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Do not preserve the sign in argument reduction if computing a Cos #4161

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merged 9 commits into from
Jan 27, 2025
Merged

Do not preserve the sign in argument reduction if computing a Cos #4161

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6065459
Do not preserve the sign during reduction if evaluating a Cos.
pleroy Jan 11, 2025
55c7c8e
More symmetry.
pleroy Jan 12, 2025
4369b7b
Do not preserve the sign during reduction if evaluating a Cos.
pleroy Jan 12, 2025
43273b6
Do not preserve the sign during reduction if evaluating a Cos.
pleroy Jan 12, 2025
9950902
Redundant computation.
pleroy Jan 26, 2025
b4846ab
Merge remote-tracking branch 'mockingbirdnest/master' into NoSignForCos
pleroy Jan 27, 2025
d8206da
Merge
pleroy Jan 27, 2025
c5019e3
Comment.
pleroy Jan 27, 2025
1dc0634
Comment.
pleroy Jan 27, 2025
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35 changes: 23 additions & 12 deletions numerics/sin_cos.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -151,7 +151,7 @@ inline double DetectDangerousRounding(double const x, double const Δx) {
}
}

template<FMAPolicy fma_policy>
template<FMAPolicy fma_policy, bool preserve_sign>
inline void Reduce(Argument const θ,
DoublePrecision<Argument>& θ_reduced,
std::int64_t& quadrant) {
Expand All @@ -167,14 +167,24 @@ inline void Reduce(Argument const θ,
// vicinity of π / 4 to the vicinity of -π / 4 with appropriate adjustment
// of the quadrant.
__m128d const sign = _mm_and_pd(masks::sign_bit, _mm_set_sd(θ));
double const n_shifted =
FusedMultiplyAdd<fma_policy>(abs_θ, (2 / π), mantissa_reduce_shifter);
double const n_double = _mm_cvtsd_f64(
_mm_xor_pd(_mm_set_sd(n_shifted - mantissa_reduce_shifter), sign));
std::int64_t const n = _mm_cvtsd_si64(_mm_set_sd(n_double));
double n_double =
FusedMultiplyAdd<fma_policy>(abs_θ, (2 / π), mantissa_reduce_shifter) -
mantissa_reduce_shifter;

// Don't move the computation of `n` after the if, it generates some extra
// moves.
Argument value;
std::int64_t n;
if constexpr (preserve_sign) {
n_double = _mm_cvtsd_f64(_mm_xor_pd(_mm_set_sd(n_double), sign));
n = _mm_cvtsd_si64(_mm_set_sd(n_double));
value = FusedNegatedMultiplyAdd<fma_policy>(n_double, π_over_2_high, θ);
} else {
n = _mm_cvtsd_si64(_mm_set_sd(n_double));
value =
FusedNegatedMultiplyAdd<fma_policy>(n_double, π_over_2_high, abs_θ);
}

Argument const value =
FusedNegatedMultiplyAdd<fma_policy>(n_double, π_over_2_high, θ);
Argument const error = n_double * π_over_2_low;
θ_reduced = QuickTwoDifference(value, error);
// TODO(phl): Error analysis needed to find the right bounds.
Expand Down Expand Up @@ -294,14 +304,14 @@ Value __cdecl Sin(Argument θ) {
std::int64_t quadrant;
double value;
OSACA_IF(UseHardwareFMA) {
Reduce<FMAPolicy::Force>(θ, θ_reduced, quadrant);
Reduce<FMAPolicy::Force, /*preserve_sign=*/true>(θ, θ_reduced, quadrant);
OSACA_IF(quadrant & 0b1) {
value = CosImplementation<FMAPolicy::Force>(θ_reduced);
} else {
value = SinImplementation<FMAPolicy::Force>(θ_reduced);
}
} else {
Reduce<FMAPolicy::Disallow>(θ, θ_reduced, quadrant);
Reduce<FMAPolicy::Disallow, /*preserve_sign=*/true>(θ, θ_reduced, quadrant);
OSACA_IF(quadrant & 0b1) {
value = CosImplementation<FMAPolicy::Disallow>(θ_reduced);
} else {
Expand All @@ -323,14 +333,15 @@ Value __cdecl Cos(Argument θ) {
std::int64_t quadrant;
double value;
OSACA_IF(UseHardwareFMA) {
Reduce<FMAPolicy::Force>(θ, θ_reduced, quadrant);
Reduce<FMAPolicy::Force, /*preserve_sign=*/false>(θ, θ_reduced, quadrant);
OSACA_IF(quadrant & 0b1) {
value = SinImplementation<FMAPolicy::Force>(θ_reduced);
} else {
value = CosImplementation<FMAPolicy::Force>(θ_reduced);
}
} else {
Reduce<FMAPolicy::Disallow>(θ, θ_reduced, quadrant);
Reduce<FMAPolicy::Disallow,
/*preserve_sign=*/false>(θ, θ_reduced, quadrant);
OSACA_IF(quadrant & 0b1) {
value = SinImplementation<FMAPolicy::Disallow>(θ_reduced);
} else {
Expand Down