From 95a01ea9551f09c5e6accd07105bac360f2d38e6 Mon Sep 17 00:00:00 2001 From: Adhemerval Zanella Date: Fri, 20 Dec 2024 13:18:32 -0300 Subject: [PATCH] math: Use atanpif from CORE-MATH The CORE-MATH implementation is correctly rounded (for any rounding mode) and shows better performance to the generic atanpif. 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 66.3296 52.7558 20.46% x86_64v2 66.0429 51.4007 22.17% x86_64v3 60.6294 48.7876 19.53% aarch64 (Neoverse) 24.3163 20.9110 14.00% power8 16.5766 13.3620 19.39% power10 16.5115 13.4072 18.80% reciprocal-throughput master patched improvement x86_64 30.8599 16.0866 47.87% x86_64v2 29.2286 15.4688 47.08% x86_64v3 23.0960 12.8510 44.36% aarch64 (Neoverse) 15.4619 10.6752 30.96% power8 7.9200 5.2483 33.73% power10 6.8539 4.6262 32.50% Reviewed-by: DJ Delorie --- SHARED-FILES | 4 + math/auto-libm-test-in | 1 + math/auto-libm-test-out-atanpi | 25 ++++ sysdeps/aarch64/libm-test-ulps | 4 - sysdeps/arc/fpu/libm-test-ulps | 4 - sysdeps/arc/nofpu/libm-test-ulps | 1 - sysdeps/arm/libm-test-ulps | 4 - sysdeps/hppa/fpu/libm-test-ulps | 4 - sysdeps/i386/fpu/libm-test-ulps | 4 - .../i386/i686/fpu/multiarch/libm-test-ulps | 4 - sysdeps/ieee754/flt-32/s_atanpif.c | 109 ++++++++++++++++++ sysdeps/loongarch/lp64/libm-test-ulps | 4 - sysdeps/mips/mips64/libm-test-ulps | 4 - sysdeps/or1k/fpu/libm-test-ulps | 4 - sysdeps/or1k/nofpu/libm-test-ulps | 1 - sysdeps/powerpc/fpu/libm-test-ulps | 4 - sysdeps/riscv/nofpu/libm-test-ulps | 1 - sysdeps/riscv/rvd/libm-test-ulps | 4 - sysdeps/s390/fpu/libm-test-ulps | 4 - sysdeps/sparc/fpu/libm-test-ulps | 4 - sysdeps/x86_64/fpu/libm-test-ulps | 4 - 21 files changed, 139 insertions(+), 59 deletions(-) create mode 100644 sysdeps/ieee754/flt-32/s_atanpif.c diff --git a/SHARED-FILES b/SHARED-FILES index b403a2a6f0..5702a2d1c3 100644 --- a/SHARED-FILES +++ b/SHARED-FILES @@ -346,3 +346,7 @@ sysdeps/ieee754/flt-32/s_atan2pif.c: (src/binary32/atan2pi/atan2pif.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_atanpif.c: + (src/binary32/atanpi/atanpif.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/math/auto-libm-test-in b/math/auto-libm-test-in index 4f194da19d..7dd9cde9c9 100644 --- a/math/auto-libm-test-in +++ b/math/auto-libm-test-in @@ -936,6 +936,7 @@ atanpi -0x3.eb8e18p+0 atanpi 0x3.53c188p+0 atanpi -0x1.58c83p+0 atanpi 0x1.626772p-1 +atanpi 0x1p-126 atanpi min atanpi -min atanpi min_subnorm diff --git a/math/auto-libm-test-out-atanpi b/math/auto-libm-test-out-atanpi index 9f9ded81d1..4d3454b4ae 100644 --- a/math/auto-libm-test-out-atanpi +++ b/math/auto-libm-test-out-atanpi @@ -1061,6 +1061,31 @@ atanpi 0x1.626772p-1 = atanpi tonearest ibm128 0xb.133b9p-4 : 0x3.156898f544dca52f89f818e127p-4 : inexact-ok = atanpi towardzero ibm128 0xb.133b9p-4 : 0x3.156898f544dca52f89f818e127p-4 : inexact-ok = atanpi upward ibm128 0xb.133b9p-4 : 0x3.156898f544dca52f89f818e128p-4 : inexact-ok +atanpi 0x1p-126 += atanpi downward binary32 0x4p-128 : 0x1.45f3p-128 : inexact-ok underflow errno-erange-ok += atanpi tonearest binary32 0x4p-128 : 0x1.45f308p-128 : inexact-ok underflow errno-erange-ok += atanpi towardzero binary32 0x4p-128 : 0x1.45f3p-128 : inexact-ok underflow errno-erange-ok += atanpi upward binary32 0x4p-128 : 0x1.45f308p-128 : inexact-ok underflow errno-erange-ok += atanpi downward binary64 0x4p-128 : 0x1.45f306dc9c882p-128 : inexact-ok += atanpi tonearest binary64 0x4p-128 : 0x1.45f306dc9c883p-128 : inexact-ok += atanpi towardzero binary64 0x4p-128 : 0x1.45f306dc9c882p-128 : inexact-ok += atanpi upward binary64 0x4p-128 : 0x1.45f306dc9c883p-128 : inexact-ok += atanpi downward intel96 0x4p-128 : 0x1.45f306dc9c882a52p-128 : inexact-ok += atanpi tonearest intel96 0x4p-128 : 0x1.45f306dc9c882a54p-128 : inexact-ok += atanpi towardzero intel96 0x4p-128 : 0x1.45f306dc9c882a52p-128 : inexact-ok += atanpi upward intel96 0x4p-128 : 0x1.45f306dc9c882a54p-128 : inexact-ok += atanpi downward m68k96 0x4p-128 : 0x1.45f306dc9c882a52p-128 : inexact-ok += atanpi tonearest m68k96 0x4p-128 : 0x1.45f306dc9c882a54p-128 : inexact-ok += atanpi towardzero m68k96 0x4p-128 : 0x1.45f306dc9c882a52p-128 : inexact-ok += atanpi upward m68k96 0x4p-128 : 0x1.45f306dc9c882a54p-128 : inexact-ok += atanpi downward binary128 0x4p-128 : 0x1.45f306dc9c882a53f84eafa3ea69p-128 : inexact-ok += atanpi tonearest binary128 0x4p-128 : 0x1.45f306dc9c882a53f84eafa3ea6ap-128 : inexact-ok += atanpi towardzero binary128 0x4p-128 : 0x1.45f306dc9c882a53f84eafa3ea69p-128 : inexact-ok += atanpi upward binary128 0x4p-128 : 0x1.45f306dc9c882a53f84eafa3ea6ap-128 : inexact-ok += atanpi downward ibm128 0x4p-128 : 0x1.45f306dc9c882a53f84eafa3eap-128 : inexact-ok += atanpi tonearest ibm128 0x4p-128 : 0x1.45f306dc9c882a53f84eafa3ea8p-128 : inexact-ok += atanpi towardzero ibm128 0x4p-128 : 0x1.45f306dc9c882a53f84eafa3eap-128 : inexact-ok += atanpi upward ibm128 0x4p-128 : 0x1.45f306dc9c882a53f84eafa3ea8p-128 : inexact-ok atanpi min = atanpi downward binary32 0x4p-128 : 0x1.45f3p-128 : inexact-ok underflow errno-erange-ok = atanpi tonearest binary32 0x4p-128 : 0x1.45f308p-128 : inexact-ok underflow errno-erange-ok diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps index be29b37721..10f182a211 100644 --- a/sysdeps/aarch64/libm-test-ulps +++ b/sysdeps/aarch64/libm-test-ulps @@ -218,22 +218,18 @@ ldouble: 4 Function: "atanpi": double: 2 -float: 1 ldouble: 2 Function: "atanpi_downward": double: 1 -float: 2 ldouble: 1 Function: "atanpi_towardzero": double: 1 -float: 2 ldouble: 1 Function: "atanpi_upward": double: 1 -float: 1 ldouble: 2 Function: "cabs": diff --git a/sysdeps/arc/fpu/libm-test-ulps b/sysdeps/arc/fpu/libm-test-ulps index 1383c88b95..7fb407cecd 100644 --- a/sysdeps/arc/fpu/libm-test-ulps +++ b/sysdeps/arc/fpu/libm-test-ulps @@ -123,19 +123,15 @@ double: 3 Function: "atanpi": double: 2 -float: 1 Function: "atanpi_downward": double: 1 -float: 2 Function: "atanpi_towardzero": double: 1 -float: 2 Function: "atanpi_upward": double: 1 -float: 1 Function: "cabs": double: 1 diff --git a/sysdeps/arc/nofpu/libm-test-ulps b/sysdeps/arc/nofpu/libm-test-ulps index 9028f5cbe7..1859c2bd4f 100644 --- a/sysdeps/arc/nofpu/libm-test-ulps +++ b/sysdeps/arc/nofpu/libm-test-ulps @@ -30,7 +30,6 @@ double: 2 Function: "atanpi": double: 2 -float: 1 Function: "cabs": double: 1 diff --git a/sysdeps/arm/libm-test-ulps b/sysdeps/arm/libm-test-ulps index e1c538f79f..fa9864adee 100644 --- a/sysdeps/arm/libm-test-ulps +++ b/sysdeps/arm/libm-test-ulps @@ -120,19 +120,15 @@ double: 3 Function: "atanpi": double: 2 -float: 1 Function: "atanpi_downward": double: 1 -float: 2 Function: "atanpi_towardzero": double: 1 -float: 2 Function: "atanpi_upward": double: 1 -float: 1 Function: "cabs": double: 1 diff --git a/sysdeps/hppa/fpu/libm-test-ulps b/sysdeps/hppa/fpu/libm-test-ulps index 796da7b5ab..a59f61fc4e 100644 --- a/sysdeps/hppa/fpu/libm-test-ulps +++ b/sysdeps/hppa/fpu/libm-test-ulps @@ -120,19 +120,15 @@ double: 3 Function: "atanpi": double: 2 -float: 1 Function: "atanpi_downward": double: 1 -float: 2 Function: "atanpi_towardzero": double: 1 -float: 2 Function: "atanpi_upward": double: 1 -float: 1 Function: "cabs": double: 1 diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps index 4f687c762b..8aa52f4600 100644 --- a/sysdeps/i386/fpu/libm-test-ulps +++ b/sysdeps/i386/fpu/libm-test-ulps @@ -201,25 +201,21 @@ ldouble: 5 Function: "atanpi": double: 1 -float: 1 float128: 2 ldouble: 1 Function: "atanpi_downward": double: 2 -float: 2 float128: 1 ldouble: 2 Function: "atanpi_towardzero": double: 1 -float: 2 float128: 1 ldouble: 2 Function: "atanpi_upward": double: 2 -float: 1 float128: 2 ldouble: 1 diff --git a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps index f24c87b302..8032636808 100644 --- a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps +++ b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps @@ -201,25 +201,21 @@ ldouble: 5 Function: "atanpi": double: 1 -float: 1 float128: 2 ldouble: 2 Function: "atanpi_downward": double: 2 -float: 2 float128: 1 ldouble: 2 Function: "atanpi_towardzero": double: 1 -float: 2 float128: 1 ldouble: 2 Function: "atanpi_upward": double: 2 -float: 1 float128: 2 ldouble: 1 diff --git a/sysdeps/ieee754/flt-32/s_atanpif.c b/sysdeps/ieee754/flt-32/s_atanpif.c new file mode 100644 index 0000000000..8d78163418 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_atanpif.c @@ -0,0 +1,109 @@ +/* Correctly-rounded half-revolution arc-tangent of binary32 value. + +Copyright (c) 2022-2025 Alexei Sibidanov. + +The original version of this file was copied from the CORE-MATH +project (file src/binary32/atanpi/atanpif.c, revision e02000e). + +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 "math_config.h" + +float +__atanpif (float x) +{ + uint32_t t = asuint (x); + int32_t e = (t >> 23) & 0xff; + bool gt = e >= 127; + if (__glibc_unlikely (e > 127 + 24)) + { + float f = copysignf (0.5f, x); + if (__glibc_unlikely (e == 0xff)) + { + if (t << 9) + return x + x; /* nan */ + return f; /* inf */ + } + /* Warning: 0x1.45f306p-2f / x underflows for |x| >= 0x1.45f306p+124 */ + if (fabsf (x) >= 0x1.45f306p+124f) + return f - copysign (0x1p-26f, x); + else + return f - 0x1.45f306p-2f / x; + } + double z = x; + if (__glibc_unlikely (e < 127 - 13)) + { + double sx = z * 0x1.45f306dc9c883p-2; + if (__glibc_unlikely (e < 127 - 25)) + { + float rsx = sx; + if (x != 0 && rsx == 0) + __set_errno (ERANGE); + return rsx; + } + return sx - (0x1.5555555555555p-2 * sx) * (x * x); + } + uint32_t ax = t & (~0u >> 1); + if (__glibc_unlikely (ax == 0x3fa267ddu)) + return copysignf (0x1.267004p-2f, x) - copysignf (0x1p-55f, x); + if (__glibc_unlikely (ax == 0x3f693531u)) + return copysignf (0x1.e1a662p-3f, x) + copysignf (0x1p-28f, x); + if (__glibc_unlikely (ax == 0x3f800000u)) + return copysignf (0x1p-2f, x); + if (gt) + z = 1 / z; + double z2 = z * z; + double z4 = z2 * z2; + double z8 = z4 * z4; + static const double cn[] = + { + 0x1.45f306dc9c882p-2, 0x1.733b561bc23d5p-1, 0x1.28d9805bdfbf2p-1, + 0x1.8c3ba966ae287p-3, 0x1.94a7f81ee634bp-6, 0x1.a6bbf6127a6dfp-11 + }; + static const double cd[] = + { + 0x1p+0, 0x1.4e3b3ecc2518fp+1, 0x1.3ef4a360ff063p+1, + 0x1.0f1dc55bad551p+0, 0x1.8da0fecc018a4p-3, 0x1.8fa87803776bfp-7, + 0x1.dadf2ca0acb43p-14 + }; + double cn0 = cn[0] + z2 * cn[1]; + double cn2 = cn[2] + z2 * cn[3]; + double cn4 = cn[4] + z2 * cn[5]; + cn0 += z4 * cn2; + cn0 += z8 * cn4; + cn0 *= z; + double cd0 = cd[0] + z2 * cd[1]; + double cd2 = cd[2] + z2 * cd[3]; + double cd4 = cd[4] + z2 * cd[5]; + double cd6 = cd[6]; + cd0 += z4 * cd2; + cd4 += z4 * cd6; + cd0 += z8 * cd4; + double r = cn0 / cd0; + if (gt) + r = copysign (0.5, z) - r; + return r; +} +libm_alias_float (__atanpi, atanpi) diff --git a/sysdeps/loongarch/lp64/libm-test-ulps b/sysdeps/loongarch/lp64/libm-test-ulps index d5adc119cf..0cac55cbe4 100644 --- a/sysdeps/loongarch/lp64/libm-test-ulps +++ b/sysdeps/loongarch/lp64/libm-test-ulps @@ -162,22 +162,18 @@ ldouble: 4 Function: "atanpi": double: 2 -float: 1 ldouble: 2 Function: "atanpi_downward": double: 1 -float: 2 ldouble: 1 Function: "atanpi_towardzero": double: 1 -float: 2 ldouble: 1 Function: "atanpi_upward": double: 1 -float: 1 ldouble: 2 Function: "cabs": diff --git a/sysdeps/mips/mips64/libm-test-ulps b/sysdeps/mips/mips64/libm-test-ulps index c901b00f20..1b5bcff11e 100644 --- a/sysdeps/mips/mips64/libm-test-ulps +++ b/sysdeps/mips/mips64/libm-test-ulps @@ -162,22 +162,18 @@ ldouble: 4 Function: "atanpi": double: 2 -float: 1 ldouble: 2 Function: "atanpi_downward": double: 1 -float: 2 ldouble: 1 Function: "atanpi_towardzero": double: 1 -float: 2 ldouble: 1 Function: "atanpi_upward": double: 1 -float: 1 ldouble: 2 Function: "cabs": diff --git a/sysdeps/or1k/fpu/libm-test-ulps b/sysdeps/or1k/fpu/libm-test-ulps index 9934382bde..a608e3c949 100644 --- a/sysdeps/or1k/fpu/libm-test-ulps +++ b/sysdeps/or1k/fpu/libm-test-ulps @@ -120,19 +120,15 @@ double: 3 Function: "atanpi": double: 2 -float: 1 Function: "atanpi_downward": double: 1 -float: 2 Function: "atanpi_towardzero": double: 1 -float: 2 Function: "atanpi_upward": double: 1 -float: 1 Function: "cabs": double: 1 diff --git a/sysdeps/or1k/nofpu/libm-test-ulps b/sysdeps/or1k/nofpu/libm-test-ulps index 7ff5ee4425..56986f0be0 100644 --- a/sysdeps/or1k/nofpu/libm-test-ulps +++ b/sysdeps/or1k/nofpu/libm-test-ulps @@ -93,7 +93,6 @@ double: 3 Function: "atanpi": double: 2 -float: 1 Function: "cabs": double: 1 diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps index b1c01b4d94..630111e6c4 100644 --- a/sysdeps/powerpc/fpu/libm-test-ulps +++ b/sysdeps/powerpc/fpu/libm-test-ulps @@ -206,25 +206,21 @@ ldouble: 4 Function: "atanpi": double: 2 -float: 1 float128: 2 ldouble: 1 Function: "atanpi_downward": double: 1 -float: 2 float128: 1 ldouble: 2 Function: "atanpi_towardzero": double: 1 -float: 2 float128: 1 ldouble: 3 Function: "atanpi_upward": double: 1 -float: 1 float128: 2 ldouble: 5 diff --git a/sysdeps/riscv/nofpu/libm-test-ulps b/sysdeps/riscv/nofpu/libm-test-ulps index f55df65c6a..087dcd79fc 100644 --- a/sysdeps/riscv/nofpu/libm-test-ulps +++ b/sysdeps/riscv/nofpu/libm-test-ulps @@ -126,7 +126,6 @@ ldouble: 4 Function: "atanpi": double: 2 -float: 1 ldouble: 2 Function: "cabs": diff --git a/sysdeps/riscv/rvd/libm-test-ulps b/sysdeps/riscv/rvd/libm-test-ulps index 879f5c5669..efd83affa4 100644 --- a/sysdeps/riscv/rvd/libm-test-ulps +++ b/sysdeps/riscv/rvd/libm-test-ulps @@ -166,22 +166,18 @@ ldouble: 4 Function: "atanpi": double: 2 -float: 1 ldouble: 2 Function: "atanpi_downward": double: 1 -float: 2 ldouble: 1 Function: "atanpi_towardzero": double: 1 -float: 2 ldouble: 1 Function: "atanpi_upward": double: 1 -float: 1 ldouble: 2 Function: "cabs": diff --git a/sysdeps/s390/fpu/libm-test-ulps b/sysdeps/s390/fpu/libm-test-ulps index c4a27b96ad..709debb205 100644 --- a/sysdeps/s390/fpu/libm-test-ulps +++ b/sysdeps/s390/fpu/libm-test-ulps @@ -162,22 +162,18 @@ ldouble: 4 Function: "atanpi": double: 2 -float: 1 ldouble: 2 Function: "atanpi_downward": double: 1 -float: 2 ldouble: 1 Function: "atanpi_towardzero": double: 1 -float: 2 ldouble: 1 Function: "atanpi_upward": double: 1 -float: 1 ldouble: 2 Function: "cabs": diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps index fbf1507bd9..becf5da3d6 100644 --- a/sysdeps/sparc/fpu/libm-test-ulps +++ b/sysdeps/sparc/fpu/libm-test-ulps @@ -162,22 +162,18 @@ ldouble: 4 Function: "atanpi": double: 2 -float: 1 ldouble: 2 Function: "atanpi_downward": double: 1 -float: 2 ldouble: 1 Function: "atanpi_towardzero": double: 1 -float: 2 ldouble: 1 Function: "atanpi_upward": double: 1 -float: 1 ldouble: 2 Function: "cabs": diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps index a340df6243..8c5d4fd471 100644 --- a/sysdeps/x86_64/fpu/libm-test-ulps +++ b/sysdeps/x86_64/fpu/libm-test-ulps @@ -339,25 +339,21 @@ float: 1 Function: "atanpi": double: 2 -float: 1 float128: 2 ldouble: 2 Function: "atanpi_downward": double: 1 -float: 2 float128: 1 ldouble: 2 Function: "atanpi_towardzero": double: 1 -float: 2 float128: 1 ldouble: 2 Function: "atanpi_upward": double: 1 -float: 1 float128: 2 ldouble: 1