1 //===-- Single-precision sinpif 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/sinpif.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/PolyEval.h" 14 #include "src/__support/FPUtil/multiply_add.h" 15 #include "src/__support/common.h" 16 #include "src/__support/macros/config.h" 17 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY 18 19 namespace LIBC_NAMESPACE_DECL { 20 21 LLVM_LIBC_FUNCTION(float, sinpif, (float x)) { 22 using FPBits = typename fputil::FPBits<float>; 23 FPBits xbits(x); 24 25 uint32_t x_u = xbits.uintval(); 26 uint32_t x_abs = x_u & 0x7fff'ffffU; 27 double xd = static_cast<double>(x); 28 29 // Range reduction: 30 // For |x| > 1/32, we perform range reduction as follows: 31 // Find k and y such that: 32 // x = (k + y) * 1/32 33 // k is an integer 34 // |y| < 0.5 35 // 36 // This is done by performing: 37 // k = round(x * 32) 38 // y = x * 32 - k 39 // 40 // Once k and y are computed, we then deduce the answer by the sine of sum 41 // formula: 42 // sin(x * pi) = sin((k + y)*pi/32) 43 // = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32) 44 // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..31 are precomputed 45 // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are 46 // computed using degree-7 and degree-6 minimax polynomials generated by 47 // Sollya respectively. 48 49 // |x| <= 1/16 50 if (LIBC_UNLIKELY(x_abs <= 0x3d80'0000U)) { 51 52 if (LIBC_UNLIKELY(x_abs < 0x33CD'01D7U)) { 53 if (LIBC_UNLIKELY(x_abs == 0U)) { 54 // For signed zeros. 55 return x; 56 } 57 58 // For very small values we can approximate sinpi(x) with x * pi 59 // An exhaustive test shows that this is accurate for |x| < 9.546391 × 60 // 10-8 61 double xdpi = xd * 0x1.921fb54442d18p1; 62 return static_cast<float>(xdpi); 63 } 64 65 // |x| < 1/16. 66 double xsq = xd * xd; 67 68 // Degree-9 polynomial approximation: 69 // sinpi(x) ~ x + a_3 x^3 + a_5 x^5 + a_7 x^7 + a_9 x^9 70 // = x (1 + a_3 x^2 + ... + a_9 x^8) 71 // = x * P(x^2) 72 // generated by Sollya with the following commands: 73 // > display = hexadecimal; 74 // > Q = fpminimax(sin(pi * x)/x, [|0, 2, 4, 6, 8|], [|D...|], [0, 1/16]); 75 double result = fputil::polyeval( 76 xsq, 0x1.921fb54442d18p1, -0x1.4abbce625bbf2p2, 0x1.466bc675e116ap1, 77 -0x1.32d2c0b62d41cp-1, 0x1.501ec4497cb7dp-4); 78 return static_cast<float>(xd * result); 79 } 80 81 // Numbers greater or equal to 2^23 are always integers or NaN 82 if (LIBC_UNLIKELY(x_abs >= 0x4B00'0000)) { 83 84 // check for NaN values 85 if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) { 86 if (x_abs == 0x7f80'0000U) { 87 fputil::set_errno_if_required(EDOM); 88 fputil::raise_except_if_required(FE_INVALID); 89 } 90 91 return x + FPBits::quiet_nan().get_val(); 92 } 93 94 return FPBits::zero(xbits.sign()).get_val(); 95 } 96 97 // Combine the results with the sine of sum formula: 98 // sin(x * pi) = sin((k + y)*pi/32) 99 // = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32) 100 // = sin_y * cos_k + (1 + cosm1_y) * sin_k 101 // = sin_y * cos_k + (cosm1_y * sin_k + sin_k) 102 double sin_k, cos_k, sin_y, cosm1_y; 103 sincospif_eval(xd, sin_k, cos_k, sin_y, cosm1_y); 104 105 if (LIBC_UNLIKELY(sin_y == 0 && sin_k == 0)) 106 return FPBits::zero(xbits.sign()).get_val(); 107 108 return static_cast<float>(fputil::multiply_add( 109 sin_y, cos_k, fputil::multiply_add(cosm1_y, sin_k, sin_k))); 110 } 111 112 } // namespace LIBC_NAMESPACE_DECL 113