| /* Double-precision floating point 2^x. |
| Copyright (C) 1997-2018 Free Software Foundation, Inc. |
| This file is part of the GNU C Library. |
| Contributed by Geoffrey Keating <geoffk@ozemail.com.au> |
| |
| 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/>. */ |
| |
| /* The basic design here is from |
| Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical |
| Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft., |
| 17 (1), March 1991, pp. 26-45. |
| It has been slightly modified to compute 2^x instead of e^x. |
| */ |
| #include <stdlib.h> |
| #include <float.h> |
| #include <ieee754.h> |
| #include <math.h> |
| #include <fenv.h> |
| #include <inttypes.h> |
| #include <math_private.h> |
| |
| #include "t_exp2.h" |
| |
| static const double TWO1023 = 8.988465674311579539e+307; |
| static const double TWOM1000 = 9.3326361850321887899e-302; |
| |
| double |
| __ieee754_exp2 (double x) |
| { |
| static const double himark = (double) DBL_MAX_EXP; |
| static const double lomark = (double) (DBL_MIN_EXP - DBL_MANT_DIG - 1); |
| |
| /* Check for usual case. */ |
| if (__glibc_likely (isless (x, himark))) |
| { |
| /* Exceptional cases: */ |
| if (__glibc_unlikely (!isgreaterequal (x, lomark))) |
| { |
| if (isinf (x)) |
| /* e^-inf == 0, with no error. */ |
| return 0; |
| else |
| /* Underflow */ |
| return TWOM1000 * TWOM1000; |
| } |
| |
| static const double THREEp42 = 13194139533312.0; |
| int tval, unsafe; |
| double rx, x22, result; |
| union ieee754_double ex2_u, scale_u; |
| |
| if (fabs (x) < DBL_EPSILON / 4.0) |
| return 1.0 + x; |
| |
| { |
| SET_RESTORE_ROUND_NOEX (FE_TONEAREST); |
| |
| /* 1. Argument reduction. |
| Choose integers ex, -256 <= t < 256, and some real |
| -1/1024 <= x1 <= 1024 so that |
| x = ex + t/512 + x1. |
| |
| First, calculate rx = ex + t/512. */ |
| rx = x + THREEp42; |
| rx -= THREEp42; |
| x -= rx; /* Compute x=x1. */ |
| /* Compute tval = (ex*512 + t)+256. |
| Now, t = (tval mod 512)-256 and ex=tval/512 [that's mod, NOT %; |
| and /-round-to-nearest not the usual c integer /]. */ |
| tval = (int) (rx * 512.0 + 256.0); |
| |
| /* 2. Adjust for accurate table entry. |
| Find e so that |
| x = ex + t/512 + e + x2 |
| where -1e6 < e < 1e6, and |
| (double)(2^(t/512+e)) |
| is accurate to one part in 2^-64. */ |
| |
| /* 'tval & 511' is the same as 'tval%512' except that it's always |
| positive. |
| Compute x = x2. */ |
| x -= exp2_deltatable[tval & 511]; |
| |
| /* 3. Compute ex2 = 2^(t/512+e+ex). */ |
| ex2_u.d = exp2_accuratetable[tval & 511]; |
| tval >>= 9; |
| /* x2 is an integer multiple of 2^-54; avoid intermediate |
| underflow from the calculation of x22 * x. */ |
| unsafe = abs (tval) >= -DBL_MIN_EXP - 56; |
| ex2_u.ieee.exponent += tval >> unsafe; |
| scale_u.d = 1.0; |
| scale_u.ieee.exponent += tval - (tval >> unsafe); |
| |
| /* 4. Approximate 2^x2 - 1, using a fourth-degree polynomial, |
| with maximum error in [-2^-10-2^-30,2^-10+2^-30] |
| less than 10^-19. */ |
| |
| x22 = (((.0096181293647031180 |
| * x + .055504110254308625) |
| * x + .240226506959100583) |
| * x + .69314718055994495) * ex2_u.d; |
| math_opt_barrier (x22); |
| } |
| |
| /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */ |
| result = x22 * x + ex2_u.d; |
| |
| if (!unsafe) |
| return result; |
| else |
| { |
| result *= scale_u.d; |
| math_check_force_underflow_nonneg (result); |
| return result; |
| } |
| } |
| else |
| /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ |
| return TWO1023 * x; |
| } |
| strong_alias (__ieee754_exp2, __exp2_finite) |