1 //===-- Single-precision cospi 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/cospif.h" 10 #include "sincosf_utils.h" 11 #include "src/__support/FPUtil/FEnvImpl.h" 12 #include "src/__support/FPUtil/FPBits.h" 13 #include "src/__support/FPUtil/multiply_add.h" 14 #include "src/__support/common.h" 15 #include "src/__support/macros/config.h" 16 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY 17 #include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA 18 19 namespace LIBC_NAMESPACE_DECL { 20 21 LLVM_LIBC_FUNCTION(float, cospif, (float x)) { 22 using FPBits = typename fputil::FPBits<float>; 23 24 FPBits xbits(x); 25 xbits.set_sign(Sign::POS); 26 27 uint32_t x_abs = xbits.uintval(); 28 double xd = static_cast<double>(xbits.get_val()); 29 30 // Range reduction: 31 // For |x| > 1/32, we perform range reduction as follows: 32 // Find k and y such that: 33 // x = (k + y) * 1/32 34 // k is an integer 35 // |y| < 0.5 36 // 37 // This is done by performing: 38 // k = round(x * 32) 39 // y = x * 32 - k 40 // 41 // Once k and y are computed, we then deduce the answer by the cosine of sum 42 // formula: 43 // cospi(x) = cos((k + y)*pi/32) 44 // = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32) 45 // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..63 are precomputed 46 // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are 47 // computed using degree-7 and degree-6 minimax polynomials generated by 48 // Sollya respectively. 49 50 // The exhautive test passes for smaller values 51 if (LIBC_UNLIKELY(x_abs < 0x38A2'F984U)) { 52 53 #if defined(LIBC_TARGET_CPU_HAS_FMA) 54 return fputil::multiply_add(xbits.get_val(), -0x1.0p-25f, 1.0f); 55 #else 56 return static_cast<float>(fputil::multiply_add(xd, -0x1.0p-25, 1.0)); 57 #endif // LIBC_TARGET_CPU_HAS_FMA 58 } 59 60 // Numbers greater or equal to 2^23 are always integers or NaN 61 if (LIBC_UNLIKELY(x_abs >= 0x4B00'0000)) { 62 63 if (LIBC_UNLIKELY(x_abs < 0x4B80'0000)) { 64 return (x_abs & 0x1) ? -1.0f : 1.0f; 65 } 66 67 // x is inf or nan. 68 if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) { 69 if (x_abs == 0x7f80'0000U) { 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 return 1.0f; 77 } 78 79 // Combine the results with the sine of sum formula: 80 // cos(pi * x) = cos((k + y)*pi/32) 81 // = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32) 82 // = (cosm1_y + 1) * cos_k - sin_y * sin_k 83 // = (cosm1_y * cos_k + cos_k) - sin_y * sin_k 84 double sin_k, cos_k, sin_y, cosm1_y; 85 86 sincospif_eval(xd, sin_k, cos_k, sin_y, cosm1_y); 87 88 if (LIBC_UNLIKELY(sin_y == 0 && cos_k == 0)) { 89 return 0.0f; 90 } 91 92 return static_cast<float>(fputil::multiply_add( 93 sin_y, -sin_k, fputil::multiply_add(cosm1_y, cos_k, cos_k))); 94 } 95 96 } // namespace LIBC_NAMESPACE_DECL 97