mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-27 03:33:33 +08:00
math: Use expm1f from CORE-MATH
The CORE-MATH implementation is correctly rounded (for any rounding mode) and shows better performance compared to the generic expm1f. The code was adapted to glibc style and to use the definition of math_config.h (to handle errno, overflow, and underflow). Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (Neoverse-N1, gcc 13.3.1), and powerpc (POWER10, gcc 13.2.1): Latency master patched improvement x86_64 96.7402 36.4026 62.37% x86_64v2 97.5391 33.4625 65.69% x86_64v3 82.1778 30.8668 62.44% i686 120.58 94.8302 21.35% aarch64 32.3558 12.8881 60.17% power10 23.5087 9.8574 58.07% powerpc 23.4776 9.06325 61.40% reciprocal-throughput master patched improvement x86_64 27.8224 15.9255 42.76% x86_64v2 27.8364 9.6438 65.36% x86_64v3 20.3227 9.6146 52.69% i686 63.5629 59.4718 6.44% aarch64 17.4838 7.1082 59.34% power10 12.4644 8.7829 29.54% powerpc 14.2152 5.94765 58.16% Signed-off-by: Alexei Sibidanov <sibid@uvic.ca> Signed-off-by: Paul Zimmermann <Paul.Zimmermann@inria.fr> Signed-off-by: Adhemerval Zanella <adhemerval.zanella@linaro.org> Reviewed-by: DJ Delorie <dj@redhat.com>
This commit is contained in:
Adhemerval Zanella
parent
5c22fd25c1
commit
bbd578b38d
@ -248,3 +248,7 @@ sysdeps/ieee754/flt-32/s_exp2m1f.c
|
||||
(file src/binary32/exp2m1/exp2m1f.c in CORE-MATH)
|
||||
- The code was adapted to use glibc code style and internal
|
||||
functions to handle errno, overflow, and underflow.
|
||||
sysdeps/ieee754/flt-32/s_expm1f.c
|
||||
(file src/binary32/expm1/expm1f.c in CORE-MATH)
|
||||
- The code was adapted to use glibc code style and internal
|
||||
functions to handle errno, overflow, and underflow.
|
||||
|
||||
@ -801,6 +801,7 @@ float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: Imaginary part of "csin":
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: Real part of "csin_downward":
|
||||
@ -1163,7 +1164,6 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "expm1_advsimd":
|
||||
@ -1172,7 +1172,6 @@ float: 1
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "expm1_sve":
|
||||
@ -1181,12 +1180,10 @@ float: 1
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
ldouble: 4
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "gamma":
|
||||
|
||||
@ -1034,22 +1034,18 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
ldouble: 4
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "gamma":
|
||||
|
||||
@ -839,19 +839,15 @@ float: 2
|
||||
|
||||
Function: "expm1":
|
||||
double: 2
|
||||
float: 2
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 2
|
||||
float: 2
|
||||
|
||||
Function: "gamma":
|
||||
double: 7
|
||||
|
||||
@ -203,7 +203,6 @@ double: 2
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "gamma":
|
||||
double: 4
|
||||
|
||||
@ -574,6 +574,9 @@ Function: Real part of "csin":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: Imaginary part of "csin":
|
||||
float: 1
|
||||
|
||||
Function: Real part of "csin_downward":
|
||||
double: 3
|
||||
float: 3
|
||||
@ -831,19 +834,15 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "gamma":
|
||||
double: 4
|
||||
|
||||
@ -799,19 +799,15 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "gamma":
|
||||
double: 4
|
||||
|
||||
@ -797,19 +797,15 @@ double: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "gamma":
|
||||
double: 4
|
||||
|
||||
@ -850,20 +850,16 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "gamma":
|
||||
double: 4
|
||||
|
||||
@ -1234,19 +1234,16 @@ ldouble: 3
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 2
|
||||
ldouble: 4
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 4
|
||||
ldouble: 4
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 3
|
||||
ldouble: 4
|
||||
|
||||
|
||||
@ -1,112 +0,0 @@
|
||||
/* ix87 specific implementation of exp(x)-1.
|
||||
Copyright (C) 1996-2024 Free Software Foundation, Inc.
|
||||
This file is part of the GNU C Library.
|
||||
|
||||
The GNU C Library is free software; you can redistribute it and/or
|
||||
modify it under the terms of the GNU Lesser General Public
|
||||
License as published by the Free Software Foundation; either
|
||||
version 2.1 of the License, or (at your option) any later version.
|
||||
|
||||
The GNU C Library is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
||||
Lesser General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU Lesser General Public
|
||||
License along with the GNU C Library; if not, see
|
||||
<https://www.gnu.org/licenses/>. */
|
||||
|
||||
/* Using: e^x - 1 = 2^(x * log2(e)) - 1 */
|
||||
|
||||
#include <sysdep.h>
|
||||
#include <machine/asm.h>
|
||||
#include <i386-math-asm.h>
|
||||
#include <libm-alias-float.h>
|
||||
|
||||
.section .rodata
|
||||
|
||||
.align ALIGNARG(4)
|
||||
.type minus1,@object
|
||||
minus1: .double -1.0
|
||||
ASM_SIZE_DIRECTIVE(minus1)
|
||||
.type one,@object
|
||||
one: .double 1.0
|
||||
ASM_SIZE_DIRECTIVE(one)
|
||||
.type l2e,@object
|
||||
l2e: .quad 0xb8aa3b295c17f0bc /* 1.442695040888963407359924681002 */
|
||||
.short 0x3fff
|
||||
ASM_SIZE_DIRECTIVE(l2e)
|
||||
|
||||
DEFINE_FLT_MIN
|
||||
|
||||
#ifdef PIC
|
||||
#define MO(op) op##@GOTOFF(%edx)
|
||||
#else
|
||||
#define MO(op) op
|
||||
#endif
|
||||
|
||||
.text
|
||||
ENTRY(__expm1f)
|
||||
movzwl 4+2(%esp), %eax
|
||||
xorb $0x80, %ah // invert sign bit (now 1 is "positive")
|
||||
cmpl $0xc2b1, %eax // is num >= 88.5?
|
||||
jae HIDDEN_JUMPTARGET (__expf)
|
||||
|
||||
flds 4(%esp) // x
|
||||
fxam // Is NaN, +-Inf or +-0?
|
||||
xorb $0x80, %ah
|
||||
cmpl $0xc190, %eax // is num <= -18.0?
|
||||
fstsw %ax
|
||||
movb $0x45, %ch
|
||||
jb 4f
|
||||
|
||||
// Below -18.0 (may be -NaN or -Inf).
|
||||
andb %ah, %ch
|
||||
#ifdef PIC
|
||||
LOAD_PIC_REG (dx)
|
||||
#endif
|
||||
cmpb $0x01, %ch
|
||||
je 5f // If -NaN, jump.
|
||||
jmp 2f // -large, possibly -Inf.
|
||||
|
||||
4: // In range -18.0 to 88.5 (may be +-0 but not NaN or +-Inf).
|
||||
andb %ah, %ch
|
||||
cmpb $0x40, %ch
|
||||
je 3f // If +-0, jump.
|
||||
#ifdef PIC
|
||||
LOAD_PIC_REG (dx)
|
||||
#endif
|
||||
|
||||
5: fldt MO(l2e) // log2(e) : x
|
||||
fmulp // log2(e)*x
|
||||
fld %st // log2(e)*x : log2(e)*x
|
||||
// Set round-to-nearest temporarily.
|
||||
subl $8, %esp
|
||||
cfi_adjust_cfa_offset (8)
|
||||
fstcw 4(%esp)
|
||||
movl $0xf3ff, %ecx
|
||||
andl 4(%esp), %ecx
|
||||
movl %ecx, (%esp)
|
||||
fldcw (%esp)
|
||||
frndint // int(log2(e)*x) : log2(e)*x
|
||||
fldcw 4(%esp)
|
||||
addl $8, %esp
|
||||
cfi_adjust_cfa_offset (-8)
|
||||
fsubr %st, %st(1) // int(log2(e)*x) : fract(log2(e)*x)
|
||||
fxch // fract(log2(e)*x) : int(log2(e)*x)
|
||||
f2xm1 // 2^fract(log2(e)*x)-1 : int(log2(e)*x)
|
||||
fscale // 2^(log2(e)*x)-2^int(log2(e)*x) : int(log2(e)*x)
|
||||
fxch // int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
|
||||
fldl MO(one) // 1 : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
|
||||
fscale // 2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
|
||||
fsubrl MO(one) // 1-2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
|
||||
fstp %st(1) // 1-2^int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
|
||||
fsubrp %st, %st(1) // 2^(log2(e)*x)
|
||||
FLT_CHECK_FORCE_UFLOW
|
||||
ret
|
||||
|
||||
2: fstp %st
|
||||
fldl MO(minus1) // Set result to -1.0.
|
||||
3: ret
|
||||
END(__expm1f)
|
||||
libm_alias_float (__expm1, expm1)
|
||||
@ -1237,19 +1237,16 @@ ldouble: 3
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 2
|
||||
ldouble: 4
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 4
|
||||
ldouble: 4
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 3
|
||||
ldouble: 4
|
||||
|
||||
|
||||
@ -3,7 +3,7 @@
|
||||
Copyright (c) 2022-2024 Alexei Sibidanov.
|
||||
|
||||
The original version of this file was copied from the CORE-MATH
|
||||
project (file src/binary32/exp2m1/exp2m1f.c, revision bc385c2).
|
||||
project (file src/binary32/exp2m1/exp2m1f.c, revision baf5f6b).
|
||||
|
||||
Permission is hereby granted, free of charge, to any person obtaining a copy
|
||||
of this software and associated documentation files (the "Software"), to deal
|
||||
|
||||
@ -1,132 +1,124 @@
|
||||
/* s_expm1f.c -- float version of s_expm1.c.
|
||||
*/
|
||||
/* Correctly-rounded natural exponent function biased by 1 for binary32 value.
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
Copyright (c) 2022-2024 Alexei Sibidanov.
|
||||
|
||||
This file is part of the CORE-MATH project
|
||||
project (file src/binary32/expm1/expm1f.c, revision bc385c2).
|
||||
|
||||
Permission is hereby granted, free of charge, to any person obtaining a copy
|
||||
of this software and associated documentation 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 <errno.h>
|
||||
#include <float.h>
|
||||
#include <math.h>
|
||||
#include <math-barriers.h>
|
||||
#include <math_private.h>
|
||||
#include <math-underflow.h>
|
||||
#include <libm-alias-float.h>
|
||||
|
||||
static const float huge = 1.0e+30;
|
||||
static const float tiny = 1.0e-30;
|
||||
|
||||
static const float
|
||||
one = 1.0,
|
||||
o_threshold = 8.8721679688e+01,/* 0x42b17180 */
|
||||
ln2_hi = 6.9313812256e-01,/* 0x3f317180 */
|
||||
ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */
|
||||
invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */
|
||||
/* scaled coefficients related to expm1 */
|
||||
Q1 = -3.3333335072e-02, /* 0xbd088889 */
|
||||
Q2 = 1.5873016091e-03, /* 0x3ad00d01 */
|
||||
Q3 = -7.9365076090e-05, /* 0xb8a670cd */
|
||||
Q4 = 4.0082177293e-06, /* 0x36867e54 */
|
||||
Q5 = -2.0109921195e-07; /* 0xb457edbb */
|
||||
#include "math_config.h"
|
||||
|
||||
float
|
||||
__expm1f(float x)
|
||||
__expm1f (float x)
|
||||
{
|
||||
float y,hi,lo,c,t,e,hxs,hfx,r1;
|
||||
int32_t k,xsb;
|
||||
uint32_t hx;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
xsb = hx&0x80000000; /* sign bit of x */
|
||||
if(xsb==0) y=x; else y= -x; /* y = |x| */
|
||||
hx &= 0x7fffffff; /* high word of |x| */
|
||||
|
||||
/* filter out huge and non-finite argument */
|
||||
if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
|
||||
if(hx >= 0x42b17218) { /* if |x|>=88.721... */
|
||||
if(hx>0x7f800000)
|
||||
return x+x; /* NaN */
|
||||
if(hx==0x7f800000)
|
||||
return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
|
||||
if(x > o_threshold) {
|
||||
__set_errno (ERANGE);
|
||||
return huge*huge; /* overflow */
|
||||
}
|
||||
}
|
||||
if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
|
||||
math_force_eval(x+tiny);/* raise inexact */
|
||||
return tiny-one; /* return -1 */
|
||||
}
|
||||
static const double c[] =
|
||||
{
|
||||
1, 0x1.62e42fef4c4e7p-6, 0x1.ebfd1b232f475p-13, 0x1.c6b19384ecd93p-20
|
||||
};
|
||||
static const double ch[] =
|
||||
{
|
||||
0x1.62e42fefa39efp-6, 0x1.ebfbdff82c58fp-13, 0x1.c6b08d702e0edp-20,
|
||||
0x1.3b2ab6fb92e5ep-27, 0x1.5d886e6d54203p-35, 0x1.430976b8ce6efp-43
|
||||
};
|
||||
static const double td[] =
|
||||
{
|
||||
0x1p+0, 0x1.059b0d3158574p+0, 0x1.0b5586cf9890fp+0,
|
||||
0x1.11301d0125b51p+0, 0x1.172b83c7d517bp+0, 0x1.1d4873168b9aap+0,
|
||||
0x1.2387a6e756238p+0, 0x1.29e9df51fdee1p+0, 0x1.306fe0a31b715p+0,
|
||||
0x1.371a7373aa9cbp+0, 0x1.3dea64c123422p+0, 0x1.44e086061892dp+0,
|
||||
0x1.4bfdad5362a27p+0, 0x1.5342b569d4f82p+0, 0x1.5ab07dd485429p+0,
|
||||
0x1.6247eb03a5585p+0, 0x1.6a09e667f3bcdp+0, 0x1.71f75e8ec5f74p+0,
|
||||
0x1.7a11473eb0187p+0, 0x1.82589994cce13p+0, 0x1.8ace5422aa0dbp+0,
|
||||
0x1.93737b0cdc5e5p+0, 0x1.9c49182a3f09p+0, 0x1.a5503b23e255dp+0,
|
||||
0x1.ae89f995ad3adp+0, 0x1.b7f76f2fb5e47p+0, 0x1.c199bdd85529cp+0,
|
||||
0x1.cb720dcef9069p+0, 0x1.d5818dcfba487p+0, 0x1.dfc97337b9b5fp+0,
|
||||
0x1.ea4afa2a490dap+0, 0x1.f50765b6e454p+0
|
||||
};
|
||||
const double iln2 = 0x1.71547652b82fep+5;
|
||||
const double big = 0x1.8p52;
|
||||
double z = x;
|
||||
uint32_t ux = asuint (x);
|
||||
uint32_t ax = ux << 1;
|
||||
if (__glibc_likely (ax < 0x7c400000u))
|
||||
{ /* |x| < 0.15625 */
|
||||
if (__glibc_unlikely (ax < 0x676a09e8u))
|
||||
{ /* |x| < 0x1.6a09e8p-24 */
|
||||
if (__glibc_unlikely (ax == 0x0u))
|
||||
return x; /* x = +-0 */
|
||||
return fmaf (fabsf (x), 0x1p-25f, x);
|
||||
}
|
||||
|
||||
/* argument reduction */
|
||||
if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
|
||||
if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
|
||||
if(xsb==0)
|
||||
{hi = x - ln2_hi; lo = ln2_lo; k = 1;}
|
||||
else
|
||||
{hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
|
||||
} else {
|
||||
k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
|
||||
t = k;
|
||||
hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
|
||||
lo = t*ln2_lo;
|
||||
}
|
||||
x = hi - lo;
|
||||
c = (hi-x)-lo;
|
||||
static const double b[] =
|
||||
{
|
||||
0x1.fffffffffffc2p-2, 0x1.55555555555fep-3, 0x1.555555559767fp-5,
|
||||
0x1.1111111098dc1p-7, 0x1.6c16bca988aa9p-10, 0x1.a01a07658483fp-13,
|
||||
0x1.a05b04d2c3503p-16, 0x1.71de3a960b5e3p-19
|
||||
};
|
||||
double z2 = z * z, z4 = z2 * z2;
|
||||
double r = z + z2
|
||||
* ((b[0] + z * b[1]) + z2 * (b[2] + z * b[3])
|
||||
+ z4 * ((b[4] + z * b[5]) + z2 * (b[6] + z * b[7])));
|
||||
return r;
|
||||
}
|
||||
if (__glibc_unlikely (ax >= 0x8562e430u))
|
||||
{ /* |x| > 88.72 */
|
||||
if (ax > (0xffu << 24))
|
||||
return x + x; /* nan */
|
||||
if (__glibc_unlikely (ux >> 31))
|
||||
{ /* x < 0 */
|
||||
if (ax == (0xffu << 24))
|
||||
return -1.0f;
|
||||
return -1.0f + 0x1p-26f;
|
||||
}
|
||||
else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
|
||||
math_check_force_underflow (x);
|
||||
t = huge+x; /* return x with inexact flags when x!=0 */
|
||||
return x - (t-(huge+x));
|
||||
}
|
||||
else k = 0;
|
||||
|
||||
/* x is now in primary range */
|
||||
hfx = (float)0.5*x;
|
||||
hxs = x*hfx;
|
||||
r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
|
||||
t = (float)3.0-r1*hfx;
|
||||
e = hxs*((r1-t)/((float)6.0 - x*t));
|
||||
if(k==0) return x - (x*e-hxs); /* c is 0 */
|
||||
else {
|
||||
e = (x*(e-c)-c);
|
||||
e -= hxs;
|
||||
if(k== -1) return (float)0.5*(x-e)-(float)0.5;
|
||||
if(k==1) {
|
||||
if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
|
||||
else return one+(float)2.0*(x-e);
|
||||
}
|
||||
if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
|
||||
int32_t i;
|
||||
y = one-(e-x);
|
||||
GET_FLOAT_WORD(i,y);
|
||||
SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
|
||||
return y-one;
|
||||
}
|
||||
t = one;
|
||||
if(k<23) {
|
||||
int32_t i;
|
||||
SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
|
||||
y = t-(e-x);
|
||||
GET_FLOAT_WORD(i,y);
|
||||
SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
|
||||
} else {
|
||||
int32_t i;
|
||||
SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
|
||||
y = x-(e+t);
|
||||
y += one;
|
||||
GET_FLOAT_WORD(i,y);
|
||||
SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
|
||||
}
|
||||
}
|
||||
return y;
|
||||
if (ax == (0xffu << 24))
|
||||
return INFINITY;
|
||||
return __math_oflowf (0);
|
||||
}
|
||||
double a = iln2 * z;
|
||||
double ia = roundeven (a);
|
||||
double h = a - ia;
|
||||
double h2 = h * h;
|
||||
uint64_t u = asuint64 (ia + big);
|
||||
double c2 = c[2] + h * c[3], c0 = c[0] + h * c[1];
|
||||
const uint64_t *tdl = (uint64_t *) ((void *) td);
|
||||
double sv = asdouble (tdl[u & 0x1f] + ((u >> 5) << 52));
|
||||
double r = (c0 + h2 * c2) * sv - 1.0;
|
||||
float ub = r, lb = r - sv * 0x1.3b3p-33;
|
||||
if (__glibc_unlikely (ub != lb))
|
||||
{
|
||||
if (__glibc_unlikely (ux > 0xc18aa123u)) /* x < -17.32 */
|
||||
return -1.0f + 0x1p-26f;
|
||||
const double iln2h = 0x1.7154765p+5;
|
||||
const double iln2l = 0x1.5c17f0bbbe88p-26;
|
||||
double s = sv;
|
||||
h = (iln2h * z - ia) + iln2l * z;
|
||||
h2 = h * h;
|
||||
double w = s * h;
|
||||
r = (s - 1) + w
|
||||
* ((ch[0] + h * ch[1])
|
||||
+ h2 * ((ch[2] + h * ch[3]) + h2 * (ch[4] + h * ch[5])));
|
||||
ub = r;
|
||||
}
|
||||
return ub;
|
||||
}
|
||||
libm_alias_float (__expm1, expm1)
|
||||
|
||||
@ -1038,22 +1038,18 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
ldouble: 4
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "gamma":
|
||||
|
||||
@ -191,7 +191,6 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "gamma":
|
||||
double: 4
|
||||
|
||||
@ -831,19 +831,15 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "gamma":
|
||||
double: 4
|
||||
|
||||
@ -1042,22 +1042,18 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
ldouble: 4
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "gamma":
|
||||
|
||||
@ -197,7 +197,6 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "gamma":
|
||||
double: 4
|
||||
|
||||
@ -804,19 +804,15 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "gamma":
|
||||
double: 4
|
||||
|
||||
@ -802,19 +802,15 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "gamma":
|
||||
double: 4
|
||||
|
||||
@ -870,6 +870,7 @@ float128: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: Imaginary part of "csin":
|
||||
float: 1
|
||||
float128: 1
|
||||
ldouble: 1
|
||||
|
||||
@ -1262,25 +1263,21 @@ ldouble: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 2
|
||||
ldouble: 1
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 2
|
||||
ldouble: 7
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
float128: 4
|
||||
ldouble: 6
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 3
|
||||
ldouble: 6
|
||||
|
||||
|
||||
@ -1054,22 +1054,18 @@ ldouble: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 5
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
ldouble: 5
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 6
|
||||
|
||||
Function: "fma":
|
||||
|
||||
@ -1011,22 +1011,18 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
ldouble: 4
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "gamma":
|
||||
|
||||
@ -1038,22 +1038,18 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
ldouble: 4
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "gamma":
|
||||
|
||||
@ -1039,22 +1039,18 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
ldouble: 4
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "gamma":
|
||||
|
||||
@ -394,11 +394,9 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
|
||||
Function: "fma_towardzero":
|
||||
double: 1
|
||||
|
||||
@ -1042,22 +1042,18 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
ldouble: 4
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "gamma":
|
||||
|
||||
@ -1062,6 +1062,7 @@ float128: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: Imaginary part of "csin":
|
||||
float: 1
|
||||
float128: 1
|
||||
|
||||
Function: Real part of "csin_downward":
|
||||
@ -1550,25 +1551,21 @@ float: 1
|
||||
|
||||
Function: "expm1":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 2
|
||||
ldouble: 3
|
||||
|
||||
Function: "expm1_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 2
|
||||
ldouble: 4
|
||||
|
||||
Function: "expm1_towardzero":
|
||||
double: 1
|
||||
float: 2
|
||||
float128: 4
|
||||
ldouble: 4
|
||||
|
||||
Function: "expm1_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
float128: 3
|
||||
ldouble: 4
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user