118 lines · cpp
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-exception6//7//===----------------------------------------------------------------------===//8 9#include "src/math/sinpif.h"10#include "src/__support/FPUtil/FEnvImpl.h"11#include "src/__support/FPUtil/FPBits.h"12#include "src/__support/FPUtil/PolyEval.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_UNLIKELY17#include "src/__support/math/sincosf_utils.h"18 19namespace LIBC_NAMESPACE_DECL {20 21LLVM_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) * 1/3233 // k is an integer34 // |y| < 0.535 //36 // This is done by performing:37 // k = round(x * 32)38 // y = x * 32 - k39 //40 // Once k and y are computed, we then deduce the answer by the sine of sum41 // 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 precomputed45 // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are46 // computed using degree-7 and degree-6 minimax polynomials generated by47 // Sollya respectively.48 49 // |x| <= 1/1650 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 * pi59 // An exhaustive test shows that this is accurate for |x| < 9.546391 ×60 // 10-861 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^970 // = 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 NaN82 if (LIBC_UNLIKELY(x_abs >= 0x4B00'0000)) {83 84 // check for NaN values85 if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) {86 if (xbits.is_signaling_nan()) {87 fputil::raise_except_if_required(FE_INVALID);88 return FPBits::quiet_nan().get_val();89 }90 91 if (x_abs == 0x7f80'0000U) {92 fputil::set_errno_if_required(EDOM);93 fputil::raise_except_if_required(FE_INVALID);94 }95 96 return x + FPBits::quiet_nan().get_val();97 }98 99 return FPBits::zero(xbits.sign()).get_val();100 }101 102 // Combine the results with the sine of sum formula:103 // sin(x * pi) = sin((k + y)*pi/32)104 // = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)105 // = sin_y * cos_k + (1 + cosm1_y) * sin_k106 // = sin_y * cos_k + (cosm1_y * sin_k + sin_k)107 double sin_k, cos_k, sin_y, cosm1_y;108 sincospif_eval(xd, sin_k, cos_k, sin_y, cosm1_y);109 110 if (LIBC_UNLIKELY(sin_y == 0 && sin_k == 0))111 return FPBits::zero(xbits.sign()).get_val();112 113 return static_cast<float>(fputil::multiply_add(114 sin_y, cos_k, fputil::multiply_add(cosm1_y, sin_k, sin_k)));115}116 117} // namespace LIBC_NAMESPACE_DECL118