| //===-- 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 "src/math/expf.h" |
| #include "exp_utils.h" |
| #include "math_utils.h" |
| |
| #include "src/__support/common.h" |
| #include <math.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 { |
| |
| LLVM_LIBC_FUNCTION(float, 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 |