f41b0a43e4
Optimized log using carefully generated lookup table with 1/c and log(c) values for small intervalls around 1. The log(c) is very near a double precision value, it has about 62 bits precision. The algorithm is log(2^k x) = k log(2) + log(c) + log(x/c), where the last term is approximated by a polynomial of x/c - 1. Near 1 a single polynomial of x - 1 is used. There is separate code path when fma instruction is not available for computing x/c - 1 precisely, in which case the table size is doubled. The code uses __builtin_fma under __FP_FAST_FMA to ensure it is inlined as an instruction. With the default configuration settings the worst case error is 0.519 ULP (and 0.520 without fma), the rodata size is 2192 bytes (4240 without fma). The non-nearest rounding error is less than 1 ULP. Improvements on Cortex-A72 compared to current glibc master: log thruput: 3.28x in [0.01 11.1] log latency: 2.23x in [0.01 11.1] log thruput: 1.56x in [0.999 1.001] log latency: 1.57x in [0.999 1.001] Tested on aarch64-linux-gnu (defined __FP_FAST_FMA) arm-linux-gnueabihf (!defined __FP_FAST_FMA) x86_64-linux-gnu (!defined __FP_FAST_FMA) powerpc64le-linux-gnu (defined __FP_FAST_FMA) targets. * NEWS: Mention log improvement. * math/Makefile (type-double-routines): Add e_log_data. * sysdeps/i386/fpu/e_log_data.c: New file. * sysdeps/ia64/fpu/e_log_data.c: New file. * sysdeps/ieee754/dbl-64/e_log.c: Rewrite. * sysdeps/ieee754/dbl-64/e_log_data.c: New file. * sysdeps/ieee754/dbl-64/math_config.h (__log_data): Add. * sysdeps/ieee754/dbl-64/ulog.h: Remove. * sysdeps/ieee754/dbl-64/ulog.tbl: Remove. * sysdeps/m68k/m680x0/fpu/e_log_data.c: New file.
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