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//===-- Single-precision sinpif 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/sinpif.h"
#include "sincosf_utils.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.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
namespace LIBC_NAMESPACE_DECL {
LLVM_LIBC_FUNCTION(float, sinpif, (float x)) {
using FPBits = typename fputil::FPBits<float>;
FPBits xbits(x);
uint32_t x_u = xbits.uintval();
uint32_t x_abs = x_u & 0x7fff'ffffU;
double xd = static_cast<double>(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 sine of sum
// formula:
// sin(x * pi) = sin((k + y)*pi/32)
// = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
// The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..31 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.
// |x| <= 1/16
if (LIBC_UNLIKELY(x_abs <= 0x3d80'0000U)) {
if (LIBC_UNLIKELY(x_abs < 0x33CD'01D7U)) {
if (LIBC_UNLIKELY(x_abs == 0U)) {
// For signed zeros.
return x;
}
// For very small values we can approximate sinpi(x) with x * pi
// An exhaustive test shows that this is accurate for |x| < 9.546391 ×
// 10-8
double xdpi = xd * 0x1.921fb54442d18p1;
return static_cast<float>(xdpi);
}
// |x| < 1/16.
double xsq = xd * xd;
// Degree-9 polynomial approximation:
// sinpi(x) ~ x + a_3 x^3 + a_5 x^5 + a_7 x^7 + a_9 x^9
// = x (1 + a_3 x^2 + ... + a_9 x^8)
// = x * P(x^2)
// generated by Sollya with the following commands:
// > display = hexadecimal;
// > Q = fpminimax(sin(pi * x)/x, [|0, 2, 4, 6, 8|], [|D...|], [0, 1/16]);
double result = fputil::polyeval(
xsq, 0x1.921fb54442d18p1, -0x1.4abbce625bbf2p2, 0x1.466bc675e116ap1,
-0x1.32d2c0b62d41cp-1, 0x1.501ec4497cb7dp-4);
return static_cast<float>(xd * result);
}
// Numbers greater or equal to 2^23 are always integers or NaN
if (LIBC_UNLIKELY(x_abs >= 0x4B00'0000)) {
// check for NaN values
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 FPBits::zero(xbits.sign()).get_val();
}
// Combine the results with the sine of sum formula:
// sin(x * pi) = sin((k + y)*pi/32)
// = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
// = sin_y * cos_k + (1 + cosm1_y) * sin_k
// = sin_y * cos_k + (cosm1_y * sin_k + 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 && sin_k == 0))
return FPBits::zero(xbits.sign()).get_val();
return static_cast<float>(fputil::multiply_add(
sin_y, cos_k, fputil::multiply_add(cosm1_y, sin_k, sin_k)));
}
} // namespace LIBC_NAMESPACE_DECL
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