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//===-- Single-precision 10^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/exp10f.h"
#include "explogxf.h"
#include "src/__support/FPUtil/BasicOperations.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/FPUtil/nearest_integer.h"
#include "src/__support/common.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
#include <errno.h>
namespace __llvm_libc {
LLVM_LIBC_FUNCTION(float, exp10f, (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;
// When |x| >= log10(2^128), or x is nan
if (LIBC_UNLIKELY(x_abs >= 0x421a'209bU)) {
// When x < log10(2^-150) or nan
if (x_u > 0xc234'9e35U) {
// exp(-Inf) = 0
if (xbits.is_inf())
return 0.0f;
// exp(nan) = nan
if (xbits.is_nan())
return x;
if (fputil::get_round() == FE_UPWARD)
return static_cast<float>(FPBits(FPBits::MIN_SUBNORMAL));
fputil::set_errno_if_required(ERANGE);
fputil::raise_except_if_required(FE_UNDERFLOW);
return 0.0f;
}
// x >= log10(2^128) or nan
if (!xbits.get_sign() && (x_u >= 0x421a'209bU)) {
// x is finite
if (x_u < 0x7f80'0000U) {
int rounding = fputil::get_round();
if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
return static_cast<float>(FPBits(FPBits::MAX_NORMAL));
fputil::set_errno_if_required(ERANGE);
fputil::raise_except_if_required(FE_OVERFLOW);
}
// x is +inf or nan
return x + static_cast<float>(FPBits::inf());
}
}
// When |x| <= log10(2)*2^-6
if (LIBC_UNLIKELY(x_abs <= 0x3b9a'209bU)) {
if (LIBC_UNLIKELY(x_u == 0xb25e'5bd9U)) { // x = -0x1.bcb7b2p-27f
if (fputil::get_round() == FE_TONEAREST)
return 0x1.fffffep-1f;
}
// |x| < 2^-25
// 10^x ~ 1 + log(10) * x
if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {
return fputil::multiply_add(x, 0x1.26bb1cp+1f, 1.0f);
}
return static_cast<float>(Exp10Base::powb_lo(x));
}
// Exceptional value.
if (LIBC_UNLIKELY(x_u == 0x3d14'd956U)) { // x = 0x1.29b2acp-5f
if (fputil::get_round() == FE_UPWARD)
return 0x1.1657c4p+0f;
}
// Exact outputs when x = 1, 2, ..., 10.
// Quick check mask: 0x800f'ffffU = ~(bits of 1.0f | ... | bits of 10.0f)
if (LIBC_UNLIKELY((x_u & 0x800f'ffffU) == 0)) {
switch (x_u) {
case 0x3f800000U: // x = 1.0f
return 10.0f;
case 0x40000000U: // x = 2.0f
return 100.0f;
case 0x40400000U: // x = 3.0f
return 1'000.0f;
case 0x40800000U: // x = 4.0f
return 10'000.0f;
case 0x40a00000U: // x = 5.0f
return 100'000.0f;
case 0x40c00000U: // x = 6.0f
return 1'000'000.0f;
case 0x40e00000U: // x = 7.0f
return 10'000'000.0f;
case 0x41000000U: // x = 8.0f
return 100'000'000.0f;
case 0x41100000U: // x = 9.0f
return 1'000'000'000.0f;
case 0x41200000U: // x = 10.0f
return 10'000'000'000.0f;
}
}
// Range reduction: 10^x = 2^(mid + hi) * 10^lo
// rr = (2^(mid + hi), lo)
auto rr = exp_b_range_reduc<Exp10Base>(x);
// The low part is approximated by a degree-5 minimax polynomial.
// 10^lo ~ 1 + COEFFS[0] * lo + ... + COEFFS[4] * lo^5
using fputil::multiply_add;
double lo2 = rr.lo * rr.lo;
// c0 = 1 + COEFFS[0] * lo
double c0 = multiply_add(rr.lo, Exp10Base::COEFFS[0], 1.0);
// c1 = COEFFS[1] + COEFFS[2] * lo
double c1 = multiply_add(rr.lo, Exp10Base::COEFFS[2], Exp10Base::COEFFS[1]);
// c2 = COEFFS[3] + COEFFS[4] * lo
double c2 = multiply_add(rr.lo, Exp10Base::COEFFS[4], Exp10Base::COEFFS[3]);
// p = c1 + c2 * lo^2
// = COEFFS[1] + COEFFS[2] * lo + COEFFS[3] * lo^2 + COEFFS[4] * lo^3
double p = multiply_add(lo2, c2, c1);
// 10^lo ~ c0 + p * lo^2
// 10^x = 2^(mid + hi) * 10^lo
// ~ mh * (c0 + p * lo^2)
// = (mh * c0) + p * (mh * lo^2)
return static_cast<float>(multiply_add(p, lo2 * rr.mh, c0 * rr.mh));
}
} // namespace __llvm_libc
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