math: Sync acosh from CORE-MATH

The CORE-MATH commit 6736002f fixes some issues for RNDZ:

Failure: Test: acosh_towardzero (0x1.08000c1e79fp+0)
Result:
 is:          2.4935636091994373e-01   0x1.feae8c399b18cp-3
 should be:   2.4935636091994370e-01   0x1.feae8c399b18bp-3
 difference:  2.7755575615628913e-17   0x1.0000000000000p-55
 ulp       :  1.0000
 max.ulp   :  0.0000
Failure: Test: acosh_towardzero (0x1.080016353964ep+0)
Result:
 is:          2.4935874767710369e-01   0x1.feafcc91f518ep-3
 should be:   2.4935874767710367e-01   0x1.feafcc91f518dp-3
 difference:  2.7755575615628913e-17   0x1.0000000000000p-55
 ulp       :  1.0000
 max.ulp   :  0.0000
Maximal error of `acosh_towardzero'
 is      : 1 ulp
 accepted: 0 ulp

This only happens when the ISA supports fma, such as x86_64-v3, aarch64,
or powerpc.

Checked on x86_64-linux-gnu, x86_64-linux-gnu-v3, aarch64-linux-gnu,
and i686-linux-gnu.

diff --git a/SHARED-FILES b/SHARED-FILES
index b9016ead8f31c7d8c5408d36f5b08077f9585703..38fc87a79cfb7f05cbf705d272da64e43dca51bd 100644 (file)
--- a/SHARED-FILES
+++ b/SHARED-FILES
@@ -244,7 +244,7 @@ tzdata:
 # The project is distribute here:
 #       https://gitlab.inria.fr/core-math/core-math/
 core-math:
-  # src/binary64/acosh/acosh.c, revision 69062c4d
+  # src/binary64/acosh/acosh.c, revision 6736002f
   sysdeps/ieee754/dbl-64/e_acosh.c
   # src/binary64/atanh/atanh.c, revision c9abdf80
   sysdeps/ieee754/dbl-64/e_atanh.c

diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index 10e7d11850f0c75cd031c055fb73fb0b71805e43..0e5b27397056745bb63a9516b2b739e4d1a3ff12 100644 (file)
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -220,6 +220,8 @@ acosh 0x1.07c956p+0
 acosh 0x1.1808eep+0
 acosh 0x1.1052c4p+0
 acosh 0x1.0800751d9facbp+0
+acosh 0x1.08000c1e79fp+0
+acosh 0x1.080016353964ep+0
 # the next value generates larger error bounds on x86_64 (ldbl-96)
 acosh 0x1.1ecbdf374bce01cap+0
 # the next value generates larger error bounds on x86_64 (binary128)

diff --git a/math/auto-libm-test-out-acosh b/math/auto-libm-test-out-acosh
index 8cdaddd84fd26d84ed0f1002028841a40860c62f..ccc2b47e8f699f39d4e5df8b25eee2c89d683e29 100644 (file)
--- a/math/auto-libm-test-out-acosh
+++ b/math/auto-libm-test-out-acosh
@@ -1967,6 +1967,144 @@ acosh 0x1.0800751d9facbp+0
 = acosh tonearest ibm128 0x1.0800751d9facbp+0 : 0x3.fd7723edbf377ffec0d3568a9dp-4 : inexact-ok
 = acosh towardzero ibm128 0x1.0800751d9facbp+0 : 0x3.fd7723edbf377ffec0d3568a9cp-4 : inexact-ok
 = acosh upward ibm128 0x1.0800751d9facbp+0 : 0x3.fd7723edbf377ffec0d3568a9dp-4 : inexact-ok
+acosh 0x1.08000c1e79fp+0
+= acosh downward binary32 0x1.08000ep+0 : 0x3.fd5d8cp-4 : inexact-ok
+= acosh tonearest binary32 0x1.08000ep+0 : 0x3.fd5d9p-4 : inexact-ok
+= acosh towardzero binary32 0x1.08000ep+0 : 0x3.fd5d8cp-4 : inexact-ok
+= acosh upward binary32 0x1.08000ep+0 : 0x3.fd5d9p-4 : inexact-ok
+= acosh downward binary64 0x1.08000ep+0 : 0x3.fd5d8fe65d2c4p-4 : inexact-ok
+= acosh tonearest binary64 0x1.08000ep+0 : 0x3.fd5d8fe65d2c4p-4 : inexact-ok
+= acosh towardzero binary64 0x1.08000ep+0 : 0x3.fd5d8fe65d2c4p-4 : inexact-ok
+= acosh upward binary64 0x1.08000ep+0 : 0x3.fd5d8fe65d2c6p-4 : inexact-ok
+= acosh downward intel96 0x1.08000ep+0 : 0x3.fd5d8fe65d2c4628p-4 : inexact-ok
+= acosh tonearest intel96 0x1.08000ep+0 : 0x3.fd5d8fe65d2c462cp-4 : inexact-ok
+= acosh towardzero intel96 0x1.08000ep+0 : 0x3.fd5d8fe65d2c4628p-4 : inexact-ok
+= acosh upward intel96 0x1.08000ep+0 : 0x3.fd5d8fe65d2c462cp-4 : inexact-ok
+= acosh downward m68k96 0x1.08000ep+0 : 0x3.fd5d8fe65d2c4628p-4 : inexact-ok
+= acosh tonearest m68k96 0x1.08000ep+0 : 0x3.fd5d8fe65d2c462cp-4 : inexact-ok
+= acosh towardzero m68k96 0x1.08000ep+0 : 0x3.fd5d8fe65d2c4628p-4 : inexact-ok
+= acosh upward m68k96 0x1.08000ep+0 : 0x3.fd5d8fe65d2c462cp-4 : inexact-ok
+= acosh downward binary128 0x1.08000ep+0 : 0x3.fd5d8fe65d2c462b828356278c7ap-4 : inexact-ok
+= acosh tonearest binary128 0x1.08000ep+0 : 0x3.fd5d8fe65d2c462b828356278c7cp-4 : inexact-ok
+= acosh towardzero binary128 0x1.08000ep+0 : 0x3.fd5d8fe65d2c462b828356278c7ap-4 : inexact-ok
+= acosh upward binary128 0x1.08000ep+0 : 0x3.fd5d8fe65d2c462b828356278c7cp-4 : inexact-ok
+= acosh downward ibm128 0x1.08000ep+0 : 0x3.fd5d8fe65d2c462b828356278cp-4 : inexact-ok
+= acosh tonearest ibm128 0x1.08000ep+0 : 0x3.fd5d8fe65d2c462b828356278cp-4 : inexact-ok
+= acosh towardzero ibm128 0x1.08000ep+0 : 0x3.fd5d8fe65d2c462b828356278cp-4 : inexact-ok
+= acosh upward ibm128 0x1.08000ep+0 : 0x3.fd5d8fe65d2c462b828356278dp-4 : inexact-ok
+= acosh downward binary32 0x1.08000cp+0 : 0x3.fd5d1p-4 : inexact-ok
+= acosh tonearest binary32 0x1.08000cp+0 : 0x3.fd5d1p-4 : inexact-ok
+= acosh towardzero binary32 0x1.08000cp+0 : 0x3.fd5d1p-4 : inexact-ok
+= acosh upward binary32 0x1.08000cp+0 : 0x3.fd5d14p-4 : inexact-ok
+= acosh downward binary64 0x1.08000cp+0 : 0x3.fd5d10e3cfd2p-4 : inexact-ok
+= acosh tonearest binary64 0x1.08000cp+0 : 0x3.fd5d10e3cfd22p-4 : inexact-ok
+= acosh towardzero binary64 0x1.08000cp+0 : 0x3.fd5d10e3cfd2p-4 : inexact-ok
+= acosh upward binary64 0x1.08000cp+0 : 0x3.fd5d10e3cfd22p-4 : inexact-ok
+= acosh downward intel96 0x1.08000cp+0 : 0x3.fd5d10e3cfd21ae8p-4 : inexact-ok
+= acosh tonearest intel96 0x1.08000cp+0 : 0x3.fd5d10e3cfd21ae8p-4 : inexact-ok
+= acosh towardzero intel96 0x1.08000cp+0 : 0x3.fd5d10e3cfd21ae8p-4 : inexact-ok
+= acosh upward intel96 0x1.08000cp+0 : 0x3.fd5d10e3cfd21aecp-4 : inexact-ok
+= acosh downward m68k96 0x1.08000cp+0 : 0x3.fd5d10e3cfd21ae8p-4 : inexact-ok
+= acosh tonearest m68k96 0x1.08000cp+0 : 0x3.fd5d10e3cfd21ae8p-4 : inexact-ok
+= acosh towardzero m68k96 0x1.08000cp+0 : 0x3.fd5d10e3cfd21ae8p-4 : inexact-ok
+= acosh upward m68k96 0x1.08000cp+0 : 0x3.fd5d10e3cfd21aecp-4 : inexact-ok
+= acosh downward binary128 0x1.08000cp+0 : 0x3.fd5d10e3cfd21ae9cf9594e2ce42p-4 : inexact-ok
+= acosh tonearest binary128 0x1.08000cp+0 : 0x3.fd5d10e3cfd21ae9cf9594e2ce42p-4 : inexact-ok
+= acosh towardzero binary128 0x1.08000cp+0 : 0x3.fd5d10e3cfd21ae9cf9594e2ce42p-4 : inexact-ok
+= acosh upward binary128 0x1.08000cp+0 : 0x3.fd5d10e3cfd21ae9cf9594e2ce44p-4 : inexact-ok
+= acosh downward ibm128 0x1.08000cp+0 : 0x3.fd5d10e3cfd21ae9cf9594e2cep-4 : inexact-ok
+= acosh tonearest ibm128 0x1.08000cp+0 : 0x3.fd5d10e3cfd21ae9cf9594e2cep-4 : inexact-ok
+= acosh towardzero ibm128 0x1.08000cp+0 : 0x3.fd5d10e3cfd21ae9cf9594e2cep-4 : inexact-ok
+= acosh upward ibm128 0x1.08000cp+0 : 0x3.fd5d10e3cfd21ae9cf9594e2cfp-4 : inexact-ok
+= acosh downward binary64 0x1.08000c1e79fp+0 : 0x3.fd5d187336316p-4 : inexact-ok
+= acosh tonearest binary64 0x1.08000c1e79fp+0 : 0x3.fd5d187336318p-4 : inexact-ok
+= acosh towardzero binary64 0x1.08000c1e79fp+0 : 0x3.fd5d187336316p-4 : inexact-ok
+= acosh upward binary64 0x1.08000c1e79fp+0 : 0x3.fd5d187336318p-4 : inexact-ok
+= acosh downward intel96 0x1.08000c1e79fp+0 : 0x3.fd5d187336317ffcp-4 : inexact-ok
+= acosh tonearest intel96 0x1.08000c1e79fp+0 : 0x3.fd5d187336318p-4 : inexact-ok
+= acosh towardzero intel96 0x1.08000c1e79fp+0 : 0x3.fd5d187336317ffcp-4 : inexact-ok
+= acosh upward intel96 0x1.08000c1e79fp+0 : 0x3.fd5d187336318p-4 : inexact-ok
+= acosh downward m68k96 0x1.08000c1e79fp+0 : 0x3.fd5d187336317ffcp-4 : inexact-ok
+= acosh tonearest m68k96 0x1.08000c1e79fp+0 : 0x3.fd5d187336318p-4 : inexact-ok
+= acosh towardzero m68k96 0x1.08000c1e79fp+0 : 0x3.fd5d187336317ffcp-4 : inexact-ok
+= acosh upward m68k96 0x1.08000c1e79fp+0 : 0x3.fd5d187336318p-4 : inexact-ok
+= acosh downward binary128 0x1.08000c1e79fp+0 : 0x3.fd5d187336317ffe277a90ecfa02p-4 : inexact-ok
+= acosh tonearest binary128 0x1.08000c1e79fp+0 : 0x3.fd5d187336317ffe277a90ecfa04p-4 : inexact-ok
+= acosh towardzero binary128 0x1.08000c1e79fp+0 : 0x3.fd5d187336317ffe277a90ecfa02p-4 : inexact-ok
+= acosh upward binary128 0x1.08000c1e79fp+0 : 0x3.fd5d187336317ffe277a90ecfa04p-4 : inexact-ok
+= acosh downward ibm128 0x1.08000c1e79fp+0 : 0x3.fd5d187336317ffe277a90ecfap-4 : inexact-ok
+= acosh tonearest ibm128 0x1.08000c1e79fp+0 : 0x3.fd5d187336317ffe277a90ecfap-4 : inexact-ok
+= acosh towardzero ibm128 0x1.08000c1e79fp+0 : 0x3.fd5d187336317ffe277a90ecfap-4 : inexact-ok
+= acosh upward ibm128 0x1.08000c1e79fp+0 : 0x3.fd5d187336317ffe277a90ecfbp-4 : inexact-ok
+acosh 0x1.080016353964ep+0
+= acosh downward binary32 0x1.080018p+0 : 0x3.fd6008p-4 : inexact-ok
+= acosh tonearest binary32 0x1.080018p+0 : 0x3.fd600cp-4 : inexact-ok
+= acosh towardzero binary32 0x1.080018p+0 : 0x3.fd6008p-4 : inexact-ok
+= acosh upward binary32 0x1.080018p+0 : 0x3.fd600cp-4 : inexact-ok
+= acosh downward binary64 0x1.080018p+0 : 0x3.fd600af22e228p-4 : inexact-ok
+= acosh tonearest binary64 0x1.080018p+0 : 0x3.fd600af22e22ap-4 : inexact-ok
+= acosh towardzero binary64 0x1.080018p+0 : 0x3.fd600af22e228p-4 : inexact-ok
+= acosh upward binary64 0x1.080018p+0 : 0x3.fd600af22e22ap-4 : inexact-ok
+= acosh downward intel96 0x1.080018p+0 : 0x3.fd600af22e22927p-4 : inexact-ok
+= acosh tonearest intel96 0x1.080018p+0 : 0x3.fd600af22e229274p-4 : inexact-ok
+= acosh towardzero intel96 0x1.080018p+0 : 0x3.fd600af22e22927p-4 : inexact-ok
+= acosh upward intel96 0x1.080018p+0 : 0x3.fd600af22e229274p-4 : inexact-ok
+= acosh downward m68k96 0x1.080018p+0 : 0x3.fd600af22e22927p-4 : inexact-ok
+= acosh tonearest m68k96 0x1.080018p+0 : 0x3.fd600af22e229274p-4 : inexact-ok
+= acosh towardzero m68k96 0x1.080018p+0 : 0x3.fd600af22e22927p-4 : inexact-ok
+= acosh upward m68k96 0x1.080018p+0 : 0x3.fd600af22e229274p-4 : inexact-ok
+= acosh downward binary128 0x1.080018p+0 : 0x3.fd600af22e229273dafef597f80cp-4 : inexact-ok
+= acosh tonearest binary128 0x1.080018p+0 : 0x3.fd600af22e229273dafef597f80ep-4 : inexact-ok
+= acosh towardzero binary128 0x1.080018p+0 : 0x3.fd600af22e229273dafef597f80cp-4 : inexact-ok
+= acosh upward binary128 0x1.080018p+0 : 0x3.fd600af22e229273dafef597f80ep-4 : inexact-ok
+= acosh downward ibm128 0x1.080018p+0 : 0x3.fd600af22e229273dafef597f8p-4 : inexact-ok
+= acosh tonearest ibm128 0x1.080018p+0 : 0x3.fd600af22e229273dafef597f8p-4 : inexact-ok
+= acosh towardzero ibm128 0x1.080018p+0 : 0x3.fd600af22e229273dafef597f8p-4 : inexact-ok
+= acosh upward ibm128 0x1.080018p+0 : 0x3.fd600af22e229273dafef597f9p-4 : inexact-ok
+= acosh downward binary32 0x1.080016p+0 : 0x3.fd5f88p-4 : inexact-ok
+= acosh tonearest binary32 0x1.080016p+0 : 0x3.fd5f8cp-4 : inexact-ok
+= acosh towardzero binary32 0x1.080016p+0 : 0x3.fd5f88p-4 : inexact-ok
+= acosh upward binary32 0x1.080016p+0 : 0x3.fd5f8cp-4 : inexact-ok
+= acosh downward binary64 0x1.080016p+0 : 0x3.fd5f8beff161cp-4 : inexact-ok
+= acosh tonearest binary64 0x1.080016p+0 : 0x3.fd5f8beff161ep-4 : inexact-ok
+= acosh towardzero binary64 0x1.080016p+0 : 0x3.fd5f8beff161cp-4 : inexact-ok
+= acosh upward binary64 0x1.080016p+0 : 0x3.fd5f8beff161ep-4 : inexact-ok
+= acosh downward intel96 0x1.080016p+0 : 0x3.fd5f8beff161d724p-4 : inexact-ok
+= acosh tonearest intel96 0x1.080016p+0 : 0x3.fd5f8beff161d724p-4 : inexact-ok
+= acosh towardzero intel96 0x1.080016p+0 : 0x3.fd5f8beff161d724p-4 : inexact-ok
+= acosh upward intel96 0x1.080016p+0 : 0x3.fd5f8beff161d728p-4 : inexact-ok
+= acosh downward m68k96 0x1.080016p+0 : 0x3.fd5f8beff161d724p-4 : inexact-ok
+= acosh tonearest m68k96 0x1.080016p+0 : 0x3.fd5f8beff161d724p-4 : inexact-ok
+= acosh towardzero m68k96 0x1.080016p+0 : 0x3.fd5f8beff161d724p-4 : inexact-ok
+= acosh upward m68k96 0x1.080016p+0 : 0x3.fd5f8beff161d728p-4 : inexact-ok
+= acosh downward binary128 0x1.080016p+0 : 0x3.fd5f8beff161d724dfb1d4b47f1ep-4 : inexact-ok
+= acosh tonearest binary128 0x1.080016p+0 : 0x3.fd5f8beff161d724dfb1d4b47f2p-4 : inexact-ok
+= acosh towardzero binary128 0x1.080016p+0 : 0x3.fd5f8beff161d724dfb1d4b47f1ep-4 : inexact-ok
+= acosh upward binary128 0x1.080016p+0 : 0x3.fd5f8beff161d724dfb1d4b47f2p-4 : inexact-ok
+= acosh downward ibm128 0x1.080016p+0 : 0x3.fd5f8beff161d724dfb1d4b47fp-4 : inexact-ok
+= acosh tonearest ibm128 0x1.080016p+0 : 0x3.fd5f8beff161d724dfb1d4b47fp-4 : inexact-ok
+= acosh towardzero ibm128 0x1.080016p+0 : 0x3.fd5f8beff161d724dfb1d4b47fp-4 : inexact-ok
+= acosh upward ibm128 0x1.080016p+0 : 0x3.fd5f8beff161d724dfb1d4b48p-4 : inexact-ok
+= acosh downward binary64 0x1.080016353964ep+0 : 0x3.fd5f9923ea31ap-4 : inexact-ok
+= acosh tonearest binary64 0x1.080016353964ep+0 : 0x3.fd5f9923ea31cp-4 : inexact-ok
+= acosh towardzero binary64 0x1.080016353964ep+0 : 0x3.fd5f9923ea31ap-4 : inexact-ok
+= acosh upward binary64 0x1.080016353964ep+0 : 0x3.fd5f9923ea31cp-4 : inexact-ok
+= acosh downward intel96 0x1.080016353964ep+0 : 0x3.fd5f9923ea31bffcp-4 : inexact-ok
+= acosh tonearest intel96 0x1.080016353964ep+0 : 0x3.fd5f9923ea31cp-4 : inexact-ok
+= acosh towardzero intel96 0x1.080016353964ep+0 : 0x3.fd5f9923ea31bffcp-4 : inexact-ok
+= acosh upward intel96 0x1.080016353964ep+0 : 0x3.fd5f9923ea31cp-4 : inexact-ok
+= acosh downward m68k96 0x1.080016353964ep+0 : 0x3.fd5f9923ea31bffcp-4 : inexact-ok
+= acosh tonearest m68k96 0x1.080016353964ep+0 : 0x3.fd5f9923ea31cp-4 : inexact-ok
+= acosh towardzero m68k96 0x1.080016353964ep+0 : 0x3.fd5f9923ea31bffcp-4 : inexact-ok
+= acosh upward m68k96 0x1.080016353964ep+0 : 0x3.fd5f9923ea31cp-4 : inexact-ok
+= acosh downward binary128 0x1.080016353964ep+0 : 0x3.fd5f9923ea31bfffb58257240266p-4 : inexact-ok
+= acosh tonearest binary128 0x1.080016353964ep+0 : 0x3.fd5f9923ea31bfffb58257240266p-4 : inexact-ok
+= acosh towardzero binary128 0x1.080016353964ep+0 : 0x3.fd5f9923ea31bfffb58257240266p-4 : inexact-ok
+= acosh upward binary128 0x1.080016353964ep+0 : 0x3.fd5f9923ea31bfffb58257240268p-4 : inexact-ok
+= acosh downward ibm128 0x1.080016353964ep+0 : 0x3.fd5f9923ea31bfffb582572402p-4 : inexact-ok
+= acosh tonearest ibm128 0x1.080016353964ep+0 : 0x3.fd5f9923ea31bfffb582572402p-4 : inexact-ok
+= acosh towardzero ibm128 0x1.080016353964ep+0 : 0x3.fd5f9923ea31bfffb582572402p-4 : inexact-ok
+= acosh upward ibm128 0x1.080016353964ep+0 : 0x3.fd5f9923ea31bfffb582572403p-4 : inexact-ok
 acosh 0x1.1ecbdf374bce01cap+0
 = acosh downward binary32 0x1.1ecbep+0 : 0x7.c5802p-4 : inexact-ok
 = acosh tonearest binary32 0x1.1ecbep+0 : 0x7.c5802p-4 : inexact-ok

diff --git a/sysdeps/ieee754/dbl-64/e_acosh.c b/sysdeps/ieee754/dbl-64/e_acosh.c
index 2e3f4235bdecb9ff01a7906d0f5c67638d36e193..7354d8c1041dbfae179ffadd247c8221551cc832 100644 (file)
--- a/sysdeps/ieee754/dbl-64/e_acosh.c
+++ b/sysdeps/ieee754/dbl-64/e_acosh.c
@@ -4,7 +4,7 @@
 Copyright (c) 2023-2025 Alexei Sibidanov.
 
 The original version of this file was copied from the CORE-MATH
-project (file src/binary64/acosh/acosh.c, revision 69062c4d).
+project (file src/binary64/acosh/acosh.c, revision 6736002f).
 
 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal
@@ -112,15 +112,16 @@ __ieee754_acosh (double x)
        -0x1.c9045534e6d9ep-14, 0x1.71fedae26a76bp-15,  -0x1.f1f4f8cc65342p-17
       };
       double z2 = z * z, z4 = z2 * z2,
-            ds = (sh * z)
-                 * (cl[0]
+            ds = fma (
+                sh * z,
+                cl[0]
                     + z
                           * (((cl[1] + z * cl[2]) + z2 * (cl[3] + z * cl[4]))
                              + z4
                                    * ((cl[5] + z * cl[6])
-                                      + z2 * (cl[7] + z * cl[8]))));
-      double eps = ds * 0x1.22p-50 - 0x1p-104 * sh;
-      ds += sl;
+                                      + z2 * (cl[7] + z * cl[8]))),
+                sl);
+      double eps = ds * 0x1.fcp-51 - 0x1p-104 * sh;
       double lb = sh + (ds - eps), ub = sh + (ds + eps);
       if (lb == ub)
        return lb;