1 //===-- Half-precision tanpif 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/tanpif16.h" 10 #include "hdr/errno_macros.h" 11 #include "hdr/fenv_macros.h" 12 #include "sincosf16_utils.h" 13 #include "src/__support/FPUtil/FEnvImpl.h" 14 #include "src/__support/FPUtil/FPBits.h" 15 #include "src/__support/FPUtil/cast.h" 16 #include "src/__support/FPUtil/except_value_utils.h" 17 #include "src/__support/FPUtil/multiply_add.h" 18 #include "src/__support/macros/optimization.h" 19 20 namespace LIBC_NAMESPACE_DECL { 21 22 constexpr size_t N_EXCEPTS = 21; 23 24 constexpr fputil::ExceptValues<float16, N_EXCEPTS> TANF16_EXCEPTS{{ 25 // (input, RZ output, RU offset, RD offset, RN offset) 26 {0x07f2, 0x0e3d, 1, 0, 0}, {0x086a, 0x0eee, 1, 0, 1}, 27 {0x08db, 0x0fa0, 1, 0, 0}, {0x094c, 0x1029, 1, 0, 0}, 28 {0x0b10, 0x118c, 1, 0, 0}, {0x1ce0, 0x23a8, 1, 0, 1}, 29 {0x1235, 0x18e0, 1, 0, 0}, {0x2579, 0x2c4e, 1, 0, 0}, 30 {0x28b2, 0x2f68, 1, 0, 1}, {0x2a43, 0x30f4, 1, 0, 1}, 31 {0x31b7, 0x3907, 1, 0, 0}, {0x329d, 0x3a12, 1, 0, 1}, 32 {0x34f1, 0x3dd7, 1, 0, 0}, {0x3658, 0x41ee, 1, 0, 0}, 33 {0x38d4, 0xc1ee, 0, 1, 0}, {0x3d96, 0x41ee, 1, 0, 0}, 34 {0x3e6a, 0xc1ee, 0, 1, 0}, {0x40cb, 0x41ee, 1, 0, 0}, 35 {0x4135, 0xc1ee, 0, 1, 0}, {0x42cb, 0x41ee, 1, 0, 0}, 36 {0x4335, 0xc1ee, 0, 1, 0}, 37 }}; 38 39 LLVM_LIBC_FUNCTION(float16, tanpif16, (float16 x)) { 40 using FPBits = typename fputil::FPBits<float16>; 41 FPBits xbits(x); 42 43 uint16_t x_u = xbits.uintval(); 44 uint16_t x_abs = x_u & 0x7fff; 45 46 // Handle exceptional values 47 if (LIBC_UNLIKELY(x_abs <= 0x4335)) { 48 if (LIBC_UNLIKELY(x_abs == 0U)) 49 return x; 50 51 bool x_sign = x_u >> 15; 52 if (auto r = TANF16_EXCEPTS.lookup_odd(x_abs, x_sign); 53 LIBC_UNLIKELY(r.has_value())) 54 return r.value(); 55 } 56 57 // Numbers greater or equal to 2^10 are integers, or infinity, or NaN 58 if (LIBC_UNLIKELY(x_abs >= 0x6400)) { 59 // Check for NaN or infinity values 60 if (LIBC_UNLIKELY(x_abs >= 0x7c00)) { 61 if (x_abs == 0x7c00) { 62 fputil::set_errno_if_required(EDOM); 63 fputil::raise_except_if_required(FE_INVALID); 64 } 65 66 return x + FPBits::quiet_nan().get_val(); 67 } 68 69 return FPBits::zero(xbits.sign()).get_val(); 70 } 71 // Range reduction: 72 // For |x| > 1/32, we perform range reduction as follows: 73 // Find k and y such that: 74 // x = (k + y) * 1/32 75 // k is an integer 76 // |y| < 0.5 77 // 78 // This is done by performing: 79 // k = round(x * 32) 80 // y = x * 32 - k 81 // 82 // Once k and y are computed, we then deduce the answer by tthe formula: 83 // tan(x) = sin(x) / cos(x) 84 // = (sin_y * cos_k + cos_y * sin_k) / (cos_y * cos_k - sin_y * sin_k) 85 float xf = x; 86 float sin_k, cos_k, sin_y, cosm1_y; 87 sincospif16_eval(xf, sin_k, cos_k, sin_y, cosm1_y); 88 89 if (LIBC_UNLIKELY(sin_y == 0 && cos_k == 0)) { 90 fputil::set_errno_if_required(EDOM); 91 fputil::raise_except_if_required(FE_DIVBYZERO); 92 93 int16_t x_mp5_u = static_cast<int16_t>(x - 0.5); 94 return ((x_mp5_u & 0x1) ? -1 : 1) * FPBits::inf().get_val(); 95 } 96 97 using fputil::multiply_add; 98 return fputil::cast<float16>( 99 multiply_add(sin_y, cos_k, multiply_add(cosm1_y, sin_k, sin_k)) / 100 multiply_add(sin_y, -sin_k, multiply_add(cosm1_y, cos_k, cos_k))); 101 } 102 103 } // namespace LIBC_NAMESPACE_DECL 104