expf.cpp
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//===-- Single-precision e^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 "exp_utils.h"
#include "math_utils.h"
#include "include/math.h"
#include "src/__support/common.h"
#include <stdint.h>
#define InvLn2N exp2f_data.invln2_scaled
#define T exp2f_data.tab
#define C exp2f_data.poly_scaled
#define SHIFT exp2f_data.shift
namespace __llvm_libc {
float LLVM_LIBC_ENTRYPOINT(expf)(float x) {
uint32_t abstop;
uint64_t ki, t;
// double_t for better performance on targets with FLT_EVAL_METHOD == 2.
double_t kd, xd, z, r, r2, y, s;
xd = static_cast<double_t>(x);
abstop = top12_bits(x) & 0x7ff;
if (unlikely(abstop >= top12_bits(88.0f))) {
// |x| >= 88 or x is nan.
if (as_uint32_bits(x) == as_uint32_bits(-INFINITY))
return 0.0f;
if (abstop >= top12_bits(INFINITY))
return x + x;
if (x > as_float(0x42b17217)) // x > log(0x1p128) ~= 88.72
return overflow<float>(0);
if (x < as_float(0xc2cff1b4)) // x < log(0x1p-150) ~= -103.97
return underflow<float>(0);
if (x < as_float(0xc2ce8ecf)) // x < log(0x1p-149) ~= -103.28
return may_underflow<float>(0);
}
// x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k.
z = InvLn2N * xd;
// Round and convert z to int, the result is in [-150*N, 128*N] and
// ideally nearest int is used, otherwise the magnitude of r can be
// bigger which gives larger approximation error.
kd = static_cast<double>(z + SHIFT);
ki = as_uint64_bits(kd);
kd -= SHIFT;
r = z - kd;
// exp(x) = 2^(k/N) * 2^(r/N) ~= s *(C0*r^3 + C1*r^2 + C2*r + 1)
t = T[ki % N];
t += ki << (52 - EXP2F_TABLE_BITS);
s = as_double(t);
z = C[0] * r + C[1];
r2 = r * r;
y = C[2] * r + 1;
y = z * r2 + y;
y = y * s;
return static_cast<float>(y);
}
} // namespace __llvm_libc