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Implement double precision log1p function correctly rounded to all rounding modes. **Performance** - For `0.5 <= x <= 2`, the fast pass hitting rate is about 99.93%. - Benchmarks with `./perf.sh` tool from the CORE-MATH project, unit is (CPU clocks / call). - Reciprocal throughput from CORE-MATH's perf tool on Ryzen 5900X: ``` $ ./perf.sh log1p GNU libc version: 2.35 GNU libc release: stable -- CORE-MATH reciprocal throughput -- with FMA [####################] 100 % Ntrial = 20 ; Min = 39.792 + 1.011 clc/call; Median-Min = 0.940 clc/call; Max = 41.373 clc/call; -- CORE-MATH reciprocal throughput -- without FMA (-march=x86-64-v2) [####################] 100 % Ntrial = 20 ; Min = 87.285 + 1.135 clc/call; Median-Min = 1.299 clc/call; Max = 89.715 clc/call; -- System LIBC reciprocal throughput -- [####################] 100 % Ntrial = 20 ; Min = 20.666 + 0.123 clc/call; Median-Min = 0.125 clc/call; Max = 20.828 clc/call; -- LIBC reciprocal throughput -- with FMA [####################] 100 % Ntrial = 20 ; Min = 20.928 + 0.771 clc/call; Median-Min = 0.725 clc/call; Max = 22.767 clc/call; -- LIBC reciprocal throughput -- without FMA [####################] 100 % Ntrial = 20 ; Min = 31.461 + 0.528 clc/call; Median-Min = 0.602 clc/call; Max = 36.809 clc/call; ``` - Latency from CORE-MATH's perf tool on Ryzen 5900X: ``` $ ./perf.sh log1p --latency GNU libc version: 2.35 GNU libc release: stable -- CORE-MATH latency -- with FMA [####################] 100 % Ntrial = 20 ; Min = 77.875 + 0.062 clc/call; Median-Min = 0.051 clc/call; Max = 78.003 clc/call; -- CORE-MATH latency -- without FMA (-march=x86-64-v2) [####################] 100 % Ntrial = 20 ; Min = 101.958 + 1.202 clc/call; Median-Min = 1.325 clc/call; Max = 104.452 clc/call; -- System LIBC latency -- [####################] 100 % Ntrial = 20 ; Min = 60.581 + 1.443 clc/call; Median-Min = 1.611 clc/call; Max = 62.285 clc/call; -- LIBC latency -- with FMA [####################] 100 % Ntrial = 20 ; Min = 48.817 + 1.108 clc/call; Median-Min = 1.300 clc/call; Max = 50.282 clc/call; -- LIBC latency -- without FMA [####################] 100 % Ntrial = 20 ; Min = 61.121 + 0.599 clc/call; Median-Min = 0.761 clc/call; Max = 62.020 clc/call; ``` - Accurate pass latency: ``` $ ./perf.sh log1p --latency --simple_stat GNU libc version: 2.35 GNU libc release: stable -- CORE-MATH latency -- with FMA 760.444 -- CORE-MATH latency -- without FMA (-march=x86-64-v2) 827.880 -- LIBC latency -- with FMA 711.837 -- LIBC latency -- without FMA 764.317 ``` Reviewed By: zimmermann6 Differential Revision: https://reviews.llvm.org/D151049 |
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