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| 1 | +//===-- Implementation header for asinf -------------------------*- 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-exception |
| 6 | +// |
| 7 | +//===----------------------------------------------------------------------===// |
| 8 | + |
| 9 | +#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ASINHF_H |
| 10 | +#define LLVM_LIBC_SRC___SUPPORT_MATH_ASINHF_H |
| 11 | + |
| 12 | +#include "acoshf_utils.h" |
| 13 | +#include "src/__support/FPUtil/FPBits.h" |
| 14 | +#include "src/__support/FPUtil/PolyEval.h" |
| 15 | +#include "src/__support/FPUtil/multiply_add.h" |
| 16 | +#include "src/__support/FPUtil/sqrt.h" |
| 17 | +#include "src/__support/macros/config.h" |
| 18 | +#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY |
| 19 | + |
| 20 | +namespace LIBC_NAMESPACE_DECL { |
| 21 | + |
| 22 | +namespace math { |
| 23 | + |
| 24 | +LIBC_INLINE static constexpr float asinhf(float x) { |
| 25 | + using namespace acoshf_internal; |
| 26 | + using FPBits_t = typename fputil::FPBits<float>; |
| 27 | + FPBits_t xbits(x); |
| 28 | + uint32_t x_u = xbits.uintval(); |
| 29 | + uint32_t x_abs = xbits.abs().uintval(); |
| 30 | + |
| 31 | + // |x| <= 2^-3 |
| 32 | + if (LIBC_UNLIKELY(x_abs <= 0x3e80'0000U)) { |
| 33 | + // |x| <= 2^-26 |
| 34 | + if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) { |
| 35 | + return static_cast<float>(LIBC_UNLIKELY(x_abs == 0) |
| 36 | + ? x |
| 37 | + : (x - 0x1.5555555555555p-3 * x * x * x)); |
| 38 | + } |
| 39 | + |
| 40 | + double x_d = x; |
| 41 | + double x_sq = x_d * x_d; |
| 42 | + // Generated by Sollya with: |
| 43 | + // > P = fpminimax(asinh(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16|], [|D...|], |
| 44 | + // [0, 2^-2]); |
| 45 | + double p = fputil::polyeval( |
| 46 | + x_sq, 0.0, -0x1.555555555551ep-3, 0x1.3333333325495p-4, |
| 47 | + -0x1.6db6db5a7622bp-5, 0x1.f1c70f82928c6p-6, -0x1.6e893934266b7p-6, |
| 48 | + 0x1.1c0b41d3fbe78p-6, -0x1.c0f47810b3c4fp-7, 0x1.2c8602690143dp-7); |
| 49 | + return static_cast<float>(fputil::multiply_add(x_d, p, x_d)); |
| 50 | + } |
| 51 | + |
| 52 | + const double SIGN[2] = {1.0, -1.0}; |
| 53 | + double x_sign = SIGN[x_u >> 31]; |
| 54 | + double x_d = x; |
| 55 | + |
| 56 | +#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS |
| 57 | + // Helper functions to set results for exceptional cases. |
| 58 | + auto round_result_slightly_down = [x_sign](float r) -> float { |
| 59 | + return fputil::multiply_add(static_cast<float>(x_sign), r, |
| 60 | + static_cast<float>(x_sign) * (-0x1.0p-24f)); |
| 61 | + }; |
| 62 | + auto round_result_slightly_up = [x_sign](float r) -> float { |
| 63 | + return fputil::multiply_add(static_cast<float>(x_sign), r, |
| 64 | + static_cast<float>(x_sign) * 0x1.0p-24f); |
| 65 | + }; |
| 66 | + |
| 67 | + if (LIBC_UNLIKELY(x_abs >= 0x4bdd'65a5U)) { |
| 68 | + if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) { |
| 69 | + if (xbits.is_signaling_nan()) { |
| 70 | + fputil::raise_except_if_required(FE_INVALID); |
| 71 | + return FPBits_t::quiet_nan().get_val(); |
| 72 | + } |
| 73 | + |
| 74 | + return x; |
| 75 | + } |
| 76 | + |
| 77 | + // Exceptional cases when x > 2^24. |
| 78 | + switch (x_abs) { |
| 79 | + case 0x4bdd65a5: // |x| = 0x1.bacb4ap24f |
| 80 | + return round_result_slightly_down(0x1.1e0696p4f); |
| 81 | + case 0x4c803f2c: // |x| = 0x1.007e58p26f |
| 82 | + return round_result_slightly_down(0x1.2b786cp4f); |
| 83 | + case 0x4f8ffb03: // |x| = 0x1.1ff606p32f |
| 84 | + return round_result_slightly_up(0x1.6fdd34p4f); |
| 85 | + case 0x5c569e88: // |x| = 0x1.ad3d1p57f |
| 86 | + return round_result_slightly_up(0x1.45c146p5f); |
| 87 | + case 0x5e68984e: // |x| = 0x1.d1309cp61f |
| 88 | + return round_result_slightly_up(0x1.5c9442p5f); |
| 89 | + case 0x655890d3: // |x| = 0x1.b121a6p75f |
| 90 | + return round_result_slightly_down(0x1.a9a3f2p5f); |
| 91 | + case 0x65de7ca6: // |x| = 0x1.bcf94cp76f |
| 92 | + return round_result_slightly_up(0x1.af66cp5f); |
| 93 | + case 0x6eb1a8ec: // |x| = 0x1.6351d8p94f |
| 94 | + return round_result_slightly_down(0x1.08b512p6f); |
| 95 | + case 0x7997f30a: // |x| = 0x1.2fe614p116f |
| 96 | + return round_result_slightly_up(0x1.451436p6f); |
| 97 | + } |
| 98 | + } else { |
| 99 | + // Exceptional cases when x < 2^24. |
| 100 | + if (LIBC_UNLIKELY(x_abs == 0x45abaf26)) { |
| 101 | + // |x| = 0x1.575e4cp12f |
| 102 | + return round_result_slightly_down(0x1.29becap3f); |
| 103 | + } |
| 104 | + if (LIBC_UNLIKELY(x_abs == 0x49d29048)) { |
| 105 | + // |x| = 0x1.a5209p20f |
| 106 | + return round_result_slightly_down(0x1.e1b92p3f); |
| 107 | + } |
| 108 | + } |
| 109 | +#else |
| 110 | + if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) |
| 111 | + return x; |
| 112 | +#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS |
| 113 | + |
| 114 | + // asinh(x) = log(x + sqrt(x^2 + 1)) |
| 115 | + return static_cast<float>( |
| 116 | + x_sign * log_eval(fputil::multiply_add( |
| 117 | + x_d, x_sign, |
| 118 | + fputil::sqrt<double>(fputil::multiply_add(x_d, x_d, 1.0))))); |
| 119 | +} |
| 120 | + |
| 121 | +} // namespace math |
| 122 | + |
| 123 | +} // namespace LIBC_NAMESPACE_DECL |
| 124 | + |
| 125 | +#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ASINHF_H |
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