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//===-- Half-precision sin(x) 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/sinf16.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/except_value_utils.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/macros/optimization.h"
namespace LIBC_NAMESPACE_DECL {
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
constexpr size_t N_EXCEPTS = 4;
constexpr fputil::ExceptValues<float16, N_EXCEPTS> SINF16_EXCEPTS{{
// (input, RZ output, RU offset, RD offset, RN offset)
{0x2b45, 0x2b43, 1, 0, 1},
{0x585c, 0x3ba3, 1, 0, 1},
{0x5cb0, 0xbbff, 0, 1, 0},
{0x51f5, 0xb80f, 0, 1, 0},
}};
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
LLVM_LIBC_FUNCTION(float16, sinf16, (float16 x)) {
using FPBits = 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| > pi/32, we perform range reduction as follows:
// Find k and y such that:
// x = (k + y) * pi/32
// k is an integer, |y| < 0.5
//
// This is done by performing:
// k = round(x * 32/pi)
// y = x * 32/pi - k
//
// Once k and y are computed, we then deduce the answer by the sine of sum
// formula:
// sin(x) = sin((k + y) * pi/32)
// = sin(k * pi/32) * cos(y * pi/32) +
// sin(y * pi/32) * cos(k * pi/32)
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
// Handle exceptional values
bool x_sign = x_u >> 15;
if (auto r = SINF16_EXCEPTS.lookup_odd(x_abs, x_sign);
LIBC_UNLIKELY(r.has_value()))
return r.value();
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
int rounding = fputil::quick_get_round();
// Exhaustive tests show that for |x| <= 0x1.f4p-11, 1ULP rounding errors
// occur. To fix this, the following apply:
if (LIBC_UNLIKELY(x_abs <= 0x13d0)) {
// sin(+/-0) = +/-0
if (LIBC_UNLIKELY(x_abs == 0U))
return x;
// When x > 0, and rounding upward, sin(x) == x.
// When x < 0, and rounding downward, sin(x) == x.
if ((rounding == FE_UPWARD && xbits.is_pos()) ||
(rounding == FE_DOWNWARD && xbits.is_neg()))
return x;
// When x < 0, and rounding upward, sin(x) == (x - 1ULP)
if (rounding == FE_UPWARD && xbits.is_neg()) {
x_u--;
return FPBits(x_u).get_val();
}
}
if (xbits.is_inf_or_nan()) {
if (xbits.is_signaling_nan()) {
fputil::raise_except_if_required(FE_INVALID);
return FPBits::quiet_nan().get_val();
}
if (xbits.is_inf()) {
fputil::set_errno_if_required(EDOM);
fputil::raise_except_if_required(FE_INVALID);
}
return x + FPBits::quiet_nan().get_val();
}
float sin_k, cos_k, sin_y, cosm1_y;
sincosf16_eval(xf, sin_k, cos_k, sin_y, cosm1_y);
if (LIBC_UNLIKELY(sin_y == 0 && sin_k == 0))
return FPBits::zero(xbits.sign()).get_val();
// Since, cosm1_y = cos_y - 1, therefore:
// sin(x) = cos_k * sin_y + sin_k + (cosm1_y * sin_k)
return fputil::cast<float16>(fputil::multiply_add(
sin_y, cos_k, fputil::multiply_add(cosm1_y, sin_k, sin_k)));
}
} // namespace LIBC_NAMESPACE_DECL
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