| /* Single-precision e^x function. |
| Copyright (C) 2017-2018 Free Software Foundation, Inc. |
| This file is part of the GNU C Library. |
| |
| The GNU C Library is free software; you can redistribute it and/or |
| modify it under the terms of the GNU Lesser General Public |
| License as published by the Free Software Foundation; either |
| version 2.1 of the License, or (at your option) any later version. |
| |
| The GNU C Library is distributed in the hope that it will be useful, |
| but WITHOUT ANY WARRANTY; without even the implied warranty of |
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| Lesser General Public License for more details. |
| |
| You should have received a copy of the GNU Lesser General Public |
| License along with the GNU C Library; if not, see |
| <http://www.gnu.org/licenses/>. */ |
| |
| #ifdef __expf |
| # undef libm_hidden_proto |
| # define libm_hidden_proto(ignored) |
| #endif |
| |
| #include <math.h> |
| #include <stdint.h> |
| #include <shlib-compat.h> |
| #include <libm-alias-float.h> |
| #include "math_config.h" |
| |
| /* |
| EXP2F_TABLE_BITS = 5 |
| EXP2F_POLY_ORDER = 3 |
| |
| ULP error: 0.502 (nearest rounding.) |
| Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.) |
| Wrong count: 170635 (all nearest rounding wrong results with fma.) |
| Non-nearest ULP error: 1 (rounded ULP error) |
| */ |
| |
| #define N (1 << EXP2F_TABLE_BITS) |
| #define InvLn2N __exp2f_data.invln2_scaled |
| #define T __exp2f_data.tab |
| #define C __exp2f_data.poly_scaled |
| |
| static inline uint32_t |
| top12 (float x) |
| { |
| return asuint (x) >> 20; |
| } |
| |
| 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 = (double_t) x; |
| abstop = top12 (x) & 0x7ff; |
| if (__glibc_unlikely (abstop >= top12 (88.0f))) |
| { |
| /* |x| >= 88 or x is nan. */ |
| if (asuint (x) == asuint (-INFINITY)) |
| return 0.0f; |
| if (abstop >= top12 (INFINITY)) |
| return x + x; |
| if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */ |
| return __math_oflowf (0); |
| if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */ |
| return __math_uflowf (0); |
| #if WANT_ERRNO_UFLOW |
| if (x < -0x1.9d1d9ep6f) /* x < log(0x1p-149) ~= -103.28 */ |
| return __math_may_uflowf (0); |
| #endif |
| } |
| |
| /* 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 ties-to-even rule is used, otherwise the magnitude of r |
| can be bigger which gives larger approximation error. */ |
| #if TOINT_INTRINSICS |
| kd = roundtoint (z); |
| ki = converttoint (z); |
| #elif TOINT_RINT |
| kd = rint (z); |
| ki = (long) kd; |
| #elif TOINT_SHIFT |
| # define SHIFT __exp2f_data.shift |
| kd = math_narrow_eval ((double) (z + SHIFT)); /* Needs to be double. */ |
| ki = asuint64 (kd); |
| kd -= SHIFT; |
| #endif |
| 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 = asdouble (t); |
| z = C[0] * r + C[1]; |
| r2 = r * r; |
| y = C[2] * r + 1; |
| y = z * r2 + y; |
| y = y * s; |
| return (float) y; |
| } |
| |
| #ifndef __expf |
| hidden_def (__expf) |
| strong_alias (__expf, __ieee754_expf) |
| strong_alias (__expf, __expf_finite) |
| versioned_symbol (libm, __expf, expf, GLIBC_2_27); |
| libm_alias_float_other (__exp, exp) |
| #endif |
