glibc/sysdeps/i386/fpu/libm-test-ulps
Joseph Myers e02920bc02 Improve tgamma accuracy (bug 18613).
In non-default rounding modes, tgamma can be slightly less accurate
than permitted by glibc's accuracy goals.

Part of the problem is error accumulation, addressed in this patch by
setting round-to-nearest for internal computations.  However, there
was also a bug in the code dealing with computing pow (x + n, x + n)
where x + n is not exactly representable, providing another source of
error even in round-to-nearest mode; it was necessary to address both
bugs to get errors for all testcases within glibc's accuracy goals.
Given this second fix, accuracy in round-to-nearest mode is also
improved (hence regeneration of ulps for tgamma should be from scratch
- truncate libm-test-ulps or at least remove existing tgamma entries -
so that the expected ulps can be reduced).

Some additional complications also arose.  Certain tgamma tests should
strictly, according to IEEE semantics, overflow or not depending on
the rounding mode; this is beyond the scope of glibc's accuracy goals
for any function without exactly-determined results, but
gen-auto-libm-tests doesn't handle being lax there as it does for
underflow.  (libm-test.inc also doesn't handle being lax about whether
the result in cases very close to the overflow threshold is infinity
or a finite value close to overflow, but that doesn't cause problems
in this case though I've seen it cause problems with random test
generation for some functions.)  Thus, spurious-overflow markings,
with a comment, are added to auto-libm-test-in (no bug in Bugzilla
because the issue is with the testsuite, not a user-visible bug in
glibc).  And on x86, after the patch I saw ERANGE issues as previously
reported by Carlos (see my commentary in
<https://sourceware.org/ml/libc-alpha/2015-01/msg00485.html>), which
needed addressing by ensuring excess range and precision were
eliminated at various points if FLT_EVAL_METHOD != 0.

I also noticed and fixed a cosmetic issue where 1.0f was used in long
double functions and should have been 1.0L.

This completes the move of all functions to testing in all rounding
modes with ALL_RM_TEST, so gen-libm-have-vector-test.sh is updated to
remove the workaround for some functions not using ALL_RM_TEST.

Tested for x86_64, x86, mips64 and powerpc.

	[BZ #18613]
	* sysdeps/ieee754/dbl-64/e_gamma_r.c (gamma_positive): Take log of
	X_ADJ not X when adjusting exponent.
	(__ieee754_gamma_r): Do intermediate computations in
	round-to-nearest then adjust overflowing and underflowing results
	as needed.
	* sysdeps/ieee754/flt-32/e_gammaf_r.c (gammaf_positive): Take log
	of X_ADJ not X when adjusting exponent.
	(__ieee754_gammaf_r): Do intermediate computations in
	round-to-nearest then adjust overflowing and underflowing results
	as needed.
	* sysdeps/ieee754/ldbl-128/e_gammal_r.c (gammal_positive): Take
	log of X_ADJ not X when adjusting exponent.
	(__ieee754_gammal_r): Do intermediate computations in
	round-to-nearest then adjust overflowing and underflowing results
	as needed.  Use 1.0L not 1.0f as numerator of division.
	* sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c (gammal_positive): Take
	log of X_ADJ not X when adjusting exponent.
	(__ieee754_gammal_r): Do intermediate computations in
	round-to-nearest then adjust overflowing and underflowing results
	as needed.  Use 1.0L not 1.0f as numerator of division.
	* sysdeps/ieee754/ldbl-96/e_gammal_r.c (gammal_positive): Take log
	of X_ADJ not X when adjusting exponent.
	(__ieee754_gammal_r): Do intermediate computations in
	round-to-nearest then adjust overflowing and underflowing results
	as needed.  Use 1.0L not 1.0f as numerator of division.
	* math/libm-test.inc (tgamma_test_data): Remove one test.  Moved
	to auto-libm-test-in.
	(tgamma_test): Use ALL_RM_TEST.
	* math/auto-libm-test-in: Add one test of tgamma.  Mark some other
	tests of tgamma with spurious-overflow.
	* math/auto-libm-test-out: Regenerated.
	* math/gen-libm-have-vector-test.sh: Do not check for START.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2015-06-29 23:29:35 +00:00

2063 lines
25 KiB
Plaintext

# Begin of automatic generation
# Maximal error of functions:
Function: "acos":
ildouble: 1
ldouble: 1
Function: "acos_downward":
ildouble: 2
ldouble: 2
Function: "acos_towardzero":
ildouble: 2
ldouble: 2
Function: "acos_upward":
ildouble: 2
ldouble: 2
Function: "acosh":
ildouble: 4
ldouble: 2
Function: "acosh_downward":
ildouble: 6
ldouble: 4
Function: "acosh_towardzero":
ildouble: 6
ldouble: 4
Function: "acosh_upward":
ildouble: 4
ldouble: 3
Function: "asin":
ildouble: 1
ldouble: 1
Function: "asin_downward":
ildouble: 2
ldouble: 2
Function: "asin_towardzero":
ildouble: 1
ldouble: 1
Function: "asin_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "asinh":
ildouble: 2
ldouble: 2
Function: "asinh_downward":
double: 1
float: 1
ildouble: 5
ldouble: 5
Function: "asinh_towardzero":
double: 1
float: 1
ildouble: 4
ldouble: 4
Function: "asinh_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 5
ldouble: 4
Function: "atan":
ildouble: 1
ldouble: 1
Function: "atan2":
ildouble: 1
ldouble: 1
Function: "atan2_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "atan2_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "atan2_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "atan_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "atan_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "atan_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "atanh":
ildouble: 3
ldouble: 3
Function: "atanh_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 4
Function: "atanh_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 4
ldouble: 3
Function: "atanh_upward":
idouble: 1
ifloat: 1
ildouble: 5
ldouble: 5
Function: "cabs":
ildouble: 1
ldouble: 1
Function: "cabs_downward":
ildouble: 1
ldouble: 1
Function: "cabs_towardzero":
ildouble: 1
ldouble: 1
Function: "cabs_upward":
ildouble: 1
ldouble: 1
Function: Real part of "cacos":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Imaginary part of "cacos":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Real part of "cacos_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Imaginary part of "cacos_downward":
double: 3
float: 3
idouble: 3
ifloat: 3
ildouble: 5
ldouble: 5
Function: Real part of "cacos_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Imaginary part of "cacos_towardzero":
double: 3
float: 3
idouble: 3
ifloat: 3
ildouble: 5
ldouble: 5
Function: Real part of "cacos_upward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 2
ldouble: 2
Function: Imaginary part of "cacos_upward":
double: 4
float: 4
idouble: 4
ifloat: 4
ildouble: 5
ldouble: 5
Function: Real part of "cacosh":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Imaginary part of "cacosh":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "cacosh_downward":
double: 3
float: 3
idouble: 3
ifloat: 3
ildouble: 5
ldouble: 5
Function: Imaginary part of "cacosh_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Real part of "cacosh_towardzero":
double: 3
float: 3
idouble: 3
ifloat: 3
ildouble: 5
ldouble: 5
Function: Imaginary part of "cacosh_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Real part of "cacosh_upward":
double: 4
float: 4
idouble: 4
ifloat: 4
ildouble: 5
ldouble: 5
Function: Imaginary part of "cacosh_upward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 2
ldouble: 2
Function: "carg":
ildouble: 1
ldouble: 1
Function: "carg_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "carg_towardzero":
float: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "carg_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "casin":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Imaginary part of "casin":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Real part of "casin_downward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 2
ldouble: 2
Function: Imaginary part of "casin_downward":
double: 3
float: 3
idouble: 3
ifloat: 3
ildouble: 5
ldouble: 5
Function: Real part of "casin_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Imaginary part of "casin_towardzero":
double: 3
float: 3
idouble: 3
ifloat: 3
ildouble: 5
ldouble: 5
Function: Real part of "casin_upward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 2
ldouble: 2
Function: Imaginary part of "casin_upward":
double: 4
float: 4
idouble: 4
ifloat: 4
ildouble: 5
ldouble: 5
Function: Real part of "casinh":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Imaginary part of "casinh":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "casinh_downward":
double: 3
float: 3
idouble: 3
ifloat: 3
ildouble: 5
ldouble: 5
Function: Imaginary part of "casinh_downward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 2
ldouble: 2
Function: Real part of "casinh_towardzero":
double: 3
float: 3
idouble: 3
ifloat: 3
ildouble: 5
ldouble: 5
Function: Imaginary part of "casinh_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Real part of "casinh_upward":
double: 4
float: 4
idouble: 4
ifloat: 4
ildouble: 5
ldouble: 5
Function: Imaginary part of "casinh_upward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 2
ldouble: 2
Function: Imaginary part of "catan":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "catan_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Imaginary part of "catan_downward":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 4
ldouble: 4
Function: Real part of "catan_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Imaginary part of "catan_towardzero":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 4
ldouble: 4
Function: Real part of "catan_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Imaginary part of "catan_upward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 3
ldouble: 3
Function: Real part of "catanh":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "catanh_downward":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 4
ldouble: 4
Function: Imaginary part of "catanh_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "catanh_towardzero":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 4
ldouble: 4
Function: Imaginary part of "catanh_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "catanh_upward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 4
ldouble: 4
Function: Imaginary part of "catanh_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "cbrt":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Function: "cbrt_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: "cbrt_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "cbrt_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: Real part of "ccos":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Imaginary part of "ccos":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "ccos_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: Imaginary part of "ccos_downward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 3
ldouble: 3
Function: Real part of "ccos_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: Imaginary part of "ccos_towardzero":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 3
ldouble: 3
Function: Real part of "ccos_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Imaginary part of "ccos_upward":
double: 1
float: 2
idouble: 1
ifloat: 2
ildouble: 2
ldouble: 2
Function: Real part of "ccosh":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Imaginary part of "ccosh":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "ccosh_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: Imaginary part of "ccosh_downward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 3
ldouble: 3
Function: Real part of "ccosh_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: Imaginary part of "ccosh_towardzero":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 3
ldouble: 3
Function: Real part of "ccosh_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Imaginary part of "ccosh_upward":
double: 1
float: 2
idouble: 1
ifloat: 2
ildouble: 2
ldouble: 2
Function: Real part of "cexp":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Imaginary part of "cexp":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "cexp_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: Imaginary part of "cexp_downward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 3
ldouble: 3
Function: Real part of "cexp_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: Imaginary part of "cexp_towardzero":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 3
ldouble: 3
Function: Real part of "cexp_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Imaginary part of "cexp_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: Real part of "clog":
double: 3
float: 2
idouble: 3
ifloat: 2
ildouble: 4
ldouble: 4
Function: Imaginary part of "clog":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Function: Real part of "clog10":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 4
ldouble: 4
Function: Imaginary part of "clog10":
double: 1
idouble: 1
ildouble: 2
ldouble: 2
Function: Real part of "clog10_downward":
double: 5
float: 4
idouble: 5
ifloat: 4
ildouble: 8
ldouble: 8
Function: Imaginary part of "clog10_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Real part of "clog10_towardzero":
double: 5
float: 4
idouble: 5
ifloat: 4
ildouble: 8
ldouble: 8
Function: Imaginary part of "clog10_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: Real part of "clog10_upward":
double: 5
float: 5
idouble: 5
ifloat: 5
ildouble: 6
ldouble: 6
Function: Imaginary part of "clog10_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: Real part of "clog_downward":
double: 5
float: 5
idouble: 5
ifloat: 5
ildouble: 7
ldouble: 7
Function: Imaginary part of "clog_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "clog_towardzero":
double: 5
float: 5
idouble: 5
ifloat: 5
ildouble: 8
ldouble: 8
Function: Imaginary part of "clog_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "clog_upward":
double: 5
float: 5
idouble: 5
ifloat: 5
ildouble: 6
ldouble: 6
Function: Imaginary part of "clog_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "cos":
ildouble: 1
ldouble: 1
Function: "cos_downward":
double: 1
idouble: 1
ildouble: 3
ldouble: 3
Function: "cos_towardzero":
double: 1
idouble: 1
ildouble: 2
ldouble: 2
Function: "cos_upward":
double: 1
idouble: 1
ildouble: 2
ldouble: 2
Function: "cosh":
ildouble: 1
ldouble: 2
Function: "cosh_downward":
double: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 3
Function: "cosh_towardzero":
double: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "cosh_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 3
Function: Real part of "cpow":
double: 2
float: 5
idouble: 2
ifloat: 5
ildouble: 3
ldouble: 3
Function: Imaginary part of "cpow":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 4
ldouble: 4
Function: Real part of "cpow_downward":
double: 5
float: 8
idouble: 5
ifloat: 8
ildouble: 7
ldouble: 7
Function: Imaginary part of "cpow_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Real part of "cpow_towardzero":
double: 5
float: 8
idouble: 5
ifloat: 8
ildouble: 7
ldouble: 7
Function: Imaginary part of "cpow_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "cpow_upward":
double: 4
float: 1
idouble: 4
ifloat: 1
ildouble: 2
ldouble: 2
Function: Imaginary part of "cpow_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Real part of "csin":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Imaginary part of "csin":
double: 1
float: 1
idouble: 1
ifloat: 1
Function: Real part of "csin_downward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 3
ldouble: 3
Function: Imaginary part of "csin_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: Real part of "csin_towardzero":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 3
ldouble: 3
Function: Imaginary part of "csin_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: Real part of "csin_upward":
double: 1
float: 2
idouble: 1
ifloat: 2
ildouble: 3
ldouble: 3
Function: Imaginary part of "csin_upward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 3
ldouble: 3
Function: Real part of "csinh":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Imaginary part of "csinh":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "csinh_downward":
double: 1
float: 2
idouble: 1
ifloat: 2
ildouble: 3
ldouble: 3
Function: Imaginary part of "csinh_downward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 3
ldouble: 3
Function: Real part of "csinh_towardzero":
double: 1
float: 2
idouble: 1
ifloat: 2
ildouble: 3
ldouble: 3
Function: Imaginary part of "csinh_towardzero":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 3
ldouble: 3
Function: Real part of "csinh_upward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 3
ldouble: 3
Function: Imaginary part of "csinh_upward":
double: 1
float: 2
idouble: 1
ifloat: 2
ildouble: 3
ldouble: 3
Function: Real part of "csqrt":
double: 1
idouble: 1
ildouble: 2
ldouble: 2
Function: Imaginary part of "csqrt":
double: 1
idouble: 1
ildouble: 2
ldouble: 2
Function: Real part of "csqrt_downward":
double: 1
idouble: 1
ildouble: 4
ldouble: 4
Function: Imaginary part of "csqrt_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: Real part of "csqrt_towardzero":
double: 1
idouble: 1
ildouble: 4
ldouble: 4
Function: Imaginary part of "csqrt_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: Real part of "csqrt_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 5
ldouble: 5
Function: Imaginary part of "csqrt_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: Real part of "ctan":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Imaginary part of "ctan":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "ctan_downward":
double: 1
float: 2
idouble: 1
ifloat: 2
ildouble: 5
ldouble: 5
Function: Imaginary part of "ctan_downward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 4
ldouble: 4
Function: Real part of "ctan_towardzero":
double: 3
float: 1
idouble: 3
ifloat: 1
ildouble: 5
ldouble: 5
Function: Imaginary part of "ctan_towardzero":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 4
ldouble: 4
Function: Real part of "ctan_upward":
double: 3
float: 2
idouble: 3
ifloat: 2
ildouble: 3
ldouble: 3
Function: Imaginary part of "ctan_upward":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 3
ldouble: 3
Function: Real part of "ctanh":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Imaginary part of "ctanh":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Real part of "ctanh_downward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 4
ldouble: 4
Function: Imaginary part of "ctanh_downward":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 4
ldouble: 4
Function: Real part of "ctanh_towardzero":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 4
ldouble: 4
Function: Imaginary part of "ctanh_towardzero":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 3
ldouble: 3
Function: Real part of "ctanh_upward":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 3
ldouble: 3
Function: Imaginary part of "ctanh_upward":
double: 3
float: 2
idouble: 3
ifloat: 2
ildouble: 3
ldouble: 3
Function: "erf":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "erf_downward":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Function: "erf_towardzero":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Function: "erf_upward":
ildouble: 1
ldouble: 1
Function: "erfc":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "erfc_downward":
double: 1
float: 2
idouble: 1
ifloat: 2
ildouble: 4
ldouble: 4
Function: "erfc_towardzero":
double: 1
float: 2
idouble: 1
ifloat: 2
ildouble: 4
ldouble: 4
Function: "erfc_upward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 4
ldouble: 4
Function: "exp":
ildouble: 1
ldouble: 1
Function: "exp10":
ildouble: 1
ldouble: 1
Function: "exp10_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "exp10_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "exp10_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "exp2":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Function: "exp2_downward":
ildouble: 1
ldouble: 1
Function: "exp2_towardzero":
ildouble: 1
ldouble: 1
Function: "exp2_upward":
ildouble: 1
ldouble: 1
Function: "exp_downward":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Function: "exp_towardzero":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Function: "exp_upward":
ildouble: 1
ldouble: 1
Function: "expm1":
ildouble: 2
ldouble: 2
Function: "expm1_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 4
ldouble: 4
Function: "expm1_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 4
ldouble: 4
Function: "expm1_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 4
ldouble: 4
Function: "gamma":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "gamma_downward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 6
ldouble: 6
Function: "gamma_towardzero":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 6
ldouble: 6
Function: "gamma_upward":
double: 2
float: 3
idouble: 2
ifloat: 3
ildouble: 4
ldouble: 4
Function: "hypot":
ildouble: 1
ldouble: 1
Function: "hypot_downward":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Function: "hypot_towardzero":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Function: "hypot_upward":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Function: "j0":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "j0_downward":
double: 1
float: 2
idouble: 1
ifloat: 2
ildouble: 4
ldouble: 4
Function: "j0_towardzero":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 5
ldouble: 5
Function: "j0_upward":
double: 1
float: 3
idouble: 1
ifloat: 3
ildouble: 4
ldouble: 4
Function: "j1":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 1
ldouble: 1
Function: "j1_downward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 4
ldouble: 4
Function: "j1_towardzero":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 4
ldouble: 4
Function: "j1_upward":
double: 2
float: 3
idouble: 2
ifloat: 3
ildouble: 3
ldouble: 3
Function: "jn":
double: 2
float: 3
idouble: 2
ifloat: 3
ildouble: 4
ldouble: 4
Function: "jn_downward":
double: 2
float: 3
idouble: 2
ifloat: 3
ildouble: 4
ldouble: 4
Function: "jn_towardzero":
double: 2
float: 3
idouble: 2
ifloat: 3
ildouble: 5
ldouble: 5
Function: "jn_upward":
double: 2
float: 3
idouble: 2
ifloat: 3
ildouble: 5
ldouble: 5
Function: "lgamma":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "lgamma_downward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 6
ldouble: 6
Function: "lgamma_towardzero":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 6
ldouble: 6
Function: "lgamma_upward":
double: 2
float: 3
idouble: 2
ifloat: 3
ildouble: 4
ldouble: 4
Function: "log":
ildouble: 1
ldouble: 1
Function: "log10":
ildouble: 1
ldouble: 1
Function: "log10_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "log10_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "log10_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "log1p":
ildouble: 2
ldouble: 2
Function: "log1p_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: "log1p_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: "log1p_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 3
ldouble: 3
Function: "log2":
ildouble: 1
ldouble: 1
Function: "log2_downward":
ildouble: 1
ldouble: 1
Function: "log2_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "log2_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "log_downward":
ildouble: 2
ldouble: 2
Function: "log_towardzero":
ildouble: 2
ldouble: 2
Function: "log_upward":
ildouble: 1
ldouble: 1
Function: "pow":
ildouble: 1
ldouble: 1
Function: "pow10":
ildouble: 1
ldouble: 1
Function: "pow10_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "pow10_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "pow10_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "pow_downward":
double: 1
idouble: 1
ildouble: 4
ldouble: 4
Function: "pow_towardzero":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Function: "pow_upward":
double: 1
idouble: 1
ildouble: 2
ldouble: 2
Function: "sin":
ildouble: 1
ldouble: 1
Function: "sin_downward":
double: 1
idouble: 1
ildouble: 2
ldouble: 2
Function: "sin_towardzero":
double: 1
idouble: 1
ildouble: 1
ldouble: 1
Function: "sin_upward":
double: 1
idouble: 1
ildouble: 3
ldouble: 3
Function: "sincos":
ildouble: 1
ldouble: 1
Function: "sincos_downward":
double: 1
idouble: 1
ildouble: 3
ldouble: 3
Function: "sincos_towardzero":
double: 1
idouble: 1
ildouble: 2
ldouble: 2
Function: "sincos_upward":
double: 1
idouble: 1
ildouble: 3
ldouble: 3
Function: "sinh":
ildouble: 2
ldouble: 2
Function: "sinh_downward":
ildouble: 4
ldouble: 5
Function: "sinh_towardzero":
ildouble: 3
ldouble: 4
Function: "sinh_upward":
double: 1
float: 1
ildouble: 4
ldouble: 5
Function: "tan":
float: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "tan_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "tan_towardzero":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "tan_upward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: "tanh":
ildouble: 2
ldouble: 2
Function: "tanh_downward":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 5
ldouble: 4
Function: "tanh_towardzero":
double: 1
float: 1
ildouble: 3
ldouble: 3
Function: "tanh_upward":
double: 1
float: 1
ildouble: 5
ldouble: 4
Function: "tgamma":
double: 2
float: 3
idouble: 2
ifloat: 3
ildouble: 3
ldouble: 3
Function: "tgamma_downward":
double: 2
float: 3
idouble: 2
ifloat: 3
ildouble: 3
ldouble: 3
Function: "tgamma_towardzero":
double: 3
float: 3
idouble: 3
ifloat: 3
ildouble: 3
ldouble: 3
Function: "tgamma_upward":
double: 3
float: 3
idouble: 3
ifloat: 3
ildouble: 3
ldouble: 3
Function: "y0":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: "y0_downward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 5
ldouble: 5
Function: "y0_towardzero":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 5
ldouble: 5
Function: "y0_upward":
double: 1
float: 2
idouble: 1
ifloat: 2
ildouble: 3
ldouble: 3
Function: "y1":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 2
ldouble: 2
Function: "y1_downward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 7
ldouble: 7
Function: "y1_towardzero":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 5
ldouble: 5
Function: "y1_upward":
double: 1
float: 3
idouble: 1
ifloat: 3
ildouble: 7
ldouble: 7
Function: "yn":
double: 2
float: 3
idouble: 2
ifloat: 3
ildouble: 4
ldouble: 4
Function: "yn_downward":
double: 2
float: 2
idouble: 2
ifloat: 2
ildouble: 5
ldouble: 5
Function: "yn_towardzero":
double: 3
float: 3
idouble: 3
ifloat: 3
ildouble: 5
ldouble: 5
Function: "yn_upward":
double: 3
float: 3
idouble: 3
ifloat: 3
ildouble: 4
ldouble: 4
# end of automatic generation