v4: - Update math_config.h with documentation for round/converttoint. - Remove unused configurations and related code/data. - Update comment for the specialcase function. - Document tested targets in the commit message. - Merge NEWS entry with sincosf improvements. v3: - Remove t_exp.c from targets too. - Add empty math_err.c and e_exp_data.c to targets that don't need them. - Fix GNU style issues. - Document internal function semantics. - Add NEWS entry. v2: - define TOINT_INTRINSICS for all targets. Optimized exp and exp2 implementations using a lookup table for fractional powers of 2. There are several variants, see e_exp_data.c, they can be selected by modifying math_config.h allowing different tradeoffs. The default selection should be acceptable as generic libm code. Worst case error is 0.509 ULP for exp and 0.507 ULP for exp2, on aarch64 the rodata size is 2160 bytes, shared between exp and exp2. On aarch64 .text + .rodata size decreased by 24912 bytes. The non-nearest rounding error is less than 1 ULP even on targets without efficient round implementation (although the error rate is higher in that case). Targets with single instruction, rounding mode independent, to nearest integer rounding and conversion can use them by setting TOINT_INTRINSICS and adding the necessary code to their math_private.h. The __exp1 code uses the same algorithm, so the error bound of pow increased a bit. New double precision error handling code was added following the style of the single precision error handling code. Improvements on Cortex-A72 compared to current glibc master: exp latency: 1.5x exp thruput: 2.3x exp latency: 1.3x on small inputs exp thruput: 1.8x on small inputs exp2 latency: 1.6x exp2 thruput: 3.2x For small inputs the current exp code uses a separate algorithm so the speed up there is less. Was tested on aarch64-linux-gnu (TOINT_INTRINSICS, fma contraction) and arm-linux-gnueabihf (!TOINT_INTRINSICS, no fma contraction) and x86_64-linux-gnu (!TOINT_INTRINSICS, no fma contraction) targets, only non-nearest rounding ulp errors increase and they are within acceptable bounds (ulp updates are in separate patches). 2018-07-06 Szabolcs Nagy * NEWS: Mention exp and exp2 improvements. * math/Makefile (libm-support): Remove t_exp. (type-double-routines): Add math_err and e_exp_data. * sysdeps/i386/fpu/e_exp_data.c: New file. * sysdeps/i386/fpu/math_err.c: New file. * sysdeps/i386/fpu/t_exp.c: Remove. * sysdeps/ia64/fpu/e_exp_data.c: New file. * sysdeps/ia64/fpu/math_err.c: New file. * sysdeps/ia64/fpu/t_exp.c: Remove. * sysdeps/ieee754/dbl-64/e_exp.c: Rewrite. * sysdeps/ieee754/dbl-64/e_exp2.c: Rewrite. * sysdeps/ieee754/dbl-64/e_exp_data.c: New file. * sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Update error bound. * sysdeps/ieee754/dbl-64/eexp.tbl: Remove. * sysdeps/ieee754/dbl-64/math_config.h: New file. * sysdeps/ieee754/dbl-64/math_err.c: New file. * sysdeps/ieee754/dbl-64/t_exp.c: Remove. * sysdeps/ieee754/dbl-64/t_exp2.h: Remove. * sysdeps/ieee754/dbl-64/uexp.h: Remove. * sysdeps/ieee754/dbl-64/uexp.tbl: Remove. * sysdeps/m68k/m680x0/fpu/e_exp_data.c: New file. * sysdeps/m68k/m680x0/fpu/math_err.c: New file. * sysdeps/m68k/m680x0/fpu/t_exp.c: Remove. --- NEWS | 2 +- math/Makefile | 4 +- sysdeps/i386/fpu/e_exp_data.c | 1 + sysdeps/i386/fpu/math_err.c | 1 + sysdeps/i386/fpu/t_exp.c | 1 - sysdeps/ia64/fpu/e_exp_data.c | 1 + sysdeps/ia64/fpu/math_err.c | 1 + sysdeps/ia64/fpu/t_exp.c | 1 - sysdeps/ieee754/dbl-64/e_exp.c | 485 +++------ sysdeps/ieee754/dbl-64/e_exp2.c | 220 +++-- sysdeps/ieee754/dbl-64/e_exp_data.c | 196 ++++ sysdeps/ieee754/dbl-64/e_pow.c | 6 +- sysdeps/ieee754/dbl-64/eexp.tbl | 172 ---- sysdeps/ieee754/dbl-64/math_config.h | 136 +++ sysdeps/ieee754/dbl-64/math_err.c | 92 ++ sysdeps/ieee754/dbl-64/t_exp.c | 435 --------- sysdeps/ieee754/dbl-64/t_exp2.h | 585 ----------- sysdeps/ieee754/dbl-64/uexp.h | 68 -- sysdeps/ieee754/dbl-64/uexp.tbl | 1786 ---------------------------------- sysdeps/m68k/m680x0/fpu/e_exp_data.c | 1 + sysdeps/m68k/m680x0/fpu/math_err.c | 1 + sysdeps/m68k/m680x0/fpu/t_exp.c | 1 - 22 files changed, 705 insertions(+), 3491 deletions(-) create mode 100644 sysdeps/i386/fpu/e_exp_data.c create mode 100644 sysdeps/i386/fpu/math_err.c delete mode 100644 sysdeps/i386/fpu/t_exp.c create mode 100644 sysdeps/ia64/fpu/e_exp_data.c create mode 100644 sysdeps/ia64/fpu/math_err.c delete mode 100644 sysdeps/ia64/fpu/t_exp.c create mode 100644 sysdeps/ieee754/dbl-64/e_exp_data.c delete mode 100644 sysdeps/ieee754/dbl-64/eexp.tbl create mode 100644 sysdeps/ieee754/dbl-64/math_config.h create mode 100644 sysdeps/ieee754/dbl-64/math_err.c delete mode 100644 sysdeps/ieee754/dbl-64/t_exp.c delete mode 100644 sysdeps/ieee754/dbl-64/t_exp2.h delete mode 100644 sysdeps/ieee754/dbl-64/uexp.h delete mode 100644 sysdeps/ieee754/dbl-64/uexp.tbl create mode 100644 sysdeps/m68k/m680x0/fpu/e_exp_data.c create mode 100644 sysdeps/m68k/m680x0/fpu/math_err.c delete mode 100644 sysdeps/m68k/m680x0/fpu/t_exp.c