aboutsummaryrefslogtreecommitdiff
path: root/sysdeps/ieee754/dbl-64/e_exp.c
blob: 5837ccd106476fbeb28b26b4e62707223e4ab54c (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
/*
 * IBM Accurate Mathematical Library
 * written by International Business Machines Corp.
 * Copyright (C) 2001 Free Software Foundation
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
 */
/***************************************************************************/
/*  MODULE_NAME:uexp.c                                                     */
/*                                                                         */
/*  FUNCTION:uexp                                                          */
/*           exp1                                                          */
/*                                                                         */
/* FILES NEEDED:dla.h endian.h mpa.h mydefs.h uexp.h                       */
/*              mpa.c mpexp.x slowexp.c                                    */
/*                                                                         */
/* An ultimate exp routine. Given an IEEE double machine number x          */
/* it computes the correctly rounded (to nearest) value of e^x             */
/* Assumption: Machine arithmetic operations are performed in              */
/* round to nearest mode of IEEE 754 standard.                             */
/*                                                                         */
/***************************************************************************/

#include "endian.h"
#include "uexp.h"
#include "mydefs.h"
#include "MathLib.h"
#include "uexp.tbl"
#include "math_private.h"

double __slowexp(double);

/***************************************************************************/
/* An ultimate exp routine. Given an IEEE double machine number x          */
/* it computes the correctly rounded (to nearest) value of e^x             */
/***************************************************************************/
double __ieee754_exp(double x) {
  double bexp, t, eps, del, base, y, al, bet, res, rem, cor;
  mynumber junk1, junk2, binexp  = {{0,0}};
#if 0
  int4 k;
#endif
  int4 i,j,m,n,ex;

  junk1.x = x;
  m = junk1.i[HIGH_HALF];
  n = m&hugeint;

  if (n > smallint && n < bigint) {

    y = x*log2e.x + three51.x;
    bexp = y - three51.x;      /*  multiply the result by 2**bexp        */

    junk1.x = y;

    eps = bexp*ln_two2.x;      /* x = bexp*ln(2) + t - eps               */
    t = x - bexp*ln_two1.x;

    y = t + three33.x;
    base = y - three33.x;      /* t rounded to a multiple of 2**-18      */
    junk2.x = y;
    del = (t - base) - eps;    /*  x = bexp*ln(2) + base + del           */
    eps = del + del*del*(p3.x*del + p2.x);

    binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+1023)<<20;

    i = ((junk2.i[LOW_HALF]>>8)&0xfffffffe)+356;
    j = (junk2.i[LOW_HALF]&511)<<1;

    al = coar.x[i]*fine.x[j];
    bet =(coar.x[i]*fine.x[j+1] + coar.x[i+1]*fine.x[j]) + coar.x[i+1]*fine.x[j+1];

    rem=(bet + bet*eps)+al*eps;
    res = al + rem;
    cor = (al - res) + rem;
    if  (res == (res+cor*err_0)) return res*binexp.x;
    else return __slowexp(x); /*if error is over bound */
  }

  if (n <= smallint) return 1.0;

  if (n >= badint) {
    if (n > infint) return(zero/zero);               /* x is NaN,  return invalid */
    if (n < infint) return ( (x>0) ? (hhuge*hhuge) : (tiny*tiny) );
    /* x is finite,  cause either overflow or underflow  */
    if (junk1.i[LOW_HALF] != 0)  return (zero/zero);                /*  x is NaN  */
    return ((x>0)?inf.x:zero );             /* |x| = inf;  return either inf or 0 */
  }

  y = x*log2e.x + three51.x;
  bexp = y - three51.x;
  junk1.x = y;
  eps = bexp*ln_two2.x;
  t = x - bexp*ln_two1.x;
  y = t + three33.x;
  base = y - three33.x;
  junk2.x = y;
  del = (t - base) - eps;
  eps = del + del*del*(p3.x*del + p2.x);
  i = ((junk2.i[LOW_HALF]>>8)&0xfffffffe)+356;
  j = (junk2.i[LOW_HALF]&511)<<1;
  al = coar.x[i]*fine.x[j];
  bet =(coar.x[i]*fine.x[j+1] + coar.x[i+1]*fine.x[j]) + coar.x[i+1]*fine.x[j+1];
  rem=(bet + bet*eps)+al*eps;
  res = al + rem;
  cor = (al - res) + rem;
  if (m>>31) {
    ex=junk1.i[LOW_HALF];
    if (res < 1.0) {res+=res; cor+=cor; ex-=1;}
    if (ex >=-1022) {
      binexp.i[HIGH_HALF] = (1023+ex)<<20;
      if  (res == (res+cor*err_0)) return res*binexp.x;
      else return __slowexp(x); /*if error is over bound */
    }
    ex = -(1022+ex);
    binexp.i[HIGH_HALF] = (1023-ex)<<20;
    res*=binexp.x;
    cor*=binexp.x;
    eps=1.0000000001+err_0*binexp.x;
    t=1.0+res;
    y = ((1.0-t)+res)+cor;
    res=t+y;
    cor = (t-res)+y;
    if (res == (res + eps*cor))
    { binexp.i[HIGH_HALF] = 0x00100000;
      return (res-1.0)*binexp.x;
    }
    else return __slowexp(x); /*   if error is over bound    */
  }
  else {
    binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+767)<<20;
    if  (res == (res+cor*err_0)) return res*binexp.x*t256.x;
    else return __slowexp(x);
  }
}

/************************************************************************/
/* Compute e^(x+xx)(Double-Length number) .The routine also receive     */
/* bound of error of previous calculation .If after computing exp       */
/* error bigger than allows routine return non positive number          */
/*else return   e^(x + xx)   (always positive )                         */
/************************************************************************/

double __exp1(double x, double xx, double error) {
  double bexp, t, eps, del, base, y, al, bet, res, rem, cor;
  mynumber junk1, junk2, binexp  = {{0,0}};
#if 0
  int4 k;
#endif
  int4 i,j,m,n,ex;

  junk1.x = x;
  m = junk1.i[HIGH_HALF];
  n = m&hugeint;                 /* no sign */

  if (n > smallint && n < bigint) {
    y = x*log2e.x + three51.x;
    bexp = y - three51.x;      /*  multiply the result by 2**bexp        */

    junk1.x = y;

    eps = bexp*ln_two2.x;      /* x = bexp*ln(2) + t - eps               */
    t = x - bexp*ln_two1.x;

    y = t + three33.x;
    base = y - three33.x;      /* t rounded to a multiple of 2**-18      */
    junk2.x = y;
    del = (t - base) + (xx-eps);    /*  x = bexp*ln(2) + base + del      */
    eps = del + del*del*(p3.x*del + p2.x);

    binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+1023)<<20;

    i = ((junk2.i[LOW_HALF]>>8)&0xfffffffe)+356;
    j = (junk2.i[LOW_HALF]&511)<<1;

    al = coar.x[i]*fine.x[j];
    bet =(coar.x[i]*fine.x[j+1] + coar.x[i+1]*fine.x[j]) + coar.x[i+1]*fine.x[j+1];

    rem=(bet + bet*eps)+al*eps;
    res = al + rem;
    cor = (al - res) + rem;
    if  (res == (res+cor*(1.0+error+err_1))) return res*binexp.x;
    else return -10.0;
  }

  if (n <= smallint) return 1.0; /*  if x->0 e^x=1 */

  if (n >= badint) {
    if (n > infint) return(zero/zero);    /* x is NaN,  return invalid */
    if (n < infint) return ( (x>0) ? (hhuge*hhuge) : (tiny*tiny) );
    /* x is finite,  cause either overflow or underflow  */
    if (junk1.i[LOW_HALF] != 0)  return (zero/zero);        /*  x is NaN  */
    return ((x>0)?inf.x:zero );   /* |x| = inf;  return either inf or 0 */
  }

  y = x*log2e.x + three51.x;
  bexp = y - three51.x;
  junk1.x = y;
  eps = bexp*ln_two2.x;
  t = x - bexp*ln_two1.x;
  y = t + three33.x;
  base = y - three33.x;
  junk2.x = y;
  del = (t - base) + (xx-eps);
  eps = del + del*del*(p3.x*del + p2.x);
  i = ((junk2.i[LOW_HALF]>>8)&0xfffffffe)+356;
  j = (junk2.i[LOW_HALF]&511)<<1;
  al = coar.x[i]*fine.x[j];
  bet =(coar.x[i]*fine.x[j+1] + coar.x[i+1]*fine.x[j]) + coar.x[i+1]*fine.x[j+1];
  rem=(bet + bet*eps)+al*eps;
  res = al + rem;
  cor = (al - res) + rem;
  if (m>>31) {
    ex=junk1.i[LOW_HALF];
    if (res < 1.0) {res+=res; cor+=cor; ex-=1;}
    if (ex >=-1022) {
      binexp.i[HIGH_HALF] = (1023+ex)<<20;
      if  (res == (res+cor*(1.0+error+err_1))) return res*binexp.x;
      else return -10.0;
    }
    ex = -(1022+ex);
    binexp.i[HIGH_HALF] = (1023-ex)<<20;
    res*=binexp.x;
    cor*=binexp.x;
    eps=1.00000000001+(error+err_1)*binexp.x;
    t=1.0+res;
    y = ((1.0-t)+res)+cor;
    res=t+y;
    cor = (t-res)+y;
    if (res == (res + eps*cor))
      {binexp.i[HIGH_HALF] = 0x00100000; return (res-1.0)*binexp.x;}
    else return -10.0;
  }
  else {
    binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+767)<<20;
    if  (res == (res+cor*(1.0+error+err_1)))
      return res*binexp.x*t256.x;
    else return -10.0;
  }
}