mirror of
https://github.com/jart/cosmopolitan.git
synced 2025-06-27 14:58:30 +00:00
Make quality improvements
- Write some more unit tests - memcpy() on ARM is now faster - Address the Musl complex math FIXME comments - Some libm funcs like pow() now support setting errno - Import the latest and greatest math functions from ARM - Use more accurate atan2f() and log1pf() implementations - atoi() and atol() will no longer saturate or clobber errno
This commit is contained in:
Justine Tunney
parent
af8f2bd19f
commit
592f6ebc20
122 changed files with 6305 additions and 3859 deletions
|
|
@ -1,9 +1,9 @@
|
|||
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
|
||||
│ vi: set noet ft=c ts=8 sw=8 fenc=utf-8 :vi │
|
||||
/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│
|
||||
│ vi: set et ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi │
|
||||
╚──────────────────────────────────────────────────────────────────────────────╝
|
||||
│ │
|
||||
│ Optimized Routines │
|
||||
│ Copyright (c) 1999-2022, Arm Limited. │
|
||||
│ Copyright (c) 2018-2024, Arm Limited. │
|
||||
│ │
|
||||
│ Permission is hereby granted, free of charge, to any person obtaining │
|
||||
│ a copy of this software and associated documentation files (the │
|
||||
|
|
@ -25,20 +25,9 @@
|
|||
│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
|
||||
│ │
|
||||
╚─────────────────────────────────────────────────────────────────────────────*/
|
||||
#include "libc/intrin/likely.h"
|
||||
#include "libc/math.h"
|
||||
#include "libc/tinymath/complex.internal.h"
|
||||
#include "libc/tinymath/internal.h"
|
||||
#include "libc/tinymath/log2_data.internal.h"
|
||||
#include "libc/tinymath/arm.internal.h"
|
||||
__static_yoink("arm_optimized_routines_notice");
|
||||
|
||||
/*
|
||||
* Double-precision log2(x) function.
|
||||
*
|
||||
* Copyright (c) 2018, Arm Limited.
|
||||
* SPDX-License-Identifier: MIT
|
||||
*/
|
||||
|
||||
#define T __log2_data.tab
|
||||
#define T2 __log2_data.tab2
|
||||
#define B __log2_data.poly1
|
||||
|
|
@ -49,110 +38,126 @@ __static_yoink("arm_optimized_routines_notice");
|
|||
#define OFF 0x3fe6000000000000
|
||||
|
||||
/* Top 16 bits of a double. */
|
||||
static inline uint32_t top16(double x)
|
||||
static inline uint32_t
|
||||
top16 (double x)
|
||||
{
|
||||
return asuint64(x) >> 48;
|
||||
return asuint64 (x) >> 48;
|
||||
}
|
||||
|
||||
/**
|
||||
* Calculates log₂𝑥.
|
||||
* Returns base 2 logarithm of x.
|
||||
*/
|
||||
double log2(double x)
|
||||
double
|
||||
log2 (double x)
|
||||
{
|
||||
double_t z, r, r2, r4, y, invc, logc, kd, hi, lo, t1, t2, t3, p;
|
||||
uint64_t ix, iz, tmp;
|
||||
uint32_t top;
|
||||
int k, i;
|
||||
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
|
||||
double_t z, r, r2, r4, y, invc, logc, kd, hi, lo, t1, t2, t3, p;
|
||||
uint64_t ix, iz, tmp;
|
||||
uint32_t top;
|
||||
int k, i;
|
||||
|
||||
ix = asuint64(x);
|
||||
top = top16(x);
|
||||
#define LO asuint64(1.0 - 0x1.5b51p-5)
|
||||
#define HI asuint64(1.0 + 0x1.6ab2p-5)
|
||||
if (UNLIKELY(ix - LO < HI - LO)) {
|
||||
/* Handle close to 1.0 inputs separately. */
|
||||
/* Fix sign of zero with downward rounding when x==1. */
|
||||
if (WANT_ROUNDING && UNLIKELY(ix == asuint64(1.0)))
|
||||
return 0;
|
||||
r = x - 1.0;
|
||||
#if __FP_FAST_FMA
|
||||
hi = r * InvLn2hi;
|
||||
lo = r * InvLn2lo + __builtin_fma(r, InvLn2hi, -hi);
|
||||
#else
|
||||
double_t rhi, rlo;
|
||||
rhi = asdouble(asuint64(r) & -1ULL << 32);
|
||||
rlo = r - rhi;
|
||||
hi = rhi * InvLn2hi;
|
||||
lo = rlo * InvLn2hi + r * InvLn2lo;
|
||||
ix = asuint64 (x);
|
||||
top = top16 (x);
|
||||
|
||||
#if LOG2_POLY1_ORDER == 11
|
||||
# define LO asuint64 (1.0 - 0x1.5b51p-5)
|
||||
# define HI asuint64 (1.0 + 0x1.6ab2p-5)
|
||||
#endif
|
||||
r2 = r * r; /* rounding error: 0x1p-62. */
|
||||
r4 = r2 * r2;
|
||||
/* Worst-case error is less than 0.54 ULP (0.55 ULP without fma). */
|
||||
p = r2 * (B[0] + r * B[1]);
|
||||
y = hi + p;
|
||||
lo += hi - y + p;
|
||||
lo += r4 * (B[2] + r * B[3] + r2 * (B[4] + r * B[5]) +
|
||||
r4 * (B[6] + r * B[7] + r2 * (B[8] + r * B[9])));
|
||||
y += lo;
|
||||
return eval_as_double(y);
|
||||
}
|
||||
if (UNLIKELY(top - 0x0010 >= 0x7ff0 - 0x0010)) {
|
||||
/* x < 0x1p-1022 or inf or nan. */
|
||||
if (ix * 2 == 0)
|
||||
return __math_divzero(1);
|
||||
if (ix == asuint64(INFINITY)) /* log(inf) == inf. */
|
||||
return x;
|
||||
if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
|
||||
return __math_invalid(x);
|
||||
/* x is subnormal, normalize it. */
|
||||
ix = asuint64(x * 0x1p52);
|
||||
ix -= 52ULL << 52;
|
||||
}
|
||||
|
||||
/* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
|
||||
The range is split into N subintervals.
|
||||
The ith subinterval contains z and c is near its center. */
|
||||
tmp = ix - OFF;
|
||||
i = (tmp >> (52 - LOG2_TABLE_BITS)) % N;
|
||||
k = (int64_t)tmp >> 52; /* arithmetic shift */
|
||||
iz = ix - (tmp & 0xfffULL << 52);
|
||||
invc = T[i].invc;
|
||||
logc = T[i].logc;
|
||||
z = asdouble(iz);
|
||||
kd = (double_t)k;
|
||||
|
||||
/* log2(x) = log2(z/c) + log2(c) + k. */
|
||||
/* r ~= z/c - 1, |r| < 1/(2*N). */
|
||||
#if __FP_FAST_FMA
|
||||
/* rounding error: 0x1p-55/N. */
|
||||
r = __builtin_fma(z, invc, -1.0);
|
||||
t1 = r * InvLn2hi;
|
||||
t2 = r * InvLn2lo + __builtin_fma(r, InvLn2hi, -t1);
|
||||
if (unlikely (ix - LO < HI - LO))
|
||||
{
|
||||
/* Handle close to 1.0 inputs separately. */
|
||||
/* Fix sign of zero with downward rounding when x==1. */
|
||||
if (WANT_ROUNDING && unlikely (ix == asuint64 (1.0)))
|
||||
return 0;
|
||||
r = x - 1.0;
|
||||
#if HAVE_FAST_FMA
|
||||
hi = r * InvLn2hi;
|
||||
lo = r * InvLn2lo + fma (r, InvLn2hi, -hi);
|
||||
#else
|
||||
double_t rhi, rlo;
|
||||
/* rounding error: 0x1p-55/N + 0x1p-65. */
|
||||
r = (z - T2[i].chi - T2[i].clo) * invc;
|
||||
rhi = asdouble(asuint64(r) & -1ULL << 32);
|
||||
rlo = r - rhi;
|
||||
t1 = rhi * InvLn2hi;
|
||||
t2 = rlo * InvLn2hi + r * InvLn2lo;
|
||||
double_t rhi, rlo;
|
||||
rhi = asdouble (asuint64 (r) & -1ULL << 32);
|
||||
rlo = r - rhi;
|
||||
hi = rhi * InvLn2hi;
|
||||
lo = rlo * InvLn2hi + r * InvLn2lo;
|
||||
#endif
|
||||
r2 = r * r; /* rounding error: 0x1p-62. */
|
||||
r4 = r2 * r2;
|
||||
#if LOG2_POLY1_ORDER == 11
|
||||
/* Worst-case error is less than 0.54 ULP (0.55 ULP without fma). */
|
||||
p = r2 * (B[0] + r * B[1]);
|
||||
y = hi + p;
|
||||
lo += hi - y + p;
|
||||
lo += r4 * (B[2] + r * B[3] + r2 * (B[4] + r * B[5])
|
||||
+ r4 * (B[6] + r * B[7] + r2 * (B[8] + r * B[9])));
|
||||
y += lo;
|
||||
#endif
|
||||
return eval_as_double (y);
|
||||
}
|
||||
if (unlikely (top - 0x0010 >= 0x7ff0 - 0x0010))
|
||||
{
|
||||
/* x < 0x1p-1022 or inf or nan. */
|
||||
if (ix * 2 == 0)
|
||||
return __math_divzero (1);
|
||||
if (ix == asuint64 (INFINITY)) /* log(inf) == inf. */
|
||||
return x;
|
||||
if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
|
||||
return __math_invalid (x);
|
||||
/* x is subnormal, normalize it. */
|
||||
ix = asuint64 (x * 0x1p52);
|
||||
ix -= 52ULL << 52;
|
||||
}
|
||||
|
||||
/* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
|
||||
The range is split into N subintervals.
|
||||
The ith subinterval contains z and c is near its center. */
|
||||
tmp = ix - OFF;
|
||||
i = (tmp >> (52 - LOG2_TABLE_BITS)) % N;
|
||||
k = (int64_t) tmp >> 52; /* arithmetic shift */
|
||||
iz = ix - (tmp & 0xfffULL << 52);
|
||||
invc = T[i].invc;
|
||||
logc = T[i].logc;
|
||||
z = asdouble (iz);
|
||||
kd = (double_t) k;
|
||||
|
||||
/* log2(x) = log2(z/c) + log2(c) + k. */
|
||||
/* r ~= z/c - 1, |r| < 1/(2*N). */
|
||||
#if HAVE_FAST_FMA
|
||||
/* rounding error: 0x1p-55/N. */
|
||||
r = fma (z, invc, -1.0);
|
||||
t1 = r * InvLn2hi;
|
||||
t2 = r * InvLn2lo + fma (r, InvLn2hi, -t1);
|
||||
#else
|
||||
double_t rhi, rlo;
|
||||
/* rounding error: 0x1p-55/N + 0x1p-65. */
|
||||
r = (z - T2[i].chi - T2[i].clo) * invc;
|
||||
rhi = asdouble (asuint64 (r) & -1ULL << 32);
|
||||
rlo = r - rhi;
|
||||
t1 = rhi * InvLn2hi;
|
||||
t2 = rlo * InvLn2hi + r * InvLn2lo;
|
||||
#endif
|
||||
|
||||
/* hi + lo = r/ln2 + log2(c) + k. */
|
||||
t3 = kd + logc;
|
||||
hi = t3 + t1;
|
||||
lo = t3 - hi + t1 + t2;
|
||||
/* hi + lo = r/ln2 + log2(c) + k. */
|
||||
t3 = kd + logc;
|
||||
hi = t3 + t1;
|
||||
lo = t3 - hi + t1 + t2;
|
||||
|
||||
/* log2(r+1) = r/ln2 + r^2*poly(r). */
|
||||
/* Evaluation is optimized assuming superscalar pipelined execution. */
|
||||
r2 = r * r; /* rounding error: 0x1p-54/N^2. */
|
||||
r4 = r2 * r2;
|
||||
/* Worst-case error if |y| > 0x1p-4: 0.547 ULP (0.550 ULP without fma).
|
||||
~ 0.5 + 2/N/ln2 + abs-poly-error*0x1p56 ULP (+ 0.003 ULP without fma). */
|
||||
p = A[0] + r * A[1] + r2 * (A[2] + r * A[3]) + r4 * (A[4] + r * A[5]);
|
||||
y = lo + r2 * p + hi;
|
||||
return eval_as_double(y);
|
||||
/* log2(r+1) = r/ln2 + r^2*poly(r). */
|
||||
/* Evaluation is optimized assuming superscalar pipelined execution. */
|
||||
r2 = r * r; /* rounding error: 0x1p-54/N^2. */
|
||||
r4 = r2 * r2;
|
||||
#if LOG2_POLY_ORDER == 7
|
||||
/* Worst-case error if |y| > 0x1p-4: 0.547 ULP (0.550 ULP without fma).
|
||||
~ 0.5 + 2/N/ln2 + abs-poly-error*0x1p56 ULP (+ 0.003 ULP without fma). */
|
||||
p = A[0] + r * A[1] + r2 * (A[2] + r * A[3]) + r4 * (A[4] + r * A[5]);
|
||||
y = lo + r2 * p + hi;
|
||||
#endif
|
||||
return eval_as_double (y);
|
||||
}
|
||||
|
||||
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
|
||||
__weak_reference(log2, log2l);
|
||||
#if USE_GLIBC_ABI
|
||||
strong_alias (log2, __log2_finite)
|
||||
hidden_alias (log2, __ieee754_log2)
|
||||
# if LDBL_MANT_DIG == 53
|
||||
long double log2l (long double x) { return log2 (x); }
|
||||
# endif
|
||||
#endif
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue