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//===-- Single-precision tanpi 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/tanpif.h"
#include "sincosf_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/common.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
namespace LIBC_NAMESPACE_DECL {
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
constexpr size_t N_EXCEPTS = 3;
constexpr fputil::ExceptValues<float, N_EXCEPTS> TANPIF_EXCEPTS{{
// (input, RZ output, RU offset, RD offset, RN offset)
{0x38F26685, 0x39BE6182, 1, 0, 0},
{0x3E933802, 0x3FA267DD, 1, 0, 0},
{0x3F3663FF, 0xBFA267DD, 0, 1, 0},
}};
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
LLVM_LIBC_FUNCTION(float, tanpif, (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>(xbits.get_val());
// Handle exceptional values
if (LIBC_UNLIKELY(x_abs <= 0x3F3663FF)) {
if (LIBC_UNLIKELY(x_abs == 0U))
return x;
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
bool x_sign = x_u >> 31;
if (auto r = TANPIF_EXCEPTS.lookup_odd(x_abs, x_sign);
LIBC_UNLIKELY(r.has_value()))
return r.value();
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
}
// Numbers greater or equal to 2^23 are always integers, or infinity, or NaN
if (LIBC_UNLIKELY(x_abs >= 0x4B00'0000)) {
// 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 FPBits::zero(xbits.sign()).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 formula:
// tan(x) = sin(x) / cos(x)
// = (sin_y * cos_k + cos_y * sin_k) / (cos_y * 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)) {
fputil::set_errno_if_required(EDOM);
fputil::raise_except_if_required(FE_DIVBYZERO);
int32_t x_mp5_i = static_cast<int32_t>(xd - 0.5);
return FPBits::inf((x_mp5_i & 0x1) ? Sign::NEG : Sign::POS).get_val();
}
using fputil::multiply_add;
return fputil::cast<float>(
multiply_add(sin_y, cos_k, multiply_add(cosm1_y, sin_k, sin_k)) /
multiply_add(sin_y, -sin_k, multiply_add(cosm1_y, cos_k, cos_k)));
}
} // namespace LIBC_NAMESPACE_DECL
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