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//===-- Single-precision cospi 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/cospif.h"
#include "sincosf_utils.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/common.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
namespace LIBC_NAMESPACE_DECL {
LLVM_LIBC_FUNCTION(float, cospif, (float x)) {
using FPBits = typename fputil::FPBits<float>;
FPBits xbits(x);
xbits.set_sign(Sign::POS);
uint32_t x_abs = xbits.uintval();
double xd = static_cast<double>(xbits.get_val());
// 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:
// cospi(x) = cos((k + y)*pi/32)
// = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32)
// The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..63 are precomputed
// and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
// computed using degree-7 and degree-6 minimax polynomials generated by
// Sollya respectively.
// The exhautive test passes for smaller values
if (LIBC_UNLIKELY(x_abs < 0x38A2'F984U)) {
#if defined(LIBC_TARGET_CPU_HAS_FMA_FLOAT)
return fputil::multiply_add(xbits.get_val(), -0x1.0p-25f, 1.0f);
#else
return static_cast<float>(fputil::multiply_add(xd, -0x1.0p-25, 1.0));
#endif // LIBC_TARGET_CPU_HAS_FMA_FLOAT
}
// Numbers greater or equal to 2^23 are always integers or NaN
if (LIBC_UNLIKELY(x_abs >= 0x4B00'0000)) {
if (LIBC_UNLIKELY(x_abs < 0x4B80'0000)) {
return (x_abs & 0x1) ? -1.0f : 1.0f;
}
// x is inf or nan.
if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) {
if (xbits.is_signaling_nan()) {
fputil::raise_except_if_required(FE_INVALID);
return FPBits::quiet_nan().get_val();
}
if (x_abs == 0x7f80'0000U) {
fputil::set_errno_if_required(EDOM);
fputil::raise_except_if_required(FE_INVALID);
}
return x + FPBits::quiet_nan().get_val();
}
return 1.0f;
}
// Combine the results with the sine of sum formula:
// cos(pi * x) = cos((k + y)*pi/32)
// = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32)
// = (cosm1_y + 1) * cos_k - sin_y * sin_k
// = (cosm1_y * cos_k + cos_k) - sin_y * sin_k
double sin_k, cos_k, sin_y, cosm1_y;
sincospif_eval(xd, sin_k, cos_k, sin_y, cosm1_y);
if (LIBC_UNLIKELY(sin_y == 0 && cos_k == 0)) {
return 0.0f;
}
return static_cast<float>(fputil::multiply_add(
sin_y, -sin_k, fputil::multiply_add(cosm1_y, cos_k, cos_k)));
}
} // namespace LIBC_NAMESPACE_DECL
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