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math: Use cosh from CORE-MATH 

The current implementation precision shows the following accuracy, on
three ranges ([-DBL_MAX,-10], [-10,10], [10,DBL_MAX]) with 10e9 uniform
randomly generated numbers for each range (first column is the
accuracy in ULP, with '0' being correctly rounded, second is the
number of samples with the corresponding precision):

* Range [-DBL_MAX, -10]
 * FE_TONEAREST
     0:      10000000000 100.00%
 * FE_UPWARD
     0:      10000000000 100.00%
 * FE_DOWNWARD
     0:      10000000000 100.00%
 * FE_TOWARDZERO
     0:      10000000000 100.00%

* Range [-10, -10]
 * FE_TONEAREST
     0:       3291614060  76.64%
     1:       1003353235  23.36%
 * FE_UPWARD
     0:       2295272497  53.44%
     1:       1999675198  46.56%
     2:            19600   0.00%
 * FE_DOWNWARD
     0:       2294966533  53.43%
     1:       1999981461  46.57%
     2:            19301   0.00%
 * FE_TOWARDZERO
     0:       2306015780  53.69%
     1:       1988942093  46.31%
     2:             9422   0.00%

* Range [10, DBL_MAX]
 * FE_TONEAREST
     0:      10000000000 100.00%
 * FE_UPWARD
     0:      10000000000 100.00%
 * FE_DOWNWARD
     0:      10000000000 100.00%
 * FE_TOWARDZERO
     0:      10000000000 100.00%

The CORE-MATH implementation is correctly rounded for any rounding mode.
The code was adapted to glibc style and to use the definition of
math_config.h (to handle errno, overflow, and underflow).

Performance-wise, it shows:

latency                      master        patched     improvement
x86_64                      52.1066       126.4120        -142.60%
x86_64v2                    49.5781       119.8520        -141.74%
x86_64v3                    45.0811        50.5758         -12.19%
aarch64                     19.9977        21.7814          -8.92%
armhf-vpfv4                 20.5969        27.0479         -31.32%
powerpc64le                 12.6405        13.6768          -8.20%

reciprocal-throughput        master        patched     improvement
x86_64                      18.4833        102.9120       -456.78%
x86_64v2                    17.5409        99.5179        -467.35%
x86_64v3                    18.9187        25.3662         -34.08%
aarch64                     10.9045        18.8217         -72.60%
armhf-vpfv4                 15.7430        24.0822         -52.97%
powerpc64le                  5.4275         8.1269         -49.73%

* x86_64:        gcc version 15.2.1 20260112, Ryzen 9 5900X, --disable-multi-arch
* aarch64:       gcc version 15.2.1 20251105, Neoverse-N1
* armv7a-vpfv4:  gcc version 15.2.1 20251105, Neoverse-N1
* powerpc64le:   gcc version 15.2.1 20260128, POWER10

Checked on x86_64-linux-gnu, aarch64-linux-gnu, and
powerpc64le-linux-gnu.

Reviewed-by: DJ Delorie <dj@redhat.com>
This commit is contained in:
Adhemerval Zanella 2026-03-12 11:21:05 -03:00
parent e0e34185e5
commit 291fc87155
8 changed files with 1388 additions and 67 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

3
NEWS
View File

@ -9,7 +9,8 @@ Version 2.44
Major new features:
[Add new features here]
* Additional optimized and correctly rounded mathematical functions have
been imported from the CORE-MATH project, in particular cosh.
Deprecated and removed features, and other changes affecting compatibility:

2
SHARED-FILES
View File

@ -248,6 +248,8 @@ core-math:
sysdeps/ieee754/dbl-64/e_acosh.c
# src/binary64/atanh/atanh.c, revision 532e37dc
sysdeps/ieee754/dbl-64/e_atanh.c
# src/binary64/cosh/cosh.c, revision 5d0c89d5
sysdeps/ieee754/dbl-64/e_cosh.c
# src/binary64/tgamma/tgamma.c, revision 0f185e23
sysdeps/ieee754/dbl-64/e_gamma_r.c
# src/binary64/lgamma/lgamma.c, revision 0413bb7e

14
math/auto-libm-test-in
View File

@ -5213,6 +5213,20 @@ cosh 0x1.633c457f1e66bp+9
cosh 0x2.c5d376167f4052f4p+12
# the next value generates larger error bounds on x86_64 (binary128)
cosh -0x2.c5d376eefcd4bbeb000452d84662p+12
# CORE-MATH extra tests
cosh 0x1.41fe58c623761p+2
cosh 0x1.424ed1d05dfa7p+2
cosh 0x1.41a83b901d5bdp+2
cosh 0x1.40d5c37ff8185p+2
cosh -0x1.419a5f3fa359p+2
cosh 0x1.426a50e51bd1ep+2
cosh -0x1.64c53499192bfp+2
cosh 0x1.41fe58c623761p+2
cosh 0x1.424ed1d05dfa7p+2
cosh 0x1.41a83b901d5bdp+2
cosh 0x1.40d5c37ff8185p+2
cosh 0x1.426a50e51bd1ep+2
cosh -0x1.41311766f07f6p+2
cpow 1 0 0 0 ignore-zero-inf-sign
cpow 2 0 10 0 ignore-zero-inf-sign

897
math/auto-libm-test-out-cosh
View File

@ -3725,3 +3725,900 @@ cosh -0x2.c5d376eefcd4bbeb000452d84662p+12
= cosh tonearest ibm128 -0x2.c5d376eefcd4bbeb000452d847p+12 : plus_infty : inexact-ok overflow errno-erange
= cosh towardzero ibm128 -0x2.c5d376eefcd4bbeb000452d847p+12 : 0xf.ffffffffffffbffffffffffffcp+1020 : xfail:ibm128-libgcc inexact-ok overflow errno-erange-ok
= cosh upward ibm128 -0x2.c5d376eefcd4bbeb000452d847p+12 : plus_infty : xfail:ibm128-libgcc inexact-ok overflow errno-erange
cosh 0x1.41fe58c623761p+2
= cosh downward binary32 0x5.07f968p+0 : 0x4.c8ec6p+4 : inexact-ok
= cosh tonearest binary32 0x5.07f968p+0 : 0x4.c8ec6p+4 : inexact-ok
= cosh towardzero binary32 0x5.07f968p+0 : 0x4.c8ec6p+4 : inexact-ok
= cosh upward binary32 0x5.07f968p+0 : 0x4.c8ec68p+4 : inexact-ok
= cosh downward binary64 0x5.07f968p+0 : 0x4.c8ec639696b94p+4 : inexact-ok
= cosh tonearest binary64 0x5.07f968p+0 : 0x4.c8ec639696b98p+4 : inexact-ok
= cosh towardzero binary64 0x5.07f968p+0 : 0x4.c8ec639696b94p+4 : inexact-ok
= cosh upward binary64 0x5.07f968p+0 : 0x4.c8ec639696b98p+4 : inexact-ok
= cosh downward intel96 0x5.07f968p+0 : 0x4.c8ec639696b9734p+4 : inexact-ok
= cosh tonearest intel96 0x5.07f968p+0 : 0x4.c8ec639696b9734p+4 : inexact-ok
= cosh towardzero intel96 0x5.07f968p+0 : 0x4.c8ec639696b9734p+4 : inexact-ok
= cosh upward intel96 0x5.07f968p+0 : 0x4.c8ec639696b97348p+4 : inexact-ok
= cosh downward m68k96 0x5.07f968p+0 : 0x4.c8ec639696b9734p+4 : inexact-ok
= cosh tonearest m68k96 0x5.07f968p+0 : 0x4.c8ec639696b9734p+4 : inexact-ok
= cosh towardzero m68k96 0x5.07f968p+0 : 0x4.c8ec639696b9734p+4 : inexact-ok
= cosh upward m68k96 0x5.07f968p+0 : 0x4.c8ec639696b97348p+4 : inexact-ok
= cosh downward binary128 0x5.07f968p+0 : 0x4.c8ec639696b9734351e5a3ba533cp+4 : inexact-ok
= cosh tonearest binary128 0x5.07f968p+0 : 0x4.c8ec639696b9734351e5a3ba534p+4 : inexact-ok
= cosh towardzero binary128 0x5.07f968p+0 : 0x4.c8ec639696b9734351e5a3ba533cp+4 : inexact-ok
= cosh upward binary128 0x5.07f968p+0 : 0x4.c8ec639696b9734351e5a3ba534p+4 : inexact-ok
= cosh downward ibm128 0x5.07f968p+0 : 0x4.c8ec639696b9734351e5a3ba52p+4 : inexact-ok
= cosh tonearest ibm128 0x5.07f968p+0 : 0x4.c8ec639696b9734351e5a3ba54p+4 : inexact-ok
= cosh towardzero ibm128 0x5.07f968p+0 : 0x4.c8ec639696b9734351e5a3ba52p+4 : inexact-ok
= cosh upward ibm128 0x5.07f968p+0 : 0x4.c8ec639696b9734351e5a3ba54p+4 : inexact-ok
= cosh downward binary32 0x5.07f96p+0 : 0x4.c8ec38p+4 : inexact-ok
= cosh tonearest binary32 0x5.07f96p+0 : 0x4.c8ec4p+4 : inexact-ok
= cosh towardzero binary32 0x5.07f96p+0 : 0x4.c8ec38p+4 : inexact-ok
= cosh upward binary32 0x5.07f96p+0 : 0x4.c8ec4p+4 : inexact-ok
= cosh downward binary64 0x5.07f96p+0 : 0x4.c8ec3d500a3a4p+4 : inexact-ok
= cosh tonearest binary64 0x5.07f96p+0 : 0x4.c8ec3d500a3a4p+4 : inexact-ok
= cosh towardzero binary64 0x5.07f96p+0 : 0x4.c8ec3d500a3a4p+4 : inexact-ok
= cosh upward binary64 0x5.07f96p+0 : 0x4.c8ec3d500a3a8p+4 : inexact-ok
= cosh downward intel96 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e7p+4 : inexact-ok
= cosh tonearest intel96 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e78p+4 : inexact-ok
= cosh towardzero intel96 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e7p+4 : inexact-ok
= cosh upward intel96 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e78p+4 : inexact-ok
= cosh downward m68k96 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e7p+4 : inexact-ok
= cosh tonearest m68k96 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e78p+4 : inexact-ok
= cosh towardzero m68k96 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e7p+4 : inexact-ok
= cosh upward m68k96 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e78p+4 : inexact-ok
= cosh downward binary128 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e75d427b3126be8p+4 : inexact-ok
= cosh tonearest binary128 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e75d427b3126becp+4 : inexact-ok
= cosh towardzero binary128 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e75d427b3126be8p+4 : inexact-ok
= cosh upward binary128 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e75d427b3126becp+4 : inexact-ok
= cosh downward ibm128 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e75d427b3126ap+4 : inexact-ok
= cosh tonearest ibm128 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e75d427b3126cp+4 : inexact-ok
= cosh towardzero ibm128 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e75d427b3126ap+4 : inexact-ok
= cosh upward ibm128 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e75d427b3126cp+4 : inexact-ok
= cosh downward binary64 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh tonearest binary64 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh towardzero binary64 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh upward binary64 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9118p+4 : inexact-ok
= cosh downward intel96 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh tonearest intel96 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh towardzero intel96 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh upward intel96 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114008p+4 : inexact-ok
= cosh downward m68k96 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh tonearest m68k96 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh towardzero m68k96 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh upward m68k96 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114008p+4 : inexact-ok
= cosh downward binary128 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff91140001f93e1971e5cp+4 : inexact-ok
= cosh tonearest binary128 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff91140001f93e1971e6p+4 : inexact-ok
= cosh towardzero binary128 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff91140001f93e1971e5cp+4 : inexact-ok
= cosh upward binary128 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff91140001f93e1971e6p+4 : inexact-ok
= cosh downward ibm128 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff91140001f93e1971ep+4 : inexact-ok
= cosh tonearest ibm128 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff91140001f93e1971ep+4 : inexact-ok
= cosh towardzero ibm128 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff91140001f93e1971ep+4 : inexact-ok
= cosh upward ibm128 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff91140001f93e1972p+4 : inexact-ok
cosh 0x1.424ed1d05dfa7p+2
= cosh downward binary32 0x5.093b48p+0 : 0x4.cef428p+4 : inexact-ok
= cosh tonearest binary32 0x5.093b48p+0 : 0x4.cef428p+4 : inexact-ok
= cosh towardzero binary32 0x5.093b48p+0 : 0x4.cef428p+4 : inexact-ok
= cosh upward binary32 0x5.093b48p+0 : 0x4.cef43p+4 : inexact-ok
= cosh downward binary64 0x5.093b48p+0 : 0x4.cef42bf9b1e84p+4 : inexact-ok
= cosh tonearest binary64 0x5.093b48p+0 : 0x4.cef42bf9b1e84p+4 : inexact-ok
= cosh towardzero binary64 0x5.093b48p+0 : 0x4.cef42bf9b1e84p+4 : inexact-ok
= cosh upward binary64 0x5.093b48p+0 : 0x4.cef42bf9b1e88p+4 : inexact-ok
= cosh downward intel96 0x5.093b48p+0 : 0x4.cef42bf9b1e857c8p+4 : inexact-ok
= cosh tonearest intel96 0x5.093b48p+0 : 0x4.cef42bf9b1e857dp+4 : inexact-ok
= cosh towardzero intel96 0x5.093b48p+0 : 0x4.cef42bf9b1e857c8p+4 : inexact-ok
= cosh upward intel96 0x5.093b48p+0 : 0x4.cef42bf9b1e857dp+4 : inexact-ok
= cosh downward m68k96 0x5.093b48p+0 : 0x4.cef42bf9b1e857c8p+4 : inexact-ok
= cosh tonearest m68k96 0x5.093b48p+0 : 0x4.cef42bf9b1e857dp+4 : inexact-ok
= cosh towardzero m68k96 0x5.093b48p+0 : 0x4.cef42bf9b1e857c8p+4 : inexact-ok
= cosh upward m68k96 0x5.093b48p+0 : 0x4.cef42bf9b1e857dp+4 : inexact-ok
= cosh downward binary128 0x5.093b48p+0 : 0x4.cef42bf9b1e857cddb3ba37b563p+4 : inexact-ok
= cosh tonearest binary128 0x5.093b48p+0 : 0x4.cef42bf9b1e857cddb3ba37b5634p+4 : inexact-ok
= cosh towardzero binary128 0x5.093b48p+0 : 0x4.cef42bf9b1e857cddb3ba37b563p+4 : inexact-ok
= cosh upward binary128 0x5.093b48p+0 : 0x4.cef42bf9b1e857cddb3ba37b5634p+4 : inexact-ok
= cosh downward ibm128 0x5.093b48p+0 : 0x4.cef42bf9b1e857cddb3ba37b56p+4 : inexact-ok
= cosh tonearest ibm128 0x5.093b48p+0 : 0x4.cef42bf9b1e857cddb3ba37b56p+4 : inexact-ok
= cosh towardzero ibm128 0x5.093b48p+0 : 0x4.cef42bf9b1e857cddb3ba37b56p+4 : inexact-ok
= cosh upward ibm128 0x5.093b48p+0 : 0x4.cef42bf9b1e857cddb3ba37b58p+4 : inexact-ok
= cosh downward binary32 0x5.093b4p+0 : 0x4.cef4p+4 : inexact-ok
= cosh tonearest binary32 0x5.093b4p+0 : 0x4.cef408p+4 : inexact-ok
= cosh towardzero binary32 0x5.093b4p+0 : 0x4.cef4p+4 : inexact-ok
= cosh upward binary32 0x5.093b4p+0 : 0x4.cef408p+4 : inexact-ok
= cosh downward binary64 0x5.093b4p+0 : 0x4.cef40582e61a4p+4 : inexact-ok
= cosh tonearest binary64 0x5.093b4p+0 : 0x4.cef40582e61a8p+4 : inexact-ok
= cosh towardzero binary64 0x5.093b4p+0 : 0x4.cef40582e61a4p+4 : inexact-ok
= cosh upward binary64 0x5.093b4p+0 : 0x4.cef40582e61a8p+4 : inexact-ok
= cosh downward intel96 0x5.093b4p+0 : 0x4.cef40582e61a7d18p+4 : inexact-ok
= cosh tonearest intel96 0x5.093b4p+0 : 0x4.cef40582e61a7d18p+4 : inexact-ok
= cosh towardzero intel96 0x5.093b4p+0 : 0x4.cef40582e61a7d18p+4 : inexact-ok
= cosh upward intel96 0x5.093b4p+0 : 0x4.cef40582e61a7d2p+4 : inexact-ok
= cosh downward m68k96 0x5.093b4p+0 : 0x4.cef40582e61a7d18p+4 : inexact-ok
= cosh tonearest m68k96 0x5.093b4p+0 : 0x4.cef40582e61a7d18p+4 : inexact-ok
= cosh towardzero m68k96 0x5.093b4p+0 : 0x4.cef40582e61a7d18p+4 : inexact-ok
= cosh upward m68k96 0x5.093b4p+0 : 0x4.cef40582e61a7d2p+4 : inexact-ok
= cosh downward binary128 0x5.093b4p+0 : 0x4.cef40582e61a7d185037ecafd3f8p+4 : inexact-ok
= cosh tonearest binary128 0x5.093b4p+0 : 0x4.cef40582e61a7d185037ecafd3fcp+4 : inexact-ok
= cosh towardzero binary128 0x5.093b4p+0 : 0x4.cef40582e61a7d185037ecafd3f8p+4 : inexact-ok
= cosh upward binary128 0x5.093b4p+0 : 0x4.cef40582e61a7d185037ecafd3fcp+4 : inexact-ok
= cosh downward ibm128 0x5.093b4p+0 : 0x4.cef40582e61a7d185037ecafd2p+4 : inexact-ok
= cosh tonearest ibm128 0x5.093b4p+0 : 0x4.cef40582e61a7d185037ecafd4p+4 : inexact-ok
= cosh towardzero ibm128 0x5.093b4p+0 : 0x4.cef40582e61a7d185037ecafd2p+4 : inexact-ok
= cosh upward ibm128 0x5.093b4p+0 : 0x4.cef40582e61a7d185037ecafd4p+4 : inexact-ok
= cosh downward binary64 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh tonearest binary64 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh towardzero binary64 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh upward binary64 0x5.093b474177e9cp+0 : 0x4.cef428659e24cp+4 : inexact-ok
= cosh downward intel96 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh tonearest intel96 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh towardzero intel96 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh upward intel96 0x5.093b474177e9cp+0 : 0x4.cef428659e248008p+4 : inexact-ok
= cosh downward m68k96 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh tonearest m68k96 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh towardzero m68k96 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh upward m68k96 0x5.093b474177e9cp+0 : 0x4.cef428659e248008p+4 : inexact-ok
= cosh downward binary128 0x5.093b474177e9cp+0 : 0x4.cef428659e2480012c38267523ep+4 : inexact-ok
= cosh tonearest binary128 0x5.093b474177e9cp+0 : 0x4.cef428659e2480012c38267523e4p+4 : inexact-ok
= cosh towardzero binary128 0x5.093b474177e9cp+0 : 0x4.cef428659e2480012c38267523ep+4 : inexact-ok
= cosh upward binary128 0x5.093b474177e9cp+0 : 0x4.cef428659e2480012c38267523e4p+4 : inexact-ok
= cosh downward ibm128 0x5.093b474177e9cp+0 : 0x4.cef428659e2480012c38267522p+4 : inexact-ok
= cosh tonearest ibm128 0x5.093b474177e9cp+0 : 0x4.cef428659e2480012c38267524p+4 : inexact-ok
= cosh towardzero ibm128 0x5.093b474177e9cp+0 : 0x4.cef428659e2480012c38267522p+4 : inexact-ok
= cosh upward ibm128 0x5.093b474177e9cp+0 : 0x4.cef428659e2480012c38267524p+4 : inexact-ok
cosh 0x1.41a83b901d5bdp+2
= cosh downward binary32 0x5.06a0fp+0 : 0x4.c28098p+4 : inexact-ok
= cosh tonearest binary32 0x5.06a0fp+0 : 0x4.c280ap+4 : inexact-ok
= cosh towardzero binary32 0x5.06a0fp+0 : 0x4.c28098p+4 : inexact-ok
= cosh upward binary32 0x5.06a0fp+0 : 0x4.c280ap+4 : inexact-ok
= cosh downward binary64 0x5.06a0fp+0 : 0x4.c2809ebb13c34p+4 : inexact-ok
= cosh tonearest binary64 0x5.06a0fp+0 : 0x4.c2809ebb13c38p+4 : inexact-ok
= cosh towardzero binary64 0x5.06a0fp+0 : 0x4.c2809ebb13c34p+4 : inexact-ok
= cosh upward binary64 0x5.06a0fp+0 : 0x4.c2809ebb13c38p+4 : inexact-ok
= cosh downward intel96 0x5.06a0fp+0 : 0x4.c2809ebb13c362ep+4 : inexact-ok
= cosh tonearest intel96 0x5.06a0fp+0 : 0x4.c2809ebb13c362ep+4 : inexact-ok
= cosh towardzero intel96 0x5.06a0fp+0 : 0x4.c2809ebb13c362ep+4 : inexact-ok
= cosh upward intel96 0x5.06a0fp+0 : 0x4.c2809ebb13c362e8p+4 : inexact-ok
= cosh downward m68k96 0x5.06a0fp+0 : 0x4.c2809ebb13c362ep+4 : inexact-ok
= cosh tonearest m68k96 0x5.06a0fp+0 : 0x4.c2809ebb13c362ep+4 : inexact-ok
= cosh towardzero m68k96 0x5.06a0fp+0 : 0x4.c2809ebb13c362ep+4 : inexact-ok
= cosh upward m68k96 0x5.06a0fp+0 : 0x4.c2809ebb13c362e8p+4 : inexact-ok
= cosh downward binary128 0x5.06a0fp+0 : 0x4.c2809ebb13c362e0e60f23b1bd4cp+4 : inexact-ok
= cosh tonearest binary128 0x5.06a0fp+0 : 0x4.c2809ebb13c362e0e60f23b1bd5p+4 : inexact-ok
= cosh towardzero binary128 0x5.06a0fp+0 : 0x4.c2809ebb13c362e0e60f23b1bd4cp+4 : inexact-ok
= cosh upward binary128 0x5.06a0fp+0 : 0x4.c2809ebb13c362e0e60f23b1bd5p+4 : inexact-ok
= cosh downward ibm128 0x5.06a0fp+0 : 0x4.c2809ebb13c362e0e60f23b1bcp+4 : inexact-ok
= cosh tonearest ibm128 0x5.06a0fp+0 : 0x4.c2809ebb13c362e0e60f23b1bep+4 : inexact-ok
= cosh towardzero ibm128 0x5.06a0fp+0 : 0x4.c2809ebb13c362e0e60f23b1bcp+4 : inexact-ok
= cosh upward ibm128 0x5.06a0fp+0 : 0x4.c2809ebb13c362e0e60f23b1bep+4 : inexact-ok
= cosh downward binary32 0x5.06a0e8p+0 : 0x4.c28078p+4 : inexact-ok
= cosh tonearest binary32 0x5.06a0e8p+0 : 0x4.c28078p+4 : inexact-ok
= cosh towardzero binary32 0x5.06a0e8p+0 : 0x4.c28078p+4 : inexact-ok
= cosh upward binary32 0x5.06a0e8p+0 : 0x4.c2808p+4 : inexact-ok
= cosh downward binary64 0x5.06a0e8p+0 : 0x4.c28078a7e68bp+4 : inexact-ok
= cosh tonearest binary64 0x5.06a0e8p+0 : 0x4.c28078a7e68bp+4 : inexact-ok
= cosh towardzero binary64 0x5.06a0e8p+0 : 0x4.c28078a7e68bp+4 : inexact-ok
= cosh upward binary64 0x5.06a0e8p+0 : 0x4.c28078a7e68b4p+4 : inexact-ok
= cosh downward intel96 0x5.06a0e8p+0 : 0x4.c28078a7e68b1928p+4 : inexact-ok
= cosh tonearest intel96 0x5.06a0e8p+0 : 0x4.c28078a7e68b1928p+4 : inexact-ok
= cosh towardzero intel96 0x5.06a0e8p+0 : 0x4.c28078a7e68b1928p+4 : inexact-ok
= cosh upward intel96 0x5.06a0e8p+0 : 0x4.c28078a7e68b193p+4 : inexact-ok
= cosh downward m68k96 0x5.06a0e8p+0 : 0x4.c28078a7e68b1928p+4 : inexact-ok
= cosh tonearest m68k96 0x5.06a0e8p+0 : 0x4.c28078a7e68b1928p+4 : inexact-ok
= cosh towardzero m68k96 0x5.06a0e8p+0 : 0x4.c28078a7e68b1928p+4 : inexact-ok
= cosh upward m68k96 0x5.06a0e8p+0 : 0x4.c28078a7e68b193p+4 : inexact-ok
= cosh downward binary128 0x5.06a0e8p+0 : 0x4.c28078a7e68b192a8657996119ap+4 : inexact-ok
= cosh tonearest binary128 0x5.06a0e8p+0 : 0x4.c28078a7e68b192a8657996119ap+4 : inexact-ok
= cosh towardzero binary128 0x5.06a0e8p+0 : 0x4.c28078a7e68b192a8657996119ap+4 : inexact-ok
= cosh upward binary128 0x5.06a0e8p+0 : 0x4.c28078a7e68b192a8657996119a4p+4 : inexact-ok
= cosh downward ibm128 0x5.06a0e8p+0 : 0x4.c28078a7e68b192a8657996118p+4 : inexact-ok
= cosh tonearest ibm128 0x5.06a0e8p+0 : 0x4.c28078a7e68b192a865799611ap+4 : inexact-ok
= cosh towardzero ibm128 0x5.06a0e8p+0 : 0x4.c28078a7e68b192a8657996118p+4 : inexact-ok
= cosh upward ibm128 0x5.06a0e8p+0 : 0x4.c28078a7e68b192a865799611ap+4 : inexact-ok
= cosh downward binary64 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh tonearest binary64 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh towardzero binary64 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh upward binary64 0x5.06a0ee40756f4p+0 : 0x4.c280966910af4p+4 : inexact-ok
= cosh downward intel96 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh tonearest intel96 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh towardzero intel96 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh upward intel96 0x5.06a0ee40756f4p+0 : 0x4.c280966910af0008p+4 : inexact-ok
= cosh downward m68k96 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh tonearest m68k96 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh towardzero m68k96 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh upward m68k96 0x5.06a0ee40756f4p+0 : 0x4.c280966910af0008p+4 : inexact-ok
= cosh downward binary128 0x5.06a0ee40756f4p+0 : 0x4.c280966910af000028c5b44dfbacp+4 : inexact-ok
= cosh tonearest binary128 0x5.06a0ee40756f4p+0 : 0x4.c280966910af000028c5b44dfbbp+4 : inexact-ok
= cosh towardzero binary128 0x5.06a0ee40756f4p+0 : 0x4.c280966910af000028c5b44dfbacp+4 : inexact-ok
= cosh upward binary128 0x5.06a0ee40756f4p+0 : 0x4.c280966910af000028c5b44dfbbp+4 : inexact-ok
= cosh downward ibm128 0x5.06a0ee40756f4p+0 : 0x4.c280966910af000028c5b44dfap+4 : inexact-ok
= cosh tonearest ibm128 0x5.06a0ee40756f4p+0 : 0x4.c280966910af000028c5b44dfcp+4 : inexact-ok
= cosh towardzero ibm128 0x5.06a0ee40756f4p+0 : 0x4.c280966910af000028c5b44dfap+4 : inexact-ok
= cosh upward ibm128 0x5.06a0ee40756f4p+0 : 0x4.c280966910af000028c5b44dfcp+4 : inexact-ok
cosh 0x1.40d5c37ff8185p+2
= cosh downward binary32 0x5.03571p+0 : 0x4.b2f37p+4 : inexact-ok
= cosh tonearest binary32 0x5.03571p+0 : 0x4.b2f378p+4 : inexact-ok
= cosh towardzero binary32 0x5.03571p+0 : 0x4.b2f37p+4 : inexact-ok
= cosh upward binary32 0x5.03571p+0 : 0x4.b2f378p+4 : inexact-ok
= cosh downward binary64 0x5.03571p+0 : 0x4.b2f3753486e64p+4 : inexact-ok
= cosh tonearest binary64 0x5.03571p+0 : 0x4.b2f3753486e64p+4 : inexact-ok
= cosh towardzero binary64 0x5.03571p+0 : 0x4.b2f3753486e64p+4 : inexact-ok
= cosh upward binary64 0x5.03571p+0 : 0x4.b2f3753486e68p+4 : inexact-ok
= cosh downward intel96 0x5.03571p+0 : 0x4.b2f3753486e64318p+4 : inexact-ok
= cosh tonearest intel96 0x5.03571p+0 : 0x4.b2f3753486e64318p+4 : inexact-ok
= cosh towardzero intel96 0x5.03571p+0 : 0x4.b2f3753486e64318p+4 : inexact-ok
= cosh upward intel96 0x5.03571p+0 : 0x4.b2f3753486e6432p+4 : inexact-ok
= cosh downward m68k96 0x5.03571p+0 : 0x4.b2f3753486e64318p+4 : inexact-ok
= cosh tonearest m68k96 0x5.03571p+0 : 0x4.b2f3753486e64318p+4 : inexact-ok
= cosh towardzero m68k96 0x5.03571p+0 : 0x4.b2f3753486e64318p+4 : inexact-ok
= cosh upward m68k96 0x5.03571p+0 : 0x4.b2f3753486e6432p+4 : inexact-ok
= cosh downward binary128 0x5.03571p+0 : 0x4.b2f3753486e6431841ef6829925p+4 : inexact-ok
= cosh tonearest binary128 0x5.03571p+0 : 0x4.b2f3753486e6431841ef6829925p+4 : inexact-ok
= cosh towardzero binary128 0x5.03571p+0 : 0x4.b2f3753486e6431841ef6829925p+4 : inexact-ok
= cosh upward binary128 0x5.03571p+0 : 0x4.b2f3753486e6431841ef68299254p+4 : inexact-ok
= cosh downward ibm128 0x5.03571p+0 : 0x4.b2f3753486e6431841ef682992p+4 : inexact-ok
= cosh tonearest ibm128 0x5.03571p+0 : 0x4.b2f3753486e6431841ef682992p+4 : inexact-ok
= cosh towardzero ibm128 0x5.03571p+0 : 0x4.b2f3753486e6431841ef682992p+4 : inexact-ok
= cosh upward ibm128 0x5.03571p+0 : 0x4.b2f3753486e6431841ef682994p+4 : inexact-ok
= cosh downward binary32 0x5.035708p+0 : 0x4.b2f348p+4 : inexact-ok
= cosh tonearest binary32 0x5.035708p+0 : 0x4.b2f35p+4 : inexact-ok
= cosh towardzero binary32 0x5.035708p+0 : 0x4.b2f348p+4 : inexact-ok
= cosh upward binary32 0x5.035708p+0 : 0x4.b2f35p+4 : inexact-ok
= cosh downward binary64 0x5.035708p+0 : 0x4.b2f34f9dc5c04p+4 : inexact-ok
= cosh tonearest binary64 0x5.035708p+0 : 0x4.b2f34f9dc5c04p+4 : inexact-ok
= cosh towardzero binary64 0x5.035708p+0 : 0x4.b2f34f9dc5c04p+4 : inexact-ok
= cosh upward binary64 0x5.035708p+0 : 0x4.b2f34f9dc5c08p+4 : inexact-ok
= cosh downward intel96 0x5.035708p+0 : 0x4.b2f34f9dc5c05218p+4 : inexact-ok
= cosh tonearest intel96 0x5.035708p+0 : 0x4.b2f34f9dc5c0522p+4 : inexact-ok
= cosh towardzero intel96 0x5.035708p+0 : 0x4.b2f34f9dc5c05218p+4 : inexact-ok
= cosh upward intel96 0x5.035708p+0 : 0x4.b2f34f9dc5c0522p+4 : inexact-ok
= cosh downward m68k96 0x5.035708p+0 : 0x4.b2f34f9dc5c05218p+4 : inexact-ok
= cosh tonearest m68k96 0x5.035708p+0 : 0x4.b2f34f9dc5c0522p+4 : inexact-ok
= cosh towardzero m68k96 0x5.035708p+0 : 0x4.b2f34f9dc5c05218p+4 : inexact-ok
= cosh upward m68k96 0x5.035708p+0 : 0x4.b2f34f9dc5c0522p+4 : inexact-ok
= cosh downward binary128 0x5.035708p+0 : 0x4.b2f34f9dc5c0521d84b3bbb501fcp+4 : inexact-ok
= cosh tonearest binary128 0x5.035708p+0 : 0x4.b2f34f9dc5c0521d84b3bbb502p+4 : inexact-ok
= cosh towardzero binary128 0x5.035708p+0 : 0x4.b2f34f9dc5c0521d84b3bbb501fcp+4 : inexact-ok
= cosh upward binary128 0x5.035708p+0 : 0x4.b2f34f9dc5c0521d84b3bbb502p+4 : inexact-ok
= cosh downward ibm128 0x5.035708p+0 : 0x4.b2f34f9dc5c0521d84b3bbb5p+4 : inexact-ok
= cosh tonearest ibm128 0x5.035708p+0 : 0x4.b2f34f9dc5c0521d84b3bbb502p+4 : inexact-ok
= cosh towardzero ibm128 0x5.035708p+0 : 0x4.b2f34f9dc5c0521d84b3bbb5p+4 : inexact-ok
= cosh upward ibm128 0x5.035708p+0 : 0x4.b2f34f9dc5c0521d84b3bbb502p+4 : inexact-ok
= cosh downward binary64 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh tonearest binary64 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh towardzero binary64 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh upward binary64 0x5.03570dffe0614p+0 : 0x4.b2f36bce41eecp+4 : inexact-ok
= cosh downward intel96 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh tonearest intel96 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh towardzero intel96 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh upward intel96 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8008p+4 : inexact-ok
= cosh downward m68k96 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh tonearest m68k96 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh towardzero m68k96 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh upward m68k96 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8008p+4 : inexact-ok
= cosh downward binary128 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee800040f77ba288b4p+4 : inexact-ok
= cosh tonearest binary128 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee800040f77ba288b4p+4 : inexact-ok
= cosh towardzero binary128 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee800040f77ba288b4p+4 : inexact-ok
= cosh upward binary128 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee800040f77ba288b8p+4 : inexact-ok
= cosh downward ibm128 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee800040f77ba288p+4 : inexact-ok
= cosh tonearest ibm128 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee800040f77ba288p+4 : inexact-ok
= cosh towardzero ibm128 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee800040f77ba288p+4 : inexact-ok
= cosh upward ibm128 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee800040f77ba28ap+4 : inexact-ok
cosh -0x1.419a5f3fa359p+2
= cosh downward binary32 -0x5.066978p+0 : 0x4.c178b8p+4 : inexact-ok
= cosh tonearest binary32 -0x5.066978p+0 : 0x4.c178cp+4 : inexact-ok
= cosh towardzero binary32 -0x5.066978p+0 : 0x4.c178b8p+4 : inexact-ok
= cosh upward binary32 -0x5.066978p+0 : 0x4.c178cp+4 : inexact-ok
= cosh downward binary64 -0x5.066978p+0 : 0x4.c178bc58bf018p+4 : inexact-ok
= cosh tonearest binary64 -0x5.066978p+0 : 0x4.c178bc58bf018p+4 : inexact-ok
= cosh towardzero binary64 -0x5.066978p+0 : 0x4.c178bc58bf018p+4 : inexact-ok
= cosh upward binary64 -0x5.066978p+0 : 0x4.c178bc58bf01cp+4 : inexact-ok
= cosh downward intel96 -0x5.066978p+0 : 0x4.c178bc58bf018fd8p+4 : inexact-ok
= cosh tonearest intel96 -0x5.066978p+0 : 0x4.c178bc58bf018fd8p+4 : inexact-ok
= cosh towardzero intel96 -0x5.066978p+0 : 0x4.c178bc58bf018fd8p+4 : inexact-ok
= cosh upward intel96 -0x5.066978p+0 : 0x4.c178bc58bf018fep+4 : inexact-ok
= cosh downward m68k96 -0x5.066978p+0 : 0x4.c178bc58bf018fd8p+4 : inexact-ok
= cosh tonearest m68k96 -0x5.066978p+0 : 0x4.c178bc58bf018fd8p+4 : inexact-ok
= cosh towardzero m68k96 -0x5.066978p+0 : 0x4.c178bc58bf018fd8p+4 : inexact-ok
= cosh upward m68k96 -0x5.066978p+0 : 0x4.c178bc58bf018fep+4 : inexact-ok
= cosh downward binary128 -0x5.066978p+0 : 0x4.c178bc58bf018fd9b85ed488b598p+4 : inexact-ok
= cosh tonearest binary128 -0x5.066978p+0 : 0x4.c178bc58bf018fd9b85ed488b59cp+4 : inexact-ok
= cosh towardzero binary128 -0x5.066978p+0 : 0x4.c178bc58bf018fd9b85ed488b598p+4 : inexact-ok
= cosh upward binary128 -0x5.066978p+0 : 0x4.c178bc58bf018fd9b85ed488b59cp+4 : inexact-ok
= cosh downward ibm128 -0x5.066978p+0 : 0x4.c178bc58bf018fd9b85ed488b4p+4 : inexact-ok
= cosh tonearest ibm128 -0x5.066978p+0 : 0x4.c178bc58bf018fd9b85ed488b6p+4 : inexact-ok
= cosh towardzero ibm128 -0x5.066978p+0 : 0x4.c178bc58bf018fd9b85ed488b4p+4 : inexact-ok
= cosh upward ibm128 -0x5.066978p+0 : 0x4.c178bc58bf018fd9b85ed488b6p+4 : inexact-ok
= cosh downward binary32 -0x5.06698p+0 : 0x4.c178ep+4 : inexact-ok
= cosh tonearest binary32 -0x5.06698p+0 : 0x4.c178ep+4 : inexact-ok
= cosh towardzero binary32 -0x5.06698p+0 : 0x4.c178ep+4 : inexact-ok
= cosh upward binary32 -0x5.06698p+0 : 0x4.c178e8p+4 : inexact-ok
= cosh downward binary64 -0x5.06698p+0 : 0x4.c178e263ae288p+4 : inexact-ok
= cosh tonearest binary64 -0x5.06698p+0 : 0x4.c178e263ae28cp+4 : inexact-ok
= cosh towardzero binary64 -0x5.06698p+0 : 0x4.c178e263ae288p+4 : inexact-ok
= cosh upward binary64 -0x5.06698p+0 : 0x4.c178e263ae28cp+4 : inexact-ok
= cosh downward intel96 -0x5.06698p+0 : 0x4.c178e263ae28a328p+4 : inexact-ok
= cosh tonearest intel96 -0x5.06698p+0 : 0x4.c178e263ae28a33p+4 : inexact-ok
= cosh towardzero intel96 -0x5.06698p+0 : 0x4.c178e263ae28a328p+4 : inexact-ok
= cosh upward intel96 -0x5.06698p+0 : 0x4.c178e263ae28a33p+4 : inexact-ok
= cosh downward m68k96 -0x5.06698p+0 : 0x4.c178e263ae28a328p+4 : inexact-ok
= cosh tonearest m68k96 -0x5.06698p+0 : 0x4.c178e263ae28a33p+4 : inexact-ok
= cosh towardzero m68k96 -0x5.06698p+0 : 0x4.c178e263ae28a328p+4 : inexact-ok
= cosh upward m68k96 -0x5.06698p+0 : 0x4.c178e263ae28a33p+4 : inexact-ok
= cosh downward binary128 -0x5.06698p+0 : 0x4.c178e263ae28a32e370063ef6ab4p+4 : inexact-ok
= cosh tonearest binary128 -0x5.06698p+0 : 0x4.c178e263ae28a32e370063ef6ab8p+4 : inexact-ok
= cosh towardzero binary128 -0x5.06698p+0 : 0x4.c178e263ae28a32e370063ef6ab4p+4 : inexact-ok
= cosh upward binary128 -0x5.06698p+0 : 0x4.c178e263ae28a32e370063ef6ab8p+4 : inexact-ok
= cosh downward ibm128 -0x5.06698p+0 : 0x4.c178e263ae28a32e370063ef6ap+4 : inexact-ok
= cosh tonearest ibm128 -0x5.06698p+0 : 0x4.c178e263ae28a32e370063ef6ap+4 : inexact-ok
= cosh towardzero ibm128 -0x5.06698p+0 : 0x4.c178e263ae28a32e370063ef6ap+4 : inexact-ok
= cosh upward ibm128 -0x5.06698p+0 : 0x4.c178e263ae28a32e370063ef6cp+4 : inexact-ok
= cosh downward binary64 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6cp+4 : inexact-ok
= cosh tonearest binary64 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6cp+4 : inexact-ok
= cosh towardzero binary64 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6cp+4 : inexact-ok
= cosh upward binary64 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f7p+4 : inexact-ok
= cosh downward intel96 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6cp+4 : inexact-ok
= cosh tonearest intel96 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6cp+4 : inexact-ok
= cosh towardzero intel96 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6cp+4 : inexact-ok
= cosh upward intel96 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6c008p+4 : inexact-ok
= cosh downward m68k96 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6cp+4 : inexact-ok
= cosh tonearest m68k96 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6cp+4 : inexact-ok
= cosh towardzero m68k96 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6cp+4 : inexact-ok
= cosh upward m68k96 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6c008p+4 : inexact-ok
= cosh downward binary128 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6c00025bace002618p+4 : inexact-ok
= cosh tonearest binary128 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6c00025bace002618p+4 : inexact-ok
= cosh towardzero binary128 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6c00025bace002618p+4 : inexact-ok
= cosh upward binary128 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6c00025bace00261cp+4 : inexact-ok
= cosh downward ibm128 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6c00025bace0026p+4 : inexact-ok
= cosh tonearest ibm128 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6c00025bace0026p+4 : inexact-ok
= cosh towardzero ibm128 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6c00025bace0026p+4 : inexact-ok
= cosh upward ibm128 -0x5.06697cfe8d64p+0 : 0x4.c178d418b1f6c00025bace0028p+4 : inexact-ok
cosh 0x1.426a50e51bd1ep+2
= cosh downward binary32 0x5.09a948p+0 : 0x4.d10578p+4 : inexact-ok
= cosh tonearest binary32 0x5.09a948p+0 : 0x4.d1058p+4 : inexact-ok
= cosh towardzero binary32 0x5.09a948p+0 : 0x4.d10578p+4 : inexact-ok
= cosh upward binary32 0x5.09a948p+0 : 0x4.d1058p+4 : inexact-ok
= cosh downward binary64 0x5.09a948p+0 : 0x4.d1057f2772a24p+4 : inexact-ok
= cosh tonearest binary64 0x5.09a948p+0 : 0x4.d1057f2772a28p+4 : inexact-ok
= cosh towardzero binary64 0x5.09a948p+0 : 0x4.d1057f2772a24p+4 : inexact-ok
= cosh upward binary64 0x5.09a948p+0 : 0x4.d1057f2772a28p+4 : inexact-ok
= cosh downward intel96 0x5.09a948p+0 : 0x4.d1057f2772a269ep+4 : inexact-ok
= cosh tonearest intel96 0x5.09a948p+0 : 0x4.d1057f2772a269e8p+4 : inexact-ok
= cosh towardzero intel96 0x5.09a948p+0 : 0x4.d1057f2772a269ep+4 : inexact-ok
= cosh upward intel96 0x5.09a948p+0 : 0x4.d1057f2772a269e8p+4 : inexact-ok
= cosh downward m68k96 0x5.09a948p+0 : 0x4.d1057f2772a269ep+4 : inexact-ok
= cosh tonearest m68k96 0x5.09a948p+0 : 0x4.d1057f2772a269e8p+4 : inexact-ok
= cosh towardzero m68k96 0x5.09a948p+0 : 0x4.d1057f2772a269ep+4 : inexact-ok
= cosh upward m68k96 0x5.09a948p+0 : 0x4.d1057f2772a269e8p+4 : inexact-ok
= cosh downward binary128 0x5.09a948p+0 : 0x4.d1057f2772a269e5e93d5f15f2ecp+4 : inexact-ok
= cosh tonearest binary128 0x5.09a948p+0 : 0x4.d1057f2772a269e5e93d5f15f2fp+4 : inexact-ok
= cosh towardzero binary128 0x5.09a948p+0 : 0x4.d1057f2772a269e5e93d5f15f2ecp+4 : inexact-ok
= cosh upward binary128 0x5.09a948p+0 : 0x4.d1057f2772a269e5e93d5f15f2fp+4 : inexact-ok
= cosh downward ibm128 0x5.09a948p+0 : 0x4.d1057f2772a269e5e93d5f15f2p+4 : inexact-ok
= cosh tonearest ibm128 0x5.09a948p+0 : 0x4.d1057f2772a269e5e93d5f15f2p+4 : inexact-ok
= cosh towardzero ibm128 0x5.09a948p+0 : 0x4.d1057f2772a269e5e93d5f15f2p+4 : inexact-ok
= cosh upward ibm128 0x5.09a948p+0 : 0x4.d1057f2772a269e5e93d5f15f4p+4 : inexact-ok
= cosh downward binary32 0x5.09a94p+0 : 0x4.d10558p+4 : inexact-ok
= cosh tonearest binary32 0x5.09a94p+0 : 0x4.d10558p+4 : inexact-ok
= cosh towardzero binary32 0x5.09a94p+0 : 0x4.d10558p+4 : inexact-ok
= cosh upward binary32 0x5.09a94p+0 : 0x4.d1056p+4 : inexact-ok
= cosh downward binary64 0x5.09a94p+0 : 0x4.d10558a01bdfcp+4 : inexact-ok
= cosh tonearest binary64 0x5.09a94p+0 : 0x4.d10558a01bep+4 : inexact-ok
= cosh towardzero binary64 0x5.09a94p+0 : 0x4.d10558a01bdfcp+4 : inexact-ok
= cosh upward binary64 0x5.09a94p+0 : 0x4.d10558a01bep+4 : inexact-ok
= cosh downward intel96 0x5.09a94p+0 : 0x4.d10558a01bdff46p+4 : inexact-ok
= cosh tonearest intel96 0x5.09a94p+0 : 0x4.d10558a01bdff46p+4 : inexact-ok
= cosh towardzero intel96 0x5.09a94p+0 : 0x4.d10558a01bdff46p+4 : inexact-ok
= cosh upward intel96 0x5.09a94p+0 : 0x4.d10558a01bdff468p+4 : inexact-ok
= cosh downward m68k96 0x5.09a94p+0 : 0x4.d10558a01bdff46p+4 : inexact-ok
= cosh tonearest m68k96 0x5.09a94p+0 : 0x4.d10558a01bdff46p+4 : inexact-ok
= cosh towardzero m68k96 0x5.09a94p+0 : 0x4.d10558a01bdff46p+4 : inexact-ok
= cosh upward m68k96 0x5.09a94p+0 : 0x4.d10558a01bdff468p+4 : inexact-ok
= cosh downward binary128 0x5.09a94p+0 : 0x4.d10558a01bdff462740c7f713f6cp+4 : inexact-ok
= cosh tonearest binary128 0x5.09a94p+0 : 0x4.d10558a01bdff462740c7f713f7p+4 : inexact-ok
= cosh towardzero binary128 0x5.09a94p+0 : 0x4.d10558a01bdff462740c7f713f6cp+4 : inexact-ok
= cosh upward binary128 0x5.09a94p+0 : 0x4.d10558a01bdff462740c7f713f7p+4 : inexact-ok
= cosh downward ibm128 0x5.09a94p+0 : 0x4.d10558a01bdff462740c7f713ep+4 : inexact-ok
= cosh tonearest ibm128 0x5.09a94p+0 : 0x4.d10558a01bdff462740c7f714p+4 : inexact-ok
= cosh towardzero ibm128 0x5.09a94p+0 : 0x4.d10558a01bdff462740c7f713ep+4 : inexact-ok
= cosh upward ibm128 0x5.09a94p+0 : 0x4.d10558a01bdff462740c7f714p+4 : inexact-ok
= cosh downward binary64 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh tonearest binary64 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh towardzero binary64 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh upward binary64 0x5.09a943946f478p+0 : 0x4.d10569ddbbf64p+4 : inexact-ok
= cosh downward intel96 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh tonearest intel96 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh towardzero intel96 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh upward intel96 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60008p+4 : inexact-ok
= cosh downward m68k96 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh tonearest m68k96 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh towardzero m68k96 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh upward m68k96 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60008p+4 : inexact-ok
= cosh downward binary128 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60000094da480974cp+4 : inexact-ok
= cosh tonearest binary128 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60000094da480975p+4 : inexact-ok
= cosh towardzero binary128 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60000094da480974cp+4 : inexact-ok
= cosh upward binary128 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60000094da480975p+4 : inexact-ok
= cosh downward ibm128 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60000094da48096p+4 : inexact-ok
= cosh tonearest ibm128 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60000094da48098p+4 : inexact-ok
= cosh towardzero ibm128 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60000094da48096p+4 : inexact-ok
= cosh upward ibm128 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60000094da48098p+4 : inexact-ok
cosh -0x1.64c53499192bfp+2
= cosh downward binary32 -0x5.9314dp+0 : 0x8.3d0c7p+4 : inexact-ok
= cosh tonearest binary32 -0x5.9314dp+0 : 0x8.3d0c7p+4 : inexact-ok
= cosh towardzero binary32 -0x5.9314dp+0 : 0x8.3d0c7p+4 : inexact-ok
= cosh upward binary32 -0x5.9314dp+0 : 0x8.3d0c8p+4 : inexact-ok
= cosh downward binary64 -0x5.9314dp+0 : 0x8.3d0c751e5408p+4 : inexact-ok
= cosh tonearest binary64 -0x5.9314dp+0 : 0x8.3d0c751e54088p+4 : inexact-ok
= cosh towardzero binary64 -0x5.9314dp+0 : 0x8.3d0c751e5408p+4 : inexact-ok
= cosh upward binary64 -0x5.9314dp+0 : 0x8.3d0c751e54088p+4 : inexact-ok
= cosh downward intel96 -0x5.9314dp+0 : 0x8.3d0c751e540878cp+4 : inexact-ok
= cosh tonearest intel96 -0x5.9314dp+0 : 0x8.3d0c751e540878dp+4 : inexact-ok
= cosh towardzero intel96 -0x5.9314dp+0 : 0x8.3d0c751e540878cp+4 : inexact-ok
= cosh upward intel96 -0x5.9314dp+0 : 0x8.3d0c751e540878dp+4 : inexact-ok
= cosh downward m68k96 -0x5.9314dp+0 : 0x8.3d0c751e540878cp+4 : inexact-ok
= cosh tonearest m68k96 -0x5.9314dp+0 : 0x8.3d0c751e540878dp+4 : inexact-ok
= cosh towardzero m68k96 -0x5.9314dp+0 : 0x8.3d0c751e540878cp+4 : inexact-ok
= cosh upward m68k96 -0x5.9314dp+0 : 0x8.3d0c751e540878dp+4 : inexact-ok
= cosh downward binary128 -0x5.9314dp+0 : 0x8.3d0c751e540878c9d15a8fe9641p+4 : inexact-ok
= cosh tonearest binary128 -0x5.9314dp+0 : 0x8.3d0c751e540878c9d15a8fe96418p+4 : inexact-ok
= cosh towardzero binary128 -0x5.9314dp+0 : 0x8.3d0c751e540878c9d15a8fe9641p+4 : inexact-ok
= cosh upward binary128 -0x5.9314dp+0 : 0x8.3d0c751e540878c9d15a8fe96418p+4 : inexact-ok
= cosh downward ibm128 -0x5.9314dp+0 : 0x8.3d0c751e540878c9d15a8fe964p+4 : inexact-ok
= cosh tonearest ibm128 -0x5.9314dp+0 : 0x8.3d0c751e540878c9d15a8fe964p+4 : inexact-ok
= cosh towardzero ibm128 -0x5.9314dp+0 : 0x8.3d0c751e540878c9d15a8fe964p+4 : inexact-ok
= cosh upward ibm128 -0x5.9314dp+0 : 0x8.3d0c751e540878c9d15a8fe968p+4 : inexact-ok
= cosh downward binary32 -0x5.9314d8p+0 : 0x8.3d0cbp+4 : inexact-ok
= cosh tonearest binary32 -0x5.9314d8p+0 : 0x8.3d0cbp+4 : inexact-ok
= cosh towardzero binary32 -0x5.9314d8p+0 : 0x8.3d0cbp+4 : inexact-ok
= cosh upward binary32 -0x5.9314d8p+0 : 0x8.3d0ccp+4 : inexact-ok
= cosh downward binary64 -0x5.9314d8p+0 : 0x8.3d0cb7063c6dp+4 : inexact-ok
= cosh tonearest binary64 -0x5.9314d8p+0 : 0x8.3d0cb7063c6dp+4 : inexact-ok
= cosh towardzero binary64 -0x5.9314d8p+0 : 0x8.3d0cb7063c6dp+4 : inexact-ok
= cosh upward binary64 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d8p+4 : inexact-ok
= cosh downward intel96 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d18fp+4 : inexact-ok
= cosh tonearest intel96 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d19p+4 : inexact-ok
= cosh towardzero intel96 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d18fp+4 : inexact-ok
= cosh upward intel96 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d19p+4 : inexact-ok
= cosh downward m68k96 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d18fp+4 : inexact-ok
= cosh tonearest m68k96 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d19p+4 : inexact-ok
= cosh towardzero m68k96 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d18fp+4 : inexact-ok
= cosh upward m68k96 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d19p+4 : inexact-ok
= cosh downward binary128 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d18fa473295485a98p+4 : inexact-ok
= cosh tonearest binary128 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d18fa473295485a98p+4 : inexact-ok
= cosh towardzero binary128 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d18fa473295485a98p+4 : inexact-ok
= cosh upward binary128 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d18fa473295485aap+4 : inexact-ok
= cosh downward ibm128 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d18fa4732954858p+4 : inexact-ok
= cosh tonearest ibm128 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d18fa473295485cp+4 : inexact-ok
= cosh towardzero ibm128 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d18fa4732954858p+4 : inexact-ok
= cosh upward ibm128 -0x5.9314d8p+0 : 0x8.3d0cb7063c6d18fa473295485cp+4 : inexact-ok
= cosh downward binary64 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3ep+4 : inexact-ok
= cosh tonearest binary64 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3ep+4 : inexact-ok
= cosh towardzero binary64 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3ep+4 : inexact-ok
= cosh upward binary64 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3e8p+4 : inexact-ok
= cosh downward intel96 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3ep+4 : inexact-ok
= cosh tonearest intel96 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3ep+4 : inexact-ok
= cosh towardzero intel96 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3ep+4 : inexact-ok
= cosh upward intel96 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3e001p+4 : inexact-ok
= cosh downward m68k96 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3ep+4 : inexact-ok
= cosh tonearest m68k96 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3ep+4 : inexact-ok
= cosh towardzero m68k96 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3ep+4 : inexact-ok
= cosh upward m68k96 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3e001p+4 : inexact-ok
= cosh downward binary128 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3e00004b1dc4056c18p+4 : inexact-ok
= cosh tonearest binary128 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3e00004b1dc4056c2p+4 : inexact-ok
= cosh towardzero binary128 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3e00004b1dc4056c18p+4 : inexact-ok
= cosh upward binary128 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3e00004b1dc4056c2p+4 : inexact-ok
= cosh downward ibm128 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3e00004b1dc4056cp+4 : inexact-ok
= cosh tonearest ibm128 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3e00004b1dc4056cp+4 : inexact-ok
= cosh towardzero ibm128 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3e00004b1dc4056cp+4 : inexact-ok
= cosh upward ibm128 -0x5.9314d26464afcp+0 : 0x8.3d0c88d35e3e00004b1dc4057p+4 : inexact-ok
cosh 0x1.41fe58c623761p+2
= cosh downward binary32 0x5.07f968p+0 : 0x4.c8ec6p+4 : inexact-ok
= cosh tonearest binary32 0x5.07f968p+0 : 0x4.c8ec6p+4 : inexact-ok
= cosh towardzero binary32 0x5.07f968p+0 : 0x4.c8ec6p+4 : inexact-ok
= cosh upward binary32 0x5.07f968p+0 : 0x4.c8ec68p+4 : inexact-ok
= cosh downward binary64 0x5.07f968p+0 : 0x4.c8ec639696b94p+4 : inexact-ok
= cosh tonearest binary64 0x5.07f968p+0 : 0x4.c8ec639696b98p+4 : inexact-ok
= cosh towardzero binary64 0x5.07f968p+0 : 0x4.c8ec639696b94p+4 : inexact-ok
= cosh upward binary64 0x5.07f968p+0 : 0x4.c8ec639696b98p+4 : inexact-ok
= cosh downward intel96 0x5.07f968p+0 : 0x4.c8ec639696b9734p+4 : inexact-ok
= cosh tonearest intel96 0x5.07f968p+0 : 0x4.c8ec639696b9734p+4 : inexact-ok
= cosh towardzero intel96 0x5.07f968p+0 : 0x4.c8ec639696b9734p+4 : inexact-ok
= cosh upward intel96 0x5.07f968p+0 : 0x4.c8ec639696b97348p+4 : inexact-ok
= cosh downward m68k96 0x5.07f968p+0 : 0x4.c8ec639696b9734p+4 : inexact-ok
= cosh tonearest m68k96 0x5.07f968p+0 : 0x4.c8ec639696b9734p+4 : inexact-ok
= cosh towardzero m68k96 0x5.07f968p+0 : 0x4.c8ec639696b9734p+4 : inexact-ok
= cosh upward m68k96 0x5.07f968p+0 : 0x4.c8ec639696b97348p+4 : inexact-ok
= cosh downward binary128 0x5.07f968p+0 : 0x4.c8ec639696b9734351e5a3ba533cp+4 : inexact-ok
= cosh tonearest binary128 0x5.07f968p+0 : 0x4.c8ec639696b9734351e5a3ba534p+4 : inexact-ok
= cosh towardzero binary128 0x5.07f968p+0 : 0x4.c8ec639696b9734351e5a3ba533cp+4 : inexact-ok
= cosh upward binary128 0x5.07f968p+0 : 0x4.c8ec639696b9734351e5a3ba534p+4 : inexact-ok
= cosh downward ibm128 0x5.07f968p+0 : 0x4.c8ec639696b9734351e5a3ba52p+4 : inexact-ok
= cosh tonearest ibm128 0x5.07f968p+0 : 0x4.c8ec639696b9734351e5a3ba54p+4 : inexact-ok
= cosh towardzero ibm128 0x5.07f968p+0 : 0x4.c8ec639696b9734351e5a3ba52p+4 : inexact-ok
= cosh upward ibm128 0x5.07f968p+0 : 0x4.c8ec639696b9734351e5a3ba54p+4 : inexact-ok
= cosh downward binary32 0x5.07f96p+0 : 0x4.c8ec38p+4 : inexact-ok
= cosh tonearest binary32 0x5.07f96p+0 : 0x4.c8ec4p+4 : inexact-ok
= cosh towardzero binary32 0x5.07f96p+0 : 0x4.c8ec38p+4 : inexact-ok
= cosh upward binary32 0x5.07f96p+0 : 0x4.c8ec4p+4 : inexact-ok
= cosh downward binary64 0x5.07f96p+0 : 0x4.c8ec3d500a3a4p+4 : inexact-ok
= cosh tonearest binary64 0x5.07f96p+0 : 0x4.c8ec3d500a3a4p+4 : inexact-ok
= cosh towardzero binary64 0x5.07f96p+0 : 0x4.c8ec3d500a3a4p+4 : inexact-ok
= cosh upward binary64 0x5.07f96p+0 : 0x4.c8ec3d500a3a8p+4 : inexact-ok
= cosh downward intel96 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e7p+4 : inexact-ok
= cosh tonearest intel96 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e78p+4 : inexact-ok
= cosh towardzero intel96 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e7p+4 : inexact-ok
= cosh upward intel96 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e78p+4 : inexact-ok
= cosh downward m68k96 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e7p+4 : inexact-ok
= cosh tonearest m68k96 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e78p+4 : inexact-ok
= cosh towardzero m68k96 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e7p+4 : inexact-ok
= cosh upward m68k96 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e78p+4 : inexact-ok
= cosh downward binary128 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e75d427b3126be8p+4 : inexact-ok
= cosh tonearest binary128 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e75d427b3126becp+4 : inexact-ok
= cosh towardzero binary128 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e75d427b3126be8p+4 : inexact-ok
= cosh upward binary128 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e75d427b3126becp+4 : inexact-ok
= cosh downward ibm128 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e75d427b3126ap+4 : inexact-ok
= cosh tonearest ibm128 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e75d427b3126cp+4 : inexact-ok
= cosh towardzero ibm128 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e75d427b3126ap+4 : inexact-ok
= cosh upward ibm128 0x5.07f96p+0 : 0x4.c8ec3d500a3a5e75d427b3126cp+4 : inexact-ok
= cosh downward binary64 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh tonearest binary64 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh towardzero binary64 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh upward binary64 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9118p+4 : inexact-ok
= cosh downward intel96 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh tonearest intel96 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh towardzero intel96 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh upward intel96 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114008p+4 : inexact-ok
= cosh downward m68k96 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh tonearest m68k96 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh towardzero m68k96 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114p+4 : inexact-ok
= cosh upward m68k96 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff9114008p+4 : inexact-ok
= cosh downward binary128 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff91140001f93e1971e5cp+4 : inexact-ok
= cosh tonearest binary128 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff91140001f93e1971e6p+4 : inexact-ok
= cosh towardzero binary128 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff91140001f93e1971e5cp+4 : inexact-ok
= cosh upward binary128 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff91140001f93e1971e6p+4 : inexact-ok
= cosh downward ibm128 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff91140001f93e1971ep+4 : inexact-ok
= cosh tonearest ibm128 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff91140001f93e1971ep+4 : inexact-ok
= cosh towardzero ibm128 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff91140001f93e1971ep+4 : inexact-ok
= cosh upward ibm128 0x5.07f963188dd84p+0 : 0x4.c8ec4c1ff91140001f93e1972p+4 : inexact-ok
cosh 0x1.424ed1d05dfa7p+2
= cosh downward binary32 0x5.093b48p+0 : 0x4.cef428p+4 : inexact-ok
= cosh tonearest binary32 0x5.093b48p+0 : 0x4.cef428p+4 : inexact-ok
= cosh towardzero binary32 0x5.093b48p+0 : 0x4.cef428p+4 : inexact-ok
= cosh upward binary32 0x5.093b48p+0 : 0x4.cef43p+4 : inexact-ok
= cosh downward binary64 0x5.093b48p+0 : 0x4.cef42bf9b1e84p+4 : inexact-ok
= cosh tonearest binary64 0x5.093b48p+0 : 0x4.cef42bf9b1e84p+4 : inexact-ok
= cosh towardzero binary64 0x5.093b48p+0 : 0x4.cef42bf9b1e84p+4 : inexact-ok
= cosh upward binary64 0x5.093b48p+0 : 0x4.cef42bf9b1e88p+4 : inexact-ok
= cosh downward intel96 0x5.093b48p+0 : 0x4.cef42bf9b1e857c8p+4 : inexact-ok
= cosh tonearest intel96 0x5.093b48p+0 : 0x4.cef42bf9b1e857dp+4 : inexact-ok
= cosh towardzero intel96 0x5.093b48p+0 : 0x4.cef42bf9b1e857c8p+4 : inexact-ok
= cosh upward intel96 0x5.093b48p+0 : 0x4.cef42bf9b1e857dp+4 : inexact-ok
= cosh downward m68k96 0x5.093b48p+0 : 0x4.cef42bf9b1e857c8p+4 : inexact-ok
= cosh tonearest m68k96 0x5.093b48p+0 : 0x4.cef42bf9b1e857dp+4 : inexact-ok
= cosh towardzero m68k96 0x5.093b48p+0 : 0x4.cef42bf9b1e857c8p+4 : inexact-ok
= cosh upward m68k96 0x5.093b48p+0 : 0x4.cef42bf9b1e857dp+4 : inexact-ok
= cosh downward binary128 0x5.093b48p+0 : 0x4.cef42bf9b1e857cddb3ba37b563p+4 : inexact-ok
= cosh tonearest binary128 0x5.093b48p+0 : 0x4.cef42bf9b1e857cddb3ba37b5634p+4 : inexact-ok
= cosh towardzero binary128 0x5.093b48p+0 : 0x4.cef42bf9b1e857cddb3ba37b563p+4 : inexact-ok
= cosh upward binary128 0x5.093b48p+0 : 0x4.cef42bf9b1e857cddb3ba37b5634p+4 : inexact-ok
= cosh downward ibm128 0x5.093b48p+0 : 0x4.cef42bf9b1e857cddb3ba37b56p+4 : inexact-ok
= cosh tonearest ibm128 0x5.093b48p+0 : 0x4.cef42bf9b1e857cddb3ba37b56p+4 : inexact-ok
= cosh towardzero ibm128 0x5.093b48p+0 : 0x4.cef42bf9b1e857cddb3ba37b56p+4 : inexact-ok
= cosh upward ibm128 0x5.093b48p+0 : 0x4.cef42bf9b1e857cddb3ba37b58p+4 : inexact-ok
= cosh downward binary32 0x5.093b4p+0 : 0x4.cef4p+4 : inexact-ok
= cosh tonearest binary32 0x5.093b4p+0 : 0x4.cef408p+4 : inexact-ok
= cosh towardzero binary32 0x5.093b4p+0 : 0x4.cef4p+4 : inexact-ok
= cosh upward binary32 0x5.093b4p+0 : 0x4.cef408p+4 : inexact-ok
= cosh downward binary64 0x5.093b4p+0 : 0x4.cef40582e61a4p+4 : inexact-ok
= cosh tonearest binary64 0x5.093b4p+0 : 0x4.cef40582e61a8p+4 : inexact-ok
= cosh towardzero binary64 0x5.093b4p+0 : 0x4.cef40582e61a4p+4 : inexact-ok
= cosh upward binary64 0x5.093b4p+0 : 0x4.cef40582e61a8p+4 : inexact-ok
= cosh downward intel96 0x5.093b4p+0 : 0x4.cef40582e61a7d18p+4 : inexact-ok
= cosh tonearest intel96 0x5.093b4p+0 : 0x4.cef40582e61a7d18p+4 : inexact-ok
= cosh towardzero intel96 0x5.093b4p+0 : 0x4.cef40582e61a7d18p+4 : inexact-ok
= cosh upward intel96 0x5.093b4p+0 : 0x4.cef40582e61a7d2p+4 : inexact-ok
= cosh downward m68k96 0x5.093b4p+0 : 0x4.cef40582e61a7d18p+4 : inexact-ok
= cosh tonearest m68k96 0x5.093b4p+0 : 0x4.cef40582e61a7d18p+4 : inexact-ok
= cosh towardzero m68k96 0x5.093b4p+0 : 0x4.cef40582e61a7d18p+4 : inexact-ok
= cosh upward m68k96 0x5.093b4p+0 : 0x4.cef40582e61a7d2p+4 : inexact-ok
= cosh downward binary128 0x5.093b4p+0 : 0x4.cef40582e61a7d185037ecafd3f8p+4 : inexact-ok
= cosh tonearest binary128 0x5.093b4p+0 : 0x4.cef40582e61a7d185037ecafd3fcp+4 : inexact-ok
= cosh towardzero binary128 0x5.093b4p+0 : 0x4.cef40582e61a7d185037ecafd3f8p+4 : inexact-ok
= cosh upward binary128 0x5.093b4p+0 : 0x4.cef40582e61a7d185037ecafd3fcp+4 : inexact-ok
= cosh downward ibm128 0x5.093b4p+0 : 0x4.cef40582e61a7d185037ecafd2p+4 : inexact-ok
= cosh tonearest ibm128 0x5.093b4p+0 : 0x4.cef40582e61a7d185037ecafd4p+4 : inexact-ok
= cosh towardzero ibm128 0x5.093b4p+0 : 0x4.cef40582e61a7d185037ecafd2p+4 : inexact-ok
= cosh upward ibm128 0x5.093b4p+0 : 0x4.cef40582e61a7d185037ecafd4p+4 : inexact-ok
= cosh downward binary64 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh tonearest binary64 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh towardzero binary64 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh upward binary64 0x5.093b474177e9cp+0 : 0x4.cef428659e24cp+4 : inexact-ok
= cosh downward intel96 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh tonearest intel96 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh towardzero intel96 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh upward intel96 0x5.093b474177e9cp+0 : 0x4.cef428659e248008p+4 : inexact-ok
= cosh downward m68k96 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh tonearest m68k96 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh towardzero m68k96 0x5.093b474177e9cp+0 : 0x4.cef428659e248p+4 : inexact-ok
= cosh upward m68k96 0x5.093b474177e9cp+0 : 0x4.cef428659e248008p+4 : inexact-ok
= cosh downward binary128 0x5.093b474177e9cp+0 : 0x4.cef428659e2480012c38267523ep+4 : inexact-ok
= cosh tonearest binary128 0x5.093b474177e9cp+0 : 0x4.cef428659e2480012c38267523e4p+4 : inexact-ok
= cosh towardzero binary128 0x5.093b474177e9cp+0 : 0x4.cef428659e2480012c38267523ep+4 : inexact-ok
= cosh upward binary128 0x5.093b474177e9cp+0 : 0x4.cef428659e2480012c38267523e4p+4 : inexact-ok
= cosh downward ibm128 0x5.093b474177e9cp+0 : 0x4.cef428659e2480012c38267522p+4 : inexact-ok
= cosh tonearest ibm128 0x5.093b474177e9cp+0 : 0x4.cef428659e2480012c38267524p+4 : inexact-ok
= cosh towardzero ibm128 0x5.093b474177e9cp+0 : 0x4.cef428659e2480012c38267522p+4 : inexact-ok
= cosh upward ibm128 0x5.093b474177e9cp+0 : 0x4.cef428659e2480012c38267524p+4 : inexact-ok
cosh 0x1.41a83b901d5bdp+2
= cosh downward binary32 0x5.06a0fp+0 : 0x4.c28098p+4 : inexact-ok
= cosh tonearest binary32 0x5.06a0fp+0 : 0x4.c280ap+4 : inexact-ok
= cosh towardzero binary32 0x5.06a0fp+0 : 0x4.c28098p+4 : inexact-ok
= cosh upward binary32 0x5.06a0fp+0 : 0x4.c280ap+4 : inexact-ok
= cosh downward binary64 0x5.06a0fp+0 : 0x4.c2809ebb13c34p+4 : inexact-ok
= cosh tonearest binary64 0x5.06a0fp+0 : 0x4.c2809ebb13c38p+4 : inexact-ok
= cosh towardzero binary64 0x5.06a0fp+0 : 0x4.c2809ebb13c34p+4 : inexact-ok
= cosh upward binary64 0x5.06a0fp+0 : 0x4.c2809ebb13c38p+4 : inexact-ok
= cosh downward intel96 0x5.06a0fp+0 : 0x4.c2809ebb13c362ep+4 : inexact-ok
= cosh tonearest intel96 0x5.06a0fp+0 : 0x4.c2809ebb13c362ep+4 : inexact-ok
= cosh towardzero intel96 0x5.06a0fp+0 : 0x4.c2809ebb13c362ep+4 : inexact-ok
= cosh upward intel96 0x5.06a0fp+0 : 0x4.c2809ebb13c362e8p+4 : inexact-ok
= cosh downward m68k96 0x5.06a0fp+0 : 0x4.c2809ebb13c362ep+4 : inexact-ok
= cosh tonearest m68k96 0x5.06a0fp+0 : 0x4.c2809ebb13c362ep+4 : inexact-ok
= cosh towardzero m68k96 0x5.06a0fp+0 : 0x4.c2809ebb13c362ep+4 : inexact-ok
= cosh upward m68k96 0x5.06a0fp+0 : 0x4.c2809ebb13c362e8p+4 : inexact-ok
= cosh downward binary128 0x5.06a0fp+0 : 0x4.c2809ebb13c362e0e60f23b1bd4cp+4 : inexact-ok
= cosh tonearest binary128 0x5.06a0fp+0 : 0x4.c2809ebb13c362e0e60f23b1bd5p+4 : inexact-ok
= cosh towardzero binary128 0x5.06a0fp+0 : 0x4.c2809ebb13c362e0e60f23b1bd4cp+4 : inexact-ok
= cosh upward binary128 0x5.06a0fp+0 : 0x4.c2809ebb13c362e0e60f23b1bd5p+4 : inexact-ok
= cosh downward ibm128 0x5.06a0fp+0 : 0x4.c2809ebb13c362e0e60f23b1bcp+4 : inexact-ok
= cosh tonearest ibm128 0x5.06a0fp+0 : 0x4.c2809ebb13c362e0e60f23b1bep+4 : inexact-ok
= cosh towardzero ibm128 0x5.06a0fp+0 : 0x4.c2809ebb13c362e0e60f23b1bcp+4 : inexact-ok
= cosh upward ibm128 0x5.06a0fp+0 : 0x4.c2809ebb13c362e0e60f23b1bep+4 : inexact-ok
= cosh downward binary32 0x5.06a0e8p+0 : 0x4.c28078p+4 : inexact-ok
= cosh tonearest binary32 0x5.06a0e8p+0 : 0x4.c28078p+4 : inexact-ok
= cosh towardzero binary32 0x5.06a0e8p+0 : 0x4.c28078p+4 : inexact-ok
= cosh upward binary32 0x5.06a0e8p+0 : 0x4.c2808p+4 : inexact-ok
= cosh downward binary64 0x5.06a0e8p+0 : 0x4.c28078a7e68bp+4 : inexact-ok
= cosh tonearest binary64 0x5.06a0e8p+0 : 0x4.c28078a7e68bp+4 : inexact-ok
= cosh towardzero binary64 0x5.06a0e8p+0 : 0x4.c28078a7e68bp+4 : inexact-ok
= cosh upward binary64 0x5.06a0e8p+0 : 0x4.c28078a7e68b4p+4 : inexact-ok
= cosh downward intel96 0x5.06a0e8p+0 : 0x4.c28078a7e68b1928p+4 : inexact-ok
= cosh tonearest intel96 0x5.06a0e8p+0 : 0x4.c28078a7e68b1928p+4 : inexact-ok
= cosh towardzero intel96 0x5.06a0e8p+0 : 0x4.c28078a7e68b1928p+4 : inexact-ok
= cosh upward intel96 0x5.06a0e8p+0 : 0x4.c28078a7e68b193p+4 : inexact-ok
= cosh downward m68k96 0x5.06a0e8p+0 : 0x4.c28078a7e68b1928p+4 : inexact-ok
= cosh tonearest m68k96 0x5.06a0e8p+0 : 0x4.c28078a7e68b1928p+4 : inexact-ok
= cosh towardzero m68k96 0x5.06a0e8p+0 : 0x4.c28078a7e68b1928p+4 : inexact-ok
= cosh upward m68k96 0x5.06a0e8p+0 : 0x4.c28078a7e68b193p+4 : inexact-ok
= cosh downward binary128 0x5.06a0e8p+0 : 0x4.c28078a7e68b192a8657996119ap+4 : inexact-ok
= cosh tonearest binary128 0x5.06a0e8p+0 : 0x4.c28078a7e68b192a8657996119ap+4 : inexact-ok
= cosh towardzero binary128 0x5.06a0e8p+0 : 0x4.c28078a7e68b192a8657996119ap+4 : inexact-ok
= cosh upward binary128 0x5.06a0e8p+0 : 0x4.c28078a7e68b192a8657996119a4p+4 : inexact-ok
= cosh downward ibm128 0x5.06a0e8p+0 : 0x4.c28078a7e68b192a8657996118p+4 : inexact-ok
= cosh tonearest ibm128 0x5.06a0e8p+0 : 0x4.c28078a7e68b192a865799611ap+4 : inexact-ok
= cosh towardzero ibm128 0x5.06a0e8p+0 : 0x4.c28078a7e68b192a8657996118p+4 : inexact-ok
= cosh upward ibm128 0x5.06a0e8p+0 : 0x4.c28078a7e68b192a865799611ap+4 : inexact-ok
= cosh downward binary64 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh tonearest binary64 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh towardzero binary64 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh upward binary64 0x5.06a0ee40756f4p+0 : 0x4.c280966910af4p+4 : inexact-ok
= cosh downward intel96 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh tonearest intel96 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh towardzero intel96 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh upward intel96 0x5.06a0ee40756f4p+0 : 0x4.c280966910af0008p+4 : inexact-ok
= cosh downward m68k96 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh tonearest m68k96 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh towardzero m68k96 0x5.06a0ee40756f4p+0 : 0x4.c280966910afp+4 : inexact-ok
= cosh upward m68k96 0x5.06a0ee40756f4p+0 : 0x4.c280966910af0008p+4 : inexact-ok
= cosh downward binary128 0x5.06a0ee40756f4p+0 : 0x4.c280966910af000028c5b44dfbacp+4 : inexact-ok
= cosh tonearest binary128 0x5.06a0ee40756f4p+0 : 0x4.c280966910af000028c5b44dfbbp+4 : inexact-ok
= cosh towardzero binary128 0x5.06a0ee40756f4p+0 : 0x4.c280966910af000028c5b44dfbacp+4 : inexact-ok
= cosh upward binary128 0x5.06a0ee40756f4p+0 : 0x4.c280966910af000028c5b44dfbbp+4 : inexact-ok
= cosh downward ibm128 0x5.06a0ee40756f4p+0 : 0x4.c280966910af000028c5b44dfap+4 : inexact-ok
= cosh tonearest ibm128 0x5.06a0ee40756f4p+0 : 0x4.c280966910af000028c5b44dfcp+4 : inexact-ok
= cosh towardzero ibm128 0x5.06a0ee40756f4p+0 : 0x4.c280966910af000028c5b44dfap+4 : inexact-ok
= cosh upward ibm128 0x5.06a0ee40756f4p+0 : 0x4.c280966910af000028c5b44dfcp+4 : inexact-ok
cosh 0x1.40d5c37ff8185p+2
= cosh downward binary32 0x5.03571p+0 : 0x4.b2f37p+4 : inexact-ok
= cosh tonearest binary32 0x5.03571p+0 : 0x4.b2f378p+4 : inexact-ok
= cosh towardzero binary32 0x5.03571p+0 : 0x4.b2f37p+4 : inexact-ok
= cosh upward binary32 0x5.03571p+0 : 0x4.b2f378p+4 : inexact-ok
= cosh downward binary64 0x5.03571p+0 : 0x4.b2f3753486e64p+4 : inexact-ok
= cosh tonearest binary64 0x5.03571p+0 : 0x4.b2f3753486e64p+4 : inexact-ok
= cosh towardzero binary64 0x5.03571p+0 : 0x4.b2f3753486e64p+4 : inexact-ok
= cosh upward binary64 0x5.03571p+0 : 0x4.b2f3753486e68p+4 : inexact-ok
= cosh downward intel96 0x5.03571p+0 : 0x4.b2f3753486e64318p+4 : inexact-ok
= cosh tonearest intel96 0x5.03571p+0 : 0x4.b2f3753486e64318p+4 : inexact-ok
= cosh towardzero intel96 0x5.03571p+0 : 0x4.b2f3753486e64318p+4 : inexact-ok
= cosh upward intel96 0x5.03571p+0 : 0x4.b2f3753486e6432p+4 : inexact-ok
= cosh downward m68k96 0x5.03571p+0 : 0x4.b2f3753486e64318p+4 : inexact-ok
= cosh tonearest m68k96 0x5.03571p+0 : 0x4.b2f3753486e64318p+4 : inexact-ok
= cosh towardzero m68k96 0x5.03571p+0 : 0x4.b2f3753486e64318p+4 : inexact-ok
= cosh upward m68k96 0x5.03571p+0 : 0x4.b2f3753486e6432p+4 : inexact-ok
= cosh downward binary128 0x5.03571p+0 : 0x4.b2f3753486e6431841ef6829925p+4 : inexact-ok
= cosh tonearest binary128 0x5.03571p+0 : 0x4.b2f3753486e6431841ef6829925p+4 : inexact-ok
= cosh towardzero binary128 0x5.03571p+0 : 0x4.b2f3753486e6431841ef6829925p+4 : inexact-ok
= cosh upward binary128 0x5.03571p+0 : 0x4.b2f3753486e6431841ef68299254p+4 : inexact-ok
= cosh downward ibm128 0x5.03571p+0 : 0x4.b2f3753486e6431841ef682992p+4 : inexact-ok
= cosh tonearest ibm128 0x5.03571p+0 : 0x4.b2f3753486e6431841ef682992p+4 : inexact-ok
= cosh towardzero ibm128 0x5.03571p+0 : 0x4.b2f3753486e6431841ef682992p+4 : inexact-ok
= cosh upward ibm128 0x5.03571p+0 : 0x4.b2f3753486e6431841ef682994p+4 : inexact-ok
= cosh downward binary32 0x5.035708p+0 : 0x4.b2f348p+4 : inexact-ok
= cosh tonearest binary32 0x5.035708p+0 : 0x4.b2f35p+4 : inexact-ok
= cosh towardzero binary32 0x5.035708p+0 : 0x4.b2f348p+4 : inexact-ok
= cosh upward binary32 0x5.035708p+0 : 0x4.b2f35p+4 : inexact-ok
= cosh downward binary64 0x5.035708p+0 : 0x4.b2f34f9dc5c04p+4 : inexact-ok
= cosh tonearest binary64 0x5.035708p+0 : 0x4.b2f34f9dc5c04p+4 : inexact-ok
= cosh towardzero binary64 0x5.035708p+0 : 0x4.b2f34f9dc5c04p+4 : inexact-ok
= cosh upward binary64 0x5.035708p+0 : 0x4.b2f34f9dc5c08p+4 : inexact-ok
= cosh downward intel96 0x5.035708p+0 : 0x4.b2f34f9dc5c05218p+4 : inexact-ok
= cosh tonearest intel96 0x5.035708p+0 : 0x4.b2f34f9dc5c0522p+4 : inexact-ok
= cosh towardzero intel96 0x5.035708p+0 : 0x4.b2f34f9dc5c05218p+4 : inexact-ok
= cosh upward intel96 0x5.035708p+0 : 0x4.b2f34f9dc5c0522p+4 : inexact-ok
= cosh downward m68k96 0x5.035708p+0 : 0x4.b2f34f9dc5c05218p+4 : inexact-ok
= cosh tonearest m68k96 0x5.035708p+0 : 0x4.b2f34f9dc5c0522p+4 : inexact-ok
= cosh towardzero m68k96 0x5.035708p+0 : 0x4.b2f34f9dc5c05218p+4 : inexact-ok
= cosh upward m68k96 0x5.035708p+0 : 0x4.b2f34f9dc5c0522p+4 : inexact-ok
= cosh downward binary128 0x5.035708p+0 : 0x4.b2f34f9dc5c0521d84b3bbb501fcp+4 : inexact-ok
= cosh tonearest binary128 0x5.035708p+0 : 0x4.b2f34f9dc5c0521d84b3bbb502p+4 : inexact-ok
= cosh towardzero binary128 0x5.035708p+0 : 0x4.b2f34f9dc5c0521d84b3bbb501fcp+4 : inexact-ok
= cosh upward binary128 0x5.035708p+0 : 0x4.b2f34f9dc5c0521d84b3bbb502p+4 : inexact-ok
= cosh downward ibm128 0x5.035708p+0 : 0x4.b2f34f9dc5c0521d84b3bbb5p+4 : inexact-ok
= cosh tonearest ibm128 0x5.035708p+0 : 0x4.b2f34f9dc5c0521d84b3bbb502p+4 : inexact-ok
= cosh towardzero ibm128 0x5.035708p+0 : 0x4.b2f34f9dc5c0521d84b3bbb5p+4 : inexact-ok
= cosh upward ibm128 0x5.035708p+0 : 0x4.b2f34f9dc5c0521d84b3bbb502p+4 : inexact-ok
= cosh downward binary64 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh tonearest binary64 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh towardzero binary64 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh upward binary64 0x5.03570dffe0614p+0 : 0x4.b2f36bce41eecp+4 : inexact-ok
= cosh downward intel96 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh tonearest intel96 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh towardzero intel96 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh upward intel96 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8008p+4 : inexact-ok
= cosh downward m68k96 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh tonearest m68k96 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh towardzero m68k96 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8p+4 : inexact-ok
= cosh upward m68k96 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee8008p+4 : inexact-ok
= cosh downward binary128 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee800040f77ba288b4p+4 : inexact-ok
= cosh tonearest binary128 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee800040f77ba288b4p+4 : inexact-ok
= cosh towardzero binary128 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee800040f77ba288b4p+4 : inexact-ok
= cosh upward binary128 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee800040f77ba288b8p+4 : inexact-ok
= cosh downward ibm128 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee800040f77ba288p+4 : inexact-ok
= cosh tonearest ibm128 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee800040f77ba288p+4 : inexact-ok
= cosh towardzero ibm128 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee800040f77ba288p+4 : inexact-ok
= cosh upward ibm128 0x5.03570dffe0614p+0 : 0x4.b2f36bce41ee800040f77ba28ap+4 : inexact-ok
cosh 0x1.426a50e51bd1ep+2
= cosh downward binary32 0x5.09a948p+0 : 0x4.d10578p+4 : inexact-ok
= cosh tonearest binary32 0x5.09a948p+0 : 0x4.d1058p+4 : inexact-ok
= cosh towardzero binary32 0x5.09a948p+0 : 0x4.d10578p+4 : inexact-ok
= cosh upward binary32 0x5.09a948p+0 : 0x4.d1058p+4 : inexact-ok
= cosh downward binary64 0x5.09a948p+0 : 0x4.d1057f2772a24p+4 : inexact-ok
= cosh tonearest binary64 0x5.09a948p+0 : 0x4.d1057f2772a28p+4 : inexact-ok
= cosh towardzero binary64 0x5.09a948p+0 : 0x4.d1057f2772a24p+4 : inexact-ok
= cosh upward binary64 0x5.09a948p+0 : 0x4.d1057f2772a28p+4 : inexact-ok
= cosh downward intel96 0x5.09a948p+0 : 0x4.d1057f2772a269ep+4 : inexact-ok
= cosh tonearest intel96 0x5.09a948p+0 : 0x4.d1057f2772a269e8p+4 : inexact-ok
= cosh towardzero intel96 0x5.09a948p+0 : 0x4.d1057f2772a269ep+4 : inexact-ok
= cosh upward intel96 0x5.09a948p+0 : 0x4.d1057f2772a269e8p+4 : inexact-ok
= cosh downward m68k96 0x5.09a948p+0 : 0x4.d1057f2772a269ep+4 : inexact-ok
= cosh tonearest m68k96 0x5.09a948p+0 : 0x4.d1057f2772a269e8p+4 : inexact-ok
= cosh towardzero m68k96 0x5.09a948p+0 : 0x4.d1057f2772a269ep+4 : inexact-ok
= cosh upward m68k96 0x5.09a948p+0 : 0x4.d1057f2772a269e8p+4 : inexact-ok
= cosh downward binary128 0x5.09a948p+0 : 0x4.d1057f2772a269e5e93d5f15f2ecp+4 : inexact-ok
= cosh tonearest binary128 0x5.09a948p+0 : 0x4.d1057f2772a269e5e93d5f15f2fp+4 : inexact-ok
= cosh towardzero binary128 0x5.09a948p+0 : 0x4.d1057f2772a269e5e93d5f15f2ecp+4 : inexact-ok
= cosh upward binary128 0x5.09a948p+0 : 0x4.d1057f2772a269e5e93d5f15f2fp+4 : inexact-ok
= cosh downward ibm128 0x5.09a948p+0 : 0x4.d1057f2772a269e5e93d5f15f2p+4 : inexact-ok
= cosh tonearest ibm128 0x5.09a948p+0 : 0x4.d1057f2772a269e5e93d5f15f2p+4 : inexact-ok
= cosh towardzero ibm128 0x5.09a948p+0 : 0x4.d1057f2772a269e5e93d5f15f2p+4 : inexact-ok
= cosh upward ibm128 0x5.09a948p+0 : 0x4.d1057f2772a269e5e93d5f15f4p+4 : inexact-ok
= cosh downward binary32 0x5.09a94p+0 : 0x4.d10558p+4 : inexact-ok
= cosh tonearest binary32 0x5.09a94p+0 : 0x4.d10558p+4 : inexact-ok
= cosh towardzero binary32 0x5.09a94p+0 : 0x4.d10558p+4 : inexact-ok
= cosh upward binary32 0x5.09a94p+0 : 0x4.d1056p+4 : inexact-ok
= cosh downward binary64 0x5.09a94p+0 : 0x4.d10558a01bdfcp+4 : inexact-ok
= cosh tonearest binary64 0x5.09a94p+0 : 0x4.d10558a01bep+4 : inexact-ok
= cosh towardzero binary64 0x5.09a94p+0 : 0x4.d10558a01bdfcp+4 : inexact-ok
= cosh upward binary64 0x5.09a94p+0 : 0x4.d10558a01bep+4 : inexact-ok
= cosh downward intel96 0x5.09a94p+0 : 0x4.d10558a01bdff46p+4 : inexact-ok
= cosh tonearest intel96 0x5.09a94p+0 : 0x4.d10558a01bdff46p+4 : inexact-ok
= cosh towardzero intel96 0x5.09a94p+0 : 0x4.d10558a01bdff46p+4 : inexact-ok
= cosh upward intel96 0x5.09a94p+0 : 0x4.d10558a01bdff468p+4 : inexact-ok
= cosh downward m68k96 0x5.09a94p+0 : 0x4.d10558a01bdff46p+4 : inexact-ok
= cosh tonearest m68k96 0x5.09a94p+0 : 0x4.d10558a01bdff46p+4 : inexact-ok
= cosh towardzero m68k96 0x5.09a94p+0 : 0x4.d10558a01bdff46p+4 : inexact-ok
= cosh upward m68k96 0x5.09a94p+0 : 0x4.d10558a01bdff468p+4 : inexact-ok
= cosh downward binary128 0x5.09a94p+0 : 0x4.d10558a01bdff462740c7f713f6cp+4 : inexact-ok
= cosh tonearest binary128 0x5.09a94p+0 : 0x4.d10558a01bdff462740c7f713f7p+4 : inexact-ok
= cosh towardzero binary128 0x5.09a94p+0 : 0x4.d10558a01bdff462740c7f713f6cp+4 : inexact-ok
= cosh upward binary128 0x5.09a94p+0 : 0x4.d10558a01bdff462740c7f713f7p+4 : inexact-ok
= cosh downward ibm128 0x5.09a94p+0 : 0x4.d10558a01bdff462740c7f713ep+4 : inexact-ok
= cosh tonearest ibm128 0x5.09a94p+0 : 0x4.d10558a01bdff462740c7f714p+4 : inexact-ok
= cosh towardzero ibm128 0x5.09a94p+0 : 0x4.d10558a01bdff462740c7f713ep+4 : inexact-ok
= cosh upward ibm128 0x5.09a94p+0 : 0x4.d10558a01bdff462740c7f714p+4 : inexact-ok
= cosh downward binary64 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh tonearest binary64 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh towardzero binary64 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh upward binary64 0x5.09a943946f478p+0 : 0x4.d10569ddbbf64p+4 : inexact-ok
= cosh downward intel96 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh tonearest intel96 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh towardzero intel96 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh upward intel96 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60008p+4 : inexact-ok
= cosh downward m68k96 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh tonearest m68k96 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh towardzero m68k96 0x5.09a943946f478p+0 : 0x4.d10569ddbbf6p+4 : inexact-ok
= cosh upward m68k96 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60008p+4 : inexact-ok
= cosh downward binary128 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60000094da480974cp+4 : inexact-ok
= cosh tonearest binary128 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60000094da480975p+4 : inexact-ok
= cosh towardzero binary128 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60000094da480974cp+4 : inexact-ok
= cosh upward binary128 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60000094da480975p+4 : inexact-ok
= cosh downward ibm128 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60000094da48096p+4 : inexact-ok
= cosh tonearest ibm128 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60000094da48098p+4 : inexact-ok
= cosh towardzero ibm128 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60000094da48096p+4 : inexact-ok
= cosh upward ibm128 0x5.09a943946f478p+0 : 0x4.d10569ddbbf60000094da48098p+4 : inexact-ok
cosh -0x1.41311766f07f6p+2
= cosh downward binary32 -0x5.04c458p+0 : 0x4.b9ac9p+4 : inexact-ok
= cosh tonearest binary32 -0x5.04c458p+0 : 0x4.b9ac9p+4 : inexact-ok
= cosh towardzero binary32 -0x5.04c458p+0 : 0x4.b9ac9p+4 : inexact-ok
= cosh upward binary32 -0x5.04c458p+0 : 0x4.b9ac98p+4 : inexact-ok
= cosh downward binary64 -0x5.04c458p+0 : 0x4.b9ac90a84443cp+4 : inexact-ok
= cosh tonearest binary64 -0x5.04c458p+0 : 0x4.b9ac90a84443cp+4 : inexact-ok
= cosh towardzero binary64 -0x5.04c458p+0 : 0x4.b9ac90a84443cp+4 : inexact-ok
= cosh upward binary64 -0x5.04c458p+0 : 0x4.b9ac90a84444p+4 : inexact-ok
= cosh downward intel96 -0x5.04c458p+0 : 0x4.b9ac90a84443c66p+4 : inexact-ok
= cosh tonearest intel96 -0x5.04c458p+0 : 0x4.b9ac90a84443c66p+4 : inexact-ok
= cosh towardzero intel96 -0x5.04c458p+0 : 0x4.b9ac90a84443c66p+4 : inexact-ok
= cosh upward intel96 -0x5.04c458p+0 : 0x4.b9ac90a84443c668p+4 : inexact-ok
= cosh downward m68k96 -0x5.04c458p+0 : 0x4.b9ac90a84443c66p+4 : inexact-ok
= cosh tonearest m68k96 -0x5.04c458p+0 : 0x4.b9ac90a84443c66p+4 : inexact-ok
= cosh towardzero m68k96 -0x5.04c458p+0 : 0x4.b9ac90a84443c66p+4 : inexact-ok
= cosh upward m68k96 -0x5.04c458p+0 : 0x4.b9ac90a84443c668p+4 : inexact-ok
= cosh downward binary128 -0x5.04c458p+0 : 0x4.b9ac90a84443c66064cd523852acp+4 : inexact-ok
= cosh tonearest binary128 -0x5.04c458p+0 : 0x4.b9ac90a84443c66064cd523852bp+4 : inexact-ok
= cosh towardzero binary128 -0x5.04c458p+0 : 0x4.b9ac90a84443c66064cd523852acp+4 : inexact-ok
= cosh upward binary128 -0x5.04c458p+0 : 0x4.b9ac90a84443c66064cd523852bp+4 : inexact-ok
= cosh downward ibm128 -0x5.04c458p+0 : 0x4.b9ac90a84443c66064cd523852p+4 : inexact-ok
= cosh tonearest ibm128 -0x5.04c458p+0 : 0x4.b9ac90a84443c66064cd523852p+4 : inexact-ok
= cosh towardzero ibm128 -0x5.04c458p+0 : 0x4.b9ac90a84443c66064cd523852p+4 : inexact-ok
= cosh upward ibm128 -0x5.04c458p+0 : 0x4.b9ac90a84443c66064cd523854p+4 : inexact-ok
= cosh downward binary32 -0x5.04c46p+0 : 0x4.b9acbp+4 : inexact-ok
= cosh tonearest binary32 -0x5.04c46p+0 : 0x4.b9acb8p+4 : inexact-ok
= cosh towardzero binary32 -0x5.04c46p+0 : 0x4.b9acbp+4 : inexact-ok
= cosh upward binary32 -0x5.04c46p+0 : 0x4.b9acb8p+4 : inexact-ok
= cosh downward binary64 -0x5.04c46p+0 : 0x4.b9acb674d0a9p+4 : inexact-ok
= cosh tonearest binary64 -0x5.04c46p+0 : 0x4.b9acb674d0a9p+4 : inexact-ok
= cosh towardzero binary64 -0x5.04c46p+0 : 0x4.b9acb674d0a9p+4 : inexact-ok
= cosh upward binary64 -0x5.04c46p+0 : 0x4.b9acb674d0a94p+4 : inexact-ok
= cosh downward intel96 -0x5.04c46p+0 : 0x4.b9acb674d0a9008p+4 : inexact-ok
= cosh tonearest intel96 -0x5.04c46p+0 : 0x4.b9acb674d0a9008p+4 : inexact-ok
= cosh towardzero intel96 -0x5.04c46p+0 : 0x4.b9acb674d0a9008p+4 : inexact-ok
= cosh upward intel96 -0x5.04c46p+0 : 0x4.b9acb674d0a90088p+4 : inexact-ok
= cosh downward m68k96 -0x5.04c46p+0 : 0x4.b9acb674d0a9008p+4 : inexact-ok
= cosh tonearest m68k96 -0x5.04c46p+0 : 0x4.b9acb674d0a9008p+4 : inexact-ok
= cosh towardzero m68k96 -0x5.04c46p+0 : 0x4.b9acb674d0a9008p+4 : inexact-ok
= cosh upward m68k96 -0x5.04c46p+0 : 0x4.b9acb674d0a90088p+4 : inexact-ok
= cosh downward binary128 -0x5.04c46p+0 : 0x4.b9acb674d0a90083aebc0322ff4cp+4 : inexact-ok
= cosh tonearest binary128 -0x5.04c46p+0 : 0x4.b9acb674d0a90083aebc0322ff4cp+4 : inexact-ok
= cosh towardzero binary128 -0x5.04c46p+0 : 0x4.b9acb674d0a90083aebc0322ff4cp+4 : inexact-ok
= cosh upward binary128 -0x5.04c46p+0 : 0x4.b9acb674d0a90083aebc0322ff5p+4 : inexact-ok
= cosh downward ibm128 -0x5.04c46p+0 : 0x4.b9acb674d0a90083aebc0322fep+4 : inexact-ok
= cosh tonearest ibm128 -0x5.04c46p+0 : 0x4.b9acb674d0a90083aebc0323p+4 : inexact-ok
= cosh towardzero ibm128 -0x5.04c46p+0 : 0x4.b9acb674d0a90083aebc0322fep+4 : inexact-ok
= cosh upward ibm128 -0x5.04c46p+0 : 0x4.b9acb674d0a90083aebc0323p+4 : inexact-ok
= cosh downward binary64 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b98p+4 : inexact-ok
= cosh tonearest binary64 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b98p+4 : inexact-ok
= cosh towardzero binary64 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b98p+4 : inexact-ok
= cosh upward binary64 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b984p+4 : inexact-ok
= cosh downward intel96 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b98p+4 : inexact-ok
= cosh tonearest intel96 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b98p+4 : inexact-ok
= cosh towardzero intel96 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b98p+4 : inexact-ok
= cosh upward intel96 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b980008p+4 : inexact-ok
= cosh downward m68k96 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b98p+4 : inexact-ok
= cosh tonearest m68k96 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b98p+4 : inexact-ok
= cosh towardzero m68k96 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b98p+4 : inexact-ok
= cosh upward m68k96 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b980008p+4 : inexact-ok
= cosh downward binary128 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b9800000056edb592f8p+4 : inexact-ok
= cosh tonearest binary128 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b9800000056edb592fcp+4 : inexact-ok
= cosh towardzero binary128 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b9800000056edb592f8p+4 : inexact-ok
= cosh upward binary128 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b9800000056edb592fcp+4 : inexact-ok
= cosh downward ibm128 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b9800000056edb592p+4 : inexact-ok
= cosh tonearest ibm128 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b9800000056edb592p+4 : inexact-ok
= cosh towardzero ibm128 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b9800000056edb592p+4 : inexact-ok
= cosh upward ibm128 -0x5.04c45d9bc1fd8p+0 : 0x4.b9acab280b9800000056edb594p+4 : inexact-ok

1
sysdeps/i386/Makefile
View File

@ -8,6 +8,7 @@ long-double-fcts = yes
ifeq ($(subdir),math)
# The CORE-MATH implementation assumes FLT_EVAL_METHOD == 0 to provide
# correctly rounded results.
CFLAGS-e_cosh.c += -fexcess-precision=standard
CFLAGS-e_lgamma_r.c += -fexcess-precision=standard
CFLAGS-e_gamma_r.c += -fexcess-precision=standard
CFLAGS-s_erf.c += -fexcess-precision=standard

5
sysdeps/i386/fpu/libm-test-ulps
View File

@ -24,6 +24,11 @@ float: 1
Function: "cbrt_upward":
float: 1
# sysdeps/ieee754/dbl-64/e_cosh.c shows 1ulp error even with
# -fexcess-precision=standard.
Function: "cosh":
double: 1
# sysdeps/i386/fpu/s_asinh.S is not correctly rounded
Function: "asinh":
double: 1

521
sysdeps/ieee754/dbl-64/e_cosh.c
View File

@ -1,85 +1,474 @@
/*
* ====================================================
* 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.
* ====================================================
*/
/* Correctly rounded hyperbolic cosine for binary64 values.
/* __ieee754_cosh(x)
* Method :
* mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
* 1. Replace x by |x| (cosh(x) = cosh(-x)).
* 2.
* [ exp(x) - 1 ]^2
* 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
* 2*exp(x)
*
* exp(x) + 1/exp(x)
* ln2/2 <= x <= 22 : cosh(x) := -------------------
* 2
* 22 <= x <= lnovft : cosh(x) := exp(x)/2
* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
* ln2ovft < x : cosh(x) := huge*huge (overflow)
*
* Special cases:
* cosh(x) is |x| if x is +INF, -INF, or NaN.
* only cosh(0)=1 is exact for finite x.
*/
Copyright (c) 2023-2026 Alexei Sibidanov.
The original version of this file was copied from the CORE-MATH
project (file src/binary64/cosh/cosh.c, revision 5d0c89d5).
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 <math.h>
#include <math_private.h>
#include <math-narrow-eval.h>
#include <libm-alias-finite.h>
#include <ddcoremath.h>
#include "math_config.h"
static const double one = 1.0, half=0.5, huge = 1.0e300;
static __attribute__ ((noinline)) double as_cosh_database (double, double);
static inline double
polydd_cosh (double xh, double xl, int n, const double c[][2], double *l)
{
int i = n - 1;
double ch, cl, e;
ch = fasttwosum (c[i][0], *l, &cl);
cl += c[i][1];
while (--i >= 0)
{
ch = muldd2 (xh, xl, ch, cl, &cl);
ch = fasttwosum (c[i][0], ch, &e);
cl = (cl + c[i][1]) + e;
}
*l = cl;
return ch;
}
static double __attribute__ ((cold, noinline))
as_exp_accurate (double x, double t, double th, double tl, double *l)
{
static const double ch[][2] =
{
{ 0x1p+0, 0x1.6c16bd194535dp-94 },
{ 0x1p-1, -0x1.8259d904fd34fp-93 },
{ 0x1.5555555555555p-3, 0x1.53e93e9f26e62p-57 }
};
const double l2h = 0x1.62e42ffp-13, l2l = 0x1.718432a1b0e26p-47,
l2ll = 0x1.9ff0342542fc3p-102;
double dx = x - l2h * t, dxl = l2l * t, dxll = l2ll * t + fma (l2l, t, -dxl);
double dxh = dx + dxl;
dxl = ((dx - dxh) + dxl) + dxll;
double fl = dxh
* (0x1.5555555555555p-5
+ dxh * (0x1.11111113e93e9p-7 + dxh * 0x1.6c16c169400a7p-10));
double fh = polydd (dxh, dxl, 3, ch, &fl);
fh = muldd2 (dxh, dxl, fh, fl, &fl);
fh = muldd2 (th, tl, fh, fl, &fl);
double zh = th + fh, zl = (th - zh) + fh;
double uh = zh + tl, ul = ((zh - uh) + tl) + zl;
double vh = uh + fl, vl = ((uh - vh) + fl) + ul;
*l = vl;
return vh;
}
static double __attribute__ ((noinline))
as_cosh_zero (double x)
{
static const double ch[][2] =
{
{ 0x1p-1, -0x1.c7e8db669f624p-111 }, // degree 2
{ 0x1.5555555555555p-5, 0x1.5555555556135p-59 }, // degree 4
{ 0x1.6c16c16c16c17p-10, -0x1.f49f4a6e838f2p-65 }, // degree 6
{ 0x1.a01a01a01a01ap-16, 0x1.a4ffbe15316aap-76 } // degree 8
};
static const double cl[] =
{
0x1.27e4fb7789f5cp-22, // degree 10
0x1.1eed8eff9089cp-29, // degree 12
0x1.939749ce13dadp-37, // degree 14
0x1.ae9891efb6691p-45 // degree 16
};
double x2 = x * x, x2l = fma (x, x, -x2);
double y2 = x2 * (cl[0] + x2 * (cl[1] + x2 * (cl[2] + x2 * cl[3])));
double y1 = polydd (x2, x2l, 4, ch, &y2);
y1 = muldd2 (y1, y2, x2, x2l, &y2);
double y0 = fasttwosum (1.0, y1, &y1);
y1 = fasttwosum (y1, y2, &y2);
uint64_t t = asuint64 (y1);
if (__glibc_unlikely (!(t & MANTISSA_MASK)))
{
uint64_t w = asuint64 (y2);
if ((w ^ t) >> 63)
t--;
else
t++;
y1 = asdouble (t);
}
if (__glibc_unlikely ((t & MANTISSA_MASK) == MANTISSA_MASK))
return as_cosh_database (x, y0 + y1);
return y0 + y1;
}
static __attribute__ ((noinline)) double
as_cosh_database (double x, double f)
{
static const double db[][3] =
{
{ 0x1.9a5e3cbe1985ep-4, 0x1.01492f72f984bp+0, -0x1p-107 },
{ 0x1.52a11832e847dp-3, 0x1.0381e68cac923p+0, 0x1p-104 },
{ 0x1.bf0305e2c6c37p-3, 0x1.061f4c39e16f2p+0, 0x1p-107 },
{ 0x1.17326ffc09f68p-2, 0x1.099318a43ac8p+0, 0x1p-104 },
{ 0x1.3d27bf16d8bdbp-2, 0x1.0c6091056e06ap+0, -0x1p-107 },
{ 0x1.03923f2b47c07p-1, 0x1.219c1989e3373p+0, -0x1p-54 },
{ 0x1.a6031cd5f93bap-1, 0x1.5bff041b260fep+0, -0x1p-107 },
{ 0x1.104b648f113a1p+0, 0x1.9efdca62b700ap+0, -0x1p-109 },
{ 0x1.1585720f35cd9p+0, 0x1.a5bf3acfde4b2p+0, 0x1p-105 },
{ 0x1.e9cc7ed2e1a7ep+0, 0x1.bb0ff220d8eb5p+1, -0x1p-53 },
{ 0x1.43180ea854696p+1, 0x1.91f1122b6b63ap+2, 0x1p-102 },
{ 0x1.725811dcf6782p+2, 0x1.45ea160ddc71fp+7, -0x1p-100 },
{ 0x1.5afd56f7d565bp+3, 0x1.8ff8e0ccea7cp+14, 0x1p-90 },
{ 0x1.759a2ad4c4d56p+3, 0x1.cb62eec26bd78p+15, -0x1p-92 },
{ 0x1.7fce95ea5c653p+3, 0x1.3bf8009648dcp+16, 0x1p-88 },
{ 0x1.743d5609348acp+4, 0x1.7a87a8bb7fa28p+32, -0x1p-22 },
{ 0x1.e07e71bfcf06fp+5, 0x1.91ec4412c344fp+85, 0x1p-24 },
{ 0x1.6474c604cc0d7p+6, 0x1.7a8f65ad009bdp+127, -0x1p+20 },
{ 0x1.54cd1fea7663ap+7, 0x1.c90810d354618p+244, 0x1p+135 },
{ 0x1.2da9e5e6af0bp+8, 0x1.27d6fe867d6f6p+434, 0x1p+329 },
{ 0x1.d6479eba7c971p+8, 0x1.62a88613629b6p+677, -0x1p+568 },
};
int a = 0, b = sizeof (db) / sizeof (db[0]) - 1, m = (a + b) / 2;
double ax = fabs (x);
while (a <= b)
{
if (db[m][0] < ax)
a = m + 1;
else if (db[m][0] == ax)
{
f = db[m][1] + db[m][2];
break;
}
else
b = m - 1;
m = (a + b) / 2;
}
return f;
}
double
__ieee754_cosh (double x)
{
double t,w;
int32_t ix;
/*
The function cosh(x) is approximated by a minimax polynomial
cosh(x)~1+x^2*P(x^2) for |x|<0.125. For other arguments the
identity cosh(x)=(exp(|x|)+exp(-|x|))/2 is used. For |x|<5 both
exponents are calculated with slightly higher precision than
double. For 5<|x|<36.736801 the exp(-|x|) is rather small and is
calculated with double precision but exp(|x|) is calculated with
higher than double precision. For 36.736801<|x|<710.47586
exp(-|x|) becomes too small and only exp(|x|) is calculated.
*/
static const double t0[][2] =
{
{ 0x0p+0, 0x1p+0 },
{ -0x1.19083535b085ep-56, 0x1.02c9a3e778061p+0 },
{ 0x1.d73e2a475b466p-55, 0x1.059b0d3158574p+0 },
{ 0x1.186be4bb285p-57, 0x1.0874518759bc8p+0 },
{ 0x1.8a62e4adc610ap-54, 0x1.0b5586cf9890fp+0 },
{ 0x1.03a1727c57b52p-59, 0x1.0e3ec32d3d1a2p+0 },
{ -0x1.6c51039449b3ap-54, 0x1.11301d0125b51p+0 },
{ -0x1.32fbf9af1369ep-54, 0x1.1429aaea92dep+0 },
{ -0x1.19041b9d78a76p-55, 0x1.172b83c7d517bp+0 },
{ 0x1.e5b4c7b4968e4p-55, 0x1.1a35beb6fcb75p+0 },
{ 0x1.e016e00a2643cp-54, 0x1.1d4873168b9aap+0 },
{ 0x1.dc775814a8494p-55, 0x1.2063b88628cd6p+0 },
{ 0x1.9b07eb6c70572p-54, 0x1.2387a6e756238p+0 },
{ 0x1.2bd339940e9dap-55, 0x1.26b4565e27cddp+0 },
{ 0x1.612e8afad1256p-55, 0x1.29e9df51fdee1p+0 },
{ 0x1.0024754db41d4p-54, 0x1.2d285a6e4030bp+0 },
{ 0x1.6f46ad23182e4p-55, 0x1.306fe0a31b715p+0 },
{ 0x1.32721843659a6p-54, 0x1.33c08b26416ffp+0 },
{ -0x1.63aeabf42eae2p-54, 0x1.371a7373aa9cbp+0 },
{ -0x1.5e436d661f5e2p-56, 0x1.3a7db34e59ff7p+0 },
{ 0x1.ada0911f09ebcp-55, 0x1.3dea64c123422p+0 },
{ -0x1.ef3691c309278p-58, 0x1.4160a21f72e2ap+0 },
{ 0x1.89b7a04ef80dp-59, 0x1.44e086061892dp+0 },
{ 0x1.3c1a3b69062fp-56, 0x1.486a2b5c13cdp+0 },
{ 0x1.d4397afec42e2p-56, 0x1.4bfdad5362a27p+0 },
{ -0x1.4b309d25957e4p-54, 0x1.4f9b2769d2ca7p+0 },
{ -0x1.07abe1db13cacp-55, 0x1.5342b569d4f82p+0 },
{ 0x1.9bb2c011d93acp-54, 0x1.56f4736b527dap+0 },
{ 0x1.6324c054647acp-54, 0x1.5ab07dd485429p+0 },
{ 0x1.ba6f93080e65ep-54, 0x1.5e76f15ad2148p+0 },
{ -0x1.383c17e40b496p-54, 0x1.6247eb03a5585p+0 },
{ -0x1.bb60987591c34p-54, 0x1.6623882552225p+0 },
{ -0x1.bdd3413b26456p-54, 0x1.6a09e667f3bcdp+0 },
{ -0x1.bbe3a683c88aap-57, 0x1.6dfb23c651a2fp+0 },
{ -0x1.16e4786887a9ap-55, 0x1.71f75e8ec5f74p+0 },
{ -0x1.0245957316dd4p-54, 0x1.75feb564267c9p+0 },
{ -0x1.41577ee04993p-55, 0x1.7a11473eb0187p+0 },
{ 0x1.05d02ba15797ep-56, 0x1.7e2f336cf4e62p+0 },
{ -0x1.d4c1dd41532d8p-54, 0x1.82589994cce13p+0 },
{ -0x1.fc6f89bd4f6bap-54, 0x1.868d99b4492edp+0 },
{ 0x1.6e9f156864b26p-54, 0x1.8ace5422aa0dbp+0 },
{ 0x1.5cc13a2e3976cp-55, 0x1.8f1ae99157736p+0 },
{ -0x1.75fc781b57ebcp-57, 0x1.93737b0cdc5e5p+0 },
{ -0x1.d185b7c1b85dp-54, 0x1.97d829fde4e5p+0 },
{ 0x1.c7c46b071f2bep-56, 0x1.9c49182a3f09p+0 },
{ -0x1.359495d1cd532p-54, 0x1.a0c667b5de565p+0 },
{ -0x1.d2f6edb8d41e2p-54, 0x1.a5503b23e255dp+0 },
{ 0x1.0fac90ef7fd32p-54, 0x1.a9e6b5579fdbfp+0 },
{ 0x1.7a1cd345dcc82p-54, 0x1.ae89f995ad3adp+0 },
{ -0x1.2805e3084d708p-57, 0x1.b33a2b84f15fbp+0 },
{ -0x1.5584f7e54ac3ap-56, 0x1.b7f76f2fb5e47p+0 },
{ 0x1.23dd07a2d9e84p-55, 0x1.bcc1e904bc1d2p+0 },
{ 0x1.11065895048dep-55, 0x1.c199bdd85529cp+0 },
{ 0x1.2884dff483cacp-54, 0x1.c67f12e57d14bp+0 },
{ 0x1.503cbd1e949dcp-56, 0x1.cb720dcef9069p+0 },
{ -0x1.cbc3743797a9cp-54, 0x1.d072d4a07897cp+0 },
{ 0x1.2ed02d75b3706p-55, 0x1.d5818dcfba487p+0 },
{ 0x1.c2300696db532p-54, 0x1.da9e603db3285p+0 },
{ -0x1.1a5cd4f184b5cp-54, 0x1.dfc97337b9b5fp+0 },
{ 0x1.39e8980a9cc9p-55, 0x1.e502ee78b3ff6p+0 },
{ -0x1.e9c23179c2894p-54, 0x1.ea4afa2a490dap+0 },
{ 0x1.dc7f486a4b6bp-54, 0x1.efa1bee615a27p+0 },
{ 0x1.9d3e12dd8a18ap-54, 0x1.f50765b6e454p+0 },
{ 0x1.74853f3a5931ep-55, 0x1.fa7c1819e90d8p+0 }
};
static const double t1[][2] =
{
{ 0x0p+0, 0x1p+0 },
{ 0x1.ae8e38c59c72ap-54, 0x1.000b175effdc7p+0 },
{ -0x1.7b5d0d58ea8f4p-58, 0x1.00162f3904052p+0 },
{ 0x1.4115cb6b16a8ep-54, 0x1.0021478e11ce6p+0 },
{ -0x1.d7c96f201bb2ep-55, 0x1.002c605e2e8cfp+0 },
{ 0x1.84711d4c35eap-54, 0x1.003779a95f959p+0 },
{ -0x1.0484245243778p-55, 0x1.0042936faa3d8p+0 },
{ -0x1.4b237da2025fap-54, 0x1.004dadb113dap+0 },
{ -0x1.5e00e62d6b30ep-56, 0x1.0058c86da1c0ap+0 },
{ 0x1.a1d6cedbb948p-54, 0x1.0063e3a559473p+0 },
{ -0x1.4acf197a00142p-54, 0x1.006eff583fc3dp+0 },
{ -0x1.eaf2ea42391a6p-57, 0x1.007a1b865a8cap+0 },
{ 0x1.da93f90835f76p-56, 0x1.0085382faef83p+0 },
{ -0x1.6a79084ab093cp-55, 0x1.00905554425d4p+0 },
{ 0x1.86364f8fbe8f8p-54, 0x1.009b72f41a12bp+0 },
{ -0x1.82e8e14e3110ep-55, 0x1.00a6910f3b6fdp+0 },
{ -0x1.4f6b2a7609f72p-55, 0x1.00b1afa5abcbfp+0 },
{ -0x1.e1a258ea8f71ap-56, 0x1.00bcceb7707ecp+0 },
{ 0x1.4362ca5bc26f2p-56, 0x1.00c7ee448ee02p+0 },
{ 0x1.095a56c919d02p-54, 0x1.00d30e4d0c483p+0 },
{ -0x1.406ac4e81a646p-57, 0x1.00de2ed0ee0f5p+0 },
{ 0x1.b5a6902767e08p-54, 0x1.00e94fd0398ep+0 },
{ -0x1.91b206085932p-54, 0x1.00f4714af41d3p+0 },
{ 0x1.427068ab22306p-55, 0x1.00ff93412315cp+0 },
{ 0x1.c1d0660524e08p-54, 0x1.010ab5b2cbd11p+0 },
{ -0x1.e7bdfb3204be8p-54, 0x1.0115d89ff3a8bp+0 },
{ 0x1.843aa8b9cbbc6p-55, 0x1.0120fc089ff63p+0 },
{ -0x1.34104ee7edae8p-56, 0x1.012c1fecd613bp+0 },
{ -0x1.2b6aeb6176892p-56, 0x1.0137444c9b5b5p+0 },
{ 0x1.a8cd33b8a1bb2p-56, 0x1.01426927f5278p+0 },
{ 0x1.2edc08e5da99ap-56, 0x1.014d8e7ee8d2fp+0 },
{ 0x1.57ba2dc7e0c72p-55, 0x1.0158b4517bb88p+0 },
{ 0x1.b61299ab8cdb8p-54, 0x1.0163da9fb3335p+0 },
{ -0x1.90565902c5f44p-54, 0x1.016f0169949edp+0 },
{ 0x1.70fc41c5c2d54p-55, 0x1.017a28af25567p+0 },
{ 0x1.4b9a6e145d76cp-54, 0x1.018550706ab62p+0 },
{ -0x1.008eff5142bfap-56, 0x1.019078ad6a19fp+0 },
{ -0x1.77669f033c7dep-54, 0x1.019ba16628de2p+0 },
{ -0x1.09bb78eeead0ap-54, 0x1.01a6ca9aac5f3p+0 },
{ 0x1.371231477ece6p-54, 0x1.01b1f44af9f9ep+0 },
{ 0x1.5e7626621eb5ap-56, 0x1.01bd1e77170b4p+0 },
{ -0x1.bc72b100828a4p-54, 0x1.01c8491f08f08p+0 },
{ -0x1.ce39cbbab8bbep-57, 0x1.01d37442d507p+0 },
{ 0x1.16996709da2e2p-55, 0x1.01de9fe280ac8p+0 },
{ -0x1.c11f5239bf536p-55, 0x1.01e9cbfe113efp+0 },
{ 0x1.e1d4eb5edc6b4p-55, 0x1.01f4f8958c1c6p+0 },
{ -0x1.afb99946ee3fp-54, 0x1.020025a8f6a35p+0 },
{ -0x1.8f06d8a148a32p-54, 0x1.020b533856324p+0 },
{ -0x1.2bf310fc54eb6p-55, 0x1.02168143b0281p+0 },
{ -0x1.c95a035eb4176p-54, 0x1.0221afcb09e3ep+0 },
{ -0x1.491793e46834cp-54, 0x1.022cdece68c4fp+0 },
{ -0x1.3e8d0d9c4909p-56, 0x1.02380e4dd22adp+0 },
{ -0x1.314aa16278aa4p-54, 0x1.02433e494b755p+0 },
{ 0x1.48daf888e965p-55, 0x1.024e6ec0da046p+0 },
{ 0x1.56dc8046821f4p-55, 0x1.02599fb483385p+0 },
{ 0x1.45b42356b9d46p-54, 0x1.0264d1244c719p+0 },
{ -0x1.082ef51b61d7ep-56, 0x1.027003103b10ep+0 },
{ 0x1.2106ed0920a34p-56, 0x1.027b357854772p+0 },
{ -0x1.fd4cf26ea5d0ep-54, 0x1.0286685c9e059p+0 },
{ -0x1.09f8775e78084p-54, 0x1.02919bbd1d1d8p+0 },
{ 0x1.64cbba902ca28p-58, 0x1.029ccf99d720ap+0 },
{ 0x1.4383ef231d206p-54, 0x1.02a803f2d170dp+0 },
{ 0x1.4a47a505b3a46p-54, 0x1.02b338c811703p+0 },
{ 0x1.e47120223468p-54, 0x1.02be6e199c811p+0 },
};
/* High word of |x|. */
GET_HIGH_WORD(ix,x);
ix &= 0x7fffffff;
const double s = 0x1.71547652b82fep+12;
double ax = fabs (x), v0 = fma (ax, s, 0x1.8000002p+26);
uint64_t jt = asuint64 (v0);
uint64_t v = asuint64 (v0);
uint64_t tt = ~((1 << 26) - 1l);
v &= tt;
double t = asdouble (v) - 0x1.8p26;
uint64_t aix = asuint64 (ax);
if (__glibc_unlikely (aix < UINT64_C(0x3fc0000000000000)))
{ // |x| < 0.125
if (__glibc_unlikely (aix
< UINT64_C(0x3e50000000000000))) // |x| < 0x1p-26
return fma (ax, 0x1p-55, 1);
/* q(x) = 1 + c0*x^2 + c1*x^4 + c2*x^6 + c3*x^8 + c4*x^10 is a degree-10
polynomial approximating cosh(x) on [2^-26, 0.125] such that:
|q(x) - cosh(x)| < 2^-67.518 * x^2.
This polynomial was generated with the following Sollya command:
d = [2^-26,0.125];
q=1+x^2*fpminimax((cosh(x)-1)/x^2, [|0,2,4,6,8|], [|53...|], d,
absolute);
*/
static const double c[] =
{
0x1p-1, 0x1.5555555555554p-5, 0x1.6c16c16c1d0cp-10,
0x1.a01a0075066b4p-16, 0x1.27faff8dcc1c8p-22
};
double x2 = x * x, x4 = x2 * x2,
p
= x2
* ((c[0] + x2 * c[1]) + x4 * ((c[2] + x2 * c[3]) + x4 * c[4]));
// fails with e = x2*(0x1.c8p-52), x=0x1.0f0a7d6ea89ep-14 (rndu, no FMA)
double e = x2 * 0x1.84p-51, lb = 1 + (p - e), ub = 1 + (p + e);
if (lb == ub)
return lb;
return as_cosh_zero (x);
}
/* |x| in [0,22] */
if (ix < 0x40360000) {
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
if(ix<0x3fd62e43) {
if (ix<0x3c800000) /* cosh(tiny) = 1 */
return one;
t = __expm1(fabs(x));
w = one+t;
return one+(t*t)/(w+w);
}
// treat large values apart to avoid a spurious invalid exception
if (__glibc_unlikely (aix > UINT64_C(0x408633ce8fb9f87d)))
{
// |x| > 0x1.633ce8fb9f87dp+9
if (aix > UINT64_C(0x7ff0000000000000))
return x + x; // nan
if (aix == UINT64_C(0x7ff0000000000000))
return fabs (x); // inf
return __math_oflow (0);
}
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
t = __ieee754_exp(fabs(x));
return half*t+half/t;
// now 0.125 <= |x| <= 0x1.633ce8fb9f87dp+9
/* exhaustive tests:
0.25 <= x < 2: done
2 <= x < 4: nancy (gr10)
4 <= x < 8: nancy
8 <= x < 16: explor
*/
int64_t il = ((uint64_t) jt << 14) >> 40, jl = -il;
int64_t i1 = il & 0x3f, i0 = (il >> 6) & 0x3f, ie = il >> 12;
int64_t j1 = jl & 0x3f, j0 = (jl >> 6) & 0x3f, je = jl >> 12;
double sp = asdouble ((uint64_t) (1022 + ie) << 52),
sm = asdouble ((uint64_t) (1022 + je) << 52);
double t0h = t0[i0][1], t0l = t0[i0][0];
double t1h = t1[i1][1], t1l = t1[i1][0];
double th = t0h * t1h, tl = t0h * t1l + t1h * t0l + fma (t0h, t1h, -th);
const double l2h = 0x1.62e42ffp-13, l2l = 0x1.718432a1b0e26p-47;
double dx = (ax - l2h * t) + l2l * t, dx2 = dx * dx, mx = -dx;
static const double ch[]
= { 0x1p+0, 0x1p-1, 0x1.5555555aaaaaep-3, 0x1.55555551c98cp-5 };
double pp = dx * ((ch[0] + dx * ch[1]) + dx2 * (ch[2] + dx * ch[3]));
double rh, rl;
if (__glibc_unlikely (aix > UINT64_C(0x4014000000000000)))
{ // |x| > 5
if (__glibc_unlikely (aix > UINT64_C(0x40425e4f7b2737fa)))
{ // |x| >~ 36.736801
sp = asdouble ((1021 + ie) << 52);
rh = th;
rl = tl + th * pp;
double e = 0x1.1b578c96db19bp-63 * th, lb = rh + (rl - e),
ub = rh + (rl + e);
if (lb == ub)
return (lb * sp) * 2;
th = as_exp_accurate (ax, t, th, tl, &tl);
th = fasttwosum (th, tl, &tl);
uint64_t uh = asuint64 (th), ul = asuint64 (tl);
int64_t eh = (uh >> MANTISSA_WIDTH) & 0x7ff,
el = (ul >> MANTISSA_WIDTH) & 0x7ff,
ml = (ul + 8) & MANTISSA_MASK;
th += tl;
th *= 2;
th *= sp;
/* if the exponent difference between eh and el is larger than 103,
or if the last bits from ml are <= 8 in absolute value,
call the accurate path */
if (ml <= 16 || eh - el > 103)
return as_cosh_database (x, th);
return th;
}
double q0h = t0[j0][1], q1h = t1[j1][1], qh = q0h * q1h;
th *= sp;
tl *= sp;
qh *= sm;
double pm = mx * ((ch[0] + mx * ch[1]) + dx2 * (ch[2] + mx * ch[3]));
double em = qh + qh * pm;
rh = th;
rl = (tl + em) + th * pp;
/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
if (ix < 0x40862e42) return half*__ieee754_exp(fabs(x));
double e = 0x1.202p-63 * rh, lb = rh + (rl - e), ub = rh + (rl + e);
// fails with e = 0x1.afbp-64*rh and x=0x1.4173941572a71p+2 (rndz)
if (lb == ub)
return lb;
/* |x| in [log(maxdouble), overflowthresold] */
int64_t fix;
EXTRACT_WORDS64(fix, x);
fix &= UINT64_C(0x7fffffffffffffff);
if (fix <= UINT64_C(0x408633ce8fb9f87d)) {
w = __ieee754_exp(half*fabs(x));
t = half*w;
return t*w;
th = as_exp_accurate (ax, t, th, tl, &tl);
if (__glibc_unlikely (aix > UINT64_C(0x403f666666666666)))
{
// |x| > 0x1.f666666666666p+4
rh = th + qh;
rl = ((th - rh) + qh) + tl;
}
else
{
qh = q0h * q1h;
double q0l = t0[j0][0], q1l = t1[j1][0];
double ql = q0h * q1l + q1h * q0l + fma (q0h, q1h, -qh);
qh *= sm;
ql *= sm;
qh = as_exp_accurate (-ax, -t, qh, ql, &ql);
rh = th + qh;
rl = (((th - rh) + qh) + ql) + tl;
}
}
else
{ // |x| <= 5
double q0h = t0[j0][1], q0l = t0[j0][0];
double q1h = t1[j1][1], q1l = t1[j1][0];
double qh = q0h * q1h, ql = q0h * q1l + q1h * q0l + fma (q0h, q1h, -qh);
th *= sp;
tl *= sp;
qh *= sm;
ql *= sm;
double pm = mx * ((ch[0] + mx * ch[1]) + dx2 * (ch[2] + mx * ch[3]));
double fph = th, fpl = tl + th * pp;
double fmh = qh, fml = ql + qh * pm;
/* x is INF or NaN */
if(ix>=0x7ff00000) return x*x;
/* |x| > overflowthresold, cosh(x) overflow */
return math_narrow_eval (huge * huge);
rh = fph + fmh;
rl = ((fph - rh) + fmh) + fml + fpl;
double e = 0x1.c0ap-62 * rh, lb = rh + (rl - e), ub = rh + (rl + e);
// fails with e = 0x1.855p-64*rh and x=0x1.dbf464fbc8795p+0 (rndz, no
// fma)
if (lb == ub)
return lb;
th = as_exp_accurate (ax, t, th, tl, &tl);
qh = as_exp_accurate (-ax, -t, qh, ql, &ql);
rh = th + qh;
rl = ((th - rh) + qh) + ql + tl;
}
rh = fasttwosum (rh, rl, &rl);
uint64_t uh = asuint64 (rh), ul = asuint64 (rl);
int64_t eh = (uh >> MANTISSA_WIDTH) & 0x7ff,
el = (ul >> MANTISSA_WIDTH) & 0x7ff,
ml = (ul + 8) & MANTISSA_MASK;
rh += rl;
if (__glibc_unlikely (ml <= 16 || eh - el > 103))
return as_cosh_database (x, rh);
return rh;
}
libm_alias_finite (__ieee754_cosh, __cosh)

12
sysdeps/ieee754/dbl-64/libm-test-ulps
View File

@ -35,6 +35,18 @@ double: 0
Function: "atanh_upward":
double: 0
Function: "cosh":
double: 0
Function: "cosh_downward":
double: 0
Function: "cosh_towardzero":
double: 0
Function: "cosh_upward":
double: 0
Function: "erf":
double: 0