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2fc507c98f
* modelines: tw -> sw shiftwidth, not textwidth. * space-surround modelines * fix irregular modelines * Fix modeline in titlegen.c
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 -*-│
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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_tanhl.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/intrin/likely.h"
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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 double tiny = 1.0e-300;
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static const double one = 1.0;
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#if LDBL_MANT_DIG == 64
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/*
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* Domain [-0.25, 0.25], range ~[-1.6304e-22, 1.6304e-22]:
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* |tanh(x)/x - t(x)| < 2**-72.3
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*/
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static const union IEEEl2bits
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T3u = LD80C(0xaaaaaaaaaaaaaa9f, -2, -3.33333333333333333017e-1L);
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#define T3 T3u.e
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static const double
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T5 = 1.3333333333333314e-1, /* 0x1111111111110a.0p-55 */
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T7 = -5.3968253968210485e-2, /* -0x1ba1ba1ba1a1a1.0p-57 */
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T9 = 2.1869488531393817e-2, /* 0x1664f488172022.0p-58 */
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T11 = -8.8632352345964591e-3, /* -0x1226e34bc138d5.0p-59 */
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T13 = 3.5921169709993771e-3, /* 0x1d6d371d3e400f.0p-61 */
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T15 = -1.4555786415756001e-3, /* -0x17d923aa63814d.0p-62 */
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T17 = 5.8645267876296793e-4, /* 0x13378589b85aa7.0p-63 */
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T19 = -2.1121033571392224e-4; /* -0x1baf0af80c4090.0p-65 */
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#elif LDBL_MANT_DIG == 113
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/*
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* Domain [-0.25, 0.25], range ~[-2.4211e-37, 2.4211e-37]:
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* |tanh(x)/x - t(x)| < 2**121.6
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*/
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static const long double
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T3 = -3.33333333333333333333333333333332980e-1L, /* -0x1555555555555555555555555554e.0p-114L */
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T5 = 1.33333333333333333333333333332707260e-1L, /* 0x1111111111111111111111110ab7b.0p-115L */
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T7 = -5.39682539682539682539682535723482314e-2L, /* -0x1ba1ba1ba1ba1ba1ba1ba17b5fc98.0p-117L */
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T9 = 2.18694885361552028218693591149061717e-2L, /* 0x1664f4882c10f9f32d6b1a12a25e5.0p-118L */
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T11 = -8.86323552990219656883762347736381851e-3L, /* -0x1226e355e6c23c8f5a5a0f386cb4d.0p-119L */
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T13 = 3.59212803657248101358314398220822722e-3L, /* 0x1d6d3d0e157ddfb403ad3637442c6.0p-121L */
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T15 = -1.45583438705131796512568010348874662e-3L; /* -0x17da36452b75e150c44cc34253b34.0p-122L */
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static const double
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T17 = 5.9002744094556621e-4, /* 0x1355824803668e.0p-63 */
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T19 = -2.3912911424260516e-4, /* -0x1f57d7734c8dde.0p-65 */
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T21 = 9.6915379535512898e-5, /* 0x1967e18ad6a6ca.0p-66 */
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T23 = -3.9278322983156353e-5, /* -0x1497d8e6b75729.0p-67 */
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T25 = 1.5918887220143869e-5, /* 0x10b1319998cafa.0p-68 */
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T27 = -6.4514295231630956e-6, /* -0x1b0f2b71b218eb.0p-70 */
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T29 = 2.6120754043964365e-6, /* 0x15e963a3cf3a39.0p-71 */
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T31 = -1.0407567231003314e-6, /* -0x1176041e656869.0p-72 */
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T33 = 3.4744117554063574e-7; /* 0x1750fe732cab9c.0p-74 */
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#endif /* LDBL_MANT_DIG == 64 */
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static inline long double
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divl(long double a, long double b, long double c, long double d,
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long double e, long double f)
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{
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long double inv, r;
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float fr, fw;
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_2sumF(a, c);
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b = b + c;
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_2sumF(d, f);
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e = e + f;
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inv = 1 / (d + e);
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r = (a + b) * inv;
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fr = r;
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r = fr;
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fw = d + e;
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e = d - fw + e;
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d = fw;
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r = r + (a - d * r + b - e * r) * inv;
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return r;
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}
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/**
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* Returns hyperbolic tangent of 𝑥.
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*/
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long double
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tanhl(long double x)
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{
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long double hi,lo,s,x2,x4,z;
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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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int16_t jx,ix;
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GET_LDBL_EXPSIGN(jx,x);
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ix = jx&0x7fff;
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/* x is INF or NaN */
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if(ix>=0x7fff) {
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if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
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else return one/x-one; /* tanh(NaN) = NaN */
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}
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ENTERI();
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/* |x| < 40 */
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if (ix < 0x4004 || fabsl(x) < 40) { /* |x|<40 */
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if (UNLIKELY(ix<BIAS-(LDBL_MANT_DIG+1)/2)) { /* |x|<TINY */
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/* tanh(+-0) = +0; tanh(tiny) = tiny(-+) with inexact: */
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return (x == 0 ? x : (0x1p200 * x - x) * 0x1p-200);
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}
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if (ix<0x3ffd) { /* |x|<0.25 */
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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(((T19*x2 + T17)*x4 + (T15*x2 + T13))*(x2*x*x2*x4*x4) +
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((T11*x2 + T9)*x4 + (T7*x2 + T5))*(x2*x*x2) +
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T3*(x2*x) + x);
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#elif LDBL_MANT_DIG == 113
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dx2 = x2;
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long double q = ((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 +
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T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 +
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T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)*
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(x2*x*x2);
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RETURNI(q + T3*(x2*x) + x);
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#endif
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}
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k_hexpl(2*fabsl(x), &hi, &lo);
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if (ix<0x4001 && fabsl(x) < 1.5) /* |x|<1.5 */
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z = divl(hi, lo, -0.5, hi, lo, 0.5);
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else
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z = one - one/(lo+0.5+hi);
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/* |x| >= 40, return +-1 */
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} else {
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z = one - tiny; /* raise inexact flag */
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}
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s = 1;
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if (jx<0) s = -1;
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RETURNI(s*z);
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}
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#endif /* long double is long */
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