python-3.6.zip added from Github

README.cosmo contains the necessary links.

third_party/python/Modules/_decimal/libmpdec/README.txt

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+
+
+libmpdec
+========
+
+libmpdec is a fast C/C++ library for correctly-rounded arbitrary precision
+decimal floating point arithmetic. It is a complete implementation of
+Mike Cowlishaw/IBM's General Decimal Arithmetic Specification.
+
+
+Files required for the Python _decimal module
+=============================================
+
+  Core files for small and medium precision arithmetic
+  ----------------------------------------------------
+
+    basearith.{c,h}  ->  Core arithmetic in base 10**9 or 10**19.
+    bits.h           ->  Portable detection of least/most significant one-bit.
+    constants.{c,h}  ->  Constants that are used in multiple files.
+    context.c        ->  Context functions.
+    io.{c,h}         ->  Conversions between mpd_t and ASCII strings,
+                         mpd_t formatting (allows UTF-8 fill character).
+    memory.{c,h}     ->  Allocation handlers with overflow detection
+                         and functions for switching between static
+                         and dynamic mpd_t.
+    mpdecimal.{c,h}  ->  All (quiet) functions of the specification.
+    typearith.h      ->  Fast primitives for double word multiplication,
+                         division etc.
+
+    Visual Studio only:
+    ~~~~~~~~~~~~~~~~~~~
+      vccompat.h    ->  snprintf <==> sprintf_s and similar things.
+      vcstdint.h    ->  stdint.h (included in VS 2010 but not in VS 2008).
+      vcdiv64.asm   ->  Double word division used in typearith.h. VS 2008 does
+                        not allow inline asm for x64. Also, it does not provide
+                        an intrinsic for double word division.
+
+  Files for bignum arithmetic:
+  ----------------------------
+
+    The following files implement the Fast Number Theoretic Transform
+    used for multiplying coefficients with more than 1024 words (see
+    mpdecimal.c: _mpd_fntmul()).
+
+      umodarith.h        ->  Fast low level routines for unsigned modular arithmetic.
+      numbertheory.{c,h} ->  Routines for setting up the Number Theoretic Transform.
+      difradix2.{c,h}    ->  Decimation in frequency transform, used as the
+                             "base case" by the following three files:
+
+        fnt.{c,h}        ->  Transform arrays up to 4096 words.
+        sixstep.{c,h}    ->  Transform larger arrays of length 2**n.
+        fourstep.{c,h}   ->  Transform larger arrays of length 3 * 2**n.
+
+      convolute.{c,h}    ->  Fast convolution using one of the three transform
+                             functions.
+      transpose.{c,h}    ->  Transpositions needed for the sixstep algorithm.
+      crt.{c,h}          ->  Chinese Remainder Theorem: use information from three
+                             transforms modulo three different primes to get the
+                             final result.
+
+
+Pointers to literature, proofs and more
+=======================================
+
+  literature/
+  -----------
+
+    REFERENCES.txt  ->  List of relevant papers.
+    bignum.txt      ->  Explanation of the Fast Number Theoretic Transform (FNT).
+    fnt.py          ->  Verify constants used in the FNT; Python demo for the
+                        O(N**2) discrete transform.
+
+    matrix-transform.txt -> Proof for the Matrix Fourier Transform used in
+                            fourstep.c.
+    six-step.txt         -> Show that the algorithm used in sixstep.c is
+                            a variant of the Matrix Fourier Transform.
+    mulmod-64.txt        -> Proof for the mulmod64 algorithm from
+                            umodarith.h.
+    mulmod-ppro.txt      -> Proof for the x87 FPU modular multiplication
+                            from umodarith.h.
+    umodarith.lisp       -> ACL2 proofs for many functions from umodarith.h.
+
+
+Library Author
+==============
+
+  Stefan Krah <skrah@bytereef.org>
+
+
+

third_party/python/Modules/_decimal/libmpdec/basearith.c

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+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <assert.h>
+#include "constants.h"
+#include "typearith.h"
+#include "basearith.h"
+
+
+/*********************************************************************/
+/*                   Calculations in base MPD_RADIX                  */
+/*********************************************************************/
+
+
+/*
+ * Knuth, TAOCP, Volume 2, 4.3.1:
+ *    w := sum of u (len m) and v (len n)
+ *    n > 0 and m >= n
+ * The calling function has to handle a possible final carry.
+ */
+mpd_uint_t
+_mpd_baseadd(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
+             mpd_size_t m, mpd_size_t n)
+{
+    mpd_uint_t s;
+    mpd_uint_t carry = 0;
+    mpd_size_t i;
+
+    assert(n > 0 && m >= n);
+
+    /* add n members of u and v */
+    for (i = 0; i < n; i++) {
+        s = u[i] + (v[i] + carry);
+        carry = (s < u[i]) | (s >= MPD_RADIX);
+        w[i] = carry ? s-MPD_RADIX : s;
+    }
+    /* if there is a carry, propagate it */
+    for (; carry && i < m; i++) {
+        s = u[i] + carry;
+        carry = (s == MPD_RADIX);
+        w[i] = carry ? 0 : s;
+    }
+    /* copy the rest of u */
+    for (; i < m; i++) {
+        w[i] = u[i];
+    }
+
+    return carry;
+}
+
+/*
+ * Add the contents of u to w. Carries are propagated further. The caller
+ * has to make sure that w is big enough.
+ */
+void
+_mpd_baseaddto(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n)
+{
+    mpd_uint_t s;
+    mpd_uint_t carry = 0;
+    mpd_size_t i;
+
+    if (n == 0) return;
+
+    /* add n members of u to w */
+    for (i = 0; i < n; i++) {
+        s = w[i] + (u[i] + carry);
+        carry = (s < w[i]) | (s >= MPD_RADIX);
+        w[i] = carry ? s-MPD_RADIX : s;
+    }
+    /* if there is a carry, propagate it */
+    for (; carry; i++) {
+        s = w[i] + carry;
+        carry = (s == MPD_RADIX);
+        w[i] = carry ? 0 : s;
+    }
+}
+
+/*
+ * Add v to w (len m). The calling function has to handle a possible
+ * final carry. Assumption: m > 0.
+ */
+mpd_uint_t
+_mpd_shortadd(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v)
+{
+    mpd_uint_t s;
+    mpd_uint_t carry;
+    mpd_size_t i;
+
+    assert(m > 0);
+
+    /* add v to w */
+    s = w[0] + v;
+    carry = (s < v) | (s >= MPD_RADIX);
+    w[0] = carry ? s-MPD_RADIX : s;
+
+    /* if there is a carry, propagate it */
+    for (i = 1; carry && i < m; i++) {
+        s = w[i] + carry;
+        carry = (s == MPD_RADIX);
+        w[i] = carry ? 0 : s;
+    }
+
+    return carry;
+}
+
+/* Increment u. The calling function has to handle a possible carry. */
+mpd_uint_t
+_mpd_baseincr(mpd_uint_t *u, mpd_size_t n)
+{
+    mpd_uint_t s;
+    mpd_uint_t carry = 1;
+    mpd_size_t i;
+
+    assert(n > 0);
+
+    /* if there is a carry, propagate it */
+    for (i = 0; carry && i < n; i++) {
+        s = u[i] + carry;
+        carry = (s == MPD_RADIX);
+        u[i] = carry ? 0 : s;
+    }
+
+    return carry;
+}
+
+/*
+ * Knuth, TAOCP, Volume 2, 4.3.1:
+ *     w := difference of u (len m) and v (len n).
+ *     number in u >= number in v;
+ */
+void
+_mpd_basesub(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
+             mpd_size_t m, mpd_size_t n)
+{
+    mpd_uint_t d;
+    mpd_uint_t borrow = 0;
+    mpd_size_t i;
+
+    assert(m > 0 && n > 0);
+
+    /* subtract n members of v from u */
+    for (i = 0; i < n; i++) {
+        d = u[i] - (v[i] + borrow);
+        borrow = (u[i] < d);
+        w[i] = borrow ? d + MPD_RADIX : d;
+    }
+    /* if there is a borrow, propagate it */
+    for (; borrow && i < m; i++) {
+        d = u[i] - borrow;
+        borrow = (u[i] == 0);
+        w[i] = borrow ? MPD_RADIX-1 : d;
+    }
+    /* copy the rest of u */
+    for (; i < m; i++) {
+        w[i] = u[i];
+    }
+}
+
+/*
+ * Subtract the contents of u from w. w is larger than u. Borrows are
+ * propagated further, but eventually w can absorb the final borrow.
+ */
+void
+_mpd_basesubfrom(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n)
+{
+    mpd_uint_t d;
+    mpd_uint_t borrow = 0;
+    mpd_size_t i;
+
+    if (n == 0) return;
+
+    /* subtract n members of u from w */
+    for (i = 0; i < n; i++) {
+        d = w[i] - (u[i] + borrow);
+        borrow = (w[i] < d);
+        w[i] = borrow ? d + MPD_RADIX : d;
+    }
+    /* if there is a borrow, propagate it */
+    for (; borrow; i++) {
+        d = w[i] - borrow;
+        borrow = (w[i] == 0);
+        w[i] = borrow ? MPD_RADIX-1 : d;
+    }
+}
+
+/* w := product of u (len n) and v (single word) */
+void
+_mpd_shortmul(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, mpd_uint_t v)
+{
+    mpd_uint_t hi, lo;
+    mpd_uint_t carry = 0;
+    mpd_size_t i;
+
+    assert(n > 0);
+
+    for (i=0; i < n; i++) {
+
+        _mpd_mul_words(&hi, &lo, u[i], v);
+        lo = carry + lo;
+        if (lo < carry) hi++;
+
+        _mpd_div_words_r(&carry, &w[i], hi, lo);
+    }
+    w[i] = carry;
+}
+
+/*
+ * Knuth, TAOCP, Volume 2, 4.3.1:
+ *     w := product of u (len m) and v (len n)
+ *     w must be initialized to zero
+ */
+void
+_mpd_basemul(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
+             mpd_size_t m, mpd_size_t n)
+{
+    mpd_uint_t hi, lo;
+    mpd_uint_t carry;
+    mpd_size_t i, j;
+
+    assert(m > 0 && n > 0);
+
+    for (j=0; j < n; j++) {
+        carry = 0;
+        for (i=0; i < m; i++) {
+
+            _mpd_mul_words(&hi, &lo, u[i], v[j]);
+            lo = w[i+j] + lo;
+            if (lo < w[i+j]) hi++;
+            lo = carry + lo;
+            if (lo < carry) hi++;
+
+            _mpd_div_words_r(&carry, &w[i+j], hi, lo);
+        }
+        w[j+m] = carry;
+    }
+}
+
+/*
+ * Knuth, TAOCP Volume 2, 4.3.1, exercise 16:
+ *     w := quotient of u (len n) divided by a single word v
+ */
+mpd_uint_t
+_mpd_shortdiv(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, mpd_uint_t v)
+{
+    mpd_uint_t hi, lo;
+    mpd_uint_t rem = 0;
+    mpd_size_t i;
+
+    assert(n > 0);
+
+    for (i=n-1; i != MPD_SIZE_MAX; i--) {
+
+        _mpd_mul_words(&hi, &lo, rem, MPD_RADIX);
+        lo = u[i] + lo;
+        if (lo < u[i]) hi++;
+
+        _mpd_div_words(&w[i], &rem, hi, lo, v);
+    }
+
+    return rem;
+}
+
+/*
+ * Knuth, TAOCP Volume 2, 4.3.1:
+ *     q, r := quotient and remainder of uconst (len nplusm)
+ *             divided by vconst (len n)
+ *     nplusm >= n
+ *
+ * If r is not NULL, r will contain the remainder. If r is NULL, the
+ * return value indicates if there is a remainder: 1 for true, 0 for
+ * false.  A return value of -1 indicates an error.
+ */
+int
+_mpd_basedivmod(mpd_uint_t *q, mpd_uint_t *r,
+                const mpd_uint_t *uconst, const mpd_uint_t *vconst,
+                mpd_size_t nplusm, mpd_size_t n)
+{
+    mpd_uint_t ustatic[MPD_MINALLOC_MAX];
+    mpd_uint_t vstatic[MPD_MINALLOC_MAX];
+    mpd_uint_t *u = ustatic;
+    mpd_uint_t *v = vstatic;
+    mpd_uint_t d, qhat, rhat, w2[2];
+    mpd_uint_t hi, lo, x;
+    mpd_uint_t carry;
+    mpd_size_t i, j, m;
+    int retval = 0;
+
+    assert(n > 1 && nplusm >= n);
+    m = sub_size_t(nplusm, n);
+
+    /* D1: normalize */
+    d = MPD_RADIX / (vconst[n-1] + 1);
+
+    if (nplusm >= MPD_MINALLOC_MAX) {
+        if ((u = mpd_alloc(nplusm+1, sizeof *u)) == NULL) {
+            return -1;
+        }
+    }
+    if (n >= MPD_MINALLOC_MAX) {
+        if ((v = mpd_alloc(n+1, sizeof *v)) == NULL) {
+            mpd_free(u);
+            return -1;
+        }
+    }
+
+    _mpd_shortmul(u, uconst, nplusm, d);
+    _mpd_shortmul(v, vconst, n, d);
+
+    /* D2: loop */
+    for (j=m; j != MPD_SIZE_MAX; j--) {
+
+        /* D3: calculate qhat and rhat */
+        rhat = _mpd_shortdiv(w2, u+j+n-1, 2, v[n-1]);
+        qhat = w2[1] * MPD_RADIX + w2[0];
+
+        while (1) {
+            if (qhat < MPD_RADIX) {
+                _mpd_singlemul(w2, qhat, v[n-2]);
+                if (w2[1] <= rhat) {
+                    if (w2[1] != rhat || w2[0] <= u[j+n-2]) {
+                        break;
+                    }
+                }
+            }
+            qhat -= 1;
+            rhat += v[n-1];
+            if (rhat < v[n-1] || rhat >= MPD_RADIX) {
+                break;
+            }
+        }
+        /* D4: multiply and subtract */
+        carry = 0;
+        for (i=0; i <= n; i++) {
+
+            _mpd_mul_words(&hi, &lo, qhat, v[i]);
+
+            lo = carry + lo;
+            if (lo < carry) hi++;
+
+            _mpd_div_words_r(&hi, &lo, hi, lo);
+
+            x = u[i+j] - lo;
+            carry = (u[i+j] < x);
+            u[i+j] = carry ? x+MPD_RADIX : x;
+            carry += hi;
+        }
+        q[j] = qhat;
+        /* D5: test remainder */
+        if (carry) {
+            q[j] -= 1;
+            /* D6: add back */
+            (void)_mpd_baseadd(u+j, u+j, v, n+1, n);
+        }
+    }
+
+    /* D8: unnormalize */
+    if (r != NULL) {
+        _mpd_shortdiv(r, u, n, d);
+        /* we are not interested in the return value here */
+        retval = 0;
+    }
+    else {
+        retval = !_mpd_isallzero(u, n);
+    }
+
+
+if (u != ustatic) mpd_free(u);
+if (v != vstatic) mpd_free(v);
+return retval;
+}
+
+/*
+ * Left shift of src by 'shift' digits; src may equal dest.
+ *
+ *  dest := area of n mpd_uint_t with space for srcdigits+shift digits.
+ *  src  := coefficient with length m.
+ *
+ * The case splits in the function are non-obvious. The following
+ * equations might help:
+ *
+ *  Let msdigits denote the number of digits in the most significant
+ *  word of src. Then 1 <= msdigits <= rdigits.
+ *
+ *   1) shift = q * rdigits + r
+ *   2) srcdigits = qsrc * rdigits + msdigits
+ *   3) destdigits = shift + srcdigits
+ *                 = q * rdigits + r + qsrc * rdigits + msdigits
+ *                 = q * rdigits + (qsrc * rdigits + (r + msdigits))
+ *
+ *  The result has q zero words, followed by the coefficient that
+ *  is left-shifted by r. The case r == 0 is trivial. For r > 0, it
+ *  is important to keep in mind that we always read m source words,
+ *  but write m+1 destination words if r + msdigits > rdigits, m words
+ *  otherwise.
+ */
+void
+_mpd_baseshiftl(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t n, mpd_size_t m,
+                mpd_size_t shift)
+{
+#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__)
+    /* spurious uninitialized warnings */
+    mpd_uint_t l=l, lprev=lprev, h=h;
+#else
+    mpd_uint_t l, lprev, h;
+#endif
+    mpd_uint_t q, r;
+    mpd_uint_t ph;
+
+    assert(m > 0 && n >= m);
+
+    _mpd_div_word(&q, &r, (mpd_uint_t)shift, MPD_RDIGITS);
+
+    if (r != 0) {
+
+        ph = mpd_pow10[r];
+
+        --m; --n;
+        _mpd_divmod_pow10(&h, &lprev, src[m--], MPD_RDIGITS-r);
+        if (h != 0) { /* r + msdigits > rdigits <==> h != 0 */
+            dest[n--] = h;
+        }
+        /* write m-1 shifted words */
+        for (; m != MPD_SIZE_MAX; m--,n--) {
+            _mpd_divmod_pow10(&h, &l, src[m], MPD_RDIGITS-r);
+            dest[n] = ph * lprev + h;
+            lprev = l;
+        }
+        /* write least significant word */
+        dest[q] = ph * lprev;
+    }
+    else {
+        while (--m != MPD_SIZE_MAX) {
+            dest[m+q] = src[m];
+        }
+    }
+
+    mpd_uint_zero(dest, q);
+}
+
+/*
+ * Right shift of src by 'shift' digits; src may equal dest.
+ * Assumption: srcdigits-shift > 0.
+ *
+ *  dest := area with space for srcdigits-shift digits.
+ *  src  := coefficient with length 'slen'.
+ *
+ * The case splits in the function rely on the following equations:
+ *
+ *  Let msdigits denote the number of digits in the most significant
+ *  word of src. Then 1 <= msdigits <= rdigits.
+ *
+ *  1) shift = q * rdigits + r
+ *  2) srcdigits = qsrc * rdigits + msdigits
+ *  3) destdigits = srcdigits - shift
+ *                = qsrc * rdigits + msdigits - (q * rdigits + r)
+ *                = (qsrc - q) * rdigits + msdigits - r
+ *
+ * Since destdigits > 0 and 1 <= msdigits <= rdigits:
+ *
+ *  4) qsrc >= q
+ *  5) qsrc == q  ==>  msdigits > r
+ *
+ * The result has slen-q words if msdigits > r, slen-q-1 words otherwise.
+ */
+mpd_uint_t
+_mpd_baseshiftr(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t slen,
+                mpd_size_t shift)
+{
+#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__)
+    /* spurious uninitialized warnings */
+    mpd_uint_t l=l, h=h, hprev=hprev; /* low, high, previous high */
+#else
+    mpd_uint_t l, h, hprev; /* low, high, previous high */
+#endif
+    mpd_uint_t rnd, rest;   /* rounding digit, rest */
+    mpd_uint_t q, r;
+    mpd_size_t i, j;
+    mpd_uint_t ph;
+
+    assert(slen > 0);
+
+    _mpd_div_word(&q, &r, (mpd_uint_t)shift, MPD_RDIGITS);
+
+    rnd = rest = 0;
+    if (r != 0) {
+
+        ph = mpd_pow10[MPD_RDIGITS-r];
+
+        _mpd_divmod_pow10(&hprev, &rest, src[q], r);
+        _mpd_divmod_pow10(&rnd, &rest, rest, r-1);
+
+        if (rest == 0 && q > 0) {
+            rest = !_mpd_isallzero(src, q);
+        }
+        /* write slen-q-1 words */
+        for (j=0,i=q+1; i<slen; i++,j++) {
+            _mpd_divmod_pow10(&h, &l, src[i], r);
+            dest[j] = ph * l + hprev;
+            hprev = h;
+        }
+        /* write most significant word */
+        if (hprev != 0) { /* always the case if slen==q-1 */
+            dest[j] = hprev;
+        }
+    }
+    else {
+        if (q > 0) {
+            _mpd_divmod_pow10(&rnd, &rest, src[q-1], MPD_RDIGITS-1);
+            /* is there any non-zero digit below rnd? */
+            if (rest == 0) rest = !_mpd_isallzero(src, q-1);
+        }
+        for (j = 0; j < slen-q; j++) {
+            dest[j] = src[q+j];
+        }
+    }
+
+    /* 0-4  ==> rnd+rest < 0.5   */
+    /* 5    ==> rnd+rest == 0.5  */
+    /* 6-9  ==> rnd+rest > 0.5   */
+    return (rnd == 0 || rnd == 5) ? rnd + !!rest : rnd;
+}
+
+
+/*********************************************************************/
+/*                      Calculations in base b                       */
+/*********************************************************************/
+
+/*
+ * Add v to w (len m). The calling function has to handle a possible
+ * final carry. Assumption: m > 0.
+ */
+mpd_uint_t
+_mpd_shortadd_b(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v, mpd_uint_t b)
+{
+    mpd_uint_t s;
+    mpd_uint_t carry;
+    mpd_size_t i;
+
+    assert(m > 0);
+
+    /* add v to w */
+    s = w[0] + v;
+    carry = (s < v) | (s >= b);
+    w[0] = carry ? s-b : s;
+
+    /* if there is a carry, propagate it */
+    for (i = 1; carry && i < m; i++) {
+        s = w[i] + carry;
+        carry = (s == b);
+        w[i] = carry ? 0 : s;
+    }
+
+    return carry;
+}
+
+/* w := product of u (len n) and v (single word). Return carry. */
+mpd_uint_t
+_mpd_shortmul_c(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, mpd_uint_t v)
+{
+    mpd_uint_t hi, lo;
+    mpd_uint_t carry = 0;
+    mpd_size_t i;
+
+    assert(n > 0);
+
+    for (i=0; i < n; i++) {
+
+        _mpd_mul_words(&hi, &lo, u[i], v);
+        lo = carry + lo;
+        if (lo < carry) hi++;
+
+        _mpd_div_words_r(&carry, &w[i], hi, lo);
+    }
+
+    return carry;
+}
+
+/* w := product of u (len n) and v (single word) */
+mpd_uint_t
+_mpd_shortmul_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+                mpd_uint_t v, mpd_uint_t b)
+{
+    mpd_uint_t hi, lo;
+    mpd_uint_t carry = 0;
+    mpd_size_t i;
+
+    assert(n > 0);
+
+    for (i=0; i < n; i++) {
+
+        _mpd_mul_words(&hi, &lo, u[i], v);
+        lo = carry + lo;
+        if (lo < carry) hi++;
+
+        _mpd_div_words(&carry, &w[i], hi, lo, b);
+    }
+
+    return carry;
+}
+
+/*
+ * Knuth, TAOCP Volume 2, 4.3.1, exercise 16:
+ *     w := quotient of u (len n) divided by a single word v
+ */
+mpd_uint_t
+_mpd_shortdiv_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+                mpd_uint_t v, mpd_uint_t b)
+{
+    mpd_uint_t hi, lo;
+    mpd_uint_t rem = 0;
+    mpd_size_t i;
+
+    assert(n > 0);
+
+    for (i=n-1; i != MPD_SIZE_MAX; i--) {
+
+        _mpd_mul_words(&hi, &lo, rem, b);
+        lo = u[i] + lo;
+        if (lo < u[i]) hi++;
+
+        _mpd_div_words(&w[i], &rem, hi, lo, v);
+    }
+
+    return rem;
+}
+
+
+

third_party/python/Modules/_decimal/libmpdec/basearith.h

@@ -0,0 +1,222 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef BASEARITH_H
+#define BASEARITH_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include "typearith.h"
+
+
+/* Internal header file: all symbols have local scope in the DSO */
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
+
+
+mpd_uint_t _mpd_baseadd(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
+                        mpd_size_t m, mpd_size_t n);
+void _mpd_baseaddto(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n);
+mpd_uint_t _mpd_shortadd(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v);
+mpd_uint_t _mpd_shortadd_b(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v,
+                           mpd_uint_t b);
+mpd_uint_t _mpd_baseincr(mpd_uint_t *u, mpd_size_t n);
+void _mpd_basesub(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
+                  mpd_size_t m, mpd_size_t n);
+void _mpd_basesubfrom(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n);
+void _mpd_basemul(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
+                  mpd_size_t m, mpd_size_t n);
+void _mpd_shortmul(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+                   mpd_uint_t v);
+mpd_uint_t _mpd_shortmul_c(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+                           mpd_uint_t v);
+mpd_uint_t _mpd_shortmul_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+                           mpd_uint_t v, mpd_uint_t b);
+mpd_uint_t _mpd_shortdiv(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+                         mpd_uint_t v);
+mpd_uint_t _mpd_shortdiv_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+                           mpd_uint_t v, mpd_uint_t b);
+int _mpd_basedivmod(mpd_uint_t *q, mpd_uint_t *r, const mpd_uint_t *uconst,
+                    const mpd_uint_t *vconst, mpd_size_t nplusm, mpd_size_t n);
+void _mpd_baseshiftl(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t n,
+                     mpd_size_t m, mpd_size_t shift);
+mpd_uint_t _mpd_baseshiftr(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t slen,
+                           mpd_size_t shift);
+
+
+
+#ifdef CONFIG_64
+extern const mpd_uint_t mprime_rdx;
+
+/*
+ * Algorithm from: Division by Invariant Integers using Multiplication,
+ * T. Granlund and P. L. Montgomery, Proceedings of the SIGPLAN '94
+ * Conference on Programming Language Design and Implementation.
+ *
+ * http://gmplib.org/~tege/divcnst-pldi94.pdf
+ *
+ * Variables from the paper and their translations (See section 8):
+ *
+ *  N := 64
+ *  d := MPD_RADIX
+ *  l := 64
+ *  m' := floor((2**(64+64) - 1)/MPD_RADIX) - 2**64
+ *
+ * Since N-l == 0:
+ *
+ *  dnorm := d
+ *  n2 := hi
+ *  n10 := lo
+ *
+ * ACL2 proof: mpd-div-words-r-correct
+ */
+static inline void
+_mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo)
+{
+    mpd_uint_t n_adj, h, l, t;
+    mpd_uint_t n1_neg;
+
+    /* n1_neg = if lo >= 2**63 then MPD_UINT_MAX else 0 */
+    n1_neg = (lo & (1ULL<<63)) ? MPD_UINT_MAX : 0;
+    /* n_adj = if lo >= 2**63 then lo+MPD_RADIX else lo */
+    n_adj = lo + (n1_neg & MPD_RADIX);
+
+    /* (h, l) = if lo >= 2**63 then m'*(hi+1) else m'*hi */
+    _mpd_mul_words(&h, &l, mprime_rdx, hi-n1_neg);
+    l = l + n_adj;
+    if (l < n_adj) h++;
+    t = h + hi;
+    /* At this point t == qest, with q == qest or q == qest+1:
+     *   1) 0 <= 2**64*hi + lo - qest*MPD_RADIX < 2*MPD_RADIX
+     */
+
+    /* t = 2**64-1 - qest = 2**64 - (qest+1) */
+    t = MPD_UINT_MAX - t;
+
+    /* (h, l) = 2**64*MPD_RADIX - (qest+1)*MPD_RADIX */
+    _mpd_mul_words(&h, &l, t, MPD_RADIX);
+    l = l + lo;
+    if (l < lo) h++;
+    h += hi;
+    h -= MPD_RADIX;
+    /* (h, l) = 2**64*hi + lo - (qest+1)*MPD_RADIX (mod 2**128)
+     * Case q == qest+1:
+     *     a) h == 0, l == r
+     *     b) q := h - t == qest+1
+     *     c) r := l
+     * Case q == qest:
+     *     a) h == MPD_UINT_MAX, l == 2**64-(MPD_RADIX-r)
+     *     b) q := h - t == qest
+     *     c) r := l + MPD_RADIX = r
+     */
+
+    *q = (h - t);
+    *r = l + (MPD_RADIX & h);
+}
+#else
+static inline void
+_mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo)
+{
+    _mpd_div_words(q, r, hi, lo, MPD_RADIX);
+}
+#endif
+
+
+/* Multiply two single base MPD_RADIX words, store result in array w[2]. */
+static inline void
+_mpd_singlemul(mpd_uint_t w[2], mpd_uint_t u, mpd_uint_t v)
+{
+    mpd_uint_t hi, lo;
+
+    _mpd_mul_words(&hi, &lo, u, v);
+    _mpd_div_words_r(&w[1], &w[0], hi, lo);
+}
+
+/* Multiply u (len 2) and v (len m, 1 <= m <= 2). */
+static inline void
+_mpd_mul_2_le2(mpd_uint_t w[4], mpd_uint_t u[2], mpd_uint_t v[2], mpd_ssize_t m)
+{
+    mpd_uint_t hi, lo;
+
+    _mpd_mul_words(&hi, &lo, u[0], v[0]);
+    _mpd_div_words_r(&w[1], &w[0], hi, lo);
+
+    _mpd_mul_words(&hi, &lo, u[1], v[0]);
+    lo = w[1] + lo;
+    if (lo < w[1]) hi++;
+    _mpd_div_words_r(&w[2], &w[1], hi, lo);
+    if (m == 1) return;
+
+    _mpd_mul_words(&hi, &lo, u[0], v[1]);
+    lo = w[1] + lo;
+    if (lo < w[1]) hi++;
+    _mpd_div_words_r(&w[3], &w[1], hi, lo);
+
+    _mpd_mul_words(&hi, &lo, u[1], v[1]);
+    lo = w[2] + lo;
+    if (lo < w[2]) hi++;
+    lo = w[3] + lo;
+    if (lo < w[3]) hi++;
+    _mpd_div_words_r(&w[3], &w[2], hi, lo);
+}
+
+
+/*
+ * Test if all words from data[len-1] to data[0] are zero. If len is 0, nothing
+ * is tested and the coefficient is regarded as "all zero".
+ */
+static inline int
+_mpd_isallzero(const mpd_uint_t *data, mpd_ssize_t len)
+{
+    while (--len >= 0) {
+        if (data[len] != 0) return 0;
+    }
+    return 1;
+}
+
+/*
+ * Test if all full words from data[len-1] to data[0] are MPD_RADIX-1
+ * (all nines). Return true if len == 0.
+ */
+static inline int
+_mpd_isallnine(const mpd_uint_t *data, mpd_ssize_t len)
+{
+    while (--len >= 0) {
+        if (data[len] != MPD_RADIX-1) return 0;
+    }
+    return 1;
+}
+
+
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
+
+
+#endif /* BASEARITH_H */
+
+
+

third_party/python/Modules/_decimal/libmpdec/bits.h

@@ -0,0 +1,192 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef BITS_H
+#define BITS_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+
+
+/* Check if n is a power of 2. */
+static inline int
+ispower2(mpd_size_t n)
+{
+    return n != 0 && (n & (n-1)) == 0;
+}
+
+#if defined(ANSI)
+/*
+ * Return the most significant bit position of n from 0 to 31 (63).
+ * Assumptions: n != 0.
+ */
+static inline int
+mpd_bsr(mpd_size_t n)
+{
+    int pos = 0;
+    mpd_size_t tmp;
+
+#ifdef CONFIG_64
+    tmp = n >> 32;
+    if (tmp != 0) { n = tmp; pos += 32; }
+#endif
+    tmp = n >> 16;
+    if (tmp != 0) { n = tmp; pos += 16; }
+    tmp = n >> 8;
+    if (tmp != 0) { n = tmp; pos += 8; }
+    tmp = n >> 4;
+    if (tmp != 0) { n = tmp; pos += 4; }
+    tmp = n >> 2;
+    if (tmp != 0) { n = tmp; pos += 2; }
+    tmp = n >> 1;
+    if (tmp != 0) { n = tmp; pos += 1; }
+
+    return pos + (int)n - 1;
+}
+
+/*
+ * Return the least significant bit position of n from 0 to 31 (63).
+ * Assumptions: n != 0.
+ */
+static inline int
+mpd_bsf(mpd_size_t n)
+{
+    int pos;
+
+#ifdef CONFIG_64
+    pos = 63;
+    if (n & 0x00000000FFFFFFFFULL) { pos -= 32; } else { n >>= 32; }
+    if (n & 0x000000000000FFFFULL) { pos -= 16; } else { n >>= 16; }
+    if (n & 0x00000000000000FFULL) { pos -=  8; } else { n >>=  8; }
+    if (n & 0x000000000000000FULL) { pos -=  4; } else { n >>=  4; }
+    if (n & 0x0000000000000003ULL) { pos -=  2; } else { n >>=  2; }
+    if (n & 0x0000000000000001ULL) { pos -=  1; }
+#else
+    pos = 31;
+    if (n & 0x000000000000FFFFUL) { pos -= 16; } else { n >>= 16; }
+    if (n & 0x00000000000000FFUL) { pos -=  8; } else { n >>=  8; }
+    if (n & 0x000000000000000FUL) { pos -=  4; } else { n >>=  4; }
+    if (n & 0x0000000000000003UL) { pos -=  2; } else { n >>=  2; }
+    if (n & 0x0000000000000001UL) { pos -=  1; }
+#endif
+    return pos;
+}
+/* END ANSI */
+
+#elif defined(ASM)
+/*
+ * Bit scan reverse. Assumptions: a != 0.
+ */
+static inline int
+mpd_bsr(mpd_size_t a)
+{
+    mpd_size_t retval;
+
+    __asm__ (
+#ifdef CONFIG_64
+        "bsrq %1, %0\n\t"
+#else
+        "bsr %1, %0\n\t"
+#endif
+        :"=r" (retval)
+        :"r" (a)
+        :"cc"
+    );
+
+    return (int)retval;
+}
+
+/*
+ * Bit scan forward. Assumptions: a != 0.
+ */
+static inline int
+mpd_bsf(mpd_size_t a)
+{
+    mpd_size_t retval;
+
+    __asm__ (
+#ifdef CONFIG_64
+        "bsfq %1, %0\n\t"
+#else
+        "bsf %1, %0\n\t"
+#endif
+        :"=r" (retval)
+        :"r" (a)
+        :"cc"
+    );
+
+    return (int)retval;
+}
+/* END ASM */
+
+#elif defined(MASM)
+#include <intrin.h>
+/*
+ * Bit scan reverse. Assumptions: a != 0.
+ */
+static inline int __cdecl
+mpd_bsr(mpd_size_t a)
+{
+    unsigned long retval;
+
+#ifdef CONFIG_64
+    _BitScanReverse64(&retval, a);
+#else
+    _BitScanReverse(&retval, a);
+#endif
+
+    return (int)retval;
+}
+
+/*
+ * Bit scan forward. Assumptions: a != 0.
+ */
+static inline int __cdecl
+mpd_bsf(mpd_size_t a)
+{
+    unsigned long retval;
+
+#ifdef CONFIG_64
+    _BitScanForward64(&retval, a);
+#else
+    _BitScanForward(&retval, a);
+#endif
+
+    return (int)retval;
+}
+/* END MASM (_MSC_VER) */
+#else
+  #error "missing preprocessor definitions"
+#endif /* BSR/BSF */
+
+
+#endif /* BITS_H */
+
+
+

third_party/python/Modules/_decimal/libmpdec/constants.c

@@ -0,0 +1,132 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include "constants.h"
+
+
+#if defined(CONFIG_64)
+
+  /* number-theory.c */
+  const mpd_uint_t mpd_moduli[3] = {
+    18446744069414584321ULL, 18446744056529682433ULL, 18446742974197923841ULL
+  };
+  const mpd_uint_t mpd_roots[3]  = {7ULL, 10ULL, 19ULL};
+
+  /* crt.c */
+  const mpd_uint_t INV_P1_MOD_P2   = 18446744055098026669ULL;
+  const mpd_uint_t INV_P1P2_MOD_P3 = 287064143708160ULL;
+  const mpd_uint_t LH_P1P2 = 18446744052234715137ULL;     /* (P1*P2) % 2^64 */
+  const mpd_uint_t UH_P1P2 = 18446744052234715141ULL;     /* (P1*P2) / 2^64 */
+
+  /* transpose.c */
+  const mpd_size_t mpd_bits[64] = {
+    1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024,  2048, 4096, 8192, 16384,
+    32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608,
+    16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824,
+    2147483648ULL, 4294967296ULL, 8589934592ULL, 17179869184ULL, 34359738368ULL,
+    68719476736ULL, 137438953472ULL, 274877906944ULL, 549755813888ULL,
+    1099511627776ULL, 2199023255552ULL, 4398046511104, 8796093022208ULL,
+    17592186044416ULL, 35184372088832ULL, 70368744177664ULL, 140737488355328ULL,
+    281474976710656ULL, 562949953421312ULL, 1125899906842624ULL,
+    2251799813685248ULL, 4503599627370496ULL, 9007199254740992ULL,
+    18014398509481984ULL, 36028797018963968ULL, 72057594037927936ULL,
+    144115188075855872ULL, 288230376151711744ULL, 576460752303423488ULL,
+    1152921504606846976ULL, 2305843009213693952ULL, 4611686018427387904ULL,
+    9223372036854775808ULL
+  };
+
+  /* mpdecimal.c */
+  const mpd_uint_t mpd_pow10[MPD_RDIGITS+1] = {
+    1,10,100,1000,10000,100000,1000000,10000000,100000000,1000000000,
+    10000000000ULL,100000000000ULL,1000000000000ULL,10000000000000ULL,
+    100000000000000ULL,1000000000000000ULL,10000000000000000ULL,
+    100000000000000000ULL,1000000000000000000ULL,10000000000000000000ULL
+  };
+
+  /* magic number for constant division by MPD_RADIX */
+  const mpd_uint_t mprime_rdx = 15581492618384294730ULL;
+
+#elif defined(CONFIG_32)
+
+  /* number-theory.c */
+  const mpd_uint_t mpd_moduli[3]  = {2113929217UL, 2013265921UL, 1811939329UL};
+  const mpd_uint_t mpd_roots[3]   = {5UL, 31UL, 13UL};
+
+  /* PentiumPro modular multiplication: These constants have to be loaded as
+   * 80 bit long doubles, which are not supported by certain compilers. */
+  const uint32_t mpd_invmoduli[3][3] = {
+    {4293885170U, 2181570688U, 16352U},  /* ((long double) 1 / 2113929217UL) */
+    {1698898177U, 2290649223U, 16352U},  /* ((long double) 1 / 2013265921UL) */
+    {2716021846U, 2545165803U, 16352U}   /* ((long double) 1 / 1811939329UL) */
+  };
+
+  const float MPD_TWO63 = 9223372036854775808.0; /* 2^63 */
+
+  /* crt.c */
+  const mpd_uint_t INV_P1_MOD_P2   = 2013265901UL;
+  const mpd_uint_t INV_P1P2_MOD_P3 = 54UL;
+  const mpd_uint_t LH_P1P2 = 4127195137UL;  /* (P1*P2) % 2^32 */
+  const mpd_uint_t UH_P1P2 = 990904320UL;   /* (P1*P2) / 2^32 */
+
+  /* transpose.c */
+  const mpd_size_t mpd_bits[32] = {
+    1, 2, 4, 8, 16, 32, 64, 128, 256, 512,  1024,  2048, 4096, 8192, 16384,
+    32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608,
+    16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824,
+    2147483648UL
+  };
+
+  /* mpdecimal.c */
+  const mpd_uint_t mpd_pow10[MPD_RDIGITS+1] = {
+    1,10,100,1000,10000,100000,1000000,10000000,100000000,1000000000
+  };
+
+#else
+  #error "CONFIG_64 or CONFIG_32 must be defined."
+#endif
+
+const char *mpd_round_string[MPD_ROUND_GUARD] = {
+    "ROUND_UP",          /* round away from 0               */
+    "ROUND_DOWN",        /* round toward 0 (truncate)       */
+    "ROUND_CEILING",     /* round toward +infinity          */
+    "ROUND_FLOOR",       /* round toward -infinity          */
+    "ROUND_HALF_UP",     /* 0.5 is rounded up               */
+    "ROUND_HALF_DOWN",   /* 0.5 is rounded down             */
+    "ROUND_HALF_EVEN",   /* 0.5 is rounded to even          */
+    "ROUND_05UP",        /* round zero or five away from 0  */
+    "ROUND_TRUNC",       /* truncate, but set infinity      */
+};
+
+const char *mpd_clamp_string[MPD_CLAMP_GUARD] = {
+    "CLAMP_DEFAULT",
+    "CLAMP_IEEE_754"
+};
+
+

third_party/python/Modules/_decimal/libmpdec/constants.h

@@ -0,0 +1,90 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef CONSTANTS_H
+#define CONSTANTS_H
+
+
+#include "mpdecimal.h"
+
+
+/* Internal header file: all symbols have local scope in the DSO */
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
+
+
+/* choice of optimized functions */
+#if defined(CONFIG_64)
+/* x64 */
+  #define MULMOD(a, b) x64_mulmod(a, b, umod)
+  #define MULMOD2C(a0, a1, w) x64_mulmod2c(a0, a1, w, umod)
+  #define MULMOD2(a0, b0, a1, b1) x64_mulmod2(a0, b0, a1, b1, umod)
+  #define POWMOD(base, exp) x64_powmod(base, exp, umod)
+  #define SETMODULUS(modnum) std_setmodulus(modnum, &umod)
+  #define SIZE3_NTT(x0, x1, x2, w3table) std_size3_ntt(x0, x1, x2, w3table, umod)
+#elif defined(PPRO)
+/* PentiumPro (or later) gcc inline asm */
+  #define MULMOD(a, b) ppro_mulmod(a, b, &dmod, dinvmod)
+  #define MULMOD2C(a0, a1, w) ppro_mulmod2c(a0, a1, w, &dmod, dinvmod)
+  #define MULMOD2(a0, b0, a1, b1) ppro_mulmod2(a0, b0, a1, b1, &dmod, dinvmod)
+  #define POWMOD(base, exp) ppro_powmod(base, exp, &dmod, dinvmod)
+  #define SETMODULUS(modnum) ppro_setmodulus(modnum, &umod, &dmod, dinvmod)
+  #define SIZE3_NTT(x0, x1, x2, w3table) ppro_size3_ntt(x0, x1, x2, w3table, umod, &dmod, dinvmod)
+#else
+  /* ANSI C99 */
+  #define MULMOD(a, b) std_mulmod(a, b, umod)
+  #define MULMOD2C(a0, a1, w) std_mulmod2c(a0, a1, w, umod)
+  #define MULMOD2(a0, b0, a1, b1) std_mulmod2(a0, b0, a1, b1, umod)
+  #define POWMOD(base, exp) std_powmod(base, exp, umod)
+  #define SETMODULUS(modnum) std_setmodulus(modnum, &umod)
+  #define SIZE3_NTT(x0, x1, x2, w3table) std_size3_ntt(x0, x1, x2, w3table, umod)
+#endif
+
+/* PentiumPro (or later) gcc inline asm */
+extern const float MPD_TWO63;
+extern const uint32_t mpd_invmoduli[3][3];
+
+enum {P1, P2, P3};
+
+extern const mpd_uint_t mpd_moduli[];
+extern const mpd_uint_t mpd_roots[];
+extern const mpd_size_t mpd_bits[];
+extern const mpd_uint_t mpd_pow10[];
+
+extern const mpd_uint_t INV_P1_MOD_P2;
+extern const mpd_uint_t INV_P1P2_MOD_P3;
+extern const mpd_uint_t LH_P1P2;
+extern const mpd_uint_t UH_P1P2;
+
+
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
+
+
+#endif /* CONSTANTS_H */
+
+
+

third_party/python/Modules/_decimal/libmpdec/context.c

@@ -0,0 +1,286 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <string.h>
+#include <signal.h>
+
+
+void
+mpd_dflt_traphandler(mpd_context_t *ctx UNUSED)
+{
+    raise(SIGFPE);
+}
+
+void (* mpd_traphandler)(mpd_context_t *) = mpd_dflt_traphandler;
+
+
+/* Set guaranteed minimum number of coefficient words. The function may
+   be used once at program start. Setting MPD_MINALLOC to out-of-bounds
+   values is a catastrophic error, so in that case the function exits rather
+   than relying on the user to check a return value. */
+void
+mpd_setminalloc(mpd_ssize_t n)
+{
+    static int minalloc_is_set = 0;
+
+    if (minalloc_is_set) {
+        mpd_err_warn("mpd_setminalloc: ignoring request to set "
+                     "MPD_MINALLOC a second time\n");
+        return;
+    }
+    if (n < MPD_MINALLOC_MIN || n > MPD_MINALLOC_MAX) {
+        mpd_err_fatal("illegal value for MPD_MINALLOC"); /* GCOV_NOT_REACHED */
+    }
+    MPD_MINALLOC = n;
+    minalloc_is_set = 1;
+}
+
+void
+mpd_init(mpd_context_t *ctx, mpd_ssize_t prec)
+{
+    mpd_ssize_t ideal_minalloc;
+
+    mpd_defaultcontext(ctx);
+
+    if (!mpd_qsetprec(ctx, prec)) {
+        mpd_addstatus_raise(ctx, MPD_Invalid_context);
+        return;
+    }
+
+    ideal_minalloc = 2 * ((prec+MPD_RDIGITS-1) / MPD_RDIGITS);
+    if (ideal_minalloc < MPD_MINALLOC_MIN) ideal_minalloc = MPD_MINALLOC_MIN;
+    if (ideal_minalloc > MPD_MINALLOC_MAX) ideal_minalloc = MPD_MINALLOC_MAX;
+
+    mpd_setminalloc(ideal_minalloc);
+}
+
+void
+mpd_maxcontext(mpd_context_t *ctx)
+{
+    ctx->prec=MPD_MAX_PREC;
+    ctx->emax=MPD_MAX_EMAX;
+    ctx->emin=MPD_MIN_EMIN;
+    ctx->round=MPD_ROUND_HALF_EVEN;
+    ctx->traps=MPD_Traps;
+    ctx->status=0;
+    ctx->newtrap=0;
+    ctx->clamp=0;
+    ctx->allcr=1;
+}
+
+void
+mpd_defaultcontext(mpd_context_t *ctx)
+{
+    ctx->prec=2*MPD_RDIGITS;
+    ctx->emax=MPD_MAX_EMAX;
+    ctx->emin=MPD_MIN_EMIN;
+    ctx->round=MPD_ROUND_HALF_UP;
+    ctx->traps=MPD_Traps;
+    ctx->status=0;
+    ctx->newtrap=0;
+    ctx->clamp=0;
+    ctx->allcr=1;
+}
+
+void
+mpd_basiccontext(mpd_context_t *ctx)
+{
+    ctx->prec=9;
+    ctx->emax=MPD_MAX_EMAX;
+    ctx->emin=MPD_MIN_EMIN;
+    ctx->round=MPD_ROUND_HALF_UP;
+    ctx->traps=MPD_Traps|MPD_Clamped;
+    ctx->status=0;
+    ctx->newtrap=0;
+    ctx->clamp=0;
+    ctx->allcr=1;
+}
+
+int
+mpd_ieee_context(mpd_context_t *ctx, int bits)
+{
+    if (bits <= 0 || bits > MPD_IEEE_CONTEXT_MAX_BITS || bits % 32) {
+        return -1;
+    }
+
+    ctx->prec = 9 * (bits/32) - 2;
+    ctx->emax = 3 * ((mpd_ssize_t)1<<(bits/16+3));
+    ctx->emin = 1 - ctx->emax;
+    ctx->round=MPD_ROUND_HALF_EVEN;
+    ctx->traps=0;
+    ctx->status=0;
+    ctx->newtrap=0;
+    ctx->clamp=1;
+    ctx->allcr=1;
+
+    return 0;
+}
+
+mpd_ssize_t
+mpd_getprec(const mpd_context_t *ctx)
+{
+    return ctx->prec;
+}
+
+mpd_ssize_t
+mpd_getemax(const mpd_context_t *ctx)
+{
+    return ctx->emax;
+}
+
+mpd_ssize_t
+mpd_getemin(const mpd_context_t *ctx)
+{
+    return ctx->emin;
+}
+
+int
+mpd_getround(const mpd_context_t *ctx)
+{
+    return ctx->round;
+}
+
+uint32_t
+mpd_gettraps(const mpd_context_t *ctx)
+{
+    return ctx->traps;
+}
+
+uint32_t
+mpd_getstatus(const mpd_context_t *ctx)
+{
+    return ctx->status;
+}
+
+int
+mpd_getclamp(const mpd_context_t *ctx)
+{
+    return ctx->clamp;
+}
+
+int
+mpd_getcr(const mpd_context_t *ctx)
+{
+    return ctx->allcr;
+}
+
+
+int
+mpd_qsetprec(mpd_context_t *ctx, mpd_ssize_t prec)
+{
+    if (prec <= 0 || prec > MPD_MAX_PREC) {
+        return 0;
+    }
+    ctx->prec = prec;
+    return 1;
+}
+
+int
+mpd_qsetemax(mpd_context_t *ctx, mpd_ssize_t emax)
+{
+    if (emax < 0 || emax > MPD_MAX_EMAX) {
+        return 0;
+    }
+    ctx->emax = emax;
+    return 1;
+}
+
+int
+mpd_qsetemin(mpd_context_t *ctx, mpd_ssize_t emin)
+{
+    if (emin > 0 || emin < MPD_MIN_EMIN) {
+        return 0;
+    }
+    ctx->emin = emin;
+    return 1;
+}
+
+int
+mpd_qsetround(mpd_context_t *ctx, int round)
+{
+    if (!(0 <= round && round < MPD_ROUND_GUARD)) {
+        return 0;
+    }
+    ctx->round = round;
+    return 1;
+}
+
+int
+mpd_qsettraps(mpd_context_t *ctx, uint32_t traps)
+{
+    if (traps > MPD_Max_status) {
+        return 0;
+    }
+    ctx->traps = traps;
+    return 1;
+}
+
+int
+mpd_qsetstatus(mpd_context_t *ctx, uint32_t flags)
+{
+    if (flags > MPD_Max_status) {
+        return 0;
+    }
+    ctx->status = flags;
+    return 1;
+}
+
+int
+mpd_qsetclamp(mpd_context_t *ctx, int c)
+{
+    if (c != 0 && c != 1) {
+        return 0;
+    }
+    ctx->clamp = c;
+    return 1;
+}
+
+int
+mpd_qsetcr(mpd_context_t *ctx, int c)
+{
+    if (c != 0 && c != 1) {
+        return 0;
+    }
+    ctx->allcr = c;
+    return 1;
+}
+
+
+void
+mpd_addstatus_raise(mpd_context_t *ctx, uint32_t flags)
+{
+    ctx->status |= flags;
+    if (flags&ctx->traps) {
+        ctx->newtrap = (flags&ctx->traps);
+        mpd_traphandler(ctx);
+    }
+}
+
+

third_party/python/Modules/_decimal/libmpdec/convolute.c

@@ -0,0 +1,174 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include "bits.h"
+#include "constants.h"
+#include "fnt.h"
+#include "fourstep.h"
+#include "numbertheory.h"
+#include "sixstep.h"
+#include "umodarith.h"
+#include "convolute.h"
+
+
+/* Bignum: Fast convolution using the Number Theoretic Transform. Used for
+   the multiplication of very large coefficients. */
+
+
+/* Convolute the data in c1 and c2. Result is in c1. */
+int
+fnt_convolute(mpd_uint_t *c1, mpd_uint_t *c2, mpd_size_t n, int modnum)
+{
+    int (*fnt)(mpd_uint_t *, mpd_size_t, int);
+    int (*inv_fnt)(mpd_uint_t *, mpd_size_t, int);
+#ifdef PPRO
+    double dmod;
+    uint32_t dinvmod[3];
+#endif
+    mpd_uint_t n_inv, umod;
+    mpd_size_t i;
+
+
+    SETMODULUS(modnum);
+    n_inv = POWMOD(n, (umod-2));
+
+    if (ispower2(n)) {
+        if (n > SIX_STEP_THRESHOLD) {
+            fnt = six_step_fnt;
+            inv_fnt = inv_six_step_fnt;
+        }
+        else {
+            fnt = std_fnt;
+            inv_fnt = std_inv_fnt;
+        }
+    }
+    else {
+        fnt = four_step_fnt;
+        inv_fnt = inv_four_step_fnt;
+    }
+
+    if (!fnt(c1, n, modnum)) {
+        return 0;
+    }
+    if (!fnt(c2, n, modnum)) {
+        return 0;
+    }
+    for (i = 0; i < n-1; i += 2) {
+        mpd_uint_t x0 = c1[i];
+        mpd_uint_t y0 = c2[i];
+        mpd_uint_t x1 = c1[i+1];
+        mpd_uint_t y1 = c2[i+1];
+        MULMOD2(&x0, y0, &x1, y1);
+        c1[i] = x0;
+        c1[i+1] = x1;
+    }
+
+    if (!inv_fnt(c1, n, modnum)) {
+        return 0;
+    }
+    for (i = 0; i < n-3; i += 4) {
+        mpd_uint_t x0 = c1[i];
+        mpd_uint_t x1 = c1[i+1];
+        mpd_uint_t x2 = c1[i+2];
+        mpd_uint_t x3 = c1[i+3];
+        MULMOD2C(&x0, &x1, n_inv);
+        MULMOD2C(&x2, &x3, n_inv);
+        c1[i] = x0;
+        c1[i+1] = x1;
+        c1[i+2] = x2;
+        c1[i+3] = x3;
+    }
+
+    return 1;
+}
+
+/* Autoconvolute the data in c1. Result is in c1. */
+int
+fnt_autoconvolute(mpd_uint_t *c1, mpd_size_t n, int modnum)
+{
+    int (*fnt)(mpd_uint_t *, mpd_size_t, int);
+    int (*inv_fnt)(mpd_uint_t *, mpd_size_t, int);
+#ifdef PPRO
+    double dmod;
+    uint32_t dinvmod[3];
+#endif
+    mpd_uint_t n_inv, umod;
+    mpd_size_t i;
+
+
+    SETMODULUS(modnum);
+    n_inv = POWMOD(n, (umod-2));
+
+    if (ispower2(n)) {
+        if (n > SIX_STEP_THRESHOLD) {
+            fnt = six_step_fnt;
+            inv_fnt = inv_six_step_fnt;
+        }
+        else {
+            fnt = std_fnt;
+            inv_fnt = std_inv_fnt;
+        }
+    }
+    else {
+        fnt = four_step_fnt;
+        inv_fnt = inv_four_step_fnt;
+    }
+
+    if (!fnt(c1, n, modnum)) {
+        return 0;
+    }
+    for (i = 0; i < n-1; i += 2) {
+        mpd_uint_t x0 = c1[i];
+        mpd_uint_t x1 = c1[i+1];
+        MULMOD2(&x0, x0, &x1, x1);
+        c1[i] = x0;
+        c1[i+1] = x1;
+    }
+
+    if (!inv_fnt(c1, n, modnum)) {
+        return 0;
+    }
+    for (i = 0; i < n-3; i += 4) {
+        mpd_uint_t x0 = c1[i];
+        mpd_uint_t x1 = c1[i+1];
+        mpd_uint_t x2 = c1[i+2];
+        mpd_uint_t x3 = c1[i+3];
+        MULMOD2C(&x0, &x1, n_inv);
+        MULMOD2C(&x2, &x3, n_inv);
+        c1[i] = x0;
+        c1[i+1] = x1;
+        c1[i+2] = x2;
+        c1[i+3] = x3;
+    }
+
+    return 1;
+}
+
+

third_party/python/Modules/_decimal/libmpdec/convolute.h

@@ -0,0 +1,50 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef CONVOLUTE_H
+#define CONVOLUTE_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+
+
+/* Internal header file: all symbols have local scope in the DSO */
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
+
+
+#define SIX_STEP_THRESHOLD 4096
+
+int fnt_convolute(mpd_uint_t *c1, mpd_uint_t *c2, mpd_size_t n, int modnum);
+int fnt_autoconvolute(mpd_uint_t *c1, mpd_size_t n, int modnum);
+
+
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
+
+
+#endif

third_party/python/Modules/_decimal/libmpdec/crt.c

@@ -0,0 +1,179 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <assert.h>
+#include "numbertheory.h"
+#include "umodarith.h"
+#include "crt.h"
+
+
+/* Bignum: Chinese Remainder Theorem, extends the maximum transform length. */
+
+
+/* Multiply P1P2 by v, store result in w. */
+static inline void
+_crt_mulP1P2_3(mpd_uint_t w[3], mpd_uint_t v)
+{
+    mpd_uint_t hi1, hi2, lo;
+
+    _mpd_mul_words(&hi1, &lo, LH_P1P2, v);
+    w[0] = lo;
+
+    _mpd_mul_words(&hi2, &lo, UH_P1P2, v);
+    lo = hi1 + lo;
+    if (lo < hi1) hi2++;
+
+    w[1] = lo;
+    w[2] = hi2;
+}
+
+/* Add 3 words from v to w. The result is known to fit in w. */
+static inline void
+_crt_add3(mpd_uint_t w[3], mpd_uint_t v[3])
+{
+    mpd_uint_t carry;
+    mpd_uint_t s;
+
+    s = w[0] + v[0];
+    carry = (s < w[0]);
+    w[0] = s;
+
+    s = w[1] + (v[1] + carry);
+    carry = (s < w[1]);
+    w[1] = s;
+
+    w[2] = w[2] + (v[2] + carry);
+}
+
+/* Divide 3 words in u by v, store result in w, return remainder. */
+static inline mpd_uint_t
+_crt_div3(mpd_uint_t *w, const mpd_uint_t *u, mpd_uint_t v)
+{
+    mpd_uint_t r1 = u[2];
+    mpd_uint_t r2;
+
+    if (r1 < v) {
+        w[2] = 0;
+    }
+    else {
+        _mpd_div_word(&w[2], &r1, u[2], v); /* GCOV_NOT_REACHED */
+    }
+
+    _mpd_div_words(&w[1], &r2, r1, u[1], v);
+    _mpd_div_words(&w[0], &r1, r2, u[0], v);
+
+    return r1;
+}
+
+
+/*
+ * Chinese Remainder Theorem:
+ * Algorithm from Joerg Arndt, "Matters Computational",
+ * Chapter 37.4.1 [http://www.jjj.de/fxt/]
+ *
+ * See also Knuth, TAOCP, Volume 2, 4.3.2, exercise 7.
+ */
+
+/*
+ * CRT with carry: x1, x2, x3 contain numbers modulo p1, p2, p3. For each
+ * triple of members of the arrays, find the unique z modulo p1*p2*p3, with
+ * zmax = p1*p2*p3 - 1.
+ *
+ * In each iteration of the loop, split z into result[i] = z % MPD_RADIX
+ * and carry = z / MPD_RADIX. Let N be the size of carry[] and cmax the
+ * maximum carry.
+ *
+ * Limits for the 32-bit build:
+ *
+ *   N    = 2**96
+ *   cmax = 7711435591312380274
+ *
+ * Limits for the 64 bit build:
+ *
+ *   N    = 2**192
+ *   cmax = 627710135393475385904124401220046371710
+ *
+ * The following statements hold for both versions:
+ *
+ *   1) cmax + zmax < N, so the addition does not overflow.
+ *
+ *   2) (cmax + zmax) / MPD_RADIX == cmax.
+ *
+ *   3) If c <= cmax, then c_next = (c + zmax) / MPD_RADIX <= cmax.
+ */
+void
+crt3(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_size_t rsize)
+{
+    mpd_uint_t p1 = mpd_moduli[P1];
+    mpd_uint_t umod;
+#ifdef PPRO
+    double dmod;
+    uint32_t dinvmod[3];
+#endif
+    mpd_uint_t a1, a2, a3;
+    mpd_uint_t s;
+    mpd_uint_t z[3], t[3];
+    mpd_uint_t carry[3] = {0,0,0};
+    mpd_uint_t hi, lo;
+    mpd_size_t i;
+
+    for (i = 0; i < rsize; i++) {
+
+        a1 = x1[i];
+        a2 = x2[i];
+        a3 = x3[i];
+
+        SETMODULUS(P2);
+        s = ext_submod(a2, a1, umod);
+        s = MULMOD(s, INV_P1_MOD_P2);
+
+        _mpd_mul_words(&hi, &lo, s, p1);
+        lo = lo + a1;
+        if (lo < a1) hi++;
+
+        SETMODULUS(P3);
+        s = dw_submod(a3, hi, lo, umod);
+        s = MULMOD(s, INV_P1P2_MOD_P3);
+
+        z[0] = lo;
+        z[1] = hi;
+        z[2] = 0;
+
+        _crt_mulP1P2_3(t, s);
+        _crt_add3(z, t);
+        _crt_add3(carry, z);
+
+        x1[i] = _crt_div3(carry, carry, MPD_RADIX);
+    }
+
+    assert(carry[0] == 0 && carry[1] == 0 && carry[2] == 0);
+}
+
+

third_party/python/Modules/_decimal/libmpdec/crt.h

@@ -0,0 +1,47 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef CRT_H
+#define CRT_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+
+
+/* Internal header file: all symbols have local scope in the DSO */
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
+
+
+void crt3(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_size_t nmemb);
+
+
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
+
+
+#endif

third_party/python/Modules/_decimal/libmpdec/difradix2.c

@@ -0,0 +1,173 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <assert.h>
+#include "bits.h"
+#include "numbertheory.h"
+#include "umodarith.h"
+#include "difradix2.h"
+
+
+/* Bignum: The actual transform routine (decimation in frequency). */
+
+
+/*
+ * Generate index pairs (x, bitreverse(x)) and carry out the permutation.
+ * n must be a power of two.
+ * Algorithm due to Brent/Lehmann, see Joerg Arndt, "Matters Computational",
+ * Chapter 1.14.4. [http://www.jjj.de/fxt/]
+ */
+static inline void
+bitreverse_permute(mpd_uint_t a[], mpd_size_t n)
+{
+    mpd_size_t x = 0;
+    mpd_size_t r = 0;
+    mpd_uint_t t;
+
+    do { /* Invariant: r = bitreverse(x) */
+        if (r > x) {
+            t = a[x];
+            a[x] = a[r];
+            a[r] = t;
+        }
+        /* Flip trailing consecutive 1 bits and the first zero bit
+         * that absorbs a possible carry. */
+        x += 1;
+        /* Mirror the operation on r: Flip n_trailing_zeros(x)+1
+           high bits of r. */
+        r ^= (n - (n >> (mpd_bsf(x)+1)));
+        /* The loop invariant is preserved. */
+    } while (x < n);
+}
+
+
+/* Fast Number Theoretic Transform, decimation in frequency. */
+void
+fnt_dif2(mpd_uint_t a[], mpd_size_t n, struct fnt_params *tparams)
+{
+    mpd_uint_t *wtable = tparams->wtable;
+    mpd_uint_t umod;
+#ifdef PPRO
+    double dmod;
+    uint32_t dinvmod[3];
+#endif
+    mpd_uint_t u0, u1, v0, v1;
+    mpd_uint_t w, w0, w1, wstep;
+    mpd_size_t m, mhalf;
+    mpd_size_t j, r;
+
+
+    assert(ispower2(n));
+    assert(n >= 4);
+
+    SETMODULUS(tparams->modnum);
+
+    /* m == n */
+    mhalf = n / 2;
+    for (j = 0; j < mhalf; j += 2) {
+
+        w0 = wtable[j];
+        w1 = wtable[j+1];
+
+        u0 = a[j];
+        v0 = a[j+mhalf];
+
+        u1 = a[j+1];
+        v1 = a[j+1+mhalf];
+
+        a[j] = addmod(u0, v0, umod);
+        v0 = submod(u0, v0, umod);
+
+        a[j+1] = addmod(u1, v1, umod);
+        v1 = submod(u1, v1, umod);
+
+        MULMOD2(&v0, w0, &v1, w1);
+
+        a[j+mhalf] = v0;
+        a[j+1+mhalf] = v1;
+
+    }
+
+    wstep = 2;
+    for (m = n/2; m >= 2; m>>=1, wstep<<=1) {
+
+        mhalf = m / 2;
+
+        /* j == 0 */
+        for (r = 0; r < n; r += 2*m) {
+
+            u0 = a[r];
+            v0 = a[r+mhalf];
+
+            u1 = a[m+r];
+            v1 = a[m+r+mhalf];
+
+            a[r] = addmod(u0, v0, umod);
+            v0 = submod(u0, v0, umod);
+
+            a[m+r] = addmod(u1, v1, umod);
+            v1 = submod(u1, v1, umod);
+
+            a[r+mhalf] = v0;
+            a[m+r+mhalf] = v1;
+        }
+
+        for (j = 1; j < mhalf; j++) {
+
+            w = wtable[j*wstep];
+
+            for (r = 0; r < n; r += 2*m) {
+
+                u0 = a[r+j];
+                v0 = a[r+j+mhalf];
+
+                u1 = a[m+r+j];
+                v1 = a[m+r+j+mhalf];
+
+                a[r+j] = addmod(u0, v0, umod);
+                v0 = submod(u0, v0, umod);
+
+                a[m+r+j] = addmod(u1, v1, umod);
+                v1 = submod(u1, v1, umod);
+
+                MULMOD2C(&v0, &v1, w);
+
+                a[r+j+mhalf] = v0;
+                a[m+r+j+mhalf] = v1;
+            }
+
+        }
+
+    }
+
+    bitreverse_permute(a, n);
+}
+
+

third_party/python/Modules/_decimal/libmpdec/difradix2.h

@@ -0,0 +1,48 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef DIF_RADIX2_H
+#define DIF_RADIX2_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include "numbertheory.h"
+
+
+/* Internal header file: all symbols have local scope in the DSO */
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
+
+
+void fnt_dif2(mpd_uint_t a[], mpd_size_t n, struct fnt_params *tparams);
+
+
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
+
+
+#endif

third_party/python/Modules/_decimal/libmpdec/fnt.c

@@ -0,0 +1,81 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include <assert.h>
+#include "bits.h"
+#include "difradix2.h"
+#include "numbertheory.h"
+#include "fnt.h"
+
+
+/* Bignum: Fast transform for medium-sized coefficients. */
+
+
+/* forward transform, sign = -1 */
+int
+std_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
+{
+    struct fnt_params *tparams;
+
+    assert(ispower2(n));
+    assert(n >= 4);
+    assert(n <= 3*MPD_MAXTRANSFORM_2N);
+
+    if ((tparams = _mpd_init_fnt_params(n, -1, modnum)) == NULL) {
+        return 0;
+    }
+    fnt_dif2(a, n, tparams);
+
+    mpd_free(tparams);
+    return 1;
+}
+
+/* reverse transform, sign = 1 */
+int
+std_inv_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
+{
+    struct fnt_params *tparams;
+
+    assert(ispower2(n));
+    assert(n >= 4);
+    assert(n <= 3*MPD_MAXTRANSFORM_2N);
+
+    if ((tparams = _mpd_init_fnt_params(n, 1, modnum)) == NULL) {
+        return 0;
+    }
+    fnt_dif2(a, n, tparams);
+
+    mpd_free(tparams);
+    return 1;
+}
+
+
+

third_party/python/Modules/_decimal/libmpdec/fnt.h

@@ -0,0 +1,49 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef FNT_H
+#define FNT_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+
+
+/* Internal header file: all symbols have local scope in the DSO */
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
+
+
+int std_fnt(mpd_uint_t a[], mpd_size_t n, int modnum);
+int std_inv_fnt(mpd_uint_t a[], mpd_size_t n, int modnum);
+
+
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
+
+
+#endif
+

third_party/python/Modules/_decimal/libmpdec/fourstep.c

@@ -0,0 +1,257 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <assert.h>
+#include "numbertheory.h"
+#include "sixstep.h"
+#include "transpose.h"
+#include "umodarith.h"
+#include "fourstep.h"
+
+
+/* Bignum: Cache efficient Matrix Fourier Transform for arrays of the
+   form 3 * 2**n (See literature/matrix-transform.txt). */
+
+
+#ifndef PPRO
+static inline void
+std_size3_ntt(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3,
+              mpd_uint_t w3table[3], mpd_uint_t umod)
+{
+    mpd_uint_t r1, r2;
+    mpd_uint_t w;
+    mpd_uint_t s, tmp;
+
+
+    /* k = 0 -> w = 1 */
+    s = *x1;
+    s = addmod(s, *x2, umod);
+    s = addmod(s, *x3, umod);
+
+    r1 = s;
+
+    /* k = 1 */
+    s = *x1;
+
+    w = w3table[1];
+    tmp = MULMOD(*x2, w);
+    s = addmod(s, tmp, umod);
+
+    w = w3table[2];
+    tmp = MULMOD(*x3, w);
+    s = addmod(s, tmp, umod);
+
+    r2 = s;
+
+    /* k = 2 */
+    s = *x1;
+
+    w = w3table[2];
+    tmp = MULMOD(*x2, w);
+    s = addmod(s, tmp, umod);
+
+    w = w3table[1];
+    tmp = MULMOD(*x3, w);
+    s = addmod(s, tmp, umod);
+
+    *x3 = s;
+    *x2 = r2;
+    *x1 = r1;
+}
+#else /* PPRO */
+static inline void
+ppro_size3_ntt(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_uint_t w3table[3],
+               mpd_uint_t umod, double *dmod, uint32_t dinvmod[3])
+{
+    mpd_uint_t r1, r2;
+    mpd_uint_t w;
+    mpd_uint_t s, tmp;
+
+
+    /* k = 0 -> w = 1 */
+    s = *x1;
+    s = addmod(s, *x2, umod);
+    s = addmod(s, *x3, umod);
+
+    r1 = s;
+
+    /* k = 1 */
+    s = *x1;
+
+    w = w3table[1];
+    tmp = ppro_mulmod(*x2, w, dmod, dinvmod);
+    s = addmod(s, tmp, umod);
+
+    w = w3table[2];
+    tmp = ppro_mulmod(*x3, w, dmod, dinvmod);
+    s = addmod(s, tmp, umod);
+
+    r2 = s;
+
+    /* k = 2 */
+    s = *x1;
+
+    w = w3table[2];
+    tmp = ppro_mulmod(*x2, w, dmod, dinvmod);
+    s = addmod(s, tmp, umod);
+
+    w = w3table[1];
+    tmp = ppro_mulmod(*x3, w, dmod, dinvmod);
+    s = addmod(s, tmp, umod);
+
+    *x3 = s;
+    *x2 = r2;
+    *x1 = r1;
+}
+#endif
+
+
+/* forward transform, sign = -1; transform length = 3 * 2**n */
+int
+four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
+{
+    mpd_size_t R = 3; /* number of rows */
+    mpd_size_t C = n / 3; /* number of columns */
+    mpd_uint_t w3table[3];
+    mpd_uint_t kernel, w0, w1, wstep;
+    mpd_uint_t *s, *p0, *p1, *p2;
+    mpd_uint_t umod;
+#ifdef PPRO
+    double dmod;
+    uint32_t dinvmod[3];
+#endif
+    mpd_size_t i, k;
+
+
+    assert(n >= 48);
+    assert(n <= 3*MPD_MAXTRANSFORM_2N);
+
+
+    /* Length R transform on the columns. */
+    SETMODULUS(modnum);
+    _mpd_init_w3table(w3table, -1, modnum);
+    for (p0=a, p1=p0+C, p2=p0+2*C; p0<a+C; p0++,p1++,p2++) {
+
+        SIZE3_NTT(p0, p1, p2, w3table);
+    }
+
+    /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */
+    kernel = _mpd_getkernel(n, -1, modnum);
+    for (i = 1; i < R; i++) {
+        w0 = 1;                  /* r**(i*0): initial value for k=0 */
+        w1 = POWMOD(kernel, i);  /* r**(i*1): initial value for k=1 */
+        wstep = MULMOD(w1, w1);  /* r**(2*i) */
+        for (k = 0; k < C-1; k += 2) {
+            mpd_uint_t x0 = a[i*C+k];
+            mpd_uint_t x1 = a[i*C+k+1];
+            MULMOD2(&x0, w0, &x1, w1);
+            MULMOD2C(&w0, &w1, wstep);  /* r**(i*(k+2)) = r**(i*k) * r**(2*i) */
+            a[i*C+k] = x0;
+            a[i*C+k+1] = x1;
+        }
+    }
+
+    /* Length C transform on the rows. */
+    for (s = a; s < a+n; s += C) {
+        if (!six_step_fnt(s, C, modnum)) {
+            return 0;
+        }
+    }
+
+#if 0
+    /* An unordered transform is sufficient for convolution. */
+    /* Transpose the matrix. */
+    transpose_3xpow2(a, R, C);
+#endif
+
+    return 1;
+}
+
+/* backward transform, sign = 1; transform length = 3 * 2**n */
+int
+inv_four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
+{
+    mpd_size_t R = 3; /* number of rows */
+    mpd_size_t C = n / 3; /* number of columns */
+    mpd_uint_t w3table[3];
+    mpd_uint_t kernel, w0, w1, wstep;
+    mpd_uint_t *s, *p0, *p1, *p2;
+    mpd_uint_t umod;
+#ifdef PPRO
+    double dmod;
+    uint32_t dinvmod[3];
+#endif
+    mpd_size_t i, k;
+
+
+    assert(n >= 48);
+    assert(n <= 3*MPD_MAXTRANSFORM_2N);
+
+
+#if 0
+    /* An unordered transform is sufficient for convolution. */
+    /* Transpose the matrix, producing an R*C matrix. */
+    transpose_3xpow2(a, C, R);
+#endif
+
+    /* Length C transform on the rows. */
+    for (s = a; s < a+n; s += C) {
+        if (!inv_six_step_fnt(s, C, modnum)) {
+            return 0;
+        }
+    }
+
+    /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */
+    SETMODULUS(modnum);
+    kernel = _mpd_getkernel(n, 1, modnum);
+    for (i = 1; i < R; i++) {
+        w0 = 1;
+        w1 = POWMOD(kernel, i);
+        wstep = MULMOD(w1, w1);
+        for (k = 0; k < C; k += 2) {
+            mpd_uint_t x0 = a[i*C+k];
+            mpd_uint_t x1 = a[i*C+k+1];
+            MULMOD2(&x0, w0, &x1, w1);
+            MULMOD2C(&w0, &w1, wstep);
+            a[i*C+k] = x0;
+            a[i*C+k+1] = x1;
+        }
+    }
+
+    /* Length R transform on the columns. */
+    _mpd_init_w3table(w3table, 1, modnum);
+    for (p0=a, p1=p0+C, p2=p0+2*C; p0<a+C; p0++,p1++,p2++) {
+
+        SIZE3_NTT(p0, p1, p2, w3table);
+    }
+
+    return 1;
+}
+
+

third_party/python/Modules/_decimal/libmpdec/fourstep.h

@@ -0,0 +1,48 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef FOUR_STEP_H
+#define FOUR_STEP_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+
+
+/* Internal header file: all symbols have local scope in the DSO */
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
+
+
+int four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum);
+int inv_four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum);
+
+
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
+
+
+#endif

third_party/python/Modules/_decimal/libmpdec/io.h

@@ -0,0 +1,59 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef IO_H
+#define IO_H
+
+
+#include <errno.h>
+#include "mpdecimal.h"
+
+
+#if SIZE_MAX == MPD_SIZE_MAX
+  #define mpd_strtossize _mpd_strtossize
+#else
+static inline mpd_ssize_t
+mpd_strtossize(const char *s, char **end, int base)
+{
+    int64_t retval;
+
+    errno = 0;
+    retval = _mpd_strtossize(s, end, base);
+    if (errno == 0 && (retval > MPD_SSIZE_MAX || retval < MPD_SSIZE_MIN)) {
+        errno = ERANGE;
+    }
+    if (errno == ERANGE) {
+        return (retval < 0) ? MPD_SSIZE_MIN : MPD_SSIZE_MAX;
+    }
+
+    return (mpd_ssize_t)retval;
+}
+#endif
+
+
+#endif

third_party/python/Modules/_decimal/libmpdec/literature/REFERENCES.txt

@@ -0,0 +1,51 @@
+
+
+This document contains links to the literature used in the process of
+creating the library. The list is probably not complete.
+
+
+Mike Cowlishaw: General Decimal Arithmetic Specification
+http://speleotrove.com/decimal/decarith.html
+
+
+Jean-Michel Muller: On the definition of ulp (x)
+lara.inist.fr/bitstream/2332/518/1/LIP-RR2005-09.pdf
+
+
+T. E. Hull, A. Abrham: Properly rounded variable precision square root
+http://portal.acm.org/citation.cfm?id=214413
+
+
+T. E. Hull, A. Abrham: Variable precision exponential function
+http://portal.acm.org/citation.cfm?id=6498
+
+
+Roman E. Maeder: Storage allocation for the Karatsuba integer multiplication
+algorithm.  http://www.springerlink.com/content/w15058mj6v59t565/
+
+
+J. M. Pollard: The fast Fourier transform in a finite field
+http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0301966-0/home.html
+
+
+David H. Bailey: FFTs in External or Hierarchical Memory
+http://crd.lbl.gov/~dhbailey/dhbpapers/
+
+
+W. Morven Gentleman: Matrix Multiplication and Fast Fourier Transforms
+http://www.alcatel-lucent.com/bstj/vol47-1968/articles/bstj47-6-1099.pdf
+
+
+Mikko Tommila: Apfloat documentation
+http://www.apfloat.org/apfloat/2.41/apfloat.pdf
+
+
+Joerg Arndt: "Matters Computational"
+http://www.jjj.de/fxt/
+
+
+Karl Hasselstrom: Fast Division of Large Integers
+www.treskal.com/kalle/exjobb/original-report.pdf
+
+
+

third_party/python/Modules/_decimal/libmpdec/literature/bignum.txt

@@ -0,0 +1,83 @@
+
+
+Bignum support (Fast Number Theoretic Transform or FNT):
+========================================================
+
+Bignum arithmetic in libmpdec uses the scheme for fast convolution
+of integer sequences from:
+
+J. M. Pollard: The fast Fourier transform in a finite field
+http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0301966-0/home.html
+
+
+The transform in a finite field can be used for convolution in the same
+way as the Fourier Transform. The main advantages of the Number Theoretic
+Transform are that it is both exact and very memory efficient.
+
+
+Convolution in pseudo-code:
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+  fnt_convolute(a, b):
+    x = fnt(a)                          # forward transform of a
+    y = fnt(b)                          # forward transform of b
+    z = pairwise multiply x[i] and y[i]
+    result = inv_fnt(z)                 # backward transform of z.
+
+
+Extending the maximum transform length (Chinese Remainder Theorem):
+-------------------------------------------------------------------
+
+The maximum transform length is quite limited when using a single
+prime field. However, it is possible to use multiple primes and
+recover the result using the Chinese Remainder Theorem.
+
+
+Multiplication in pseudo-code:
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+  _mpd_fntmul(u, v):
+    c1 = fnt_convolute(u, v, P1)  # convolute modulo prime1
+    c2 = fnt_convolute(u, v, P2)  # convolute modulo prime2
+    c3 = fnt_convolute(u, v, P3)  # convolute modulo prime3
+    result = crt3(c1, c2, c3)     # Chinese Remainder Theorem
+
+
+Optimized transform functions:
+------------------------------
+
+There are three different fnt() functions:
+
+   std_fnt: "standard" decimation in frequency transform for array lengths
+            of 2**n. Performs well up to 1024 words.
+
+   sixstep: Cache-friendly algorithm for array lengths of 2**n. Outperforms
+            std_fnt for large arrays.
+
+   fourstep: Algorithm for array lengths of 3 * 2**n. Also cache friendly
+             in large parts.
+
+
+List of bignum-only files:
+--------------------------
+
+Functions from these files are only used in _mpd_fntmul().
+
+  umodarith.h    -> fast low level routines for unsigned modular arithmetic
+  numbertheory.c -> routines for setting up the FNT
+  difradix2.c    -> decimation in frequency transform, used as the
+                    "base case" by the following three files:
+
+      fnt.c          -> standard transform for smaller arrays
+      sixstep.c      -> transform large arrays of length 2**n
+      fourstep.c     -> transform arrays of length 3 * 2**n
+
+  convolute.c    -> do the actual fast convolution, using one of
+                    the three transform functions.
+  transpose.c    -> transpositions needed for the sixstep algorithm.
+  crt.c          -> Chinese Remainder Theorem: use information from three
+                    transforms modulo three different primes to get the
+                    final result.
+
+
+

third_party/python/Modules/_decimal/libmpdec/literature/fnt.py

@@ -0,0 +1,208 @@
+#
+# Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions
+# are met:
+#
+# 1. Redistributions of source code must retain the above copyright
+#    notice, this list of conditions and the following disclaimer.
+#
+# 2. Redistributions in binary form must reproduce the above copyright
+#    notice, this list of conditions and the following disclaimer in the
+#    documentation and/or other materials provided with the distribution.
+#
+# THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+# ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+# ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+# OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+# HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+# OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+# SUCH DAMAGE.
+#
+
+
+######################################################################
+#  This file lists and checks some of the constants and limits used  #
+#  in libmpdec's Number Theoretic Transform. At the end of the file  #
+#  there is an example function for the plain DFT transform.         #
+######################################################################
+
+
+#
+# Number theoretic transforms are done in subfields of F(p). P[i]
+# are the primes, D[i] = P[i] - 1 are highly composite and w[i]
+# are the respective primitive roots of F(p).
+#
+# The strategy is to convolute two coefficients modulo all three
+# primes, then use the Chinese Remainder Theorem on the three
+# result arrays to recover the result in the usual base RADIX
+# form.
+#
+
+# ======================================================================
+#                           Primitive roots
+# ======================================================================
+
+#
+# Verify primitive roots:
+#
+# For a prime field, r is a primitive root if and only if for all prime
+# factors f of p-1, r**((p-1)/f) =/= 1  (mod p).
+#
+def prod(F, E):
+    """Check that the factorization of P-1 is correct. F is the list of
+       factors of P-1, E lists the number of occurrences of each factor."""
+    x = 1
+    for y, z in zip(F, E):
+        x *= y**z
+    return x
+
+def is_primitive_root(r, p, factors, exponents):
+    """Check if r is a primitive root of F(p)."""
+    if p != prod(factors, exponents) + 1:
+        return False
+    for f in factors:
+        q, control = divmod(p-1, f)
+        if control != 0:
+            return False
+        if pow(r, q, p) == 1:
+            return False
+    return True
+
+
+# =================================================================
+#             Constants and limits for the 64-bit version
+# =================================================================
+
+RADIX = 10**19
+
+# Primes P1, P2 and P3:
+P = [2**64-2**32+1, 2**64-2**34+1, 2**64-2**40+1]
+
+# P-1, highly composite. The transform length d is variable and
+# must divide D = P-1. Since all D are divisible by 3 * 2**32,
+# transform lengths can be 2**n or 3 * 2**n (where n <= 32).
+D = [2**32 * 3    * (5 * 17 * 257 * 65537),
+     2**34 * 3**2 * (7 * 11 * 31 * 151 * 331),
+     2**40 * 3**2 * (5 * 7 * 13 * 17 * 241)]
+
+# Prime factors of P-1 and their exponents:
+F = [(2,3,5,17,257,65537), (2,3,7,11,31,151,331), (2,3,5,7,13,17,241)]
+E = [(32,1,1,1,1,1), (34,2,1,1,1,1,1), (40,2,1,1,1,1,1)]
+
+# Maximum transform length for 2**n. Above that only 3 * 2**31
+# or 3 * 2**32 are possible.
+MPD_MAXTRANSFORM_2N = 2**32
+
+
+# Limits in the terminology of Pollard's paper:
+m2 = (MPD_MAXTRANSFORM_2N * 3) // 2 # Maximum length of the smaller array.
+M1 = M2 = RADIX-1                   # Maximum value per single word.
+L = m2 * M1 * M2
+P[0] * P[1] * P[2] > 2 * L
+
+
+# Primitive roots of F(P1), F(P2) and F(P3):
+w = [7, 10, 19]
+
+# The primitive roots are correct:
+for i in range(3):
+    if not is_primitive_root(w[i], P[i], F[i], E[i]):
+        print("FAIL")
+
+
+# =================================================================
+#             Constants and limits for the 32-bit version
+# =================================================================
+
+RADIX = 10**9
+
+# Primes P1, P2 and P3:
+P = [2113929217, 2013265921, 1811939329]
+
+# P-1, highly composite. All D = P-1 are divisible by 3 * 2**25,
+# allowing for transform lengths up to 3 * 2**25 words.
+D = [2**25 * 3**2 * 7,
+     2**27 * 3    * 5,
+     2**26 * 3**3]
+
+# Prime factors of P-1 and their exponents:
+F = [(2,3,7), (2,3,5), (2,3)]
+E = [(25,2,1), (27,1,1), (26,3)]
+
+# Maximum transform length for 2**n. Above that only 3 * 2**24 or
+# 3 * 2**25 are possible.
+MPD_MAXTRANSFORM_2N = 2**25
+
+
+# Limits in the terminology of Pollard's paper:
+m2 = (MPD_MAXTRANSFORM_2N * 3) // 2 # Maximum length of the smaller array.
+M1 = M2 = RADIX-1                   # Maximum value per single word.
+L = m2 * M1 * M2
+P[0] * P[1] * P[2] > 2 * L
+
+
+# Primitive roots of F(P1), F(P2) and F(P3):
+w = [5, 31, 13]
+
+# The primitive roots are correct:
+for i in range(3):
+    if not is_primitive_root(w[i], P[i], F[i], E[i]):
+        print("FAIL")
+
+
+# ======================================================================
+#                 Example transform using a single prime
+# ======================================================================
+
+def ntt(lst, dir):
+    """Perform a transform on the elements of lst. len(lst) must
+       be 2**n or 3 * 2**n, where n <= 25. This is the slow DFT."""
+    p = 2113929217             # prime
+    d = len(lst)               # transform length
+    d_prime = pow(d, (p-2), p) # inverse of d
+    xi = (p-1)//d
+    w = 5                         # primitive root of F(p)
+    r = pow(w, xi, p)             # primitive root of the subfield
+    r_prime = pow(w, (p-1-xi), p) # inverse of r
+    if dir == 1:      # forward transform
+        a = lst       # input array
+        A = [0] * d   # transformed values
+        for i in range(d):
+            s = 0
+            for j in range(d):
+                s += a[j] * pow(r, i*j, p)
+            A[i] = s % p
+        return A
+    elif dir == -1: # backward transform
+        A = lst     # input array
+        a = [0] * d # transformed values
+        for j in range(d):
+            s = 0
+            for i in range(d):
+                s += A[i] * pow(r_prime, i*j, p)
+            a[j] = (d_prime * s) % p
+        return a
+
+def ntt_convolute(a, b):
+    """convolute arrays a and b."""
+    assert(len(a) == len(b))
+    x = ntt(a, 1)
+    y = ntt(b, 1)
+    for i in range(len(a)):
+        y[i] = y[i] * x[i]
+    r = ntt(y, -1)
+    return r
+
+
+# Example: Two arrays representing 21 and 81 in little-endian:
+a = [1, 2, 0, 0]
+b = [1, 8, 0, 0]
+
+assert(ntt_convolute(a, b) == [1,        10,        16,        0])
+assert(21 * 81             == (1*10**0 + 10*10**1 + 16*10**2 + 0*10**3))

third_party/python/Modules/_decimal/libmpdec/literature/matrix-transform.txt

@@ -0,0 +1,256 @@
+
+
+(* Copyright (c) 2011 Stefan Krah. All rights reserved. *)
+
+
+The Matrix Fourier Transform:
+=============================
+
+In libmpdec, the Matrix Fourier Transform [1] is called four-step transform
+after a variant that appears in [2]. The algorithm requires that the input
+array can be viewed as an R*C matrix.
+
+All operations are done modulo p. For readability, the proofs drop all
+instances of (mod p).
+
+
+Algorithm four-step (forward transform):
+----------------------------------------
+
+  a := input array
+  d := len(a) = R * C
+  p := prime
+  w := primitive root of unity of the prime field
+  r := w**((p-1)/d)
+  A := output array
+
+  1) Apply a length R FNT to each column.
+
+  2) Multiply each matrix element (addressed by j*C+m) by r**(j*m).
+
+  3) Apply a length C FNT to each row.
+
+  4) Transpose the matrix.
+
+
+Proof (forward transform):
+--------------------------
+
+  The algorithm can be derived starting from the regular definition of
+  the finite-field transform of length d:
+
+            d-1
+           ,----
+           \
+    A[k] =  |  a[l]  * r**(k * l)
+           /
+           `----
+           l = 0
+
+
+  The sum can be rearranged into the sum of the sums of columns:
+
+            C-1     R-1
+           ,----   ,----
+           \       \
+         =  |       |  a[i * C + j] * r**(k * (i * C + j))
+           /       /
+           `----   `----
+           j = 0   i = 0
+
+
+  Extracting a constant from the inner sum:
+
+            C-1           R-1
+           ,----         ,----
+           \             \
+         =  |  r**k*j  *  |  a[i * C + j] * r**(k * i * C)
+           /             /
+           `----         `----
+           j = 0         i = 0
+
+
+  Without any loss of generality, let k = n * R + m,
+  where n < C and m < R:
+
+                C-1                          R-1
+               ,----                        ,----
+               \                            \
+    A[n*R+m] =  |  r**(R*n*j) * r**(m*j)  *  |  a[i*C+j] * r**(R*C*n*i) * r**(C*m*i)
+               /                            /
+               `----                        `----
+               j = 0                        i = 0
+
+
+  Since r = w ** ((p-1) / (R*C)):
+
+     a) r**(R*C*n*i) = w**((p-1)*n*i) = 1
+
+     b) r**(C*m*i) = w**((p-1) / R) ** (m*i) = r_R ** (m*i)
+
+     c) r**(R*n*j) = w**((p-1) / C) ** (n*j) = r_C ** (n*j)
+
+     r_R := root of the subfield of length R.
+     r_C := root of the subfield of length C.
+
+
+                C-1                             R-1
+               ,----                           ,----
+               \                               \
+    A[n*R+m] =  |  r_C**(n*j) * [ r**(m*j)  *   |  a[i*C+j] * r_R**(m*i) ]
+               /                     ^         /
+               `----                 |         `----    1) transform the columns
+               j = 0                 |         i = 0
+                 ^                   |
+                 |                   `-- 2) multiply
+                 |
+                 `-- 3) transform the rows
+
+
+   Note that the entire RHS is a function of n and m and that the results
+   for each pair (n, m) are stored in Fortran order.
+
+   Let the term in square brackets be f(m, j). Step 1) and 2) precalculate
+   the term for all (m, j). After that, the original matrix is now a lookup
+   table with the mth element in the jth column at location m * C + j.
+
+   Let the complete RHS be g(m, n). Step 3) does an in-place transform of
+   length n on all rows. After that, the original matrix is now a lookup
+   table with the mth element in the nth column at location m * C + n.
+
+   But each (m, n) pair should be written to location n * R + m. Therefore,
+   step 4) transposes the result of step 3).
+
+
+
+Algorithm four-step (inverse transform):
+----------------------------------------
+
+  A  := input array
+  d  := len(A) = R * C
+  p  := prime
+  d' := d**(p-2)             # inverse of d
+  w  := primitive root of unity of the prime field
+  r  := w**((p-1)/d)         # root of the subfield
+  r' := w**((p-1) - (p-1)/d) # inverse of r
+  a  := output array
+
+  0) View the matrix as a C*R matrix.
+
+  1) Transpose the matrix, producing an R*C matrix.
+
+  2) Apply a length C FNT to each row.
+
+  3) Multiply each matrix element (addressed by i*C+n) by r**(i*n).
+
+  4) Apply a length R FNT to each column.
+
+
+Proof (inverse transform):
+--------------------------
+
+  The algorithm can be derived starting from the regular definition of
+  the finite-field inverse transform of length d:
+
+                  d-1
+                 ,----
+                 \
+    a[k] =  d' *  |  A[l]  * r' ** (k * l)
+                 /
+                 `----
+                 l = 0
+
+
+  The sum can be rearranged into the sum of the sums of columns. Note
+  that at this stage we still have a C*R matrix, so C denotes the number
+  of rows:
+
+                  R-1     C-1
+                 ,----   ,----
+                 \       \
+         =  d' *  |       |  a[j * R + i] * r' ** (k * (j * R + i))
+                 /       /
+                 `----   `----
+                 i = 0   j = 0
+
+
+  Extracting a constant from the inner sum:
+
+                  R-1                C-1
+                 ,----              ,----
+                 \                  \
+         =  d' *  |  r' ** (k*i)  *  |  a[j * R + i] * r' ** (k * j * R)
+                 /                  /
+                 `----              `----
+                 i = 0              j = 0
+
+
+  Without any loss of generality, let k = m * C + n,
+  where m < R and n < C:
+
+                     R-1                                  C-1
+                    ,----                                ,----
+                    \                                    \
+    A[m*C+n] = d' *  |  r' ** (C*m*i) *  r' ** (n*i)   *  |  a[j*R+i] * r' ** (R*C*m*j) * r' ** (R*n*j)
+                    /                                    /
+                    `----                                `----
+                    i = 0                                j = 0
+
+
+  Since r' = w**((p-1) - (p-1)/d) and d = R*C:
+
+     a) r' ** (R*C*m*j) = w**((p-1)*R*C*m*j - (p-1)*m*j) = 1
+
+     b) r' ** (C*m*i) = w**((p-1)*C - (p-1)/R) ** (m*i) = r_R' ** (m*i)
+
+     c) r' ** (R*n*j) = r_C' ** (n*j)
+
+     d) d' = d**(p-2) = (R*C) ** (p-2) = R**(p-2) * C**(p-2) = R' * C'
+
+     r_R' := inverse of the root of the subfield of length R.
+     r_C' := inverse of the root of the subfield of length C.
+     R'   := inverse of R
+     C'   := inverse of C
+
+
+                     R-1                                      C-1
+                    ,----                                    ,----  2) transform the rows of a^T
+                    \                                        \
+    A[m*C+n] = R' *  |  r_R' ** (m*i) * [ r' ** (n*i) * C' *  |  a[j*R+i] * r_C' ** (n*j) ]
+                    /                           ^            /       ^
+                    `----                       |            `----   |
+                    i = 0                       |            j = 0   |
+                      ^                         |                    `-- 1) Transpose input matrix
+                      |                         `-- 3) multiply             to address elements by
+                      |                                                     i * C + j
+                      `-- 3) transform the columns
+
+
+
+   Note that the entire RHS is a function of m and n and that the results
+   for each pair (m, n) are stored in C order.
+
+   Let the term in square brackets be f(n, i). Without step 1), the sum
+   would perform a length C transform on the columns of the input matrix.
+   This is a) inefficient and b) the results are needed in C order, so
+   step 1) exchanges rows and columns.
+
+   Step 2) and 3) precalculate f(n, i) for all (n, i). After that, the
+   original matrix is now a lookup table with the ith element in the nth
+   column at location i * C + n.
+
+   Let the complete RHS be g(m, n). Step 4) does an in-place transform of
+   length m on all columns. After that, the original matrix is now a lookup
+   table with the mth element in the nth column at location m * C + n,
+   which means that all A[k] = A[m * C + n] are in the correct order.
+
+
+--
+
+  [1] Joerg Arndt: "Matters Computational"
+      http://www.jjj.de/fxt/
+  [2] David H. Bailey: FFTs in External or Hierarchical Memory
+      http://crd.lbl.gov/~dhbailey/dhbpapers/
+
+
+

third_party/python/Modules/_decimal/libmpdec/literature/mulmod-64.txt

@@ -0,0 +1,127 @@
+
+
+(* Copyright (c) 2011 Stefan Krah. All rights reserved. *)
+
+
+==========================================================================
+                Calculate (a * b) % p using special primes
+==========================================================================
+
+A description of the algorithm can be found in the apfloat manual by
+Tommila [1].
+
+
+Definitions:
+------------
+
+In the whole document, "==" stands for "is congruent with".
+
+Result of a * b in terms of high/low words:
+
+   (1) hi * 2**64 + lo = a * b
+
+Special primes:
+
+   (2) p = 2**64 - z + 1, where z = 2**n
+
+Single step modular reduction:
+
+   (3) R(hi, lo) = hi * z - hi + lo
+
+
+Strategy:
+---------
+
+   a) Set (hi, lo) to the result of a * b.
+
+   b) Set (hi', lo') to the result of R(hi, lo).
+
+   c) Repeat step b) until 0 <= hi' * 2**64 + lo' < 2*p.
+
+   d) If the result is less than p, return lo'. Otherwise return lo' - p.
+
+
+The reduction step b) preserves congruence:
+-------------------------------------------
+
+    hi * 2**64 + lo == hi * z - hi + lo   (mod p)
+
+    Proof:
+    ~~~~~~
+
+       hi * 2**64 + lo = (2**64 - z + 1) * hi + z * hi - hi + lo
+
+                       = p * hi               + z * hi - hi + lo
+
+                       == z * hi - hi + lo   (mod p)
+
+
+Maximum numbers of step b):
+---------------------------
+
+# To avoid unnecessary formalism, define:
+
+def R(hi, lo, z):
+     return divmod(hi * z - hi + lo, 2**64)
+
+# For simplicity, assume hi=2**64-1, lo=2**64-1 after the
+# initial multiplication a * b. This is of course impossible
+# but certainly covers all cases.
+
+# Then, for p1:
+hi=2**64-1; lo=2**64-1; z=2**32
+p1 = 2**64 - z + 1
+
+hi, lo = R(hi, lo, z)    # First reduction
+hi, lo = R(hi, lo, z)    # Second reduction
+hi * 2**64 + lo < 2 * p1 # True
+
+# For p2:
+hi=2**64-1; lo=2**64-1; z=2**34
+p2 = 2**64 - z + 1
+
+hi, lo = R(hi, lo, z)    # First reduction
+hi, lo = R(hi, lo, z)    # Second reduction
+hi, lo = R(hi, lo, z)    # Third reduction
+hi * 2**64 + lo < 2 * p2 # True
+
+# For p3:
+hi=2**64-1; lo=2**64-1; z=2**40
+p3 = 2**64 - z + 1
+
+hi, lo = R(hi, lo, z)    # First reduction
+hi, lo = R(hi, lo, z)    # Second reduction
+hi, lo = R(hi, lo, z)    # Third reduction
+hi * 2**64 + lo < 2 * p3 # True
+
+
+Step d) preserves congruence and yields a result < p:
+-----------------------------------------------------
+
+   Case hi = 0:
+
+       Case lo < p: trivial.
+
+       Case lo >= p:
+
+          lo == lo - p   (mod p)             # result is congruent
+
+          p <= lo < 2*p  ->  0 <= lo - p < p # result is in the correct range
+
+   Case hi = 1:
+
+       p < 2**64 /\ 2**64 + lo < 2*p  ->  lo < p  # lo is always less than p
+
+       2**64 + lo == 2**64 + (lo - p)   (mod p)   # result is congruent
+
+                  = lo - p   # exactly the same value as the previous RHS
+                             # in uint64_t arithmetic.
+
+       p < 2**64 + lo < 2*p  ->  0 < 2**64 + (lo - p) < p  # correct range
+
+
+
+[1]  http://www.apfloat.org/apfloat/2.40/apfloat.pdf
+
+
+

third_party/python/Modules/_decimal/libmpdec/literature/mulmod-ppro.txt

@@ -0,0 +1,269 @@
+
+
+(* Copyright (c) 2011 Stefan Krah. All rights reserved. *)
+
+
+========================================================================
+             Calculate (a * b) % p using the 80-bit x87 FPU
+========================================================================
+
+A description of the algorithm can be found in the apfloat manual by
+Tommila [1].
+
+The proof follows an argument made by Granlund/Montgomery in [2].
+
+
+Definitions and assumptions:
+----------------------------
+
+The 80-bit extended precision format uses 64 bits for the significand:
+
+  (1) F = 64
+
+The modulus is prime and less than 2**31:
+
+  (2) 2 <= p < 2**31
+
+The factors are less than p:
+
+  (3) 0 <= a < p
+  (4) 0 <= b < p
+
+The product a * b is less than 2**62 and is thus exact in 64 bits:
+
+  (5) n = a * b
+
+The product can be represented in terms of quotient and remainder:
+
+  (6) n = q * p + r
+
+Using (3), (4) and the fact that p is prime, the remainder is always
+greater than zero:
+
+  (7) 0 <= q < p  /\  1 <= r < p
+
+
+Strategy:
+---------
+
+Precalculate the 80-bit long double inverse of p, with a maximum
+relative error of 2**(1-F):
+
+  (8) pinv = (long double)1.0 / p
+
+Calculate an estimate for q = floor(n/p). The multiplication has another
+maximum relative error of 2**(1-F):
+
+  (9) qest = n * pinv
+
+If we can show that q < qest < q+1, then trunc(qest) = q. It is then
+easy to recover the remainder r. The complete algorithm is:
+
+  a) Set the control word to 64-bit precision and truncation mode.
+
+  b) n = a * b              # Calculate exact product.
+
+  c) qest = n * pinv        # Calculate estimate for the quotient.
+
+  d) q = (qest+2**63)-2**63 # Truncate qest to the exact quotient.
+
+  f) r = n - q * p          # Calculate remainder.
+
+
+Proof for q < qest < q+1:
+-------------------------
+
+Using the cumulative error, the error bounds for qest are:
+
+                n                       n * (1 + 2**(1-F))**2
+  (9) --------------------- <= qest <=  ---------------------
+      p * (1 + 2**(1-F))**2                       p
+
+
+  Lemma 1:
+  --------
+                       n                   q * p + r
+    (10) q < --------------------- = ---------------------
+             p * (1 + 2**(1-F))**2   p * (1 + 2**(1-F))**2
+
+
+    Proof:
+    ~~~~~~
+
+    (I)     q * p * (1 + 2**(1-F))**2 < q * p + r
+
+    (II)    q * p * 2**(2-F) + q * p * 2**(2-2*F) < r
+
+    Using (1) and (7), it is sufficient to show that:
+
+    (III)   q * p * 2**(-62) + q * p * 2**(-126) < 1 <= r
+
+    (III) can easily be verified by substituting the largest possible
+    values p = 2**31-1 and q = 2**31-2.
+
+    The critical cases occur when r = 1, n = m * p + 1. These cases
+    can be exhaustively verified with a test program.
+
+
+  Lemma 2:
+  --------
+
+           n * (1 + 2**(1-F))**2     (q * p + r) * (1 + 2**(1-F))**2
+    (11)   ---------------------  =  -------------------------------  <  q + 1
+                     p                              p
+
+    Proof:
+    ~~~~~~
+
+    (I)  (q * p + r) + (q * p + r) * 2**(2-F) + (q * p + r) * 2**(2-2*F) < q * p + p
+
+    (II)  (q * p + r) * 2**(2-F) + (q * p + r) * 2**(2-2*F) < p - r
+
+    Using (1) and (7), it is sufficient to show that:
+
+    (III) (q * p + r) * 2**(-62) + (q * p + r) * 2**(-126) < 1 <= p - r
+
+    (III) can easily be verified by substituting the largest possible
+    values p = 2**31-1, q = 2**31-2 and r = 2**31-2.
+
+    The critical cases occur when r = (p - 1), n = m * p - 1. These cases
+    can be exhaustively verified with a test program.
+
+
+[1]  http://www.apfloat.org/apfloat/2.40/apfloat.pdf
+[2]  http://gmplib.org/~tege/divcnst-pldi94.pdf
+     [Section 7: "Use of floating point"]
+
+
+
+(* Coq proof for (10) and (11) *)
+
+Require Import ZArith.
+Require Import QArith.
+Require Import Qpower.
+Require Import Qabs.
+Require Import Psatz.
+
+Open Scope Q_scope.
+
+
+Ltac qreduce T :=
+  rewrite <- (Qred_correct (T)); simpl (Qred (T)).
+
+Theorem Qlt_move_right :
+  forall x y z:Q, x + z < y <-> x < y - z.
+Proof.
+  intros.
+  split.
+    intros.
+    psatzl Q.
+    intros.
+    psatzl Q.
+Qed.
+
+Theorem Qlt_mult_by_z :
+  forall x y z:Q, 0 < z -> (x < y <-> x * z < y * z).
+Proof.
+  intros.
+  split.
+    intros.
+    apply Qmult_lt_compat_r. trivial. trivial.
+    intros.
+    rewrite <- (Qdiv_mult_l x z). rewrite <- (Qdiv_mult_l y z).
+    apply Qmult_lt_compat_r.
+    apply Qlt_shift_inv_l.
+    trivial. psatzl Q. trivial. psatzl Q. psatzl Q.
+Qed.
+
+Theorem Qle_mult_quad :
+  forall (a b c d:Q),
+    0 <= a -> a <= c ->
+    0 <= b -> b <= d ->
+      a * b <= c * d.
+  intros.
+  psatz Q.
+Qed.
+
+
+Theorem q_lt_qest:
+  forall (p q r:Q),
+    (0 < p) -> (p <= (2#1)^31 - 1) ->
+    (0 <= q) -> (q <= p - 1) ->
+    (1 <= r) -> (r <= p - 1) ->
+      q < (q * p + r) / (p * (1 + (2#1)^(-63))^2).
+Proof.
+  intros.
+  rewrite Qlt_mult_by_z with (z := (p * (1 + (2#1)^(-63))^2)).
+
+  unfold Qdiv.
+  rewrite <- Qmult_assoc.
+  rewrite (Qmult_comm (/ (p * (1 + (2 # 1) ^ (-63)) ^ 2)) (p * (1 + (2 # 1) ^ (-63)) ^ 2)).
+  rewrite Qmult_inv_r.
+  rewrite Qmult_1_r.
+
+  assert (q * (p * (1 + (2 # 1) ^ (-63)) ^ 2) == q * p + (q * p) * ((2 # 1) ^ (-62) + (2 # 1) ^ (-126))).
+  qreduce ((1 + (2 # 1) ^ (-63)) ^ 2).
+  qreduce ((2 # 1) ^ (-62) + (2 # 1) ^ (-126)).
+  ring_simplify.
+  reflexivity.
+  rewrite H5.
+
+  rewrite Qplus_comm.
+  rewrite Qlt_move_right.
+  ring_simplify (q * p + r - q * p).
+  qreduce ((2 # 1) ^ (-62) + (2 # 1) ^ (-126)).
+
+  apply Qlt_le_trans with (y := 1).
+  rewrite Qlt_mult_by_z with (z := 85070591730234615865843651857942052864 # 18446744073709551617).
+  ring_simplify.
+
+  apply Qle_lt_trans with (y := ((2 # 1) ^ 31 - (2#1)) * ((2 # 1) ^ 31 - 1)).
+  apply Qle_mult_quad.
+  assumption. psatzl Q. psatzl Q. psatzl Q. psatzl Q. psatzl Q. assumption. psatzl Q. psatzl Q.
+Qed.
+
+Theorem qest_lt_qplus1:
+  forall (p q r:Q),
+    (0 < p) -> (p <= (2#1)^31 - 1) ->
+    (0 <= q) -> (q <= p - 1) ->
+    (1 <= r) -> (r <= p - 1) ->
+      ((q * p + r) * (1 + (2#1)^(-63))^2) / p < q + 1.
+Proof.
+  intros.
+  rewrite Qlt_mult_by_z with (z := p).
+
+  unfold Qdiv.
+  rewrite <- Qmult_assoc.
+  rewrite (Qmult_comm (/ p) p).
+  rewrite Qmult_inv_r.
+  rewrite Qmult_1_r.
+
+  assert ((q * p + r) * (1 + (2 # 1) ^ (-63)) ^ 2 == q * p + r + (q * p + r) * ((2 # 1) ^ (-62) + (2 # 1) ^ (-126))).
+  qreduce ((1 + (2 # 1) ^ (-63)) ^ 2).
+  qreduce ((2 # 1) ^ (-62) + (2 # 1) ^ (-126)).
+  ring_simplify. reflexivity.
+  rewrite H5.
+
+  rewrite <- Qplus_assoc. rewrite <- Qplus_comm. rewrite Qlt_move_right.
+  ring_simplify ((q + 1) * p - q * p).
+
+  rewrite <- Qplus_comm. rewrite Qlt_move_right.
+
+  apply Qlt_le_trans with (y := 1).
+  qreduce ((2 # 1) ^ (-62) + (2 # 1) ^ (-126)).
+
+  rewrite Qlt_mult_by_z with (z := 85070591730234615865843651857942052864 # 18446744073709551617).
+  ring_simplify.
+
+  ring_simplify in H0.
+  apply Qle_lt_trans with (y := (2147483646 # 1) * (2147483647 # 1) + (2147483646 # 1)).
+
+  apply Qplus_le_compat.
+  apply Qle_mult_quad.
+  assumption. psatzl Q. auto with qarith. assumption. psatzl Q.
+  auto with qarith. auto with qarith.
+  psatzl Q. psatzl Q. assumption.
+Qed.
+
+
+

third_party/python/Modules/_decimal/libmpdec/literature/six-step.txt

@@ -0,0 +1,63 @@
+
+
+(* Copyright (c) 2011 Stefan Krah. All rights reserved. *)
+
+
+The Six Step Transform:
+=======================
+
+In libmpdec, the six-step transform is the Matrix Fourier Transform (See
+matrix-transform.txt) in disguise. It is called six-step transform after
+a variant that appears in [1]. The algorithm requires that the input
+array can be viewed as an R*C matrix.
+
+
+Algorithm six-step (forward transform):
+---------------------------------------
+
+  1a) Transpose the matrix.
+
+  1b) Apply a length R FNT to each row.
+
+  1c) Transpose the matrix.
+
+  2) Multiply each matrix element (addressed by j*C+m) by r**(j*m).
+
+  3) Apply a length C FNT to each row.
+
+  4) Transpose the matrix.
+
+Note that steps 1a) - 1c) are exactly equivalent to step 1) of the Matrix
+Fourier Transform. For large R, it is faster to transpose twice and do
+a transform on the rows than to perform a column transpose directly.
+
+
+
+Algorithm six-step (inverse transform):
+---------------------------------------
+
+  0) View the matrix as a C*R matrix.
+
+  1) Transpose the matrix, producing an R*C matrix.
+
+  2) Apply a length C FNT to each row.
+
+  3) Multiply each matrix element (addressed by i*C+n) by r**(i*n).
+
+  4a) Transpose the matrix.
+
+  4b) Apply a length R FNT to each row.
+
+  4c) Transpose the matrix.
+
+Again, steps 4a) - 4c) are equivalent to step 4) of the Matrix Fourier
+Transform.
+
+
+
+--
+
+  [1] David H. Bailey: FFTs in External or Hierarchical Memory
+      http://crd.lbl.gov/~dhbailey/dhbpapers/
+
+

third_party/python/Modules/_decimal/libmpdec/literature/umodarith.lisp

@@ -0,0 +1,692 @@
+;
+; Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+;
+; Redistribution and use in source and binary forms, with or without
+; modification, are permitted provided that the following conditions
+; are met:
+;
+; 1. Redistributions of source code must retain the above copyright
+;    notice, this list of conditions and the following disclaimer.
+;
+; 2. Redistributions in binary form must reproduce the above copyright
+;    notice, this list of conditions and the following disclaimer in the
+;    documentation and/or other materials provided with the distribution.
+;
+; THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+; ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+; IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+; ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+; FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+; DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+; OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+; HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+; LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+; OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+; SUCH DAMAGE.
+;
+
+
+(in-package "ACL2")
+
+(include-book "arithmetic/top-with-meta" :dir :system)
+(include-book "arithmetic-2/floor-mod/floor-mod" :dir :system)
+
+
+;; =====================================================================
+;;            Proofs for several functions in umodarith.h
+;; =====================================================================
+
+
+
+;; =====================================================================
+;;                          Helper theorems
+;; =====================================================================
+
+(defthm elim-mod-m<x<2*m
+  (implies (and (<= m x)
+                (< x (* 2 m))
+                (rationalp x) (rationalp m))
+           (equal (mod x m)
+                  (+ x (- m)))))
+
+(defthm modaux-1a
+  (implies (and (< x m) (< 0 x) (< 0 m)
+                (rationalp x) (rationalp m))
+           (equal (mod (- x) m)
+                  (+ (- x) m))))
+
+(defthm modaux-1b
+  (implies (and (< (- x) m) (< x 0) (< 0 m)
+                (rationalp x) (rationalp m))
+           (equal (mod x m)
+                  (+ x m)))
+  :hints (("Goal" :use ((:instance modaux-1a
+                                   (x (- x)))))))
+
+(defthm modaux-1c
+  (implies (and (< x m) (< 0 x) (< 0 m)
+                (rationalp x) (rationalp m))
+           (equal (mod x m)
+                  x)))
+
+(defthm modaux-2a
+  (implies (and (< 0 b) (< b m)
+                (natp x) (natp b) (natp m)
+                (< (mod (+ b x) m) b))
+           (equal (mod (+ (- m) b x) m)
+                  (+ (- m) b (mod x m)))))
+
+(defthm modaux-2b
+  (implies (and (< 0 b) (< b m)
+                (natp x) (natp b) (natp m)
+                (< (mod (+ b x) m) b))
+           (equal (mod (+ b x) m)
+                  (+ (- m) b (mod x m))))
+  :hints (("Goal" :use (modaux-2a))))
+
+(defthm linear-mod-1
+  (implies (and (< x m) (< b m)
+                (natp x) (natp b)
+                (rationalp m))
+         (equal (< x (mod (+ (- b) x) m))
+                (< x b)))
+  :hints (("Goal" :use ((:instance modaux-1a
+                                   (x (+ b (- x))))))))
+
+(defthm linear-mod-2
+  (implies (and (< 0 b) (< b m)
+                (natp x) (natp b)
+                (natp m))
+           (equal (< (mod x m)
+                     (mod (+ (- b) x) m))
+                  (< (mod x m) b))))
+
+(defthm linear-mod-3
+  (implies (and (< x m) (< b m)
+                (natp x) (natp b)
+                (rationalp m))
+           (equal (<= b (mod (+ b x) m))
+                  (< (+ b x) m)))
+  :hints (("Goal" :use ((:instance elim-mod-m<x<2*m
+                                   (x (+ b x)))))))
+
+(defthm modaux-2c
+  (implies (and (< 0 b) (< b m)
+                (natp x) (natp b) (natp m)
+                (<= b (mod (+ b x) m)))
+           (equal (mod (+ b x) m)
+                  (+ b (mod x m))))
+  :hints (("Subgoal *1/8''" :use (linear-mod-3))))
+
+(defthmd modaux-2d
+  (implies (and (< x m) (< 0 x) (< 0 m)
+                (< (- m) b) (< b 0) (rationalp m)
+                (<= x (mod (+ b x) m))
+                (rationalp x) (rationalp b))
+           (equal (+ (- m) (mod (+ b x) m))
+                  (+ b x)))
+  :hints (("Goal" :cases ((<= 0 (+ b x))))
+          ("Subgoal 2'" :use ((:instance modaux-1b
+                                        (x (+ b x)))))))
+
+(defthm mod-m-b
+  (implies (and (< 0 x) (< 0 b) (< 0 m)
+                (< x b) (< b m)
+                (natp x) (natp b) (natp m))
+           (equal (mod (+ (mod (- x) m) b) m)
+                  (mod (- x) b))))
+
+
+;; =====================================================================
+;;                          addmod, submod
+;; =====================================================================
+
+(defun addmod (a b m base)
+  (let* ((s (mod (+ a b) base))
+         (s (if (< s a) (mod (- s m) base) s))
+         (s (if (>= s m) (mod (- s m) base) s)))
+        s))
+
+(defthmd addmod-correct
+  (implies (and (< 0 m) (< m base)
+		(< a m) (<= b m)
+                (natp m) (natp base)
+                (natp a) (natp b))
+           (equal (addmod a b m base)
+                  (mod (+ a b) m)))
+  :hints (("Goal" :cases ((<= base (+ a b))))
+          ("Subgoal 2.1'" :use ((:instance elim-mod-m<x<2*m
+                                           (x (+ a b)))))))
+
+(defun submod (a b m base)
+  (let* ((d (mod (- a b) base))
+         (d (if (< a d) (mod (+ d m) base) d)))
+        d))
+
+(defthmd submod-aux1
+  (implies (and (< a (mod (+ a (- b)) base))
+                (< 0 base) (< a base) (<= b base)
+                (natp base) (natp a) (natp b))
+           (< a b))
+  :rule-classes :forward-chaining)
+
+(defthmd submod-aux2
+  (implies (and (<= (mod (+ a (- b)) base) a)
+                (< 0 base) (< a base) (< b base)
+                (natp base) (natp a) (natp b))
+           (<= b a))
+  :rule-classes :forward-chaining)
+
+(defthmd submod-correct
+  (implies (and (< 0 m) (< m base)
+		(< a m) (<= b m)
+                (natp m) (natp base)
+                (natp a) (natp b))
+           (equal (submod a b m base)
+                  (mod (- a b) m)))
+  :hints (("Goal" :cases ((<= base (+ a b))))
+          ("Subgoal 2.2" :use ((:instance submod-aux1)))
+          ("Subgoal 2.2'''" :cases ((and (< 0 (+ a (- b) m))
+                                         (< (+ a (- b) m) m))))
+          ("Subgoal 2.1" :use ((:instance submod-aux2)))
+          ("Subgoal 1.2" :use ((:instance submod-aux1)))
+          ("Subgoal 1.1" :use ((:instance submod-aux2)))))
+
+
+(defun submod-2 (a b m base)
+  (let* ((d (mod (- a b) base))
+         (d (if (< a b) (mod (+ d m) base) d)))
+        d))
+
+(defthm submod-2-correct
+  (implies (and (< 0 m) (< m base)
+		(< a m) (<= b m)
+                (natp m) (natp base)
+                (natp a) (natp b))
+           (equal (submod-2 a b m base)
+                  (mod (- a b) m)))
+  :hints (("Subgoal 2'" :cases ((and (< 0 (+ a (- b) m))
+                                     (< (+ a (- b) m) m))))))
+
+
+;; =========================================================================
+;;                         ext-submod is correct
+;; =========================================================================
+
+; a < 2*m, b < 2*m
+(defun ext-submod (a b m base)
+  (let* ((a (if (>= a m) (- a m) a))
+         (b (if (>= b m) (- b m) b))
+         (d (mod (- a b) base))
+         (d (if (< a b) (mod (+ d m) base) d)))
+        d))
+
+; a < 2*m, b < 2*m
+(defun ext-submod-2 (a b m base)
+  (let* ((a (mod a m))
+         (b (mod b m))
+         (d (mod (- a b) base))
+         (d (if (< a b) (mod (+ d m) base) d)))
+        d))
+
+(defthmd ext-submod-ext-submod-2-equal
+  (implies (and (< 0 m) (< m base)
+		(< a (* 2 m)) (< b (* 2 m))
+                (natp m) (natp base)
+                (natp a) (natp b))
+           (equal (ext-submod a b m base)
+                  (ext-submod-2 a b m base))))
+
+(defthmd ext-submod-2-correct
+  (implies (and (< 0 m) (< m base)
+		(< a (* 2 m)) (< b (* 2 m))
+                (natp m) (natp base)
+                (natp a) (natp b))
+           (equal (ext-submod-2 a b m base)
+                  (mod (- a b) m))))
+
+
+;; =========================================================================
+;;                            dw-reduce is correct
+;; =========================================================================
+
+(defun dw-reduce (hi lo m base)
+  (let* ((r1 (mod hi m))
+         (r2 (mod (+ (* r1 base) lo) m)))
+        r2))
+
+(defthmd dw-reduce-correct
+  (implies (and (< 0 m) (< m base)
+		(< hi base) (< lo base)
+                (natp m) (natp base)
+                (natp hi) (natp lo))
+           (equal (dw-reduce hi lo m base)
+                  (mod (+ (* hi base) lo) m))))
+
+(defthmd <=-multiply-both-sides-by-z
+  (implies (and (rationalp x) (rationalp y)
+                (< 0 z) (rationalp z))
+           (equal (<= x y)
+                  (<= (* z x) (* z y)))))
+
+(defthmd dw-reduce-aux1
+  (implies (and (< 0 m) (< m base)
+                (natp m) (natp base)
+                (< lo base) (natp lo)
+                (< x m) (natp x))
+           (< (+ lo (* base x)) (* base m)))
+  :hints (("Goal" :cases ((<= (+ x 1) m)))
+          ("Subgoal 1''" :cases ((<= (* base (+ x 1)) (* base m))))
+          ("subgoal 1.2" :use ((:instance <=-multiply-both-sides-by-z
+                                          (x (+ 1 x))
+                                          (y m)
+                                          (z base))))))
+
+(defthm dw-reduce-aux2
+  (implies (and (< x (* base m))
+                (< 0 m) (< m base)
+                (natp m) (natp base) (natp x))
+           (< (floor x m) base)))
+
+;; This is the necessary condition for using _mpd_div_words().
+(defthmd dw-reduce-second-quotient-fits-in-single-word
+  (implies (and (< 0 m) (< m base)
+                (< hi base) (< lo base)
+                (natp m) (natp base)
+                (natp hi) (natp lo)
+                (equal r1 (mod hi m)))
+           (< (floor (+ (* r1 base) lo) m)
+              base))
+  :hints (("Goal" :cases ((< r1 m)))
+          ("Subgoal 1''" :cases ((< (+ lo (* base (mod hi m))) (* base m))))
+          ("Subgoal 1.2" :use ((:instance dw-reduce-aux1
+                                          (x (mod hi m)))))))
+
+
+;; =========================================================================
+;;                            dw-submod is correct
+;; =========================================================================
+
+(defun dw-submod (a hi lo m base)
+  (let* ((r (dw-reduce hi lo m base))
+         (d (mod (- a r) base))
+         (d (if (< a r) (mod (+ d m) base) d)))
+        d))
+
+(defthmd dw-submod-aux1
+  (implies (and (natp a) (< 0 m) (natp m)
+                (natp x) (equal r (mod x m)))
+           (equal (mod (- a x) m)
+                  (mod (- a r) m))))
+
+(defthmd dw-submod-correct
+  (implies (and (< 0 m) (< m base)
+                (natp a) (< a m)
+		(< hi base) (< lo base)
+                (natp m) (natp base)
+                (natp hi) (natp lo))
+           (equal (dw-submod a hi lo m base)
+                  (mod (- a (+ (* base hi) lo)) m)))
+  :hints (("Goal" :in-theory (disable dw-reduce)
+                  :use ((:instance dw-submod-aux1
+                                   (x (+ lo (* base hi)))
+                                   (r (dw-reduce hi lo m base)))
+                        (:instance dw-reduce-correct)))))
+
+
+;; =========================================================================
+;;                      ANSI C arithmetic for uint64_t
+;; =========================================================================
+
+(defun add (a b)
+  (mod (+ a b)
+       (expt 2 64)))
+
+(defun sub (a b)
+  (mod (- a b)
+       (expt 2 64)))
+
+(defun << (w n)
+  (mod (* w (expt 2 n))
+       (expt 2 64)))
+
+(defun >> (w n)
+  (floor w (expt 2 n)))
+
+;; join upper and lower half of a double word, yielding a 128 bit number
+(defun join (hi lo)
+  (+ (* (expt 2 64) hi) lo))
+
+
+;; =============================================================================
+;;                           Fast modular reduction
+;; =============================================================================
+
+;; These are the three primes used in the Number Theoretic Transform.
+;; A fast modular reduction scheme exists for all of them.
+(defmacro p1 ()
+  (+ (expt 2 64) (- (expt 2 32)) 1))
+
+(defmacro p2 ()
+  (+ (expt 2 64) (- (expt 2 34)) 1))
+
+(defmacro p3 ()
+  (+ (expt 2 64) (- (expt 2 40)) 1))
+
+
+;; reduce the double word number hi*2**64 + lo (mod p1)
+(defun simple-mod-reduce-p1 (hi lo)
+  (+ (* (expt 2 32) hi) (- hi) lo))
+
+;; reduce the double word number hi*2**64 + lo (mod p2)
+(defun simple-mod-reduce-p2 (hi lo)
+  (+ (* (expt 2 34) hi) (- hi) lo))
+
+;; reduce the double word number hi*2**64 + lo (mod p3)
+(defun simple-mod-reduce-p3 (hi lo)
+  (+ (* (expt 2 40) hi) (- hi) lo))
+
+
+; ----------------------------------------------------------
+;      The modular reductions given above are correct
+; ----------------------------------------------------------
+
+(defthmd congruence-p1-aux
+  (equal (* (expt 2 64) hi)
+         (+ (* (p1) hi)
+            (* (expt 2 32) hi)
+            (- hi))))
+
+(defthmd congruence-p2-aux
+  (equal (* (expt 2 64) hi)
+         (+ (* (p2) hi)
+            (* (expt 2 34) hi)
+            (- hi))))
+
+(defthmd congruence-p3-aux
+  (equal (* (expt 2 64) hi)
+         (+ (* (p3) hi)
+            (* (expt 2 40) hi)
+            (- hi))))
+
+(defthmd mod-augment
+  (implies (and (rationalp x)
+                (rationalp y)
+                (rationalp m))
+           (equal (mod (+ x y) m)
+                  (mod (+ x (mod y m)) m))))
+
+(defthmd simple-mod-reduce-p1-congruent
+  (implies (and (integerp hi)
+                (integerp lo))
+           (equal (mod (simple-mod-reduce-p1 hi lo) (p1))
+                  (mod (join hi lo) (p1))))
+  :hints (("Goal''" :use ((:instance congruence-p1-aux)
+                          (:instance mod-augment
+                                     (m (p1))
+                                     (x (+ (- hi) lo (* (expt 2 32) hi)))
+                                     (y (* (p1) hi)))))))
+
+(defthmd simple-mod-reduce-p2-congruent
+  (implies (and (integerp hi)
+                (integerp lo))
+           (equal (mod (simple-mod-reduce-p2 hi lo) (p2))
+                  (mod (join hi lo) (p2))))
+  :hints (("Goal''" :use ((:instance congruence-p2-aux)
+                          (:instance mod-augment
+                                     (m (p2))
+                                     (x (+ (- hi) lo (* (expt 2 34) hi)))
+                                     (y (* (p2) hi)))))))
+
+(defthmd simple-mod-reduce-p3-congruent
+  (implies (and (integerp hi)
+                (integerp lo))
+           (equal (mod (simple-mod-reduce-p3 hi lo) (p3))
+                  (mod (join hi lo) (p3))))
+  :hints (("Goal''" :use ((:instance congruence-p3-aux)
+                          (:instance mod-augment
+                                     (m (p3))
+                                     (x (+ (- hi) lo (* (expt 2 40) hi)))
+                                     (y (* (p3) hi)))))))
+
+
+; ---------------------------------------------------------------------
+;  We need a number less than 2*p, so that we can use the trick from
+;  elim-mod-m<x<2*m for the final reduction.
+;  For p1, two modular reductions are sufficient, for p2 and p3 three.
+; ---------------------------------------------------------------------
+
+;; p1: the first reduction is less than 2**96
+(defthmd simple-mod-reduce-p1-<-2**96
+  (implies (and (< hi (expt 2 64))
+                (< lo (expt 2 64))
+                (natp hi) (natp lo))
+           (< (simple-mod-reduce-p1 hi lo)
+              (expt 2 96))))
+
+;; p1: the second reduction is less than 2*p1
+(defthmd simple-mod-reduce-p1-<-2*p1
+  (implies (and (< hi (expt 2 64))
+                (< lo (expt 2 64))
+                (< (join hi lo) (expt 2 96))
+                (natp hi) (natp lo))
+           (< (simple-mod-reduce-p1 hi lo)
+              (* 2 (p1)))))
+
+
+;; p2: the first reduction is less than 2**98
+(defthmd simple-mod-reduce-p2-<-2**98
+  (implies (and (< hi (expt 2 64))
+                (< lo (expt 2 64))
+                (natp hi) (natp lo))
+           (< (simple-mod-reduce-p2 hi lo)
+              (expt 2 98))))
+
+;; p2: the second reduction is less than 2**69
+(defthmd simple-mod-reduce-p2-<-2*69
+  (implies (and (< hi (expt 2 64))
+                (< lo (expt 2 64))
+                (< (join hi lo) (expt 2 98))
+                (natp hi) (natp lo))
+           (< (simple-mod-reduce-p2 hi lo)
+              (expt 2 69))))
+
+;; p3: the third reduction is less than 2*p2
+(defthmd simple-mod-reduce-p2-<-2*p2
+  (implies (and (< hi (expt 2 64))
+                (< lo (expt 2 64))
+                (< (join hi lo) (expt 2 69))
+                (natp hi) (natp lo))
+           (< (simple-mod-reduce-p2 hi lo)
+              (* 2 (p2)))))
+
+
+;; p3: the first reduction is less than 2**104
+(defthmd simple-mod-reduce-p3-<-2**104
+  (implies (and (< hi (expt 2 64))
+                (< lo (expt 2 64))
+                (natp hi) (natp lo))
+           (< (simple-mod-reduce-p3 hi lo)
+              (expt 2 104))))
+
+;; p3: the second reduction is less than 2**81
+(defthmd simple-mod-reduce-p3-<-2**81
+  (implies (and (< hi (expt 2 64))
+                (< lo (expt 2 64))
+                (< (join hi lo) (expt 2 104))
+                (natp hi) (natp lo))
+           (< (simple-mod-reduce-p3 hi lo)
+              (expt 2 81))))
+
+;; p3: the third reduction is less than 2*p3
+(defthmd simple-mod-reduce-p3-<-2*p3
+  (implies (and (< hi (expt 2 64))
+                (< lo (expt 2 64))
+                (< (join hi lo) (expt 2 81))
+                (natp hi) (natp lo))
+           (< (simple-mod-reduce-p3 hi lo)
+              (* 2 (p3)))))
+
+
+; -------------------------------------------------------------------------
+;      The simple modular reductions, adapted for compiler friendly C
+; -------------------------------------------------------------------------
+
+(defun mod-reduce-p1 (hi lo)
+  (let* ((y hi)
+         (x y)
+         (hi (>> hi 32))
+         (x (sub lo x))
+         (hi (if (> x lo) (+ hi -1) hi))
+         (y (<< y 32))
+         (lo (add y x))
+         (hi (if (< lo y) (+ hi 1) hi)))
+        (+ (* hi (expt 2 64)) lo)))
+
+(defun mod-reduce-p2 (hi lo)
+  (let* ((y hi)
+         (x y)
+         (hi (>> hi 30))
+         (x (sub lo x))
+         (hi (if (> x lo) (+ hi -1) hi))
+         (y (<< y 34))
+         (lo (add y x))
+         (hi (if (< lo y) (+ hi 1) hi)))
+        (+ (* hi (expt 2 64)) lo)))
+
+(defun mod-reduce-p3 (hi lo)
+  (let* ((y hi)
+         (x y)
+         (hi (>> hi 24))
+         (x (sub lo x))
+         (hi (if (> x lo) (+ hi -1) hi))
+         (y (<< y 40))
+         (lo (add y x))
+         (hi (if (< lo y) (+ hi 1) hi)))
+        (+ (* hi (expt 2 64)) lo)))
+
+
+; -------------------------------------------------------------------------
+;     The compiler friendly versions are equal to the simple versions
+; -------------------------------------------------------------------------
+
+(defthm mod-reduce-aux1
+  (implies (and (<= 0 a) (natp a) (natp m)
+                (< (- m) b) (<= b 0)
+                (integerp b)
+                (< (mod (+ b a) m)
+                   (mod a m)))
+           (equal (mod (+ b a) m)
+                  (+ b (mod a m))))
+  :hints (("Subgoal 2" :use ((:instance modaux-1b
+                                        (x (+ a b)))))))
+
+(defthm mod-reduce-aux2
+  (implies (and (<= 0 a) (natp a) (natp m)
+                (< b m) (natp b)
+                (< (mod (+ b a) m)
+                   (mod a m)))
+           (equal (+ m (mod (+ b a) m))
+                  (+ b (mod a m)))))
+
+
+(defthm mod-reduce-aux3
+  (implies (and (< 0 a) (natp a) (natp m)
+                (< (- m) b) (< b 0)
+                (integerp b)
+                (<= (mod a m)
+                    (mod (+ b a) m)))
+           (equal (+ (- m) (mod (+ b a) m))
+                  (+ b (mod a m))))
+  :hints (("Subgoal 1.2'" :use ((:instance modaux-1b
+                                           (x b))))
+          ("Subgoal 1''" :use ((:instance modaux-2d
+                                          (x I))))))
+
+
+(defthm mod-reduce-aux4
+  (implies (and (< 0 a) (natp a) (natp m)
+                (< b m) (natp b)
+                (<= (mod a m)
+                    (mod (+ b a) m)))
+           (equal (mod (+ b a) m)
+                  (+ b (mod a m)))))
+
+
+(defthm mod-reduce-p1==simple-mod-reduce-p1
+  (implies (and (< hi (expt 2 64))
+                (< lo (expt 2 64))
+                (natp hi) (natp lo))
+           (equal (mod-reduce-p1 hi lo)
+                  (simple-mod-reduce-p1 hi lo)))
+  :hints (("Goal" :in-theory (disable expt)
+                  :cases ((< 0 hi)))
+          ("Subgoal 1.2.2'" :use ((:instance mod-reduce-aux1
+                                             (m (expt 2 64))
+                                             (b (+ (- HI) LO))
+                                             (a (* (expt 2 32) hi)))))
+          ("Subgoal 1.2.1'" :use ((:instance mod-reduce-aux3
+                                             (m (expt 2 64))
+                                             (b (+ (- HI) LO))
+                                             (a (* (expt 2 32) hi)))))
+          ("Subgoal 1.1.2'" :use ((:instance mod-reduce-aux2
+                                             (m (expt 2 64))
+                                             (b (+ (- HI) LO))
+                                             (a (* (expt 2 32) hi)))))
+          ("Subgoal 1.1.1'" :use ((:instance mod-reduce-aux4
+                                             (m (expt 2 64))
+                                             (b (+ (- HI) LO))
+                                             (a (* (expt 2 32) hi)))))))
+
+
+(defthm mod-reduce-p2==simple-mod-reduce-p2
+  (implies (and (< hi (expt 2 64))
+                (< lo (expt 2 64))
+                (natp hi) (natp lo))
+           (equal (mod-reduce-p2 hi lo)
+                  (simple-mod-reduce-p2 hi lo)))
+  :hints (("Goal" :cases ((< 0 hi)))
+          ("Subgoal 1.2.2'" :use ((:instance mod-reduce-aux1
+                                             (m (expt 2 64))
+                                             (b (+ (- HI) LO))
+                                             (a (* (expt 2 34) hi)))))
+          ("Subgoal 1.2.1'" :use ((:instance mod-reduce-aux3
+                                             (m (expt 2 64))
+                                             (b (+ (- HI) LO))
+                                             (a (* (expt 2 34) hi)))))
+          ("Subgoal 1.1.2'" :use ((:instance mod-reduce-aux2
+                                             (m (expt 2 64))
+                                             (b (+ (- HI) LO))
+                                             (a (* (expt 2 34) hi)))))
+          ("Subgoal 1.1.1'" :use ((:instance mod-reduce-aux4
+                                             (m (expt 2 64))
+                                             (b (+ (- HI) LO))
+                                             (a (* (expt 2 34) hi)))))))
+
+
+(defthm mod-reduce-p3==simple-mod-reduce-p3
+  (implies (and (< hi (expt 2 64))
+                (< lo (expt 2 64))
+                (natp hi) (natp lo))
+           (equal (mod-reduce-p3 hi lo)
+                  (simple-mod-reduce-p3 hi lo)))
+  :hints (("Goal" :cases ((< 0 hi)))
+          ("Subgoal 1.2.2'" :use ((:instance mod-reduce-aux1
+                                             (m (expt 2 64))
+                                             (b (+ (- HI) LO))
+                                             (a (* (expt 2 40) hi)))))
+          ("Subgoal 1.2.1'" :use ((:instance mod-reduce-aux3
+                                             (m (expt 2 64))
+                                             (b (+ (- HI) LO))
+                                             (a (* (expt 2 40) hi)))))
+          ("Subgoal 1.1.2'" :use ((:instance mod-reduce-aux2
+                                             (m (expt 2 64))
+                                             (b (+ (- HI) LO))
+                                             (a (* (expt 2 40) hi)))))
+          ("Subgoal 1.1.1'" :use ((:instance mod-reduce-aux4
+                                             (m (expt 2 64))
+                                             (b (+ (- HI) LO))
+                                             (a (* (expt 2 40) hi)))))))
+
+
+

third_party/python/Modules/_decimal/libmpdec/memory.c

@@ -0,0 +1,297 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include "typearith.h"
+#include "mpalloc.h"
+
+
+#if defined(_MSC_VER)
+  #pragma warning(disable : 4232)
+#endif
+
+
+/* Guaranteed minimum allocation for a coefficient. May be changed once
+   at program start using mpd_setminalloc(). */
+mpd_ssize_t MPD_MINALLOC = MPD_MINALLOC_MIN;
+
+/* Custom allocation and free functions */
+void *(* mpd_mallocfunc)(size_t size) = malloc;
+void *(* mpd_reallocfunc)(void *ptr, size_t size) = realloc;
+void *(* mpd_callocfunc)(size_t nmemb, size_t size) = calloc;
+void (* mpd_free)(void *ptr) = free;
+
+
+/* emulate calloc if it is not available */
+void *
+mpd_callocfunc_em(size_t nmemb, size_t size)
+{
+    void *ptr;
+    size_t req;
+    mpd_size_t overflow;
+
+#if MPD_SIZE_MAX < SIZE_MAX
+    /* full_coverage test only */
+    if (nmemb > MPD_SIZE_MAX || size > MPD_SIZE_MAX) {
+        return NULL;
+    }
+#endif
+
+    req = mul_size_t_overflow((mpd_size_t)nmemb, (mpd_size_t)size,
+                              &overflow);
+    if (overflow) {
+        return NULL;
+    }
+
+    ptr = mpd_mallocfunc(req);
+    if (ptr == NULL) {
+        return NULL;
+    }
+    /* used on uint32_t or uint64_t */
+    memset(ptr, 0, req);
+
+    return ptr;
+}
+
+
+/* malloc with overflow checking */
+void *
+mpd_alloc(mpd_size_t nmemb, mpd_size_t size)
+{
+    mpd_size_t req, overflow;
+
+    req = mul_size_t_overflow(nmemb, size, &overflow);
+    if (overflow) {
+        return NULL;
+    }
+
+    return mpd_mallocfunc(req);
+}
+
+/* calloc with overflow checking */
+void *
+mpd_calloc(mpd_size_t nmemb, mpd_size_t size)
+{
+    mpd_size_t overflow;
+
+    (void)mul_size_t_overflow(nmemb, size, &overflow);
+    if (overflow) {
+        return NULL;
+    }
+
+    return mpd_callocfunc(nmemb, size);
+}
+
+/* realloc with overflow checking */
+void *
+mpd_realloc(void *ptr, mpd_size_t nmemb, mpd_size_t size, uint8_t *err)
+{
+    void *new;
+    mpd_size_t req, overflow;
+
+    req = mul_size_t_overflow(nmemb, size, &overflow);
+    if (overflow) {
+        *err = 1;
+        return ptr;
+    }
+
+    new = mpd_reallocfunc(ptr, req);
+    if (new == NULL) {
+        *err = 1;
+        return ptr;
+    }
+
+    return new;
+}
+
+/* struct hack malloc with overflow checking */
+void *
+mpd_sh_alloc(mpd_size_t struct_size, mpd_size_t nmemb, mpd_size_t size)
+{
+    mpd_size_t req, overflow;
+
+    req = mul_size_t_overflow(nmemb, size, &overflow);
+    if (overflow) {
+        return NULL;
+    }
+
+    req = add_size_t_overflow(req, struct_size, &overflow);
+    if (overflow) {
+        return NULL;
+    }
+
+    return mpd_mallocfunc(req);
+}
+
+
+/* Allocate a new decimal with a coefficient of length 'nwords'. In case
+   of an error the return value is NULL. */
+mpd_t *
+mpd_qnew_size(mpd_ssize_t nwords)
+{
+    mpd_t *result;
+
+    nwords = (nwords < MPD_MINALLOC) ? MPD_MINALLOC : nwords;
+
+    result = mpd_alloc(1, sizeof *result);
+    if (result == NULL) {
+        return NULL;
+    }
+
+    result->data = mpd_alloc(nwords, sizeof *result->data);
+    if (result->data == NULL) {
+        mpd_free(result);
+        return NULL;
+    }
+
+    result->flags = 0;
+    result->exp = 0;
+    result->digits = 0;
+    result->len = 0;
+    result->alloc = nwords;
+
+    return result;
+}
+
+/* Allocate a new decimal with a coefficient of length MPD_MINALLOC.
+   In case of an error the return value is NULL. */
+mpd_t *
+mpd_qnew(void)
+{
+    return mpd_qnew_size(MPD_MINALLOC);
+}
+
+/* Allocate new decimal. Caller can check for NULL or MPD_Malloc_error.
+   Raises on error. */
+mpd_t *
+mpd_new(mpd_context_t *ctx)
+{
+    mpd_t *result;
+
+    result = mpd_qnew();
+    if (result == NULL) {
+        mpd_addstatus_raise(ctx, MPD_Malloc_error);
+    }
+    return result;
+}
+
+/*
+ * Input: 'result' is a static mpd_t with a static coefficient.
+ * Assumption: 'nwords' >= result->alloc.
+ *
+ * Resize the static coefficient to a larger dynamic one and copy the
+ * existing data. If successful, the value of 'result' is unchanged.
+ * Otherwise, set 'result' to NaN and update 'status' with MPD_Malloc_error.
+ */
+int
+mpd_switch_to_dyn(mpd_t *result, mpd_ssize_t nwords, uint32_t *status)
+{
+    mpd_uint_t *p = result->data;
+
+    assert(nwords >= result->alloc);
+
+    result->data = mpd_alloc(nwords, sizeof *result->data);
+    if (result->data == NULL) {
+        result->data = p;
+        mpd_set_qnan(result);
+        mpd_set_positive(result);
+        result->exp = result->digits = result->len = 0;
+        *status |= MPD_Malloc_error;
+        return 0;
+    }
+
+    memcpy(result->data, p, result->alloc * (sizeof *result->data));
+    result->alloc = nwords;
+    mpd_set_dynamic_data(result);
+    return 1;
+}
+
+/*
+ * Input: 'result' is a static mpd_t with a static coefficient.
+ *
+ * Convert the coefficient to a dynamic one that is initialized to zero. If
+ * malloc fails, set 'result' to NaN and update 'status' with MPD_Malloc_error.
+ */
+int
+mpd_switch_to_dyn_zero(mpd_t *result, mpd_ssize_t nwords, uint32_t *status)
+{
+    mpd_uint_t *p = result->data;
+
+    result->data = mpd_calloc(nwords, sizeof *result->data);
+    if (result->data == NULL) {
+        result->data = p;
+        mpd_set_qnan(result);
+        mpd_set_positive(result);
+        result->exp = result->digits = result->len = 0;
+        *status |= MPD_Malloc_error;
+        return 0;
+    }
+
+    result->alloc = nwords;
+    mpd_set_dynamic_data(result);
+
+    return 1;
+}
+
+/*
+ * Input: 'result' is a static or a dynamic mpd_t with a dynamic coefficient.
+ * Resize the coefficient to length 'nwords':
+ *   Case nwords > result->alloc:
+ *     If realloc is successful:
+ *       'result' has a larger coefficient but the same value. Return 1.
+ *     Otherwise:
+ *       Set 'result' to NaN, update status with MPD_Malloc_error and return 0.
+ *   Case nwords < result->alloc:
+ *     If realloc is successful:
+ *       'result' has a smaller coefficient. result->len is undefined. Return 1.
+ *     Otherwise (unlikely):
+ *       'result' is unchanged. Reuse the now oversized coefficient. Return 1.
+ */
+int
+mpd_realloc_dyn(mpd_t *result, mpd_ssize_t nwords, uint32_t *status)
+{
+    uint8_t err = 0;
+
+    result->data = mpd_realloc(result->data, nwords, sizeof *result->data, &err);
+    if (!err) {
+        result->alloc = nwords;
+    }
+    else if (nwords > result->alloc) {
+        mpd_set_qnan(result);
+        mpd_set_positive(result);
+        result->exp = result->digits = result->len = 0;
+        *status |= MPD_Malloc_error;
+        return 0;
+    }
+
+    return 1;
+}
+
+

third_party/python/Modules/_decimal/libmpdec/mpalloc.h

@@ -0,0 +1,51 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef MPALLOC_H
+#define MPALLOC_H
+
+
+#include "mpdecimal.h"
+
+
+/* Internal header file: all symbols have local scope in the DSO */
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
+
+
+int mpd_switch_to_dyn(mpd_t *result, mpd_ssize_t size, uint32_t *status);
+int mpd_switch_to_dyn_zero(mpd_t *result, mpd_ssize_t size, uint32_t *status);
+int mpd_realloc_dyn(mpd_t *result, mpd_ssize_t size, uint32_t *status);
+
+
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
+
+
+#endif
+
+
+

third_party/python/Modules/_decimal/libmpdec/mpdecimal.h

@@ -0,0 +1,847 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef MPDECIMAL_H
+#define MPDECIMAL_H
+
+
+#ifdef __cplusplus
+extern "C" {
+  #ifndef __STDC_LIMIT_MACROS
+    #define __STDC_LIMIT_MACROS
+    #define MPD_CLEAR_STDC_LIMIT_MACROS
+  #endif
+#endif
+
+
+#ifndef _MSC_VER
+  #include "pyconfig.h"
+#endif
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <limits.h>
+#include <assert.h>
+#include <stdint.h>
+#include <inttypes.h>
+
+#ifdef _MSC_VER
+  #include "vccompat.h"
+  #ifndef UNUSED
+    #define UNUSED
+  #endif
+  #define MPD_PRAGMA(x)
+  #define MPD_HIDE_SYMBOLS_START
+  #define MPD_HIDE_SYMBOLS_END
+  #define EXTINLINE extern inline
+#else
+  #ifndef __GNUC_STDC_INLINE__
+    #define __GNUC_STDC_INLINE__ 1
+  #endif
+  #if defined(__GNUC__) && !defined(__INTEL_COMPILER)
+    #define UNUSED __attribute__((unused))
+  #else
+    #define UNUSED
+  #endif
+  #if (defined(__linux__) || defined(__FreeBSD__) || defined(__APPLE__)) && \
+      defined(__GNUC__) && __GNUC__ >= 4 && !defined(__INTEL_COMPILER)
+    #define MPD_PRAGMA(x) _Pragma(x)
+    #define MPD_HIDE_SYMBOLS_START "GCC visibility push(hidden)"
+    #define MPD_HIDE_SYMBOLS_END "GCC visibility pop"
+  #else
+    #define MPD_PRAGMA(x)
+    #define MPD_HIDE_SYMBOLS_START
+    #define MPD_HIDE_SYMBOLS_END
+  #endif
+  #define EXTINLINE
+#endif
+
+
+/* This header file is internal for the purpose of building _decimal.so.
+ * All symbols should have local scope in the DSO. */
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
+
+
+#if !defined(LEGACY_COMPILER)
+  #if !defined(UINT64_MAX)
+    /* The following #error is just a warning. If the compiler indeed does
+     * not have uint64_t, it is perfectly safe to comment out the #error. */
+    #error "Warning: Compiler without uint64_t. Comment out this line."
+    #define LEGACY_COMPILER
+  #endif
+#endif
+
+
+/******************************************************************************/
+/*                                  Version                                   */
+/******************************************************************************/
+
+#define MPD_MAJOR_VERSION 2
+#define MPD_MINOR_VERSION 4
+#define MPD_MICRO_VERSION 2
+
+#define MPD_VERSION "2.4.2"
+
+#define MPD_VERSION_HEX ((MPD_MAJOR_VERSION << 24) | \
+                         (MPD_MINOR_VERSION << 16) | \
+                         (MPD_MICRO_VERSION <<  8))
+
+const char *mpd_version(void);
+
+
+/******************************************************************************/
+/*                              Configuration                                 */
+/******************************************************************************/
+
+#if defined(UNIVERSAL)
+  #if defined(CONFIG_64) || defined(CONFIG_32)
+    #error "cannot use CONFIG_64 or CONFIG_32 with UNIVERSAL."
+  #endif
+  #if defined(__ppc__)
+    #define CONFIG_32
+    #define ANSI
+  #elif defined(__ppc64__)
+    #define CONFIG_64
+    #define ANSI
+  #elif defined(__i386__)
+    #define CONFIG_32
+    #define ANSI
+  #elif defined(__x86_64__)
+    #define CONFIG_64
+    #define ASM
+  #else
+    #error "unknown architecture for universal build."
+  #endif
+#endif
+
+
+/* BEGIN CONFIG_64 */
+#if defined(CONFIG_64)
+/* types for modular and base arithmetic */
+#define MPD_UINT_MAX UINT64_MAX
+#define MPD_BITS_PER_UINT 64
+typedef uint64_t mpd_uint_t;  /* unsigned mod type */
+
+#define MPD_SIZE_MAX SIZE_MAX
+typedef size_t mpd_size_t; /* unsigned size type */
+
+/* type for exp, digits, len, prec */
+#define MPD_SSIZE_MAX INT64_MAX
+#define MPD_SSIZE_MIN INT64_MIN
+typedef int64_t mpd_ssize_t;
+#define _mpd_strtossize strtoll
+
+/* decimal arithmetic */
+#define MPD_RADIX 10000000000000000000ULL  /* 10**19 */
+#define MPD_RDIGITS 19
+#define MPD_MAX_POW10 19
+#define MPD_EXPDIGITS 19  /* MPD_EXPDIGITS <= MPD_RDIGITS+1 */
+
+#define MPD_MAXTRANSFORM_2N 4294967296ULL      /* 2**32 */
+#define MPD_MAX_PREC 999999999999999999LL
+#define MPD_MAX_PREC_LOG2 64
+#define MPD_ELIMIT  1000000000000000000LL
+#define MPD_MAX_EMAX   999999999999999999LL    /* ELIMIT-1 */
+#define MPD_MIN_EMIN  (-999999999999999999LL)  /* -EMAX */
+#define MPD_MIN_ETINY (MPD_MIN_EMIN-(MPD_MAX_PREC-1))
+#define MPD_EXP_INF 2000000000000000001LL
+#define MPD_EXP_CLAMP (-4000000000000000001LL)
+#define MPD_MAXIMPORT 105263157894736842L /* ceil((2*MPD_MAX_PREC)/MPD_RDIGITS) */
+
+/* conversion specifiers */
+#define PRI_mpd_uint_t PRIu64
+#define PRI_mpd_ssize_t PRIi64
+/* END CONFIG_64 */
+
+
+/* BEGIN CONFIG_32 */
+#elif defined(CONFIG_32)
+/* types for modular and base arithmetic */
+#define MPD_UINT_MAX UINT32_MAX
+#define MPD_BITS_PER_UINT 32
+typedef uint32_t mpd_uint_t;  /* unsigned mod type */
+
+#ifndef LEGACY_COMPILER
+#define MPD_UUINT_MAX UINT64_MAX
+typedef uint64_t mpd_uuint_t; /* double width unsigned mod type */
+#endif
+
+#define MPD_SIZE_MAX SIZE_MAX
+typedef size_t mpd_size_t; /* unsigned size type */
+
+/* type for dec->len, dec->exp, ctx->prec */
+#define MPD_SSIZE_MAX INT32_MAX
+#define MPD_SSIZE_MIN INT32_MIN
+typedef int32_t mpd_ssize_t;
+#define _mpd_strtossize strtol
+
+/* decimal arithmetic */
+#define MPD_RADIX 1000000000UL  /* 10**9 */
+#define MPD_RDIGITS 9
+#define MPD_MAX_POW10 9
+#define MPD_EXPDIGITS 10 /* MPD_EXPDIGITS <= MPD_RDIGITS+1 */
+
+#define MPD_MAXTRANSFORM_2N 33554432UL /* 2**25 */
+#define MPD_MAX_PREC 425000000L
+#define MPD_MAX_PREC_LOG2 32
+#define MPD_ELIMIT 425000001L
+#define MPD_MAX_EMAX 425000000L        /* ELIMIT-1 */
+#define MPD_MIN_EMIN (-425000000L)     /* -EMAX */
+#define MPD_MIN_ETINY (MPD_MIN_EMIN-(MPD_MAX_PREC-1))
+#define MPD_EXP_INF 1000000001L      /* allows for emax=999999999 in the tests */
+#define MPD_EXP_CLAMP (-2000000001L) /* allows for emin=-999999999 in the tests */
+#define MPD_MAXIMPORT 94444445L      /* ceil((2*MPD_MAX_PREC)/MPD_RDIGITS) */
+
+/* conversion specifiers */
+#define PRI_mpd_uint_t PRIu32
+#define PRI_mpd_ssize_t PRIi32
+/* END CONFIG_32 */
+
+#else
+  #error "define CONFIG_64 or CONFIG_32"
+#endif
+/* END CONFIG */
+
+
+#if MPD_SIZE_MAX != MPD_UINT_MAX
+  #error "unsupported platform: need mpd_size_t == mpd_uint_t"
+#endif
+
+
+/******************************************************************************/
+/*                                Context                                     */
+/******************************************************************************/
+
+enum {
+    MPD_ROUND_UP,          /* round away from 0               */
+    MPD_ROUND_DOWN,        /* round toward 0 (truncate)       */
+    MPD_ROUND_CEILING,     /* round toward +infinity          */
+    MPD_ROUND_FLOOR,       /* round toward -infinity          */
+    MPD_ROUND_HALF_UP,     /* 0.5 is rounded up               */
+    MPD_ROUND_HALF_DOWN,   /* 0.5 is rounded down             */
+    MPD_ROUND_HALF_EVEN,   /* 0.5 is rounded to even          */
+    MPD_ROUND_05UP,        /* round zero or five away from 0  */
+    MPD_ROUND_TRUNC,       /* truncate, but set infinity      */
+    MPD_ROUND_GUARD
+};
+
+enum { MPD_CLAMP_DEFAULT, MPD_CLAMP_IEEE_754, MPD_CLAMP_GUARD };
+
+extern const char *mpd_round_string[MPD_ROUND_GUARD];
+extern const char *mpd_clamp_string[MPD_CLAMP_GUARD];
+
+
+typedef struct mpd_context_t {
+    mpd_ssize_t prec;   /* precision */
+    mpd_ssize_t emax;   /* max positive exp */
+    mpd_ssize_t emin;   /* min negative exp */
+    uint32_t traps;     /* status events that should be trapped */
+    uint32_t status;    /* status flags */
+    uint32_t newtrap;   /* set by mpd_addstatus_raise() */
+    int      round;     /* rounding mode */
+    int      clamp;     /* clamp mode */
+    int      allcr;     /* all functions correctly rounded */
+} mpd_context_t;
+
+
+/* Status flags */
+#define MPD_Clamped             0x00000001U
+#define MPD_Conversion_syntax   0x00000002U
+#define MPD_Division_by_zero    0x00000004U
+#define MPD_Division_impossible 0x00000008U
+#define MPD_Division_undefined  0x00000010U
+#define MPD_Fpu_error           0x00000020U
+#define MPD_Inexact             0x00000040U
+#define MPD_Invalid_context     0x00000080U
+#define MPD_Invalid_operation   0x00000100U
+#define MPD_Malloc_error        0x00000200U
+#define MPD_Not_implemented     0x00000400U
+#define MPD_Overflow            0x00000800U
+#define MPD_Rounded             0x00001000U
+#define MPD_Subnormal           0x00002000U
+#define MPD_Underflow           0x00004000U
+#define MPD_Max_status         (0x00008000U-1U)
+
+/* Conditions that result in an IEEE 754 exception */
+#define MPD_IEEE_Invalid_operation (MPD_Conversion_syntax |   \
+                                    MPD_Division_impossible | \
+                                    MPD_Division_undefined |  \
+                                    MPD_Fpu_error |           \
+                                    MPD_Invalid_context |     \
+                                    MPD_Invalid_operation |   \
+                                    MPD_Malloc_error)         \
+
+/* Errors that require the result of an operation to be set to NaN */
+#define MPD_Errors (MPD_IEEE_Invalid_operation | \
+                    MPD_Division_by_zero)
+
+/* Default traps */
+#define MPD_Traps (MPD_IEEE_Invalid_operation | \
+                   MPD_Division_by_zero |       \
+                   MPD_Overflow |               \
+                   MPD_Underflow)
+
+/* Official name */
+#define MPD_Insufficient_storage MPD_Malloc_error
+
+/* IEEE 754 interchange format contexts */
+#define MPD_IEEE_CONTEXT_MAX_BITS 512 /* 16*(log2(MPD_MAX_EMAX / 3)-3) */
+#define MPD_DECIMAL32 32
+#define MPD_DECIMAL64 64
+#define MPD_DECIMAL128 128
+
+
+#define MPD_MINALLOC_MIN 2
+#define MPD_MINALLOC_MAX 64
+extern mpd_ssize_t MPD_MINALLOC;
+extern void (* mpd_traphandler)(mpd_context_t *);
+void mpd_dflt_traphandler(mpd_context_t *);
+
+void mpd_setminalloc(mpd_ssize_t n);
+void mpd_init(mpd_context_t *ctx, mpd_ssize_t prec);
+
+void mpd_maxcontext(mpd_context_t *ctx);
+void mpd_defaultcontext(mpd_context_t *ctx);
+void mpd_basiccontext(mpd_context_t *ctx);
+int mpd_ieee_context(mpd_context_t *ctx, int bits);
+
+mpd_ssize_t mpd_getprec(const mpd_context_t *ctx);
+mpd_ssize_t mpd_getemax(const mpd_context_t *ctx);
+mpd_ssize_t mpd_getemin(const mpd_context_t *ctx);
+int mpd_getround(const mpd_context_t *ctx);
+uint32_t mpd_gettraps(const mpd_context_t *ctx);
+uint32_t mpd_getstatus(const mpd_context_t *ctx);
+int mpd_getclamp(const mpd_context_t *ctx);
+int mpd_getcr(const mpd_context_t *ctx);
+
+int mpd_qsetprec(mpd_context_t *ctx, mpd_ssize_t prec);
+int mpd_qsetemax(mpd_context_t *ctx, mpd_ssize_t emax);
+int mpd_qsetemin(mpd_context_t *ctx, mpd_ssize_t emin);
+int mpd_qsetround(mpd_context_t *ctx, int newround);
+int mpd_qsettraps(mpd_context_t *ctx, uint32_t flags);
+int mpd_qsetstatus(mpd_context_t *ctx, uint32_t flags);
+int mpd_qsetclamp(mpd_context_t *ctx, int c);
+int mpd_qsetcr(mpd_context_t *ctx, int c);
+void mpd_addstatus_raise(mpd_context_t *ctx, uint32_t flags);
+
+
+/******************************************************************************/
+/*                           Decimal Arithmetic                               */
+/******************************************************************************/
+
+/* mpd_t flags */
+#define MPD_POS                 ((uint8_t)0)
+#define MPD_NEG                 ((uint8_t)1)
+#define MPD_INF                 ((uint8_t)2)
+#define MPD_NAN                 ((uint8_t)4)
+#define MPD_SNAN                ((uint8_t)8)
+#define MPD_SPECIAL (MPD_INF|MPD_NAN|MPD_SNAN)
+#define MPD_STATIC              ((uint8_t)16)
+#define MPD_STATIC_DATA         ((uint8_t)32)
+#define MPD_SHARED_DATA         ((uint8_t)64)
+#define MPD_CONST_DATA          ((uint8_t)128)
+#define MPD_DATAFLAGS (MPD_STATIC_DATA|MPD_SHARED_DATA|MPD_CONST_DATA)
+
+/* mpd_t */
+typedef struct mpd_t {
+    uint8_t flags;
+    mpd_ssize_t exp;
+    mpd_ssize_t digits;
+    mpd_ssize_t len;
+    mpd_ssize_t alloc;
+    mpd_uint_t *data;
+} mpd_t;
+
+
+typedef unsigned char uchar;
+
+
+/******************************************************************************/
+/*                       Quiet, thread-safe functions                         */
+/******************************************************************************/
+
+/* format specification */
+typedef struct mpd_spec_t {
+    mpd_ssize_t min_width; /* minimum field width */
+    mpd_ssize_t prec;      /* fraction digits or significant digits */
+    char type;             /* conversion specifier */
+    char align;            /* alignment */
+    char sign;             /* sign printing/alignment */
+    char fill[5];          /* fill character */
+    const char *dot;       /* decimal point */
+    const char *sep;       /* thousands separator */
+    const char *grouping;  /* grouping of digits */
+} mpd_spec_t;
+
+/* output to a string */
+char *mpd_to_sci(const mpd_t *dec, int fmt);
+char *mpd_to_eng(const mpd_t *dec, int fmt);
+mpd_ssize_t mpd_to_sci_size(char **res, const mpd_t *dec, int fmt);
+mpd_ssize_t mpd_to_eng_size(char **res, const mpd_t *dec, int fmt);
+int mpd_validate_lconv(mpd_spec_t *spec);
+int mpd_parse_fmt_str(mpd_spec_t *spec, const char *fmt, int caps);
+char *mpd_qformat_spec(const mpd_t *dec, const mpd_spec_t *spec, const mpd_context_t *ctx, uint32_t *status);
+char *mpd_qformat(const mpd_t *dec, const char *fmt, const mpd_context_t *ctx, uint32_t *status);
+
+#define MPD_NUM_FLAGS 15
+#define MPD_MAX_FLAG_STRING 208
+#define MPD_MAX_FLAG_LIST (MPD_MAX_FLAG_STRING+18)
+#define MPD_MAX_SIGNAL_LIST 121
+int mpd_snprint_flags(char *dest, int nmemb, uint32_t flags);
+int mpd_lsnprint_flags(char *dest, int nmemb, uint32_t flags, const char *flag_string[]);
+int mpd_lsnprint_signals(char *dest, int nmemb, uint32_t flags, const char *signal_string[]);
+
+/* output to a file */
+void mpd_fprint(FILE *file, const mpd_t *dec);
+void mpd_print(const mpd_t *dec);
+
+/* assignment from a string */
+void mpd_qset_string(mpd_t *dec, const char *s, const mpd_context_t *ctx, uint32_t *status);
+
+/* set to NaN with error flags */
+void mpd_seterror(mpd_t *result, uint32_t flags, uint32_t *status);
+/* set a special with sign and type */
+void mpd_setspecial(mpd_t *dec, uint8_t sign, uint8_t type);
+/* set coefficient to zero or all nines */
+void mpd_zerocoeff(mpd_t *result);
+void mpd_qmaxcoeff(mpd_t *result, const mpd_context_t *ctx, uint32_t *status);
+
+/* quietly assign a C integer type to an mpd_t */
+void mpd_qset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx, uint32_t *status);
+#ifndef LEGACY_COMPILER
+void mpd_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, uint32_t *status);
+#endif
+
+/* quietly assign a C integer type to an mpd_t with a static coefficient */
+void mpd_qsset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx, uint32_t *status);
+
+/* quietly get a C integer type from an mpd_t */
+mpd_ssize_t mpd_qget_ssize(const mpd_t *dec, uint32_t *status);
+mpd_uint_t mpd_qget_uint(const mpd_t *dec, uint32_t *status);
+mpd_uint_t mpd_qabs_uint(const mpd_t *dec, uint32_t *status);
+
+int32_t mpd_qget_i32(const mpd_t *dec, uint32_t *status);
+uint32_t mpd_qget_u32(const mpd_t *dec, uint32_t *status);
+#ifndef LEGACY_COMPILER
+int64_t mpd_qget_i64(const mpd_t *dec, uint32_t *status);
+uint64_t mpd_qget_u64(const mpd_t *dec, uint32_t *status);
+#endif
+
+/* quiet functions */
+int mpd_qcheck_nan(mpd_t *nanresult, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+int mpd_qcheck_nans(mpd_t *nanresult, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qfinalize(mpd_t *result, const mpd_context_t *ctx, uint32_t *status);
+
+const char *mpd_class(const mpd_t *a, const mpd_context_t *ctx);
+
+int mpd_qcopy(mpd_t *result, const mpd_t *a,  uint32_t *status);
+mpd_t *mpd_qncopy(const mpd_t *a);
+int mpd_qcopy_abs(mpd_t *result, const mpd_t *a, uint32_t *status);
+int mpd_qcopy_negate(mpd_t *result, const mpd_t *a, uint32_t *status);
+int mpd_qcopy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status);
+
+void mpd_qand(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qinvert(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qlogb(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qor(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qscaleb(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qxor(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+int mpd_same_quantum(const mpd_t *a, const mpd_t *b);
+
+void mpd_qrotate(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+int mpd_qshiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status);
+mpd_uint_t mpd_qshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status);
+mpd_uint_t mpd_qshiftr_inplace(mpd_t *result, mpd_ssize_t n);
+void mpd_qshift(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qshiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, const mpd_context_t *ctx, uint32_t *status);
+
+int mpd_qcmp(const mpd_t *a, const mpd_t *b, uint32_t *status);
+int mpd_qcompare(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+int mpd_qcompare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+int mpd_cmp_total(const mpd_t *a, const mpd_t *b);
+int mpd_cmp_total_mag(const mpd_t *a, const mpd_t *b);
+int mpd_compare_total(mpd_t *result, const mpd_t *a, const mpd_t *b);
+int mpd_compare_total_mag(mpd_t *result, const mpd_t *a, const mpd_t *b);
+
+void mpd_qround_to_intx(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qround_to_int(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qtrunc(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qfloor(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qceil(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+
+void mpd_qabs(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmax(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmax_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmin(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmin_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qminus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qplus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qnext_minus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qnext_plus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qnext_toward(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qquantize(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qrescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qrescale_fmt(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qreduce(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qadd_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qadd_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qadd_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qadd_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsub_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsub_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmul_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmul_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qfma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdiv(mpd_t *q, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdiv_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdiv_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdiv_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdiv_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdivint(mpd_t *q, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qrem(mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qrem_near(mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qpow(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qpowmod(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_t *mod, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qln10(mpd_t *result, mpd_ssize_t prec, uint32_t *status);
+void mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qlog10(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsqrt(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+
+#ifndef LEGACY_COMPILER
+void mpd_qadd_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qadd_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsub_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsub_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmul_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmul_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdiv_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdiv_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status);
+#endif
+
+
+size_t mpd_sizeinbase(const mpd_t *a, uint32_t base);
+void mpd_qimport_u16(mpd_t *result, const uint16_t *srcdata, size_t srclen,
+                     uint8_t srcsign, uint32_t srcbase,
+                     const mpd_context_t *ctx, uint32_t *status);
+void mpd_qimport_u32(mpd_t *result, const uint32_t *srcdata, size_t srclen,
+                     uint8_t srcsign, uint32_t srcbase,
+                     const mpd_context_t *ctx, uint32_t *status);
+size_t mpd_qexport_u16(uint16_t **rdata, size_t rlen, uint32_t base,
+                       const mpd_t *src, uint32_t *status);
+size_t mpd_qexport_u32(uint32_t **rdata, size_t rlen, uint32_t base,
+                       const mpd_t *src, uint32_t *status);
+
+
+/******************************************************************************/
+/*                           Signalling functions                             */
+/******************************************************************************/
+
+char *mpd_format(const mpd_t *dec, const char *fmt, mpd_context_t *ctx);
+void mpd_import_u16(mpd_t *result, const uint16_t *srcdata, size_t srclen, uint8_t srcsign, uint32_t base, mpd_context_t *ctx);
+void mpd_import_u32(mpd_t *result, const uint32_t *srcdata, size_t srclen, uint8_t srcsign, uint32_t base, mpd_context_t *ctx);
+size_t mpd_export_u16(uint16_t **rdata, size_t rlen, uint32_t base, const mpd_t *src, mpd_context_t *ctx);
+size_t mpd_export_u32(uint32_t **rdata, size_t rlen, uint32_t base, const mpd_t *src, mpd_context_t *ctx);
+void mpd_finalize(mpd_t *result, mpd_context_t *ctx);
+int mpd_check_nan(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+int mpd_check_nans(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_set_string(mpd_t *result, const char *s, mpd_context_t *ctx);
+void mpd_maxcoeff(mpd_t *result, mpd_context_t *ctx);
+void mpd_sset_ssize(mpd_t *result, mpd_ssize_t a, mpd_context_t *ctx);
+void mpd_sset_i32(mpd_t *result, int32_t a, mpd_context_t *ctx);
+void mpd_sset_uint(mpd_t *result, mpd_uint_t a, mpd_context_t *ctx);
+void mpd_sset_u32(mpd_t *result, uint32_t a, mpd_context_t *ctx);
+void mpd_set_ssize(mpd_t *result, mpd_ssize_t a, mpd_context_t *ctx);
+void mpd_set_i32(mpd_t *result, int32_t a, mpd_context_t *ctx);
+void mpd_set_uint(mpd_t *result, mpd_uint_t a, mpd_context_t *ctx);
+void mpd_set_u32(mpd_t *result, uint32_t a, mpd_context_t *ctx);
+#ifndef LEGACY_COMPILER
+void mpd_set_i64(mpd_t *result, int64_t a, mpd_context_t *ctx);
+void mpd_set_u64(mpd_t *result, uint64_t a, mpd_context_t *ctx);
+#endif
+mpd_ssize_t mpd_get_ssize(const mpd_t *a, mpd_context_t *ctx);
+mpd_uint_t mpd_get_uint(const mpd_t *a, mpd_context_t *ctx);
+mpd_uint_t mpd_abs_uint(const mpd_t *a, mpd_context_t *ctx);
+int32_t mpd_get_i32(const mpd_t *a, mpd_context_t *ctx);
+uint32_t mpd_get_u32(const mpd_t *a, mpd_context_t *ctx);
+#ifndef LEGACY_COMPILER
+int64_t mpd_get_i64(const mpd_t *a, mpd_context_t *ctx);
+uint64_t mpd_get_u64(const mpd_t *a, mpd_context_t *ctx);
+#endif
+void mpd_and(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_copy(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_canonical(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_copy_abs(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_copy_negate(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_copy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_invert(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_logb(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_or(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_rotate(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_scaleb(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_shiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx);
+mpd_uint_t mpd_shiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx);
+void mpd_shiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx);
+void mpd_shift(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_xor(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_abs(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+int mpd_cmp(const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+int mpd_compare(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+int mpd_compare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_add(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_add_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx);
+void mpd_add_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx);
+void mpd_add_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx);
+void mpd_add_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx);
+void mpd_sub(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_sub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx);
+void mpd_sub_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx);
+void mpd_sub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx);
+void mpd_sub_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx);
+void mpd_div(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_div_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx);
+void mpd_div_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx);
+void mpd_div_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx);
+void mpd_div_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx);
+void mpd_divmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_divint(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_exp(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_fma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, mpd_context_t *ctx);
+void mpd_ln(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_log10(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_max(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_max_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_min(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_min_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_minus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_mul(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_mul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx);
+void mpd_mul_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx);
+void mpd_mul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx);
+void mpd_mul_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx);
+void mpd_next_minus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_next_plus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_next_toward(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_plus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_pow(mpd_t *result, const mpd_t *base, const mpd_t *exp, mpd_context_t *ctx);
+void mpd_powmod(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_t *mod, mpd_context_t *ctx);
+void mpd_quantize(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_rescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, mpd_context_t *ctx);
+void mpd_reduce(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_rem(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_rem_near(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_round_to_intx(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_round_to_int(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_trunc(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_floor(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_ceil(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_sqrt(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_invroot(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+
+#ifndef LEGACY_COMPILER
+void mpd_add_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx);
+void mpd_add_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx);
+void mpd_sub_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx);
+void mpd_sub_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx);
+void mpd_div_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx);
+void mpd_div_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx);
+void mpd_mul_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx);
+void mpd_mul_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx);
+#endif
+
+
+/******************************************************************************/
+/*                          Configuration specific                            */
+/******************************************************************************/
+
+#ifdef CONFIG_64
+void mpd_qsset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_sset_i64(mpd_t *result, int64_t a, mpd_context_t *ctx);
+void mpd_sset_u64(mpd_t *result, uint64_t a, mpd_context_t *ctx);
+#endif
+
+
+/******************************************************************************/
+/*                       Get attributes of a decimal                          */
+/******************************************************************************/
+
+EXTINLINE mpd_ssize_t mpd_adjexp(const mpd_t *dec);
+EXTINLINE mpd_ssize_t mpd_etiny(const mpd_context_t *ctx);
+EXTINLINE mpd_ssize_t mpd_etop(const mpd_context_t *ctx);
+EXTINLINE mpd_uint_t mpd_msword(const mpd_t *dec);
+EXTINLINE int mpd_word_digits(mpd_uint_t word);
+/* most significant digit of a word */
+EXTINLINE mpd_uint_t mpd_msd(mpd_uint_t word);
+/* least significant digit of a word */
+EXTINLINE mpd_uint_t mpd_lsd(mpd_uint_t word);
+/* coefficient size needed to store 'digits' */
+EXTINLINE mpd_ssize_t mpd_digits_to_size(mpd_ssize_t digits);
+/* number of digits in the exponent, undefined for MPD_SSIZE_MIN */
+EXTINLINE int mpd_exp_digits(mpd_ssize_t exp);
+EXTINLINE int mpd_iscanonical(const mpd_t *dec UNUSED);
+EXTINLINE int mpd_isfinite(const mpd_t *dec);
+EXTINLINE int mpd_isinfinite(const mpd_t *dec);
+EXTINLINE int mpd_isinteger(const mpd_t *dec);
+EXTINLINE int mpd_isnan(const mpd_t *dec);
+EXTINLINE int mpd_isnegative(const mpd_t *dec);
+EXTINLINE int mpd_ispositive(const mpd_t *dec);
+EXTINLINE int mpd_isqnan(const mpd_t *dec);
+EXTINLINE int mpd_issigned(const mpd_t *dec);
+EXTINLINE int mpd_issnan(const mpd_t *dec);
+EXTINLINE int mpd_isspecial(const mpd_t *dec);
+EXTINLINE int mpd_iszero(const mpd_t *dec);
+/* undefined for special numbers */
+EXTINLINE int mpd_iszerocoeff(const mpd_t *dec);
+EXTINLINE int mpd_isnormal(const mpd_t *dec, const mpd_context_t *ctx);
+EXTINLINE int mpd_issubnormal(const mpd_t *dec, const mpd_context_t *ctx);
+/* odd word */
+EXTINLINE int mpd_isoddword(mpd_uint_t word);
+/* odd coefficient */
+EXTINLINE int mpd_isoddcoeff(const mpd_t *dec);
+/* odd decimal, only defined for integers */
+int mpd_isodd(const mpd_t *dec);
+/* even decimal, only defined for integers */
+int mpd_iseven(const mpd_t *dec);
+/* 0 if dec is positive, 1 if dec is negative */
+EXTINLINE uint8_t mpd_sign(const mpd_t *dec);
+/* 1 if dec is positive, -1 if dec is negative */
+EXTINLINE int mpd_arith_sign(const mpd_t *dec);
+EXTINLINE long mpd_radix(void);
+EXTINLINE int mpd_isdynamic(const mpd_t *dec);
+EXTINLINE int mpd_isstatic(const mpd_t *dec);
+EXTINLINE int mpd_isdynamic_data(const mpd_t *dec);
+EXTINLINE int mpd_isstatic_data(const mpd_t *dec);
+EXTINLINE int mpd_isshared_data(const mpd_t *dec);
+EXTINLINE int mpd_isconst_data(const mpd_t *dec);
+EXTINLINE mpd_ssize_t mpd_trail_zeros(const mpd_t *dec);
+
+
+/******************************************************************************/
+/*                       Set attributes of a decimal                          */
+/******************************************************************************/
+
+/* set number of decimal digits in the coefficient */
+EXTINLINE void mpd_setdigits(mpd_t *result);
+EXTINLINE void mpd_set_sign(mpd_t *result, uint8_t sign);
+/* copy sign from another decimal */
+EXTINLINE void mpd_signcpy(mpd_t *result, const mpd_t *a);
+EXTINLINE void mpd_set_infinity(mpd_t *result);
+EXTINLINE void mpd_set_qnan(mpd_t *result);
+EXTINLINE void mpd_set_snan(mpd_t *result);
+EXTINLINE void mpd_set_negative(mpd_t *result);
+EXTINLINE void mpd_set_positive(mpd_t *result);
+EXTINLINE void mpd_set_dynamic(mpd_t *result);
+EXTINLINE void mpd_set_static(mpd_t *result);
+EXTINLINE void mpd_set_dynamic_data(mpd_t *result);
+EXTINLINE void mpd_set_static_data(mpd_t *result);
+EXTINLINE void mpd_set_shared_data(mpd_t *result);
+EXTINLINE void mpd_set_const_data(mpd_t *result);
+EXTINLINE void mpd_clear_flags(mpd_t *result);
+EXTINLINE void mpd_set_flags(mpd_t *result, uint8_t flags);
+EXTINLINE void mpd_copy_flags(mpd_t *result, const mpd_t *a);
+
+
+/******************************************************************************/
+/*                              Error Macros                                  */
+/******************************************************************************/
+
+#define mpd_err_fatal(...) \
+    do {fprintf(stderr, "%s:%d: error: ", __FILE__, __LINE__); \
+        fprintf(stderr, __VA_ARGS__);  fputc('\n', stderr);    \
+        abort();                                               \
+    } while (0)
+#define mpd_err_warn(...) \
+    do {fprintf(stderr, "%s:%d: warning: ", __FILE__, __LINE__); \
+        fprintf(stderr, __VA_ARGS__); fputc('\n', stderr);       \
+    } while (0)
+
+
+/******************************************************************************/
+/*                            Memory handling                                 */
+/******************************************************************************/
+
+extern void *(* mpd_mallocfunc)(size_t size);
+extern void *(* mpd_callocfunc)(size_t nmemb, size_t size);
+extern void *(* mpd_reallocfunc)(void *ptr, size_t size);
+extern void (* mpd_free)(void *ptr);
+
+void *mpd_callocfunc_em(size_t nmemb, size_t size);
+
+void *mpd_alloc(mpd_size_t nmemb, mpd_size_t size);
+void *mpd_calloc(mpd_size_t nmemb, mpd_size_t size);
+void *mpd_realloc(void *ptr, mpd_size_t nmemb, mpd_size_t size, uint8_t *err);
+void *mpd_sh_alloc(mpd_size_t struct_size, mpd_size_t nmemb, mpd_size_t size);
+
+mpd_t *mpd_qnew(void);
+mpd_t *mpd_new(mpd_context_t *ctx);
+mpd_t *mpd_qnew_size(mpd_ssize_t size);
+EXTINLINE void mpd_del(mpd_t *dec);
+
+EXTINLINE void mpd_uint_zero(mpd_uint_t *dest, mpd_size_t len);
+EXTINLINE int mpd_qresize(mpd_t *result, mpd_ssize_t size, uint32_t *status);
+EXTINLINE int mpd_qresize_zero(mpd_t *result, mpd_ssize_t size, uint32_t *status);
+EXTINLINE void mpd_minalloc(mpd_t *result);
+
+int mpd_resize(mpd_t *result, mpd_ssize_t size, mpd_context_t *ctx);
+int mpd_resize_zero(mpd_t *result, mpd_ssize_t size, mpd_context_t *ctx);
+
+
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
+
+
+#ifdef __cplusplus
+  #ifdef MPD_CLEAR_STDC_LIMIT_MACROS
+    #undef MPD_CLEAR_STDC_LIMIT_MACROS
+    #undef __STDC_LIMIT_MACROS
+  #endif
+} /* END extern "C" */
+#endif
+
+
+#endif /* MPDECIMAL_H */
+
+
+

third_party/python/Modules/_decimal/libmpdec/numbertheory.c

@@ -0,0 +1,132 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdlib.h>
+#include <assert.h>
+#include "bits.h"
+#include "umodarith.h"
+#include "numbertheory.h"
+
+
+/* Bignum: Initialize the Number Theoretic Transform. */
+
+
+/*
+ * Return the nth root of unity in F(p). This corresponds to e**((2*pi*i)/n)
+ * in the Fourier transform. We have w**n == 1 (mod p).
+ *    n := transform length.
+ *    sign := -1 for forward transform, 1 for backward transform.
+ *    modnum := one of {P1, P2, P3}.
+ */
+mpd_uint_t
+_mpd_getkernel(mpd_uint_t n, int sign, int modnum)
+{
+    mpd_uint_t umod, p, r, xi;
+#ifdef PPRO
+    double dmod;
+    uint32_t dinvmod[3];
+#endif
+
+    SETMODULUS(modnum);
+    r = mpd_roots[modnum]; /* primitive root of F(p) */
+    p = umod;
+    xi = (p-1) / n;
+
+    if (sign == -1)
+        return POWMOD(r, (p-1-xi));
+    else
+        return POWMOD(r, xi);
+}
+
+/*
+ * Initialize and return transform parameters.
+ *    n := transform length.
+ *    sign := -1 for forward transform, 1 for backward transform.
+ *    modnum := one of {P1, P2, P3}.
+ */
+struct fnt_params *
+_mpd_init_fnt_params(mpd_size_t n, int sign, int modnum)
+{
+    struct fnt_params *tparams;
+    mpd_uint_t umod;
+#ifdef PPRO
+    double dmod;
+    uint32_t dinvmod[3];
+#endif
+    mpd_uint_t kernel, w;
+    mpd_uint_t i;
+    mpd_size_t nhalf;
+
+    assert(ispower2(n));
+    assert(sign == -1 || sign == 1);
+    assert(P1 <= modnum && modnum <= P3);
+
+    nhalf = n/2;
+    tparams = mpd_sh_alloc(sizeof *tparams, nhalf, sizeof (mpd_uint_t));
+    if (tparams == NULL) {
+        return NULL;
+    }
+
+    SETMODULUS(modnum);
+    kernel = _mpd_getkernel(n, sign, modnum);
+
+    tparams->modnum = modnum;
+    tparams->modulus = umod;
+    tparams->kernel = kernel;
+
+    /* wtable[] := w**0, w**1, ..., w**(nhalf-1) */
+    w = 1;
+    for (i = 0; i < nhalf; i++) {
+        tparams->wtable[i] = w;
+        w = MULMOD(w, kernel);
+    }
+
+    return tparams;
+}
+
+/* Initialize wtable of size three. */
+void
+_mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum)
+{
+    mpd_uint_t umod;
+#ifdef PPRO
+    double dmod;
+    uint32_t dinvmod[3];
+#endif
+    mpd_uint_t kernel;
+
+    SETMODULUS(modnum);
+    kernel = _mpd_getkernel(3, sign, modnum);
+
+    w3table[0] = 1;
+    w3table[1] = kernel;
+    w3table[2] = POWMOD(kernel, 2);
+}
+
+

third_party/python/Modules/_decimal/libmpdec/numbertheory.h

@@ -0,0 +1,78 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef NUMBER_THEORY_H
+#define NUMBER_THEORY_H
+
+
+#include "constants.h"
+#include "mpdecimal.h"
+
+
+/* Internal header file: all symbols have local scope in the DSO */
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
+
+
+/* transform parameters */
+struct fnt_params {
+    int modnum;
+    mpd_uint_t modulus;
+    mpd_uint_t kernel;
+    mpd_uint_t wtable[];
+};
+
+
+mpd_uint_t _mpd_getkernel(mpd_uint_t n, int sign, int modnum);
+struct fnt_params *_mpd_init_fnt_params(mpd_size_t n, int sign, int modnum);
+void _mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum);
+
+
+#ifdef PPRO
+static inline void
+ppro_setmodulus(int modnum, mpd_uint_t *umod, double *dmod, uint32_t dinvmod[3])
+{
+    *dmod = *umod =  mpd_moduli[modnum];
+    dinvmod[0] = mpd_invmoduli[modnum][0];
+    dinvmod[1] = mpd_invmoduli[modnum][1];
+    dinvmod[2] = mpd_invmoduli[modnum][2];
+}
+#else
+static inline void
+std_setmodulus(int modnum, mpd_uint_t *umod)
+{
+    *umod =  mpd_moduli[modnum];
+}
+#endif
+
+
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
+
+
+#endif
+
+

third_party/python/Modules/_decimal/libmpdec/sixstep.c

@@ -0,0 +1,214 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include <assert.h>
+#include "bits.h"
+#include "difradix2.h"
+#include "numbertheory.h"
+#include "transpose.h"
+#include "umodarith.h"
+#include "sixstep.h"
+
+
+/* Bignum: Cache efficient Matrix Fourier Transform for arrays of the
+   form 2**n (See literature/six-step.txt). */
+
+
+/* forward transform with sign = -1 */
+int
+six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
+{
+    struct fnt_params *tparams;
+    mpd_size_t log2n, C, R;
+    mpd_uint_t kernel;
+    mpd_uint_t umod;
+#ifdef PPRO
+    double dmod;
+    uint32_t dinvmod[3];
+#endif
+    mpd_uint_t *x, w0, w1, wstep;
+    mpd_size_t i, k;
+
+
+    assert(ispower2(n));
+    assert(n >= 16);
+    assert(n <= MPD_MAXTRANSFORM_2N);
+
+    log2n = mpd_bsr(n);
+    C = ((mpd_size_t)1) << (log2n / 2);  /* number of columns */
+    R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */
+
+
+    /* Transpose the matrix. */
+    if (!transpose_pow2(a, R, C)) {
+        return 0;
+    }
+
+    /* Length R transform on the rows. */
+    if ((tparams = _mpd_init_fnt_params(R, -1, modnum)) == NULL) {
+        return 0;
+    }
+    for (x = a; x < a+n; x += R) {
+        fnt_dif2(x, R, tparams);
+    }
+
+    /* Transpose the matrix. */
+    if (!transpose_pow2(a, C, R)) {
+        mpd_free(tparams);
+        return 0;
+    }
+
+    /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */
+    SETMODULUS(modnum);
+    kernel = _mpd_getkernel(n, -1, modnum);
+    for (i = 1; i < R; i++) {
+        w0 = 1;                  /* r**(i*0): initial value for k=0 */
+        w1 = POWMOD(kernel, i);  /* r**(i*1): initial value for k=1 */
+        wstep = MULMOD(w1, w1);  /* r**(2*i) */
+        for (k = 0; k < C; k += 2) {
+            mpd_uint_t x0 = a[i*C+k];
+            mpd_uint_t x1 = a[i*C+k+1];
+            MULMOD2(&x0, w0, &x1, w1);
+            MULMOD2C(&w0, &w1, wstep);  /* r**(i*(k+2)) = r**(i*k) * r**(2*i) */
+            a[i*C+k] = x0;
+            a[i*C+k+1] = x1;
+        }
+    }
+
+    /* Length C transform on the rows. */
+    if (C != R) {
+        mpd_free(tparams);
+        if ((tparams = _mpd_init_fnt_params(C, -1, modnum)) == NULL) {
+            return 0;
+        }
+    }
+    for (x = a; x < a+n; x += C) {
+        fnt_dif2(x, C, tparams);
+    }
+    mpd_free(tparams);
+
+#if 0
+    /* An unordered transform is sufficient for convolution. */
+    /* Transpose the matrix. */
+    if (!transpose_pow2(a, R, C)) {
+        return 0;
+    }
+#endif
+
+    return 1;
+}
+
+
+/* reverse transform, sign = 1 */
+int
+inv_six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
+{
+    struct fnt_params *tparams;
+    mpd_size_t log2n, C, R;
+    mpd_uint_t kernel;
+    mpd_uint_t umod;
+#ifdef PPRO
+    double dmod;
+    uint32_t dinvmod[3];
+#endif
+    mpd_uint_t *x, w0, w1, wstep;
+    mpd_size_t i, k;
+
+
+    assert(ispower2(n));
+    assert(n >= 16);
+    assert(n <= MPD_MAXTRANSFORM_2N);
+
+    log2n = mpd_bsr(n);
+    C = ((mpd_size_t)1) << (log2n / 2); /* number of columns */
+    R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */
+
+
+#if 0
+    /* An unordered transform is sufficient for convolution. */
+    /* Transpose the matrix, producing an R*C matrix. */
+    if (!transpose_pow2(a, C, R)) {
+        return 0;
+    }
+#endif
+
+    /* Length C transform on the rows. */
+    if ((tparams = _mpd_init_fnt_params(C, 1, modnum)) == NULL) {
+        return 0;
+    }
+    for (x = a; x < a+n; x += C) {
+        fnt_dif2(x, C, tparams);
+    }
+
+    /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */
+    SETMODULUS(modnum);
+    kernel = _mpd_getkernel(n, 1, modnum);
+    for (i = 1; i < R; i++) {
+        w0 = 1;
+        w1 = POWMOD(kernel, i);
+        wstep = MULMOD(w1, w1);
+        for (k = 0; k < C; k += 2) {
+            mpd_uint_t x0 = a[i*C+k];
+            mpd_uint_t x1 = a[i*C+k+1];
+            MULMOD2(&x0, w0, &x1, w1);
+            MULMOD2C(&w0, &w1, wstep);
+            a[i*C+k] = x0;
+            a[i*C+k+1] = x1;
+        }
+    }
+
+    /* Transpose the matrix. */
+    if (!transpose_pow2(a, R, C)) {
+        mpd_free(tparams);
+        return 0;
+    }
+
+    /* Length R transform on the rows. */
+    if (R != C) {
+        mpd_free(tparams);
+        if ((tparams = _mpd_init_fnt_params(R, 1, modnum)) == NULL) {
+            return 0;
+        }
+    }
+    for (x = a; x < a+n; x += R) {
+        fnt_dif2(x, R, tparams);
+    }
+    mpd_free(tparams);
+
+    /* Transpose the matrix. */
+    if (!transpose_pow2(a, C, R)) {
+        return 0;
+    }
+
+    return 1;
+}
+
+

third_party/python/Modules/_decimal/libmpdec/sixstep.h

@@ -0,0 +1,48 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef SIX_STEP_H
+#define SIX_STEP_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+
+
+/* Internal header file: all symbols have local scope in the DSO */
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
+
+
+int six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum);
+int inv_six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum);
+
+
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
+
+
+#endif

third_party/python/Modules/_decimal/libmpdec/transpose.c

@@ -0,0 +1,276 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <limits.h>
+#include <assert.h>
+#include "bits.h"
+#include "constants.h"
+#include "typearith.h"
+#include "transpose.h"
+
+
+#define BUFSIZE 4096
+#define SIDE 128
+
+
+/* Bignum: The transpose functions are used for very large transforms
+   in sixstep.c and fourstep.c. */
+
+
+/* Definition of the matrix transpose */
+void
+std_trans(mpd_uint_t dest[], mpd_uint_t src[], mpd_size_t rows, mpd_size_t cols)
+{
+    mpd_size_t idest, isrc;
+    mpd_size_t r, c;
+
+    for (r = 0; r < rows; r++) {
+        isrc = r * cols;
+        idest = r;
+        for (c = 0; c < cols; c++) {
+            dest[idest] = src[isrc];
+            isrc += 1;
+            idest += rows;
+        }
+    }
+}
+
+/*
+ * Swap half-rows of 2^n * (2*2^n) matrix.
+ * FORWARD_CYCLE: even/odd permutation of the halfrows.
+ * BACKWARD_CYCLE: reverse the even/odd permutation.
+ */
+static int
+swap_halfrows_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols, int dir)
+{
+    mpd_uint_t buf1[BUFSIZE];
+    mpd_uint_t buf2[BUFSIZE];
+    mpd_uint_t *readbuf, *writebuf, *hp;
+    mpd_size_t *done, dbits;
+    mpd_size_t b = BUFSIZE, stride;
+    mpd_size_t hn, hmax; /* halfrow number */
+    mpd_size_t m, r=0;
+    mpd_size_t offset;
+    mpd_size_t next;
+
+
+    assert(cols == mul_size_t(2, rows));
+
+    if (dir == FORWARD_CYCLE) {
+        r = rows;
+    }
+    else if (dir == BACKWARD_CYCLE) {
+        r = 2;
+    }
+    else {
+        abort(); /* GCOV_NOT_REACHED */
+    }
+
+    m = cols - 1;
+    hmax = rows; /* cycles start at odd halfrows */
+    dbits = 8 * sizeof *done;
+    if ((done = mpd_calloc(hmax/(sizeof *done) + 1, sizeof *done)) == NULL) {
+        return 0;
+    }
+
+    for (hn = 1; hn <= hmax; hn += 2) {
+
+        if (done[hn/dbits] & mpd_bits[hn%dbits]) {
+            continue;
+        }
+
+        readbuf = buf1; writebuf = buf2;
+
+        for (offset = 0; offset < cols/2; offset += b) {
+
+            stride = (offset + b < cols/2) ? b : cols/2-offset;
+
+            hp = matrix + hn*cols/2;
+            memcpy(readbuf, hp+offset, stride*(sizeof *readbuf));
+            pointerswap(&readbuf, &writebuf);
+
+            next = mulmod_size_t(hn, r, m);
+            hp = matrix + next*cols/2;
+
+            while (next != hn) {
+
+                memcpy(readbuf, hp+offset, stride*(sizeof *readbuf));
+                memcpy(hp+offset, writebuf, stride*(sizeof *writebuf));
+                pointerswap(&readbuf, &writebuf);
+
+                done[next/dbits] |= mpd_bits[next%dbits];
+
+                next = mulmod_size_t(next, r, m);
+                    hp = matrix + next*cols/2;
+
+            }
+
+            memcpy(hp+offset, writebuf, stride*(sizeof *writebuf));
+
+            done[hn/dbits] |= mpd_bits[hn%dbits];
+        }
+    }
+
+    mpd_free(done);
+    return 1;
+}
+
+/* In-place transpose of a square matrix */
+static inline void
+squaretrans(mpd_uint_t *buf, mpd_size_t cols)
+{
+    mpd_uint_t tmp;
+    mpd_size_t idest, isrc;
+    mpd_size_t r, c;
+
+    for (r = 0; r < cols; r++) {
+        c = r+1;
+        isrc = r*cols + c;
+        idest = c*cols + r;
+        for (c = r+1; c < cols; c++) {
+            tmp = buf[isrc];
+            buf[isrc] = buf[idest];
+            buf[idest] = tmp;
+            isrc += 1;
+            idest += cols;
+        }
+    }
+}
+
+/*
+ * Transpose 2^n * 2^n matrix. For cache efficiency, the matrix is split into
+ * square blocks with side length 'SIDE'. First, the blocks are transposed,
+ * then a square transposition is done on each individual block.
+ */
+static void
+squaretrans_pow2(mpd_uint_t *matrix, mpd_size_t size)
+{
+    mpd_uint_t buf1[SIDE*SIDE];
+    mpd_uint_t buf2[SIDE*SIDE];
+    mpd_uint_t *to, *from;
+    mpd_size_t b = size;
+    mpd_size_t r, c;
+    mpd_size_t i;
+
+    while (b > SIDE) b >>= 1;
+
+    for (r = 0; r < size; r += b) {
+
+        for (c = r; c < size; c += b) {
+
+            from = matrix + r*size + c;
+            to = buf1;
+            for (i = 0; i < b; i++) {
+                memcpy(to, from, b*(sizeof *to));
+                from += size;
+                to += b;
+            }
+            squaretrans(buf1, b);
+
+            if (r == c) {
+                to = matrix + r*size + c;
+                from = buf1;
+                for (i = 0; i < b; i++) {
+                    memcpy(to, from, b*(sizeof *to));
+                    from += b;
+                    to += size;
+                }
+                continue;
+            }
+            else {
+                from = matrix + c*size + r;
+                to = buf2;
+                for (i = 0; i < b; i++) {
+                    memcpy(to, from, b*(sizeof *to));
+                    from += size;
+                    to += b;
+                }
+                squaretrans(buf2, b);
+
+                to = matrix + c*size + r;
+                from = buf1;
+                for (i = 0; i < b; i++) {
+                    memcpy(to, from, b*(sizeof *to));
+                    from += b;
+                    to += size;
+                }
+
+                to = matrix + r*size + c;
+                from = buf2;
+                for (i = 0; i < b; i++) {
+                    memcpy(to, from, b*(sizeof *to));
+                    from += b;
+                    to += size;
+                }
+            }
+        }
+    }
+
+}
+
+/*
+ * In-place transposition of a 2^n x 2^n or a 2^n x (2*2^n)
+ * or a (2*2^n) x 2^n matrix.
+ */
+int
+transpose_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols)
+{
+    mpd_size_t size = mul_size_t(rows, cols);
+
+    assert(ispower2(rows));
+    assert(ispower2(cols));
+
+    if (cols == rows) {
+        squaretrans_pow2(matrix, rows);
+    }
+    else if (cols == mul_size_t(2, rows)) {
+        if (!swap_halfrows_pow2(matrix, rows, cols, FORWARD_CYCLE)) {
+            return 0;
+        }
+        squaretrans_pow2(matrix, rows);
+        squaretrans_pow2(matrix+(size/2), rows);
+    }
+    else if (rows == mul_size_t(2, cols)) {
+        squaretrans_pow2(matrix, cols);
+        squaretrans_pow2(matrix+(size/2), cols);
+        if (!swap_halfrows_pow2(matrix, cols, rows, BACKWARD_CYCLE)) {
+            return 0;
+        }
+    }
+    else {
+        abort(); /* GCOV_NOT_REACHED */
+    }
+
+    return 1;
+}
+
+

third_party/python/Modules/_decimal/libmpdec/transpose.h

@@ -0,0 +1,62 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef TRANSPOSE_H
+#define TRANSPOSE_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+
+
+/* Internal header file: all symbols have local scope in the DSO */
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
+
+
+enum {FORWARD_CYCLE, BACKWARD_CYCLE};
+
+
+void std_trans(mpd_uint_t dest[], mpd_uint_t src[], mpd_size_t rows, mpd_size_t cols);
+int transpose_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols);
+void transpose_3xpow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols);
+
+
+static inline void pointerswap(mpd_uint_t **a, mpd_uint_t **b)
+{
+    mpd_uint_t *tmp;
+
+    tmp = *b;
+    *b = *a;
+    *a = tmp;
+}
+
+
+MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
+
+
+#endif

third_party/python/Modules/_decimal/libmpdec/typearith.h

@@ -0,0 +1,669 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef TYPEARITH_H
+#define TYPEARITH_H
+
+
+#include "mpdecimal.h"
+
+
+/*****************************************************************************/
+/*                 Low level native arithmetic on basic types                */
+/*****************************************************************************/
+
+
+/** ------------------------------------------------------------
+ **           Double width multiplication and division
+ ** ------------------------------------------------------------
+ */
+
+#if defined(CONFIG_64)
+#if defined(ANSI)
+#if defined(HAVE_UINT128_T)
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+    __uint128_t hl;
+
+    hl = (__uint128_t)a * b;
+
+    *hi = hl >> 64;
+    *lo = (mpd_uint_t)hl;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+               mpd_uint_t d)
+{
+    __uint128_t hl;
+
+    hl = ((__uint128_t)hi<<64) + lo;
+    *q = (mpd_uint_t)(hl / d); /* quotient is known to fit */
+    *r = (mpd_uint_t)(hl - (__uint128_t)(*q) * d);
+}
+#else
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+    uint32_t w[4], carry;
+    uint32_t ah, al, bh, bl;
+    uint64_t hl;
+
+    ah = (uint32_t)(a>>32); al = (uint32_t)a;
+    bh = (uint32_t)(b>>32); bl = (uint32_t)b;
+
+    hl = (uint64_t)al * bl;
+    w[0] = (uint32_t)hl;
+    carry = (uint32_t)(hl>>32);
+
+    hl = (uint64_t)ah * bl + carry;
+    w[1] = (uint32_t)hl;
+    w[2] = (uint32_t)(hl>>32);
+
+    hl = (uint64_t)al * bh + w[1];
+    w[1] = (uint32_t)hl;
+    carry = (uint32_t)(hl>>32);
+
+    hl = ((uint64_t)ah * bh + w[2]) + carry;
+    w[2] = (uint32_t)hl;
+    w[3] = (uint32_t)(hl>>32);
+
+    *hi = ((uint64_t)w[3]<<32) + w[2];
+    *lo = ((uint64_t)w[1]<<32) + w[0];
+}
+
+/*
+ * By Henry S. Warren: http://www.hackersdelight.org/HDcode/divlu.c.txt
+ * http://www.hackersdelight.org/permissions.htm:
+ * "You are free to use, copy, and distribute any of the code on this web
+ *  site, whether modified by you or not. You need not give attribution."
+ *
+ * Slightly modified, comments are mine.
+ */
+static inline int
+nlz(uint64_t x)
+{
+    int n;
+
+    if (x == 0) return(64);
+
+    n = 0;
+    if (x <= 0x00000000FFFFFFFF) {n = n +32; x = x <<32;}
+    if (x <= 0x0000FFFFFFFFFFFF) {n = n +16; x = x <<16;}
+    if (x <= 0x00FFFFFFFFFFFFFF) {n = n + 8; x = x << 8;}
+    if (x <= 0x0FFFFFFFFFFFFFFF) {n = n + 4; x = x << 4;}
+    if (x <= 0x3FFFFFFFFFFFFFFF) {n = n + 2; x = x << 2;}
+    if (x <= 0x7FFFFFFFFFFFFFFF) {n = n + 1;}
+
+    return n;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t u1, mpd_uint_t u0,
+               mpd_uint_t v)
+{
+    const mpd_uint_t b = 4294967296;
+    mpd_uint_t un1, un0,
+               vn1, vn0,
+               q1, q0,
+               un32, un21, un10,
+               rhat, t;
+    int s;
+
+    assert(u1 < v);
+
+    s = nlz(v);
+    v = v << s;
+    vn1 = v >> 32;
+    vn0 = v & 0xFFFFFFFF;
+
+    t = (s == 0) ? 0 : u0 >> (64 - s);
+    un32 = (u1 << s) | t;
+    un10 = u0 << s;
+
+    un1 = un10 >> 32;
+    un0 = un10 & 0xFFFFFFFF;
+
+    q1 = un32 / vn1;
+    rhat = un32 - q1*vn1;
+again1:
+    if (q1 >= b || q1*vn0 > b*rhat + un1) {
+        q1 = q1 - 1;
+        rhat = rhat + vn1;
+        if (rhat < b) goto again1;
+    }
+
+    /*
+     *  Before again1 we had:
+     *      (1) q1*vn1   + rhat         = un32
+     *      (2) q1*vn1*b + rhat*b + un1 = un32*b + un1
+     *
+     *  The statements inside the if-clause do not change the value
+     *  of the left-hand side of (2), and the loop is only exited
+     *  if q1*vn0 <= rhat*b + un1, so:
+     *
+     *      (3) q1*vn1*b + q1*vn0 <= un32*b + un1
+     *      (4)              q1*v <= un32*b + un1
+     *      (5)                 0 <= un32*b + un1 - q1*v
+     *
+     *  By (5) we are certain that the possible add-back step from
+     *  Knuth's algorithm D is never required.
+     *
+     *  Since the final quotient is less than 2**64, the following
+     *  must be true:
+     *
+     *      (6) un32*b + un1 - q1*v <= UINT64_MAX
+     *
+     *  This means that in the following line, the high words
+     *  of un32*b and q1*v can be discarded without any effect
+     *  on the result.
+     */
+    un21 = un32*b + un1 - q1*v;
+
+    q0 = un21 / vn1;
+    rhat = un21 - q0*vn1;
+again2:
+    if (q0 >= b || q0*vn0 > b*rhat + un0) {
+        q0 = q0 - 1;
+        rhat = rhat + vn1;
+        if (rhat < b) goto again2;
+    }
+
+    *q = q1*b + q0;
+    *r = (un21*b + un0 - q0*v) >> s;
+}
+#endif
+
+/* END ANSI */
+#elif defined(ASM)
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+    mpd_uint_t h, l;
+
+    __asm__ ( "mulq %3\n\t"
+              : "=d" (h), "=a" (l)
+              : "%a" (a), "rm" (b)
+              : "cc"
+    );
+
+    *hi = h;
+    *lo = l;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+               mpd_uint_t d)
+{
+    mpd_uint_t qq, rr;
+
+    __asm__ ( "divq %4\n\t"
+              : "=a" (qq), "=d" (rr)
+              : "a" (lo), "d" (hi), "rm" (d)
+              : "cc"
+    );
+
+    *q = qq;
+    *r = rr;
+}
+/* END GCC ASM */
+#elif defined(MASM)
+#include <intrin.h>
+#pragma intrinsic(_umul128)
+
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+    *lo = _umul128(a, b, hi);
+}
+
+void _mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+                    mpd_uint_t d);
+
+/* END MASM (_MSC_VER) */
+#else
+  #error "need platform specific 128 bit multiplication and division"
+#endif
+
+#define DIVMOD(q, r, v, d) *q = v / d; *r = v - *q * d
+static inline void
+_mpd_divmod_pow10(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t exp)
+{
+    assert(exp <= 19);
+
+    if (exp <= 9) {
+        if (exp <= 4) {
+            switch (exp) {
+            case 0: *q = v; *r = 0; break;
+            case 1: DIVMOD(q, r, v, 10UL); break;
+            case 2: DIVMOD(q, r, v, 100UL); break;
+            case 3: DIVMOD(q, r, v, 1000UL); break;
+            case 4: DIVMOD(q, r, v, 10000UL); break;
+            }
+        }
+        else {
+            switch (exp) {
+            case 5: DIVMOD(q, r, v, 100000UL); break;
+            case 6: DIVMOD(q, r, v, 1000000UL); break;
+            case 7: DIVMOD(q, r, v, 10000000UL); break;
+            case 8: DIVMOD(q, r, v, 100000000UL); break;
+            case 9: DIVMOD(q, r, v, 1000000000UL); break;
+            }
+        }
+    }
+    else {
+        if (exp <= 14) {
+            switch (exp) {
+            case 10: DIVMOD(q, r, v, 10000000000ULL); break;
+            case 11: DIVMOD(q, r, v, 100000000000ULL); break;
+            case 12: DIVMOD(q, r, v, 1000000000000ULL); break;
+            case 13: DIVMOD(q, r, v, 10000000000000ULL); break;
+            case 14: DIVMOD(q, r, v, 100000000000000ULL); break;
+            }
+        }
+        else {
+            switch (exp) {
+            case 15: DIVMOD(q, r, v, 1000000000000000ULL); break;
+            case 16: DIVMOD(q, r, v, 10000000000000000ULL); break;
+            case 17: DIVMOD(q, r, v, 100000000000000000ULL); break;
+            case 18: DIVMOD(q, r, v, 1000000000000000000ULL); break;
+            case 19: DIVMOD(q, r, v, 10000000000000000000ULL); break; /* GCOV_NOT_REACHED */
+            }
+        }
+    }
+}
+
+/* END CONFIG_64 */
+#elif defined(CONFIG_32)
+#if defined(ANSI)
+#if !defined(LEGACY_COMPILER)
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+    mpd_uuint_t hl;
+
+    hl = (mpd_uuint_t)a * b;
+
+    *hi = hl >> 32;
+    *lo = (mpd_uint_t)hl;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+               mpd_uint_t d)
+{
+    mpd_uuint_t hl;
+
+    hl = ((mpd_uuint_t)hi<<32) + lo;
+    *q = (mpd_uint_t)(hl / d); /* quotient is known to fit */
+    *r = (mpd_uint_t)(hl - (mpd_uuint_t)(*q) * d);
+}
+/* END ANSI + uint64_t */
+#else
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+    uint16_t w[4], carry;
+    uint16_t ah, al, bh, bl;
+    uint32_t hl;
+
+    ah = (uint16_t)(a>>16); al = (uint16_t)a;
+    bh = (uint16_t)(b>>16); bl = (uint16_t)b;
+
+    hl = (uint32_t)al * bl;
+    w[0] = (uint16_t)hl;
+    carry = (uint16_t)(hl>>16);
+
+    hl = (uint32_t)ah * bl + carry;
+    w[1] = (uint16_t)hl;
+    w[2] = (uint16_t)(hl>>16);
+
+    hl = (uint32_t)al * bh + w[1];
+    w[1] = (uint16_t)hl;
+    carry = (uint16_t)(hl>>16);
+
+    hl = ((uint32_t)ah * bh + w[2]) + carry;
+    w[2] = (uint16_t)hl;
+    w[3] = (uint16_t)(hl>>16);
+
+    *hi = ((uint32_t)w[3]<<16) + w[2];
+    *lo = ((uint32_t)w[1]<<16) + w[0];
+}
+
+/*
+ * By Henry S. Warren: http://www.hackersdelight.org/HDcode/divlu.c.txt
+ * http://www.hackersdelight.org/permissions.htm:
+ * "You are free to use, copy, and distribute any of the code on this web
+ *  site, whether modified by you or not. You need not give attribution."
+ *
+ * Slightly modified, comments are mine.
+ */
+static inline int
+nlz(uint32_t x)
+{
+    int n;
+
+    if (x == 0) return(32);
+
+    n = 0;
+    if (x <= 0x0000FFFF) {n = n +16; x = x <<16;}
+    if (x <= 0x00FFFFFF) {n = n + 8; x = x << 8;}
+    if (x <= 0x0FFFFFFF) {n = n + 4; x = x << 4;}
+    if (x <= 0x3FFFFFFF) {n = n + 2; x = x << 2;}
+    if (x <= 0x7FFFFFFF) {n = n + 1;}
+
+    return n;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t u1, mpd_uint_t u0,
+               mpd_uint_t v)
+{
+    const mpd_uint_t b = 65536;
+    mpd_uint_t un1, un0,
+               vn1, vn0,
+               q1, q0,
+               un32, un21, un10,
+               rhat, t;
+    int s;
+
+    assert(u1 < v);
+
+    s = nlz(v);
+    v = v << s;
+    vn1 = v >> 16;
+    vn0 = v & 0xFFFF;
+
+    t = (s == 0) ? 0 : u0 >> (32 - s);
+    un32 = (u1 << s) | t;
+    un10 = u0 << s;
+
+    un1 = un10 >> 16;
+    un0 = un10 & 0xFFFF;
+
+    q1 = un32 / vn1;
+    rhat = un32 - q1*vn1;
+again1:
+    if (q1 >= b || q1*vn0 > b*rhat + un1) {
+        q1 = q1 - 1;
+        rhat = rhat + vn1;
+        if (rhat < b) goto again1;
+    }
+
+    /*
+     *  Before again1 we had:
+     *      (1) q1*vn1   + rhat         = un32
+     *      (2) q1*vn1*b + rhat*b + un1 = un32*b + un1
+     *
+     *  The statements inside the if-clause do not change the value
+     *  of the left-hand side of (2), and the loop is only exited
+     *  if q1*vn0 <= rhat*b + un1, so:
+     *
+     *      (3) q1*vn1*b + q1*vn0 <= un32*b + un1
+     *      (4)              q1*v <= un32*b + un1
+     *      (5)                 0 <= un32*b + un1 - q1*v
+     *
+     *  By (5) we are certain that the possible add-back step from
+     *  Knuth's algorithm D is never required.
+     *
+     *  Since the final quotient is less than 2**32, the following
+     *  must be true:
+     *
+     *      (6) un32*b + un1 - q1*v <= UINT32_MAX
+     *
+     *  This means that in the following line, the high words
+     *  of un32*b and q1*v can be discarded without any effect
+     *  on the result.
+     */
+    un21 = un32*b + un1 - q1*v;
+
+    q0 = un21 / vn1;
+    rhat = un21 - q0*vn1;
+again2:
+    if (q0 >= b || q0*vn0 > b*rhat + un0) {
+        q0 = q0 - 1;
+        rhat = rhat + vn1;
+        if (rhat < b) goto again2;
+    }
+
+    *q = q1*b + q0;
+    *r = (un21*b + un0 - q0*v) >> s;
+}
+#endif /* END ANSI + LEGACY_COMPILER */
+
+/* END ANSI */
+#elif defined(ASM)
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+    mpd_uint_t h, l;
+
+    __asm__ ( "mull %3\n\t"
+              : "=d" (h), "=a" (l)
+              : "%a" (a), "rm" (b)
+              : "cc"
+    );
+
+    *hi = h;
+    *lo = l;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+               mpd_uint_t d)
+{
+    mpd_uint_t qq, rr;
+
+    __asm__ ( "divl %4\n\t"
+              : "=a" (qq), "=d" (rr)
+              : "a" (lo), "d" (hi), "rm" (d)
+              : "cc"
+    );
+
+    *q = qq;
+    *r = rr;
+}
+/* END GCC ASM */
+#elif defined(MASM)
+static inline void __cdecl
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+    mpd_uint_t h, l;
+
+    __asm {
+        mov eax, a
+        mul b
+        mov h, edx
+        mov l, eax
+    }
+
+    *hi = h;
+    *lo = l;
+}
+
+static inline void __cdecl
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+               mpd_uint_t d)
+{
+    mpd_uint_t qq, rr;
+
+    __asm {
+        mov eax, lo
+        mov edx, hi
+        div d
+        mov qq, eax
+        mov rr, edx
+    }
+
+    *q = qq;
+    *r = rr;
+}
+/* END MASM (_MSC_VER) */
+#else
+  #error "need platform specific 64 bit multiplication and division"
+#endif
+
+#define DIVMOD(q, r, v, d) *q = v / d; *r = v - *q * d
+static inline void
+_mpd_divmod_pow10(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t exp)
+{
+    assert(exp <= 9);
+
+    if (exp <= 4) {
+        switch (exp) {
+        case 0: *q = v; *r = 0; break;
+        case 1: DIVMOD(q, r, v, 10UL); break;
+        case 2: DIVMOD(q, r, v, 100UL); break;
+        case 3: DIVMOD(q, r, v, 1000UL); break;
+        case 4: DIVMOD(q, r, v, 10000UL); break;
+        }
+    }
+    else {
+        switch (exp) {
+        case 5: DIVMOD(q, r, v, 100000UL); break;
+        case 6: DIVMOD(q, r, v, 1000000UL); break;
+        case 7: DIVMOD(q, r, v, 10000000UL); break;
+        case 8: DIVMOD(q, r, v, 100000000UL); break;
+        case 9: DIVMOD(q, r, v, 1000000000UL); break; /* GCOV_NOT_REACHED */
+        }
+    }
+}
+/* END CONFIG_32 */
+
+/* NO CONFIG */
+#else
+  #error "define CONFIG_64 or CONFIG_32"
+#endif /* CONFIG */
+
+
+static inline void
+_mpd_div_word(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t d)
+{
+    *q = v / d;
+    *r = v - *q * d;
+}
+
+static inline void
+_mpd_idiv_word(mpd_ssize_t *q, mpd_ssize_t *r, mpd_ssize_t v, mpd_ssize_t d)
+{
+    *q = v / d;
+    *r = v - *q * d;
+}
+
+
+/** ------------------------------------------------------------
+ **              Arithmetic with overflow checking
+ ** ------------------------------------------------------------
+ */
+
+/* The following macros do call exit() in case of an overflow.
+   If the library is used correctly (i.e. with valid context
+   parameters), such overflows cannot occur. The macros are used
+   as sanity checks in a couple of strategic places and should
+   be viewed as a handwritten version of gcc's -ftrapv option. */
+
+static inline mpd_size_t
+add_size_t(mpd_size_t a, mpd_size_t b)
+{
+    if (a > MPD_SIZE_MAX - b) {
+        mpd_err_fatal("add_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */
+    }
+    return a + b;
+}
+
+static inline mpd_size_t
+sub_size_t(mpd_size_t a, mpd_size_t b)
+{
+    if (b > a) {
+        mpd_err_fatal("sub_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */
+    }
+    return a - b;
+}
+
+#if MPD_SIZE_MAX != MPD_UINT_MAX
+  #error "adapt mul_size_t() and mulmod_size_t()"
+#endif
+
+static inline mpd_size_t
+mul_size_t(mpd_size_t a, mpd_size_t b)
+{
+    mpd_uint_t hi, lo;
+
+    _mpd_mul_words(&hi, &lo, (mpd_uint_t)a, (mpd_uint_t)b);
+    if (hi) {
+        mpd_err_fatal("mul_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */
+    }
+    return lo;
+}
+
+static inline mpd_size_t
+add_size_t_overflow(mpd_size_t a, mpd_size_t b, mpd_size_t *overflow)
+{
+    mpd_size_t ret;
+
+    *overflow = 0;
+    ret = a + b;
+    if (ret < a) *overflow = 1;
+    return ret;
+}
+
+static inline mpd_size_t
+mul_size_t_overflow(mpd_size_t a, mpd_size_t b, mpd_size_t *overflow)
+{
+    mpd_uint_t lo;
+
+    _mpd_mul_words((mpd_uint_t *)overflow, &lo, (mpd_uint_t)a,
+                   (mpd_uint_t)b);
+    return lo;
+}
+
+static inline mpd_ssize_t
+mod_mpd_ssize_t(mpd_ssize_t a, mpd_ssize_t m)
+{
+    mpd_ssize_t r = a % m;
+    return (r < 0) ? r + m : r;
+}
+
+static inline mpd_size_t
+mulmod_size_t(mpd_size_t a, mpd_size_t b, mpd_size_t m)
+{
+    mpd_uint_t hi, lo;
+    mpd_uint_t q, r;
+
+    _mpd_mul_words(&hi, &lo, (mpd_uint_t)a, (mpd_uint_t)b);
+    _mpd_div_words(&q, &r, hi, lo, (mpd_uint_t)m);
+
+    return r;
+}
+
+
+#endif /* TYPEARITH_H */
+
+
+

third_party/python/Modules/_decimal/libmpdec/umodarith.h

@@ -0,0 +1,650 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef UMODARITH_H
+#define UMODARITH_H
+
+
+#include "constants.h"
+#include "mpdecimal.h"
+#include "typearith.h"
+
+
+/* Bignum: Low level routines for unsigned modular arithmetic. These are
+   used in the fast convolution functions for very large coefficients. */
+
+
+/**************************************************************************/
+/*                        ANSI modular arithmetic                         */
+/**************************************************************************/
+
+
+/*
+ * Restrictions: a < m and b < m
+ * ACL2 proof: umodarith.lisp: addmod-correct
+ */
+static inline mpd_uint_t
+addmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
+{
+    mpd_uint_t s;
+
+    s = a + b;
+    s = (s < a) ? s - m : s;
+    s = (s >= m) ? s - m : s;
+
+    return s;
+}
+
+/*
+ * Restrictions: a < m and b < m
+ * ACL2 proof: umodarith.lisp: submod-2-correct
+ */
+static inline mpd_uint_t
+submod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
+{
+    mpd_uint_t d;
+
+    d = a - b;
+    d = (a < b) ? d + m : d;
+
+    return d;
+}
+
+/*
+ * Restrictions: a < 2m and b < 2m
+ * ACL2 proof: umodarith.lisp: section ext-submod
+ */
+static inline mpd_uint_t
+ext_submod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
+{
+    mpd_uint_t d;
+
+    a = (a >= m) ? a - m : a;
+    b = (b >= m) ? b - m : b;
+
+    d = a - b;
+    d = (a < b) ? d + m : d;
+
+    return d;
+}
+
+/*
+ * Reduce double word modulo m.
+ * Restrictions: m != 0
+ * ACL2 proof: umodarith.lisp: section dw-reduce
+ */
+static inline mpd_uint_t
+dw_reduce(mpd_uint_t hi, mpd_uint_t lo, mpd_uint_t m)
+{
+    mpd_uint_t r1, r2, w;
+
+    _mpd_div_word(&w, &r1, hi, m);
+    _mpd_div_words(&w, &r2, r1, lo, m);
+
+    return r2;
+}
+
+/*
+ * Subtract double word from a.
+ * Restrictions: a < m
+ * ACL2 proof: umodarith.lisp: section dw-submod
+ */
+static inline mpd_uint_t
+dw_submod(mpd_uint_t a, mpd_uint_t hi, mpd_uint_t lo, mpd_uint_t m)
+{
+    mpd_uint_t d, r;
+
+    r = dw_reduce(hi, lo, m);
+    d = a - r;
+    d = (a < r) ? d + m : d;
+
+    return d;
+}
+
+#ifdef CONFIG_64
+
+/**************************************************************************/
+/*                        64-bit modular arithmetic                       */
+/**************************************************************************/
+
+/*
+ * A proof of the algorithm is in literature/mulmod-64.txt. An ACL2
+ * proof is in umodarith.lisp: section "Fast modular reduction".
+ *
+ * Algorithm: calculate (a * b) % p:
+ *
+ *   a) hi, lo <- a * b       # Calculate a * b.
+ *
+ *   b) hi, lo <-  R(hi, lo)  # Reduce modulo p.
+ *
+ *   c) Repeat step b) until 0 <= hi * 2**64 + lo < 2*p.
+ *
+ *   d) If the result is less than p, return lo. Otherwise return lo - p.
+ */
+
+static inline mpd_uint_t
+x64_mulmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
+{
+    mpd_uint_t hi, lo, x, y;
+
+
+    _mpd_mul_words(&hi, &lo, a, b);
+
+    if (m & (1ULL<<32)) { /* P1 */
+
+        /* first reduction */
+        x = y = hi;
+        hi >>= 32;
+
+        x = lo - x;
+        if (x > lo) hi--;
+
+        y <<= 32;
+        lo = y + x;
+        if (lo < y) hi++;
+
+        /* second reduction */
+        x = y = hi;
+        hi >>= 32;
+
+        x = lo - x;
+        if (x > lo) hi--;
+
+        y <<= 32;
+        lo = y + x;
+        if (lo < y) hi++;
+
+        return (hi || lo >= m ? lo - m : lo);
+    }
+    else if (m & (1ULL<<34)) { /* P2 */
+
+        /* first reduction */
+        x = y = hi;
+        hi >>= 30;
+
+        x = lo - x;
+        if (x > lo) hi--;
+
+        y <<= 34;
+        lo = y + x;
+        if (lo < y) hi++;
+
+        /* second reduction */
+        x = y = hi;
+        hi >>= 30;
+
+        x = lo - x;
+        if (x > lo) hi--;
+
+        y <<= 34;
+        lo = y + x;
+        if (lo < y) hi++;
+
+        /* third reduction */
+        x = y = hi;
+        hi >>= 30;
+
+        x = lo - x;
+        if (x > lo) hi--;
+
+        y <<= 34;
+        lo = y + x;
+        if (lo < y) hi++;
+
+        return (hi || lo >= m ? lo - m : lo);
+    }
+    else { /* P3 */
+
+        /* first reduction */
+        x = y = hi;
+        hi >>= 24;
+
+        x = lo - x;
+        if (x > lo) hi--;
+
+        y <<= 40;
+        lo = y + x;
+        if (lo < y) hi++;
+
+        /* second reduction */
+        x = y = hi;
+        hi >>= 24;
+
+        x = lo - x;
+        if (x > lo) hi--;
+
+        y <<= 40;
+        lo = y + x;
+        if (lo < y) hi++;
+
+        /* third reduction */
+        x = y = hi;
+        hi >>= 24;
+
+        x = lo - x;
+        if (x > lo) hi--;
+
+        y <<= 40;
+        lo = y + x;
+        if (lo < y) hi++;
+
+        return (hi || lo >= m ? lo - m : lo);
+    }
+}
+
+static inline void
+x64_mulmod2c(mpd_uint_t *a, mpd_uint_t *b, mpd_uint_t w, mpd_uint_t m)
+{
+    *a = x64_mulmod(*a, w, m);
+    *b = x64_mulmod(*b, w, m);
+}
+
+static inline void
+x64_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1,
+            mpd_uint_t m)
+{
+    *a0 = x64_mulmod(*a0, b0, m);
+    *a1 = x64_mulmod(*a1, b1, m);
+}
+
+static inline mpd_uint_t
+x64_powmod(mpd_uint_t base, mpd_uint_t exp, mpd_uint_t umod)
+{
+    mpd_uint_t r = 1;
+
+    while (exp > 0) {
+        if (exp & 1)
+            r = x64_mulmod(r, base, umod);
+        base = x64_mulmod(base, base, umod);
+        exp >>= 1;
+    }
+
+    return r;
+}
+
+/* END CONFIG_64 */
+#else /* CONFIG_32 */
+
+
+/**************************************************************************/
+/*                        32-bit modular arithmetic                       */
+/**************************************************************************/
+
+#if defined(ANSI)
+#if !defined(LEGACY_COMPILER)
+/* HAVE_UINT64_T */
+static inline mpd_uint_t
+std_mulmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
+{
+    return ((mpd_uuint_t) a * b) % m;
+}
+
+static inline void
+std_mulmod2c(mpd_uint_t *a, mpd_uint_t *b, mpd_uint_t w, mpd_uint_t m)
+{
+    *a = ((mpd_uuint_t) *a * w) % m;
+    *b = ((mpd_uuint_t) *b * w) % m;
+}
+
+static inline void
+std_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1,
+            mpd_uint_t m)
+{
+    *a0 = ((mpd_uuint_t) *a0 * b0) % m;
+    *a1 = ((mpd_uuint_t) *a1 * b1) % m;
+}
+/* END HAVE_UINT64_T */
+#else
+/* LEGACY_COMPILER */
+static inline mpd_uint_t
+std_mulmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
+{
+    mpd_uint_t hi, lo, q, r;
+    _mpd_mul_words(&hi, &lo, a, b);
+    _mpd_div_words(&q, &r, hi, lo, m);
+    return r;
+}
+
+static inline void
+std_mulmod2c(mpd_uint_t *a, mpd_uint_t *b, mpd_uint_t w, mpd_uint_t m)
+{
+    *a = std_mulmod(*a, w, m);
+    *b = std_mulmod(*b, w, m);
+}
+
+static inline void
+std_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1,
+            mpd_uint_t m)
+{
+    *a0 = std_mulmod(*a0, b0, m);
+    *a1 = std_mulmod(*a1, b1, m);
+}
+/* END LEGACY_COMPILER */
+#endif
+
+static inline mpd_uint_t
+std_powmod(mpd_uint_t base, mpd_uint_t exp, mpd_uint_t umod)
+{
+    mpd_uint_t r = 1;
+
+    while (exp > 0) {
+        if (exp & 1)
+            r = std_mulmod(r, base, umod);
+        base = std_mulmod(base, base, umod);
+        exp >>= 1;
+    }
+
+    return r;
+}
+#endif /* ANSI CONFIG_32 */
+
+
+/**************************************************************************/
+/*                    Pentium Pro modular arithmetic                      */
+/**************************************************************************/
+
+/*
+ * A proof of the algorithm is in literature/mulmod-ppro.txt. The FPU
+ * control word must be set to 64-bit precision and truncation mode
+ * prior to using these functions.
+ *
+ * Algorithm: calculate (a * b) % p:
+ *
+ *   p    := prime < 2**31
+ *   pinv := (long double)1.0 / p (precalculated)
+ *
+ *   a) n = a * b              # Calculate exact product.
+ *   b) qest = n * pinv        # Calculate estimate for q = n / p.
+ *   c) q = (qest+2**63)-2**63 # Truncate qest to the exact quotient.
+ *   d) r = n - q * p          # Calculate remainder.
+ *
+ * Remarks:
+ *
+ *   - p = dmod and pinv = dinvmod.
+ *   - dinvmod points to an array of three uint32_t, which is interpreted
+ *     as an 80 bit long double by fldt.
+ *   - Intel compilers prior to version 11 do not seem to handle the
+ *     __GNUC__ inline assembly correctly.
+ *   - random tests are provided in tests/extended/ppro_mulmod.c
+ */
+
+#if defined(PPRO)
+#if defined(ASM)
+
+/* Return (a * b) % dmod */
+static inline mpd_uint_t
+ppro_mulmod(mpd_uint_t a, mpd_uint_t b, double *dmod, uint32_t *dinvmod)
+{
+    mpd_uint_t retval;
+
+    __asm__ (
+            "fildl  %2\n\t"
+            "fildl  %1\n\t"
+            "fmulp  %%st, %%st(1)\n\t"
+            "fldt   (%4)\n\t"
+            "fmul   %%st(1), %%st\n\t"
+            "flds   %5\n\t"
+            "fadd   %%st, %%st(1)\n\t"
+            "fsubrp %%st, %%st(1)\n\t"
+            "fldl   (%3)\n\t"
+            "fmulp  %%st, %%st(1)\n\t"
+            "fsubrp %%st, %%st(1)\n\t"
+            "fistpl %0\n\t"
+            : "=m" (retval)
+            : "m" (a), "m" (b), "r" (dmod), "r" (dinvmod), "m" (MPD_TWO63)
+            : "st", "memory"
+    );
+
+    return retval;
+}
+
+/*
+ * Two modular multiplications in parallel:
+ *      *a0 = (*a0 * w) % dmod
+ *      *a1 = (*a1 * w) % dmod
+ */
+static inline void
+ppro_mulmod2c(mpd_uint_t *a0, mpd_uint_t *a1, mpd_uint_t w,
+              double *dmod, uint32_t *dinvmod)
+{
+    __asm__ (
+            "fildl  %2\n\t"
+            "fildl  (%1)\n\t"
+            "fmul   %%st(1), %%st\n\t"
+            "fxch   %%st(1)\n\t"
+            "fildl  (%0)\n\t"
+            "fmulp  %%st, %%st(1) \n\t"
+            "fldt   (%4)\n\t"
+            "flds   %5\n\t"
+            "fld    %%st(2)\n\t"
+            "fmul   %%st(2)\n\t"
+            "fadd   %%st(1)\n\t"
+            "fsub   %%st(1)\n\t"
+            "fmull  (%3)\n\t"
+            "fsubrp %%st, %%st(3)\n\t"
+            "fxch   %%st(2)\n\t"
+            "fistpl (%0)\n\t"
+            "fmul   %%st(2)\n\t"
+            "fadd   %%st(1)\n\t"
+            "fsubp  %%st, %%st(1)\n\t"
+            "fmull  (%3)\n\t"
+            "fsubrp %%st, %%st(1)\n\t"
+            "fistpl (%1)\n\t"
+            : : "r" (a0), "r" (a1), "m" (w),
+                "r" (dmod), "r" (dinvmod),
+                "m" (MPD_TWO63)
+            : "st", "memory"
+    );
+}
+
+/*
+ * Two modular multiplications in parallel:
+ *      *a0 = (*a0 * b0) % dmod
+ *      *a1 = (*a1 * b1) % dmod
+ */
+static inline void
+ppro_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1,
+             double *dmod, uint32_t *dinvmod)
+{
+    __asm__ (
+            "fildl  %3\n\t"
+            "fildl  (%2)\n\t"
+            "fmulp  %%st, %%st(1)\n\t"
+            "fildl  %1\n\t"
+            "fildl  (%0)\n\t"
+            "fmulp  %%st, %%st(1)\n\t"
+            "fldt   (%5)\n\t"
+            "fld    %%st(2)\n\t"
+            "fmul   %%st(1), %%st\n\t"
+            "fxch   %%st(1)\n\t"
+            "fmul   %%st(2), %%st\n\t"
+            "flds   %6\n\t"
+            "fldl   (%4)\n\t"
+            "fxch   %%st(3)\n\t"
+            "fadd   %%st(1), %%st\n\t"
+            "fxch   %%st(2)\n\t"
+            "fadd   %%st(1), %%st\n\t"
+            "fxch   %%st(2)\n\t"
+            "fsub   %%st(1), %%st\n\t"
+            "fxch   %%st(2)\n\t"
+            "fsubp  %%st, %%st(1)\n\t"
+            "fxch   %%st(1)\n\t"
+            "fmul   %%st(2), %%st\n\t"
+            "fxch   %%st(1)\n\t"
+            "fmulp  %%st, %%st(2)\n\t"
+            "fsubrp %%st, %%st(3)\n\t"
+            "fsubrp %%st, %%st(1)\n\t"
+            "fxch   %%st(1)\n\t"
+            "fistpl (%2)\n\t"
+            "fistpl (%0)\n\t"
+            : : "r" (a0), "m" (b0), "r" (a1), "m" (b1),
+                "r" (dmod), "r" (dinvmod),
+                "m" (MPD_TWO63)
+            : "st", "memory"
+    );
+}
+/* END PPRO GCC ASM */
+#elif defined(MASM)
+
+/* Return (a * b) % dmod */
+static inline mpd_uint_t __cdecl
+ppro_mulmod(mpd_uint_t a, mpd_uint_t b, double *dmod, uint32_t *dinvmod)
+{
+    mpd_uint_t retval;
+
+    __asm {
+        mov     eax, dinvmod
+        mov     edx, dmod
+        fild    b
+        fild    a
+        fmulp   st(1), st
+        fld     TBYTE PTR [eax]
+        fmul    st, st(1)
+        fld     MPD_TWO63
+        fadd    st(1), st
+        fsubp   st(1), st
+        fld     QWORD PTR [edx]
+        fmulp   st(1), st
+        fsubp   st(1), st
+        fistp   retval
+    }
+
+    return retval;
+}
+
+/*
+ * Two modular multiplications in parallel:
+ *      *a0 = (*a0 * w) % dmod
+ *      *a1 = (*a1 * w) % dmod
+ */
+static inline mpd_uint_t __cdecl
+ppro_mulmod2c(mpd_uint_t *a0, mpd_uint_t *a1, mpd_uint_t w,
+              double *dmod, uint32_t *dinvmod)
+{
+    __asm {
+        mov     ecx, dmod
+        mov     edx, a1
+        mov     ebx, dinvmod
+        mov     eax, a0
+        fild    w
+        fild    DWORD PTR [edx]
+        fmul    st, st(1)
+        fxch    st(1)
+        fild    DWORD PTR [eax]
+        fmulp   st(1), st
+        fld     TBYTE PTR [ebx]
+        fld     MPD_TWO63
+        fld     st(2)
+        fmul    st, st(2)
+        fadd    st, st(1)
+        fsub    st, st(1)
+        fmul    QWORD PTR [ecx]
+        fsubp   st(3), st
+        fxch    st(2)
+        fistp   DWORD PTR [eax]
+        fmul    st, st(2)
+        fadd    st, st(1)
+        fsubrp  st(1), st
+        fmul    QWORD PTR [ecx]
+        fsubp   st(1), st
+        fistp   DWORD PTR [edx]
+    }
+}
+
+/*
+ * Two modular multiplications in parallel:
+ *      *a0 = (*a0 * b0) % dmod
+ *      *a1 = (*a1 * b1) % dmod
+ */
+static inline void __cdecl
+ppro_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1,
+             double *dmod, uint32_t *dinvmod)
+{
+    __asm {
+        mov     ecx, dmod
+        mov     edx, a1
+        mov     ebx, dinvmod
+        mov     eax, a0
+        fild    b1
+        fild    DWORD PTR [edx]
+        fmulp   st(1), st
+        fild    b0
+        fild    DWORD PTR [eax]
+        fmulp   st(1), st
+        fld     TBYTE PTR [ebx]
+        fld     st(2)
+        fmul    st, st(1)
+        fxch    st(1)
+        fmul    st, st(2)
+        fld     DWORD PTR MPD_TWO63
+        fld     QWORD PTR [ecx]
+        fxch    st(3)
+        fadd    st, st(1)
+        fxch    st(2)
+        fadd    st, st(1)
+        fxch    st(2)
+        fsub    st, st(1)
+        fxch    st(2)
+        fsubrp  st(1), st
+        fxch    st(1)
+        fmul    st, st(2)
+        fxch    st(1)
+        fmulp   st(2), st
+        fsubp   st(3), st
+        fsubp   st(1), st
+        fxch    st(1)
+        fistp   DWORD PTR [edx]
+        fistp   DWORD PTR [eax]
+    }
+}
+#endif /* PPRO MASM (_MSC_VER) */
+
+
+/* Return (base ** exp) % dmod */
+static inline mpd_uint_t
+ppro_powmod(mpd_uint_t base, mpd_uint_t exp, double *dmod, uint32_t *dinvmod)
+{
+    mpd_uint_t r = 1;
+
+    while (exp > 0) {
+        if (exp & 1)
+            r = ppro_mulmod(r, base, dmod, dinvmod);
+        base = ppro_mulmod(base, base, dmod, dinvmod);
+        exp >>= 1;
+    }
+
+    return r;
+}
+#endif /* PPRO */
+#endif /* CONFIG_32 */
+
+
+#endif /* UMODARITH_H */
+
+
+

third_party/python/Modules/_decimal/libmpdec/vccompat.h

@@ -0,0 +1,57 @@
+/*
+ * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef VCCOMPAT_H
+#define VCCOMPAT_H
+
+
+/* Visual C fixes: no stdint.h, no snprintf ... */
+#ifdef _MSC_VER
+  #undef inline
+  #define inline __inline
+  #undef random
+  #define random rand
+  #undef srandom
+  #define srandom srand
+  #undef snprintf
+  #define snprintf sprintf_s
+  #define HAVE_SNPRINTF
+  #undef strncasecmp
+  #define strncasecmp _strnicmp
+  #undef strcasecmp
+  #define strcasecmp _stricmp
+  #undef strtoll
+  #define strtoll _strtoi64
+  #define strdup _strdup
+#endif
+
+
+#endif /* VCCOMPAT_H */
+
+
+

third_party/python/Modules/_decimal/libmpdec/vcdiv64.asm

@@ -0,0 +1,48 @@
+;
+; Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
+;
+; Redistribution and use in source and binary forms, with or without
+; modification, are permitted provided that the following conditions
+; are met:
+;
+; 1. Redistributions of source code must retain the above copyright
+;    notice, this list of conditions and the following disclaimer.
+;
+; 2. Redistributions in binary form must reproduce the above copyright
+;    notice, this list of conditions and the following disclaimer in the
+;    documentation and/or other materials provided with the distribution.
+;
+; THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+; ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+; IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+; ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+; FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+; DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+; OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+; HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+; LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+; OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+; SUCH DAMAGE.
+;
+
+
+PUBLIC    _mpd_div_words
+_TEXT    SEGMENT
+q$ = 8
+r$ = 16
+hi$ = 24
+lo$ = 32
+d$ = 40
+_mpd_div_words PROC
+    mov    r10, rdx
+    mov    rdx, r8
+    mov    rax, r9
+    div    QWORD PTR d$[rsp]
+    mov    QWORD PTR [r10], rdx
+    mov    QWORD PTR [rcx], rax
+    ret    0
+_mpd_div_words ENDP
+_TEXT    ENDS
+END
+
+

third_party/python/Modules/_decimal/libmpdec/vcstdint.h

@@ -0,0 +1,232 @@
+// ISO C9x  compliant stdint.h for Microsoft Visual Studio
+// Based on ISO/IEC 9899:TC2 Committee draft (May 6, 2005) WG14/N1124
+//
+//  Copyright (c) 2006-2008 Alexander Chemeris
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+//   1. Redistributions of source code must retain the above copyright notice,
+//      this list of conditions and the following disclaimer.
+//
+//   2. Redistributions in binary form must reproduce the above copyright
+//      notice, this list of conditions and the following disclaimer in the
+//      documentation and/or other materials provided with the distribution.
+//
+//   3. The name of the author may be used to endorse or promote products
+//      derived from this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR IMPLIED
+// WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+// MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
+// EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
+// OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
+// WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
+// OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
+// ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//
+///////////////////////////////////////////////////////////////////////////////
+
+#ifndef _MSC_VER // [
+#error "Use this header only with Microsoft Visual C++ compilers!"
+#endif // _MSC_VER ]
+
+#ifndef _MSC_STDINT_H_ // [
+#define _MSC_STDINT_H_
+
+#if _MSC_VER > 1000
+#pragma once
+#endif
+
+#include <limits.h>
+
+// For Visual Studio 6 in C++ mode wrap <wchar.h> include with 'extern "C++" {}'
+// or compiler give many errors like this:
+//   error C2733: second C linkage of overloaded function 'wmemchr' not allowed
+#if (_MSC_VER < 1300) && defined(__cplusplus)
+   extern "C++" {
+#endif
+#     include <wchar.h>
+#if (_MSC_VER < 1300) && defined(__cplusplus)
+   }
+#endif
+
+// Define _W64 macros to mark types changing their size, like intptr_t.
+#ifndef _W64
+#  if !defined(__midl) && (defined(_X86_) || defined(_M_IX86)) && _MSC_VER >= 1300
+#     define _W64 __w64
+#  else
+#     define _W64
+#  endif
+#endif
+
+
+// 7.18.1 Integer types
+
+// 7.18.1.1 Exact-width integer types
+typedef __int8            int8_t;
+typedef __int16           int16_t;
+typedef __int32           int32_t;
+typedef __int64           int64_t;
+typedef unsigned __int8   uint8_t;
+typedef unsigned __int16  uint16_t;
+typedef unsigned __int32  uint32_t;
+typedef unsigned __int64  uint64_t;
+
+// 7.18.1.2 Minimum-width integer types
+typedef int8_t    int_least8_t;
+typedef int16_t   int_least16_t;
+typedef int32_t   int_least32_t;
+typedef int64_t   int_least64_t;
+typedef uint8_t   uint_least8_t;
+typedef uint16_t  uint_least16_t;
+typedef uint32_t  uint_least32_t;
+typedef uint64_t  uint_least64_t;
+
+// 7.18.1.3 Fastest minimum-width integer types
+typedef int8_t    int_fast8_t;
+typedef int16_t   int_fast16_t;
+typedef int32_t   int_fast32_t;
+typedef int64_t   int_fast64_t;
+typedef uint8_t   uint_fast8_t;
+typedef uint16_t  uint_fast16_t;
+typedef uint32_t  uint_fast32_t;
+typedef uint64_t  uint_fast64_t;
+
+// 7.18.1.4 Integer types capable of holding object pointers
+#ifdef _WIN64 // [
+   typedef __int64           intptr_t;
+   typedef unsigned __int64  uintptr_t;
+#else // _WIN64 ][
+   typedef _W64 int               intptr_t;
+   typedef _W64 unsigned int      uintptr_t;
+#endif // _WIN64 ]
+
+// 7.18.1.5 Greatest-width integer types
+typedef int64_t   intmax_t;
+typedef uint64_t  uintmax_t;
+
+
+// 7.18.2 Limits of specified-width integer types
+
+#if !defined(__cplusplus) || defined(__STDC_LIMIT_MACROS) // [   See footnote 220 at page 257 and footnote 221 at page 259
+
+// 7.18.2.1 Limits of exact-width integer types
+#define INT8_MIN     ((int8_t)_I8_MIN)
+#define INT8_MAX     _I8_MAX
+#define INT16_MIN    ((int16_t)_I16_MIN)
+#define INT16_MAX    _I16_MAX
+#define INT32_MIN    ((int32_t)_I32_MIN)
+#define INT32_MAX    _I32_MAX
+#define INT64_MIN    ((int64_t)_I64_MIN)
+#define INT64_MAX    _I64_MAX
+#define UINT8_MAX    _UI8_MAX
+#define UINT16_MAX   _UI16_MAX
+#define UINT32_MAX   _UI32_MAX
+#define UINT64_MAX   _UI64_MAX
+
+// 7.18.2.2 Limits of minimum-width integer types
+#define INT_LEAST8_MIN    INT8_MIN
+#define INT_LEAST8_MAX    INT8_MAX
+#define INT_LEAST16_MIN   INT16_MIN
+#define INT_LEAST16_MAX   INT16_MAX
+#define INT_LEAST32_MIN   INT32_MIN
+#define INT_LEAST32_MAX   INT32_MAX
+#define INT_LEAST64_MIN   INT64_MIN
+#define INT_LEAST64_MAX   INT64_MAX
+#define UINT_LEAST8_MAX   UINT8_MAX
+#define UINT_LEAST16_MAX  UINT16_MAX
+#define UINT_LEAST32_MAX  UINT32_MAX
+#define UINT_LEAST64_MAX  UINT64_MAX
+
+// 7.18.2.3 Limits of fastest minimum-width integer types
+#define INT_FAST8_MIN    INT8_MIN
+#define INT_FAST8_MAX    INT8_MAX
+#define INT_FAST16_MIN   INT16_MIN
+#define INT_FAST16_MAX   INT16_MAX
+#define INT_FAST32_MIN   INT32_MIN
+#define INT_FAST32_MAX   INT32_MAX
+#define INT_FAST64_MIN   INT64_MIN
+#define INT_FAST64_MAX   INT64_MAX
+#define UINT_FAST8_MAX   UINT8_MAX
+#define UINT_FAST16_MAX  UINT16_MAX
+#define UINT_FAST32_MAX  UINT32_MAX
+#define UINT_FAST64_MAX  UINT64_MAX
+
+// 7.18.2.4 Limits of integer types capable of holding object pointers
+#ifdef _WIN64 // [
+#  define INTPTR_MIN   INT64_MIN
+#  define INTPTR_MAX   INT64_MAX
+#  define UINTPTR_MAX  UINT64_MAX
+#else // _WIN64 ][
+#  define INTPTR_MIN   INT32_MIN
+#  define INTPTR_MAX   INT32_MAX
+#  define UINTPTR_MAX  UINT32_MAX
+#endif // _WIN64 ]
+
+// 7.18.2.5 Limits of greatest-width integer types
+#define INTMAX_MIN   INT64_MIN
+#define INTMAX_MAX   INT64_MAX
+#define UINTMAX_MAX  UINT64_MAX
+
+// 7.18.3 Limits of other integer types
+
+#ifdef _WIN64 // [
+#  define PTRDIFF_MIN  _I64_MIN
+#  define PTRDIFF_MAX  _I64_MAX
+#else  // _WIN64 ][
+#  define PTRDIFF_MIN  _I32_MIN
+#  define PTRDIFF_MAX  _I32_MAX
+#endif  // _WIN64 ]
+
+#define SIG_ATOMIC_MIN  INT_MIN
+#define SIG_ATOMIC_MAX  INT_MAX
+
+#ifndef SIZE_MAX // [
+#  ifdef _WIN64 // [
+#     define SIZE_MAX  _UI64_MAX
+#  else // _WIN64 ][
+#     define SIZE_MAX  _UI32_MAX
+#  endif // _WIN64 ]
+#endif // SIZE_MAX ]
+
+// WCHAR_MIN and WCHAR_MAX are also defined in <wchar.h>
+#ifndef WCHAR_MIN // [
+#  define WCHAR_MIN  0
+#endif  // WCHAR_MIN ]
+#ifndef WCHAR_MAX // [
+#  define WCHAR_MAX  _UI16_MAX
+#endif  // WCHAR_MAX ]
+
+#define WINT_MIN  0
+#define WINT_MAX  _UI16_MAX
+
+#endif // __STDC_LIMIT_MACROS ]
+
+
+// 7.18.4 Limits of other integer types
+
+#if !defined(__cplusplus) || defined(__STDC_CONSTANT_MACROS) // [   See footnote 224 at page 260
+
+// 7.18.4.1 Macros for minimum-width integer constants
+
+#define INT8_C(val)  val##i8
+#define INT16_C(val) val##i16
+#define INT32_C(val) val##i32
+#define INT64_C(val) val##i64
+
+#define UINT8_C(val)  val##ui8
+#define UINT16_C(val) val##ui16
+#define UINT32_C(val) val##ui32
+#define UINT64_C(val) val##ui64
+
+// 7.18.4.2 Macros for greatest-width integer constants
+#define INTMAX_C   INT64_C
+#define UINTMAX_C  UINT64_C
+
+#endif // __STDC_CONSTANT_MACROS ]
+
+
+#endif // _MSC_STDINT_H_ ]