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/* from: FreeBSD: head/lib/msun/src/s_tanhl.c XXX */
/* @(#)s_tanh.c 5.1 93/09/24 */
/*
* ====================================================
* 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.
* ====================================================
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
/*
* See s_tanh.c for complete comments.
*
* Converted to long double by Bruce D. Evans.
*/
#include <float.h>
#ifdef __i386__
#include <ieeefp.h>
#endif
#include "math.h"
#include "math_private.h"
#include "fpmath.h"
#include "k_expl.h"
#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;
}
long double
tanhl(long double x)
{
long double hi,lo,s,x2,x4,z;
double dx2;
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 (__predict_false(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;
#if 0
RETURNI(((((((((((((((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) +
T3*(x2*x) + x);
#else
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
#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);
}
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