1 //===-- Half-precision sin(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/sinf16.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> SINF16_EXCEPTS{{ 25 // (input, RZ output, RU offset, RD offset, RN offset) 26 {0x2b45, 0x2b43, 1, 0, 1}, 27 {0x585c, 0x3ba3, 1, 0, 1}, 28 {0x5cb0, 0xbbff, 0, 1, 0}, 29 {0x51f5, 0xb80f, 0, 1, 0}, 30 }}; 31 32 LLVM_LIBC_FUNCTION(float16, sinf16, (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 sine of sum 51 // formula: 52 // sin(x) = sin((k + y) * pi/32) 53 // = sin(k * pi/32) * cos(y * pi/32) + 54 // sin(y * pi/32) * cos(k * pi/32) 55 56 // Handle exceptional values 57 bool x_sign = x_u >> 15; 58 if (auto r = SINF16_EXCEPTS.lookup_odd(x_abs, x_sign); 59 LIBC_UNLIKELY(r.has_value())) 60 return r.value(); 61 62 int rounding = fputil::quick_get_round(); 63 64 // Exhaustive tests show that for |x| <= 0x1.f4p-11, 1ULP rounding errors 65 // occur. To fix this, the following apply: 66 if (LIBC_UNLIKELY(x_abs <= 0x13d0)) { 67 // sin(+/-0) = +/-0 68 if (LIBC_UNLIKELY(x_abs == 0U)) 69 return x; 70 71 // When x > 0, and rounding upward, sin(x) == x. 72 // When x < 0, and rounding downward, sin(x) == x. 73 if ((rounding == FE_UPWARD && xbits.is_pos()) || 74 (rounding == FE_DOWNWARD && xbits.is_neg())) 75 return x; 76 77 // When x < 0, and rounding upward, sin(x) == (x - 1ULP) 78 if (rounding == FE_UPWARD && xbits.is_neg()) { 79 x_u--; 80 return FPBits(x_u).get_val(); 81 } 82 } 83 84 if (xbits.is_inf_or_nan()) { 85 if (xbits.is_inf()) { 86 fputil::set_errno_if_required(EDOM); 87 fputil::raise_except_if_required(FE_INVALID); 88 } 89 90 return x + FPBits::quiet_nan().get_val(); 91 } 92 93 float sin_k, cos_k, sin_y, cosm1_y; 94 sincosf16_eval(xf, sin_k, cos_k, sin_y, cosm1_y); 95 96 if (LIBC_UNLIKELY(sin_y == 0 && sin_k == 0)) 97 return FPBits::zero(xbits.sign()).get_val(); 98 99 // Since, cosm1_y = cos_y - 1, therefore: 100 // sin(x) = cos_k * sin_y + sin_k + (cosm1_y * sin_k) 101 return fputil::cast<float16>(fputil::multiply_add( 102 sin_y, cos_k, fputil::multiply_add(cosm1_y, sin_k, sin_k))); 103 } 104 105 } // namespace LIBC_NAMESPACE_DECL 106