mirror of
https://github.com/capstone-engine/llvm-capstone.git
synced 2024-10-07 19:03:57 +00:00
f320fefc4a
Implement correctly rounded `erff` functions. For `x >= 4`, `erff(x) = 1` for `FE_TONEAREST` or `FE_UPWARD`, `0x1.ffffep-1` for `FE_DOWNWARD` or `FE_TOWARDZERO`. For `0 <= x < 4`, we divide into 32 sub-intervals of length `1/8`, and use a degree-15 odd polynomial to approximate `erff(x)` in each sub-interval: ``` erff(x) ~ x * (c0 + c1 * x^2 + c2 * x^4 + ... + c7 * x^14). ``` For `x < 0`, we can use the same formula as above, since the odd part is factored out. Performance tested with `perf.sh` tool from the CORE-MATH project on AMD Ryzen 9 5900X: Reciprocal throughput (clock cycles / op) ``` $ ./perf.sh erff --path2 GNU libc version: 2.35 GNU libc release: stable -- CORE-MATH reciprocal throughput -- with -march=native (with FMA instructions) [####################] 100 % Ntrial = 20 ; Min = 11.790 + 0.182 clc/call; Median-Min = 0.154 clc/call; Max = 12.255 clc/call; -- CORE-MATH reciprocal throughput -- with -march=x86-64-v2 (without FMA instructions) [####################] 100 % Ntrial = 20 ; Min = 14.205 + 0.151 clc/call; Median-Min = 0.159 clc/call; Max = 15.893 clc/call; -- System LIBC reciprocal throughput -- [####################] 100 % Ntrial = 20 ; Min = 45.519 + 0.445 clc/call; Median-Min = 0.552 clc/call; Max = 46.345 clc/call; -- LIBC reciprocal throughput -- with -mavx2 -mfma (with FMA instructions) [####################] 100 % Ntrial = 20 ; Min = 9.595 + 0.214 clc/call; Median-Min = 0.220 clc/call; Max = 9.887 clc/call; -- LIBC reciprocal throughput -- with -msse4.2 (without FMA instructions) [####################] 100 % Ntrial = 20 ; Min = 10.223 + 0.190 clc/call; Median-Min = 0.222 clc/call; Max = 10.474 clc/call; ``` and latency (clock cycles / op): ``` $ ./perf.sh erff --path2 GNU libc version: 2.35 GNU libc release: stable -- CORE-MATH latency -- with -march=native (with FMA instructions) [####################] 100 % Ntrial = 20 ; Min = 38.566 + 0.391 clc/call; Median-Min = 0.503 clc/call; Max = 39.170 clc/call; -- CORE-MATH latency -- with -march=x86-64-v2 (without FMA instructions) [####################] 100 % Ntrial = 20 ; Min = 43.223 + 0.667 clc/call; Median-Min = 0.680 clc/call; Max = 43.913 clc/call; -- System LIBC latency -- [####################] 100 % Ntrial = 20 ; Min = 111.613 + 1.267 clc/call; Median-Min = 1.696 clc/call; Max = 113.444 clc/call; -- LIBC latency -- with -mavx2 -mfma (with FMA instructions) [####################] 100 % Ntrial = 20 ; Min = 40.138 + 0.410 clc/call; Median-Min = 0.536 clc/call; Max = 40.729 clc/call; -- LIBC latency -- with -msse4.2 (without FMA instructions) [####################] 100 % Ntrial = 20 ; Min = 44.858 + 0.872 clc/call; Median-Min = 0.814 clc/call; Max = 46.019 clc/call; ``` Reviewed By: michaelrj Differential Revision: https://reviews.llvm.org/D153683 |
||
|---|---|---|
| .. | ||
| check_mpfr.cpp | ||
| CMakeLists.txt | ||
| mpfr_inc.h | ||
| MPFRUtils.cpp | ||
| MPFRUtils.h | ||