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1//===-- Collection of utils for sinf16/cosf16 -------------------*- C++ -*-===//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#ifndef LLVM_LIBC_SRC_MATH_GENERIC_SINCOSF16_UTILS_H10#define LLVM_LIBC_SRC_MATH_GENERIC_SINCOSF16_UTILS_H11 12#include "src/__support/FPUtil/PolyEval.h"13#include "src/__support/FPUtil/nearest_integer.h"14#include "src/__support/common.h"15#include "src/__support/macros/config.h"16 17namespace LIBC_NAMESPACE_DECL {18 19namespace sincosf16_internal {20 21// Lookup table for sin(k * pi / 32) with k = 0, ..., 63.22// Table is generated with Sollya as follows:23// > display = hexadecimmal;24// > for k from 0 to 63 do { round(sin(k * pi/32), SG, RN); };25constexpr float SIN_K_PI_OVER_32[64] = {26 0x0.0p0, 0x1.917a6cp-4, 0x1.8f8b84p-3, 0x1.294062p-2,27 0x1.87de2ap-2, 0x1.e2b5d4p-2, 0x1.1c73b4p-1, 0x1.44cf32p-1,28 0x1.6a09e6p-1, 0x1.8bc806p-1, 0x1.a9b662p-1, 0x1.c38b3p-1,29 0x1.d906bcp-1, 0x1.e9f416p-1, 0x1.f6297cp-1, 0x1.fd88dap-1,30 0x1p0, 0x1.fd88dap-1, 0x1.f6297cp-1, 0x1.e9f416p-1,31 0x1.d906bcp-1, 0x1.c38b3p-1, 0x1.a9b662p-1, 0x1.8bc806p-1,32 0x1.6a09e6p-1, 0x1.44cf32p-1, 0x1.1c73b4p-1, 0x1.e2b5d4p-2,33 0x1.87de2ap-2, 0x1.294062p-2, 0x1.8f8b84p-3, 0x1.917a6cp-4,34 0x0.0p0, -0x1.917a6cp-4, -0x1.8f8b84p-3, -0x1.294062p-2,35 -0x1.87de2ap-2, -0x1.e2b5d4p-2, -0x1.1c73b4p-1, -0x1.44cf32p-1,36 -0x1.6a09e6p-1, -0x1.8bc806p-1, -0x1.a9b662p-1, -0x1.c38b3p-1,37 -0x1.d906bcp-1, -0x1.e9f416p-1, -0x1.f6297ep-1, -0x1.fd88dap-1,38 -0x1p0, -0x1.fd88dap-1, -0x1.f6297cp-1, -0x1.e9f416p-1,39 -0x1.d906bcp-1, -0x1.c38b3p-1, -0x1.a9b662p-1, -0x1.8bc806p-1,40 -0x1.6a09e6p-1, -0x1.44cf32p-1, -0x1.1c73b4p-1, -0x1.e2b5d4p-2,41 -0x1.87de2ap-2, -0x1.294062p-2, -0x1.8f8b84p-3, -0x1.917a6cp-4};42 43LIBC_INLINE int32_t range_reduction_sincospif16(float x, float &y) {44 float kf = fputil::nearest_integer(x * 32);45 y = fputil::multiply_add(x, 32.0f, -kf);46 47 return static_cast<int32_t>(kf);48}49 50// Recall, range reduction:51// k = round(x * 32/pi)52//53// The precision choice of 'double' in the following function is to minimize54// rounding errors in this initial scaling step,55// preserving enough bits so errors accumulated while computing the subtraction:56// y = x * 32/pi - round(x * 32/pi)57// are beyond the least-significant bit of single-precision used during58// further intermediate computation.59LIBC_INLINE int32_t range_reduction_sincosf16(float x, float &y) {60 // Generated by Sollya with:61 // > D(32/pi);62 constexpr double THIRTYTWO_OVER_PI = 0x1.45f306dc9c883p3;63 64 double prod = x * THIRTYTWO_OVER_PI;65 double kd = fputil::nearest_integer(prod);66 y = static_cast<float>(prod - kd);67 68 return static_cast<int32_t>(kd);69}70 71LIBC_INLINE static void sincosf16_poly_eval(int32_t k, float y, float &sin_k,72 float &cos_k, float &sin_y,73 float &cosm1_y) {74 75 sin_k = SIN_K_PI_OVER_32[k & 63];76 cos_k = SIN_K_PI_OVER_32[(k + 16) & 63];77 78 // Recall, after range reduction, -0.5 <= y <= 0.5. For very small values of79 // y, calculating sin(y * p/32) can be inaccurate. Generating a polynomial for80 // sin(y * p/32)/y instead significantly reduces the relative errors.81 float ysq = y * y;82 83 // Degree-6 minimax even polynomial for sin(y*pi/32)/y generated by Sollya84 // with:85 // > Q = fpminimax(sin(y * pi/32)/y, [|0, 2, 4, 6|], [|SG...|], [0, 0.5]);86 sin_y = y * fputil::polyeval(ysq, 0x1.921fb6p-4f, -0x1.4aeabcp-13f,87 0x1.a03354p-21f, -0x1.ad02d2p-20f);88 89 // Degree-6 minimax even polynomial for cos(y*pi/32) generated by Sollya90 // with:91 // > P = fpminimax(cos(y * pi/32), [|0, 2, 4, 6|],[|1, SG...|], [0, 0.5]);92 cosm1_y = ysq * fputil::polyeval(ysq, -0x1.3bd3ccp-8f, 0x1.03a61ap-18f,93 0x1.a6f7a2p-29f);94}95 96LIBC_INLINE void sincosf16_eval(float xf, float &sin_k, float &cos_k,97 float &sin_y, float &cosm1_y) {98 float y;99 int32_t k = range_reduction_sincosf16(xf, y);100 101 sincosf16_poly_eval(k, y, sin_k, cos_k, sin_y, cosm1_y);102}103 104LIBC_INLINE void sincospif16_eval(float xf, float &sin_k, float &cos_k,105 float &sin_y, float &cosm1_y) {106 float y;107 int32_t k = range_reduction_sincospif16(xf, y);108 109 sincosf16_poly_eval(k, y, sin_k, cos_k, sin_y, cosm1_y);110}111 112} // namespace sincosf16_internal113 114} // namespace LIBC_NAMESPACE_DECL115 116#endif // LLVM_LIBC_SRC_MATH_GENERIC_SINCOSF16_UTILS_H117