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([2804:1b3:a7c3:a8a8:cb9e:64f4:66fb:5ca2]) by smtp.gmail.com with ESMTPSA id d9443c01a7336-210bbf44550sm12314075ad.14.2024.10.25.11.27.08 (version=TLS1_3 cipher=TLS_AES_256_GCM_SHA384 bits=256/256); Fri, 25 Oct 2024 11:27:09 -0700 (PDT) From: Adhemerval Zanella To: libc-alpha@sourceware.org Cc: Paul Zimmermann , Alexei Sibidanov Subject: [PATCH 11/17] math: Use expm1f from CORE-MATH Date: Fri, 25 Oct 2024 15:21:49 -0300 Message-ID: <20241025182614.2022697-12-adhemerval.zanella@linaro.org> X-Mailer: git-send-email 2.43.0 In-Reply-To: <20241025182614.2022697-1-adhemerval.zanella@linaro.org> References: <20241025182614.2022697-1-adhemerval.zanella@linaro.org> MIME-Version: 1.0 X-Spam-Status: No, score=-12.2 required=5.0 tests=BAYES_00, DKIM_SIGNED, DKIM_VALID, DKIM_VALID_AU, DKIM_VALID_EF, GIT_PATCH_0, KAM_ASCII_DIVIDERS, KAM_SHORT, RCVD_IN_DNSWL_NONE, SPF_HELO_NONE, SPF_PASS, TXREP autolearn=ham autolearn_force=no version=3.4.6 X-Spam-Checker-Version: SpamAssassin 3.4.6 (2021-04-09) on server2.sourceware.org X-BeenThere: libc-alpha@sourceware.org X-Mailman-Version: 2.1.30 Precedence: list List-Id: Libc-alpha mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: libc-alpha-bounces~patch=linaro.org@sourceware.org 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 Signed-off-by: Paul Zimmermann Signed-off-by: Adhemerval Zanella --- SHARED-FILES | 4 + sysdeps/aarch64/libm-test-ulps | 5 +- sysdeps/alpha/fpu/libm-test-ulps | 4 - sysdeps/arc/fpu/libm-test-ulps | 4 - sysdeps/arc/nofpu/libm-test-ulps | 1 - sysdeps/arm/libm-test-ulps | 7 +- sysdeps/csky/fpu/libm-test-ulps | 4 - sysdeps/csky/nofpu/libm-test-ulps | 4 - sysdeps/hppa/fpu/libm-test-ulps | 4 - sysdeps/i386/fpu/libm-test-ulps | 3 - sysdeps/i386/fpu/s_expm1f.S | 112 --------- .../i386/i686/fpu/multiarch/libm-test-ulps | 3 - sysdeps/ieee754/flt-32/s_expm1f.c | 232 +++++++++--------- sysdeps/loongarch/lp64/libm-test-ulps | 4 - sysdeps/microblaze/libm-test-ulps | 1 - sysdeps/mips/mips32/libm-test-ulps | 4 - sysdeps/mips/mips64/libm-test-ulps | 4 - sysdeps/nios2/libm-test-ulps | 1 - sysdeps/or1k/fpu/libm-test-ulps | 4 - sysdeps/or1k/nofpu/libm-test-ulps | 4 - sysdeps/powerpc/fpu/libm-test-ulps | 5 +- sysdeps/powerpc/nofpu/libm-test-ulps | 4 - sysdeps/riscv/nofpu/libm-test-ulps | 4 - sysdeps/riscv/rvd/libm-test-ulps | 4 - sysdeps/s390/fpu/libm-test-ulps | 4 - sysdeps/sh/libm-test-ulps | 2 - sysdeps/sparc/fpu/libm-test-ulps | 4 - sysdeps/x86_64/fpu/libm-test-ulps | 5 +- 28 files changed, 122 insertions(+), 319 deletions(-) delete mode 100644 sysdeps/i386/fpu/s_expm1f.S diff --git a/SHARED-FILES b/SHARED-FILES index 5e771cd1c4..a559e97318 100644 --- a/SHARED-FILES +++ b/SHARED-FILES @@ -239,3 +239,7 @@ 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. diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps index 29ccd1dfe9..c6c40df9fa 100644 --- a/sysdeps/aarch64/libm-test-ulps +++ b/sysdeps/aarch64/libm-test-ulps @@ -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": diff --git a/sysdeps/alpha/fpu/libm-test-ulps b/sysdeps/alpha/fpu/libm-test-ulps index 5c6175406b..09185dd902 100644 --- a/sysdeps/alpha/fpu/libm-test-ulps +++ b/sysdeps/alpha/fpu/libm-test-ulps @@ -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": diff --git a/sysdeps/arc/fpu/libm-test-ulps b/sysdeps/arc/fpu/libm-test-ulps index fd6d4181f8..ca01eb3b4b 100644 --- a/sysdeps/arc/fpu/libm-test-ulps +++ b/sysdeps/arc/fpu/libm-test-ulps @@ -842,19 +842,15 @@ 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 diff --git a/sysdeps/arc/nofpu/libm-test-ulps b/sysdeps/arc/nofpu/libm-test-ulps index 574ae8b8be..266381f6ea 100644 --- a/sysdeps/arc/nofpu/libm-test-ulps +++ b/sysdeps/arc/nofpu/libm-test-ulps @@ -203,7 +203,6 @@ double: 2 Function: "expm1": double: 1 -float: 1 Function: "gamma": double: 4 diff --git a/sysdeps/arm/libm-test-ulps b/sysdeps/arm/libm-test-ulps index 28718c7d2c..12451d24a7 100644 --- a/sysdeps/arm/libm-test-ulps +++ b/sysdeps/arm/libm-test-ulps @@ -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 diff --git a/sysdeps/csky/fpu/libm-test-ulps b/sysdeps/csky/fpu/libm-test-ulps index 151df00638..3f17778d03 100644 --- a/sysdeps/csky/fpu/libm-test-ulps +++ b/sysdeps/csky/fpu/libm-test-ulps @@ -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 diff --git a/sysdeps/csky/nofpu/libm-test-ulps b/sysdeps/csky/nofpu/libm-test-ulps index 48697a7b09..fdef935578 100644 --- a/sysdeps/csky/nofpu/libm-test-ulps +++ b/sysdeps/csky/nofpu/libm-test-ulps @@ -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 diff --git a/sysdeps/hppa/fpu/libm-test-ulps b/sysdeps/hppa/fpu/libm-test-ulps index 338ca77ade..05ad1cf9b3 100644 --- a/sysdeps/hppa/fpu/libm-test-ulps +++ b/sysdeps/hppa/fpu/libm-test-ulps @@ -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 diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps index 98a5a538ff..abf9a9192b 100644 --- a/sysdeps/i386/fpu/libm-test-ulps +++ b/sysdeps/i386/fpu/libm-test-ulps @@ -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 diff --git a/sysdeps/i386/fpu/s_expm1f.S b/sysdeps/i386/fpu/s_expm1f.S deleted file mode 100644 index a1cb5bf0ab..0000000000 --- a/sysdeps/i386/fpu/s_expm1f.S +++ /dev/null @@ -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 - . */ - - /* Using: e^x - 1 = 2^(x * log2(e)) - 1 */ - -#include -#include -#include -#include - - .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) diff --git a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps index 9afb63bc0f..6d9d49d153 100644 --- a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps +++ b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps @@ -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 diff --git a/sysdeps/ieee754/flt-32/s_expm1f.c b/sysdeps/ieee754/flt-32/s_expm1f.c index 35f7b5214a..edd7c9acf8 100644 --- a/sysdeps/ieee754/flt-32/s_expm1f.c +++ b/sysdeps/ieee754/flt-32/s_expm1f.c @@ -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 -#include #include -#include -#include #include #include - -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 */ - } - } - - /* 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; - } - 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)); + 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); } - 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 */ - } + 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; } - 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) diff --git a/sysdeps/loongarch/lp64/libm-test-ulps b/sysdeps/loongarch/lp64/libm-test-ulps index c6fc9fd4ed..5d407a49fe 100644 --- a/sysdeps/loongarch/lp64/libm-test-ulps +++ b/sysdeps/loongarch/lp64/libm-test-ulps @@ -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": diff --git a/sysdeps/microblaze/libm-test-ulps b/sysdeps/microblaze/libm-test-ulps index 98ea940ccc..a84494b8f8 100644 --- a/sysdeps/microblaze/libm-test-ulps +++ b/sysdeps/microblaze/libm-test-ulps @@ -191,7 +191,6 @@ float: 1 Function: "expm1": double: 1 -float: 1 Function: "gamma": double: 4 diff --git a/sysdeps/mips/mips32/libm-test-ulps b/sysdeps/mips/mips32/libm-test-ulps index d8daca6326..f9d7bf8598 100644 --- a/sysdeps/mips/mips32/libm-test-ulps +++ b/sysdeps/mips/mips32/libm-test-ulps @@ -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 diff --git a/sysdeps/mips/mips64/libm-test-ulps b/sysdeps/mips/mips64/libm-test-ulps index 39e94d5480..4f3c82d64c 100644 --- a/sysdeps/mips/mips64/libm-test-ulps +++ b/sysdeps/mips/mips64/libm-test-ulps @@ -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": diff --git a/sysdeps/nios2/libm-test-ulps b/sysdeps/nios2/libm-test-ulps index df6e932cb6..33f714e713 100644 --- a/sysdeps/nios2/libm-test-ulps +++ b/sysdeps/nios2/libm-test-ulps @@ -197,7 +197,6 @@ float: 1 Function: "expm1": double: 1 -float: 1 Function: "gamma": double: 4 diff --git a/sysdeps/or1k/fpu/libm-test-ulps b/sysdeps/or1k/fpu/libm-test-ulps index 4ccb136298..9ced4b0052 100644 --- a/sysdeps/or1k/fpu/libm-test-ulps +++ b/sysdeps/or1k/fpu/libm-test-ulps @@ -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 diff --git a/sysdeps/or1k/nofpu/libm-test-ulps b/sysdeps/or1k/nofpu/libm-test-ulps index 7087cf9add..6862551b79 100644 --- a/sysdeps/or1k/nofpu/libm-test-ulps +++ b/sysdeps/or1k/nofpu/libm-test-ulps @@ -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 diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps index dd25aaf94a..ddbd184e58 100644 --- a/sysdeps/powerpc/fpu/libm-test-ulps +++ b/sysdeps/powerpc/fpu/libm-test-ulps @@ -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 diff --git a/sysdeps/powerpc/nofpu/libm-test-ulps b/sysdeps/powerpc/nofpu/libm-test-ulps index 1e5bae039b..c79dfcc2cc 100644 --- a/sysdeps/powerpc/nofpu/libm-test-ulps +++ b/sysdeps/powerpc/nofpu/libm-test-ulps @@ -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": diff --git a/sysdeps/riscv/nofpu/libm-test-ulps b/sysdeps/riscv/nofpu/libm-test-ulps index 11f891988e..4caf84f316 100644 --- a/sysdeps/riscv/nofpu/libm-test-ulps +++ b/sysdeps/riscv/nofpu/libm-test-ulps @@ -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": diff --git a/sysdeps/riscv/rvd/libm-test-ulps b/sysdeps/riscv/rvd/libm-test-ulps index 7d303fcb6b..e9c4b72c04 100644 --- a/sysdeps/riscv/rvd/libm-test-ulps +++ b/sysdeps/riscv/rvd/libm-test-ulps @@ -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": diff --git a/sysdeps/s390/fpu/libm-test-ulps b/sysdeps/s390/fpu/libm-test-ulps index aa7a94a2be..a42c9f273a 100644 --- a/sysdeps/s390/fpu/libm-test-ulps +++ b/sysdeps/s390/fpu/libm-test-ulps @@ -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": diff --git a/sysdeps/sh/libm-test-ulps b/sysdeps/sh/libm-test-ulps index 36f21ed395..fc4556e977 100644 --- a/sysdeps/sh/libm-test-ulps +++ b/sysdeps/sh/libm-test-ulps @@ -394,11 +394,9 @@ float: 1 Function: "expm1": double: 1 -float: 1 Function: "expm1_towardzero": double: 1 -float: 2 Function: "fma_towardzero": double: 1 diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps index e7b3da6f1c..3bee496247 100644 --- a/sysdeps/sparc/fpu/libm-test-ulps +++ b/sysdeps/sparc/fpu/libm-test-ulps @@ -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": diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps index 71697e99e0..ffb1d4f3c9 100644 --- a/sysdeps/x86_64/fpu/libm-test-ulps +++ b/sysdeps/x86_64/fpu/libm-test-ulps @@ -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