newlib/libm/ld/s_tanhl.c

   1 /* from: FreeBSD: head/lib/msun/src/s_tanhl.c XXX */
   2
   3 /* @(#)s_tanh.c 5.1 93/09/24 */
   4 /*
   5  * ====================================================
   6  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   7  *
   8  * Developed at SunPro, a Sun Microsystems, Inc. business.
   9  * Permission to use, copy, modify, and distribute this
  10  * software is freely granted, provided that this notice
  11  * is preserved.
  12  * ====================================================
  13  */
  14
  15 #include <sys/cdefs.h>
  16 __FBSDID("$FreeBSD$");
  17
  18 /*
  19  * See s_tanh.c for complete comments.
  20  *
  21  * Converted to long double by Bruce D. Evans.
  22  */
  23
  24 #include <float.h>
  25 #ifdef __i386__
  26 #include <ieeefp.h>
  27 #endif
  28
  29 #include "math.h"
  30 #include "math_private.h"
  31 #include "fpmath.h"
  32 #include "k_expl.h"
  33
  34 #if LDBL_MAX_EXP != 0x4000
  35 /* We also require the usual expsign encoding. */
  36 #error "Unsupported long double format"
  37 #endif
  38
  39 #define BIAS    (LDBL_MAX_EXP - 1)
  40
  41 static const volatile double tiny = 1.0e-300;
  42 static const double one = 1.0;
  43 #if LDBL_MANT_DIG == 64
  44 /*
  45  * Domain [-0.25, 0.25], range ~[-1.6304e-22, 1.6304e-22]:
  46  * |tanh(x)/x - t(x)| < 2**-72.3
  47  */
  48 static const union IEEEl2bits
  49 T3u = LD80C(0xaaaaaaaaaaaaaa9f, -2, -3.33333333333333333017e-1L);
  50 #define T3      T3u.e
  51 static const double
  52 T5  =  1.3333333333333314e-1,           /*  0x1111111111110a.0p-55 */
  53 T7  = -5.3968253968210485e-2,           /* -0x1ba1ba1ba1a1a1.0p-57 */
  54 T9  =  2.1869488531393817e-2,           /*  0x1664f488172022.0p-58 */
  55 T11 = -8.8632352345964591e-3,           /* -0x1226e34bc138d5.0p-59 */
  56 T13 =  3.5921169709993771e-3,           /*  0x1d6d371d3e400f.0p-61 */
  57 T15 = -1.4555786415756001e-3,           /* -0x17d923aa63814d.0p-62 */
  58 T17 =  5.8645267876296793e-4,           /*  0x13378589b85aa7.0p-63 */
  59 T19 = -2.1121033571392224e-4;           /* -0x1baf0af80c4090.0p-65 */
  60 #elif LDBL_MANT_DIG == 113
  61 /*
  62  * Domain [-0.25, 0.25], range ~[-2.4211e-37, 2.4211e-37]:
  63  * |tanh(x)/x - t(x)| < 2**121.6
  64  */
  65 static const long double
  66 T3 = -3.33333333333333333333333333333332980e-1L,        /* -0x1555555555555555555555555554e.0p-114L */
  67 T5  =  1.33333333333333333333333333332707260e-1L,       /*  0x1111111111111111111111110ab7b.0p-115L */
  68 T7  = -5.39682539682539682539682535723482314e-2L,       /* -0x1ba1ba1ba1ba1ba1ba1ba17b5fc98.0p-117L */
  69 T9  =  2.18694885361552028218693591149061717e-2L,       /*  0x1664f4882c10f9f32d6b1a12a25e5.0p-118L */
  70 T11 = -8.86323552990219656883762347736381851e-3L,       /* -0x1226e355e6c23c8f5a5a0f386cb4d.0p-119L */
  71 T13 =  3.59212803657248101358314398220822722e-3L,       /*  0x1d6d3d0e157ddfb403ad3637442c6.0p-121L */
  72 T15 = -1.45583438705131796512568010348874662e-3L;       /* -0x17da36452b75e150c44cc34253b34.0p-122L */
  73 static const double
  74 T17 =  5.9002744094556621e-4,           /*  0x1355824803668e.0p-63 */
  75 T19 = -2.3912911424260516e-4,           /* -0x1f57d7734c8dde.0p-65 */
  76 T21 =  9.6915379535512898e-5,           /*  0x1967e18ad6a6ca.0p-66 */
  77 T23 = -3.9278322983156353e-5,           /* -0x1497d8e6b75729.0p-67 */
  78 T25 =  1.5918887220143869e-5,           /*  0x10b1319998cafa.0p-68 */
  79 T27 = -6.4514295231630956e-6,           /* -0x1b0f2b71b218eb.0p-70 */
  80 T29 =  2.6120754043964365e-6,           /*  0x15e963a3cf3a39.0p-71 */
  81 T31 = -1.0407567231003314e-6,           /* -0x1176041e656869.0p-72 */
  82 T33 =  3.4744117554063574e-7;           /*  0x1750fe732cab9c.0p-74 */
  83 #endif /* LDBL_MANT_DIG == 64 */
  84
  85 static inline long double
  86 divl(long double a, long double b, long double c, long double d,
  87     long double e, long double f)
  88 {
  89         long double inv, r;
  90         float fr, fw;
  91
  92         _2sumF(a, c);
  93         b = b + c;
  94         _2sumF(d, f);
  95         e = e + f;
  96
  97         inv = 1 / (d + e);
  98
  99         r = (a + b) * inv;
 100         fr = r;
 101         r = fr;
 102
 103         fw = d + e;
 104         e = d - fw + e;
 105         d = fw;
 106
 107         r = r + (a - d * r + b - e * r) * inv;
 108
 109         return r;
 110 }
 111
 112 long double
 113 tanhl(long double x)
 114 {
 115         long double hi,lo,s,x2,x4,z;
 116 #if LDBL_MANT_DIG == 113
 117         double dx2;
 118 #endif
 119         int16_t jx,ix;
 120
 121         GET_LDBL_EXPSIGN(jx,x);
 122         ix = jx&0x7fff;
 123
 124     /* x is INF or NaN */
 125         if(ix>=0x7fff) {
 126             if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
 127             else       return one/x-one;    /* tanh(NaN) = NaN */
 128         }
 129
 130         ENTERI();
 131
 132     /* |x| < 40 */
 133         if (ix < 0x4004 || fabsl(x) < 40) {     /* |x|<40 */
 134             if (__predict_false(ix<BIAS-(LDBL_MANT_DIG+1)/2)) { /* |x|<TINY */
 135                 /* tanh(+-0) = +0; tanh(tiny) = tiny(-+) with inexact: */
 136                 return (x == 0 ? x : (0x1p200 * x - x) * 0x1p-200);
 137             }
 138             if (ix<0x3ffd) {            /* |x|<0.25 */
 139                 x2 = x*x;
 140 #if LDBL_MANT_DIG == 64
 141                 x4 = x2*x2;
 142                 RETURNI(((T19*x2 + T17)*x4 + (T15*x2 + T13))*(x2*x*x2*x4*x4) +
 143                     ((T11*x2 + T9)*x4 + (T7*x2 + T5))*(x2*x*x2) +
 144                     T3*(x2*x) + x);
 145 #elif LDBL_MANT_DIG == 113
 146                 dx2 = x2;
 147 #if 0
 148                 RETURNI(((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 +
 149                     T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 +
 150                     T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)*
 151                     (x2*x*x2) +
 152                     T3*(x2*x) + x);
 153 #else
 154                 long double q = ((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 +
 155                     T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 +
 156                     T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)*
 157                     (x2*x*x2);
 158                 RETURNI(q + T3*(x2*x) + x);
 159 #endif
 160 #endif
 161             }
 162             k_hexpl(2*fabsl(x), &hi, &lo);
 163             if (ix<0x4001 && fabsl(x) < 1.5)    /* |x|<1.5 */
 164                 z = divl(hi, lo, -0.5, hi, lo, 0.5);
 165             else
 166                 z = one - one/(lo+0.5+hi);
 167     /* |x| >= 40, return +-1 */
 168         } else {
 169             z = one - tiny;             /* raise inexact flag */
 170         }
 171         s = 1;
 172         if (jx<0) s = -1;
 173         RETURNI(s*z);
 174 }