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Diffstat (limited to 'lib/frexp.c')
| -rw-r--r-- | lib/frexp.c | 168 |
1 files changed, 168 insertions, 0 deletions
diff --git a/lib/frexp.c b/lib/frexp.c new file mode 100644 index 0000000..ad1dba7 --- /dev/null +++ b/lib/frexp.c @@ -0,0 +1,168 @@ +/* Split a double into fraction and mantissa. + Copyright (C) 2007-2020 Free Software Foundation, Inc. + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation; either version 3 of the License, or + (at your option) any later version. + + This program 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 General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see <https://www.gnu.org/licenses/>. */ + +/* Written by Paolo Bonzini <bonzini@gnu.org>, 2003, and + Bruno Haible <bruno@clisp.org>, 2007. */ + +#if ! defined USE_LONG_DOUBLE +# include <config.h> +#endif + +/* Specification. */ +#include <math.h> + +#include <float.h> +#ifdef USE_LONG_DOUBLE +# include "isnanl-nolibm.h" +# include "fpucw.h" +#else +# include "isnand-nolibm.h" +#endif + +/* This file assumes FLT_RADIX = 2. If FLT_RADIX is a power of 2 greater + than 2, or not even a power of 2, some rounding errors can occur, so that + then the returned mantissa is only guaranteed to be <= 1.0, not < 1.0. */ + +#ifdef USE_LONG_DOUBLE +# define FUNC frexpl +# define DOUBLE long double +# define ISNAN isnanl +# define DECL_ROUNDING DECL_LONG_DOUBLE_ROUNDING +# define BEGIN_ROUNDING() BEGIN_LONG_DOUBLE_ROUNDING () +# define END_ROUNDING() END_LONG_DOUBLE_ROUNDING () +# define L_(literal) literal##L +#else +# define FUNC frexp +# define DOUBLE double +# define ISNAN isnand +# define DECL_ROUNDING +# define BEGIN_ROUNDING() +# define END_ROUNDING() +# define L_(literal) literal +#endif + +DOUBLE +FUNC (DOUBLE x, int *expptr) +{ + int sign; + int exponent; + DECL_ROUNDING + + /* Test for NaN, infinity, and zero. */ + if (ISNAN (x) || x + x == x) + { + *expptr = 0; + return x; + } + + sign = 0; + if (x < 0) + { + x = - x; + sign = -1; + } + + BEGIN_ROUNDING (); + + { + /* Since the exponent is an 'int', it fits in 64 bits. Therefore the + loops are executed no more than 64 times. */ + DOUBLE pow2[64]; /* pow2[i] = 2^2^i */ + DOUBLE powh[64]; /* powh[i] = 2^-2^i */ + int i; + + exponent = 0; + if (x >= L_(1.0)) + { + /* A positive exponent. */ + DOUBLE pow2_i; /* = pow2[i] */ + DOUBLE powh_i; /* = powh[i] */ + + /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i, + x * 2^exponent = argument, x >= 1.0. */ + for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5); + ; + i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i) + { + if (x >= pow2_i) + { + exponent += (1 << i); + x *= powh_i; + } + else + break; + + pow2[i] = pow2_i; + powh[i] = powh_i; + } + /* Avoid making x too small, as it could become a denormalized + number and thus lose precision. */ + while (i > 0 && x < pow2[i - 1]) + { + i--; + powh_i = powh[i]; + } + exponent += (1 << i); + x *= powh_i; + /* Here 2^-2^i <= x < 1.0. */ + } + else + { + /* A negative or zero exponent. */ + DOUBLE pow2_i; /* = pow2[i] */ + DOUBLE powh_i; /* = powh[i] */ + + /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i, + x * 2^exponent = argument, x < 1.0. */ + for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5); + ; + i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i) + { + if (x < powh_i) + { + exponent -= (1 << i); + x *= pow2_i; + } + else + break; + + pow2[i] = pow2_i; + powh[i] = powh_i; + } + /* Here 2^-2^i <= x < 1.0. */ + } + + /* Invariants: x * 2^exponent = argument, and 2^-2^i <= x < 1.0. */ + while (i > 0) + { + i--; + if (x < powh[i]) + { + exponent -= (1 << i); + x *= pow2[i]; + } + } + /* Here 0.5 <= x < 1.0. */ + } + + if (sign < 0) + x = - x; + + END_ROUNDING (); + + *expptr = exponent; + return x; +} |