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Diffstat (limited to 'sysdeps/libm-ieee754/s_exp2f.c')
| -rw-r--r-- | sysdeps/libm-ieee754/s_exp2f.c | 126 |
1 files changed, 126 insertions, 0 deletions
diff --git a/sysdeps/libm-ieee754/s_exp2f.c b/sysdeps/libm-ieee754/s_exp2f.c new file mode 100644 index 0000000000..e50ac77792 --- /dev/null +++ b/sysdeps/libm-ieee754/s_exp2f.c @@ -0,0 +1,126 @@ +/* Single-precision floating point 2^x. + Copyright (C) 1997 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 Library General Public License as + published by the Free Software Foundation; either version 2 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 + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +/* 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. + */ +#define _GNU_SOURCE +#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 huge = 1e+30; + +float +__ieee754_exp2f (float x) +{ + static const uint32_t a_inf = 0x7f800000; + /* Check for usual case. */ + if (isless (x, (float) FLT_MAX_EXP) + && isgreater (x, (float) (FLT_MIN_EXP - 1))) + { + static const float TWO16 = 65536.0; + int tval; + float rx, x22; + union ieee754_float ex2_u; + fenv_t oldenv; + + feholdexcept (&oldenv); + fesetround (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. */ + if (x >= 0) + { + rx = x + TWO16; + rx -= TWO16; + } + else + { + rx = x - TWO16; + rx += TWO16; + } + 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 -= exp2_deltatable[tval & 255]; + + /* 3. Compute ex2 = 2^(t/255+e+ex). */ + ex2_u.f = exp2_accuratetable[tval & 255]; + ex2_u.ieee.exponent += tval >> 8; + + /* 4. Approximate 2^x2 - 1, using a second-degree polynomial, + 2^x2 ~= sum(k=0..2 | (x2 * ln(2))^k / k! ) + + so + 2^x2 - 1 ~= sum(k=1..4 | (x2 * ln(2))^k / k! ) + with error less than 2^(1/512+7e-4) * (x2 * ln(2))^3 / 3! < 1.2e-18. */ + + x22 = (.240226507f * x + .6931471806f) * ex2_u.f; + + /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */ + fesetenv (&oldenv); + + /* Need to check: does this set FE_INEXACT correctly? */ + return x22 * x + ex2_u.f; + } + /* 2^inf == inf, with no error. */ + else if (x == *(const float *)&a_inf) + { + return x; + } + /* Check for overflow. */ + else if (isgreaterequal (x, (float) FLT_MAX_EXP)) + return huge * huge; + /* And underflow (including -inf). */ + else if (isless (x, (float) (FLT_MIN_EXP - FLT_MANT_DIF))) + return TWOM100 * TWOM100; + /* Maybe the result needs to be a denormalised number... */ + else if (!isnan (x)) + return __ieee754_exp2f (x + 100.0) * TWOM100; + else /* isnan(x) */ + return x + x; +} |