1 //===-- Single-precision asinh 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/asinhf.h" 10 #include "src/__support/FPUtil/FPBits.h" 11 #include "src/__support/FPUtil/PolyEval.h" 12 #include "src/__support/FPUtil/multiply_add.h" 13 #include "src/__support/FPUtil/sqrt.h" 14 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY 15 #include "src/math/generic/common_constants.h" 16 #include "src/math/generic/explogxf.h" 17 18 namespace LIBC_NAMESPACE { 19 20 LLVM_LIBC_FUNCTION(float, asinhf, (float x)) { 21 using FPBits_t = typename fputil::FPBits<float>; 22 FPBits_t xbits(x); 23 uint32_t x_u = xbits.uintval(); 24 uint32_t x_abs = xbits.abs().uintval(); 25 26 // |x| <= 2^-3 27 if (LIBC_UNLIKELY(x_abs <= 0x3e80'0000U)) { 28 // |x| <= 2^-26 29 if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) { 30 return static_cast<float>(LIBC_UNLIKELY(x_abs == 0) 31 ? x 32 : (x - 0x1.5555555555555p-3 * x * x * x)); 33 } 34 35 double x_d = x; 36 double x_sq = x_d * x_d; 37 // Generated by Sollya with: 38 // > P = fpminimax(asinh(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16], [|D...|], 39 // [0, 2^-2]); 40 double p = fputil::polyeval( 41 x_sq, 0.0, -0x1.555555555551ep-3, 0x1.3333333325495p-4, 42 -0x1.6db6db5a7622bp-5, 0x1.f1c70f82928c6p-6, -0x1.6e893934266b7p-6, 43 0x1.1c0b41d3fbe78p-6, -0x1.c0f47810b3c4fp-7, 0x1.2c8602690143dp-7); 44 return static_cast<float>(fputil::multiply_add(x_d, p, x_d)); 45 } 46 47 const double SIGN[2] = {1.0, -1.0}; 48 double x_sign = SIGN[x_u >> 31]; 49 double x_d = x; 50 51 // Helper functions to set results for exceptional cases. __anone472f27c0102(float r) 52 auto round_result_slightly_down = [x_sign](float r) -> float { 53 return fputil::multiply_add(static_cast<float>(x_sign), r, 54 static_cast<float>(x_sign) * (-0x1.0p-24f)); 55 }; __anone472f27c0202(float r) 56 auto round_result_slightly_up = [x_sign](float r) -> float { 57 return fputil::multiply_add(static_cast<float>(x_sign), r, 58 static_cast<float>(x_sign) * 0x1.0p-24f); 59 }; 60 61 if (LIBC_UNLIKELY(x_abs >= 0x4bdd'65a5U)) { 62 if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) 63 return x; 64 65 // Exceptional cases when x > 2^24. 66 switch (x_abs) { 67 case 0x4bdd65a5: // |x| = 0x1.bacb4ap24f 68 return round_result_slightly_down(0x1.1e0696p4f); 69 case 0x4c803f2c: // |x| = 0x1.007e58p26f 70 return round_result_slightly_down(0x1.2b786cp4f); 71 case 0x4f8ffb03: // |x| = 0x1.1ff606p32f 72 return round_result_slightly_up(0x1.6fdd34p4f); 73 case 0x5c569e88: // |x| = 0x1.ad3d1p57f 74 return round_result_slightly_up(0x1.45c146p5f); 75 case 0x5e68984e: // |x| = 0x1.d1309cp61f 76 return round_result_slightly_up(0x1.5c9442p5f); 77 case 0x655890d3: // |x| = 0x1.b121a6p75f 78 return round_result_slightly_down(0x1.a9a3f2p5f); 79 case 0x65de7ca6: // |x| = 0x1.bcf94cp76f 80 return round_result_slightly_up(0x1.af66cp5f); 81 case 0x6eb1a8ec: // |x| = 0x1.6351d8p94f 82 return round_result_slightly_down(0x1.08b512p6f); 83 case 0x7997f30a: // |x| = 0x1.2fe614p116f 84 return round_result_slightly_up(0x1.451436p6f); 85 } 86 } else { 87 // Exceptional cases when x < 2^24. 88 if (LIBC_UNLIKELY(x_abs == 0x45abaf26)) { 89 // |x| = 0x1.575e4cp12f 90 return round_result_slightly_down(0x1.29becap3f); 91 } 92 if (LIBC_UNLIKELY(x_abs == 0x49d29048)) { 93 // |x| = 0x1.a5209p20f 94 return round_result_slightly_down(0x1.e1b92p3f); 95 } 96 } 97 98 // asinh(x) = log(x + sqrt(x^2 + 1)) 99 return static_cast<float>( 100 x_sign * 101 log_eval(fputil::multiply_add( 102 x_d, x_sign, fputil::sqrt(fputil::multiply_add(x_d, x_d, 1.0))))); 103 } 104 105 } // namespace LIBC_NAMESPACE 106