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Diffstat (limited to 'sysdeps/libm-ieee754/s_exp2.c')
| -rw-r--r-- | sysdeps/libm-ieee754/s_exp2.c | 128 |
1 files changed, 128 insertions, 0 deletions
diff --git a/sysdeps/libm-ieee754/s_exp2.c b/sysdeps/libm-ieee754/s_exp2.c new file mode 100644 index 0000000000..e10fae5492 --- /dev/null +++ b/sysdeps/libm-ieee754/s_exp2.c @@ -0,0 +1,128 @@ +/* Double-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. + */ +#ifndef _GNU_SOURCE +#define _GNU_SOURCE +#endif +#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 volatile double TWO1000 = 1.071508607186267320948e+301; +static const volatile double TWOM1000 = 9.3326361850321887899e-302; + +double +__ieee754_exp2 (double x) +{ + static const uint32_t a_inf = 0x7f800000; + /* Check for usual case. */ + if (isless (x, (double) DBL_MAX_EXP) + && isgreater (x, (double) (DBL_MIN_EXP - 1))) + { + static const float TWO43 = 8796093022208.0; + int tval; + double rx, x22; + union ieee754_double ex2_u; + fenv_t oldenv; + + feholdexcept (&oldenv); + fesetround (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. */ + if (x >= 0) + { + rx = x + TWO43; + rx -= TWO43; + } + else + { + rx = x - TWO43; + rx += TWO43; + } + 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]; + ex2_u.ieee.exponent += tval >> 9; + + /* 4. Approximate 2^x2 - 1, using a fourth-degree polynomial, + 2^x2 ~= sum(k=0..4 | (x2 * ln(2))^k / k! ) + + so + 2^x2 - 1 ~= sum(k=1..4 | (x2 * ln(2))^k / k! ) + with error less than 2^(1/1024) * (x2 * ln(2))^5 / 5! < 1.2e-18. */ + + x22 = (((.0096181291076284772 + * x + .055504108664821580) + * x + .240226506959100712) + * x + .69314718055994531) * ex2_u.d; + + /* 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.d; + } + /* 2^inf == inf, with no error. */ + else if (x == *(const float *) &a_inf) + return x; + /* Check for overflow. */ + else if (isgreaterequal (x, (double) DBL_MAX_EXP)) + return TWO1000 * TWO1000; + /* And underflow (including -inf). */ + else if (isless (x, (double) (DBL_MIN_EXP - DBL_MANT_DIG))) + return TWOM1000 * TWOM1000; + /* Maybe the result needs to be a denormalised number... */ + else if (!isnan (x)) + return __ieee754_exp2 (x + 1000.0) * TWOM1000; + else /* isnan(x) */ + return x + x; +} |