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replace tgammaf by the CORE-MATH implementation
The CORE-MATH implementation is correctly rounded (for any rounding mode). This can be checked by exhaustive tests in a few minutes since there are less than 2^32 values to check against for example GNU MPFR. This patch also adds some bench values for tgammaf. Tested on x86_64 and x86 (cfarm26). With the initial GNU libc code it gave on an Intel(R) Core(TM) i7-8700: "tgammaf": { "": { "duration": 3.50188e+09, "iterations": 2e+07, "max": 602.891, "min": 65.1415, "mean": 175.094 } } With the new code: "tgammaf": { "": { "duration": 3.30825e+09, "iterations": 5e+07, "max": 211.592, "min": 32.0325, "mean": 66.1649 } } With the initial GNU libc code it gave on cfarm26 (i686): "tgammaf": { "": { "duration": 3.70505e+09, "iterations": 6e+06, "max": 2420.23, "min": 243.154, "mean": 617.509 } } With the new code: "tgammaf": { "": { "duration": 3.24497e+09, "iterations": 1.8e+07, "max": 1238.15, "min": 101.155, "mean": 180.276 } } Signed-off-by: Alexei Sibidanov <sibid@uvic.ca> Signed-off-by: Paul Zimmermann <Paul.Zimmermann@inria.fr> Changes in v2: - include <math.h> (fix the linknamespace failures) - restored original benchtests/strcoll-inputs/filelist#en_US.UTF-8 file - restored original wrapper code (math/w_tgammaf_compat.c), except for the dealing with the sign - removed the tgammaf/float entries in all libm-test-ulps files - address other comments from Joseph Myers (https://sourceware.org/pipermail/libc-alpha/2024-July/158736.html) Changes in v3: - pass NULL argument for signgam from w_tgammaf_compat.c - use of math_narrow_eval - added more comments Changes in v4: - initialize local_signgam to 0 in math/w_tgamma_template.c - replace sysdeps/ieee754/dbl-64/gamma_productf.c by dummy file Changes in v5: - do not mention local_signgam any more in math/w_tgammaf_compat.c - initialize local_signgam to 1 instead of 0 in w_tgamma_template.c and added comment Changes in v6: - pass NULL as 2nd argument of __ieee754_gammaf_r in w_tgammaf_compat.c, and check for NULL in e_gammaf_r.c Changes in v7: - added Signed-off-by line for Alexei Sibidanov (author of the code) Changes in v8: - added Signed-off-by line for Paul Zimmermann (submitted of the patch) Changes in v9: - address comments from review by Adhemerval Zanella Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
This commit is contained in:
parent
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12
SHARED-FILES
12
SHARED-FILES
@ -219,3 +219,15 @@ tzdata:
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timezone/leapseconds
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# This is yearistype.sh in the parent project
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timezone/yearistype
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# The following files are shared with the CORE-MATH project
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sysdeps/ieee754/flt-32/e_gammaf_r.c
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(file src/binary32/tgamma/tgammaf.c in CORE-MATH)
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Instructions to merge new versions:
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- change the function name from cr_tgammaf to __ieee754_gammaf_r
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- add "int *signgamp" as 2nd argument and add at the beginning:
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if (signgamp != NULL) *signgamp = 1;
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- remove the errno stuff (this is done by the wrapper)
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- replace 0x1p127f * 0x1p127f by math_narrow_eval (x * 0x1p127f)
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- replace 0x1p-127f * sgn[k&1] by math_narrow_eval (0x1p-127f * sgn[k&1])
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- add libm_alias_finite (__ieee754_gammaf_r, __gammaf_r) at the end
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@ -94,6 +94,7 @@ bench-math := \
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tan \
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tanh \
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tgamma \
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tgammaf \
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trunc \
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truncf \
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y0 \
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benchtests/tgammaf-inputs
Normal file
1006
benchtests/tgammaf-inputs
Normal file
File diff suppressed because it is too large
Load Diff
@ -14,6 +14,7 @@
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#include <errno.h>
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#include <math.h>
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#include <stddef.h>
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#include <math_private.h>
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#include <math-svid-compat.h>
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#include <libm-alias-float.h>
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@ -22,8 +23,7 @@
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float
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__tgammaf(float x)
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{
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int local_signgam;
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float y = __ieee754_gammaf_r(x,&local_signgam);
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float y = __ieee754_gammaf_r(x, NULL);
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if(__glibc_unlikely (!isfinite (y) || y == 0)
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&& (isfinite (x) || (isinf (x) && x < 0.0))
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@ -41,7 +41,7 @@ __tgammaf(float x)
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/* tgammaf overflow */
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return __kernel_standard_f(x, x, 140);
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}
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return local_signgam < 0 ? - y : y;
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return y;
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}
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libm_alias_float (__tgamma, tgamma)
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#endif
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@ -1653,22 +1653,18 @@ ldouble: 3
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Function: "tgamma":
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double: 9
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float: 8
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ldouble: 4
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Function: "tgamma_downward":
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double: 9
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float: 7
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ldouble: 5
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Function: "tgamma_towardzero":
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double: 9
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float: 7
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ldouble: 5
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Function: "tgamma_upward":
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double: 9
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float: 8
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ldouble: 4
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Function: "y0":
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@ -1410,22 +1410,18 @@ ldouble: 3
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Function: "tgamma":
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double: 9
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float: 8
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ldouble: 4
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Function: "tgamma_downward":
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double: 9
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float: 7
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ldouble: 5
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Function: "tgamma_towardzero":
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double: 9
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float: 7
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ldouble: 5
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Function: "tgamma_upward":
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double: 9
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float: 8
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ldouble: 4
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Function: "y0":
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@ -1157,19 +1157,15 @@ float: 3
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Function: "tgamma":
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double: 9
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float: 9
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Function: "tgamma_downward":
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double: 9
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float: 9
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Function: "tgamma_towardzero":
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double: 9
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float: 8
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Function: "tgamma_upward":
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double: 9
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float: 9
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Function: "y0":
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double: 3
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@ -279,7 +279,6 @@ float: 2
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Function: "tgamma":
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double: 9
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float: 8
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Function: "y0":
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double: 3
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@ -1152,19 +1152,15 @@ float: 3
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Function: "tgamma":
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double: 9
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float: 8
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Function: "tgamma_downward":
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double: 9
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float: 7
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Function: "tgamma_towardzero":
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double: 9
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float: 7
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Function: "tgamma_upward":
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double: 9
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float: 8
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Function: "y0":
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double: 3
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@ -1061,19 +1061,15 @@ float: 3
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Function: "tgamma":
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double: 9
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float: 8
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Function: "tgamma_downward":
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double: 8
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float: 7
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Function: "tgamma_towardzero":
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double: 9
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float: 7
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Function: "tgamma_upward":
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double: 9
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float: 8
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Function: "y0":
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double: 3
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@ -1092,19 +1092,15 @@ float: 3
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Function: "tgamma":
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double: 9
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float: 8
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Function: "tgamma_downward":
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double: 5
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float: 5
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Function: "tgamma_towardzero":
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double: 5
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float: 4
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Function: "tgamma_upward":
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double: 4
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float: 4
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Function: "y0":
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double: 3
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@ -1181,20 +1181,16 @@ float: 3
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Function: "tgamma":
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double: 9
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float: 8
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ldouble: 1
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Function: "tgamma_downward":
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double: 9
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float: 7
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Function: "tgamma_towardzero":
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double: 9
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float: 7
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Function: "tgamma_upward":
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double: 9
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float: 8
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Function: "y0":
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double: 3
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@ -1699,25 +1699,21 @@ ldouble: 4
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Function: "tgamma":
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double: 9
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float: 8
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float128: 4
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ldouble: 5
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Function: "tgamma_downward":
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double: 9
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float: 7
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float128: 5
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ldouble: 6
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Function: "tgamma_towardzero":
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double: 9
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float: 7
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float128: 5
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ldouble: 6
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Function: "tgamma_upward":
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double: 9
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float: 8
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float128: 4
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ldouble: 5
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@ -1701,25 +1701,21 @@ ldouble: 4
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Function: "tgamma":
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double: 9
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float: 8
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float128: 4
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ldouble: 5
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Function: "tgamma_downward":
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double: 9
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float: 7
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float128: 5
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ldouble: 6
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Function: "tgamma_towardzero":
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double: 9
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float: 7
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float128: 5
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ldouble: 6
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Function: "tgamma_upward":
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double: 8
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float: 8
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float128: 4
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ldouble: 5
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@ -1,44 +1 @@
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/* Compute a product of X, X+1, ..., with an error estimate.
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Copyright (C) 2013-2024 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include <math.h>
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#include <math-narrow-eval.h>
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#include <math_private.h>
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#include <float.h>
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/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
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- 1, in the form R * (1 + *EPS) where the return value R is an
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approximation to the product and *EPS is set to indicate the
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approximate error in the return value. X is such that all the
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values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
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X is small enough that factors quadratic in it can be
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neglected. */
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float
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__gamma_productf (float x, float x_eps, int n, float *eps)
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{
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double x_full = (double) x + (double) x_eps;
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double ret = x_full;
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for (int i = 1; i < n; i++)
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ret *= x_full + i;
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float fret = math_narrow_eval ((float) ret);
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*eps = (ret - fret) / fret;
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return fret;
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}
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/* Not needed. */
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@ -1,215 +1,150 @@
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/* Implementation of gamma function according to ISO C.
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Copyright (C) 1997-2024 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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/* Implementation of the gamma function for binary32.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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Copyright (c) 2023-2024 Alexei Sibidanov.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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The original version of this file was copied from the CORE-MATH
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project (file src/binary32/tgamma/tgammaf.c, revision a48e352).
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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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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/* Changes with respect to the original CORE-MATH code:
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- removed the dealing with errno
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(this is done in the wrapper math/w_tgammaf_compat.c)
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- usage of math_narrow_eval to deal with underflow/overflow
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- deal with signgamp
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*/
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#include <math.h>
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#include <math-narrow-eval.h>
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#include <math_private.h>
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#include <fenv_private.h>
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#include <math-underflow.h>
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#include <float.h>
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#include <stdint.h>
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#include <stddef.h>
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#include <libm-alias-finite.h>
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#include <math-narrow-eval.h>
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/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's
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approximation to gamma function. */
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static const float gamma_coeff[] =
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{
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0x1.555556p-4f,
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-0xb.60b61p-12f,
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0x3.403404p-12f,
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};
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#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0]))
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/* Return gamma (X), for positive X less than 42, in the form R *
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2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to
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avoid overflow or underflow in intermediate calculations. */
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static float
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gammaf_positive (float x, int *exp2_adj)
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{
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int local_signgam;
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if (x < 0.5f)
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{
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*exp2_adj = 0;
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return __ieee754_expf (__ieee754_lgammaf_r (x + 1, &local_signgam)) / x;
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}
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else if (x <= 1.5f)
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{
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*exp2_adj = 0;
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return __ieee754_expf (__ieee754_lgammaf_r (x, &local_signgam));
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}
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else if (x < 2.5f)
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{
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*exp2_adj = 0;
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float x_adj = x - 1;
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return (__ieee754_expf (__ieee754_lgammaf_r (x_adj, &local_signgam))
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* x_adj);
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}
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else
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{
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float eps = 0;
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float x_eps = 0;
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float x_adj = x;
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float prod = 1;
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if (x < 4.0f)
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{
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/* Adjust into the range for applying Stirling's
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approximation. */
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float n = ceilf (4.0f - x);
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x_adj = math_narrow_eval (x + n);
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x_eps = (x - (x_adj - n));
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prod = __gamma_productf (x_adj - n, x_eps, n, &eps);
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}
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/* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).
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Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,
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starting by computing pow (X_ADJ, X_ADJ) with a power of 2
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factored out. */
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float exp_adj = -eps;
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float x_adj_int = roundf (x_adj);
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float x_adj_frac = x_adj - x_adj_int;
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int x_adj_log2;
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float x_adj_mant = __frexpf (x_adj, &x_adj_log2);
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if (x_adj_mant < M_SQRT1_2f)
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{
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x_adj_log2--;
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x_adj_mant *= 2.0f;
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}
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*exp2_adj = x_adj_log2 * (int) x_adj_int;
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float ret = (__ieee754_powf (x_adj_mant, x_adj)
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* __ieee754_exp2f (x_adj_log2 * x_adj_frac)
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* __ieee754_expf (-x_adj)
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* sqrtf (2 * M_PIf / x_adj)
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/ prod);
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exp_adj += x_eps * __ieee754_logf (x_adj);
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float bsum = gamma_coeff[NCOEFF - 1];
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float x_adj2 = x_adj * x_adj;
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for (size_t i = 1; i <= NCOEFF - 1; i++)
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bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];
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exp_adj += bsum / x_adj;
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return ret + ret * __expm1f (exp_adj);
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}
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}
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typedef union {float f; uint32_t u;} b32u32_u;
|
||||
typedef union {double f; uint64_t u;} b64u64_u;
|
||||
|
||||
float
|
||||
__ieee754_gammaf_r (float x, int *signgamp)
|
||||
{
|
||||
int32_t hx;
|
||||
float ret;
|
||||
/* The wrapper in math/w_tgamma_template.c expects *signgamp to be set to a
|
||||
non-negative value if the returned value is gamma(x), and to a negative
|
||||
value if it is -gamma(x).
|
||||
Since the code here directly computes gamma(x), we set it to 1.
|
||||
*/
|
||||
if (signgamp != NULL)
|
||||
*signgamp = 1;
|
||||
|
||||
GET_FLOAT_WORD (hx, x);
|
||||
/* List of exceptional cases. Each entry contains the 32-bit encoding u of x,
|
||||
a binary32 approximation f of gamma(x), and a correction term df. */
|
||||
static const struct {uint32_t u; float f, df;} tb[] = {
|
||||
{0x27de86a9u, 0x1.268266p+47f, 0x1p22f}, // x = 0x1.bd0d52p-48
|
||||
{0x27e05475u, 0x1.242422p+47f, 0x1p22f}, // x = 0x1.c0a8eap-48
|
||||
{0xb63befb3u, -0x1.5cb6e4p+18f, 0x1p-7f}, // x = -0x1.77df66p-19
|
||||
{0x3c7bb570u, 0x1.021d9p+6f, 0x1p-19f}, // x = 0x1.f76aep-7
|
||||
{0x41e886d1u, 0x1.33136ap+98f, 0x1p73f}, // x = 0x1.d10da2p+4
|
||||
{0xc067d177u, 0x1.f6850cp-3f, 0x1p-28f}, // x = -0x1.cfa2eep+1
|
||||
{0xbd99da31u, -0x1.befe66p+3, -0x1p-22f}, // x = -0x1.33b462p-4
|
||||
{0xbf54c45au, -0x1.a6b4ecp+2, +0x1p-23f}, // x = -0x1.a988b4p-1
|
||||
{0x41ee77feu, 0x1.d3631cp+101, -0x1p-76f}, // x = 0x1.dceffcp+4
|
||||
{0x3f843a64u, 0x1.f6c638p-1, 0x1p-26f}, // x = 0x1.0874c8p+0
|
||||
};
|
||||
|
||||
if (__glibc_unlikely ((hx & 0x7fffffff) == 0))
|
||||
{
|
||||
/* Return value for x == 0 is Inf with divide by zero exception. */
|
||||
*signgamp = 0;
|
||||
return 1.0 / x;
|
||||
b32u32_u t = {.f = x};
|
||||
uint32_t ax = t.u<<1;
|
||||
if(__builtin_expect(ax>=(0xffu<<24), 0)){ /* x=NaN or +/-Inf */
|
||||
if(ax==(0xffu<<24)){ /* x=+/-Inf */
|
||||
if(t.u>>31){ /* x=-Inf */
|
||||
return x / x; /* will raise the "Invalid operation" exception */
|
||||
}
|
||||
return x; /* x=+Inf */
|
||||
}
|
||||
if (__builtin_expect (hx < 0, 0)
|
||||
&& (uint32_t) hx < 0xff800000 && rintf (x) == x)
|
||||
{
|
||||
/* Return value for integer x < 0 is NaN with invalid exception. */
|
||||
*signgamp = 0;
|
||||
return (x - x) / (x - x);
|
||||
return x + x; /* x=NaN, where x+x ensures the "Invalid operation"
|
||||
exception is set if x is sNaN */
|
||||
}
|
||||
double z = x;
|
||||
if(__builtin_expect(ax<0x6d000000u, 0)){ /* |x| < 0x1p-18 */
|
||||
volatile double d = (0x1.fa658c23b1578p-1 - 0x1.d0a118f324b63p-1*z)*z - 0x1.2788cfc6fb619p-1;
|
||||
double f = 1.0/z + d;
|
||||
float r = f;
|
||||
b64u64_u rt = {.f = f};
|
||||
if(((rt.u+2)&0xfffffff) < 4){
|
||||
for(unsigned i=0;i<sizeof(tb)/sizeof(tb[0]);i++)
|
||||
if(t.u==tb[i].u) return tb[i].f + tb[i].df;
|
||||
}
|
||||
if (__glibc_unlikely (hx == 0xff800000))
|
||||
{
|
||||
/* x == -Inf. According to ISO this is NaN. */
|
||||
*signgamp = 0;
|
||||
return x - x;
|
||||
return r;
|
||||
}
|
||||
float fx = __builtin_floorf(x);
|
||||
if(__builtin_expect(x >= 0x1.18522p+5f, 0)){
|
||||
/* Overflow case. The original CORE-MATH code returns 0x1p127f * 0x1p127f,
|
||||
but apparently some compilers replace this by +Inf. */
|
||||
return math_narrow_eval (x * 0x1p127f);
|
||||
}
|
||||
/* compute k only after the overflow check, otherwise the case to integer
|
||||
might overflow */
|
||||
int k = fx;
|
||||
if(__builtin_expect(fx==x, 0)){ /* x is integer */
|
||||
if(x == 0.0f){
|
||||
return 1.0f/x;
|
||||
}
|
||||
if (__glibc_unlikely ((hx & 0x7f800000) == 0x7f800000))
|
||||
{
|
||||
/* Positive infinity (return positive infinity) or NaN (return
|
||||
NaN). */
|
||||
*signgamp = 0;
|
||||
return x + x;
|
||||
if(x < 0.0f){
|
||||
return 0.0f / 0.0f; /* should raise the "Invalid operation" exception */
|
||||
}
|
||||
double t0 = 1, x0 = 1;
|
||||
for(int i=1; i<k; i++, x0 += 1.0) t0 *= x0;
|
||||
return t0;
|
||||
}
|
||||
if(__builtin_expect(x<-42.0f, 0)){ /* negative non-integer */
|
||||
/* For x < -42, x non-integer, |gamma(x)| < 2^-151. */
|
||||
static const float sgn[2] = {0x1p-127f, -0x1p-127f};
|
||||
/* Underflows always happens */
|
||||
return math_narrow_eval (0x1p-127f * sgn[k&1]);
|
||||
}
|
||||
/* The array c[] stores a degree-15 polynomial approximation for gamma(x). */
|
||||
static const double c[] =
|
||||
{0x1.c9a76be577123p+0, 0x1.8f2754ddcf90dp+0, 0x1.0d1191949419bp+0, 0x1.e1f42cf0ae4a1p-2,
|
||||
0x1.82b358a3ab638p-3, 0x1.e1f2b30cd907bp-5, 0x1.240f6d4071bd8p-6, 0x1.1522c9f3cd012p-8,
|
||||
0x1.1fd0051a0525bp-10, 0x1.9808a8b96c37ep-13, 0x1.b3f78e01152b5p-15, 0x1.49c85a7e1fd04p-18,
|
||||
0x1.471ca49184475p-19, -0x1.368f0b7ed9e36p-23, 0x1.882222f9049efp-23, -0x1.a69ed2042842cp-25};
|
||||
|
||||
if (x >= 36.0f)
|
||||
{
|
||||
/* Overflow. */
|
||||
*signgamp = 0;
|
||||
ret = math_narrow_eval (FLT_MAX * FLT_MAX);
|
||||
return ret;
|
||||
double m = z - 0x1.7p+1, i = __builtin_roundeven(m), step = __builtin_copysign(1.0,i);
|
||||
double d = m - i, d2 = d*d, d4 = d2*d2, d8 = d4*d4;
|
||||
double f = (c[0] + d*c[1]) + d2*(c[2] + d*c[3]) + d4*((c[4] + d*c[5]) + d2*(c[6] + d*c[7]))
|
||||
+ d8*((c[8] + d*c[9]) + d2*(c[10] + d*c[11]) + d4*((c[12] + d*c[13]) + d2*(c[14] + d*c[15])));
|
||||
int jm = __builtin_fabs(i);
|
||||
double w = 1;
|
||||
if(jm){
|
||||
z -= 0.5 + step*0.5;
|
||||
w = z;
|
||||
for(int j=jm-1; j; j--) {z -= step; w *= z;}
|
||||
}
|
||||
if(i<=-0.5) w = 1/w;
|
||||
f *= w;
|
||||
b64u64_u rt = {.f = f};
|
||||
float r = f;
|
||||
/* Deal with exceptional cases. */
|
||||
if(__builtin_expect(((rt.u+2)&0xfffffff) < 8, 0)){
|
||||
for(unsigned j=0;j<sizeof(tb)/sizeof(tb[0]);j++) {
|
||||
if(t.u==tb[j].u) return tb[j].f + tb[j].df;
|
||||
}
|
||||
else
|
||||
{
|
||||
SET_RESTORE_ROUNDF (FE_TONEAREST);
|
||||
if (x > 0.0f)
|
||||
{
|
||||
*signgamp = 0;
|
||||
int exp2_adj;
|
||||
float tret = gammaf_positive (x, &exp2_adj);
|
||||
ret = __scalbnf (tret, exp2_adj);
|
||||
}
|
||||
else if (x >= -FLT_EPSILON / 4.0f)
|
||||
{
|
||||
*signgamp = 0;
|
||||
ret = 1.0f / x;
|
||||
}
|
||||
else
|
||||
{
|
||||
float tx = truncf (x);
|
||||
*signgamp = (tx == 2.0f * truncf (tx / 2.0f)) ? -1 : 1;
|
||||
if (x <= -42.0f)
|
||||
/* Underflow. */
|
||||
ret = FLT_MIN * FLT_MIN;
|
||||
else
|
||||
{
|
||||
float frac = tx - x;
|
||||
if (frac > 0.5f)
|
||||
frac = 1.0f - frac;
|
||||
float sinpix = (frac <= 0.25f
|
||||
? __sinf (M_PIf * frac)
|
||||
: __cosf (M_PIf * (0.5f - frac)));
|
||||
int exp2_adj;
|
||||
float tret = M_PIf / (-x * sinpix
|
||||
* gammaf_positive (-x, &exp2_adj));
|
||||
ret = __scalbnf (tret, -exp2_adj);
|
||||
math_check_force_underflow_nonneg (ret);
|
||||
}
|
||||
}
|
||||
ret = math_narrow_eval (ret);
|
||||
}
|
||||
if (isinf (ret) && x != 0)
|
||||
{
|
||||
if (*signgamp < 0)
|
||||
{
|
||||
ret = math_narrow_eval (-copysignf (FLT_MAX, ret) * FLT_MAX);
|
||||
ret = -ret;
|
||||
}
|
||||
else
|
||||
ret = math_narrow_eval (copysignf (FLT_MAX, ret) * FLT_MAX);
|
||||
return ret;
|
||||
}
|
||||
else if (ret == 0)
|
||||
{
|
||||
if (*signgamp < 0)
|
||||
{
|
||||
ret = math_narrow_eval (-copysignf (FLT_MIN, ret) * FLT_MIN);
|
||||
ret = -ret;
|
||||
}
|
||||
else
|
||||
ret = math_narrow_eval (copysignf (FLT_MIN, ret) * FLT_MIN);
|
||||
return ret;
|
||||
}
|
||||
else
|
||||
return ret;
|
||||
}
|
||||
return r;
|
||||
}
|
||||
libm_alias_finite (__ieee754_gammaf_r, __gammaf_r)
|
||||
|
@ -1432,22 +1432,18 @@ ldouble: 3
|
||||
|
||||
Function: "tgamma":
|
||||
double: 9
|
||||
float: 8
|
||||
ldouble: 4
|
||||
|
||||
Function: "tgamma_downward":
|
||||
double: 9
|
||||
float: 7
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_towardzero":
|
||||
double: 9
|
||||
float: 7
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_upward":
|
||||
double: 9
|
||||
float: 8
|
||||
ldouble: 4
|
||||
|
||||
Function: "y0":
|
||||
|
@ -146,7 +146,6 @@ double: 1
|
||||
|
||||
Function: "tgamma":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "y0":
|
||||
double: 2
|
||||
|
@ -1208,22 +1208,18 @@ float: 1
|
||||
|
||||
Function: "tgamma":
|
||||
double: 3
|
||||
float: 9
|
||||
ldouble: 9
|
||||
|
||||
Function: "tgamma_downward":
|
||||
double: 3
|
||||
float: 9
|
||||
ldouble: 9
|
||||
|
||||
Function: "tgamma_towardzero":
|
||||
double: 3
|
||||
float: 9
|
||||
ldouble: 9
|
||||
|
||||
Function: "tgamma_upward":
|
||||
double: 2
|
||||
float: 9
|
||||
ldouble: 9
|
||||
|
||||
Function: "y0":
|
||||
|
@ -257,7 +257,6 @@ float: 2
|
||||
|
||||
Function: "tgamma":
|
||||
double: 5
|
||||
float: 4
|
||||
|
||||
Function: "y0":
|
||||
double: 2
|
||||
|
@ -1156,19 +1156,15 @@ float: 3
|
||||
|
||||
Function: "tgamma":
|
||||
double: 9
|
||||
float: 8
|
||||
|
||||
Function: "tgamma_downward":
|
||||
double: 9
|
||||
float: 7
|
||||
|
||||
Function: "tgamma_towardzero":
|
||||
double: 9
|
||||
float: 7
|
||||
|
||||
Function: "tgamma_upward":
|
||||
double: 9
|
||||
float: 8
|
||||
|
||||
Function: "y0":
|
||||
double: 3
|
||||
|
@ -1444,22 +1444,18 @@ ldouble: 3
|
||||
|
||||
Function: "tgamma":
|
||||
double: 9
|
||||
float: 8
|
||||
ldouble: 4
|
||||
|
||||
Function: "tgamma_downward":
|
||||
double: 9
|
||||
float: 7
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_towardzero":
|
||||
double: 9
|
||||
float: 7
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_upward":
|
||||
double: 9
|
||||
float: 8
|
||||
ldouble: 4
|
||||
|
||||
Function: "y0":
|
||||
|
@ -266,7 +266,6 @@ float: 2
|
||||
|
||||
Function: "tgamma":
|
||||
double: 9
|
||||
float: 8
|
||||
|
||||
Function: "y0":
|
||||
double: 3
|
||||
|
@ -1066,19 +1066,15 @@ float: 3
|
||||
|
||||
Function: "tgamma":
|
||||
double: 9
|
||||
float: 8
|
||||
|
||||
Function: "tgamma_downward":
|
||||
double: 9
|
||||
float: 9
|
||||
|
||||
Function: "tgamma_towardzero":
|
||||
double: 9
|
||||
float: 8
|
||||
|
||||
Function: "tgamma_upward":
|
||||
double: 9
|
||||
float: 8
|
||||
|
||||
Function: "y0":
|
||||
double: 3
|
||||
|
@ -1064,19 +1064,15 @@ float: 3
|
||||
|
||||
Function: "tgamma":
|
||||
double: 9
|
||||
float: 8
|
||||
|
||||
Function: "tgamma_downward":
|
||||
double: 9
|
||||
float: 9
|
||||
|
||||
Function: "tgamma_towardzero":
|
||||
double: 9
|
||||
float: 8
|
||||
|
||||
Function: "tgamma_upward":
|
||||
double: 9
|
||||
float: 8
|
||||
|
||||
Function: "y0":
|
||||
double: 3
|
||||
|
@ -1828,25 +1828,21 @@ ldouble: 6
|
||||
|
||||
Function: "tgamma":
|
||||
double: 9
|
||||
float: 8
|
||||
float128: 4
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_downward":
|
||||
double: 9
|
||||
float: 7
|
||||
float128: 5
|
||||
ldouble: 6
|
||||
|
||||
Function: "tgamma_towardzero":
|
||||
double: 9
|
||||
float: 7
|
||||
float128: 5
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_upward":
|
||||
double: 9
|
||||
float: 8
|
||||
float128: 4
|
||||
ldouble: 5
|
||||
|
||||
|
@ -1560,22 +1560,18 @@ ldouble: 6
|
||||
|
||||
Function: "tgamma":
|
||||
double: 9
|
||||
float: 8
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_downward":
|
||||
double: 9
|
||||
float: 7
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_towardzero":
|
||||
double: 9
|
||||
float: 7
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_upward":
|
||||
double: 9
|
||||
float: 8
|
||||
ldouble: 4
|
||||
|
||||
Function: "y0":
|
||||
|
@ -1361,22 +1361,18 @@ ldouble: 3
|
||||
|
||||
Function: "tgamma":
|
||||
double: 9
|
||||
float: 8
|
||||
ldouble: 4
|
||||
|
||||
Function: "tgamma_downward":
|
||||
double: 5
|
||||
float: 5
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_towardzero":
|
||||
double: 5
|
||||
float: 4
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_upward":
|
||||
double: 4
|
||||
float: 4
|
||||
ldouble: 4
|
||||
|
||||
Function: "y0":
|
||||
|
@ -1431,22 +1431,18 @@ ldouble: 3
|
||||
|
||||
Function: "tgamma":
|
||||
double: 9
|
||||
float: 8
|
||||
ldouble: 4
|
||||
|
||||
Function: "tgamma_downward":
|
||||
double: 9
|
||||
float: 7
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_towardzero":
|
||||
double: 9
|
||||
float: 7
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_upward":
|
||||
double: 8
|
||||
float: 8
|
||||
ldouble: 4
|
||||
|
||||
Function: "y0":
|
||||
|
@ -1429,22 +1429,18 @@ ldouble: 3
|
||||
|
||||
Function: "tgamma":
|
||||
double: 9
|
||||
float: 8
|
||||
ldouble: 4
|
||||
|
||||
Function: "tgamma_downward":
|
||||
double: 9
|
||||
float: 7
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_towardzero":
|
||||
double: 9
|
||||
float: 7
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_upward":
|
||||
double: 9
|
||||
float: 8
|
||||
ldouble: 4
|
||||
|
||||
Function: "y0":
|
||||
|
@ -532,11 +532,9 @@ float: 2
|
||||
|
||||
Function: "tgamma":
|
||||
double: 9
|
||||
float: 8
|
||||
|
||||
Function: "tgamma_towardzero":
|
||||
double: 9
|
||||
float: 7
|
||||
|
||||
Function: "y0":
|
||||
double: 3
|
||||
|
@ -1444,22 +1444,18 @@ ldouble: 3
|
||||
|
||||
Function: "tgamma":
|
||||
double: 9
|
||||
float: 8
|
||||
ldouble: 4
|
||||
|
||||
Function: "tgamma_downward":
|
||||
double: 9
|
||||
float: 7
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_towardzero":
|
||||
double: 9
|
||||
float: 7
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_upward":
|
||||
double: 9
|
||||
float: 8
|
||||
ldouble: 4
|
||||
|
||||
Function: "y0":
|
||||
|
@ -2263,25 +2263,21 @@ double: 1
|
||||
|
||||
Function: "tgamma":
|
||||
double: 9
|
||||
float: 8
|
||||
float128: 4
|
||||
ldouble: 5
|
||||
|
||||
Function: "tgamma_downward":
|
||||
double: 9
|
||||
float: 7
|
||||
float128: 5
|
||||
ldouble: 6
|
||||
|
||||
Function: "tgamma_towardzero":
|
||||
double: 9
|
||||
float: 7
|
||||
float128: 5
|
||||
ldouble: 6
|
||||
|
||||
Function: "tgamma_upward":
|
||||
double: 9
|
||||
float: 8
|
||||
float128: 4
|
||||
ldouble: 5
|
||||
|
||||
|
Loading…
Reference in New Issue
Block a user