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| 1 | +//===-- Implementation header for cosf16 ------------------------*- C++ -*-===// |
| 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 | +#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_COSF16_H |
| 10 | +#define LLVM_LIBC_SRC___SUPPORT_MATH_COSF16_H |
| 11 | + |
| 12 | +#include "include/llvm-libc-macros/float16-macros.h" |
| 13 | + |
| 14 | +#ifdef LIBC_TYPES_HAS_FLOAT16 |
| 15 | + |
| 16 | +#include "sincosf16_utils.h" |
| 17 | +#include "src/__support/FPUtil/FEnvImpl.h" |
| 18 | +#include "src/__support/FPUtil/FPBits.h" |
| 19 | +#include "src/__support/FPUtil/cast.h" |
| 20 | +#include "src/__support/FPUtil/except_value_utils.h" |
| 21 | +#include "src/__support/FPUtil/multiply_add.h" |
| 22 | +#include "src/__support/macros/optimization.h" |
| 23 | + |
| 24 | +namespace LIBC_NAMESPACE_DECL { |
| 25 | + |
| 26 | +namespace math { |
| 27 | + |
| 28 | +LIBC_INLINE static constexpr float16 cosf16(float16 x) { |
| 29 | +#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS |
| 30 | + constexpr size_t N_EXCEPTS = 4; |
| 31 | + |
| 32 | + constexpr fputil::ExceptValues<float16, N_EXCEPTS> COSF16_EXCEPTS{{ |
| 33 | + // (input, RZ output, RU offset, RD offset, RN offset) |
| 34 | + {0x2b7c, 0x3bfc, 1, 0, 1}, |
| 35 | + {0x4ac1, 0x38b5, 1, 0, 0}, |
| 36 | + {0x5c49, 0xb8c6, 0, 1, 0}, |
| 37 | + {0x7acc, 0xa474, 0, 1, 0}, |
| 38 | + }}; |
| 39 | +#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS |
| 40 | + |
| 41 | + using namespace sincosf16_internal; |
| 42 | + using FPBits = fputil::FPBits<float16>; |
| 43 | + FPBits xbits(x); |
| 44 | + |
| 45 | + uint16_t x_u = xbits.uintval(); |
| 46 | + uint16_t x_abs = x_u & 0x7fff; |
| 47 | + float xf = x; |
| 48 | + |
| 49 | + // Range reduction: |
| 50 | + // For |x| > pi/32, we perform range reduction as follows: |
| 51 | + // Find k and y such that: |
| 52 | + // x = (k + y) * pi/32 |
| 53 | + // k is an integer, |y| < 0.5 |
| 54 | + // |
| 55 | + // This is done by performing: |
| 56 | + // k = round(x * 32/pi) |
| 57 | + // y = x * 32/pi - k |
| 58 | + // |
| 59 | + // Once k and y are computed, we then deduce the answer by the cosine of sum |
| 60 | + // formula: |
| 61 | + // cos(x) = cos((k + y) * pi/32) |
| 62 | + // = cos(k * pi/32) * cos(y * pi/32) - |
| 63 | + // sin(k * pi/32) * sin(y * pi/32) |
| 64 | + |
| 65 | +#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS |
| 66 | + // Handle exceptional values |
| 67 | + if (auto r = COSF16_EXCEPTS.lookup(x_abs); LIBC_UNLIKELY(r.has_value())) |
| 68 | + return r.value(); |
| 69 | +#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS |
| 70 | + |
| 71 | + // cos(+/-0) = 1 |
| 72 | + if (LIBC_UNLIKELY(x_abs == 0U)) |
| 73 | + return fputil::cast<float16>(1.0f); |
| 74 | + |
| 75 | + // cos(+/-inf) = NaN, and cos(NaN) = NaN |
| 76 | + if (xbits.is_inf_or_nan()) { |
| 77 | + if (xbits.is_signaling_nan()) { |
| 78 | + fputil::raise_except_if_required(FE_INVALID); |
| 79 | + return FPBits::quiet_nan().get_val(); |
| 80 | + } |
| 81 | + |
| 82 | + if (xbits.is_inf()) { |
| 83 | + fputil::set_errno_if_required(EDOM); |
| 84 | + fputil::raise_except_if_required(FE_INVALID); |
| 85 | + } |
| 86 | + |
| 87 | + return x + FPBits::quiet_nan().get_val(); |
| 88 | + } |
| 89 | + |
| 90 | + float sin_k = 0.0f, cos_k = 0.0f, sin_y = 0.0f, cosm1_y = 0.0f; |
| 91 | + sincosf16_eval(xf, sin_k, cos_k, sin_y, cosm1_y); |
| 92 | + // Since, cosm1_y = cos_y - 1, therefore: |
| 93 | + // cos(x) = cos_k * cos_y - sin_k * sin_y |
| 94 | + // = cos_k * (cos_y - 1 + 1) - sin_k * sin_y |
| 95 | + // = cos_k * cosm1_y - sin_k * sin_y + cos_k |
| 96 | + return fputil::cast<float16>(fputil::multiply_add( |
| 97 | + cos_k, cosm1_y, fputil::multiply_add(-sin_k, sin_y, cos_k))); |
| 98 | +} |
| 99 | + |
| 100 | +} // namespace math |
| 101 | + |
| 102 | +} // namespace LIBC_NAMESPACE_DECL |
| 103 | + |
| 104 | +#endif // LIBC_TYPES_HAS_FLOAT16 |
| 105 | + |
| 106 | +#endif // LLVM_LIBC_SRC___SUPPORT_MATH_COSF16_H |
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