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Diffstat (limited to 'newlib/libm/ld80/b_expl.c')
| -rw-r--r-- | newlib/libm/ld80/b_expl.c | 113 |
1 files changed, 113 insertions, 0 deletions
diff --git a/newlib/libm/ld80/b_expl.c b/newlib/libm/ld80/b_expl.c new file mode 100644 index 0000000..c18a554 --- /dev/null +++ b/newlib/libm/ld80/b_expl.c @@ -0,0 +1,113 @@ +/*- + * SPDX-License-Identifier: BSD-3-Clause + * + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +/* + * See bsdsrc/b_exp.c for implementation details. + * + * bsdrc/b_exp.c converted to long double by Steven G. Kargl. + */ + +#include "fpmath.h" +#include "math_private.h" + +static const union IEEEl2bits + p0u = LD80C(0xaaaaaaaaaaaaaaab, -3, 1.66666666666666666671e-01L), + p1u = LD80C(0xb60b60b60b60b59a, -9, -2.77777777777777775377e-03L), + p2u = LD80C(0x8ab355e008a3cfce, -14, 6.61375661375629297465e-05L), + p3u = LD80C(0xddebbc994b0c1376, -20, -1.65343915327882529784e-06L), + p4u = LD80C(0xb354784cb4ef4c41, -25, 4.17535101591534118469e-08L), + p5u = LD80C(0x913e8a718382ce75, -30, -1.05679137034774806475e-09L), + p6u = LD80C(0xe8f0042aa134502e, -36, 2.64819349895429516863e-11L); +#define p1 (p0u.e) +#define p2 (p1u.e) +#define p3 (p2u.e) +#define p4 (p3u.e) +#define p5 (p4u.e) +#define p6 (p5u.e) +#define p7 (p6u.e) + +/* + * lnhuge = (LDBL_MAX_EXP + 9) * log(2.) + * lntiny = (LDBL_MIN_EXP - 64 - 10) * log(2.) + * invln2 = 1 / log(2.) + */ +static const union IEEEl2bits +ln2hiu = LD80C(0xb17217f700000000, -1, 6.93147180369123816490e-01L), +ln2lou = LD80C(0xd1cf79abc9e3b398, -33, 1.90821492927058781614e-10L), +lnhugeu = LD80C(0xb18b0c0330a8fad9, 13, 1.13627617309191834574e+04L), +lntinyu = LD80C(0xb236f28a68bc3bd7, 13, -1.14057368561139000667e+04L), +invln2u = LD80C(0xb8aa3b295c17f0bc, 0, 1.44269504088896340739e+00L); +#define ln2hi (ln2hiu.e) +#define ln2lo (ln2lou.e) +#define lnhuge (lnhugeu.e) +#define lntiny (lntinyu.e) +#define invln2 (invln2u.e) + +/* returns exp(r = x + c) for |c| < |x| with no overlap. */ + +static long double +__exp__D(long double x, long double c) +{ + long double hi, lo, z; + int k; + + if (x != x) /* x is NaN. */ + return(x); + + if (x <= lnhuge) { + if (x >= lntiny) { + /* argument reduction: x --> x - k*ln2 */ + z = invln2 * x; + k = z + copysignl(0.5L, x); + + /* + * Express (x + c) - k * ln2 as hi - lo. + * Let x = hi - lo rounded. + */ + hi = x - k * ln2hi; /* Exact. */ + lo = k * ln2lo - c; + x = hi - lo; + + /* Return 2^k*[1+x+x*c/(2+c)] */ + z = x * x; + c = x - z * (p1 + z * (p2 + z * (p3 + z * (p4 + + z * (p5 + z * (p6 + z * p7)))))); + c = (x * c) / (2 - c); + + return (ldexpl(1 + (hi - (lo - c)), k)); + } else { + /* exp(-INF) is 0. exp(-big) underflows to 0. */ + return (isfinite(x) ? ldexpl(1., -5000) : 0); + } + } else + /* exp(INF) is INF, exp(+big#) overflows to INF */ + return (isfinite(x) ? ldexpl(1., 5000) : x); +} |