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[libc][math] Implement double precision sincos correctly rounded to a…
…ll rounding modes. (llvm#96719) Sharing the same algorithm as double precision sin: llvm#95736 and cos: llvm#96591
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//===-- Double-precision sincos function ----------------------------------===// | ||
// | ||
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. | ||
// See https://llvm.org/LICENSE.txt for license information. | ||
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception | ||
// | ||
//===----------------------------------------------------------------------===// | ||
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#include "src/math/sincos.h" | ||
#include "hdr/errno_macros.h" | ||
#include "src/__support/FPUtil/FEnvImpl.h" | ||
#include "src/__support/FPUtil/FPBits.h" | ||
#include "src/__support/FPUtil/double_double.h" | ||
#include "src/__support/FPUtil/dyadic_float.h" | ||
#include "src/__support/FPUtil/except_value_utils.h" | ||
#include "src/__support/FPUtil/multiply_add.h" | ||
#include "src/__support/FPUtil/rounding_mode.h" | ||
#include "src/__support/common.h" | ||
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY | ||
#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA | ||
#include "src/math/generic/sincos_eval.h" | ||
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#ifdef LIBC_TARGET_CPU_HAS_FMA | ||
#include "range_reduction_double_fma.h" | ||
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using LIBC_NAMESPACE::fma::FAST_PASS_EXPONENT; | ||
using LIBC_NAMESPACE::fma::ONE_TWENTY_EIGHT_OVER_PI; | ||
using LIBC_NAMESPACE::fma::range_reduction_small; | ||
using LIBC_NAMESPACE::fma::SIN_K_PI_OVER_128; | ||
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LIBC_INLINE constexpr bool NO_FMA = false; | ||
#else | ||
#include "range_reduction_double_nofma.h" | ||
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using LIBC_NAMESPACE::nofma::FAST_PASS_EXPONENT; | ||
using LIBC_NAMESPACE::nofma::ONE_TWENTY_EIGHT_OVER_PI; | ||
using LIBC_NAMESPACE::nofma::range_reduction_small; | ||
using LIBC_NAMESPACE::nofma::SIN_K_PI_OVER_128; | ||
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LIBC_INLINE constexpr bool NO_FMA = true; | ||
#endif // LIBC_TARGET_CPU_HAS_FMA | ||
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// TODO: We might be able to improve the performance of large range reduction of | ||
// non-FMA targets further by operating directly on 25-bit chunks of 128/pi and | ||
// pre-split SIN_K_PI_OVER_128, but that might double the memory footprint of | ||
// those lookup table. | ||
#include "range_reduction_double_common.h" | ||
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#if ((LIBC_MATH & LIBC_MATH_SKIP_ACCURATE_PASS) != 0) | ||
#define LIBC_MATH_SINCOS_SKIP_ACCURATE_PASS | ||
#endif | ||
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namespace LIBC_NAMESPACE { | ||
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using DoubleDouble = fputil::DoubleDouble; | ||
using Float128 = typename fputil::DyadicFloat<128>; | ||
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LLVM_LIBC_FUNCTION(void, sincos, (double x, double *sin_x, double *cos_x)) { | ||
using FPBits = typename fputil::FPBits<double>; | ||
FPBits xbits(x); | ||
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uint16_t x_e = xbits.get_biased_exponent(); | ||
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DoubleDouble y; | ||
unsigned k; | ||
generic::LargeRangeReduction<NO_FMA> range_reduction_large; | ||
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// |x| < 2^32 (with FMA) or |x| < 2^23 (w/o FMA) | ||
if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) { | ||
// |x| < 2^-27 | ||
if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 27)) { | ||
// Signed zeros. | ||
if (LIBC_UNLIKELY(x == 0.0)) { | ||
*sin_x = x; | ||
*cos_x = 1.0; | ||
return; | ||
} | ||
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// For |x| < 2^-27, max(|sin(x) - x|, |cos(x) - 1|) < ulp(x)/2. | ||
#ifdef LIBC_TARGET_CPU_HAS_FMA | ||
*sin_x = fputil::multiply_add(x, -0x1.0p-54, x); | ||
*cos_x = fputil::multiply_add(x, -x, 1.0); | ||
#else | ||
*cos_x = fputil::round_result_slightly_down(1.0); | ||
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if (LIBC_UNLIKELY(x_e < 4)) { | ||
int rounding_mode = fputil::quick_get_round(); | ||
if (rounding_mode == FE_TOWARDZERO || | ||
(xbits.sign() == Sign::POS && rounding_mode == FE_DOWNWARD) || | ||
(xbits.sign() == Sign::NEG && rounding_mode == FE_UPWARD)) | ||
*sin_x = FPBits(xbits.uintval() - 1).get_val(); | ||
} | ||
*sin_x = fputil::multiply_add(x, -0x1.0p-54, x); | ||
#endif // LIBC_TARGET_CPU_HAS_FMA | ||
return; | ||
} | ||
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// // Small range reduction. | ||
k = range_reduction_small(x, y); | ||
} else { | ||
// Inf or NaN | ||
if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) { | ||
// sin(+-Inf) = NaN | ||
if (xbits.get_mantissa() == 0) { | ||
fputil::set_errno_if_required(EDOM); | ||
fputil::raise_except_if_required(FE_INVALID); | ||
} | ||
*sin_x = *cos_x = x + FPBits::quiet_nan().get_val(); | ||
return; | ||
} | ||
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// Large range reduction. | ||
k = range_reduction_large.compute_high_part(x); | ||
y = range_reduction_large.fast(); | ||
} | ||
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DoubleDouble sin_y, cos_y; | ||
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generic::sincos_eval(y, sin_y, cos_y); | ||
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// Look up sin(k * pi/128) and cos(k * pi/128) | ||
// Memory saving versions: | ||
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// Use 128-entry table instead: | ||
// DoubleDouble sin_k = SIN_K_PI_OVER_128[k & 127]; | ||
// uint64_t sin_s = static_cast<uint64_t>(k & 128) << (63 - 7); | ||
// sin_k.hi = FPBits(FPBits(sin_k.hi).uintval() ^ sin_s).get_val(); | ||
// sin_k.lo = FPBits(FPBits(sin_k.hi).uintval() ^ sin_s).get_val(); | ||
// DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 127]; | ||
// uint64_t cos_s = static_cast<uint64_t>((k + 64) & 128) << (63 - 7); | ||
// cos_k.hi = FPBits(FPBits(cos_k.hi).uintval() ^ cos_s).get_val(); | ||
// cos_k.lo = FPBits(FPBits(cos_k.hi).uintval() ^ cos_s).get_val(); | ||
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// Use 64-entry table instead: | ||
// auto get_idx_dd = [](unsigned kk) -> DoubleDouble { | ||
// unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63); | ||
// DoubleDouble ans = SIN_K_PI_OVER_128[idx]; | ||
// if (kk & 128) { | ||
// ans.hi = -ans.hi; | ||
// ans.lo = -ans.lo; | ||
// } | ||
// return ans; | ||
// }; | ||
// DoubleDouble sin_k = get_idx_dd(k); | ||
// DoubleDouble cos_k = get_idx_dd(k + 64); | ||
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// Fast look up version, but needs 256-entry table. | ||
// cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128). | ||
DoubleDouble sin_k = SIN_K_PI_OVER_128[k & 255]; | ||
DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255]; | ||
DoubleDouble msin_k{-sin_k.lo, -sin_k.hi}; | ||
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// After range reduction, k = round(x * 128 / pi) and y = x - k * (pi / 128). | ||
// So k is an integer and -pi / 256 <= y <= pi / 256. | ||
// Then sin(x) = sin((k * pi/128 + y) | ||
// = sin(y) * cos(k*pi/128) + cos(y) * sin(k*pi/128) | ||
DoubleDouble sin_k_cos_y = fputil::quick_mult<NO_FMA>(cos_y, sin_k); | ||
DoubleDouble cos_k_sin_y = fputil::quick_mult<NO_FMA>(sin_y, cos_k); | ||
// cos(x) = cos((k * pi/128 + y) | ||
// = cos(y) * cos(k*pi/128) - sin(y) * sin(k*pi/128) | ||
DoubleDouble cos_k_cos_y = fputil::quick_mult<NO_FMA>(cos_y, cos_k); | ||
DoubleDouble msin_k_sin_y = fputil::quick_mult<NO_FMA>(sin_y, msin_k); | ||
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DoubleDouble sin_dd = | ||
fputil::exact_add<false>(sin_k_cos_y.hi, cos_k_sin_y.hi); | ||
DoubleDouble cos_dd = | ||
fputil::exact_add<false>(cos_k_cos_y.hi, msin_k_sin_y.hi); | ||
sin_dd.lo += sin_k_cos_y.lo + cos_k_sin_y.lo; | ||
cos_dd.lo += msin_k_sin_y.lo + cos_k_cos_y.lo; | ||
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#ifdef LIBC_MATH_SINCOS_SKIP_ACCURATE_PASS | ||
*sin_x = sin_dd.hi + sin_dd.lo; | ||
*cos_x = cos_dd.hi + cos_dd.lo; | ||
return; | ||
#else | ||
// Accurate test and pass for correctly rounded implementation. | ||
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#ifdef LIBC_TARGET_CPU_HAS_FMA | ||
constexpr double ERR = 0x1.0p-70; | ||
#else | ||
// TODO: Improve non-FMA fast pass accuracy. | ||
constexpr double ERR = 0x1.0p-66; | ||
#endif // LIBC_TARGET_CPU_HAS_FMA | ||
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double sin_lp = sin_dd.lo + ERR; | ||
double sin_lm = sin_dd.lo - ERR; | ||
double cos_lp = cos_dd.lo + ERR; | ||
double cos_lm = cos_dd.lo - ERR; | ||
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double sin_upper = sin_dd.hi + sin_lp; | ||
double sin_lower = sin_dd.hi + sin_lm; | ||
double cos_upper = cos_dd.hi + cos_lp; | ||
double cos_lower = cos_dd.hi + cos_lm; | ||
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// Ziv's rounding test. | ||
if (LIBC_LIKELY(sin_upper == sin_lower && cos_upper == cos_lower)) { | ||
*sin_x = sin_upper; | ||
*cos_x = cos_upper; | ||
return; | ||
} | ||
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Float128 u_f128, sin_u, cos_u; | ||
if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) | ||
u_f128 = generic::range_reduction_small_f128(x); | ||
else | ||
u_f128 = range_reduction_large.accurate(); | ||
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generic::sincos_eval(u_f128, sin_u, cos_u); | ||
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auto get_sin_k = [](unsigned kk) -> Float128 { | ||
unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63); | ||
Float128 ans = generic::SIN_K_PI_OVER_128_F128[idx]; | ||
if (kk & 128) | ||
ans.sign = Sign::NEG; | ||
return ans; | ||
}; | ||
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// cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128). | ||
Float128 sin_k_f128 = get_sin_k(k); | ||
Float128 cos_k_f128 = get_sin_k(k + 64); | ||
Float128 msin_k_f128 = get_sin_k(k + 128); | ||
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// TODO: Add assertion if Ziv's accuracy tests fail in debug mode. | ||
// https://github.com/llvm/llvm-project/issues/96452. | ||
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if (sin_upper == sin_lower) | ||
*sin_x = sin_upper; | ||
else | ||
// sin(x) = sin((k * pi/128 + u) | ||
// = sin(u) * cos(k*pi/128) + cos(u) * sin(k*pi/128) | ||
*sin_x = static_cast<double>( | ||
fputil::quick_add(fputil::quick_mul(sin_k_f128, cos_u), | ||
fputil::quick_mul(cos_k_f128, sin_u))); | ||
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if (cos_upper == cos_lower) | ||
*cos_x = cos_upper; | ||
else | ||
// cos(x) = cos((k * pi/128 + u) | ||
// = cos(u) * cos(k*pi/128) - sin(u) * sin(k*pi/128) | ||
*cos_x = static_cast<double>( | ||
fputil::quick_add(fputil::quick_mul(cos_k_f128, cos_u), | ||
fputil::quick_mul(msin_k_f128, sin_u))); | ||
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#endif // !LIBC_MATH_SINCOS_SKIP_ACCURATE_PASS | ||
} | ||
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} // namespace LIBC_NAMESPACE |
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