The flt-32 version of powf can be inaccurate because of bugs in the
extra-precision calculation of (x-1)/(x+1) or (x-1.5)/(x+1.5) as part
of calculating log(x) with extra precision: a constant used (as part
of adding 1 or 1.5 through integer arithmetic) is incorrect, and then
the code fails to mask a computed high part before using it in
arithmetic that relies on s_h*t_h being exactly representable. This
patch fixes these bugs.
Tested for x86_64 and x86. x86_64 ulps for powf removed and
regenerated to reflect reduced ulps from the increased accuracy for
existing tests.
[BZ #18956]
* sysdeps/ieee754/flt-32/e_powf.c (__ieee754_powf): Add 0x00400000
not 0x0040000 for high bit of mantissa. Mask with 0xfffff000 when
extracting high part.
* math/auto-libm-test-in: Add another test of pow.
* math/auto-libm-test-out: Regenerated.
* sysdeps/x86_64/fpu/libm-test-ulps: Update.
Similar to various other bugs in this area, pow functions can fail to
raise the underflow exception when the result is tiny and inexact but
one or more low bits of the intermediate result that is scaled down
(or, in the i386 case, converted from a wider evaluation format) are
zero. This patch forces the exception in a similar way to previous
fixes, thereby concluding the fixes for known bugs with missing
underflow exceptions currently filed in Bugzilla.
Tested for x86_64, x86, mips64 and powerpc.
[BZ #18825]
* sysdeps/i386/fpu/i386-math-asm.h (FLT_NARROW_EVAL_UFLOW_NONNAN):
New macro.
(DBL_NARROW_EVAL_UFLOW_NONNAN): Likewise.
(LDBL_CHECK_FORCE_UFLOW_NONNAN): Likewise.
* sysdeps/i386/fpu/e_pow.S: Use DEFINE_DBL_MIN.
(__ieee754_pow): Use DBL_NARROW_EVAL_UFLOW_NONNAN instead of
DBL_NARROW_EVAL, reloading the PIC register as needed.
* sysdeps/i386/fpu/e_powf.S: Use DEFINE_FLT_MIN.
(__ieee754_powf): Use FLT_NARROW_EVAL_UFLOW_NONNAN instead of
FLT_NARROW_EVAL. Use separate return path for case when first
argument is NaN.
* sysdeps/i386/fpu/e_powl.S: Include <i386-math-asm.h>. Use
DEFINE_LDBL_MIN.
(__ieee754_powl): Use LDBL_CHECK_FORCE_UFLOW_NONNAN, reloading the
PIC register.
* sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Use
math_check_force_underflow_nonneg.
* sysdeps/ieee754/flt-32/e_powf.c (__ieee754_powf): Force
underflow for subnormal result.
* sysdeps/ieee754/ldbl-128/e_powl.c (__ieee754_powl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/e_powl.c (__ieee754_powl): Use
math_check_force_underflow_nonneg.
* sysdeps/x86/fpu/powl_helper.c (__powl_helper): Use
math_check_force_underflow.
* sysdeps/x86_64/fpu/x86_64-math-asm.h
(LDBL_CHECK_FORCE_UFLOW_NONNAN): New macro.
* sysdeps/x86_64/fpu/e_powl.S: Include <x86_64-math-asm.h>. Use
DEFINE_LDBL_MIN.
(__ieee754_powl): Use LDBL_CHECK_FORCE_UFLOW_NONNAN.
* math/auto-libm-test-in: Add more tests of pow.
* math/auto-libm-test-out: Regenerated.
The flt-32 implementation of powf wrongly uses x-1 instead of |x|-1
when computing log (x) for the case where |x| is close to 1 and y is
large. This patch fixes the logic accordingly. Relevant tests
existed for x close to 1, and corresponding tests are added for x
close to -1, as well as for some new variant cases.
Tested for x86_64 and x86.
[BZ #18647]
* sysdeps/ieee754/flt-32/e_powf.c (__ieee754_powf): For large y
and |x| close to 1, use absolute value of x when computing log.
* math/auto-libm-test-in: Add more tests of pow.
* math/auto-libm-test-out: Regenerated.
