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Various floating-point functions have code to force underflow
exceptions if a tiny result was computed in a way that might not have
resulted in such exceptions even though the result is inexact. This
typically uses math_force_eval to ensure that the underflowing
expression is evaluated, but sometimes uses volatile.
This patch refactors such code to use three new macros
math_check_force_underflow, math_check_force_underflow_nonneg and
math_check_force_underflow_complex (which in turn use
math_force_eval). In the limited number of cases not suited to a
simple conversion to these macros, existing uses of volatile are
changed to use math_force_eval instead. The converted code does not
always execute exactly the same sequence of operations as the original
code, but the overall effects should be the same.
Tested for x86_64, x86, mips64 and powerpc.
* sysdeps/generic/math_private.h (fabs_tg): New macro.
(min_of_type): Likewise.
(math_check_force_underflow): Likewise.
(math_check_force_underflow_nonneg): Likewise.
(math_check_force_underflow_complex): Likewise.
* math/e_exp2l.c (__ieee754_exp2l): Use
math_check_force_underflow_nonneg.
* math/k_casinh.c (__kernel_casinh): Likewise.
* math/k_casinhf.c (__kernel_casinhf): Likewise.
* math/k_casinhl.c (__kernel_casinhl): Likewise.
* math/s_catan.c (__catan): Use
math_check_force_underflow_complex.
* math/s_catanf.c (__catanf): Likewise.
* math/s_catanh.c (__catanh): Likewise.
* math/s_catanhf.c (__catanhf): Likewise.
* math/s_catanhl.c (__catanhl): Likewise.
* math/s_catanl.c (__catanl): Likewise.
* math/s_ccosh.c (__ccosh): Likewise.
* math/s_ccoshf.c (__ccoshf): Likewise.
* math/s_ccoshl.c (__ccoshl): Likewise.
* math/s_cexp.c (__cexp): Likewise.
* math/s_cexpf.c (__cexpf): Likewise.
* math/s_cexpl.c (__cexpl): Likewise.
* math/s_clog.c (__clog): Use math_check_force_underflow_nonneg.
* math/s_clog10.c (__clog10): Likewise.
* math/s_clog10f.c (__clog10f): Likewise.
* math/s_clog10l.c (__clog10l): Likewise.
* math/s_clogf.c (__clogf): Likewise.
* math/s_clogl.c (__clogl): Likewise.
* math/s_csin.c (__csin): Use math_check_force_underflow_complex.
* math/s_csinf.c (__csinf): Likewise.
* math/s_csinh.c (__csinh): Likewise.
* math/s_csinhf.c (__csinhf): Likewise.
* math/s_csinhl.c (__csinhl): Likewise.
* math/s_csinl.c (__csinl): Likewise.
* math/s_csqrt.c (__csqrt): Use math_check_force_underflow.
* math/s_csqrtf.c (__csqrtf): Likewise.
* math/s_csqrtl.c (__csqrtl): Likewise.
* math/s_ctan.c (__ctan): Use math_check_force_underflow_complex.
* math/s_ctanf.c (__ctanf): Likewise.
* math/s_ctanh.c (__ctanh): Likewise.
* math/s_ctanhf.c (__ctanhf): Likewise.
* math/s_ctanhl.c (__ctanhl): Likewise.
* math/s_ctanl.c (__ctanl): Likewise.
* stdlib/strtod_l.c (round_and_return): Use math_force_eval
instead of volatile.
* sysdeps/ieee754/dbl-64/e_asin.c (__ieee754_asin): Use
math_check_force_underflow.
* sysdeps/ieee754/dbl-64/e_atanh.c (__ieee754_atanh): Likewise.
* sysdeps/ieee754/dbl-64/e_exp.c (__ieee754_exp): Do not use
volatile when forcing underflow.
* sysdeps/ieee754/dbl-64/e_exp2.c (__ieee754_exp2): Use
math_check_force_underflow_nonneg.
* sysdeps/ieee754/dbl-64/e_gamma_r.c (__ieee754_gamma_r):
Likewise.
* sysdeps/ieee754/dbl-64/e_j1.c (__ieee754_j1): Use
math_check_force_underflow.
* sysdeps/ieee754/dbl-64/e_jn.c (__ieee754_jn): Likewise.
* sysdeps/ieee754/dbl-64/e_sinh.c (__ieee754_sinh): Likewise.
* sysdeps/ieee754/dbl-64/s_asinh.c (__asinh): Likewise.
* sysdeps/ieee754/dbl-64/s_atan.c (atan): Use
math_check_force_underflow_nonneg.
* sysdeps/ieee754/dbl-64/s_erf.c (__erf): Use
math_check_force_underflow.
* sysdeps/ieee754/dbl-64/s_expm1.c (__expm1): Likewise.
* sysdeps/ieee754/dbl-64/s_fma.c (__fma): Use math_force_eval
instead of volatile.
* sysdeps/ieee754/dbl-64/s_log1p.c (__log1p): Use
math_check_force_underflow.
* sysdeps/ieee754/dbl-64/s_sin.c (__sin): Likewise.
* sysdeps/ieee754/dbl-64/s_tan.c (tan): Use
math_check_force_underflow_nonneg.
* sysdeps/ieee754/dbl-64/s_tanh.c (__tanh): Use
math_check_force_underflow.
* sysdeps/ieee754/flt-32/e_asinf.c (__ieee754_asinf): Likewise.
* sysdeps/ieee754/flt-32/e_atanhf.c (__ieee754_atanhf): Likewise.
* sysdeps/ieee754/flt-32/e_exp2f.c (__ieee754_exp2f): Use
math_check_force_underflow_nonneg.
* sysdeps/ieee754/flt-32/e_gammaf_r.c (__ieee754_gammaf_r):
Likewise.
* sysdeps/ieee754/flt-32/e_j1f.c (__ieee754_j1f): Use
math_check_force_underflow.
* sysdeps/ieee754/flt-32/e_jnf.c (__ieee754_jnf): Likewise.
* sysdeps/ieee754/flt-32/e_sinhf.c (__ieee754_sinhf): Likewise.
* sysdeps/ieee754/flt-32/k_sinf.c (__kernel_sinf): Likewise.
* sysdeps/ieee754/flt-32/k_tanf.c (__kernel_tanf): Likewise.
* sysdeps/ieee754/flt-32/s_asinhf.c (__asinhf): Likewise.
* sysdeps/ieee754/flt-32/s_atanf.c (__atanf): Likewise.
* sysdeps/ieee754/flt-32/s_erff.c (__erff): Likewise.
* sysdeps/ieee754/flt-32/s_expm1f.c (__expm1f): Likewise.
* sysdeps/ieee754/flt-32/s_log1pf.c (__log1pf): Likewise.
* sysdeps/ieee754/flt-32/s_tanhf.c (__tanhf): Likewise.
* sysdeps/ieee754/ldbl-128/e_asinl.c (__ieee754_asinl): Likewise.
* sysdeps/ieee754/ldbl-128/e_atanhl.c (__ieee754_atanhl):
Likewise.
* sysdeps/ieee754/ldbl-128/e_expl.c (__ieee754_expl): Use
math_check_force_underflow_nonneg.
* sysdeps/ieee754/ldbl-128/e_gammal_r.c (__ieee754_gammal_r):
Likewise.
* sysdeps/ieee754/ldbl-128/e_j1l.c (__ieee754_j1l): Use
math_check_force_underflow.
* sysdeps/ieee754/ldbl-128/e_jnl.c (__ieee754_jnl): Likewise.
* sysdeps/ieee754/ldbl-128/e_sinhl.c (__ieee754_sinhl): Likewise.
* sysdeps/ieee754/ldbl-128/k_sincosl.c (__kernel_sincosl):
Likewise.
* sysdeps/ieee754/ldbl-128/k_sinl.c (__kernel_sinl): Likewise.
* sysdeps/ieee754/ldbl-128/k_tanl.c (__kernel_tanl): Likewise.
* sysdeps/ieee754/ldbl-128/s_asinhl.c (__asinhl): Likewise.
* sysdeps/ieee754/ldbl-128/s_atanl.c (__atanl): Likewise.
* sysdeps/ieee754/ldbl-128/s_erfl.c (__erfl): Likewise.
* sysdeps/ieee754/ldbl-128/s_expm1l.c (__expm1l): Likewise.
* sysdeps/ieee754/ldbl-128/s_fmal.c (__fmal): Use math_force_eval
instead of volatile.
* sysdeps/ieee754/ldbl-128/s_log1pl.c (__log1pl): Use
math_check_force_underflow.
* sysdeps/ieee754/ldbl-128/s_tanhl.c (__tanhl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/e_asinl.c (__ieee754_asinl): Use
math_check_force_underflow.
* sysdeps/ieee754/ldbl-128ibm/e_atanhl.c (__ieee754_atanhl):
Likewise.
* sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c (__ieee754_gammal_r):
Use math_check_force_underflow_nonneg.
* sysdeps/ieee754/ldbl-128ibm/e_jnl.c (__ieee754_jnl): Use
math_check_force_underflow.
* sysdeps/ieee754/ldbl-128ibm/e_sinhl.c (__ieee754_sinhl):
Likewise.
* sysdeps/ieee754/ldbl-128ibm/k_sincosl.c (__kernel_sincosl):
Likewise.
* sysdeps/ieee754/ldbl-128ibm/k_sinl.c (__kernel_sinl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/k_tanl.c (__kernel_tanl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_asinhl.c (__asinhl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_atanl.c (__atanl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_erfl.c (__erfl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_tanhl.c (__tanhl): Likewise.
* sysdeps/ieee754/ldbl-96/e_asinl.c (__ieee754_asinl): Likewise.
* sysdeps/ieee754/ldbl-96/e_atanhl.c (__ieee754_atanhl): Likewise.
* sysdeps/ieee754/ldbl-96/e_gammal_r.c (__ieee754_gammal_r): Use
math_check_force_underflow_nonneg.
* sysdeps/ieee754/ldbl-96/e_j1l.c (__ieee754_j1l): Use
math_check_force_underflow.
* sysdeps/ieee754/ldbl-96/e_jnl.c (__ieee754_jnl): Likewise.
* sysdeps/ieee754/ldbl-96/e_sinhl.c (__ieee754_sinhl): Likewise.
* sysdeps/ieee754/ldbl-96/k_sinl.c (__kernel_sinl): Likewise.
* sysdeps/ieee754/ldbl-96/k_tanl.c (__kernel_tanl): Use
math_check_force_underflow_nonneg.
* sysdeps/ieee754/ldbl-96/s_asinhl.c (__asinhl): Use
math_check_force_underflow.
* sysdeps/ieee754/ldbl-96/s_erfl.c (__erfl): Likewise.
* sysdeps/ieee754/ldbl-96/s_fmal.c (__fmal): Use math_force_eval
instead of volatile.
* sysdeps/ieee754/ldbl-96/s_tanhl.c (__tanhl): Use
math_check_force_underflow.
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The csqrt implementations in glibc can miss underflow exceptions when
the real or imaginary part of the result becomes tiny in the course of
scaling down (in particular, multiplication by 0.5) and that scaling
is exact although the relevant part of the mathematical result isn't.
This patch forces the exception in a similar way to previous fixes.
Tested for x86_64 and x86.
[BZ #18370]
* math/s_csqrt.c (__csqrt): Force underflow exception for results
whose real or imaginary part has small absolute value.
* math/s_csqrtf.c (__csqrtf): Likewise.
* math/s_csqrtl.c (__csqrtl): Likewise.
* math/auto-libm-test-in: Add more tests of csqrt.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
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The csqrt functions scale up small arguments to avoid underflows when
calling hypot functions. However, even when hypot does not underflow,
a subsequent calculation of 0.5 * hypot can underflow. This patch
duly increases the threshold and scale factor to avoid such underflows
as well.
Tested for x86_64, x86 and mips64.
[BZ #18823]
* math/s_csqrt.c (__csqrt): Increase threshold and scale factor
for scaling up small arguments.
* math/s_csqrtf.c (__csqrtf): Likewise.
* math/s_csqrtl.c (__csqrtl): Likewise.
* math/auto-libm-test-in: Add more tests of csqrt.
* math/auto-libm-test-out: Regenerated.
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The csqrt implementations in glibc can cause spurious underflows in
some cases as a side-effect of the scaling for large arguments (when
underflow is correct for the square root of the argument that was
scaled down to avoid overflow, but not for the original argument).
This patch arranges to avoid the underflowing intermediate computation
(eliminating a multiplication in 0.5 in the problem cases where a
subsequent scaling by 2 would follow).
Tested for x86_64 and x86 and ulps updated accordingly (only needed
for x86).
[BZ #18371]
* math/s_csqrt.c (__csqrt): Avoid multiplication by 0.5 where
intermediate but not final result might underflow.
* math/s_csqrtf.c (__csqrtf): Likewise.
* math/s_csqrtl.c (__csqrtl): Likewise.
* math/auto-libm-test-in: Add more tests of csqrt.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
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