mirror of
https://github.com/jart/cosmopolitan.git
synced 2025-01-31 11:37:35 +00:00
394d998315
At least in neovim, `│vi:` is not recognized as a modeline because it has no preceding whitespace. After fixing this, opening a file yields an error because `net` is not an option. (`noet`, however, is.)
191 lines
8.1 KiB
C
191 lines
8.1 KiB
C
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
|
||
│ vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi │
|
||
╚──────────────────────────────────────────────────────────────────────────────╝
|
||
│ │
|
||
│ FreeBSD lib/msun/src/s_tanhl.c │
|
||
│ Converted to long double by Bruce D. Evans │
|
||
│ │
|
||
│ Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. │
|
||
│ │
|
||
│ Developed at SunPro, a Sun Microsystems, Inc. business. │
|
||
│ Permission to use, copy, modify, and distribute this │
|
||
│ software is freely granted, provided that this notice │
|
||
│ is preserved. │
|
||
│ │
|
||
│ Copyright (c) 1992-2023 The FreeBSD Project. │
|
||
│ │
|
||
│ 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. │
|
||
│ │
|
||
│ THIS SOFTWARE IS PROVIDED BY THE AUTHOR 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 AUTHOR 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. │
|
||
│ │
|
||
╚─────────────────────────────────────────────────────────────────────────────*/
|
||
#include "libc/intrin/likely.h"
|
||
#include "libc/math.h"
|
||
#include "libc/tinymath/freebsd.internal.h"
|
||
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
|
||
|
||
asm(".ident\t\"\\n\\n\
|
||
FreeBSD libm (BSD-2 License)\\n\
|
||
Copyright (c) 2005-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.\"");
|
||
asm(".ident\t\"\\n\\n\
|
||
fdlibm (fdlibm license)\\n\
|
||
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
|
||
asm(".include \"libc/disclaimer.inc\"");
|
||
// clang-format off
|
||
|
||
#if LDBL_MAX_EXP != 0x4000
|
||
/* We also require the usual expsign encoding. */
|
||
#error "Unsupported long double format"
|
||
#endif
|
||
|
||
#define BIAS (LDBL_MAX_EXP - 1)
|
||
|
||
static const volatile double tiny = 1.0e-300;
|
||
static const double one = 1.0;
|
||
#if LDBL_MANT_DIG == 64
|
||
/*
|
||
* Domain [-0.25, 0.25], range ~[-1.6304e-22, 1.6304e-22]:
|
||
* |tanh(x)/x - t(x)| < 2**-72.3
|
||
*/
|
||
static const union IEEEl2bits
|
||
T3u = LD80C(0xaaaaaaaaaaaaaa9f, -2, -3.33333333333333333017e-1L);
|
||
#define T3 T3u.e
|
||
static const double
|
||
T5 = 1.3333333333333314e-1, /* 0x1111111111110a.0p-55 */
|
||
T7 = -5.3968253968210485e-2, /* -0x1ba1ba1ba1a1a1.0p-57 */
|
||
T9 = 2.1869488531393817e-2, /* 0x1664f488172022.0p-58 */
|
||
T11 = -8.8632352345964591e-3, /* -0x1226e34bc138d5.0p-59 */
|
||
T13 = 3.5921169709993771e-3, /* 0x1d6d371d3e400f.0p-61 */
|
||
T15 = -1.4555786415756001e-3, /* -0x17d923aa63814d.0p-62 */
|
||
T17 = 5.8645267876296793e-4, /* 0x13378589b85aa7.0p-63 */
|
||
T19 = -2.1121033571392224e-4; /* -0x1baf0af80c4090.0p-65 */
|
||
#elif LDBL_MANT_DIG == 113
|
||
/*
|
||
* Domain [-0.25, 0.25], range ~[-2.4211e-37, 2.4211e-37]:
|
||
* |tanh(x)/x - t(x)| < 2**121.6
|
||
*/
|
||
static const long double
|
||
T3 = -3.33333333333333333333333333333332980e-1L, /* -0x1555555555555555555555555554e.0p-114L */
|
||
T5 = 1.33333333333333333333333333332707260e-1L, /* 0x1111111111111111111111110ab7b.0p-115L */
|
||
T7 = -5.39682539682539682539682535723482314e-2L, /* -0x1ba1ba1ba1ba1ba1ba1ba17b5fc98.0p-117L */
|
||
T9 = 2.18694885361552028218693591149061717e-2L, /* 0x1664f4882c10f9f32d6b1a12a25e5.0p-118L */
|
||
T11 = -8.86323552990219656883762347736381851e-3L, /* -0x1226e355e6c23c8f5a5a0f386cb4d.0p-119L */
|
||
T13 = 3.59212803657248101358314398220822722e-3L, /* 0x1d6d3d0e157ddfb403ad3637442c6.0p-121L */
|
||
T15 = -1.45583438705131796512568010348874662e-3L; /* -0x17da36452b75e150c44cc34253b34.0p-122L */
|
||
static const double
|
||
T17 = 5.9002744094556621e-4, /* 0x1355824803668e.0p-63 */
|
||
T19 = -2.3912911424260516e-4, /* -0x1f57d7734c8dde.0p-65 */
|
||
T21 = 9.6915379535512898e-5, /* 0x1967e18ad6a6ca.0p-66 */
|
||
T23 = -3.9278322983156353e-5, /* -0x1497d8e6b75729.0p-67 */
|
||
T25 = 1.5918887220143869e-5, /* 0x10b1319998cafa.0p-68 */
|
||
T27 = -6.4514295231630956e-6, /* -0x1b0f2b71b218eb.0p-70 */
|
||
T29 = 2.6120754043964365e-6, /* 0x15e963a3cf3a39.0p-71 */
|
||
T31 = -1.0407567231003314e-6, /* -0x1176041e656869.0p-72 */
|
||
T33 = 3.4744117554063574e-7; /* 0x1750fe732cab9c.0p-74 */
|
||
#endif /* LDBL_MANT_DIG == 64 */
|
||
|
||
static inline long double
|
||
divl(long double a, long double b, long double c, long double d,
|
||
long double e, long double f)
|
||
{
|
||
long double inv, r;
|
||
float fr, fw;
|
||
|
||
_2sumF(a, c);
|
||
b = b + c;
|
||
_2sumF(d, f);
|
||
e = e + f;
|
||
|
||
inv = 1 / (d + e);
|
||
|
||
r = (a + b) * inv;
|
||
fr = r;
|
||
r = fr;
|
||
|
||
fw = d + e;
|
||
e = d - fw + e;
|
||
d = fw;
|
||
|
||
r = r + (a - d * r + b - e * r) * inv;
|
||
|
||
return r;
|
||
}
|
||
|
||
/**
|
||
* Returns hyperbolic tangent of 𝑥.
|
||
*/
|
||
long double
|
||
tanhl(long double x)
|
||
{
|
||
long double hi,lo,s,x2,x4,z;
|
||
(void)x4;
|
||
#if LDBL_MANT_DIG == 113
|
||
double dx2;
|
||
#endif
|
||
int16_t jx,ix;
|
||
|
||
GET_LDBL_EXPSIGN(jx,x);
|
||
ix = jx&0x7fff;
|
||
|
||
/* x is INF or NaN */
|
||
if(ix>=0x7fff) {
|
||
if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
|
||
else return one/x-one; /* tanh(NaN) = NaN */
|
||
}
|
||
|
||
ENTERI();
|
||
|
||
/* |x| < 40 */
|
||
if (ix < 0x4004 || fabsl(x) < 40) { /* |x|<40 */
|
||
if (UNLIKELY(ix<BIAS-(LDBL_MANT_DIG+1)/2)) { /* |x|<TINY */
|
||
/* tanh(+-0) = +0; tanh(tiny) = tiny(-+) with inexact: */
|
||
return (x == 0 ? x : (0x1p200 * x - x) * 0x1p-200);
|
||
}
|
||
if (ix<0x3ffd) { /* |x|<0.25 */
|
||
x2 = x*x;
|
||
#if LDBL_MANT_DIG == 64
|
||
x4 = x2*x2;
|
||
RETURNI(((T19*x2 + T17)*x4 + (T15*x2 + T13))*(x2*x*x2*x4*x4) +
|
||
((T11*x2 + T9)*x4 + (T7*x2 + T5))*(x2*x*x2) +
|
||
T3*(x2*x) + x);
|
||
#elif LDBL_MANT_DIG == 113
|
||
dx2 = x2;
|
||
long double q = ((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 +
|
||
T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 +
|
||
T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)*
|
||
(x2*x*x2);
|
||
RETURNI(q + T3*(x2*x) + x);
|
||
#endif
|
||
}
|
||
k_hexpl(2*fabsl(x), &hi, &lo);
|
||
if (ix<0x4001 && fabsl(x) < 1.5) /* |x|<1.5 */
|
||
z = divl(hi, lo, -0.5, hi, lo, 0.5);
|
||
else
|
||
z = one - one/(lo+0.5+hi);
|
||
/* |x| >= 40, return +-1 */
|
||
} else {
|
||
z = one - tiny; /* raise inexact flag */
|
||
}
|
||
s = 1;
|
||
if (jx<0) s = -1;
|
||
RETURNI(s*z);
|
||
}
|
||
|
||
#endif /* long double is long */
|