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Make numerous improvements

Browse source 
- Python static hello world now 1.8mb
- Python static fully loaded now 10mb
- Python HTTPS client now uses MbedTLS
- Python REPL now completes import stmts
- Increase stack size for Python for now
- Begin synthesizing posixpath and ntpath
- Restore Python \N{UNICODE NAME} support
- Restore Python NFKD symbol normalization
- Add optimized code path for Intel SHA-NI
- Get more Python unit tests passing faster
- Get Python help() pagination working on NT
- Python hashlib now supports MbedTLS PBKDF2
- Make memcpy/memmove/memcmp/bcmp/etc. faster
- Add Mersenne Twister and Vigna to LIBC_RAND
- Provide privileged __printf() for error code
- Fix zipos opendir() so that it reports ENOTDIR
- Add basic chmod() implementation for Windows NT
- Add Cosmo's best functions to Python cosmo module
- Pin function trace indent depth to that of caller
- Show memory diagram on invalid access in MODE=dbg
- Differentiate stack overflow on crash in MODE=dbg
- Add stb_truetype and tools for analyzing font files
- Upgrade to UNICODE 13 and reduce its binary footprint
- COMPILE.COM now logs resource usage of build commands
- Start implementing basic poll() support on bare metal
- Set getauxval(AT_EXECFN) to GetModuleFileName() on NT
- Add descriptions to strerror() in non-TINY build modes
- Add COUNTBRANCH() macro to help with micro-optimizations
- Make error / backtrace / asan / memory code more unbreakable
- Add fast perfect C implementation of μ-Law and a-Law audio codecs
- Make strtol() functions consistent with other libc implementations
- Improve Linenoise implementation (see also github.com/jart/bestline)
- COMPILE.COM now suppresses stdout/stderr of successful build commands
This commit is contained in:
Justine Tunney 2021-09-27 22:58:51 -07:00
parent fa7b4f5bd1
commit 39bf41f4eb
806 changed files with 77494 additions and 63859 deletions
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550
third_party/python/Modules/_decimal/libmpdec/umodarith.h vendored
View file

@ -1,20 +1,14 @@
#ifndef UMODARITH_H
#define UMODARITH_H
#include "libc/log/libfatal.internal.h"
#include "third_party/python/Modules/_decimal/libmpdec/constants.h"
#include "third_party/python/Modules/_decimal/libmpdec/mpdecimal.h"
#include "third_party/python/Modules/_decimal/libmpdec/typearith.h"
/* clang-format off */
/* 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
@ -23,11 +17,9 @@ 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;
}
@ -39,10 +31,8 @@ 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;
}
@ -54,13 +44,10 @@ 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;
}
@ -73,10 +60,8 @@ 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;
}
@ -89,142 +74,213 @@ 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".
/**
* Calculates (a × b) % 𝑝 where 𝑝 is special
*
* Algorithm: calculate (a * b) % p:
* In the whole comment, "⩭" stands for "is congruent with".
*
* a) hi, lo <- a * b # Calculate a * b.
* Result of a × b in terms of high/low words:
*
* b) hi, lo <- R(hi, lo) # Reduce modulo p.
* (1) hi × 2⁶⁴ + lo = a × b
*
* c) Repeat step b) until 0 <= hi * 2**64 + lo < 2*p.
* Special primes:
*
* d) If the result is less than p, return lo. Otherwise return lo - p.
* (2) 𝑝 = 2⁶⁴ - z + 1, where z = 2ⁿ
*
* i.e. 0xfffffffffffffc01
* 0xfffffffffffff001
* 0xffffffffff000001
* 0xffffffff00000001
* 0xfffffffc00000001
* 0xffffff0000000001
* 0xffffff0000000001
*
* 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′ × 2⁶⁴ + lo′ < 𝟸×𝑝.
*
* d) If the result is less than 𝑝, return lo′. Otherwise return lo′ - 𝑝.
*
*
* The reduction step b) preserves congruence
* ------------------------------------------
*
* hi × 2⁶⁴ + lo ⩭ hi × z - hi + lo (mod 𝑝)
*
* Proof:
* ~~~~~~
*
* hi × 2⁶⁴ + lo = (2⁶⁴ - 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=2⁶⁴-1, lo=2⁶⁴-1 after the
* initial multiplication a × b. This is of course impossible
* but certainly covers all cases.
*
* Then, for p1:
*
* z = 2³²
* hi = 2⁶⁴-1
* lo = 2⁶⁴-1
* p1 = 2⁶⁴ - z + 1
* hi, lo = R(hi, lo, z) # First reduction
* hi, lo = R(hi, lo, z) # Second reduction
* hi × 2⁶⁴ + lo < 2 × p1 # True
*
* For p2:
*
* z = 2³⁴
* hi = 2⁶⁴-1
* lo = 2⁶⁴-1
* p2 = 2⁶⁴ - 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 × 2⁶⁴ + lo < 2 × p2 # True
*
* For p3:
*
* z = 2⁴⁰
* hi = 2⁶⁴-1
* lo = 2⁶⁴-1
* p3 = 2⁶⁴ - 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 × 2⁶⁴ + 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 < 2⁶⁴ Λ 2⁶⁴ + lo < 𝟸×𝑝 → lo < 𝑝 # lo is always less than 𝑝
*
* 2⁶⁴ + lo ⩭ 2⁶⁴ + (lo - 𝑝) (mod 𝑝) # result is congruent
*
* = lo - 𝑝 # exactly the same value as the previous RHS
* # in uint64_t arithmetic.
*
* 𝑝 < 2⁶⁴ + lo < 𝟸×𝑝 → 0 < 2⁶⁴ + (lo - 𝑝) < 𝑝 # correct range
*
*
* [1] http://www.apfloat.org/apfloat/2.40/apfloat.pdf
*/
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);
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);
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);
return hi || lo >= m ? lo - m : lo;
}
}
@ -247,375 +303,13 @@ 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 */