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Based on new expf and exp2f code from
https://github.com/ARM-software/optimized-routines/
with wrapper on aarch64:
expf reciprocal-throughput: 2.3x faster
expf latency: 1.7x faster
without wrapper on aarch64:
expf reciprocal-throughput: 3.3x faster
expf latency: 1.7x faster
without wrapper on aarch64:
exp2f reciprocal-throughput: 2.8x faster
exp2f latency: 1.3x faster
libm.so size on aarch64:
.text size: -152 bytes
.rodata size: -1740 bytes
expf/exp2f worst case nearest rounding error: 0.502 ulp
worst case non-nearest rounding error: 1 ulp
Error checks are inline and errno setting is in separate tail called
functions, but the wrappers are kept in this patch to handle the
_LIB_VERSION==_SVID_ case. (So e.g. errno is set twice for expf calls
and once for __expf_finite calls on targets where the new code is used.)
Double precision arithmetics is used which is expected to be faster on
most targets (including soft-float) than using single precision and it
is easier to get good precision result with it.
Const data is kept in a separate translation unit which complicates
maintenance a bit, but is expected to give good code for literal loads
on most targets and allows sharing data across expf, exp2f and powf.
(This data is disabled on i386, m68k and ia64 which have their own
expf, exp2f and powf code.)
Some details may need target specific tweaks:
- best convert and round to int operation in the arg reduction may be
different across targets.
- code was optimized on fma target, optimal polynomial eval may be
different without fma.
- gcc does not always generate good code for fp bit representation
access via unions or it may be inherently slow on some targets.
The libm-test-ulps will need adjustment because..
- The argument reduction ideally uses nearest rounded rint, but that is
not efficient on most targets, so the polynomial can get evaluated on a
wider interval in non-nearest rounding mode making 1 ulp errors common
in that case.
- The polynomial is evaluated such that it may have 1 ulp error on
negative tiny inputs with upward rounding.
* math/Makefile (type-float-routines): Add math_errf and e_exp2f_data.
* sysdeps/aarch64/fpu/math_private.h (TOINT_INTRINSICS): Define.
(roundtoint, converttoint): Likewise.
* sysdeps/ieee754/flt-32/e_expf.c: New implementation.
* sysdeps/ieee754/flt-32/e_exp2f.c: New implementation.
* sysdeps/ieee754/flt-32/e_exp2f_data.c: New file.
* sysdeps/ieee754/flt-32/math_config.h: New file.
* sysdeps/ieee754/flt-32/math_errf.c: New file.
* sysdeps/ieee754/flt-32/t_exp2f.h: Remove.
* sysdeps/i386/fpu/e_exp2f_data.c: New file.
* sysdeps/i386/fpu/math_errf.c: New file.
* sysdeps/ia64/fpu/e_exp2f_data.c: New file.
* sysdeps/ia64/fpu/math_errf.c: New file.
* sysdeps/m68k/m680x0/fpu/e_exp2f_data.c: New file.
* sysdeps/m68k/m680x0/fpu/math_errf.c: New file.
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