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[libc][math] Implement double precision cos correctly rounded to all rounding modes. #96591
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| Original file line number | Diff line number | Diff line change |
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| //===-- Double-precision cos 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/cos.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/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_COS_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(double, cos, (double 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)) | ||
| return 1.0; | ||
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| // For |x| < 2^-27, |cos(x) - 1| < |x|^2/2 < 2^-54 = ulp(1 - 2^-53)/2. | ||
| return fputil::round_result_slightly_down(1.0); | ||
| } | ||
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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); | ||
| } | ||
| return x + FPBits::quiet_nan().get_val(); | ||
| } | ||
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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) & 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 + 128); | ||
| // DoubleDouble cos_k = get_idx_dd(k + 64); | ||
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| // Fast look up version, but needs 256-entry table. | ||
| // -sin(k * pi/128) = sin((k + 128) * pi/128) | ||
| // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128). | ||
| DoubleDouble msin_k = SIN_K_PI_OVER_128[(k + 128) & 255]; | ||
| DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255]; | ||
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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 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 rr = fputil::exact_add<false>(cos_k_cos_y.hi, msin_k_sin_y.hi); | ||
| rr.lo += msin_k_sin_y.lo + cos_k_cos_y.lo; | ||
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| #ifdef LIBC_MATH_COS_SKIP_ACCURATE_PASS | ||
| return rr.hi + rr.lo; | ||
| #else | ||
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| // 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 | ||
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| double rlp = rr.lo + ERR; | ||
| double rlm = rr.lo - ERR; | ||
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| double r_upper = rr.hi + rlp; // (rr.lo + ERR); | ||
| double r_lower = rr.hi + rlm; // (rr.lo - ERR); | ||
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| // Ziv's rounding test. | ||
| if (LIBC_LIKELY(r_upper == r_lower)) | ||
| return r_upper; | ||
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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]; | ||
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| if (kk & 128) | ||
| ans.sign = Sign::NEG; | ||
| return ans; | ||
| }; | ||
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| // -sin(k * pi/128) = sin((k + 128) * pi/128) | ||
| // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128). | ||
| Float128 msin_k_f128 = get_sin_k(k + 128); | ||
| Float128 cos_k_f128 = get_sin_k(k + 64); | ||
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| // cos(x) = cos((k * pi/128 + u) | ||
| // = cos(u) * cos(k*pi/128) - sin(u) * sin(k*pi/128) | ||
| Float128 r = fputil::quick_add(fputil::quick_mul(cos_k_f128, cos_u), | ||
| fputil::quick_mul(msin_k_f128, sin_u)); | ||
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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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| return static_cast<double>(r); | ||
| #endif // !LIBC_MATH_COS_SKIP_ACCURATE_PASS | ||
| } | ||
|
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| } // namespace LIBC_NAMESPACE | ||
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