| /* Single-precision floating point 2^x. |
| Copyright (C) 1997-2014 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, and for |
| single-precision. |
| */ |
| #ifndef _GNU_SOURCE |
| # define _GNU_SOURCE |
| #endif |
| #include <stdlib.h> |
| #include <float.h> |
| #include <ieee754.h> |
| #include <math.h> |
| #include <fenv.h> |
| #include <inttypes.h> |
| #include <math_private.h> |
| |
| #include "t_exp2f.h" |
| |
| static const volatile float TWOM100 = 7.88860905e-31; |
| static const volatile float TWO127 = 1.7014118346e+38; |
| |
| float |
| __ieee754_exp2f (float x) |
| { |
| static const float himark = (float) FLT_MAX_EXP; |
| static const float lomark = (float) (FLT_MIN_EXP - FLT_MANT_DIG - 1); |
| |
| /* Check for usual case. */ |
| if (isless (x, himark) && isgreaterequal (x, lomark)) |
| { |
| static const float THREEp14 = 49152.0; |
| int tval, unsafe; |
| float rx, x22, result; |
| union ieee754_float ex2_u, scale_u; |
| |
| { |
| SET_RESTORE_ROUND_NOEXF (FE_TONEAREST); |
| |
| /* 1. Argument reduction. |
| Choose integers ex, -128 <= t < 128, and some real |
| -1/512 <= x1 <= 1/512 so that |
| x = ex + t/512 + x1. |
| |
| First, calculate rx = ex + t/256. */ |
| rx = x + THREEp14; |
| rx -= THREEp14; |
| x -= rx; /* Compute x=x1. */ |
| /* Compute tval = (ex*256 + t)+128. |
| Now, t = (tval mod 256)-128 and ex=tval/256 [that's mod, NOT %; |
| and /-round-to-nearest not the usual c integer /]. */ |
| tval = (int) (rx * 256.0f + 128.0f); |
| |
| /* 2. Adjust for accurate table entry. |
| Find e so that |
| x = ex + t/256 + e + x2 |
| where -7e-4 < e < 7e-4, and |
| (float)(2^(t/256+e)) |
| is accurate to one part in 2^-64. */ |
| |
| /* 'tval & 255' is the same as 'tval%256' except that it's always |
| positive. |
| Compute x = x2. */ |
| x -= __exp2f_deltatable[tval & 255]; |
| |
| /* 3. Compute ex2 = 2^(t/255+e+ex). */ |
| ex2_u.f = __exp2f_atable[tval & 255]; |
| tval >>= 8; |
| unsafe = abs(tval) >= -FLT_MIN_EXP - 1; |
| ex2_u.ieee.exponent += tval >> unsafe; |
| scale_u.f = 1.0; |
| scale_u.ieee.exponent += tval - (tval >> unsafe); |
| |
| /* 4. Approximate 2^x2 - 1, using a second-degree polynomial, |
| with maximum error in [-2^-9 - 2^-14, 2^-9 + 2^-14] |
| less than 1.3e-10. */ |
| |
| x22 = (.24022656679f * x + .69314736128f) * ex2_u.f; |
| } |
| |
| /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */ |
| result = x22 * x + ex2_u.f; |
| |
| if (!unsafe) |
| return result; |
| else |
| return result * scale_u.f; |
| } |
| /* Exceptional cases: */ |
| else if (isless (x, himark)) |
| { |
| if (__isinf_nsf (x)) |
| /* e^-inf == 0, with no error. */ |
| return 0; |
| else |
| /* Underflow */ |
| return TWOM100 * TWOM100; |
| } |
| else |
| /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ |
| return TWO127*x; |
| } |
| strong_alias (__ieee754_exp2f, __exp2f_finite) |