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Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/flt-32/e_exp2f.c')
| -rw-r--r-- | REORG.TODO/sysdeps/ieee754/flt-32/e_exp2f.c | 132 |
1 files changed, 132 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_exp2f.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_exp2f.c new file mode 100644 index 0000000000..567d3ff6d0 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_exp2f.c @@ -0,0 +1,132 @@ +/* Single-precision floating point 2^x. + Copyright (C) 1997-2017 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 float TWOM100 = 7.88860905e-31; +static const 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; + + if (fabsf (x) < FLT_EPSILON / 4.0f) + return 1.0f + x; + + { + 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; + /* x2 is an integer multiple of 2^-30; avoid intermediate + underflow from the calculation of x22 * x. */ + unsafe = abs(tval) >= -FLT_MIN_EXP - 32; + 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 + { + result *= scale_u.f; + math_check_force_underflow_nonneg (result); + return result; + } + } + /* Exceptional cases: */ + else if (isless (x, himark)) + { + if (isinf (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) |