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

/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:4;tab-width:8;coding:utf-8 -*-│
│ vi: set noet ft=c ts=4 sts=4 sw=4 fenc=utf-8                             :vi │
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│ Copyright (c) 2008-2016 Stefan Krah. All rights reserved.                    │
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│ Redistribution and use in source and binary forms, with or without           │
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╚─────────────────────────────────────────────────────────────────────────────*/
#include "third_party/python/Modules/_decimal/libmpdec/bits.h"
#include "third_party/python/Modules/_decimal/libmpdec/difradix2.h"
#include "third_party/python/Modules/_decimal/libmpdec/mpdecimal.h"
#include "third_party/python/Modules/_decimal/libmpdec/numbertheory.h"
#include "third_party/python/Modules/_decimal/libmpdec/umodarith.h"

asm(".ident\t\"\\n\\n\
libmpdec (BSD-2)\\n\
Copyright 2008-2016 Stefan Krah\"");
asm(".include \"libc/disclaimer.inc\"");

/* 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;
    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);
}