1 //===-- Half-precision cospif 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/cospif16.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/multiply_add.h" 17 #include "src/__support/macros/optimization.h" 18 19 namespace LIBC_NAMESPACE_DECL { 20 21 LLVM_LIBC_FUNCTION(float16, cospif16, (float16 x)) { 22 using FPBits = typename fputil::FPBits<float16>; 23 FPBits xbits(x); 24 25 uint16_t x_u = xbits.uintval(); 26 uint16_t x_abs = x_u & 0x7fff; 27 float xf = x; 28 29 // Range reduction: 30 // For |x| > 1/32, we perform range reduction as follows: 31 // Find k and y such that: 32 // x = (k + y) * 1/32 33 // k is an integer 34 // |y| < 0.5 35 // 36 // This is done by performing: 37 // k = round(x * 32) 38 // y = x * 32 - k 39 // 40 // Once k and y are computed, we then deduce the answer by the cosine of sum 41 // formula: 42 // cos(x * pi) = cos((k + y) * pi/32) 43 // = cos(k * pi/32) * cos(y * pi/32) + 44 // sin(y * pi/32) * sin(k * pi/32) 45 46 // For signed zeros 47 if (LIBC_UNLIKELY(x_abs == 0U)) 48 return fputil::cast<float16>(1.0f); 49 50 // Numbers greater or equal to 2^10 are integers, or infinity, or NaN 51 if (LIBC_UNLIKELY(x_abs >= 0x6400)) { 52 if (LIBC_UNLIKELY(x_abs <= 0x67FF)) 53 return fputil::cast<float16>((x_abs & 0x1) ? -1.0f : 1.0f); 54 55 // Check for NaN or infintiy values 56 if (LIBC_UNLIKELY(x_abs >= 0x7c00)) { 57 // If value is equal to infinity 58 if (x_abs == 0x7c00) { 59 fputil::set_errno_if_required(EDOM); 60 fputil::raise_except_if_required(FE_INVALID); 61 } 62 63 return x + FPBits::quiet_nan().get_val(); 64 } 65 66 return fputil::cast<float16>(1.0f); 67 } 68 69 float sin_k, cos_k, sin_y, cosm1_y; 70 sincospif16_eval(xf, sin_k, cos_k, sin_y, cosm1_y); 71 72 if (LIBC_UNLIKELY(sin_y == 0 && cos_k == 0)) 73 return fputil::cast<float16>(0.0f); 74 75 // Since, cosm1_y = cos_y - 1, therefore: 76 // cos(x * pi) = cos_k(cosm1_y) + cos_k - sin_k * sin_y 77 return fputil::cast<float16>(fputil::multiply_add( 78 cos_k, cosm1_y, fputil::multiply_add(-sin_k, sin_y, cos_k))); 79 } 80 81 } // namespace LIBC_NAMESPACE_DECL 82