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//===-- Half-precision cospif function ------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "src/math/cospif16.h"
#include "hdr/errno_macros.h"
#include "hdr/fenv_macros.h"
#include "sincosf16_utils.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/cast.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/macros/optimization.h"
namespace LIBC_NAMESPACE_DECL {
LLVM_LIBC_FUNCTION(float16, cospif16, (float16 x)) {
using FPBits = typename fputil::FPBits<float16>;
FPBits xbits(x);
uint16_t x_u = xbits.uintval();
uint16_t x_abs = x_u & 0x7fff;
float xf = x;
// Range reduction:
// For |x| > 1/32, we perform range reduction as follows:
// Find k and y such that:
// x = (k + y) * 1/32
// k is an integer
// |y| < 0.5
//
// This is done by performing:
// k = round(x * 32)
// y = x * 32 - k
//
// Once k and y are computed, we then deduce the answer by the cosine of sum
// formula:
// cos(x * pi) = cos((k + y) * pi/32)
// = cos(k * pi/32) * cos(y * pi/32) +
// sin(y * pi/32) * sin(k * pi/32)
// For signed zeros
if (LIBC_UNLIKELY(x_abs == 0U))
return fputil::cast<float16>(1.0f);
// Numbers greater or equal to 2^10 are integers, or infinity, or NaN
if (LIBC_UNLIKELY(x_abs >= 0x6400)) {
if (LIBC_UNLIKELY(x_abs <= 0x67FF))
return fputil::cast<float16>((x_abs & 0x1) ? -1.0f : 1.0f);
// Check for NaN or infintiy values
if (LIBC_UNLIKELY(x_abs >= 0x7c00)) {
if (xbits.is_signaling_nan()) {
fputil::raise_except_if_required(FE_INVALID);
return FPBits::quiet_nan().get_val();
}
// If value is equal to infinity
if (x_abs == 0x7c00) {
fputil::set_errno_if_required(EDOM);
fputil::raise_except_if_required(FE_INVALID);
}
return x + FPBits::quiet_nan().get_val();
}
return fputil::cast<float16>(1.0f);
}
float sin_k, cos_k, sin_y, cosm1_y;
sincospif16_eval(xf, sin_k, cos_k, sin_y, cosm1_y);
if (LIBC_UNLIKELY(sin_y == 0 && cos_k == 0))
return fputil::cast<float16>(0.0f);
// Since, cosm1_y = cos_y - 1, therefore:
// cos(x * pi) = cos_k(cosm1_y) + cos_k - sin_k * sin_y
return fputil::cast<float16>(fputil::multiply_add(
cos_k, cosm1_y, fputil::multiply_add(-sin_k, sin_y, cos_k)));
}
} // namespace LIBC_NAMESPACE_DECL
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