1 //===-- Double-precision cos function -------------------------------------===// 2 // 3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 4 // See https://llvm.org/LICENSE.txt for license information. 5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 6 // 7 //===----------------------------------------------------------------------===// 8 9 #include "src/math/cos.h" 10 #include "hdr/errno_macros.h" 11 #include "src/__support/FPUtil/FEnvImpl.h" 12 #include "src/__support/FPUtil/FPBits.h" 13 #include "src/__support/FPUtil/double_double.h" 14 #include "src/__support/FPUtil/dyadic_float.h" 15 #include "src/__support/FPUtil/except_value_utils.h" 16 #include "src/__support/common.h" 17 #include "src/__support/macros/config.h" 18 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY 19 #include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA 20 #include "src/math/generic/range_reduction_double_common.h" 21 #include "src/math/generic/sincos_eval.h" 22 23 #ifdef LIBC_TARGET_CPU_HAS_FMA 24 #include "range_reduction_double_fma.h" 25 #else 26 #include "range_reduction_double_nofma.h" 27 #endif // LIBC_TARGET_CPU_HAS_FMA 28 29 namespace LIBC_NAMESPACE_DECL { 30 31 using DoubleDouble = fputil::DoubleDouble; 32 using Float128 = typename fputil::DyadicFloat<128>; 33 34 LLVM_LIBC_FUNCTION(double, cos, (double x)) { 35 using FPBits = typename fputil::FPBits<double>; 36 FPBits xbits(x); 37 38 uint16_t x_e = xbits.get_biased_exponent(); 39 40 DoubleDouble y; 41 unsigned k; 42 LargeRangeReduction range_reduction_large{}; 43 44 // |x| < 2^16. 45 if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) { 46 // |x| < 2^-7 47 if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 7)) { 48 // |x| < 2^-27 49 if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 27)) { 50 // Signed zeros. 51 if (LIBC_UNLIKELY(x == 0.0)) 52 return 1.0; 53 54 // For |x| < 2^-27, |cos(x) - 1| < |x|^2/2 < 2^-54 = ulp(1 - 2^-53)/2. 55 return fputil::round_result_slightly_down(1.0); 56 } 57 // No range reduction needed. 58 k = 0; 59 y.lo = 0.0; 60 y.hi = x; 61 } else { 62 // Small range reduction. 63 k = range_reduction_small(x, y); 64 } 65 } else { 66 // Inf or NaN 67 if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) { 68 // sin(+-Inf) = NaN 69 if (xbits.get_mantissa() == 0) { 70 fputil::set_errno_if_required(EDOM); 71 fputil::raise_except_if_required(FE_INVALID); 72 } 73 return x + FPBits::quiet_nan().get_val(); 74 } 75 76 // Large range reduction. 77 k = range_reduction_large.fast(x, y); 78 } 79 80 DoubleDouble sin_y, cos_y; 81 82 [[maybe_unused]] double err = generic::sincos_eval(y, sin_y, cos_y); 83 84 // Look up sin(k * pi/128) and cos(k * pi/128) 85 #ifdef LIBC_MATH_HAS_SMALL_TABLES 86 // Memory saving versions. Use 65-entry table. __anon30977e8a0102(unsigned kk) 87 auto get_idx_dd = [](unsigned kk) -> DoubleDouble { 88 unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63); 89 DoubleDouble ans = SIN_K_PI_OVER_128[idx]; 90 if (kk & 128) { 91 ans.hi = -ans.hi; 92 ans.lo = -ans.lo; 93 } 94 return ans; 95 }; 96 DoubleDouble msin_k = get_idx_dd(k + 128); 97 DoubleDouble cos_k = get_idx_dd(k + 64); 98 #else 99 // Fast look up version, but needs 256-entry table. 100 // -sin(k * pi/128) = sin((k + 128) * pi/128) 101 // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128). 102 DoubleDouble msin_k = SIN_K_PI_OVER_128[(k + 128) & 255]; 103 DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255]; 104 #endif // LIBC_MATH_HAS_SMALL_TABLES 105 106 // After range reduction, k = round(x * 128 / pi) and y = x - k * (pi / 128). 107 // So k is an integer and -pi / 256 <= y <= pi / 256. 108 // Then cos(x) = cos((k * pi/128 + y) 109 // = cos(y) * cos(k*pi/128) - sin(y) * sin(k*pi/128) 110 DoubleDouble cos_k_cos_y = fputil::quick_mult(cos_y, cos_k); 111 DoubleDouble msin_k_sin_y = fputil::quick_mult(sin_y, msin_k); 112 113 DoubleDouble rr = fputil::exact_add<false>(cos_k_cos_y.hi, msin_k_sin_y.hi); 114 rr.lo += msin_k_sin_y.lo + cos_k_cos_y.lo; 115 116 #ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS 117 return rr.hi + rr.lo; 118 #else 119 120 double rlp = rr.lo + err; 121 double rlm = rr.lo - err; 122 123 double r_upper = rr.hi + rlp; // (rr.lo + ERR); 124 double r_lower = rr.hi + rlm; // (rr.lo - ERR); 125 126 // Ziv's rounding test. 127 if (LIBC_LIKELY(r_upper == r_lower)) 128 return r_upper; 129 130 Float128 u_f128, sin_u, cos_u; 131 if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) 132 u_f128 = range_reduction_small_f128(x); 133 else 134 u_f128 = range_reduction_large.accurate(); 135 136 generic::sincos_eval(u_f128, sin_u, cos_u); 137 __anon30977e8a0202(unsigned kk) 138 auto get_sin_k = [](unsigned kk) -> Float128 { 139 unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63); 140 Float128 ans = SIN_K_PI_OVER_128_F128[idx]; 141 if (kk & 128) 142 ans.sign = Sign::NEG; 143 return ans; 144 }; 145 146 // -sin(k * pi/128) = sin((k + 128) * pi/128) 147 // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128). 148 Float128 msin_k_f128 = get_sin_k(k + 128); 149 Float128 cos_k_f128 = get_sin_k(k + 64); 150 151 // cos(x) = cos((k * pi/128 + u) 152 // = cos(u) * cos(k*pi/128) - sin(u) * sin(k*pi/128) 153 Float128 r = fputil::quick_add(fputil::quick_mul(cos_k_f128, cos_u), 154 fputil::quick_mul(msin_k_f128, sin_u)); 155 156 // TODO: Add assertion if Ziv's accuracy tests fail in debug mode. 157 // https://github.com/llvm/llvm-project/issues/96452. 158 159 return static_cast<double>(r); 160 #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS 161 } 162 163 } // namespace LIBC_NAMESPACE_DECL 164