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math: Use log2p1f from CORE-MATH
The CORE-MATH implementation is correctly rounded (for any rounding mode)
and shows better performance compared to the generic log2p1f.
The code was adapted to glibc style and to use the definition of
math_config.h (to handle errno, overflow, and underflow).
Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (Neoverse-N1,
gcc 13.3.1), and powerpc (POWER10, gcc 13.2.1):
Latency master patched improvement
x86_64 70.1462 47.0090 32.98%
x86_64v2 70.2513 47.6160 32.22%
x86_64v3 60.4840 39.9443 33.96%
i686 164.068 122.909 25.09%
aarch64 25.9169 16.9207 34.71%
power10 18.1261 9.8592 45.61%
powerpc 17.2683 9.38665 45.64%
reciprocal-throughput master patched improvement
x86_64 26.2240 16.4082 37.43%
x86_64v2 25.0911 15.7480 37.24%
x86_64v3 20.9371 11.7264 43.99%
i686 90.4209 95.3073 -5.40%
aarch64 16.8537 8.9561 46.86%
power10 12.9401 6.5555 49.34%
powerpc 9.01763 7.54745 16.30%
The performance decrease for i686 is mostly due the use of x87 fpu,
when building with '-msse2 -mfpmath=sse:
master patched improvement
latency 164.068 102.982 37.23%
reciprocal-throughput 89.1968 82.5117 7.49%
Signed-off-by: Alexei Sibidanov <sibid@uvic.ca>
Signed-off-by: Paul Zimmermann <Paul.Zimmermann@inria.fr>
Signed-off-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
Reviewed-by: DJ Delorie <dj@redhat.com>
This commit is contained in:
Adhemerval Zanella
parent
9247f53219
commit
c369580814
@ -256,3 +256,7 @@ sysdeps/ieee754/flt-32/e_log10f.c
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|||||||
(file src/binary32/log10/log10f.c in CORE-MATH)
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(file src/binary32/log10/log10f.c in CORE-MATH)
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- The code was adapted to use glibc code style and internal
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- The code was adapted to use glibc code style and internal
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functions to handle errno, overflow, and underflow.
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functions to handle errno, overflow, and underflow.
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sysdeps/ieee754/flt-32/s_log2p1f.c
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(file src/binary32/log2p1/log2p1f.c in CORE-MATH)
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- The code was adapted to use glibc code style and internal
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functions to handle errno, overflow, and underflow.
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@ -1422,22 +1422,18 @@ ldouble: 1
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Function: "log2p1":
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Function: "log2p1":
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double: 2
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double: 2
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float: 2
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ldouble: 3
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ldouble: 3
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Function: "log2p1_downward":
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Function: "log2p1_downward":
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double: 2
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double: 2
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float: 2
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ldouble: 3
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ldouble: 3
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Function: "log2p1_towardzero":
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Function: "log2p1_towardzero":
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double: 2
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double: 2
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float: 2
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ldouble: 2
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ldouble: 2
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Function: "log2p1_upward":
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Function: "log2p1_upward":
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double: 2
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double: 2
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float: 2
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ldouble: 3
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ldouble: 3
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Function: "log_advsimd":
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Function: "log_advsimd":
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@ -1009,19 +1009,15 @@ float: 1
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Function: "log2p1":
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Function: "log2p1":
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double: 2
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double: 2
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float: 2
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Function: "log2p1_downward":
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Function: "log2p1_downward":
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double: 2
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double: 2
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float: 2
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Function: "log2p1_towardzero":
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Function: "log2p1_towardzero":
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double: 2
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double: 2
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float: 2
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Function: "log2p1_upward":
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Function: "log2p1_upward":
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double: 2
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double: 2
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float: 2
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Function: "log_towardzero":
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Function: "log_towardzero":
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double: 1
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double: 1
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@ -246,11 +246,9 @@ float: 1
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Function: "log2p1":
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Function: "log2p1":
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double: 1
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double: 1
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float: 2
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Function: "logp1":
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Function: "logp1":
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double: 1
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double: 1
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float: 1
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Function: "pow":
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Function: "pow":
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double: 1
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double: 1
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@ -1006,19 +1006,15 @@ float: 3
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Function: "log2p1":
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Function: "log2p1":
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double: 1
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double: 1
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float: 2
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Function: "log2p1_downward":
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Function: "log2p1_downward":
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double: 2
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double: 2
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float: 2
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Function: "log2p1_towardzero":
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Function: "log2p1_towardzero":
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double: 2
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double: 2
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float: 2
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Function: "log2p1_upward":
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Function: "log2p1_upward":
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double: 2
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double: 2
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float: 2
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Function: "log_downward":
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Function: "log_downward":
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float: 2
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float: 2
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@ -1029,19 +1029,15 @@ float: 3
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Function: "log2p1":
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Function: "log2p1":
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double: 2
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double: 2
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float: 2
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Function: "log2p1_downward":
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Function: "log2p1_downward":
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double: 2
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double: 2
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float: 2
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Function: "log2p1_towardzero":
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Function: "log2p1_towardzero":
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double: 2
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double: 2
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float: 2
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Function: "log2p1_upward":
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Function: "log2p1_upward":
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double: 2
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double: 2
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float: 2
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Function: "log_downward":
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Function: "log_downward":
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float: 2
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float: 2
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@ -1484,25 +1484,21 @@ ldouble: 1
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Function: "log2p1":
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Function: "log2p1":
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double: 1
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double: 1
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float: 1
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float128: 3
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float128: 3
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ldouble: 4
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ldouble: 4
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Function: "log2p1_downward":
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Function: "log2p1_downward":
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double: 2
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double: 2
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float: 2
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float128: 3
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float128: 3
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ldouble: 3
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ldouble: 3
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Function: "log2p1_towardzero":
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Function: "log2p1_towardzero":
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double: 2
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double: 2
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float: 2
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float128: 2
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float128: 2
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ldouble: 3
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ldouble: 3
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Function: "log2p1_upward":
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Function: "log2p1_upward":
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double: 2
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double: 2
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float: 2
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float128: 3
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float128: 3
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ldouble: 5
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ldouble: 5
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@ -1487,25 +1487,21 @@ ldouble: 1
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Function: "log2p1":
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Function: "log2p1":
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double: 1
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double: 1
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float: 1
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float128: 3
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float128: 3
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ldouble: 4
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ldouble: 4
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Function: "log2p1_downward":
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Function: "log2p1_downward":
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double: 2
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double: 2
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float: 2
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float128: 3
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float128: 3
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ldouble: 4
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ldouble: 4
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Function: "log2p1_towardzero":
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Function: "log2p1_towardzero":
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double: 2
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double: 2
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float: 2
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float128: 2
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float128: 2
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ldouble: 4
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ldouble: 4
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Function: "log2p1_upward":
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Function: "log2p1_upward":
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double: 1
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double: 1
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float: 2
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float128: 3
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float128: 3
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ldouble: 5
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ldouble: 5
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248
sysdeps/ieee754/flt-32/s_log2p1f.c
Normal file
248
sysdeps/ieee754/flt-32/s_log2p1f.c
Normal file
@ -0,0 +1,248 @@
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/* Correctly-rounded biased argument natural logarithm function for binary32
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value.
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Copyright (c) 2022-2024 Alexei Sibidanov.
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This file is part of the CORE-MATH project
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project (file src/binary32/log2p1/log2p1f.c revision bc385c2).
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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*/
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#include <errno.h>
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#include <math.h>
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#include <math-underflow.h>
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#include <libm-alias-float.h>
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#include "math_config.h"
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float
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__log2p1f (float x)
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{
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static const double ix[] =
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{
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0x1p+0, 0x1.fc07f01fcp-1, 0x1.f81f81f82p-1,
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0x1.f44659e4ap-1, 0x1.f07c1f07cp-1, 0x1.ecc07b302p-1,
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0x1.e9131abfp-1, 0x1.e573ac902p-1, 0x1.e1e1e1e1ep-1,
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0x1.de5d6e3f8p-1, 0x1.dae6076bap-1, 0x1.d77b654b8p-1,
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0x1.d41d41d42p-1, 0x1.d0cb58f6ep-1, 0x1.cd8568904p-1,
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0x1.ca4b3055ep-1, 0x1.c71c71c72p-1, 0x1.c3f8f01c4p-1,
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0x1.c0e070382p-1, 0x1.bdd2b8994p-1, 0x1.bacf914c2p-1,
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0x1.b7d6c3ddap-1, 0x1.b4e81b4e8p-1, 0x1.b2036406cp-1,
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0x1.af286bca2p-1, 0x1.ac5701ac6p-1, 0x1.a98ef606ap-1,
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0x1.a6d01a6dp-1, 0x1.a41a41a42p-1, 0x1.a16d3f97ap-1,
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0x1.9ec8e951p-1, 0x1.9c2d14ee4p-1, 0x1.99999999ap-1,
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0x1.970e4f80cp-1, 0x1.948b0fcd6p-1, 0x1.920fb49dp-1,
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0x1.8f9c18f9cp-1, 0x1.8d3018d3p-1, 0x1.8acb90f6cp-1,
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0x1.886e5f0acp-1, 0x1.861861862p-1, 0x1.83c977ab2p-1,
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0x1.818181818p-1, 0x1.7f405fd02p-1, 0x1.7d05f417ep-1,
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0x1.7ad2208ep-1, 0x1.78a4c8178p-1, 0x1.767dce434p-1,
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0x1.745d1745ep-1, 0x1.724287f46p-1, 0x1.702e05c0cp-1,
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0x1.6e1f76b44p-1, 0x1.6c16c16c2p-1, 0x1.6a13cd154p-1,
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0x1.681681682p-1, 0x1.661ec6a52p-1, 0x1.642c8590cp-1,
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0x1.623fa7702p-1, 0x1.605816058p-1, 0x1.5e75bb8dp-1,
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0x1.5c9882b94p-1, 0x1.5ac056b02p-1, 0x1.58ed23082p-1,
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0x1.571ed3c5p-1, 0x1.555555556p-1, 0x1.5390948f4p-1,
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0x1.51d07eae2p-1, 0x1.501501502p-1, 0x1.4e5e0a73p-1,
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0x1.4cab88726p-1, 0x1.4afd6a052p-1, 0x1.49539e3b2p-1,
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0x1.47ae147aep-1, 0x1.460cbc7f6p-1, 0x1.446f86562p-1,
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0x1.42d6625d6p-1, 0x1.414141414p-1, 0x1.3fb013fbp-1,
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0x1.3e22cbce4p-1, 0x1.3c995a47cp-1, 0x1.3b13b13b2p-1,
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0x1.3991c2c18p-1, 0x1.381381382p-1, 0x1.3698df3dep-1,
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0x1.3521cfb2cp-1, 0x1.33ae45b58p-1, 0x1.323e34a2cp-1,
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0x1.30d19013p-1, 0x1.2f684bda2p-1, 0x1.2e025c04cp-1,
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0x1.2c9fb4d82p-1, 0x1.2b404ad02p-1, 0x1.29e4129e4p-1,
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0x1.288b01288p-1, 0x1.27350b882p-1, 0x1.25e22708p-1,
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0x1.24924924ap-1, 0x1.23456789ap-1, 0x1.21fb78122p-1,
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0x1.20b470c68p-1, 0x1.1f7047dc2p-1, 0x1.1e2ef3b4p-1,
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0x1.1cf06ada2p-1, 0x1.1bb4a4046p-1, 0x1.1a7b9611ap-1,
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0x1.19453808cp-1, 0x1.181181182p-1, 0x1.16e068942p-1,
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0x1.15b1e5f76p-1, 0x1.1485f0e0ap-1, 0x1.135c81136p-1,
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0x1.12358e75ep-1, 0x1.111111112p-1, 0x1.0fef010fep-1,
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0x1.0ecf56be6p-1, 0x1.0db20a89p-1, 0x1.0c9714fbcp-1,
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0x1.0b7e6ec26p-1, 0x1.0a6810a68p-1, 0x1.0953f3902p-1,
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0x1.084210842p-1, 0x1.073260a48p-1, 0x1.0624dd2f2p-1,
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0x1.05197f7d8p-1, 0x1.041041042p-1, 0x1.03091b52p-1,
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0x1.020408102p-1, 0x1.01010101p-1, 0x1p-1
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};
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static const double lix[] = {
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0x0p+0, -0x1.6fe50b6f1eafap-7, -0x1.6e79685c160d5p-6,
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-0x1.11cd1d51955bap-5, -0x1.6bad37591e03p-5, -0x1.c4dfab908ddb5p-5,
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-0x1.0eb389fab4795p-4, -0x1.3aa2fdd26ae99p-4, -0x1.663f6faca846bp-4,
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-0x1.918a16e4cb157p-4, -0x1.bc84240a78a13p-4, -0x1.e72ec1181cfb1p-4,
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-0x1.08c588cd964e4p-3, -0x1.1dcd19759f2e3p-3, -0x1.32ae9e27627c6p-3,
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-0x1.476a9f989a58ap-3, -0x1.5c01a39fa6533p-3, -0x1.70742d4eed455p-3,
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-0x1.84c2bd02d6434p-3, -0x1.98edd077e9f0ap-3, -0x1.acf5e2db31eeap-3,
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-0x1.c0db6cddaa82dp-3, -0x1.d49ee4c33121ap-3, -0x1.e840be751d775p-3,
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-0x1.fbc16b9003e0bp-3, -0x1.0790adbae3fcp-2, -0x1.11307dad465b5p-2,
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-0x1.1ac05b2924cc5p-2, -0x1.24407ab0cc41p-2, -0x1.2db10fc4ea424p-2,
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-0x1.37124cea58697p-2, -0x1.406463b1d455dp-2, -0x1.49a784bcbaa37p-2,
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-0x1.52dbdfc4f341dp-2, -0x1.5c01a39ff2c9bp-2, -0x1.6518fe46abaa5p-2,
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-0x1.6e221cd9d6933p-2, -0x1.771d2ba7f5791p-2, -0x1.800a56315ee2ap-2,
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||||||
|
-0x1.88e9c72df8611p-2, -0x1.91bba891d495fp-2, -0x1.9a8023920fa4dp-2,
|
||||||
|
-0x1.a33760a7fbca6p-2, -0x1.abe18797d2effp-2, -0x1.b47ebf734b923p-2,
|
||||||
|
-0x1.bd0f2e9eb2b84p-2, -0x1.c592fad2be1aap-2, -0x1.ce0a4923cf5e6p-2,
|
||||||
|
-0x1.d6753e02f4ebcp-2, -0x1.ded3fd445afp-2, -0x1.e726aa1e558fep-2,
|
||||||
|
-0x1.ef6d67325ba38p-2, -0x1.f7a8568c8aea6p-2, -0x1.ffd799a81be87p-2,
|
||||||
|
0x1.f804ae8d33c4p-2, 0x1.efec61b04af4ep-2, 0x1.e7df5fe572606p-2,
|
||||||
|
0x1.dfdd89d5b0009p-2, 0x1.d7e6c0abbd924p-2, 0x1.cffae611a74d6p-2,
|
||||||
|
0x1.c819dc2d8578cp-2, 0x1.c043859e5bdbcp-2, 0x1.b877c57b47c04p-2,
|
||||||
|
0x1.b0b67f4f29a66p-2, 0x1.a8ff97183ed07p-2, 0x1.a152f14293c74p-2,
|
||||||
|
0x1.99b072a9289cap-2, 0x1.921800927e284p-2, 0x1.8a8980ac4113p-2,
|
||||||
|
0x1.8304d90c2859dp-2, 0x1.7b89f02cbd49ap-2, 0x1.7418aceb84ab1p-2,
|
||||||
|
0x1.6cb0f68656c95p-2, 0x1.6552b49993dc2p-2, 0x1.5dfdcf1eacd7bp-2,
|
||||||
|
0x1.56b22e6b97c18p-2, 0x1.4f6fbb2ce6943p-2, 0x1.48365e6957b42p-2,
|
||||||
|
0x1.4106017c0dbcfp-2, 0x1.39de8e15727d9p-2, 0x1.32bfee37489bcp-2,
|
||||||
|
0x1.2baa0c34989c3p-2, 0x1.249cd2b177fd5p-2, 0x1.1d982c9d50468p-2,
|
||||||
|
0x1.169c0536677acp-2, 0x1.0fa848045f67bp-2, 0x1.08bce0d9a7c6p-2,
|
||||||
|
0x1.01d9bbcf66a2cp-2, 0x1.f5fd8a90e2d85p-3, 0x1.e857d3d3af1e5p-3,
|
||||||
|
0x1.dac22d3ec5f4ep-3, 0x1.cd3c712db459ap-3, 0x1.bfc67a7ff3c22p-3,
|
||||||
|
0x1.b2602497678f4p-3, 0x1.a5094b555a1f8p-3, 0x1.97c1cb136b96fp-3,
|
||||||
|
0x1.8a8980ac8652dp-3, 0x1.7d60496c83f66p-3, 0x1.7046031c7cdafp-3,
|
||||||
|
0x1.633a8bf460335p-3, 0x1.563dc2a08b102p-3, 0x1.494f863bbc1dep-3,
|
||||||
|
0x1.3c6fb6507a37ep-3, 0x1.2f9e32d5257ecp-3, 0x1.22dadc2a627efp-3,
|
||||||
|
0x1.1625931802e49p-3, 0x1.097e38cef9519p-3, 0x1.f9c95dc138295p-4,
|
||||||
|
0x1.e0b1ae90505f6p-4, 0x1.c7b528b5fcffap-4, 0x1.aed391abb17a1p-4,
|
||||||
|
0x1.960caf9bd35eap-4, 0x1.7d60496e3edebp-4, 0x1.64ce26bf2108ep-4,
|
||||||
|
0x1.4c560fe5b573bp-4, 0x1.33f7cde24adfbp-4, 0x1.1bb32a5ed9353p-4,
|
||||||
|
0x1.0387efbd3006ep-4, 0x1.d6ebd1f1d0955p-5, 0x1.a6f9c37a8beabp-5,
|
||||||
|
0x1.77394c9d6762cp-5, 0x1.47aa07358e1a4p-5, 0x1.184b8e4d490efp-5,
|
||||||
|
0x1.d23afc4d95c78p-6, 0x1.743ee8678a7cbp-6, 0x1.16a21e243bf78p-6,
|
||||||
|
0x1.72c7ba20c907ep-7, 0x1.720d9c0536e17p-8, 0x0p+0
|
||||||
|
};
|
||||||
|
|
||||||
|
double z = x;
|
||||||
|
uint32_t ux = asuint (x);
|
||||||
|
uint32_t ax = ux & (~0u >> 1);
|
||||||
|
if (__glibc_unlikely (ux >= 0x17fu << 23))
|
||||||
|
{ /* x <= -1 */
|
||||||
|
if (ux == (0x17fu << 23))
|
||||||
|
return __math_divzerof (1);
|
||||||
|
if (ux > (0x1ffu << 23))
|
||||||
|
return x + x; /* nan */
|
||||||
|
return __math_invalidf (x);
|
||||||
|
}
|
||||||
|
else if (__glibc_unlikely (ax >= (0xff << 23)))
|
||||||
|
{ /* +inf, nan */
|
||||||
|
if (ax > (0xff << 23))
|
||||||
|
return x + x; /* nan */
|
||||||
|
return INFINITY;
|
||||||
|
}
|
||||||
|
else if (__glibc_likely (ax < 0x3cb7aa26u))
|
||||||
|
{ /* |x| < 0x1.6f544cp-6 */
|
||||||
|
double z2 = z * z, z4 = z2 * z2;
|
||||||
|
if ( __glibc_likely (ax < 0x3b9d9d34u))
|
||||||
|
{ /* |x| < 0x1.3b3a68p-8 */
|
||||||
|
if (__glibc_likely (ax < 0x39638a7eu))
|
||||||
|
{ /* |x| < 0x1.c714fcp-13 */
|
||||||
|
if (__glibc_likely (ax < 0x329c5639u))
|
||||||
|
{ /* |x| < 0x1.38ac72p-26 */
|
||||||
|
static const double c[] =
|
||||||
|
{
|
||||||
|
0x1.71547652b82fep+0, -0x1.71547652b82ffp-1
|
||||||
|
};
|
||||||
|
return z * (c[0] + z * c[1]);
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
|
if (__glibc_unlikely (ux == 0x32ff7045u))
|
||||||
|
return 0x1.70851ap-25f - 0x1.8p-80f;
|
||||||
|
if (__glibc_unlikely (ux == 0xb395efbbu))
|
||||||
|
return -0x1.b0a00ap-24f + 0x1p-76f;
|
||||||
|
if (__glibc_unlikely (ux == 0x35a14df7u))
|
||||||
|
return 0x1.d16d2p-20f + 0x1p-72f;
|
||||||
|
if (__glibc_unlikely (ux == 0x3841cb81u))
|
||||||
|
return 0x1.17949ep-14f + 0x1p-67f;
|
||||||
|
static const double c[] =
|
||||||
|
{
|
||||||
|
0x1.71547652b82fep+0, -0x1.71547652b82fdp-1,
|
||||||
|
0x1.ec709ead0c9a7p-2, -0x1.7154773c1cb29p-2
|
||||||
|
};
|
||||||
|
return z * ((c[0] + z * c[1]) + z2 * (c[2] + z * c[3]));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
|
if (__glibc_unlikely (ux == 0xbac9363du))
|
||||||
|
return -0x1.2282aap-9f + 0x1p-61f;
|
||||||
|
static const double c[] =
|
||||||
|
{
|
||||||
|
0x1.71547652b82fep+0, -0x1.71547652b83p-1,
|
||||||
|
0x1.ec709dc28f51bp-2, -0x1.7154765157748p-2,
|
||||||
|
0x1.2778a510a3682p-2, -0x1.ec745df1551fcp-3
|
||||||
|
};
|
||||||
|
return z
|
||||||
|
* ((c[0] + z * c[1]) + z2 * (c[2] + z * c[3])
|
||||||
|
+ z4 * ((c[4] + z * c[5])));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
|
static const double c[] =
|
||||||
|
{
|
||||||
|
0x1.71547652b82fep+0, -0x1.71547652b82fbp-1,
|
||||||
|
0x1.ec709dc3b6a73p-2, -0x1.71547652dc09p-2,
|
||||||
|
0x1.2776c1a88901p-2, -0x1.ec7095bd4d208p-3,
|
||||||
|
0x1.a66bec7fc8f7p-3, -0x1.71a900fc3f3f9p-3
|
||||||
|
};
|
||||||
|
return z
|
||||||
|
* ((c[0] + z * c[1]) + z2 * (c[2] + z * c[3])
|
||||||
|
+ z4 * ((c[4] + z * c[5]) + z2 * (c[6] + z * c[7])));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{ /* |x| >= 0x1.6f544cp-6 */
|
||||||
|
float h, l;
|
||||||
|
/* With gcc 6.3.0, if we return 0x1.e90026p+4f + 0x1.fp-21
|
||||||
|
in the second exceptional case, with rounding up it yields
|
||||||
|
0x1.e90026p+4 which is incorrect, thus we use this workaround. See
|
||||||
|
https://gcc.gnu.org/bugzilla/show_bug.cgi?id=112367. */
|
||||||
|
if (__glibc_unlikely (ux == 0x52928e33u))
|
||||||
|
{
|
||||||
|
h = 0x1.318ffap+5f;
|
||||||
|
l = 0x1.fp-20f;
|
||||||
|
return h + l;
|
||||||
|
}
|
||||||
|
if (__glibc_unlikely (ux == 0x4ebd09e3u))
|
||||||
|
{
|
||||||
|
h = 0x1.e90026p+4f;
|
||||||
|
l = 0x1.fp-21;
|
||||||
|
return h + l;
|
||||||
|
}
|
||||||
|
uint64_t tp = asuint64 (z + 1.0);
|
||||||
|
uint64_t m = tp & (~(uint64_t) 0 >> 12);
|
||||||
|
int e = (tp >> 52) - 0x3ff;
|
||||||
|
int j = (m + ((int64_t) 1 << (52 - 8))) >> (52 - 7), k = j > 53;
|
||||||
|
e += k;
|
||||||
|
double xd = asdouble (m | (uint64_t) 0x3ff << 52);
|
||||||
|
z = fma (xd, ix[j], -1.0);
|
||||||
|
static const double c[] =
|
||||||
|
{
|
||||||
|
0x1.71547652b82fep+0, -0x1.71547652b82ffp-1, 0x1.ec709dc32988bp-2,
|
||||||
|
-0x1.715476521ec2bp-2, 0x1.277801a1ad904p-2, -0x1.ec731704d6a88p-3
|
||||||
|
};
|
||||||
|
double z2 = z * z;
|
||||||
|
double c0 = c[0] + z * c[1];
|
||||||
|
double c2 = c[2] + z * c[3];
|
||||||
|
double c4 = c[4] + z * c[5];
|
||||||
|
c0 += z2 * (c2 + z2 * c4);
|
||||||
|
return (z * c0 - lix[j]) + e;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
libm_alias_float (__log2p1, log2p1)
|
||||||
@ -1252,22 +1252,18 @@ ldouble: 1
|
|||||||
|
|
||||||
Function: "log2p1":
|
Function: "log2p1":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 3
|
ldouble: 3
|
||||||
|
|
||||||
Function: "log2p1_downward":
|
Function: "log2p1_downward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 3
|
ldouble: 3
|
||||||
|
|
||||||
Function: "log2p1_towardzero":
|
Function: "log2p1_towardzero":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 2
|
ldouble: 2
|
||||||
|
|
||||||
Function: "log2p1_upward":
|
Function: "log2p1_upward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 3
|
ldouble: 3
|
||||||
|
|
||||||
Function: "log_downward":
|
Function: "log_downward":
|
||||||
|
|||||||
@ -1091,19 +1091,15 @@ double: 1
|
|||||||
|
|
||||||
Function: "log2p1":
|
Function: "log2p1":
|
||||||
double: 1
|
double: 1
|
||||||
float: 2
|
|
||||||
|
|
||||||
Function: "log2p1_downward":
|
Function: "log2p1_downward":
|
||||||
double: 1
|
double: 1
|
||||||
float: 2
|
|
||||||
|
|
||||||
Function: "log2p1_towardzero":
|
Function: "log2p1_towardzero":
|
||||||
double: 1
|
double: 1
|
||||||
float: 2
|
|
||||||
|
|
||||||
Function: "log2p1_upward":
|
Function: "log2p1_upward":
|
||||||
double: 1
|
double: 1
|
||||||
float: 2
|
|
||||||
|
|
||||||
Function: "logp1":
|
Function: "logp1":
|
||||||
double: 1
|
double: 1
|
||||||
|
|||||||
@ -1003,22 +1003,18 @@ float: 3
|
|||||||
|
|
||||||
Function: "log2p1":
|
Function: "log2p1":
|
||||||
double: 1
|
double: 1
|
||||||
float: 2
|
|
||||||
ldouble: 1
|
ldouble: 1
|
||||||
|
|
||||||
Function: "log2p1_downward":
|
Function: "log2p1_downward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 2
|
ldouble: 2
|
||||||
|
|
||||||
Function: "log2p1_towardzero":
|
Function: "log2p1_towardzero":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 2
|
ldouble: 2
|
||||||
|
|
||||||
Function: "log2p1_upward":
|
Function: "log2p1_upward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 1
|
ldouble: 1
|
||||||
|
|
||||||
Function: "log_downward":
|
Function: "log_downward":
|
||||||
|
|||||||
@ -1260,22 +1260,18 @@ ldouble: 1
|
|||||||
|
|
||||||
Function: "log2p1":
|
Function: "log2p1":
|
||||||
double: 1
|
double: 1
|
||||||
float: 2
|
|
||||||
ldouble: 3
|
ldouble: 3
|
||||||
|
|
||||||
Function: "log2p1_downward":
|
Function: "log2p1_downward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 3
|
ldouble: 3
|
||||||
|
|
||||||
Function: "log2p1_towardzero":
|
Function: "log2p1_towardzero":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 2
|
ldouble: 2
|
||||||
|
|
||||||
Function: "log2p1_upward":
|
Function: "log2p1_upward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 3
|
ldouble: 3
|
||||||
|
|
||||||
Function: "log_downward":
|
Function: "log_downward":
|
||||||
|
|||||||
@ -1569,25 +1569,21 @@ ldouble: 4
|
|||||||
|
|
||||||
Function: "log2p1":
|
Function: "log2p1":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
float128: 3
|
float128: 3
|
||||||
ldouble: 2
|
ldouble: 2
|
||||||
|
|
||||||
Function: "log2p1_downward":
|
Function: "log2p1_downward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
float128: 3
|
float128: 3
|
||||||
ldouble: 4
|
ldouble: 4
|
||||||
|
|
||||||
Function: "log2p1_towardzero":
|
Function: "log2p1_towardzero":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
float128: 2
|
float128: 2
|
||||||
ldouble: 5
|
ldouble: 5
|
||||||
|
|
||||||
Function: "log2p1_upward":
|
Function: "log2p1_upward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
float128: 3
|
float128: 3
|
||||||
ldouble: 6
|
ldouble: 6
|
||||||
|
|
||||||
|
|||||||
@ -1317,22 +1317,18 @@ ldouble: 4
|
|||||||
|
|
||||||
Function: "log2p1":
|
Function: "log2p1":
|
||||||
double: 1
|
double: 1
|
||||||
float: 2
|
|
||||||
ldouble: 2
|
ldouble: 2
|
||||||
|
|
||||||
Function: "log2p1_downward":
|
Function: "log2p1_downward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 4
|
ldouble: 4
|
||||||
|
|
||||||
Function: "log2p1_towardzero":
|
Function: "log2p1_towardzero":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 5
|
ldouble: 5
|
||||||
|
|
||||||
Function: "log2p1_upward":
|
Function: "log2p1_upward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 6
|
ldouble: 6
|
||||||
|
|
||||||
Function: "log_downward":
|
Function: "log_downward":
|
||||||
|
|||||||
@ -1209,7 +1209,6 @@ ldouble: 1
|
|||||||
|
|
||||||
Function: "log2p1":
|
Function: "log2p1":
|
||||||
double: 1
|
double: 1
|
||||||
float: 1
|
|
||||||
ldouble: 3
|
ldouble: 3
|
||||||
|
|
||||||
Function: "log_downward":
|
Function: "log_downward":
|
||||||
|
|||||||
@ -1252,22 +1252,18 @@ ldouble: 1
|
|||||||
|
|
||||||
Function: "log2p1":
|
Function: "log2p1":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 3
|
ldouble: 3
|
||||||
|
|
||||||
Function: "log2p1_downward":
|
Function: "log2p1_downward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 3
|
ldouble: 3
|
||||||
|
|
||||||
Function: "log2p1_towardzero":
|
Function: "log2p1_towardzero":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 2
|
ldouble: 2
|
||||||
|
|
||||||
Function: "log2p1_upward":
|
Function: "log2p1_upward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 3
|
ldouble: 3
|
||||||
|
|
||||||
Function: "log_downward":
|
Function: "log_downward":
|
||||||
|
|||||||
@ -1251,22 +1251,18 @@ ldouble: 1
|
|||||||
|
|
||||||
Function: "log2p1":
|
Function: "log2p1":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 3
|
ldouble: 3
|
||||||
|
|
||||||
Function: "log2p1_downward":
|
Function: "log2p1_downward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 3
|
ldouble: 3
|
||||||
|
|
||||||
Function: "log2p1_towardzero":
|
Function: "log2p1_towardzero":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 2
|
ldouble: 2
|
||||||
|
|
||||||
Function: "log2p1_upward":
|
Function: "log2p1_upward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 3
|
ldouble: 3
|
||||||
|
|
||||||
Function: "log_downward":
|
Function: "log_downward":
|
||||||
|
|||||||
@ -1260,22 +1260,18 @@ ldouble: 1
|
|||||||
|
|
||||||
Function: "log2p1":
|
Function: "log2p1":
|
||||||
double: 1
|
double: 1
|
||||||
float: 2
|
|
||||||
ldouble: 3
|
ldouble: 3
|
||||||
|
|
||||||
Function: "log2p1_downward":
|
Function: "log2p1_downward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 3
|
ldouble: 3
|
||||||
|
|
||||||
Function: "log2p1_towardzero":
|
Function: "log2p1_towardzero":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 2
|
ldouble: 2
|
||||||
|
|
||||||
Function: "log2p1_upward":
|
Function: "log2p1_upward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
ldouble: 3
|
ldouble: 3
|
||||||
|
|
||||||
Function: "log_downward":
|
Function: "log_downward":
|
||||||
|
|||||||
@ -1910,25 +1910,21 @@ float: 1
|
|||||||
|
|
||||||
Function: "log2p1":
|
Function: "log2p1":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
float128: 3
|
float128: 3
|
||||||
ldouble: 4
|
ldouble: 4
|
||||||
|
|
||||||
Function: "log2p1_downward":
|
Function: "log2p1_downward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
float128: 3
|
float128: 3
|
||||||
ldouble: 4
|
ldouble: 4
|
||||||
|
|
||||||
Function: "log2p1_towardzero":
|
Function: "log2p1_towardzero":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
float128: 2
|
float128: 2
|
||||||
ldouble: 4
|
ldouble: 4
|
||||||
|
|
||||||
Function: "log2p1_upward":
|
Function: "log2p1_upward":
|
||||||
double: 2
|
double: 2
|
||||||
float: 2
|
|
||||||
float128: 3
|
float128: 3
|
||||||
ldouble: 5
|
ldouble: 5
|
||||||
|
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user