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[LIBM] Import win-libm from AMD

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Source: https://github.com/amd/win-libm
This commit is contained in:
Timo Kreuzer 2022-06-12 12:02:01 +02:00
parent 081c637c06
commit 4afb647c78
82 changed files with 22392 additions and 0 deletions
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sdk/lib/crt/math/libm_sse2/tan.c Normal file
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/*******************************************************************************
MIT License
-----------
Copyright (c) 2002-2019 Advanced Micro Devices, Inc.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this Software and associated documentaon files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
*******************************************************************************/
#include "libm.h"
#include "libm_util.h"
#define USE_NAN_WITH_FLAGS
#define USE_VAL_WITH_FLAGS
#define USE_HANDLE_ERROR
#include "libm_inlines.h"
#undef USE_NAN_WITH_FLAGS
#undef USE_VAL_WITH_FLAGS
#undef USE_HANDLE_ERROR
#include "libm_errno.h"
/* tan(x + xx) approximation valid on the interval [-pi/4,pi/4].
If recip is true return -1/tan(x + xx) instead. */
static inline double tan_piby4(double x, double xx, int recip)
{
double r, t1, t2, xl;
int transform = 0;
static const double
piby4_lead = 7.85398163397448278999e-01, /* 0x3fe921fb54442d18 */
piby4_tail = 3.06161699786838240164e-17; /* 0x3c81a62633145c06 */
/* In order to maintain relative precision transform using the identity:
tan(pi/4-x) = (1-tan(x))/(1+tan(x)) for arguments close to pi/4.
Similarly use tan(x-pi/4) = (tan(x)-1)/(tan(x)+1) close to -pi/4. */
if (x > 0.68)
{
transform = 1;
x = piby4_lead - x;
xl = piby4_tail - xx;
x += xl;
xx = 0.0;
}
else if (x < -0.68)
{
transform = -1;
x = piby4_lead + x;
xl = piby4_tail + xx;
x += xl;
xx = 0.0;
}
/* Core Remez [2,3] approximation to tan(x+xx) on the
interval [0,0.68]. */
r = x*x + 2.0 * x * xx;
t1 = x;
t2 = xx + x*r*
(0.372379159759792203640806338901e0 +
(-0.229345080057565662883358588111e-1 +
0.224044448537022097264602535574e-3*r)*r)/
(0.111713747927937668539901657944e1 +
(-0.515658515729031149329237816945e0 +
(0.260656620398645407524064091208e-1 -
0.232371494088563558304549252913e-3*r)*r)*r);
/* Reconstruct tan(x) in the transformed case. */
if (transform)
{
double t;
t = t1 + t2;
if (recip)
return transform*(2*t/(t-1) - 1.0);
else
return transform*(1.0 - 2*t/(1+t));
}
if (recip)
{
/* Compute -1.0/(t1 + t2) accurately */
double trec, trec_top, z1, z2, t;
unsigned long u;
t = t1 + t2;
GET_BITS_DP64(t, u);
u &= 0xffffffff00000000;
PUT_BITS_DP64(u, z1);
z2 = t2 - (z1 - t1);
trec = -1.0 / t;
GET_BITS_DP64(trec, u);
u &= 0xffffffff00000000;
PUT_BITS_DP64(u, trec_top);
return trec_top + trec * ((1.0 + trec_top * z1) + trec_top * z2);
}
else
return t1 + t2;
}
#pragma function(tan)
double tan(double x)
{
double r, rr;
int region, xneg;
unsigned long ux, ax;
GET_BITS_DP64(x, ux);
ax = (ux & ~SIGNBIT_DP64);
if (ax <= 0x3fe921fb54442d18) /* abs(x) <= pi/4 */
{
if (ax < 0x3f20000000000000) /* abs(x) < 2.0^(-13) */
{
if (ax < 0x3e40000000000000) /* abs(x) < 2.0^(-27) */
{
if (ax == 0x0000000000000000) return x;
else return val_with_flags(x, AMD_F_INEXACT);
}
else
{
/* Using a temporary variable prevents 64-bit VC++ from
rearranging
x + x*x*x*0.333333333333333333;
into
x * (1 + x*x*0.333333333333333333);
The latter results in an incorrectly rounded answer. */
double tmp;
tmp = x*x*x*0.333333333333333333;
return x + tmp;
}
}
else
return tan_piby4(x, 0.0, 0);
}
else if ((ux & EXPBITS_DP64) == EXPBITS_DP64)
{
/* x is either NaN or infinity */
if (ux & MANTBITS_DP64)
/* x is NaN */
return _handle_error("tan", OP_TAN, ux|0x0008000000000000, _DOMAIN, 0,
EDOM, x, 0.0, 1);
else
/* x is infinity. Return a NaN */
return _handle_error("tan", OP_TAN, INDEFBITPATT_DP64, _DOMAIN, AMD_F_INVALID,
EDOM, x, 0.0, 1);
}
xneg = (ax != ux);
if (xneg)
x = -x;
if (x < 5.0e5)
{
/* For these size arguments we can just carefully subtract the
appropriate multiple of pi/2, using extra precision where
x is close to an exact multiple of pi/2 */
static const double
twobypi = 6.36619772367581382433e-01, /* 0x3fe45f306dc9c883 */
piby2_1 = 1.57079632673412561417e+00, /* 0x3ff921fb54400000 */
piby2_1tail = 6.07710050650619224932e-11, /* 0x3dd0b4611a626331 */
piby2_2 = 6.07710050630396597660e-11, /* 0x3dd0b4611a600000 */
piby2_2tail = 2.02226624879595063154e-21, /* 0x3ba3198a2e037073 */
piby2_3 = 2.02226624871116645580e-21, /* 0x3ba3198a2e000000 */
piby2_3tail = 8.47842766036889956997e-32; /* 0x397b839a252049c1 */
double t, rhead, rtail;
int npi2;
unsigned long uy, xexp, expdiff;
xexp = ax >> EXPSHIFTBITS_DP64;
/* How many pi/2 is x a multiple of? */
if (ax <= 0x400f6a7a2955385e) /* 5pi/4 */
{
if (ax <= 0x4002d97c7f3321d2) /* 3pi/4 */
npi2 = 1;
else
npi2 = 2;
}
else if (ax <= 0x401c463abeccb2bb) /* 9pi/4 */
{
if (ax <= 0x4015fdbbe9bba775) /* 7pi/4 */
npi2 = 3;
else
npi2 = 4;
}
else
npi2 = (int)(x * twobypi + 0.5);
/* Subtract the multiple from x to get an extra-precision remainder */
rhead = x - npi2 * piby2_1;
rtail = npi2 * piby2_1tail;
GET_BITS_DP64(rhead, uy);
expdiff = xexp - ((uy & EXPBITS_DP64) >> EXPSHIFTBITS_DP64);
if (expdiff > 15)
{
/* The remainder is pretty small compared with x, which
implies that x is a near multiple of pi/2
(x matches the multiple to at least 15 bits) */
t = rhead;
rtail = npi2 * piby2_2;
rhead = t - rtail;
rtail = npi2 * piby2_2tail - ((t - rhead) - rtail);
if (expdiff > 48)
{
/* x matches a pi/2 multiple to at least 48 bits */
t = rhead;
rtail = npi2 * piby2_3;
rhead = t - rtail;
rtail = npi2 * piby2_3tail - ((t - rhead) - rtail);
}
}
r = rhead - rtail;
rr = (rhead - r) - rtail;
region = npi2 & 3;
}
else
{
/* Reduce x into range [-pi/4,pi/4] */
__remainder_piby2(x, &r, &rr, &region);
}
if (xneg)
return -tan_piby4(r, rr, region & 1);
else
return tan_piby4(r, rr, region & 1);
}