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Diffstat (limited to 'libc/src/math/generic/sin.cpp')
| -rw-r--r-- | libc/src/math/generic/sin.cpp | 207 |
1 files changed, 207 insertions, 0 deletions
diff --git a/libc/src/math/generic/sin.cpp b/libc/src/math/generic/sin.cpp new file mode 100644 index 000000000000..207435d4385a --- /dev/null +++ b/libc/src/math/generic/sin.cpp @@ -0,0 +1,207 @@ +//===-- Double-precision sin 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 +// +//===----------------------------------------------------------------------===// + +#include "src/math/sin.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/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" + +#ifdef LIBC_TARGET_CPU_HAS_FMA +#include "range_reduction_double_fma.h" + +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; + +LIBC_INLINE constexpr bool NO_FMA = false; +#else +#include "range_reduction_double_nofma.h" + +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; + +LIBC_INLINE constexpr bool NO_FMA = true; +#endif // LIBC_TARGET_CPU_HAS_FMA + +// 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" + +#if ((LIBC_MATH & LIBC_MATH_SKIP_ACCURATE_PASS) != 0) +#define LIBC_MATH_SIN_SKIP_ACCURATE_PASS +#endif + +namespace LIBC_NAMESPACE { + +using DoubleDouble = fputil::DoubleDouble; +using Float128 = typename fputil::DyadicFloat<128>; + +LLVM_LIBC_FUNCTION(double, sin, (double x)) { + using FPBits = typename fputil::FPBits<double>; + FPBits xbits(x); + + uint16_t x_e = xbits.get_biased_exponent(); + + DoubleDouble y; + unsigned k; + generic::LargeRangeReduction<NO_FMA> range_reduction_large; + + // |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^-26 + if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 26)) { + // Signed zeros. + if (LIBC_UNLIKELY(x == 0.0)) + return x; + + // For |x| < 2^-26, |sin(x) - x| < ulp(x)/2. +#ifdef LIBC_TARGET_CPU_HAS_FMA + return fputil::multiply_add(x, -0x1.0p-54, x); +#else + 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)) + return FPBits(xbits.uintval() - 1).get_val(); + } + return fputil::multiply_add(x, -0x1.0p-54, x); +#endif // LIBC_TARGET_CPU_HAS_FMA + } + + // // 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); + } + return x + FPBits::quiet_nan().get_val(); + } + + // Large range reduction. + k = range_reduction_large.compute_high_part(x); + y = range_reduction_large.fast(); + } + + DoubleDouble sin_y, cos_y; + + generic::sincos_eval(y, sin_y, cos_y); + + // Look up sin(k * pi/128) and cos(k * pi/128) + // Memory saving versions: + + // 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(); + + // 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); + + // 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]; + + // 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); + + DoubleDouble rr = fputil::exact_add<false>(sin_k_cos_y.hi, cos_k_sin_y.hi); + rr.lo += sin_k_cos_y.lo + cos_k_sin_y.lo; + +#ifdef LIBC_MATH_SIN_SKIP_ACCURATE_PASS + return rr.hi + rr.lo; +#else + // Accurate test and pass for correctly rounded implementation. + +#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 + + double rlp = rr.lo + ERR; + double rlm = rr.lo - ERR; + + double r_upper = rr.hi + rlp; // (rr.lo + ERR); + double r_lower = rr.hi + rlm; // (rr.lo - ERR); + + // Ziv's rounding test. + if (LIBC_LIKELY(r_upper == r_lower)) + return r_upper; + + 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(); + + generic::sincos_eval(u_f128, sin_u, cos_u); + + 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; + }; + + // 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); + + // sin(x) = sin((k * pi/128 + u) + // = sin(u) * cos(k*pi/128) + cos(u) * sin(k*pi/128) + Float128 r = fputil::quick_add(fputil::quick_mul(sin_k_f128, cos_u), + fputil::quick_mul(cos_k_f128, sin_u)); + + // TODO: Add assertion if Ziv's accuracy tests fail in debug mode. + // https://github.com/llvm/llvm-project/issues/96452. + + return static_cast<double>(r); +#endif // !LIBC_MATH_SIN_SKIP_ACCURATE_PASS +} + +} // namespace LIBC_NAMESPACE |
