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perf: Log is a port of Arm's optimized-routines log; fixes subnormals on amd64 - #17
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Log went through Map(math.Log): 11.6 ns per element on a Zen 3 core
against NumPy's 4.2. It now runs a port of the double-precision log of
Arm's optimized-routines (the companion of the Exp port, glibc's since
2.28; MIT licence, attributed): a 128-entry {1/c, log(c)} table and a
degree-6 polynomial, a degree-12 one within 2^-4 of 1, and z/c - 1 as one
math.FMA, exact on every target. Log10 is log(x)*(1/ln10), math.Log10's
own formula, on this log.
Accuracy: worst 0.508 ULP against a 300-bit reference over 10 000 inputs
(math.Log: 0.727 on arm64). TestLogTable checks all 128 entries against
the properties log_data.c documents. Speed at 16 Ki on one core: M4
37 us (math.Log 72), Zen 3 73 us (math.Log 175, NumPy 69).
It also removes a Go bug go-ndarray inherited: Go 1.26's amd64 math.Log
is wrong for subnormal inputs (log(5e-324) = -709.09 instead of -744.44,
log(1e-310) = -709.09 instead of -713.80), confirmed on a real Zen 3.
TestLogSubnormal fails with the old Map(math.Log) under amd64.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Log went through Map(math.Log): 11.6 ns per element on a Zen 3 core
against NumPy's 4.2. It now runs a port of the double-precision log of
Arm's optimized-routines (the companion of the Exp port, glibc's since
2.28; MIT licence, attributed): a 128-entry {1/c, log(c)} table and a
degree-6 polynomial, a degree-12 one within 2^-4 of 1, and z/c - 1 as one
math.FMA, exact on every target. Log10 is log(x)*(1/ln10), math.Log10's
own formula, on this log.
Accuracy: worst 0.508 ULP against a 300-bit reference over 10 000 inputs
(math.Log: 0.727 on arm64). TestLogTable checks all 128 entries against
the properties log_data.c documents. Speed at 16 Ki on one core: M4
37 us (math.Log 72), Zen 3 73 us (math.Log 175, NumPy 69).
It also removes a Go bug go-ndarray inherited: Go 1.26's amd64 math.Log
is wrong for subnormal inputs (log(5e-324) = -709.09 instead of -744.44,
log(1e-310) = -709.09 instead of -713.80), confirmed on a real Zen 3.
TestLogSubnormal fails with the old Map(math.Log) under amd64.
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