1 //===-- Half-precision cos(x) 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/cosf16.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 = 4; 23 24 constexpr fputil::ExceptValues<float16, N_EXCEPTS> COSF16_EXCEPTS{{ 25 // (input, RZ output, RU offset, RD offset, RN offset) 26 {0x2b7c, 0x3bfc, 1, 0, 1}, 27 {0x4ac1, 0x38b5, 1, 0, 0}, 28 {0x5c49, 0xb8c6, 0, 1, 0}, 29 {0x7acc, 0xa474, 0, 1, 0}, 30 }}; 31 32 LLVM_LIBC_FUNCTION(float16, cosf16, (float16 x)) { 33 using FPBits = fputil::FPBits<float16>; 34 FPBits xbits(x); 35 36 uint16_t x_u = xbits.uintval(); 37 uint16_t x_abs = x_u & 0x7fff; 38 float xf = x; 39 40 // Range reduction: 41 // For |x| > pi/32, we perform range reduction as follows: 42 // Find k and y such that: 43 // x = (k + y) * pi/32 44 // k is an integer, |y| < 0.5 45 // 46 // This is done by performing: 47 // k = round(x * 32/pi) 48 // y = x * 32/pi - k 49 // 50 // Once k and y are computed, we then deduce the answer by the cosine of sum 51 // formula: 52 // cos(x) = cos((k + y) * pi/32) 53 // = cos(k * pi/32) * cos(y * pi/32) - 54 // sin(k * pi/32) * sin(y * pi/32) 55 56 // Handle exceptional values 57 if (auto r = COSF16_EXCEPTS.lookup(x_abs); LIBC_UNLIKELY(r.has_value())) 58 return r.value(); 59 60 // cos(+/-0) = 1 61 if (LIBC_UNLIKELY(x_abs == 0U)) 62 return fputil::cast<float16>(1.0f); 63 64 // cos(+/-inf) = NaN, and cos(NaN) = NaN 65 if (xbits.is_inf_or_nan()) { 66 if (xbits.is_inf()) { 67 fputil::set_errno_if_required(EDOM); 68 fputil::raise_except_if_required(FE_INVALID); 69 } 70 71 return x + FPBits::quiet_nan().get_val(); 72 } 73 74 float sin_k, cos_k, sin_y, cosm1_y; 75 sincosf16_eval(xf, sin_k, cos_k, sin_y, cosm1_y); 76 // Since, cosm1_y = cos_y - 1, therefore: 77 // cos(x) = cos_k * cos_y - sin_k * sin_y 78 // = cos_k * (cos_y - 1 + 1) - sin_k * sin_y 79 // = cos_k * cosm1_y - sin_k * sin_y + cos_k 80 return fputil::cast<float16>(fputil::multiply_add( 81 cos_k, cosm1_y, fputil::multiply_add(-sin_k, sin_y, cos_k))); 82 } 83 84 } // namespace LIBC_NAMESPACE_DECL 85