without wrapper on aarch64:
powf reciprocal-throughput: 4.2x faster
powf latency: 2.6x faster
old worst-case error: 1.11 ulp
new worst-case error: 0.82 ulp
aarch64 .text size: -780 bytes
aarch64 .rodata size: +144 bytes
powf(x,y) is implemented as exp2(y*log2(x)) with the same algorithms
that are used in exp2f and log2f, except that the log2f polynomial is
larger for extra precision and its output (and exp2f input) may be
scaled by a power of 2 (POWF_SCALE) to simplify the argument reduction
step of exp2 (possible when efficient round and convert toint operation
is available).
The special case handling tries to minimize the checks in the hot path.
When the input of exp2_inline is checked, int arithmetics is used as
that was faster on the tested aarch64 cores.
* math/Makefile (type-float-routines): Add e_powf_log2_data.
* sysdeps/ieee754/flt-32/e_powf.c: New implementation.
* sysdeps/ieee754/flt-32/e_powf_log2_data.c: New file.
* sysdeps/ieee754/flt-32/math_config.h (__powf_log2_data): Define.
(issignalingf_inline): Likewise.
(POWF_LOG2_TABLE_BITS): Likewise.
(POWF_LOG2_POLY_ORDER): Likewise.
(POWF_SCALE_BITS): Likewise.
(POWF_SCALE): Likewise.
* sysdeps/i386/fpu/e_powf_log2_data.c: New file.
* sysdeps/ia64/fpu/e_powf_log2_data.c: New file.
* sysdeps/m68k/m680x0/fpu/e_powf_log2_data.c: New file.
Similar to the new logf: double precision arithmetics and a small
lookup table is used. The argument reduction step is the same as in
the new logf.
without wrapper on aarch64:
log2f reciprocal-throughput: 2.3x faster
log2f latency: 2.1x faster
old worst case error: 1.72 ulp
new worst case error: 0.75 ulp
aarch64 .text size: -252 bytes
aarch64 .rodata size: +244 bytes
* math/Makefile (type-float-routines): Add e_log2f_data.
* sysdeps/ieee754/flt-32/e_log2f.c: New implementation.
* sysdeps/ieee754/flt-32/e_log2f_data.c: New file.
* sysdeps/ieee754/flt-32/math_config.h (__log2f_data): Define.
(LOG2F_TABLE_BITS, LOG2F_POLY_ORDER): Define.
* sysdeps/i386/fpu/e_log2f_data.c: New file.
* sysdeps/ia64/fpu/e_log2f_data.c: New file.
* sysdeps/m68k/m680x0/fpu/e_log2f_data.c: New file.
without wrapper on aarch64:
logf reciprocal-throughput: 2.2x faster
logf latency: 1.9x faster
old worst case error: 0.89 ulp
new worst case error: 0.82 ulp
aarch64 .text size: -356 bytes
aarch64 .rodata size: +240 bytes
Uses double precision arithmetics and a lookup table to allow smaller
polynomial and avoid the use of division.
Data is in a separate translation unit with fixed layout to prevent the
compiler generating suboptimal literal access.
Errors are handled inline according to POSIX rules, but this patch
keeps the wrapper with SVID compatible error handling.
Needs libm-test-ulps adjustment for clogf in non-nearest rounding mode.
* math/Makefile (type-float-routines): Add e_logf_data.
* sysdeps/ieee754/flt-32/e_logf.c: New implementation.
* sysdeps/ieee754/flt-32/e_logf_data.c: New file.
* sysdeps/ieee754/flt-32/math_config.h (__logf_data): Define.
(LOGF_TABLE_BITS, LOGF_POLY_ORDER): Define.
* sysdeps/i386/fpu/e_logf_data.c: New file.
* sysdeps/ia64/fpu/e_logf_data.c: New file.
* sysdeps/m68k/m680x0/fpu/e_logf_data.c: New file.
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.
