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//===-- Single-precision asinh 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/asinhf.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/sqrt.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
#include "src/math/generic/common_constants.h"
#include "src/math/generic/explogxf.h"
namespace LIBC_NAMESPACE {
LLVM_LIBC_FUNCTION(float, asinhf, (float x)) {
using FPBits_t = typename fputil::FPBits<float>;
FPBits_t xbits(x);
uint32_t x_u = xbits.uintval();
uint32_t x_abs = x_u & FPBits_t::FloatProp::EXP_MANT_MASK;
// |x| <= 2^-3
if (LIBC_UNLIKELY(x_abs <= 0x3e80'0000U)) {
// |x| <= 2^-26
if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {
return static_cast<float>(LIBC_UNLIKELY(x_abs == 0)
? x
: (x - 0x1.5555555555555p-3 * x * x * x));
}
double x_d = x;
double x_sq = x_d * x_d;
// Generated by Sollya with:
// > P = fpminimax(asinh(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16], [|D...|],
// [0, 2^-2]);
double p = fputil::polyeval(
x_sq, 0.0, -0x1.555555555551ep-3, 0x1.3333333325495p-4,
-0x1.6db6db5a7622bp-5, 0x1.f1c70f82928c6p-6, -0x1.6e893934266b7p-6,
0x1.1c0b41d3fbe78p-6, -0x1.c0f47810b3c4fp-7, 0x1.2c8602690143dp-7);
return static_cast<float>(fputil::multiply_add(x_d, p, x_d));
}
const double SIGN[2] = {1.0, -1.0};
double x_sign = SIGN[x_u >> 31];
double x_d = x;
// Helper functions to set results for exceptional cases.
auto round_result_slightly_down = [x_sign](float r) -> float {
return fputil::multiply_add(static_cast<float>(x_sign), r,
static_cast<float>(x_sign) * (-0x1.0p-24f));
};
auto round_result_slightly_up = [x_sign](float r) -> float {
return fputil::multiply_add(static_cast<float>(x_sign), r,
static_cast<float>(x_sign) * 0x1.0p-24f);
};
if (LIBC_UNLIKELY(x_abs >= 0x4bdd'65a5U)) {
if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) {
// x is +-inf or nan
return x;
}
// Exceptional cases when x > 2^24.
switch (x_abs) {
case 0x4bdd65a5: // |x| = 0x1.bacb4ap24f
return round_result_slightly_down(0x1.1e0696p4f);
case 0x4c803f2c: // |x| = 0x1.007e58p26f
return round_result_slightly_down(0x1.2b786cp4f);
case 0x4f8ffb03: // |x| = 0x1.1ff606p32f
return round_result_slightly_up(0x1.6fdd34p4f);
case 0x5c569e88: // |x| = 0x1.ad3d1p57f
return round_result_slightly_up(0x1.45c146p5f);
case 0x5e68984e: // |x| = 0x1.d1309cp61f
return round_result_slightly_up(0x1.5c9442p5f);
case 0x655890d3: // |x| = 0x1.b121a6p75f
return round_result_slightly_down(0x1.a9a3f2p5f);
case 0x65de7ca6: // |x| = 0x1.bcf94cp76f
return round_result_slightly_up(0x1.af66cp5f);
case 0x6eb1a8ec: // |x| = 0x1.6351d8p94f
return round_result_slightly_down(0x1.08b512p6f);
case 0x7997f30a: // |x| = 0x1.2fe614p116f
return round_result_slightly_up(0x1.451436p6f);
}
} else {
// Exceptional cases when x < 2^24.
if (LIBC_UNLIKELY(x_abs == 0x45abaf26)) {
// |x| = 0x1.575e4cp12f
return round_result_slightly_down(0x1.29becap3f);
}
if (LIBC_UNLIKELY(x_abs == 0x49d29048)) {
// |x| = 0x1.a5209p20f
return round_result_slightly_down(0x1.e1b92p3f);
}
}
// asinh(x) = log(x + sqrt(x^2 + 1))
return static_cast<float>(
x_sign *
log_eval(fputil::multiply_add(
x_d, x_sign, fputil::sqrt(fputil::multiply_add(x_d, x_d, 1.0)))));
}
} // namespace LIBC_NAMESPACE
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