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1//===-- Implementation header for atanf16 -----------------------*- 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___SUPPORT_MATH_ATANF16_H10#define LLVM_LIBC_SRC___SUPPORT_MATH_ATANF16_H11 12#include "include/llvm-libc-macros/float16-macros.h"13 14#ifdef LIBC_TYPES_HAS_FLOAT1615 16#include "src/__support/FPUtil/FEnvImpl.h"17#include "src/__support/FPUtil/FPBits.h"18#include "src/__support/FPUtil/PolyEval.h"19#include "src/__support/FPUtil/cast.h"20#include "src/__support/FPUtil/except_value_utils.h"21#include "src/__support/FPUtil/multiply_add.h"22#include "src/__support/FPUtil/sqrt.h"23#include "src/__support/macros/optimization.h"24 25namespace LIBC_NAMESPACE_DECL {26 27namespace math {28 29LIBC_INLINE static constexpr float16 atanf16(float16 x) {30 // Generated by Solly using the following command:31 // > round(pi/2, SG, RN);32 constexpr float PI_2 = 0x1.921fb6p0;33 34#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS35 constexpr size_t N_EXCEPTS = 6;36 37 constexpr fputil::ExceptValues<float16, N_EXCEPTS> ATANF16_EXCEPTS{{38 // (input, RZ output, RU offset, RD offset, RN offset)39 {0x2745, 0x2744, 1, 0, 1},40 {0x3099, 0x3090, 1, 0, 1},41 {0x3c6c, 0x3aae, 1, 0, 1},42 {0x466e, 0x3daa, 1, 0, 1},43 {0x48ae, 0x3ddb, 1, 0, 0},44 {0x5619, 0x3e3d, 1, 0, 1},45 }};46#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS47 48 using FPBits = fputil::FPBits<float16>;49 FPBits xbits(x);50 51 uint16_t x_u = xbits.uintval();52 uint16_t x_abs = x_u & 0x7fff;53 bool x_sign = x_u >> 15;54 float sign = (x_sign ? -1.0 : 1.0);55 56 // |x| >= +/-inf57 if (LIBC_UNLIKELY(x_abs >= 0x7c00)) {58 if (xbits.is_nan()) {59 if (xbits.is_signaling_nan()) {60 fputil::raise_except_if_required(FE_INVALID);61 return FPBits::quiet_nan().get_val();62 }63 return x;64 }65 66 // atanf16(+/-inf) = +/-pi/267 return fputil::cast<float16>(sign * PI_2);68 }69 70 float xf = x;71 float xsq = xf * xf;72#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS73 // Handle exceptional values74 if (auto r = ATANF16_EXCEPTS.lookup_odd(x_abs, x_sign);75 LIBC_UNLIKELY(r.has_value()))76 return r.value();77#endif78 79 // |x| <= 0x1p0, |x| <= 180 if (x_abs <= 0x3c00) {81 // atanf16(+/-0) = +/-082 if (LIBC_UNLIKELY(x_abs == 0))83 return x;84 85 // Degree-14 minimax odd polynomial of atan(x) generated by Sollya with:86 // > P = fpminimax(atan(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14|], [|SG...|],87 // [0, 1]);88 float result = fputil::polyeval(89 xsq, 0x1.fffffcp-1f, -0x1.55519ep-2f, 0x1.98f6a8p-3f, -0x1.1f0a92p-3f,90 0x1.95b654p-4f, -0x1.e65492p-5f, 0x1.8c0c36p-6f, -0x1.32316ep-8f);91 return fputil::cast<float16>(xf * result);92 }93 94 // If |x| > 195 // y = atan(x) = sign(x) * atan(|x|)96 // atan(|x|) = pi/2 - atan(1/|x|)97 // Recall, 1/|x| < 198 float x_inv_sq = 1.0f / xsq;99 float x_inv = fputil::sqrt<float>(x_inv_sq);100 101 // Degree-14 minimax odd polynomial of atan(x) generated by Sollya with:102 // > P = fpminimax(atan(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14|], [|SG...|],103 // [0, 1]);104 float interm =105 fputil::polyeval(x_inv_sq, 0x1.fffffcp-1f, -0x1.55519ep-2f,106 0x1.98f6a8p-3f, -0x1.1f0a92p-3f, 0x1.95b654p-4f,107 -0x1.e65492p-5f, 0x1.8c0c36p-6f, -0x1.32316ep-8f);108 109 return fputil::cast<float16>(sign *110 fputil::multiply_add(x_inv, -interm, PI_2));111}112 113} // namespace math114 115} // namespace LIBC_NAMESPACE_DECL116 117#endif // LIBC_TYPES_HAS_FLOAT16118 119#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ATANF16_H120