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Fancy macros which cannot be much fancier without breaking the osaca …
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…parser
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@eggrobin
eggrobin committed Dec 30, 2024
1 parent 2fb082b commit 84754d4
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113 changes: 84 additions & 29 deletions numerics/sin_cos.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -16,8 +16,61 @@

#if PRINCIPIA_USE_OSACA_SIN || PRINCIPIA_USE_OSACA_COS
#include "intel/iacaMarks.h"
static bool iaca_breaker = false;
#define IACA_FUNCTION_DOUBLE(arg) \
volatile double iaca_result = arg; \
IACA_VC64_START; \
IACA_LOOP: \
arg = iaca_result
#define IACA_RETURN(result) \
iaca_result = result; \
if (iaca_breaker) { \
goto IACA_END_LOOP; \
} else { \
goto IACA_LOOP; \
}
#define IACA_FUNCTION_END \
goto IACA_LOOP; \
IACA_END_LOOP: \
IACA_VC64_END; \
return iaca_result
#define IACA_IF(condition) \
if constexpr (volatile bool IACA_computed_condition = (condition); \
[] { UNDER_IACA_HYPOTHESES(return (condition)); }())

#define UNDER_IACA_HYPOTHESES(statement) \
do { \
constexpr bool UseHardwareFMA = true; \
constexpr double θ = 0.1; \
/* From argument reduction. */ \
constexpr double n_double = θ * (2 / π); \
constexpr double reduction_value = θ - n_double * π_over_2_high; \
constexpr double reduction_error = n_double * π_over_2_low; \
/* Used to determine whether a better argument reduction is needed. */ \
constexpr DoublePrecision<double> θ_reduced = \
QuickTwoDifference(reduction_value, reduction_error); \
/* Used in Sin to detect the near-0 case. */ \
constexpr double abs_x = \
θ_reduced.value > 0 ? θ_reduced.value : -θ_reduced.value; \
/* Used throughout the top-level functions. */ \
constexpr std::int64_t quadrant = \
static_cast<std::int64_t>(n_double) & 0b11; \
/* Used in DetectDangerousRounding. */ \
constexpr double normalized_error = 0; \
/* Not NaN is the only part that matters; used at the end of the top-level \

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readability/multiline_comment 

Complex multi-line /*...*/-style comment found. Lint may give bogus warnings.  Consider replacing these with //-style comments, with #if 0...#endif, or with more clearly structured multi-line comments.
* functions to determine whether to call the slow path. */ \

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constexpr double value = 1; \
{ statement; } \
} while (false)

#else
#define IACA_FUNCTION_DOUBLE(arg) (double const arg)
#define IACA_RETURN(result) return result
#define IACA_IF (condition) if (condition)
#define UNDER_IACA_HYPOTHESES(statement)
#endif


namespace principia {
namespace numerics {
namespace _sin_cos {
Expand Down Expand Up @@ -75,8 +128,8 @@ inline std::int64_t AccurateTableIndex(double const abs_x) {

template<FMAPolicy fma_policy>
double FusedMultiplyAdd(double const a, double const b, double const c) {
if ((fma_policy == FMAPolicy::Force && CanEmitFMAInstructions) ||
(fma_policy == FMAPolicy::Auto && UseHardwareFMA)) {
IACA_IF ((fma_policy == FMAPolicy::Force && CanEmitFMAInstructions) ||

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(fma_policy == FMAPolicy::Auto && UseHardwareFMA)) {
using quantities::_elementary_functions::FusedMultiplyAdd;
return FusedMultiplyAdd(a, b, c);
} else {
Expand All @@ -86,8 +139,8 @@ double FusedMultiplyAdd(double const a, double const b, double const c) {

template<FMAPolicy fma_policy>
double FusedNegatedMultiplyAdd(double const a, double const b, double const c) {
if ((fma_policy == FMAPolicy::Force && CanEmitFMAInstructions) ||
(fma_policy == FMAPolicy::Auto && UseHardwareFMA)) {
IACA_IF ((fma_policy == FMAPolicy::Force && CanEmitFMAInstructions) ||

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(fma_policy == FMAPolicy::Auto && UseHardwareFMA)) {
using quantities::_elementary_functions::FusedNegatedMultiplyAdd;
return FusedNegatedMultiplyAdd(a, b, c);
} else {
Expand All @@ -110,7 +163,8 @@ inline double DetectDangerousRounding(double const x, double const Δx) {
_mm_castsi128_pd(_mm_sub_epi64(error_128i, value_exponent_128i)));
// TODO(phl): Error analysis to refine the thresholds. Also, can we avoid
// negative numbers?
if (normalized_error < -0x1.ffffp971 && normalized_error > -0x1.00008p972) {
IACA_IF (normalized_error < -0x1.ffffp971 &&

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normalized_error > -0x1.00008p972) {
#if _DEBUG
LOG(ERROR) << std::setprecision(25) << x << " " << std::hexfloat << value
<< " " << error << " " << normalized_error;
Expand All @@ -124,12 +178,12 @@ inline double DetectDangerousRounding(double const x, double const Δx) {
inline void Reduce(Argument const θ,
DoublePrecision<Argument>& θ_reduced,
std::int64_t& quadrant) {
if (θ < π / 4 && θ > -π / 4) {
IACA_IF (θ < π / 4 && θ > -π / 4) {

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θ_reduced.value = θ;
θ_reduced.error = 0;
quadrant = 0;
return;
} else if (θ <= π_over_2_threshold && θ >= -π_over_2_threshold) {
} else IACA_IF (θ <= π_over_2_threshold && θ >= -π_over_2_threshold) {

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// We are not very sensitive to rounding errors in this expression, because
// in the worst case it could cause the reduced angle to jump from the
// vicinity of π / 4 to the vicinity of -π / 4 with appropriate adjustment
Expand All @@ -142,7 +196,7 @@ inline void Reduce(Argument const 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.
if (θ_reduced.value < -0x1.0p-30 || θ_reduced.value > 0x1.0p-30) {
IACA_IF (θ_reduced.value < -0x1.0p-30 || θ_reduced.value > 0x1.0p-30) {

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quadrant = n & 0b11;
return;
}
Expand Down Expand Up @@ -180,7 +234,7 @@ Value SinImplementation(DoublePrecision<Argument> const θ_reduced) {
auto const& x = θ_reduced.value;
auto const& e = θ_reduced.error;
double const abs_x = std::abs(x);
if (abs_x < sin_near_zero_cutoff) {
IACA_IF (abs_x < sin_near_zero_cutoff) {

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double const x² = x * x;
double const x³ = x² * x;
double const x³_term = FusedMultiplyAdd<fma_policy>(
Expand Down Expand Up @@ -257,8 +311,8 @@ Value __cdecl Sin(Argument const θ) {
std::int64_t quadrant;
Reduce(θ, θ_reduced, quadrant);
double value;
if (UseHardwareFMA) {
if (quadrant & 0b1) {
IACA_IF (UseHardwareFMA) {
IACA_IF (quadrant & 0b1) {
value = CosImplementation<FMAPolicy::Force>(θ_reduced);
} else {
#if PRINCIPIA_USE_OSACA_SIN
Expand All @@ -270,55 +324,56 @@ Value __cdecl Sin(Argument const θ) {
#endif
}
} else {
if (quadrant & 0b1) {
IACA_IF (quadrant & 0b1) {
value = CosImplementation<FMAPolicy::Disallow>(θ_reduced);
} else {
value = SinImplementation<FMAPolicy::Disallow>(θ_reduced);
}
}
if (value != value) {
IACA_IF (value != value) {
return cr_sin(θ);
} else if (quadrant & 0b10) {
}
IACA_IF (quadrant & 0b10) {
return -value;
} else {
return value;
}
}

namespace IACA_assumptions {
constexpr std::int64_t quadrant = 1;
} // namespace IACA_assumptions

#if PRINCIPIA_INLINE_SIN_COS
FORCE_INLINE(inline)
#endif
Value __cdecl Cos(Argument const θ) {
Value __cdecl Cos(Argument θ) {
IACA_FUNCTION_DOUBLE(θ);
DoublePrecision<Argument> θ_reduced;
std::int64_t quadrant;
Reduce(θ, θ_reduced, quadrant);
double value;
if (UseHardwareFMA) {
if (quadrant & 0b1) {
IACA_IF (UseHardwareFMA) {
IACA_IF (quadrant & 0b1) {
value = SinImplementation<FMAPolicy::Force>(θ_reduced);
} else {
#if PRINCIPIA_USE_OSACA_COS
IACA_VC64_START;
#endif
value = CosImplementation<FMAPolicy::Force>(θ_reduced);
#if PRINCIPIA_USE_OSACA_COS
IACA_VC64_END;
#endif
}
} else {
if (quadrant & 0b1) {
IACA_IF (quadrant & 0b1) {
value = SinImplementation<FMAPolicy::Disallow>(θ_reduced);
} else {
value = CosImplementation<FMAPolicy::Disallow>(θ_reduced);
}
}
if (value != value) {
return cr_cos(θ);
} else if (quadrant == 1 || quadrant == 2) {
return -value;
IACA_IF (value != value) {
IACA_RETURN(cr_cos(θ));
} else IACA_IF (quadrant == 1 || quadrant == 2) {
IACA_RETURN(-value);
} else {
return value;
IACA_RETURN(value);
}
IACA_FUNCTION_END;
}

} // namespace internal
Expand Down
4 changes: 2 additions & 2 deletions numerics/sin_cos.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -7,9 +7,9 @@ namespace numerics {
namespace _sin_cos {
namespace internal {

#define PRINCIPIA_INLINE_SIN_COS 0
#define PRINCIPIA_INLINE_SIN_COS 1
#define PRINCIPIA_USE_OSACA_SIN 0
#define PRINCIPIA_USE_OSACA_COS 0
#define PRINCIPIA_USE_OSACA_COS 1

#if PRINCIPIA_INLINE_SIN_COS
FORCE_INLINE(inline)
Expand Down

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