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2fc507c98f
* modelines: tw -> sw shiftwidth, not textwidth. * space-surround modelines * fix irregular modelines * Fix modeline in titlegen.c
161 lines
7.4 KiB
C
161 lines
7.4 KiB
C
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
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│ vi: set noet ft=c ts=8 sw=8 fenc=utf-8 :vi │
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╚──────────────────────────────────────────────────────────────────────────────╝
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│ │
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│ FreeBSD lib/msun/src/s_tanhf.c │
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│ Converted to long double by Bruce D. Evans. │
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│ │
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│ Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. │
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│ │
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│ Developed at SunPro, a Sun Microsystems, Inc. business. │
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│ Permission to use, copy, modify, and distribute this │
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│ software is freely granted, provided that this notice │
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│ is preserved. │
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│ │
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│ Copyright (c) 1992-2023 The FreeBSD Project. │
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│ │
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│ Redistribution and use in source and binary forms, with or without │
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│ modification, are permitted provided that the following conditions │
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│ are met: │
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│ 1. Redistributions of source code must retain the above copyright │
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│ notice, this list of conditions and the following disclaimer. │
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│ 2. Redistributions in binary form must reproduce the above copyright │
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│ notice, this list of conditions and the following disclaimer in the │
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│ documentation and/or other materials provided with the distribution. │
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│ │
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│ THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND │
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│ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE │
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│ IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE │
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│ ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE │
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│ FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL │
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│ DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS │
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│ OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) │
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│ HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT │
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│ LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY │
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│ OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF │
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│ SUCH DAMAGE. │
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│ │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/math.h"
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#include "libc/tinymath/freebsd.internal.h"
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#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
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asm(".ident\t\"\\n\\n\
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FreeBSD libm (BSD-2 License)\\n\
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Copyright (c) 2005-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.\"");
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asm(".ident\t\"\\n\\n\
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fdlibm (fdlibm license)\\n\
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Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
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asm(".include \"libc/disclaimer.inc\"");
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// clang-format off
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#if LDBL_MAX_EXP != 0x4000
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/* We also require the usual expsign encoding. */
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#error "Unsupported long double format"
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#endif
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#define BIAS (LDBL_MAX_EXP - 1)
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static const volatile long double huge = 0x1p10000L, tiny = 0x1p-10000L;
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#if LDBL_MANT_DIG == 64
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/*
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* Domain [-1, 1], range ~[-1.8211e-21, 1.8211e-21]:
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* |cosh(x) - c(x)| < 2**-68.8
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*/
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static const union IEEEl2bits
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C4u = LD80C(0xaaaaaaaaaaaaac78, -5, 4.16666666666666682297e-2L);
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#define C4 C4u.e
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static const double
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C2 = 0.5,
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C6 = 1.3888888888888616e-3, /* 0x16c16c16c16b99.0p-62 */
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C8 = 2.4801587301767953e-5, /* 0x1a01a01a027061.0p-68 */
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C10 = 2.7557319163300398e-7, /* 0x127e4fb6c9b55f.0p-74 */
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C12 = 2.0876768371393075e-9, /* 0x11eed99406a3f4.0p-81 */
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C14 = 1.1469537039374480e-11, /* 0x1938c67cd18c48.0p-89 */
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C16 = 4.8473490896852041e-14; /* 0x1b49c429701e45.0p-97 */
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#elif LDBL_MANT_DIG == 113
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/*
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* Domain [-1, 1], range ~[-2.3194e-37, 2.3194e-37]:
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* |cosh(x) - c(x)| < 2**-121.69
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*/
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static const long double
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C4 = 4.16666666666666666666666666666666225e-2L, /* 0x1555555555555555555555555554e.0p-117L */
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C6 = 1.38888888888888888888888888889434831e-3L, /* 0x16c16c16c16c16c16c16c16c1dd7a.0p-122L */
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C8 = 2.48015873015873015873015871870962089e-5L, /* 0x1a01a01a01a01a01a01a017af2756.0p-128L */
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C10 = 2.75573192239858906525574318600800201e-7L, /* 0x127e4fb7789f5c72ef01c8a040640.0p-134L */
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C12 = 2.08767569878680989791444691755468269e-9L, /* 0x11eed8eff8d897b543d0679607399.0p-141L */
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C14= 1.14707455977297247387801189650495351e-11L, /* 0x193974a8c07c9d24ae169a7fa9b54.0p-149L */
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C16 = 4.77947733238737883626416876486279985e-14L; /* 0x1ae7f3e733b814d4e1b90f5727fe4.0p-157L */
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static const double
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C2 = 0.5,
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C18 = 1.5619206968597871e-16, /* 0x16827863b9900b.0p-105 */
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C20 = 4.1103176218528049e-19, /* 0x1e542ba3d3c269.0p-114 */
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C22 = 8.8967926401641701e-22, /* 0x10ce399542a014.0p-122 */
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C24 = 1.6116681626523904e-24, /* 0x1f2c981d1f0cb7.0p-132 */
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C26 = 2.5022374732804632e-27; /* 0x18c7ecf8b2c4a0.0p-141 */
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#else
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#error "Unsupported long double format"
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#endif /* LDBL_MANT_DIG == 64 */
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/* log(2**16385 - 0.5) rounded up: */
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static const float
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o_threshold = 1.13572168e4; /* 0xb174de.0p-10 */
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/**
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* Returns hyperbolic cosine of 𝑥.
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*
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* cosh(x) = (exp(x) + 1/exp(x))/2
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* = 1 + 0.5*(exp(x)-1)*(exp(x)-1)/exp(x)
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* = 1 + x*x/2 + o(x^4)
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*/
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long double
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coshl(long double x)
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{
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long double hi,lo,x2,x4;
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(void)x4;
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#if LDBL_MANT_DIG == 113
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double dx2;
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#endif
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uint16_t ix;
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GET_LDBL_EXPSIGN(ix,x);
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ix &= 0x7fff;
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/* x is INF or NaN */
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if(ix>=0x7fff) return x*x;
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ENTERI();
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/* |x| < 1, return 1 or c(x) */
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if(ix<0x3fff) {
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if (ix<BIAS-(LDBL_MANT_DIG+1)/2) /* |x| < TINY */
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RETURNI(1+tiny); /* cosh(tiny) = 1(+) with inexact */
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x2 = x*x;
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#if LDBL_MANT_DIG == 64
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x4 = x2*x2;
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RETURNI(((C16*x2 + C14)*x4 + (C12*x2 + C10))*(x4*x4*x2) +
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((C8*x2 + C6)*x2 + C4)*x4 + C2*x2 + 1);
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#elif LDBL_MANT_DIG == 113
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dx2 = x2;
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RETURNI((((((((((((C26*dx2 + C24)*dx2 + C22)*dx2 +
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C20)*x2 + C18)*x2 +
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C16)*x2 + C14)*x2 + C12)*x2 + C10)*x2 + C8)*x2 + C6)*x2 +
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C4)*(x2*x2) + C2*x2 + 1);
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#endif
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}
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/* |x| in [1, 64), return accurate exp(|x|)/2+1/exp(|x|)/2 */
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if (ix < 0x4005) {
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k_hexpl(fabsl(x), &hi, &lo);
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RETURNI(lo + 0.25/(hi + lo) + hi);
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}
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/* |x| in [64, o_threshold], return correctly-overflowing exp(|x|)/2 */
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if (fabsl(x) <= o_threshold)
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RETURNI(hexpl(fabsl(x)));
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/* |x| > o_threshold, cosh(x) overflow */
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RETURNI(huge*huge);
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}
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#endif /* long double is long */
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