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985b6196 RS |
1 | /* real.c - implementation of REAL_ARITHMETIC, REAL_VALUE_ATOF, |
2 | and support for XFmode IEEE extended real floating point arithmetic. | |
3 | Contributed by Stephen L. Moshier (moshier@world.std.com). | |
4 | ||
5 | Copyright (C) 1993 Free Software Foundation, Inc. | |
6 | ||
7 | This file is part of GNU CC. | |
8 | ||
9 | GNU CC is free software; you can redistribute it and/or modify | |
10 | it under the terms of the GNU General Public License as published by | |
11 | the Free Software Foundation; either version 2, or (at your option) | |
12 | any later version. | |
13 | ||
14 | GNU CC is distributed in the hope that it will be useful, | |
15 | but WITHOUT ANY WARRANTY; without even the implied warranty of | |
16 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
17 | GNU General Public License for more details. | |
18 | ||
19 | You should have received a copy of the GNU General Public License | |
20 | along with GNU CC; see the file COPYING. If not, write to | |
21 | the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. */ | |
22 | ||
23 | #include <stdio.h> | |
24 | #include "config.h" | |
25 | ||
26 | #include "tree.h" | |
27 | ||
28 | /* To enable support of XFmode extended real floating point, define | |
29 | LONG_DOUBLE_TYPE_SIZE 96 in the tm.h file (m68k.h or i386.h). | |
30 | ||
31 | To support cross compilation between IEEE and VAX floating | |
32 | point formats, define REAL_ARITHMETIC in the tm.h file. | |
33 | ||
34 | In either case the machine files (tm.h) must not contain any code | |
35 | that tries to use host floating point arithmetic to convert | |
36 | REAL_VALUE_TYPEs from `double' to `float', pass them to fprintf, | |
37 | etc. In cross-compile situations a REAL_VALUE_TYPE may not | |
38 | be intelligible to the host computer's native arithmetic. | |
39 | ||
40 | The emulator defaults to the host's floating point format so that | |
41 | its decimal conversion functions can be used if desired (see | |
42 | real.h). | |
43 | ||
44 | The first part of this file interfaces gcc to ieee.c, which is a | |
45 | floating point arithmetic suite that was not written with gcc in | |
46 | mind. The interface is followed by ieee.c itself and related | |
47 | items. Avoid changing ieee.c unless you have suitable test | |
48 | programs available. A special version of the PARANOIA floating | |
49 | point arithmetic tester, modified for this purpose, can be found | |
50 | on usc.edu : /pub/C-numanal/ieeetest.zoo. Some tutorial | |
51 | information on ieee.c is given in my book: S. L. Moshier, | |
52 | _Methods and Programs for Mathematical Functions_, Prentice-Hall | |
53 | or Simon & Schuster Int'l, 1989. A library of XFmode elementary | |
54 | transcendental functions can be obtained by ftp from | |
55 | research.att.com: netlib/cephes/ldouble.shar.Z */ | |
56 | ||
57 | /* Type of computer arithmetic. | |
58 | * Only one of DEC, MIEEE, IBMPC, or UNK should get defined. | |
59 | * The following modification converts gcc macros into the ones | |
60 | * used by ieee.c. | |
61 | * | |
62 | * Note: long double formats differ between IBMPC and MIEEE | |
63 | * by more than just endian-ness. | |
64 | */ | |
65 | ||
66 | /* REAL_ARITHMETIC defined means that macros in real.h are | |
67 | defined to call emulator functions. */ | |
68 | #ifdef REAL_ARITHMETIC | |
69 | ||
70 | #if TARGET_FLOAT_FORMAT == VAX_FLOAT_FORMAT | |
71 | /* PDP-11, Pro350, VAX: */ | |
72 | #define DEC 1 | |
73 | #else /* it's not VAX */ | |
74 | #if TARGET_FLOAT_FORMAT == IEEE_FLOAT_FORMAT | |
75 | #if WORDS_BIG_ENDIAN | |
76 | /* Motorola IEEE, high order words come first (Sun workstation): */ | |
77 | #define MIEEE 1 | |
78 | #else /* not big-endian */ | |
79 | /* Intel IEEE, low order words come first: | |
80 | */ | |
81 | #define IBMPC 1 | |
82 | #endif /* big-endian */ | |
83 | #else /* it's not IEEE either */ | |
84 | /* UNKnown arithmetic. We don't support this and can't go on. */ | |
85 | unknown arithmetic type | |
86 | #define UNK 1 | |
87 | #endif /* not IEEE */ | |
88 | #endif /* not VAX */ | |
89 | ||
90 | #else | |
91 | /* REAL_ARITHMETIC not defined means that the *host's* data | |
92 | structure will be used. It may differ by endian-ness from the | |
93 | target machine's structure and will get its ends swapped | |
94 | accordingly (but not here). Probably only the decimal <-> binary | |
95 | functions in this file will actually be used in this case. */ | |
96 | #if HOST_FLOAT_FORMAT == VAX_FLOAT_FORMAT | |
97 | #define DEC 1 | |
98 | #else /* it's not VAX */ | |
99 | #if HOST_FLOAT_FORMAT == IEEE_FLOAT_FORMAT | |
100 | #ifdef HOST_WORDS_BIG_ENDIAN | |
101 | #define MIEEE 1 | |
102 | #else /* not big-endian */ | |
103 | #define IBMPC 1 | |
104 | #endif /* big-endian */ | |
105 | #else /* it's not IEEE either */ | |
106 | unknown arithmetic type | |
107 | #define UNK 1 | |
108 | #endif /* not IEEE */ | |
109 | #endif /* not VAX */ | |
110 | ||
111 | #endif /* REAL_ARITHMETIC not defined */ | |
112 | ||
113 | /* Define for support of infinity. */ | |
114 | #ifndef DEC | |
115 | #define INFINITY | |
116 | #endif | |
117 | ||
118 | ||
119 | /* ehead.h | |
120 | * | |
121 | * Include file for extended precision arithmetic programs. | |
122 | */ | |
123 | ||
124 | /* Number of 16 bit words in external e type format */ | |
125 | #define NE 6 | |
126 | ||
127 | /* Number of 16 bit words in internal format */ | |
128 | #define NI (NE+3) | |
129 | ||
130 | /* Array offset to exponent */ | |
131 | #define E 1 | |
132 | ||
133 | /* Array offset to high guard word */ | |
134 | #define M 2 | |
135 | ||
136 | /* Number of bits of precision */ | |
137 | #define NBITS ((NI-4)*16) | |
138 | ||
139 | /* Maximum number of decimal digits in ASCII conversion | |
140 | * = NBITS*log10(2) | |
141 | */ | |
142 | #define NDEC (NBITS*8/27) | |
143 | ||
144 | /* The exponent of 1.0 */ | |
145 | #define EXONE (0x3fff) | |
146 | ||
147 | /* Find a host integer type that is at least 16 bits wide, | |
148 | and another type at least twice whatever that size is. */ | |
149 | ||
150 | #if HOST_BITS_PER_CHAR >= 16 | |
151 | #define EMUSHORT char | |
152 | #define EMUSHORT_SIZE HOST_BITS_PER_CHAR | |
153 | #define EMULONG_SIZE (2 * HOST_BITS_PER_CHAR) | |
154 | #else | |
155 | #if HOST_BITS_PER_SHORT >= 16 | |
156 | #define EMUSHORT short | |
157 | #define EMUSHORT_SIZE HOST_BITS_PER_SHORT | |
158 | #define EMULONG_SIZE (2 * HOST_BITS_PER_SHORT) | |
159 | #else | |
160 | #if HOST_BITS_PER_INT >= 16 | |
161 | #define EMUSHORT int | |
162 | #define EMUSHORT_SIZE HOST_BITS_PER_INT | |
163 | #define EMULONG_SIZE (2 * HOST_BITS_PER_INT) | |
164 | #else | |
165 | #if HOST_BITS_PER_LONG >= 16 | |
166 | #define EMUSHORT long | |
167 | #define EMUSHORT_SIZE HOST_BITS_PER_LONG | |
168 | #define EMULONG_SIZE (2 * HOST_BITS_PER_LONG) | |
169 | #else | |
170 | /* You will have to modify this program to have a smaller unit size. */ | |
171 | #define EMU_NON_COMPILE | |
172 | #endif | |
173 | #endif | |
174 | #endif | |
175 | #endif | |
176 | ||
177 | #if HOST_BITS_PER_SHORT >= EMULONG_SIZE | |
178 | #define EMULONG short | |
179 | #else | |
180 | #if HOST_BITS_PER_INT >= EMULONG_SIZE | |
181 | #define EMULONG int | |
182 | #else | |
183 | #if HOST_BITS_PER_LONG >= EMULONG_SIZE | |
184 | #define EMULONG long | |
185 | #else | |
186 | #if HOST_BITS_PER_LONG_LONG >= EMULONG_SIZE | |
187 | #define EMULONG long long int | |
188 | #else | |
189 | /* You will have to modify this program to have a smaller unit size. */ | |
190 | #define EMU_NON_COMPILE | |
191 | #endif | |
192 | #endif | |
193 | #endif | |
194 | #endif | |
195 | ||
196 | ||
197 | /* The host interface doesn't work if no 16-bit size exists. */ | |
198 | #if EMUSHORT_SIZE != 16 | |
199 | #define EMU_NON_COMPILE | |
200 | #endif | |
201 | ||
202 | /* OK to continue compilation. */ | |
203 | #ifndef EMU_NON_COMPILE | |
204 | ||
205 | /* Construct macros to translate between REAL_VALUE_TYPE and e type. | |
206 | In GET_REAL and PUT_REAL, r and e are pointers. | |
207 | A REAL_VALUE_TYPE is guaranteed to occupy contiguous locations | |
208 | in memory, with no holes. */ | |
209 | ||
210 | #if LONG_DOUBLE_TYPE_SIZE == 96 | |
211 | #define GET_REAL(r,e) bcopy (r, e, 2*NE) | |
212 | #define PUT_REAL(e,r) bcopy (e, r, 2*NE) | |
213 | #else /* no XFmode */ | |
214 | ||
215 | #ifdef REAL_ARITHMETIC | |
216 | /* Emulator uses target format internally | |
217 | but host stores it in host endian-ness. */ | |
218 | ||
219 | #if defined (HOST_WORDS_BIG_ENDIAN) == WORDS_BIG_ENDIAN | |
220 | #define GET_REAL(r,e) e53toe ((r), (e)) | |
221 | #define PUT_REAL(e,r) etoe53 ((e), (r)) | |
222 | ||
223 | #else /* endian-ness differs */ | |
224 | /* emulator uses target endian-ness internally */ | |
225 | #define GET_REAL(r,e) \ | |
226 | do { EMUSHORT w[4]; \ | |
227 | w[3] = ((EMUSHORT *) r)[0]; \ | |
228 | w[2] = ((EMUSHORT *) r)[1]; \ | |
229 | w[1] = ((EMUSHORT *) r)[2]; \ | |
230 | w[0] = ((EMUSHORT *) r)[3]; \ | |
231 | e53toe (w, (e)); } while (0) | |
232 | ||
233 | #define PUT_REAL(e,r) \ | |
234 | do { EMUSHORT w[4]; \ | |
235 | etoe53 ((e), w); \ | |
236 | *((EMUSHORT *) r) = w[3]; \ | |
237 | *((EMUSHORT *) r + 1) = w[2]; \ | |
238 | *((EMUSHORT *) r + 2) = w[1]; \ | |
239 | *((EMUSHORT *) r + 3) = w[0]; } while (0) | |
240 | ||
241 | #endif /* endian-ness differs */ | |
242 | ||
243 | #else /* not REAL_ARITHMETIC */ | |
244 | ||
245 | /* emulator uses host format */ | |
246 | #define GET_REAL(r,e) e53toe ((r), (e)) | |
247 | #define PUT_REAL(e,r) etoe53 ((e), (r)) | |
248 | ||
249 | #endif /* not REAL_ARITHMETIC */ | |
250 | #endif /* no XFmode */ | |
251 | ||
252 | void pedwarn (); | |
253 | int ecmp (), enormlz (), eshift (), eisneg (), eisinf (); | |
254 | void eadd (), esub (), emul (), ediv (); | |
255 | void eshup1 (), eshup8 (), eshup6 (), eshdn1 (), eshdn8 (), eshdn6 (); | |
256 | void eabs (), eneg (), emov (), eclear (), einfin (), efloor (); | |
257 | void eldexp (), efrexp (), eifrac (), euifrac (), ltoe (), ultoe (); | |
258 | void eround (), ereal_to_decimal (); | |
259 | void esqrt (), elog (), eexp (), etanh (), epow (); | |
260 | void asctoe (), asctoe24 (), asctoe53 (), asctoe64 (); | |
261 | void etoasc (), e24toasc (), e53toasc (), e64toasc (); | |
262 | void etoe64 (), etoe53 (), etoe24 (), e64toe (), e53toe (), e24toe (); | |
263 | void mtherr (); | |
9d1bd99c MM |
264 | extern unsigned EMUSHORT ezero[], ehalf[], eone[], etwo[]; |
265 | extern unsigned EMUSHORT elog2[], esqrt2[]; | |
985b6196 RS |
266 | |
267 | /* Pack output array with 32-bit numbers obtained from | |
268 | array containing 16-bit numbers, swapping ends if required. */ | |
269 | void | |
270 | endian (e, x, mode) | |
271 | unsigned EMUSHORT e[]; | |
272 | long x[]; | |
273 | enum machine_mode mode; | |
274 | { | |
275 | unsigned long th, t; | |
276 | ||
277 | #if WORDS_BIG_ENDIAN | |
278 | switch (mode) | |
279 | { | |
280 | ||
281 | case XFmode: | |
282 | ||
283 | /* Swap halfwords in the third long. */ | |
284 | th = (unsigned long) e[4] & 0xffff; | |
285 | t = (unsigned long) e[5] & 0xffff; | |
286 | t |= th << 16; | |
287 | x[2] = (long) t; | |
288 | /* fall into the double case */ | |
289 | ||
290 | case DFmode: | |
291 | ||
292 | /* swap halfwords in the second word */ | |
293 | th = (unsigned long) e[2] & 0xffff; | |
294 | t = (unsigned long) e[3] & 0xffff; | |
295 | t |= th << 16; | |
296 | x[1] = (long) t; | |
297 | /* fall into the float case */ | |
298 | ||
299 | case SFmode: | |
300 | ||
301 | /* swap halfwords in the first word */ | |
302 | th = (unsigned long) e[0] & 0xffff; | |
303 | t = (unsigned long) e[1] & 0xffff; | |
304 | t |= th << 16; | |
305 | x[0] = t; | |
306 | break; | |
307 | ||
308 | default: | |
309 | abort (); | |
310 | } | |
311 | ||
312 | #else | |
313 | ||
314 | /* Pack the output array without swapping. */ | |
315 | ||
316 | switch (mode) | |
317 | { | |
318 | ||
319 | case XFmode: | |
320 | ||
321 | /* Pack the third long. | |
322 | Each element of the input REAL_VALUE_TYPE array has 16 bit useful bits | |
323 | in it. */ | |
324 | th = (unsigned long) e[5] & 0xffff; | |
325 | t = (unsigned long) e[4] & 0xffff; | |
326 | t |= th << 16; | |
327 | x[2] = (long) t; | |
328 | /* fall into the double case */ | |
329 | ||
330 | case DFmode: | |
331 | ||
332 | /* pack the second long */ | |
333 | th = (unsigned long) e[3] & 0xffff; | |
334 | t = (unsigned long) e[2] & 0xffff; | |
335 | t |= th << 16; | |
336 | x[1] = (long) t; | |
337 | /* fall into the float case */ | |
338 | ||
339 | case SFmode: | |
340 | ||
341 | /* pack the first long */ | |
342 | th = (unsigned long) e[1] & 0xffff; | |
343 | t = (unsigned long) e[0] & 0xffff; | |
344 | t |= th << 16; | |
345 | x[0] = t; | |
346 | break; | |
347 | ||
348 | default: | |
349 | abort (); | |
350 | } | |
351 | ||
352 | #endif | |
353 | } | |
354 | ||
355 | ||
356 | /* This is the implementation of the REAL_ARITHMETIC macro. | |
357 | */ | |
358 | void | |
359 | earith (value, icode, r1, r2) | |
360 | REAL_VALUE_TYPE *value; | |
361 | int icode; | |
362 | REAL_VALUE_TYPE *r1; | |
363 | REAL_VALUE_TYPE *r2; | |
364 | { | |
365 | unsigned EMUSHORT d1[NE], d2[NE], v[NE]; | |
366 | enum tree_code code; | |
367 | ||
368 | GET_REAL (r1, d1); | |
369 | GET_REAL (r2, d2); | |
370 | code = (enum tree_code) icode; | |
371 | switch (code) | |
372 | { | |
373 | case PLUS_EXPR: | |
374 | eadd (d2, d1, v); | |
375 | break; | |
376 | ||
377 | case MINUS_EXPR: | |
378 | esub (d2, d1, v); /* d1 - d2 */ | |
379 | break; | |
380 | ||
381 | case MULT_EXPR: | |
382 | emul (d2, d1, v); | |
383 | break; | |
384 | ||
385 | case RDIV_EXPR: | |
386 | #ifndef REAL_INFINITY | |
387 | if (ecmp (d2, ezero) == 0) | |
388 | abort (); | |
389 | #endif | |
390 | ediv (d2, d1, v); /* d1/d2 */ | |
391 | break; | |
392 | ||
393 | case MIN_EXPR: /* min (d1,d2) */ | |
394 | if (ecmp (d1, d2) < 0) | |
395 | emov (d1, v); | |
396 | else | |
397 | emov (d2, v); | |
398 | break; | |
399 | ||
400 | case MAX_EXPR: /* max (d1,d2) */ | |
401 | if (ecmp (d1, d2) > 0) | |
402 | emov (d1, v); | |
403 | else | |
404 | emov (d2, v); | |
405 | break; | |
406 | default: | |
407 | emov (ezero, v); | |
408 | break; | |
409 | } | |
410 | PUT_REAL (v, value); | |
411 | } | |
412 | ||
413 | ||
414 | /* Truncate REAL_VALUE_TYPE toward zero to signed HOST_WIDE_INT | |
415 | * implements REAL_VALUE_FIX_TRUNCATE (x) (etrunci (x)) | |
416 | */ | |
417 | REAL_VALUE_TYPE | |
418 | etrunci (x) | |
419 | REAL_VALUE_TYPE x; | |
420 | { | |
421 | unsigned EMUSHORT f[NE], g[NE]; | |
422 | REAL_VALUE_TYPE r; | |
423 | long l; | |
424 | ||
425 | GET_REAL (&x, g); | |
426 | eifrac (g, &l, f); | |
427 | ltoe (&l, g); | |
428 | PUT_REAL (g, &r); | |
429 | return (r); | |
430 | } | |
431 | ||
432 | ||
433 | /* Truncate REAL_VALUE_TYPE toward zero to unsigned HOST_WIDE_INT | |
434 | * implements REAL_VALUE_UNSIGNED_FIX_TRUNCATE (x) (etruncui (x)) | |
435 | */ | |
436 | REAL_VALUE_TYPE | |
437 | etruncui (x) | |
438 | REAL_VALUE_TYPE x; | |
439 | { | |
440 | unsigned EMUSHORT f[NE], g[NE]; | |
441 | REAL_VALUE_TYPE r; | |
442 | unsigned long l; | |
443 | ||
444 | GET_REAL (&x, g); | |
445 | euifrac (g, &l, f); | |
446 | ultoe (&l, g); | |
447 | PUT_REAL (g, &r); | |
448 | return (r); | |
449 | } | |
450 | ||
451 | ||
452 | /* This is the REAL_VALUE_ATOF function. | |
453 | * It converts a decimal string to binary, rounding off | |
454 | * as indicated by the machine_mode argument. Then it | |
455 | * promotes the rounded value to REAL_VALUE_TYPE. | |
456 | */ | |
457 | REAL_VALUE_TYPE | |
458 | ereal_atof (s, t) | |
459 | char *s; | |
460 | enum machine_mode t; | |
461 | { | |
462 | unsigned EMUSHORT tem[NE], e[NE]; | |
463 | REAL_VALUE_TYPE r; | |
464 | ||
465 | switch (t) | |
466 | { | |
467 | case SFmode: | |
468 | asctoe24 (s, tem); | |
469 | e24toe (tem, e); | |
470 | break; | |
471 | case DFmode: | |
472 | asctoe53 (s, tem); | |
473 | e53toe (tem, e); | |
474 | break; | |
475 | case XFmode: | |
476 | asctoe64 (s, tem); | |
477 | e64toe (tem, e); | |
478 | break; | |
479 | default: | |
480 | asctoe (s, e); | |
481 | } | |
482 | PUT_REAL (e, &r); | |
483 | return (r); | |
484 | } | |
485 | ||
486 | ||
487 | /* Expansion of REAL_NEGATE. | |
488 | */ | |
489 | REAL_VALUE_TYPE | |
490 | ereal_negate (x) | |
491 | REAL_VALUE_TYPE x; | |
492 | { | |
493 | unsigned EMUSHORT e[NE]; | |
494 | REAL_VALUE_TYPE r; | |
495 | ||
496 | GET_REAL (&x, e); | |
497 | eneg (e); | |
498 | PUT_REAL (e, &r); | |
499 | return (r); | |
500 | } | |
501 | ||
502 | ||
503 | /* Round real to int | |
504 | * implements REAL_VALUE_FIX (x) (eroundi (x)) | |
505 | * The type of rounding is left unspecified by real.h. | |
506 | * It is implemented here as round to nearest (add .5 and chop). | |
507 | */ | |
508 | int | |
509 | eroundi (x) | |
510 | REAL_VALUE_TYPE x; | |
511 | { | |
512 | unsigned EMUSHORT f[NE], g[NE]; | |
513 | EMULONG l; | |
514 | ||
515 | GET_REAL (&x, f); | |
516 | eround (f, g); | |
517 | eifrac (g, &l, f); | |
518 | return ((int) l); | |
519 | } | |
520 | ||
521 | /* Round real to nearest unsigned int | |
522 | * implements REAL_VALUE_UNSIGNED_FIX (x) ((unsigned int) eroundi (x)) | |
523 | * Negative input returns zero. | |
524 | * The type of rounding is left unspecified by real.h. | |
525 | * It is implemented here as round to nearest (add .5 and chop). | |
526 | */ | |
527 | unsigned int | |
528 | eroundui (x) | |
529 | REAL_VALUE_TYPE x; | |
530 | { | |
531 | unsigned EMUSHORT f[NE], g[NE]; | |
532 | unsigned EMULONG l; | |
533 | ||
534 | GET_REAL (&x, f); | |
535 | eround (f, g); | |
536 | euifrac (g, &l, f); | |
537 | return ((unsigned int)l); | |
538 | } | |
539 | ||
540 | ||
541 | /* REAL_VALUE_FROM_INT macro. | |
542 | */ | |
543 | void | |
544 | ereal_from_int (d, i, j) | |
545 | REAL_VALUE_TYPE *d; | |
546 | long i, j; | |
547 | { | |
548 | unsigned EMUSHORT df[NE], dg[NE]; | |
549 | long low, high; | |
550 | int sign; | |
551 | ||
552 | sign = 0; | |
553 | low = i; | |
554 | if ((high = j) < 0) | |
555 | { | |
556 | sign = 1; | |
557 | /* complement and add 1 */ | |
558 | high = ~high; | |
559 | if (low) | |
560 | low = -low; | |
561 | else | |
562 | high += 1; | |
563 | } | |
564 | eldexp (eone, HOST_BITS_PER_LONG, df); | |
565 | ultoe (&high, dg); | |
566 | emul (dg, df, dg); | |
567 | ultoe (&low, df); | |
568 | eadd (df, dg, dg); | |
569 | if (sign) | |
570 | eneg (dg); | |
571 | PUT_REAL (dg, d); | |
572 | } | |
573 | ||
574 | ||
575 | /* REAL_VALUE_FROM_UNSIGNED_INT macro. | |
576 | */ | |
577 | void | |
578 | ereal_from_uint (d, i, j) | |
579 | REAL_VALUE_TYPE *d; | |
580 | unsigned long i, j; | |
581 | { | |
582 | unsigned EMUSHORT df[NE], dg[NE]; | |
583 | unsigned long low, high; | |
584 | ||
585 | low = i; | |
586 | high = j; | |
587 | eldexp (eone, HOST_BITS_PER_LONG, df); | |
588 | ultoe (&high, dg); | |
589 | emul (dg, df, dg); | |
590 | ultoe (&low, df); | |
591 | eadd (df, dg, dg); | |
592 | PUT_REAL (dg, d); | |
593 | } | |
594 | ||
595 | ||
596 | /* REAL_VALUE_TO_INT macro | |
597 | */ | |
598 | void | |
599 | ereal_to_int (low, high, rr) | |
600 | long *low, *high; | |
601 | REAL_VALUE_TYPE rr; | |
602 | { | |
603 | unsigned EMUSHORT d[NE], df[NE], dg[NE], dh[NE]; | |
604 | int s; | |
605 | ||
606 | GET_REAL (&rr, d); | |
607 | /* convert positive value */ | |
608 | s = 0; | |
609 | if (eisneg (d)) | |
610 | { | |
611 | eneg (d); | |
612 | s = 1; | |
613 | } | |
614 | eldexp (eone, HOST_BITS_PER_LONG, df); | |
615 | ediv (df, d, dg); /* dg = d / 2^32 is the high word */ | |
616 | euifrac (dg, high, dh); | |
617 | emul (df, dh, dg); /* fractional part is the low word */ | |
618 | euifrac (dg, low, dh); | |
619 | if (s) | |
620 | { | |
621 | /* complement and add 1 */ | |
622 | *high = ~(*high); | |
623 | if (*low) | |
624 | *low = -(*low); | |
625 | else | |
626 | *high += 1; | |
627 | } | |
628 | } | |
629 | ||
630 | ||
631 | /* REAL_VALUE_LDEXP macro. | |
632 | */ | |
633 | REAL_VALUE_TYPE | |
634 | ereal_ldexp (x, n) | |
635 | REAL_VALUE_TYPE x; | |
636 | int n; | |
637 | { | |
638 | unsigned EMUSHORT e[NE], y[NE]; | |
639 | REAL_VALUE_TYPE r; | |
640 | ||
641 | GET_REAL (&x, e); | |
642 | eldexp (e, n, y); | |
643 | PUT_REAL (y, &r); | |
644 | return (r); | |
645 | } | |
646 | ||
647 | /* These routines are conditionally compiled because functions | |
648 | * of the same names may be defined in fold-const.c. */ | |
649 | #ifdef REAL_ARITHMETIC | |
650 | ||
651 | /* Check for infinity in a REAL_VALUE_TYPE. */ | |
652 | int | |
653 | target_isinf (x) | |
654 | REAL_VALUE_TYPE x; | |
655 | { | |
656 | unsigned EMUSHORT e[NE]; | |
657 | ||
658 | #ifdef INFINITY | |
659 | GET_REAL (&x, e); | |
660 | return (eisinf (e)); | |
661 | #else | |
662 | return 0; | |
663 | #endif | |
664 | } | |
665 | ||
666 | ||
667 | /* Check whether an IEEE double precision number is a NaN. */ | |
668 | ||
669 | int | |
670 | target_isnan (x) | |
671 | REAL_VALUE_TYPE x; | |
672 | { | |
673 | return (0); | |
674 | } | |
675 | ||
676 | ||
677 | /* Check for a negative IEEE double precision number. | |
678 | * this means strictly less than zero, not -0. | |
679 | */ | |
680 | ||
681 | int | |
682 | target_negative (x) | |
683 | REAL_VALUE_TYPE x; | |
684 | { | |
685 | unsigned EMUSHORT e[NE]; | |
686 | ||
687 | GET_REAL (&x, e); | |
688 | if (ecmp (e, ezero) < 0) | |
689 | return (1); | |
690 | return (0); | |
691 | } | |
692 | ||
693 | /* Expansion of REAL_VALUE_TRUNCATE. | |
694 | * The result is in floating point, rounded to nearest or even. | |
695 | */ | |
696 | REAL_VALUE_TYPE | |
697 | real_value_truncate (mode, arg) | |
698 | enum machine_mode mode; | |
699 | REAL_VALUE_TYPE arg; | |
700 | { | |
701 | unsigned EMUSHORT e[NE], t[NE]; | |
702 | REAL_VALUE_TYPE r; | |
703 | ||
704 | GET_REAL (&arg, e); | |
705 | eclear (t); | |
706 | switch (mode) | |
707 | { | |
708 | case XFmode: | |
709 | etoe64 (e, t); | |
710 | e64toe (t, t); | |
711 | break; | |
712 | ||
713 | case DFmode: | |
714 | etoe53 (e, t); | |
715 | e53toe (t, t); | |
716 | break; | |
717 | ||
718 | case SFmode: | |
719 | etoe24 (e, t); | |
720 | e24toe (t, t); | |
721 | break; | |
722 | ||
723 | case SImode: | |
724 | r = etrunci (e); | |
725 | return (r); | |
726 | ||
727 | default: | |
728 | abort (); | |
729 | } | |
730 | PUT_REAL (t, &r); | |
731 | return (r); | |
732 | } | |
733 | ||
734 | #endif /* REAL_ARITHMETIC defined */ | |
735 | ||
736 | /* Target values are arrays of host longs. A long is guaranteed | |
737 | to be at least 32 bits wide. */ | |
738 | void | |
739 | etarldouble (r, l) | |
740 | REAL_VALUE_TYPE r; | |
741 | long l[]; | |
742 | { | |
743 | unsigned EMUSHORT e[NE]; | |
744 | ||
745 | GET_REAL (&r, e); | |
746 | etoe64 (e, e); | |
747 | endian (e, l, XFmode); | |
748 | } | |
749 | ||
750 | void | |
751 | etardouble (r, l) | |
752 | REAL_VALUE_TYPE r; | |
753 | long l[]; | |
754 | { | |
755 | unsigned EMUSHORT e[NE]; | |
756 | ||
757 | GET_REAL (&r, e); | |
758 | etoe53 (e, e); | |
759 | endian (e, l, DFmode); | |
760 | } | |
761 | ||
762 | long | |
763 | etarsingle (r) | |
764 | REAL_VALUE_TYPE r; | |
765 | { | |
766 | unsigned EMUSHORT e[NE]; | |
767 | unsigned long l; | |
768 | ||
769 | GET_REAL (&r, e); | |
770 | etoe24 (e, e); | |
771 | endian (e, &l, SFmode); | |
772 | return ((long) l); | |
773 | } | |
774 | ||
775 | void | |
776 | ereal_to_decimal (x, s) | |
777 | REAL_VALUE_TYPE x; | |
778 | char *s; | |
779 | { | |
780 | unsigned EMUSHORT e[NE]; | |
781 | ||
782 | GET_REAL (&x, e); | |
783 | etoasc (e, s, 20); | |
784 | } | |
785 | ||
786 | int | |
787 | ereal_cmp (x, y) | |
788 | REAL_VALUE_TYPE x, y; | |
789 | { | |
790 | unsigned EMUSHORT ex[NE], ey[NE]; | |
791 | ||
792 | GET_REAL (&x, ex); | |
793 | GET_REAL (&y, ey); | |
794 | return (ecmp (ex, ey)); | |
795 | } | |
796 | ||
797 | int | |
798 | ereal_isneg (x) | |
799 | REAL_VALUE_TYPE x; | |
800 | { | |
801 | unsigned EMUSHORT ex[NE]; | |
802 | ||
803 | GET_REAL (&x, ex); | |
804 | return (eisneg (ex)); | |
805 | } | |
806 | ||
807 | /* End of REAL_ARITHMETIC interface */ | |
808 | ||
809 | /* ieee.c | |
810 | * | |
811 | * Extended precision IEEE binary floating point arithmetic routines | |
812 | * | |
813 | * Numbers are stored in C language as arrays of 16-bit unsigned | |
814 | * short integers. The arguments of the routines are pointers to | |
815 | * the arrays. | |
816 | * | |
817 | * | |
818 | * External e type data structure, simulates Intel 8087 chip | |
819 | * temporary real format but possibly with a larger significand: | |
820 | * | |
821 | * NE-1 significand words (least significant word first, | |
822 | * most significant bit is normally set) | |
823 | * exponent (value = EXONE for 1.0, | |
824 | * top bit is the sign) | |
825 | * | |
826 | * | |
827 | * Internal data structure of a number (a "word" is 16 bits): | |
828 | * | |
829 | * ei[0] sign word (0 for positive, 0xffff for negative) | |
830 | * ei[1] biased exponent (value = EXONE for the number 1.0) | |
831 | * ei[2] high guard word (always zero after normalization) | |
832 | * ei[3] | |
833 | * to ei[NI-2] significand (NI-4 significand words, | |
834 | * most significant word first, | |
835 | * most significant bit is set) | |
836 | * ei[NI-1] low guard word (0x8000 bit is rounding place) | |
837 | * | |
838 | * | |
839 | * | |
840 | * Routines for external format numbers | |
841 | * | |
842 | * asctoe (string, e) ASCII string to extended double e type | |
843 | * asctoe64 (string, &d) ASCII string to long double | |
844 | * asctoe53 (string, &d) ASCII string to double | |
845 | * asctoe24 (string, &f) ASCII string to single | |
846 | * asctoeg (string, e, prec) ASCII string to specified precision | |
847 | * e24toe (&f, e) IEEE single precision to e type | |
848 | * e53toe (&d, e) IEEE double precision to e type | |
849 | * e64toe (&d, e) IEEE long double precision to e type | |
850 | * eabs (e) absolute value | |
851 | * eadd (a, b, c) c = b + a | |
852 | * eclear (e) e = 0 | |
853 | * ecmp (a, b) compare a to b, return 1, 0, or -1 | |
854 | * ediv (a, b, c) c = b / a | |
855 | * efloor (a, b) truncate to integer, toward -infinity | |
856 | * efrexp (a, exp, s) extract exponent and significand | |
857 | * eifrac (e, &l, frac) e to long integer and e type fraction | |
858 | * euifrac (e, &l, frac) e to unsigned long integer and e type fraction | |
859 | * einfin (e) set e to infinity, leaving its sign alone | |
860 | * eldexp (a, n, b) multiply by 2**n | |
861 | * emov (a, b) b = a | |
862 | * emul (a, b, c) c = b * a | |
863 | * eneg (e) e = -e | |
864 | * eround (a, b) b = nearest integer value to a | |
865 | * esub (a, b, c) c = b - a | |
866 | * e24toasc (&f, str, n) single to ASCII string, n digits after decimal | |
867 | * e53toasc (&d, str, n) double to ASCII string, n digits after decimal | |
868 | * e64toasc (&d, str, n) long double to ASCII string | |
869 | * etoasc (e, str, n) e to ASCII string, n digits after decimal | |
870 | * etoe24 (e, &f) convert e type to IEEE single precision | |
871 | * etoe53 (e, &d) convert e type to IEEE double precision | |
872 | * etoe64 (e, &d) convert e type to IEEE long double precision | |
873 | * ltoe (&l, e) long (32 bit) integer to e type | |
874 | * ultoe (&l, e) unsigned long (32 bit) integer to e type | |
875 | * eisneg (e) 1 if sign bit of e != 0, else 0 | |
876 | * eisinf (e) 1 if e has maximum exponent | |
877 | * | |
878 | * | |
879 | * Routines for internal format numbers | |
880 | * | |
881 | * eaddm (ai, bi) add significands, bi = bi + ai | |
882 | * ecleaz (ei) ei = 0 | |
883 | * ecleazs (ei) set ei = 0 but leave its sign alone | |
884 | * ecmpm (ai, bi) compare significands, return 1, 0, or -1 | |
885 | * edivm (ai, bi) divide significands, bi = bi / ai | |
886 | * emdnorm (ai,l,s,exp) normalize and round off | |
887 | * emovi (a, ai) convert external a to internal ai | |
888 | * emovo (ai, a) convert internal ai to external a | |
889 | * emovz (ai, bi) bi = ai, low guard word of bi = 0 | |
890 | * emulm (ai, bi) multiply significands, bi = bi * ai | |
891 | * enormlz (ei) left-justify the significand | |
892 | * eshdn1 (ai) shift significand and guards down 1 bit | |
893 | * eshdn8 (ai) shift down 8 bits | |
894 | * eshdn6 (ai) shift down 16 bits | |
895 | * eshift (ai, n) shift ai n bits up (or down if n < 0) | |
896 | * eshup1 (ai) shift significand and guards up 1 bit | |
897 | * eshup8 (ai) shift up 8 bits | |
898 | * eshup6 (ai) shift up 16 bits | |
899 | * esubm (ai, bi) subtract significands, bi = bi - ai | |
900 | * | |
901 | * | |
902 | * The result is always normalized and rounded to NI-4 word precision | |
903 | * after each arithmetic operation. | |
904 | * | |
905 | * Exception flags and NaNs are NOT fully supported. | |
906 | * This arithmetic should never produce a NaN output, but it might | |
907 | * be confused by a NaN input. | |
908 | * Define INFINITY in mconf.h for support of infinity; otherwise a | |
909 | * saturation arithmetic is implemented. | |
910 | * Denormals are always supported here where appropriate (e.g., not | |
911 | * for conversion to DEC numbers). | |
912 | * | |
913 | */ | |
914 | ||
915 | /* | |
916 | * Revision history: | |
917 | * | |
918 | * 5 Jan 84 PDP-11 assembly language version | |
919 | * 2 Mar 86 fixed bug in asctoq | |
920 | * 6 Dec 86 C language version | |
921 | * 30 Aug 88 100 digit version, improved rounding | |
922 | * 15 May 92 80-bit long double support | |
923 | * | |
924 | * Author: S. L. Moshier. | |
925 | */ | |
926 | ||
927 | ||
928 | /* mconf.h | |
929 | * | |
930 | * Common include file for math routines | |
931 | * | |
932 | * | |
933 | * | |
934 | * SYNOPSIS: | |
935 | * | |
936 | * #include "mconf.h" | |
937 | * | |
938 | * | |
939 | * | |
940 | * DESCRIPTION: | |
941 | * | |
942 | * This file contains definitions for error codes that are | |
943 | * passed to the common error handling routine mtherr | |
944 | * (which see). | |
945 | * | |
946 | * The file also includes a conditional assembly definition | |
947 | * for the type of computer arithmetic (Intel IEEE, DEC, Motorola | |
948 | * IEEE, or UNKnown). | |
949 | * | |
950 | * For Digital Equipment PDP-11 and VAX computers, certain | |
951 | * IBM systems, and others that use numbers with a 56-bit | |
952 | * significand, the symbol DEC should be defined. In this | |
953 | * mode, most floating point constants are given as arrays | |
954 | * of octal integers to eliminate decimal to binary conversion | |
955 | * errors that might be introduced by the compiler. | |
956 | * | |
957 | * For computers, such as IBM PC, that follow the IEEE | |
958 | * Standard for Binary Floating Point Arithmetic (ANSI/IEEE | |
959 | * Std 754-1985), the symbol IBMPC or MIEEE should be defined. | |
960 | * These numbers have 53-bit significands. In this mode, constants | |
961 | * are provided as arrays of hexadecimal 16 bit integers. | |
962 | * | |
963 | * To accommodate other types of computer arithmetic, all | |
964 | * constants are also provided in a normal decimal radix | |
965 | * which one can hope are correctly converted to a suitable | |
966 | * format by the available C language compiler. To invoke | |
967 | * this mode, the symbol UNK is defined. | |
968 | * | |
969 | * An important difference among these modes is a predefined | |
970 | * set of machine arithmetic constants for each. The numbers | |
971 | * MACHEP (the machine roundoff error), MAXNUM (largest number | |
972 | * represented), and several other parameters are preset by | |
973 | * the configuration symbol. Check the file const.c to | |
974 | * ensure that these values are correct for your computer. | |
975 | * | |
976 | * For ANSI C compatibility, define ANSIC equal to 1. Currently | |
977 | * this affects only the atan2 function and others that use it. | |
978 | */ | |
979 | \f | |
e8650b8f | 980 | /* Constant definitions for math error conditions. */ |
985b6196 RS |
981 | |
982 | #define DOMAIN 1 /* argument domain error */ | |
983 | #define SING 2 /* argument singularity */ | |
984 | #define OVERFLOW 3 /* overflow range error */ | |
985 | #define UNDERFLOW 4 /* underflow range error */ | |
986 | #define TLOSS 5 /* total loss of precision */ | |
987 | #define PLOSS 6 /* partial loss of precision */ | |
988 | ||
989 | #define EDOM 33 | |
990 | #define ERANGE 34 | |
991 | ||
992 | /* e type constants used by high precision check routines */ | |
993 | ||
994 | /*include "ehead.h"*/ | |
995 | /* 0.0 */ | |
996 | unsigned EMUSHORT ezero[NE] = | |
997 | { | |
998 | 0, 0000000, 0000000, 0000000, 0000000, 0000000,}; | |
999 | extern unsigned EMUSHORT ezero[]; | |
1000 | ||
1001 | /* 5.0E-1 */ | |
1002 | unsigned EMUSHORT ehalf[NE] = | |
1003 | { | |
1004 | 0, 0000000, 0000000, 0000000, 0100000, 0x3ffe,}; | |
1005 | extern unsigned EMUSHORT ehalf[]; | |
1006 | ||
1007 | /* 1.0E0 */ | |
1008 | unsigned EMUSHORT eone[NE] = | |
1009 | { | |
1010 | 0, 0000000, 0000000, 0000000, 0100000, 0x3fff,}; | |
1011 | extern unsigned EMUSHORT eone[]; | |
1012 | ||
1013 | /* 2.0E0 */ | |
1014 | unsigned EMUSHORT etwo[NE] = | |
1015 | { | |
1016 | 0, 0000000, 0000000, 0000000, 0100000, 0040000,}; | |
1017 | extern unsigned EMUSHORT etwo[]; | |
1018 | ||
1019 | /* 3.2E1 */ | |
1020 | unsigned EMUSHORT e32[NE] = | |
1021 | { | |
1022 | 0, 0000000, 0000000, 0000000, 0100000, 0040004,}; | |
1023 | extern unsigned EMUSHORT e32[]; | |
1024 | ||
1025 | /* 6.93147180559945309417232121458176568075500134360255E-1 */ | |
1026 | unsigned EMUSHORT elog2[NE] = | |
1027 | { | |
1028 | 0xc9e4, 0x79ab, 0150717, 0013767, 0130562, 0x3ffe,}; | |
1029 | extern unsigned EMUSHORT elog2[]; | |
1030 | ||
1031 | /* 1.41421356237309504880168872420969807856967187537695E0 */ | |
1032 | unsigned EMUSHORT esqrt2[NE] = | |
1033 | { | |
1034 | 0x597e, 0x6484, 0174736, 0171463, 0132404, 0x3fff,}; | |
1035 | extern unsigned EMUSHORT esqrt2[]; | |
1036 | ||
1037 | /* 2/sqrt (PI) = | |
1038 | * 1.12837916709551257389615890312154517168810125865800E0 */ | |
1039 | unsigned EMUSHORT eoneopi[NE] = | |
1040 | { | |
1041 | 0x71d5, 0x688d, 0012333, 0135202, 0110156, 0x3fff,}; | |
1042 | extern unsigned EMUSHORT eoneopi[]; | |
1043 | ||
1044 | /* 3.14159265358979323846264338327950288419716939937511E0 */ | |
1045 | unsigned EMUSHORT epi[NE] = | |
1046 | { | |
1047 | 0xc4c6, 0xc234, 0020550, 0155242, 0144417, 0040000,}; | |
1048 | extern unsigned EMUSHORT epi[]; | |
1049 | ||
1050 | /* 5.7721566490153286060651209008240243104215933593992E-1 */ | |
1051 | unsigned EMUSHORT eeul[NE] = | |
1052 | { | |
1053 | 0xd1be, 0xc7a4, 0076660, 0063743, 0111704, 0x3ffe,}; | |
1054 | extern unsigned EMUSHORT eeul[]; | |
1055 | ||
1056 | /* | |
1057 | include "ehead.h" | |
1058 | include "mconf.h" | |
1059 | */ | |
1060 | ||
1061 | ||
1062 | ||
1063 | /* Control register for rounding precision. | |
1064 | * This can be set to 80 (if NE=6), 64, 56, 53, or 24 bits. | |
1065 | */ | |
1066 | int rndprc = NBITS; | |
1067 | extern int rndprc; | |
1068 | ||
1069 | void eaddm (), esubm (), emdnorm (), asctoeg (); | |
1070 | static void toe24 (), toe53 (), toe64 (); | |
1071 | void eremain (), einit (), eiremain (); | |
1072 | int ecmpm (), edivm (), emulm (); | |
1073 | void emovi (), emovo (), emovz (), ecleaz (), ecleazs (), eadd1 (); | |
1074 | void etodec (), todec (), dectoe (); | |
1075 | ||
1076 | ||
1077 | ||
1078 | ||
1079 | void | |
1080 | einit () | |
1081 | { | |
1082 | } | |
1083 | ||
1084 | /* | |
1085 | ; Clear out entire external format number. | |
1086 | ; | |
1087 | ; unsigned EMUSHORT x[]; | |
1088 | ; eclear (x); | |
1089 | */ | |
1090 | ||
1091 | void | |
1092 | eclear (x) | |
1093 | register unsigned EMUSHORT *x; | |
1094 | { | |
1095 | register int i; | |
1096 | ||
1097 | for (i = 0; i < NE; i++) | |
1098 | *x++ = 0; | |
1099 | } | |
1100 | ||
1101 | ||
1102 | ||
1103 | /* Move external format number from a to b. | |
1104 | * | |
1105 | * emov (a, b); | |
1106 | */ | |
1107 | ||
1108 | void | |
1109 | emov (a, b) | |
1110 | register unsigned EMUSHORT *a, *b; | |
1111 | { | |
1112 | register int i; | |
1113 | ||
1114 | for (i = 0; i < NE; i++) | |
1115 | *b++ = *a++; | |
1116 | } | |
1117 | ||
1118 | ||
1119 | /* | |
1120 | ; Absolute value of external format number | |
1121 | ; | |
1122 | ; EMUSHORT x[NE]; | |
1123 | ; eabs (x); | |
1124 | */ | |
1125 | ||
1126 | void | |
1127 | eabs (x) | |
1128 | unsigned EMUSHORT x[]; /* x is the memory address of a short */ | |
1129 | { | |
1130 | ||
1131 | x[NE - 1] &= 0x7fff; /* sign is top bit of last word of external format */ | |
1132 | } | |
1133 | ||
1134 | ||
1135 | ||
1136 | ||
1137 | /* | |
1138 | ; Negate external format number | |
1139 | ; | |
1140 | ; unsigned EMUSHORT x[NE]; | |
1141 | ; eneg (x); | |
1142 | */ | |
1143 | ||
1144 | void | |
1145 | eneg (x) | |
1146 | unsigned EMUSHORT x[]; | |
1147 | { | |
1148 | ||
1149 | x[NE - 1] ^= 0x8000; /* Toggle the sign bit */ | |
1150 | } | |
1151 | ||
1152 | ||
1153 | ||
1154 | /* Return 1 if external format number is negative, | |
1155 | * else return zero. | |
1156 | */ | |
1157 | int | |
1158 | eisneg (x) | |
1159 | unsigned EMUSHORT x[]; | |
1160 | { | |
1161 | ||
1162 | if (x[NE - 1] & 0x8000) | |
1163 | return (1); | |
1164 | else | |
1165 | return (0); | |
1166 | } | |
1167 | ||
1168 | ||
1169 | /* Return 1 if external format number has maximum possible exponent, | |
1170 | * else return zero. | |
1171 | */ | |
1172 | int | |
1173 | eisinf (x) | |
1174 | unsigned EMUSHORT x[]; | |
1175 | { | |
1176 | ||
1177 | if ((x[NE - 1] & 0x7fff) == 0x7fff) | |
1178 | return (1); | |
1179 | else | |
1180 | return (0); | |
1181 | } | |
1182 | ||
1183 | ||
1184 | /* | |
1185 | ; Fill entire number, including exponent and significand, with | |
1186 | ; largest possible number. These programs implement a saturation | |
1187 | ; value that is an ordinary, legal number. A special value | |
1188 | ; "infinity" may also be implemented; this would require tests | |
1189 | ; for that value and implementation of special rules for arithmetic | |
1190 | ; operations involving inifinity. | |
1191 | */ | |
1192 | ||
1193 | void | |
1194 | einfin (x) | |
1195 | register unsigned EMUSHORT *x; | |
1196 | { | |
1197 | register int i; | |
1198 | ||
1199 | #ifdef INFINITY | |
1200 | for (i = 0; i < NE - 1; i++) | |
1201 | *x++ = 0; | |
1202 | *x |= 32767; | |
1203 | #else | |
1204 | for (i = 0; i < NE - 1; i++) | |
1205 | *x++ = 0xffff; | |
1206 | *x |= 32766; | |
1207 | if (rndprc < NBITS) | |
1208 | { | |
1209 | if (rndprc == 64) | |
1210 | { | |
1211 | *(x - 5) = 0; | |
1212 | } | |
1213 | if (rndprc == 53) | |
1214 | { | |
1215 | *(x - 4) = 0xf800; | |
1216 | } | |
1217 | else | |
1218 | { | |
1219 | *(x - 4) = 0; | |
1220 | *(x - 3) = 0; | |
1221 | *(x - 2) = 0xff00; | |
1222 | } | |
1223 | } | |
1224 | #endif | |
1225 | } | |
1226 | ||
1227 | ||
1228 | ||
1229 | /* Move in external format number, | |
1230 | * converting it to internal format. | |
1231 | */ | |
1232 | void | |
1233 | emovi (a, b) | |
1234 | unsigned EMUSHORT *a, *b; | |
1235 | { | |
1236 | register unsigned EMUSHORT *p, *q; | |
1237 | int i; | |
1238 | ||
1239 | q = b; | |
1240 | p = a + (NE - 1); /* point to last word of external number */ | |
1241 | /* get the sign bit */ | |
1242 | if (*p & 0x8000) | |
1243 | *q++ = 0xffff; | |
1244 | else | |
1245 | *q++ = 0; | |
1246 | /* get the exponent */ | |
1247 | *q = *p--; | |
1248 | *q++ &= 0x7fff; /* delete the sign bit */ | |
1249 | #ifdef INFINITY | |
1250 | if ((*(q - 1) & 0x7fff) == 0x7fff) | |
1251 | { | |
1252 | for (i = 2; i < NI; i++) | |
1253 | *q++ = 0; | |
1254 | return; | |
1255 | } | |
1256 | #endif | |
1257 | /* clear high guard word */ | |
1258 | *q++ = 0; | |
1259 | /* move in the significand */ | |
1260 | for (i = 0; i < NE - 1; i++) | |
1261 | *q++ = *p--; | |
1262 | /* clear low guard word */ | |
1263 | *q = 0; | |
1264 | } | |
1265 | ||
1266 | ||
1267 | /* Move internal format number out, | |
1268 | * converting it to external format. | |
1269 | */ | |
1270 | void | |
1271 | emovo (a, b) | |
1272 | unsigned EMUSHORT *a, *b; | |
1273 | { | |
1274 | register unsigned EMUSHORT *p, *q; | |
1275 | unsigned EMUSHORT i; | |
1276 | ||
1277 | p = a; | |
1278 | q = b + (NE - 1); /* point to output exponent */ | |
1279 | /* combine sign and exponent */ | |
1280 | i = *p++; | |
1281 | if (i) | |
1282 | *q-- = *p++ | 0x8000; | |
1283 | else | |
1284 | *q-- = *p++; | |
1285 | #ifdef INFINITY | |
1286 | if (*(p - 1) == 0x7fff) | |
1287 | { | |
1288 | einfin (b); | |
1289 | return; | |
1290 | } | |
1291 | #endif | |
1292 | /* skip over guard word */ | |
1293 | ++p; | |
1294 | /* move the significand */ | |
1295 | for (i = 0; i < NE - 1; i++) | |
1296 | *q-- = *p++; | |
1297 | } | |
1298 | ||
1299 | ||
1300 | ||
1301 | ||
1302 | /* Clear out internal format number. | |
1303 | */ | |
1304 | ||
1305 | void | |
1306 | ecleaz (xi) | |
1307 | register unsigned EMUSHORT *xi; | |
1308 | { | |
1309 | register int i; | |
1310 | ||
1311 | for (i = 0; i < NI; i++) | |
1312 | *xi++ = 0; | |
1313 | } | |
1314 | ||
1315 | ||
1316 | /* same, but don't touch the sign. */ | |
1317 | ||
1318 | void | |
1319 | ecleazs (xi) | |
1320 | register unsigned EMUSHORT *xi; | |
1321 | { | |
1322 | register int i; | |
1323 | ||
1324 | ++xi; | |
1325 | for (i = 0; i < NI - 1; i++) | |
1326 | *xi++ = 0; | |
1327 | } | |
1328 | ||
1329 | ||
1330 | ||
1331 | /* Move internal format number from a to b. | |
1332 | */ | |
1333 | void | |
1334 | emovz (a, b) | |
1335 | register unsigned EMUSHORT *a, *b; | |
1336 | { | |
1337 | register int i; | |
1338 | ||
1339 | for (i = 0; i < NI - 1; i++) | |
1340 | *b++ = *a++; | |
1341 | /* clear low guard word */ | |
1342 | *b = 0; | |
1343 | } | |
1344 | ||
1345 | ||
1346 | /* | |
1347 | ; Compare significands of numbers in internal format. | |
1348 | ; Guard words are included in the comparison. | |
1349 | ; | |
1350 | ; unsigned EMUSHORT a[NI], b[NI]; | |
1351 | ; cmpm (a, b); | |
1352 | ; | |
1353 | ; for the significands: | |
1354 | ; returns +1 if a > b | |
1355 | ; 0 if a == b | |
1356 | ; -1 if a < b | |
1357 | */ | |
1358 | int | |
1359 | ecmpm (a, b) | |
1360 | register unsigned EMUSHORT *a, *b; | |
1361 | { | |
1362 | int i; | |
1363 | ||
1364 | a += M; /* skip up to significand area */ | |
1365 | b += M; | |
1366 | for (i = M; i < NI; i++) | |
1367 | { | |
1368 | if (*a++ != *b++) | |
1369 | goto difrnt; | |
1370 | } | |
1371 | return (0); | |
1372 | ||
1373 | difrnt: | |
1374 | if (*(--a) > *(--b)) | |
1375 | return (1); | |
1376 | else | |
1377 | return (-1); | |
1378 | } | |
1379 | ||
1380 | ||
1381 | /* | |
1382 | ; Shift significand down by 1 bit | |
1383 | */ | |
1384 | ||
1385 | void | |
1386 | eshdn1 (x) | |
1387 | register unsigned EMUSHORT *x; | |
1388 | { | |
1389 | register unsigned EMUSHORT bits; | |
1390 | int i; | |
1391 | ||
1392 | x += M; /* point to significand area */ | |
1393 | ||
1394 | bits = 0; | |
1395 | for (i = M; i < NI; i++) | |
1396 | { | |
1397 | if (*x & 1) | |
1398 | bits |= 1; | |
1399 | *x >>= 1; | |
1400 | if (bits & 2) | |
1401 | *x |= 0x8000; | |
1402 | bits <<= 1; | |
1403 | ++x; | |
1404 | } | |
1405 | } | |
1406 | ||
1407 | ||
1408 | ||
1409 | /* | |
1410 | ; Shift significand up by 1 bit | |
1411 | */ | |
1412 | ||
1413 | void | |
1414 | eshup1 (x) | |
1415 | register unsigned EMUSHORT *x; | |
1416 | { | |
1417 | register unsigned EMUSHORT bits; | |
1418 | int i; | |
1419 | ||
1420 | x += NI - 1; | |
1421 | bits = 0; | |
1422 | ||
1423 | for (i = M; i < NI; i++) | |
1424 | { | |
1425 | if (*x & 0x8000) | |
1426 | bits |= 1; | |
1427 | *x <<= 1; | |
1428 | if (bits & 2) | |
1429 | *x |= 1; | |
1430 | bits <<= 1; | |
1431 | --x; | |
1432 | } | |
1433 | } | |
1434 | ||
1435 | ||
1436 | ||
1437 | /* | |
1438 | ; Shift significand down by 8 bits | |
1439 | */ | |
1440 | ||
1441 | void | |
1442 | eshdn8 (x) | |
1443 | register unsigned EMUSHORT *x; | |
1444 | { | |
1445 | register unsigned EMUSHORT newbyt, oldbyt; | |
1446 | int i; | |
1447 | ||
1448 | x += M; | |
1449 | oldbyt = 0; | |
1450 | for (i = M; i < NI; i++) | |
1451 | { | |
1452 | newbyt = *x << 8; | |
1453 | *x >>= 8; | |
1454 | *x |= oldbyt; | |
1455 | oldbyt = newbyt; | |
1456 | ++x; | |
1457 | } | |
1458 | } | |
1459 | ||
1460 | /* | |
1461 | ; Shift significand up by 8 bits | |
1462 | */ | |
1463 | ||
1464 | void | |
1465 | eshup8 (x) | |
1466 | register unsigned EMUSHORT *x; | |
1467 | { | |
1468 | int i; | |
1469 | register unsigned EMUSHORT newbyt, oldbyt; | |
1470 | ||
1471 | x += NI - 1; | |
1472 | oldbyt = 0; | |
1473 | ||
1474 | for (i = M; i < NI; i++) | |
1475 | { | |
1476 | newbyt = *x >> 8; | |
1477 | *x <<= 8; | |
1478 | *x |= oldbyt; | |
1479 | oldbyt = newbyt; | |
1480 | --x; | |
1481 | } | |
1482 | } | |
1483 | ||
1484 | /* | |
1485 | ; Shift significand up by 16 bits | |
1486 | */ | |
1487 | ||
1488 | void | |
1489 | eshup6 (x) | |
1490 | register unsigned EMUSHORT *x; | |
1491 | { | |
1492 | int i; | |
1493 | register unsigned EMUSHORT *p; | |
1494 | ||
1495 | p = x + M; | |
1496 | x += M + 1; | |
1497 | ||
1498 | for (i = M; i < NI - 1; i++) | |
1499 | *p++ = *x++; | |
1500 | ||
1501 | *p = 0; | |
1502 | } | |
1503 | ||
1504 | /* | |
1505 | ; Shift significand down by 16 bits | |
1506 | */ | |
1507 | ||
1508 | void | |
1509 | eshdn6 (x) | |
1510 | register unsigned EMUSHORT *x; | |
1511 | { | |
1512 | int i; | |
1513 | register unsigned EMUSHORT *p; | |
1514 | ||
1515 | x += NI - 1; | |
1516 | p = x + 1; | |
1517 | ||
1518 | for (i = M; i < NI - 1; i++) | |
1519 | *(--p) = *(--x); | |
1520 | ||
1521 | *(--p) = 0; | |
1522 | } | |
1523 | \f | |
1524 | /* | |
1525 | ; Add significands | |
1526 | ; x + y replaces y | |
1527 | */ | |
1528 | ||
1529 | void | |
1530 | eaddm (x, y) | |
1531 | unsigned EMUSHORT *x, *y; | |
1532 | { | |
1533 | register unsigned EMULONG a; | |
1534 | int i; | |
1535 | unsigned int carry; | |
1536 | ||
1537 | x += NI - 1; | |
1538 | y += NI - 1; | |
1539 | carry = 0; | |
1540 | for (i = M; i < NI; i++) | |
1541 | { | |
1542 | a = (unsigned EMULONG) (*x) + (unsigned EMULONG) (*y) + carry; | |
1543 | if (a & 0x10000) | |
1544 | carry = 1; | |
1545 | else | |
1546 | carry = 0; | |
1547 | *y = (unsigned EMUSHORT) a; | |
1548 | --x; | |
1549 | --y; | |
1550 | } | |
1551 | } | |
1552 | ||
1553 | /* | |
1554 | ; Subtract significands | |
1555 | ; y - x replaces y | |
1556 | */ | |
1557 | ||
1558 | void | |
1559 | esubm (x, y) | |
1560 | unsigned EMUSHORT *x, *y; | |
1561 | { | |
1562 | unsigned EMULONG a; | |
1563 | int i; | |
1564 | unsigned int carry; | |
1565 | ||
1566 | x += NI - 1; | |
1567 | y += NI - 1; | |
1568 | carry = 0; | |
1569 | for (i = M; i < NI; i++) | |
1570 | { | |
1571 | a = (unsigned EMULONG) (*y) - (unsigned EMULONG) (*x) - carry; | |
1572 | if (a & 0x10000) | |
1573 | carry = 1; | |
1574 | else | |
1575 | carry = 0; | |
1576 | *y = (unsigned EMUSHORT) a; | |
1577 | --x; | |
1578 | --y; | |
1579 | } | |
1580 | } | |
1581 | ||
1582 | ||
1583 | /* Divide significands */ | |
1584 | ||
1585 | static unsigned EMUSHORT equot[NI]; | |
1586 | ||
1587 | int | |
1588 | edivm (den, num) | |
1589 | unsigned EMUSHORT den[], num[]; | |
1590 | { | |
1591 | int i; | |
1592 | register unsigned EMUSHORT *p, *q; | |
1593 | unsigned EMUSHORT j; | |
1594 | ||
1595 | p = &equot[0]; | |
1596 | *p++ = num[0]; | |
1597 | *p++ = num[1]; | |
1598 | ||
1599 | for (i = M; i < NI; i++) | |
1600 | { | |
1601 | *p++ = 0; | |
1602 | } | |
1603 | ||
1604 | /* Use faster compare and subtraction if denominator | |
1605 | * has only 15 bits of significance. | |
1606 | */ | |
1607 | p = &den[M + 2]; | |
1608 | if (*p++ == 0) | |
1609 | { | |
1610 | for (i = M + 3; i < NI; i++) | |
1611 | { | |
1612 | if (*p++ != 0) | |
1613 | goto fulldiv; | |
1614 | } | |
1615 | if ((den[M + 1] & 1) != 0) | |
1616 | goto fulldiv; | |
1617 | eshdn1 (num); | |
1618 | eshdn1 (den); | |
1619 | ||
1620 | p = &den[M + 1]; | |
1621 | q = &num[M + 1]; | |
1622 | ||
1623 | for (i = 0; i < NBITS + 2; i++) | |
1624 | { | |
1625 | if (*p <= *q) | |
1626 | { | |
1627 | *q -= *p; | |
1628 | j = 1; | |
1629 | } | |
1630 | else | |
1631 | { | |
1632 | j = 0; | |
1633 | } | |
1634 | eshup1 (equot); | |
1635 | equot[NI - 2] |= j; | |
1636 | eshup1 (num); | |
1637 | } | |
1638 | goto divdon; | |
1639 | } | |
1640 | ||
1641 | /* The number of quotient bits to calculate is | |
1642 | * NBITS + 1 scaling guard bit + 1 roundoff bit. | |
1643 | */ | |
1644 | fulldiv: | |
1645 | ||
1646 | p = &equot[NI - 2]; | |
1647 | for (i = 0; i < NBITS + 2; i++) | |
1648 | { | |
1649 | if (ecmpm (den, num) <= 0) | |
1650 | { | |
1651 | esubm (den, num); | |
1652 | j = 1; /* quotient bit = 1 */ | |
1653 | } | |
1654 | else | |
1655 | j = 0; | |
1656 | eshup1 (equot); | |
1657 | *p |= j; | |
1658 | eshup1 (num); | |
1659 | } | |
1660 | ||
1661 | divdon: | |
1662 | ||
1663 | eshdn1 (equot); | |
1664 | eshdn1 (equot); | |
1665 | ||
1666 | /* test for nonzero remainder after roundoff bit */ | |
1667 | p = &num[M]; | |
1668 | j = 0; | |
1669 | for (i = M; i < NI; i++) | |
1670 | { | |
1671 | j |= *p++; | |
1672 | } | |
1673 | if (j) | |
1674 | j = 1; | |
1675 | ||
1676 | ||
1677 | for (i = 0; i < NI; i++) | |
1678 | num[i] = equot[i]; | |
1679 | return ((int) j); | |
1680 | } | |
1681 | ||
1682 | ||
1683 | /* Multiply significands */ | |
1684 | int | |
1685 | emulm (a, b) | |
1686 | unsigned EMUSHORT a[], b[]; | |
1687 | { | |
1688 | unsigned EMUSHORT *p, *q; | |
1689 | int i, j, k; | |
1690 | ||
1691 | equot[0] = b[0]; | |
1692 | equot[1] = b[1]; | |
1693 | for (i = M; i < NI; i++) | |
1694 | equot[i] = 0; | |
1695 | ||
1696 | p = &a[NI - 2]; | |
1697 | k = NBITS; | |
1698 | while (*p == 0) /* significand is not supposed to be all zero */ | |
1699 | { | |
1700 | eshdn6 (a); | |
1701 | k -= 16; | |
1702 | } | |
1703 | if ((*p & 0xff) == 0) | |
1704 | { | |
1705 | eshdn8 (a); | |
1706 | k -= 8; | |
1707 | } | |
1708 | ||
1709 | q = &equot[NI - 1]; | |
1710 | j = 0; | |
1711 | for (i = 0; i < k; i++) | |
1712 | { | |
1713 | if (*p & 1) | |
1714 | eaddm (b, equot); | |
1715 | /* remember if there were any nonzero bits shifted out */ | |
1716 | if (*q & 1) | |
1717 | j |= 1; | |
1718 | eshdn1 (a); | |
1719 | eshdn1 (equot); | |
1720 | } | |
1721 | ||
1722 | for (i = 0; i < NI; i++) | |
1723 | b[i] = equot[i]; | |
1724 | ||
1725 | /* return flag for lost nonzero bits */ | |
1726 | return (j); | |
1727 | } | |
1728 | ||
1729 | ||
1730 | ||
1731 | /* | |
1732 | * Normalize and round off. | |
1733 | * | |
1734 | * The internal format number to be rounded is "s". | |
1735 | * Input "lost" indicates whether or not the number is exact. | |
1736 | * This is the so-called sticky bit. | |
1737 | * | |
1738 | * Input "subflg" indicates whether the number was obtained | |
1739 | * by a subtraction operation. In that case if lost is nonzero | |
1740 | * then the number is slightly smaller than indicated. | |
1741 | * | |
1742 | * Input "exp" is the biased exponent, which may be negative. | |
1743 | * the exponent field of "s" is ignored but is replaced by | |
1744 | * "exp" as adjusted by normalization and rounding. | |
1745 | * | |
1746 | * Input "rcntrl" is the rounding control. | |
1747 | */ | |
1748 | ||
1749 | static int rlast = -1; | |
1750 | static int rw = 0; | |
1751 | static unsigned EMUSHORT rmsk = 0; | |
1752 | static unsigned EMUSHORT rmbit = 0; | |
1753 | static unsigned EMUSHORT rebit = 0; | |
1754 | static int re = 0; | |
1755 | static unsigned EMUSHORT rbit[NI]; | |
1756 | ||
1757 | void | |
1758 | emdnorm (s, lost, subflg, exp, rcntrl) | |
1759 | unsigned EMUSHORT s[]; | |
1760 | int lost; | |
1761 | int subflg; | |
1762 | EMULONG exp; | |
1763 | int rcntrl; | |
1764 | { | |
1765 | int i, j; | |
1766 | unsigned EMUSHORT r; | |
1767 | ||
1768 | /* Normalize */ | |
1769 | j = enormlz (s); | |
1770 | ||
1771 | /* a blank significand could mean either zero or infinity. */ | |
1772 | #ifndef INFINITY | |
1773 | if (j > NBITS) | |
1774 | { | |
1775 | ecleazs (s); | |
1776 | return; | |
1777 | } | |
1778 | #endif | |
1779 | exp -= j; | |
1780 | #ifndef INFINITY | |
1781 | if (exp >= 32767L) | |
1782 | goto overf; | |
1783 | #else | |
1784 | if ((j > NBITS) && (exp < 32767)) | |
1785 | { | |
1786 | ecleazs (s); | |
1787 | return; | |
1788 | } | |
1789 | #endif | |
1790 | if (exp < 0L) | |
1791 | { | |
1792 | if (exp > (EMULONG) (-NBITS - 1)) | |
1793 | { | |
1794 | j = (int) exp; | |
1795 | i = eshift (s, j); | |
1796 | if (i) | |
1797 | lost = 1; | |
1798 | } | |
1799 | else | |
1800 | { | |
1801 | ecleazs (s); | |
1802 | return; | |
1803 | } | |
1804 | } | |
1805 | /* Round off, unless told not to by rcntrl. */ | |
1806 | if (rcntrl == 0) | |
1807 | goto mdfin; | |
1808 | /* Set up rounding parameters if the control register changed. */ | |
1809 | if (rndprc != rlast) | |
1810 | { | |
1811 | ecleaz (rbit); | |
1812 | switch (rndprc) | |
1813 | { | |
1814 | default: | |
1815 | case NBITS: | |
1816 | rw = NI - 1; /* low guard word */ | |
1817 | rmsk = 0xffff; | |
1818 | rmbit = 0x8000; | |
1819 | rbit[rw - 1] = 1; | |
1820 | re = NI - 2; | |
1821 | rebit = 1; | |
1822 | break; | |
1823 | case 64: | |
1824 | rw = 7; | |
1825 | rmsk = 0xffff; | |
1826 | rmbit = 0x8000; | |
1827 | rbit[rw - 1] = 1; | |
1828 | re = rw - 1; | |
1829 | rebit = 1; | |
1830 | break; | |
1831 | /* For DEC arithmetic */ | |
1832 | case 56: | |
1833 | rw = 6; | |
1834 | rmsk = 0xff; | |
1835 | rmbit = 0x80; | |
1836 | rbit[rw] = 0x100; | |
1837 | re = rw; | |
1838 | rebit = 0x100; | |
1839 | break; | |
1840 | case 53: | |
1841 | rw = 6; | |
1842 | rmsk = 0x7ff; | |
1843 | rmbit = 0x0400; | |
1844 | rbit[rw] = 0x800; | |
1845 | re = rw; | |
1846 | rebit = 0x800; | |
1847 | break; | |
1848 | case 24: | |
1849 | rw = 4; | |
1850 | rmsk = 0xff; | |
1851 | rmbit = 0x80; | |
1852 | rbit[rw] = 0x100; | |
1853 | re = rw; | |
1854 | rebit = 0x100; | |
1855 | break; | |
1856 | } | |
1857 | rlast = rndprc; | |
1858 | } | |
1859 | ||
1860 | if (rndprc >= 64) | |
1861 | { | |
1862 | r = s[rw] & rmsk; | |
1863 | if (rndprc == 64) | |
1864 | { | |
1865 | i = rw + 1; | |
1866 | while (i < NI) | |
1867 | { | |
1868 | if (s[i]) | |
1869 | r |= 1; | |
1870 | s[i] = 0; | |
1871 | ++i; | |
1872 | } | |
1873 | } | |
1874 | } | |
1875 | else | |
1876 | { | |
1877 | if (exp <= 0) | |
1878 | eshdn1 (s); | |
1879 | r = s[rw] & rmsk; | |
1880 | /* These tests assume NI = 8 */ | |
1881 | i = rw + 1; | |
1882 | while (i < NI) | |
1883 | { | |
1884 | if (s[i]) | |
1885 | r |= 1; | |
1886 | s[i] = 0; | |
1887 | ++i; | |
1888 | } | |
1889 | /* | |
1890 | if (rndprc == 24) | |
1891 | { | |
1892 | if (s[5] || s[6]) | |
1893 | r |= 1; | |
1894 | s[5] = 0; | |
1895 | s[6] = 0; | |
1896 | } | |
1897 | */ | |
1898 | s[rw] &= ~rmsk; | |
1899 | } | |
1900 | if ((r & rmbit) != 0) | |
1901 | { | |
1902 | if (r == rmbit) | |
1903 | { | |
1904 | if (lost == 0) | |
1905 | { /* round to even */ | |
1906 | if ((s[re] & rebit) == 0) | |
1907 | goto mddone; | |
1908 | } | |
1909 | else | |
1910 | { | |
1911 | if (subflg != 0) | |
1912 | goto mddone; | |
1913 | } | |
1914 | } | |
1915 | eaddm (rbit, s); | |
1916 | } | |
1917 | mddone: | |
1918 | if ((rndprc < 64) && (exp <= 0)) | |
1919 | { | |
1920 | eshup1 (s); | |
1921 | } | |
1922 | if (s[2] != 0) | |
1923 | { /* overflow on roundoff */ | |
1924 | eshdn1 (s); | |
1925 | exp += 1; | |
1926 | } | |
1927 | mdfin: | |
1928 | s[NI - 1] = 0; | |
1929 | if (exp >= 32767L) | |
1930 | { | |
1931 | #ifndef INFINITY | |
1932 | overf: | |
1933 | #endif | |
1934 | #ifdef INFINITY | |
1935 | s[1] = 32767; | |
1936 | for (i = 2; i < NI - 1; i++) | |
1937 | s[i] = 0; | |
1938 | pedwarn ("floating point overflow"); | |
1939 | #else | |
1940 | s[1] = 32766; | |
1941 | s[2] = 0; | |
1942 | for (i = M + 1; i < NI - 1; i++) | |
1943 | s[i] = 0xffff; | |
1944 | s[NI - 1] = 0; | |
1945 | if (rndprc < 64) | |
1946 | { | |
1947 | s[rw] &= ~rmsk; | |
1948 | if (rndprc == 24) | |
1949 | { | |
1950 | s[5] = 0; | |
1951 | s[6] = 0; | |
1952 | } | |
1953 | } | |
1954 | #endif | |
1955 | return; | |
1956 | } | |
1957 | if (exp < 0) | |
1958 | s[1] = 0; | |
1959 | else | |
1960 | s[1] = (unsigned EMUSHORT) exp; | |
1961 | } | |
1962 | ||
1963 | ||
1964 | ||
1965 | /* | |
1966 | ; Subtract external format numbers. | |
1967 | ; | |
1968 | ; unsigned EMUSHORT a[NE], b[NE], c[NE]; | |
1969 | ; esub (a, b, c); c = b - a | |
1970 | */ | |
1971 | ||
1972 | static int subflg = 0; | |
1973 | ||
1974 | void | |
1975 | esub (a, b, c) | |
1976 | unsigned EMUSHORT *a, *b, *c; | |
1977 | { | |
1978 | ||
1979 | subflg = 1; | |
1980 | eadd1 (a, b, c); | |
1981 | } | |
1982 | ||
1983 | ||
1984 | /* | |
1985 | ; Add. | |
1986 | ; | |
1987 | ; unsigned EMUSHORT a[NE], b[NE], c[NE]; | |
1988 | ; eadd (a, b, c); c = b + a | |
1989 | */ | |
1990 | void | |
1991 | eadd (a, b, c) | |
1992 | unsigned EMUSHORT *a, *b, *c; | |
1993 | { | |
1994 | ||
1995 | subflg = 0; | |
1996 | eadd1 (a, b, c); | |
1997 | } | |
1998 | ||
1999 | void | |
2000 | eadd1 (a, b, c) | |
2001 | unsigned EMUSHORT *a, *b, *c; | |
2002 | { | |
2003 | unsigned EMUSHORT ai[NI], bi[NI], ci[NI]; | |
2004 | int i, lost, j, k; | |
2005 | EMULONG lt, lta, ltb; | |
2006 | ||
2007 | #ifdef INFINITY | |
2008 | if (eisinf (a)) | |
2009 | { | |
2010 | emov (a, c); | |
2011 | if (subflg) | |
2012 | eneg (c); | |
2013 | return; | |
2014 | } | |
2015 | if (eisinf (b)) | |
2016 | { | |
2017 | emov (b, c); | |
2018 | return; | |
2019 | } | |
2020 | #endif | |
2021 | emovi (a, ai); | |
2022 | emovi (b, bi); | |
2023 | if (subflg) | |
2024 | ai[0] = ~ai[0]; | |
2025 | ||
2026 | /* compare exponents */ | |
2027 | lta = ai[E]; | |
2028 | ltb = bi[E]; | |
2029 | lt = lta - ltb; | |
2030 | if (lt > 0L) | |
2031 | { /* put the larger number in bi */ | |
2032 | emovz (bi, ci); | |
2033 | emovz (ai, bi); | |
2034 | emovz (ci, ai); | |
2035 | ltb = bi[E]; | |
2036 | lt = -lt; | |
2037 | } | |
2038 | lost = 0; | |
2039 | if (lt != 0L) | |
2040 | { | |
2041 | if (lt < (EMULONG) (-NBITS - 1)) | |
2042 | goto done; /* answer same as larger addend */ | |
2043 | k = (int) lt; | |
2044 | lost = eshift (ai, k); /* shift the smaller number down */ | |
2045 | } | |
2046 | else | |
2047 | { | |
2048 | /* exponents were the same, so must compare significands */ | |
2049 | i = ecmpm (ai, bi); | |
2050 | if (i == 0) | |
2051 | { /* the numbers are identical in magnitude */ | |
2052 | /* if different signs, result is zero */ | |
2053 | if (ai[0] != bi[0]) | |
2054 | { | |
2055 | eclear (c); | |
2056 | return; | |
2057 | } | |
2058 | /* if same sign, result is double */ | |
2059 | /* double denomalized tiny number */ | |
2060 | if ((bi[E] == 0) && ((bi[3] & 0x8000) == 0)) | |
2061 | { | |
2062 | eshup1 (bi); | |
2063 | goto done; | |
2064 | } | |
2065 | /* add 1 to exponent unless both are zero! */ | |
2066 | for (j = 1; j < NI - 1; j++) | |
2067 | { | |
2068 | if (bi[j] != 0) | |
2069 | { | |
2070 | /* This could overflow, but let emovo take care of that. */ | |
2071 | ltb += 1; | |
2072 | break; | |
2073 | } | |
2074 | } | |
2075 | bi[E] = (unsigned EMUSHORT) ltb; | |
2076 | goto done; | |
2077 | } | |
2078 | if (i > 0) | |
2079 | { /* put the larger number in bi */ | |
2080 | emovz (bi, ci); | |
2081 | emovz (ai, bi); | |
2082 | emovz (ci, ai); | |
2083 | } | |
2084 | } | |
2085 | if (ai[0] == bi[0]) | |
2086 | { | |
2087 | eaddm (ai, bi); | |
2088 | subflg = 0; | |
2089 | } | |
2090 | else | |
2091 | { | |
2092 | esubm (ai, bi); | |
2093 | subflg = 1; | |
2094 | } | |
2095 | emdnorm (bi, lost, subflg, ltb, 64); | |
2096 | ||
2097 | done: | |
2098 | emovo (bi, c); | |
2099 | } | |
2100 | ||
2101 | ||
2102 | ||
2103 | /* | |
2104 | ; Divide. | |
2105 | ; | |
2106 | ; unsigned EMUSHORT a[NE], b[NE], c[NE]; | |
2107 | ; ediv (a, b, c); c = b / a | |
2108 | */ | |
2109 | void | |
2110 | ediv (a, b, c) | |
2111 | unsigned EMUSHORT *a, *b, *c; | |
2112 | { | |
2113 | unsigned EMUSHORT ai[NI], bi[NI]; | |
2114 | int i; | |
2115 | EMULONG lt, lta, ltb; | |
2116 | ||
2117 | #ifdef INFINITY | |
2118 | if (eisinf (b)) | |
2119 | { | |
2120 | if (eisneg (a) ^ eisneg (b)) | |
2121 | *(c + (NE - 1)) = 0x8000; | |
2122 | else | |
2123 | *(c + (NE - 1)) = 0; | |
2124 | einfin (c); | |
2125 | return; | |
2126 | } | |
2127 | if (eisinf (a)) | |
2128 | { | |
2129 | eclear (c); | |
2130 | return; | |
2131 | } | |
2132 | #endif | |
2133 | emovi (a, ai); | |
2134 | emovi (b, bi); | |
2135 | lta = ai[E]; | |
2136 | ltb = bi[E]; | |
2137 | if (bi[E] == 0) | |
2138 | { /* See if numerator is zero. */ | |
2139 | for (i = 1; i < NI - 1; i++) | |
2140 | { | |
2141 | if (bi[i] != 0) | |
2142 | { | |
2143 | ltb -= enormlz (bi); | |
2144 | goto dnzro1; | |
2145 | } | |
2146 | } | |
2147 | eclear (c); | |
2148 | return; | |
2149 | } | |
2150 | dnzro1: | |
2151 | ||
2152 | if (ai[E] == 0) | |
2153 | { /* possible divide by zero */ | |
2154 | for (i = 1; i < NI - 1; i++) | |
2155 | { | |
2156 | if (ai[i] != 0) | |
2157 | { | |
2158 | lta -= enormlz (ai); | |
2159 | goto dnzro2; | |
2160 | } | |
2161 | } | |
2162 | if (ai[0] == bi[0]) | |
2163 | *(c + (NE - 1)) = 0; | |
2164 | else | |
2165 | *(c + (NE - 1)) = 0x8000; | |
2166 | einfin (c); | |
2167 | mtherr ("ediv", SING); | |
2168 | return; | |
2169 | } | |
2170 | dnzro2: | |
2171 | ||
2172 | i = edivm (ai, bi); | |
2173 | /* calculate exponent */ | |
2174 | lt = ltb - lta + EXONE; | |
2175 | emdnorm (bi, i, 0, lt, 64); | |
2176 | /* set the sign */ | |
2177 | if (ai[0] == bi[0]) | |
2178 | bi[0] = 0; | |
2179 | else | |
2180 | bi[0] = 0Xffff; | |
2181 | emovo (bi, c); | |
2182 | } | |
2183 | ||
2184 | ||
2185 | ||
2186 | /* | |
2187 | ; Multiply. | |
2188 | ; | |
2189 | ; unsigned EMUSHORT a[NE], b[NE], c[NE]; | |
2190 | ; emul (a, b, c); c = b * a | |
2191 | */ | |
2192 | void | |
2193 | emul (a, b, c) | |
2194 | unsigned EMUSHORT *a, *b, *c; | |
2195 | { | |
2196 | unsigned EMUSHORT ai[NI], bi[NI]; | |
2197 | int i, j; | |
2198 | EMULONG lt, lta, ltb; | |
2199 | ||
2200 | #ifdef INFINITY | |
2201 | if (eisinf (a) || eisinf (b)) | |
2202 | { | |
2203 | if (eisneg (a) ^ eisneg (b)) | |
2204 | *(c + (NE - 1)) = 0x8000; | |
2205 | else | |
2206 | *(c + (NE - 1)) = 0; | |
2207 | einfin (c); | |
2208 | return; | |
2209 | } | |
2210 | #endif | |
2211 | emovi (a, ai); | |
2212 | emovi (b, bi); | |
2213 | lta = ai[E]; | |
2214 | ltb = bi[E]; | |
2215 | if (ai[E] == 0) | |
2216 | { | |
2217 | for (i = 1; i < NI - 1; i++) | |
2218 | { | |
2219 | if (ai[i] != 0) | |
2220 | { | |
2221 | lta -= enormlz (ai); | |
2222 | goto mnzer1; | |
2223 | } | |
2224 | } | |
2225 | eclear (c); | |
2226 | return; | |
2227 | } | |
2228 | mnzer1: | |
2229 | ||
2230 | if (bi[E] == 0) | |
2231 | { | |
2232 | for (i = 1; i < NI - 1; i++) | |
2233 | { | |
2234 | if (bi[i] != 0) | |
2235 | { | |
2236 | ltb -= enormlz (bi); | |
2237 | goto mnzer2; | |
2238 | } | |
2239 | } | |
2240 | eclear (c); | |
2241 | return; | |
2242 | } | |
2243 | mnzer2: | |
2244 | ||
2245 | /* Multiply significands */ | |
2246 | j = emulm (ai, bi); | |
2247 | /* calculate exponent */ | |
2248 | lt = lta + ltb - (EXONE - 1); | |
2249 | emdnorm (bi, j, 0, lt, 64); | |
2250 | /* calculate sign of product */ | |
2251 | if (ai[0] == bi[0]) | |
2252 | bi[0] = 0; | |
2253 | else | |
2254 | bi[0] = 0xffff; | |
2255 | emovo (bi, c); | |
2256 | } | |
2257 | ||
2258 | ||
2259 | ||
2260 | ||
2261 | /* | |
2262 | ; Convert IEEE double precision to e type | |
2263 | ; double d; | |
2264 | ; unsigned EMUSHORT x[N+2]; | |
2265 | ; e53toe (&d, x); | |
2266 | */ | |
2267 | void | |
2268 | e53toe (e, y) | |
2269 | unsigned EMUSHORT *e, *y; | |
2270 | { | |
2271 | #ifdef DEC | |
2272 | ||
2273 | dectoe (e, y); /* see etodec.c */ | |
2274 | ||
2275 | #else | |
2276 | ||
2277 | register unsigned EMUSHORT r; | |
2278 | register unsigned EMUSHORT *p; | |
2279 | unsigned EMUSHORT yy[NI]; | |
2280 | int denorm, k; | |
2281 | ||
2282 | denorm = 0; /* flag if denormalized number */ | |
2283 | ecleaz (yy); | |
2284 | #ifdef IBMPC | |
2285 | e += 3; | |
2286 | #endif | |
2287 | r = *e; | |
2288 | yy[0] = 0; | |
2289 | if (r & 0x8000) | |
2290 | yy[0] = 0xffff; | |
2291 | yy[M] = (r & 0x0f) | 0x10; | |
2292 | r &= ~0x800f; /* strip sign and 4 significand bits */ | |
2293 | #ifdef INFINITY | |
2294 | if (r == 0x7ff0) | |
2295 | { | |
2296 | einfin (y); | |
2297 | if (r & 0x8000) | |
2298 | eneg (y); | |
2299 | return; | |
2300 | } | |
2301 | #endif | |
2302 | r >>= 4; | |
2303 | /* If zero exponent, then the significand is denormalized. | |
2304 | * So, take back the understood high significand bit. */ | |
2305 | if (r == 0) | |
2306 | { | |
2307 | denorm = 1; | |
2308 | yy[M] &= ~0x10; | |
2309 | } | |
2310 | r += EXONE - 01777; | |
2311 | yy[E] = r; | |
2312 | p = &yy[M + 1]; | |
2313 | #ifdef IBMPC | |
2314 | *p++ = *(--e); | |
2315 | *p++ = *(--e); | |
2316 | *p++ = *(--e); | |
2317 | #endif | |
2318 | #ifdef MIEEE | |
2319 | ++e; | |
2320 | *p++ = *e++; | |
2321 | *p++ = *e++; | |
2322 | *p++ = *e++; | |
2323 | #endif | |
2324 | (void) eshift (yy, -5); | |
2325 | if (denorm) | |
2326 | { /* if zero exponent, then normalize the significand */ | |
2327 | if ((k = enormlz (yy)) > NBITS) | |
2328 | ecleazs (yy); | |
2329 | else | |
2330 | yy[E] -= (unsigned EMUSHORT) (k - 1); | |
2331 | } | |
2332 | emovo (yy, y); | |
2333 | #endif /* not DEC */ | |
2334 | } | |
2335 | ||
2336 | void | |
2337 | e64toe (e, y) | |
2338 | unsigned EMUSHORT *e, *y; | |
2339 | { | |
2340 | unsigned EMUSHORT yy[NI]; | |
2341 | unsigned EMUSHORT *p, *q; | |
2342 | int i; | |
2343 | ||
2344 | p = yy; | |
2345 | for (i = 0; i < NE - 5; i++) | |
2346 | *p++ = 0; | |
2347 | #ifdef IBMPC | |
2348 | for (i = 0; i < 5; i++) | |
2349 | *p++ = *e++; | |
2350 | #endif | |
2351 | #ifdef DEC | |
2352 | for (i = 0; i < 5; i++) | |
2353 | *p++ = *e++; | |
2354 | #endif | |
2355 | #ifdef MIEEE | |
2356 | p = &yy[0] + (NE - 1); | |
2357 | *p-- = *e++; | |
2358 | ++e; | |
2359 | for (i = 0; i < 4; i++) | |
2360 | *p-- = *e++; | |
2361 | #endif | |
2362 | p = yy; | |
2363 | q = y; | |
2364 | #ifdef INFINITY | |
2365 | if (*p == 0x7fff) | |
2366 | { | |
2367 | einfin (y); | |
2368 | if (*p & 0x8000) | |
2369 | eneg (y); | |
2370 | return; | |
2371 | } | |
2372 | #endif | |
2373 | for (i = 0; i < NE; i++) | |
2374 | *q++ = *p++; | |
2375 | } | |
2376 | ||
2377 | ||
2378 | /* | |
2379 | ; Convert IEEE single precision to e type | |
2380 | ; float d; | |
2381 | ; unsigned EMUSHORT x[N+2]; | |
2382 | ; dtox (&d, x); | |
2383 | */ | |
2384 | void | |
2385 | e24toe (e, y) | |
2386 | unsigned EMUSHORT *e, *y; | |
2387 | { | |
2388 | register unsigned EMUSHORT r; | |
2389 | register unsigned EMUSHORT *p; | |
2390 | unsigned EMUSHORT yy[NI]; | |
2391 | int denorm, k; | |
2392 | ||
2393 | denorm = 0; /* flag if denormalized number */ | |
2394 | ecleaz (yy); | |
2395 | #ifdef IBMPC | |
2396 | e += 1; | |
2397 | #endif | |
2398 | #ifdef DEC | |
2399 | e += 1; | |
2400 | #endif | |
2401 | r = *e; | |
2402 | yy[0] = 0; | |
2403 | if (r & 0x8000) | |
2404 | yy[0] = 0xffff; | |
2405 | yy[M] = (r & 0x7f) | 0200; | |
2406 | r &= ~0x807f; /* strip sign and 7 significand bits */ | |
2407 | #ifdef INFINITY | |
2408 | if (r == 0x7f80) | |
2409 | { | |
2410 | einfin (y); | |
2411 | if (r & 0x8000) | |
2412 | eneg (y); | |
2413 | return; | |
2414 | } | |
2415 | #endif | |
2416 | r >>= 7; | |
2417 | /* If zero exponent, then the significand is denormalized. | |
2418 | * So, take back the understood high significand bit. */ | |
2419 | if (r == 0) | |
2420 | { | |
2421 | denorm = 1; | |
2422 | yy[M] &= ~0200; | |
2423 | } | |
2424 | r += EXONE - 0177; | |
2425 | yy[E] = r; | |
2426 | p = &yy[M + 1]; | |
2427 | #ifdef IBMPC | |
2428 | *p++ = *(--e); | |
2429 | #endif | |
2430 | #ifdef DEC | |
2431 | *p++ = *(--e); | |
2432 | #endif | |
2433 | #ifdef MIEEE | |
2434 | ++e; | |
2435 | *p++ = *e++; | |
2436 | #endif | |
2437 | (void) eshift (yy, -8); | |
2438 | if (denorm) | |
2439 | { /* if zero exponent, then normalize the significand */ | |
2440 | if ((k = enormlz (yy)) > NBITS) | |
2441 | ecleazs (yy); | |
2442 | else | |
2443 | yy[E] -= (unsigned EMUSHORT) (k - 1); | |
2444 | } | |
2445 | emovo (yy, y); | |
2446 | } | |
2447 | ||
2448 | ||
2449 | void | |
2450 | etoe64 (x, e) | |
2451 | unsigned EMUSHORT *x, *e; | |
2452 | { | |
2453 | unsigned EMUSHORT xi[NI]; | |
2454 | EMULONG exp; | |
2455 | int rndsav; | |
2456 | ||
2457 | emovi (x, xi); | |
2458 | /* adjust exponent for offset */ | |
2459 | exp = (EMULONG) xi[E]; | |
2460 | #ifdef INFINITY | |
2461 | if (eisinf (x)) | |
2462 | goto nonorm; | |
2463 | #endif | |
2464 | /* round off to nearest or even */ | |
2465 | rndsav = rndprc; | |
2466 | rndprc = 64; | |
2467 | emdnorm (xi, 0, 0, exp, 64); | |
2468 | rndprc = rndsav; | |
2469 | nonorm: | |
2470 | toe64 (xi, e); | |
2471 | } | |
2472 | ||
2473 | /* move out internal format to ieee long double */ | |
2474 | static void | |
2475 | toe64 (a, b) | |
2476 | unsigned EMUSHORT *a, *b; | |
2477 | { | |
2478 | register unsigned EMUSHORT *p, *q; | |
2479 | unsigned EMUSHORT i; | |
2480 | ||
2481 | p = a; | |
2482 | #ifdef MIEEE | |
2483 | q = b; | |
2484 | #else | |
2485 | q = b + 4; /* point to output exponent */ | |
2486 | #if LONG_DOUBLE_TYPE_SIZE == 96 | |
2487 | /* Clear the last two bytes of 12-byte Intel format */ | |
2488 | *(q+1) = 0; | |
2489 | #endif | |
2490 | #endif | |
2491 | ||
2492 | /* combine sign and exponent */ | |
2493 | i = *p++; | |
2494 | #ifdef MIEEE | |
2495 | if (i) | |
2496 | *q++ = *p++ | 0x8000; | |
2497 | else | |
2498 | *q++ = *p++; | |
2499 | *q++ = 0; | |
2500 | #else | |
2501 | if (i) | |
2502 | *q-- = *p++ | 0x8000; | |
2503 | else | |
2504 | *q-- = *p++; | |
2505 | #endif | |
2506 | /* skip over guard word */ | |
2507 | ++p; | |
2508 | /* move the significand */ | |
2509 | #ifdef MIEEE | |
2510 | for (i = 0; i < 4; i++) | |
2511 | *q++ = *p++; | |
2512 | #else | |
2513 | for (i = 0; i < 4; i++) | |
2514 | *q-- = *p++; | |
2515 | #endif | |
2516 | } | |
2517 | ||
2518 | ||
2519 | /* | |
2520 | ; e type to IEEE double precision | |
2521 | ; double d; | |
2522 | ; unsigned EMUSHORT x[NE]; | |
2523 | ; etoe53 (x, &d); | |
2524 | */ | |
2525 | ||
2526 | #ifdef DEC | |
2527 | ||
2528 | void | |
2529 | etoe53 (x, e) | |
2530 | unsigned EMUSHORT *x, *e; | |
2531 | { | |
2532 | etodec (x, e); /* see etodec.c */ | |
2533 | } | |
2534 | ||
2535 | static void | |
2536 | toe53 (x, y) | |
2537 | unsigned EMUSHORT *x, *y; | |
2538 | { | |
2539 | todec (x, y); | |
2540 | } | |
2541 | ||
2542 | #else | |
2543 | ||
2544 | void | |
2545 | etoe53 (x, e) | |
2546 | unsigned EMUSHORT *x, *e; | |
2547 | { | |
2548 | unsigned EMUSHORT xi[NI]; | |
2549 | EMULONG exp; | |
2550 | int rndsav; | |
2551 | ||
2552 | emovi (x, xi); | |
2553 | /* adjust exponent for offsets */ | |
2554 | exp = (EMULONG) xi[E] - (EXONE - 0x3ff); | |
2555 | #ifdef INFINITY | |
2556 | if (eisinf (x)) | |
2557 | goto nonorm; | |
2558 | #endif | |
2559 | /* round off to nearest or even */ | |
2560 | rndsav = rndprc; | |
2561 | rndprc = 53; | |
2562 | emdnorm (xi, 0, 0, exp, 64); | |
2563 | rndprc = rndsav; | |
2564 | nonorm: | |
2565 | toe53 (xi, e); | |
2566 | } | |
2567 | ||
2568 | ||
2569 | static void | |
2570 | toe53 (x, y) | |
2571 | unsigned EMUSHORT *x, *y; | |
2572 | { | |
2573 | unsigned EMUSHORT i; | |
2574 | unsigned EMUSHORT *p; | |
2575 | ||
2576 | ||
2577 | p = &x[0]; | |
2578 | #ifdef IBMPC | |
2579 | y += 3; | |
2580 | #endif | |
2581 | *y = 0; /* output high order */ | |
2582 | if (*p++) | |
2583 | *y = 0x8000; /* output sign bit */ | |
2584 | ||
2585 | i = *p++; | |
2586 | if (i >= (unsigned int) 2047) | |
2587 | { /* Saturate at largest number less than infinity. */ | |
2588 | #ifdef INFINITY | |
2589 | *y |= 0x7ff0; | |
2590 | #ifdef IBMPC | |
2591 | *(--y) = 0; | |
2592 | *(--y) = 0; | |
2593 | *(--y) = 0; | |
2594 | #endif | |
2595 | #ifdef MIEEE | |
2596 | ++y; | |
2597 | *y++ = 0; | |
2598 | *y++ = 0; | |
2599 | *y++ = 0; | |
2600 | #endif | |
2601 | #else | |
2602 | *y |= (unsigned EMUSHORT) 0x7fef; | |
2603 | #ifdef IBMPC | |
2604 | *(--y) = 0xffff; | |
2605 | *(--y) = 0xffff; | |
2606 | *(--y) = 0xffff; | |
2607 | #endif | |
2608 | #ifdef MIEEE | |
2609 | ++y; | |
2610 | *y++ = 0xffff; | |
2611 | *y++ = 0xffff; | |
2612 | *y++ = 0xffff; | |
2613 | #endif | |
2614 | #endif | |
2615 | return; | |
2616 | } | |
2617 | if (i == 0) | |
2618 | { | |
2619 | (void) eshift (x, 4); | |
2620 | } | |
2621 | else | |
2622 | { | |
2623 | i <<= 4; | |
2624 | (void) eshift (x, 5); | |
2625 | } | |
2626 | i |= *p++ & (unsigned EMUSHORT) 0x0f; /* *p = xi[M] */ | |
2627 | *y |= (unsigned EMUSHORT) i; /* high order output already has sign bit set */ | |
2628 | #ifdef IBMPC | |
2629 | *(--y) = *p++; | |
2630 | *(--y) = *p++; | |
2631 | *(--y) = *p; | |
2632 | #endif | |
2633 | #ifdef MIEEE | |
2634 | ++y; | |
2635 | *y++ = *p++; | |
2636 | *y++ = *p++; | |
2637 | *y++ = *p++; | |
2638 | #endif | |
2639 | } | |
2640 | ||
2641 | #endif /* not DEC */ | |
2642 | ||
2643 | ||
2644 | ||
2645 | /* | |
2646 | ; e type to IEEE single precision | |
2647 | ; float d; | |
2648 | ; unsigned EMUSHORT x[N+2]; | |
2649 | ; xtod (x, &d); | |
2650 | */ | |
2651 | void | |
2652 | etoe24 (x, e) | |
2653 | unsigned EMUSHORT *x, *e; | |
2654 | { | |
2655 | EMULONG exp; | |
2656 | unsigned EMUSHORT xi[NI]; | |
2657 | int rndsav; | |
2658 | ||
2659 | emovi (x, xi); | |
2660 | /* adjust exponent for offsets */ | |
2661 | exp = (EMULONG) xi[E] - (EXONE - 0177); | |
2662 | #ifdef INFINITY | |
2663 | if (eisinf (x)) | |
2664 | goto nonorm; | |
2665 | #endif | |
2666 | /* round off to nearest or even */ | |
2667 | rndsav = rndprc; | |
2668 | rndprc = 24; | |
2669 | emdnorm (xi, 0, 0, exp, 64); | |
2670 | rndprc = rndsav; | |
2671 | nonorm: | |
2672 | toe24 (xi, e); | |
2673 | } | |
2674 | ||
2675 | static void | |
2676 | toe24 (x, y) | |
2677 | unsigned EMUSHORT *x, *y; | |
2678 | { | |
2679 | unsigned EMUSHORT i; | |
2680 | unsigned EMUSHORT *p; | |
2681 | ||
2682 | p = &x[0]; | |
2683 | #ifdef IBMPC | |
2684 | y += 1; | |
2685 | #endif | |
2686 | #ifdef DEC | |
2687 | y += 1; | |
2688 | #endif | |
2689 | *y = 0; /* output high order */ | |
2690 | if (*p++) | |
2691 | *y = 0x8000; /* output sign bit */ | |
2692 | ||
2693 | i = *p++; | |
2694 | if (i >= 255) | |
2695 | { /* Saturate at largest number less than infinity. */ | |
2696 | #ifdef INFINITY | |
2697 | *y |= (unsigned EMUSHORT) 0x7f80; | |
2698 | #ifdef IBMPC | |
2699 | *(--y) = 0; | |
2700 | #endif | |
2701 | #ifdef DEC | |
2702 | *(--y) = 0; | |
2703 | #endif | |
2704 | #ifdef MIEEE | |
2705 | ++y; | |
2706 | *y = 0; | |
2707 | #endif | |
2708 | #else | |
2709 | *y |= (unsigned EMUSHORT) 0x7f7f; | |
2710 | #ifdef IBMPC | |
2711 | *(--y) = 0xffff; | |
2712 | #endif | |
2713 | #ifdef DEC | |
2714 | *(--y) = 0xffff; | |
2715 | #endif | |
2716 | #ifdef MIEEE | |
2717 | ++y; | |
2718 | *y = 0xffff; | |
2719 | #endif | |
2720 | #endif | |
2721 | return; | |
2722 | } | |
2723 | if (i == 0) | |
2724 | { | |
2725 | (void) eshift (x, 7); | |
2726 | } | |
2727 | else | |
2728 | { | |
2729 | i <<= 7; | |
2730 | (void) eshift (x, 8); | |
2731 | } | |
2732 | i |= *p++ & (unsigned EMUSHORT) 0x7f; /* *p = xi[M] */ | |
2733 | *y |= i; /* high order output already has sign bit set */ | |
2734 | #ifdef IBMPC | |
2735 | *(--y) = *p; | |
2736 | #endif | |
2737 | #ifdef DEC | |
2738 | *(--y) = *p; | |
2739 | #endif | |
2740 | #ifdef MIEEE | |
2741 | ++y; | |
2742 | *y = *p; | |
2743 | #endif | |
2744 | } | |
2745 | ||
2746 | ||
2747 | /* Compare two e type numbers. | |
2748 | * | |
2749 | * unsigned EMUSHORT a[NE], b[NE]; | |
2750 | * ecmp (a, b); | |
2751 | * | |
2752 | * returns +1 if a > b | |
2753 | * 0 if a == b | |
2754 | * -1 if a < b | |
2755 | */ | |
2756 | int | |
2757 | ecmp (a, b) | |
2758 | unsigned EMUSHORT *a, *b; | |
2759 | { | |
2760 | unsigned EMUSHORT ai[NI], bi[NI]; | |
2761 | register unsigned EMUSHORT *p, *q; | |
2762 | register int i; | |
2763 | int msign; | |
2764 | ||
2765 | emovi (a, ai); | |
2766 | p = ai; | |
2767 | emovi (b, bi); | |
2768 | q = bi; | |
2769 | ||
2770 | if (*p != *q) | |
2771 | { /* the signs are different */ | |
2772 | /* -0 equals + 0 */ | |
2773 | for (i = 1; i < NI - 1; i++) | |
2774 | { | |
2775 | if (ai[i] != 0) | |
2776 | goto nzro; | |
2777 | if (bi[i] != 0) | |
2778 | goto nzro; | |
2779 | } | |
2780 | return (0); | |
2781 | nzro: | |
2782 | if (*p == 0) | |
2783 | return (1); | |
2784 | else | |
2785 | return (-1); | |
2786 | } | |
2787 | /* both are the same sign */ | |
2788 | if (*p == 0) | |
2789 | msign = 1; | |
2790 | else | |
2791 | msign = -1; | |
2792 | i = NI - 1; | |
2793 | do | |
2794 | { | |
2795 | if (*p++ != *q++) | |
2796 | { | |
2797 | goto diff; | |
2798 | } | |
2799 | } | |
2800 | while (--i > 0); | |
2801 | ||
2802 | return (0); /* equality */ | |
2803 | ||
2804 | ||
2805 | ||
2806 | diff: | |
2807 | ||
2808 | if (*(--p) > *(--q)) | |
2809 | return (msign); /* p is bigger */ | |
2810 | else | |
2811 | return (-msign); /* p is littler */ | |
2812 | } | |
2813 | ||
2814 | ||
2815 | ||
2816 | ||
2817 | /* Find nearest integer to x = floor (x + 0.5) | |
2818 | * | |
2819 | * unsigned EMUSHORT x[NE], y[NE] | |
2820 | * eround (x, y); | |
2821 | */ | |
2822 | void | |
2823 | eround (x, y) | |
2824 | unsigned EMUSHORT *x, *y; | |
2825 | { | |
2826 | eadd (ehalf, x, y); | |
2827 | efloor (y, y); | |
2828 | } | |
2829 | ||
2830 | ||
2831 | ||
2832 | ||
2833 | /* | |
2834 | ; convert long integer to e type | |
2835 | ; | |
2836 | ; long l; | |
2837 | ; unsigned EMUSHORT x[NE]; | |
2838 | ; ltoe (&l, x); | |
2839 | ; note &l is the memory address of l | |
2840 | */ | |
2841 | void | |
2842 | ltoe (lp, y) | |
2843 | long *lp; /* lp is the memory address of a long integer */ | |
2844 | unsigned EMUSHORT *y; /* y is the address of a short */ | |
2845 | { | |
2846 | unsigned EMUSHORT yi[NI]; | |
2847 | unsigned long ll; | |
2848 | int k; | |
2849 | ||
2850 | ecleaz (yi); | |
2851 | if (*lp < 0) | |
2852 | { | |
2853 | /* make it positive */ | |
2854 | ll = (unsigned long) (-(*lp)); | |
2855 | yi[0] = 0xffff; /* put correct sign in the e type number */ | |
2856 | } | |
2857 | else | |
2858 | { | |
2859 | ll = (unsigned long) (*lp); | |
2860 | } | |
2861 | /* move the long integer to yi significand area */ | |
2862 | yi[M] = (unsigned EMUSHORT) (ll >> 16); | |
2863 | yi[M + 1] = (unsigned EMUSHORT) ll; | |
2864 | ||
2865 | yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */ | |
2866 | if ((k = enormlz (yi)) > NBITS)/* normalize the significand */ | |
2867 | ecleaz (yi); /* it was zero */ | |
2868 | else | |
2869 | yi[E] -= (unsigned EMUSHORT) k;/* subtract shift count from exponent */ | |
2870 | emovo (yi, y); /* output the answer */ | |
2871 | } | |
2872 | ||
2873 | /* | |
2874 | ; convert unsigned long integer to e type | |
2875 | ; | |
2876 | ; unsigned long l; | |
2877 | ; unsigned EMUSHORT x[NE]; | |
2878 | ; ltox (&l, x); | |
2879 | ; note &l is the memory address of l | |
2880 | */ | |
2881 | void | |
2882 | ultoe (lp, y) | |
2883 | unsigned long *lp; /* lp is the memory address of a long integer */ | |
2884 | unsigned EMUSHORT *y; /* y is the address of a short */ | |
2885 | { | |
2886 | unsigned EMUSHORT yi[NI]; | |
2887 | unsigned long ll; | |
2888 | int k; | |
2889 | ||
2890 | ecleaz (yi); | |
2891 | ll = *lp; | |
2892 | ||
2893 | /* move the long integer to ayi significand area */ | |
2894 | yi[M] = (unsigned EMUSHORT) (ll >> 16); | |
2895 | yi[M + 1] = (unsigned EMUSHORT) ll; | |
2896 | ||
2897 | yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */ | |
2898 | if ((k = enormlz (yi)) > NBITS)/* normalize the significand */ | |
2899 | ecleaz (yi); /* it was zero */ | |
2900 | else | |
2901 | yi[E] -= (unsigned EMUSHORT) k; /* subtract shift count from exponent */ | |
2902 | emovo (yi, y); /* output the answer */ | |
2903 | } | |
2904 | ||
2905 | ||
2906 | /* | |
2907 | ; Find long integer and fractional parts | |
2908 | ||
2909 | ; long i; | |
2910 | ; unsigned EMUSHORT x[NE], frac[NE]; | |
2911 | ; xifrac (x, &i, frac); | |
2912 | ||
2913 | The integer output has the sign of the input. The fraction is | |
2914 | the positive fractional part of abs (x). | |
2915 | */ | |
2916 | void | |
2917 | eifrac (x, i, frac) | |
2918 | unsigned EMUSHORT *x; | |
2919 | long *i; | |
2920 | unsigned EMUSHORT *frac; | |
2921 | { | |
2922 | unsigned EMUSHORT xi[NI]; | |
2923 | int k; | |
2924 | ||
2925 | emovi (x, xi); | |
2926 | k = (int) xi[E] - (EXONE - 1); | |
2927 | if (k <= 0) | |
2928 | { | |
2929 | /* if exponent <= 0, integer = 0 and real output is fraction */ | |
2930 | *i = 0L; | |
2931 | emovo (xi, frac); | |
2932 | return; | |
2933 | } | |
2934 | if (k > (HOST_BITS_PER_LONG - 1)) | |
2935 | { | |
2936 | /* | |
2937 | ; long integer overflow: output large integer | |
2938 | ; and correct fraction | |
2939 | */ | |
2940 | if (xi[0]) | |
2941 | *i = ((unsigned long) 1) << (HOST_BITS_PER_LONG - 1); | |
2942 | else | |
2943 | *i = (((unsigned long) 1) << (HOST_BITS_PER_LONG - 1)) - 1; | |
2944 | (void) eshift (xi, k); | |
2945 | pedwarn ("Overflow on truncation to integer"); | |
2946 | goto lab11; | |
2947 | } | |
2948 | ||
2949 | if (k > 16) | |
2950 | { | |
2951 | /* | |
2952 | ; shift more than 16 bits: shift up k-16, output the integer, | |
2953 | ; then complete the shift to get the fraction. | |
2954 | */ | |
2955 | k -= 16; | |
2956 | (void) eshift (xi, k); | |
2957 | ||
2958 | *i = (long) (((unsigned long) xi[M] << 16) | xi[M + 1]); | |
2959 | eshup6 (xi); | |
2960 | goto lab10; | |
2961 | } | |
2962 | ||
2963 | /* shift not more than 16 bits */ | |
2964 | (void) eshift (xi, k); | |
2965 | *i = (long) xi[M] & 0xffff; | |
2966 | ||
2967 | lab10: | |
2968 | ||
2969 | if (xi[0]) | |
2970 | *i = -(*i); | |
2971 | lab11: | |
2972 | ||
2973 | xi[0] = 0; | |
2974 | xi[E] = EXONE - 1; | |
2975 | xi[M] = 0; | |
2976 | if ((k = enormlz (xi)) > NBITS) | |
2977 | ecleaz (xi); | |
2978 | else | |
2979 | xi[E] -= (unsigned EMUSHORT) k; | |
2980 | ||
2981 | emovo (xi, frac); | |
2982 | } | |
2983 | ||
2984 | ||
2985 | /* | |
2986 | ; Find unsigned long integer and fractional parts | |
2987 | ||
2988 | ; unsigned long i; | |
2989 | ; unsigned EMUSHORT x[NE], frac[NE]; | |
2990 | ; xifrac (x, &i, frac); | |
2991 | ||
2992 | A negative e type input yields integer output = 0 | |
2993 | but correct fraction. | |
2994 | */ | |
2995 | void | |
2996 | euifrac (x, i, frac) | |
2997 | unsigned EMUSHORT *x; | |
2998 | long *i; | |
2999 | unsigned EMUSHORT *frac; | |
3000 | { | |
3001 | unsigned EMUSHORT xi[NI]; | |
3002 | int k; | |
3003 | ||
3004 | emovi (x, xi); | |
3005 | k = (int) xi[E] - (EXONE - 1); | |
3006 | if (k <= 0) | |
3007 | { | |
3008 | /* if exponent <= 0, integer = 0 and argument is fraction */ | |
3009 | *i = 0L; | |
3010 | emovo (xi, frac); | |
3011 | return; | |
3012 | } | |
3013 | if (k > 32) | |
3014 | { | |
3015 | /* | |
3016 | ; long integer overflow: output large integer | |
3017 | ; and correct fraction | |
3018 | */ | |
3019 | *i = ~(0L); | |
3020 | (void) eshift (xi, k); | |
3021 | pedwarn ("Overflow on truncation to unsigned integer"); | |
3022 | goto lab10; | |
3023 | } | |
3024 | ||
3025 | if (k > 16) | |
3026 | { | |
3027 | /* | |
3028 | ; shift more than 16 bits: shift up k-16, output the integer, | |
3029 | ; then complete the shift to get the fraction. | |
3030 | */ | |
3031 | k -= 16; | |
3032 | (void) eshift (xi, k); | |
3033 | ||
3034 | *i = (long) (((unsigned long) xi[M] << 16) | xi[M + 1]); | |
3035 | eshup6 (xi); | |
3036 | goto lab10; | |
3037 | } | |
3038 | ||
3039 | /* shift not more than 16 bits */ | |
3040 | (void) eshift (xi, k); | |
3041 | *i = (long) xi[M] & 0xffff; | |
3042 | ||
3043 | lab10: | |
3044 | ||
3045 | if (xi[0]) | |
3046 | *i = 0L; | |
3047 | ||
3048 | xi[0] = 0; | |
3049 | xi[E] = EXONE - 1; | |
3050 | xi[M] = 0; | |
3051 | if ((k = enormlz (xi)) > NBITS) | |
3052 | ecleaz (xi); | |
3053 | else | |
3054 | xi[E] -= (unsigned EMUSHORT) k; | |
3055 | ||
3056 | emovo (xi, frac); | |
3057 | } | |
3058 | ||
3059 | ||
3060 | ||
3061 | /* | |
3062 | ; Shift significand | |
3063 | ; | |
3064 | ; Shifts significand area up or down by the number of bits | |
3065 | ; given by the variable sc. | |
3066 | */ | |
3067 | int | |
3068 | eshift (x, sc) | |
3069 | unsigned EMUSHORT *x; | |
3070 | int sc; | |
3071 | { | |
3072 | unsigned EMUSHORT lost; | |
3073 | unsigned EMUSHORT *p; | |
3074 | ||
3075 | if (sc == 0) | |
3076 | return (0); | |
3077 | ||
3078 | lost = 0; | |
3079 | p = x + NI - 1; | |
3080 | ||
3081 | if (sc < 0) | |
3082 | { | |
3083 | sc = -sc; | |
3084 | while (sc >= 16) | |
3085 | { | |
3086 | lost |= *p; /* remember lost bits */ | |
3087 | eshdn6 (x); | |
3088 | sc -= 16; | |
3089 | } | |
3090 | ||
3091 | while (sc >= 8) | |
3092 | { | |
3093 | lost |= *p & 0xff; | |
3094 | eshdn8 (x); | |
3095 | sc -= 8; | |
3096 | } | |
3097 | ||
3098 | while (sc > 0) | |
3099 | { | |
3100 | lost |= *p & 1; | |
3101 | eshdn1 (x); | |
3102 | sc -= 1; | |
3103 | } | |
3104 | } | |
3105 | else | |
3106 | { | |
3107 | while (sc >= 16) | |
3108 | { | |
3109 | eshup6 (x); | |
3110 | sc -= 16; | |
3111 | } | |
3112 | ||
3113 | while (sc >= 8) | |
3114 | { | |
3115 | eshup8 (x); | |
3116 | sc -= 8; | |
3117 | } | |
3118 | ||
3119 | while (sc > 0) | |
3120 | { | |
3121 | eshup1 (x); | |
3122 | sc -= 1; | |
3123 | } | |
3124 | } | |
3125 | if (lost) | |
3126 | lost = 1; | |
3127 | return ((int) lost); | |
3128 | } | |
3129 | ||
3130 | ||
3131 | ||
3132 | /* | |
3133 | ; normalize | |
3134 | ; | |
3135 | ; Shift normalizes the significand area pointed to by argument | |
3136 | ; shift count (up = positive) is returned. | |
3137 | */ | |
3138 | int | |
3139 | enormlz (x) | |
3140 | unsigned EMUSHORT x[]; | |
3141 | { | |
3142 | register unsigned EMUSHORT *p; | |
3143 | int sc; | |
3144 | ||
3145 | sc = 0; | |
3146 | p = &x[M]; | |
3147 | if (*p != 0) | |
3148 | goto normdn; | |
3149 | ++p; | |
3150 | if (*p & 0x8000) | |
3151 | return (0); /* already normalized */ | |
3152 | while (*p == 0) | |
3153 | { | |
3154 | eshup6 (x); | |
3155 | sc += 16; | |
3156 | /* With guard word, there are NBITS+16 bits available. | |
3157 | * return true if all are zero. | |
3158 | */ | |
3159 | if (sc > NBITS) | |
3160 | return (sc); | |
3161 | } | |
3162 | /* see if high byte is zero */ | |
3163 | while ((*p & 0xff00) == 0) | |
3164 | { | |
3165 | eshup8 (x); | |
3166 | sc += 8; | |
3167 | } | |
3168 | /* now shift 1 bit at a time */ | |
3169 | while ((*p & 0x8000) == 0) | |
3170 | { | |
3171 | eshup1 (x); | |
3172 | sc += 1; | |
3173 | if (sc > NBITS) | |
3174 | { | |
3175 | mtherr ("enormlz", UNDERFLOW); | |
3176 | return (sc); | |
3177 | } | |
3178 | } | |
3179 | return (sc); | |
3180 | ||
3181 | /* Normalize by shifting down out of the high guard word | |
3182 | of the significand */ | |
3183 | normdn: | |
3184 | ||
3185 | if (*p & 0xff00) | |
3186 | { | |
3187 | eshdn8 (x); | |
3188 | sc -= 8; | |
3189 | } | |
3190 | while (*p != 0) | |
3191 | { | |
3192 | eshdn1 (x); | |
3193 | sc -= 1; | |
3194 | ||
3195 | if (sc < -NBITS) | |
3196 | { | |
3197 | mtherr ("enormlz", OVERFLOW); | |
3198 | return (sc); | |
3199 | } | |
3200 | } | |
3201 | return (sc); | |
3202 | } | |
3203 | ||
3204 | ||
3205 | ||
3206 | ||
3207 | /* Convert e type number to decimal format ASCII string. | |
3208 | * The constants are for 64 bit precision. | |
3209 | */ | |
3210 | ||
3211 | #define NTEN 12 | |
3212 | #define MAXP 4096 | |
3213 | ||
3214 | static unsigned EMUSHORT etens[NTEN + 1][NE] = | |
3215 | { | |
3216 | {0xc94c, 0x979a, 0x8a20, 0x5202, 0xc460, 0x7525,}, /* 10**4096 */ | |
3217 | {0xa74d, 0x5de4, 0xc53d, 0x3b5d, 0x9e8b, 0x5a92,}, /* 10**2048 */ | |
3218 | {0x650d, 0x0c17, 0x8175, 0x7586, 0xc976, 0x4d48,}, | |
3219 | {0xcc65, 0x91c6, 0xa60e, 0xa0ae, 0xe319, 0x46a3,}, | |
3220 | {0xddbc, 0xde8d, 0x9df9, 0xebfb, 0xaa7e, 0x4351,}, | |
3221 | {0xc66f, 0x8cdf, 0x80e9, 0x47c9, 0x93ba, 0x41a8,}, | |
3222 | {0x3cbf, 0xa6d5, 0xffcf, 0x1f49, 0xc278, 0x40d3,}, | |
3223 | {0xf020, 0xb59d, 0x2b70, 0xada8, 0x9dc5, 0x4069,}, | |
3224 | {0x0000, 0x0000, 0x0400, 0xc9bf, 0x8e1b, 0x4034,}, | |
3225 | {0x0000, 0x0000, 0x0000, 0x2000, 0xbebc, 0x4019,}, | |
3226 | {0x0000, 0x0000, 0x0000, 0x0000, 0x9c40, 0x400c,}, | |
3227 | {0x0000, 0x0000, 0x0000, 0x0000, 0xc800, 0x4005,}, | |
3228 | {0x0000, 0x0000, 0x0000, 0x0000, 0xa000, 0x4002,}, /* 10**1 */ | |
3229 | }; | |
3230 | ||
3231 | static unsigned EMUSHORT emtens[NTEN + 1][NE] = | |
3232 | { | |
3233 | {0x2de4, 0x9fde, 0xd2ce, 0x04c8, 0xa6dd, 0x0ad8,}, /* 10**-4096 */ | |
3234 | {0x4925, 0x2de4, 0x3436, 0x534f, 0xceae, 0x256b,}, /* 10**-2048 */ | |
3235 | {0x87a6, 0xc0bd, 0xda57, 0x82a5, 0xa2a6, 0x32b5,}, | |
3236 | {0x7133, 0xd21c, 0xdb23, 0xee32, 0x9049, 0x395a,}, | |
3237 | {0xfa91, 0x1939, 0x637a, 0x4325, 0xc031, 0x3cac,}, | |
3238 | {0xac7d, 0xe4a0, 0x64bc, 0x467c, 0xddd0, 0x3e55,}, | |
3239 | {0x3f24, 0xe9a5, 0xa539, 0xea27, 0xa87f, 0x3f2a,}, | |
3240 | {0x67de, 0x94ba, 0x4539, 0x1ead, 0xcfb1, 0x3f94,}, | |
3241 | {0x4c2f, 0xe15b, 0xc44d, 0x94be, 0xe695, 0x3fc9,}, | |
3242 | {0xfdc2, 0xcefc, 0x8461, 0x7711, 0xabcc, 0x3fe4,}, | |
3243 | {0xd3c3, 0x652b, 0xe219, 0x1758, 0xd1b7, 0x3ff1,}, | |
3244 | {0x3d71, 0xd70a, 0x70a3, 0x0a3d, 0xa3d7, 0x3ff8,}, | |
3245 | {0xcccd, 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0x3ffb,}, /* 10**-1 */ | |
3246 | }; | |
3247 | ||
3248 | void | |
3249 | e24toasc (x, string, ndigs) | |
3250 | unsigned EMUSHORT x[]; | |
3251 | char *string; | |
3252 | int ndigs; | |
3253 | { | |
3254 | unsigned EMUSHORT w[NI]; | |
3255 | ||
3256 | #ifdef INFINITY | |
3257 | #ifdef IBMPC | |
3258 | if ((x[1] & 0x7f80) == 0x7f80) | |
3259 | #else | |
3260 | if ((x[0] & 0x7f80) == 0x7f80) | |
3261 | #endif | |
3262 | { | |
3263 | #ifdef IBMPC | |
3264 | if (x[1] & 0x8000) | |
3265 | #else | |
3266 | if (x[0] & 0x8000) | |
3267 | #endif | |
3268 | sprintf (string, " -Infinity "); | |
3269 | else | |
3270 | sprintf (string, " Infinity "); | |
3271 | return; | |
3272 | } | |
3273 | #endif | |
3274 | e24toe (x, w); | |
3275 | etoasc (w, string, ndigs); | |
3276 | } | |
3277 | ||
3278 | ||
3279 | void | |
3280 | e53toasc (x, string, ndigs) | |
3281 | unsigned EMUSHORT x[]; | |
3282 | char *string; | |
3283 | int ndigs; | |
3284 | { | |
3285 | unsigned EMUSHORT w[NI]; | |
3286 | ||
3287 | #ifdef INFINITY | |
3288 | #ifdef IBMPC | |
3289 | if ((x[3] & 0x7ff0) == 0x7ff0) | |
3290 | #else | |
3291 | if ((x[0] & 0x7ff0) == 0x7ff0) | |
3292 | #endif | |
3293 | { | |
3294 | #ifdef IBMPC | |
3295 | if (x[3] & 0x8000) | |
3296 | #else | |
3297 | if (x[0] & 0x8000) | |
3298 | #endif | |
3299 | sprintf (string, " -Infinity "); | |
3300 | else | |
3301 | sprintf (string, " Infinity "); | |
3302 | return; | |
3303 | } | |
3304 | #endif | |
3305 | e53toe (x, w); | |
3306 | etoasc (w, string, ndigs); | |
3307 | } | |
3308 | ||
3309 | ||
3310 | void | |
3311 | e64toasc (x, string, ndigs) | |
3312 | unsigned EMUSHORT x[]; | |
3313 | char *string; | |
3314 | int ndigs; | |
3315 | { | |
3316 | unsigned EMUSHORT w[NI]; | |
3317 | ||
3318 | #ifdef INFINITY | |
3319 | #ifdef IBMPC | |
3320 | if ((x[4] & 0x7fff) == 0x7fff) | |
3321 | #else | |
3322 | if ((x[0] & 0x7fff) == 0x7fff) | |
3323 | #endif | |
3324 | { | |
3325 | #ifdef IBMPC | |
3326 | if (x[4] & 0x8000) | |
3327 | #else | |
3328 | if (x[0] & 0x8000) | |
3329 | #endif | |
3330 | sprintf (string, " -Infinity "); | |
3331 | else | |
3332 | sprintf (string, " Infinity "); | |
3333 | return; | |
3334 | } | |
3335 | #endif | |
3336 | e64toe (x, w); | |
3337 | etoasc (w, string, ndigs); | |
3338 | } | |
3339 | ||
3340 | ||
3341 | static char wstring[80]; /* working storage for ASCII output */ | |
3342 | ||
3343 | void | |
3344 | etoasc (x, string, ndigs) | |
3345 | unsigned EMUSHORT x[]; | |
3346 | char *string; | |
3347 | int ndigs; | |
3348 | { | |
3349 | EMUSHORT digit; | |
3350 | unsigned EMUSHORT y[NI], t[NI], u[NI], w[NI]; | |
3351 | unsigned EMUSHORT *p, *r, *ten; | |
3352 | unsigned EMUSHORT sign; | |
3353 | int i, j, k, expon, rndsav; | |
3354 | char *s, *ss; | |
3355 | unsigned EMUSHORT m; | |
3356 | ||
3357 | ss = string; | |
3358 | s = wstring; | |
3359 | while ((*s++ = *ss++) != '\0') | |
3360 | ; | |
3361 | rndsav = rndprc; | |
3362 | rndprc = NBITS; /* set to full precision */ | |
3363 | emov (x, y); /* retain external format */ | |
3364 | if (y[NE - 1] & 0x8000) | |
3365 | { | |
3366 | sign = 0xffff; | |
3367 | y[NE - 1] &= 0x7fff; | |
3368 | } | |
3369 | else | |
3370 | { | |
3371 | sign = 0; | |
3372 | } | |
3373 | expon = 0; | |
3374 | ten = &etens[NTEN][0]; | |
3375 | emov (eone, t); | |
3376 | /* Test for zero exponent */ | |
3377 | if (y[NE - 1] == 0) | |
3378 | { | |
3379 | for (k = 0; k < NE - 1; k++) | |
3380 | { | |
3381 | if (y[k] != 0) | |
3382 | goto tnzro; /* denormalized number */ | |
3383 | } | |
3384 | goto isone; /* legal all zeros */ | |
3385 | } | |
3386 | tnzro: | |
3387 | ||
3388 | /* Test for infinity. Don't bother with illegal infinities. | |
3389 | */ | |
3390 | if (y[NE - 1] == 0x7fff) | |
3391 | { | |
3392 | if (sign) | |
3393 | sprintf (wstring, " -Infinity "); | |
3394 | else | |
3395 | sprintf (wstring, " Infinity "); | |
3396 | goto bxit; | |
3397 | } | |
3398 | ||
3399 | /* Test for exponent nonzero but significand denormalized. | |
3400 | * This is an error condition. | |
3401 | */ | |
3402 | if ((y[NE - 1] != 0) && ((y[NE - 2] & 0x8000) == 0)) | |
3403 | { | |
3404 | mtherr ("etoasc", DOMAIN); | |
3405 | sprintf (wstring, "NaN"); | |
3406 | goto bxit; | |
3407 | } | |
3408 | ||
3409 | /* Compare to 1.0 */ | |
3410 | i = ecmp (eone, y); | |
3411 | if (i == 0) | |
3412 | goto isone; | |
3413 | ||
3414 | if (i < 0) | |
3415 | { /* Number is greater than 1 */ | |
3416 | /* Convert significand to an integer and strip trailing decimal zeros. */ | |
3417 | emov (y, u); | |
3418 | u[NE - 1] = EXONE + NBITS - 1; | |
3419 | ||
3420 | p = &etens[NTEN - 4][0]; | |
3421 | m = 16; | |
3422 | do | |
3423 | { | |
3424 | ediv (p, u, t); | |
3425 | efloor (t, w); | |
3426 | for (j = 0; j < NE - 1; j++) | |
3427 | { | |
3428 | if (t[j] != w[j]) | |
3429 | goto noint; | |
3430 | } | |
3431 | emov (t, u); | |
3432 | expon += (int) m; | |
3433 | noint: | |
3434 | p += NE; | |
3435 | m >>= 1; | |
3436 | } | |
3437 | while (m != 0); | |
3438 | ||
3439 | /* Rescale from integer significand */ | |
3440 | u[NE - 1] += y[NE - 1] - (unsigned int) (EXONE + NBITS - 1); | |
3441 | emov (u, y); | |
3442 | /* Find power of 10 */ | |
3443 | emov (eone, t); | |
3444 | m = MAXP; | |
3445 | p = &etens[0][0]; | |
3446 | while (ecmp (ten, u) <= 0) | |
3447 | { | |
3448 | if (ecmp (p, u) <= 0) | |
3449 | { | |
3450 | ediv (p, u, u); | |
3451 | emul (p, t, t); | |
3452 | expon += (int) m; | |
3453 | } | |
3454 | m >>= 1; | |
3455 | if (m == 0) | |
3456 | break; | |
3457 | p += NE; | |
3458 | } | |
3459 | } | |
3460 | else | |
3461 | { /* Number is less than 1.0 */ | |
3462 | /* Pad significand with trailing decimal zeros. */ | |
3463 | if (y[NE - 1] == 0) | |
3464 | { | |
3465 | while ((y[NE - 2] & 0x8000) == 0) | |
3466 | { | |
3467 | emul (ten, y, y); | |
3468 | expon -= 1; | |
3469 | } | |
3470 | } | |
3471 | else | |
3472 | { | |
3473 | emovi (y, w); | |
3474 | for (i = 0; i < NDEC + 1; i++) | |
3475 | { | |
3476 | if ((w[NI - 1] & 0x7) != 0) | |
3477 | break; | |
3478 | /* multiply by 10 */ | |
3479 | emovz (w, u); | |
3480 | eshdn1 (u); | |
3481 | eshdn1 (u); | |
3482 | eaddm (w, u); | |
3483 | u[1] += 3; | |
3484 | while (u[2] != 0) | |
3485 | { | |
3486 | eshdn1 (u); | |
3487 | u[1] += 1; | |
3488 | } | |
3489 | if (u[NI - 1] != 0) | |
3490 | break; | |
3491 | if (eone[NE - 1] <= u[1]) | |
3492 | break; | |
3493 | emovz (u, w); | |
3494 | expon -= 1; | |
3495 | } | |
3496 | emovo (w, y); | |
3497 | } | |
3498 | k = -MAXP; | |
3499 | p = &emtens[0][0]; | |
3500 | r = &etens[0][0]; | |
3501 | emov (y, w); | |
3502 | emov (eone, t); | |
3503 | while (ecmp (eone, w) > 0) | |
3504 | { | |
3505 | if (ecmp (p, w) >= 0) | |
3506 | { | |
3507 | emul (r, w, w); | |
3508 | emul (r, t, t); | |
3509 | expon += k; | |
3510 | } | |
3511 | k /= 2; | |
3512 | if (k == 0) | |
3513 | break; | |
3514 | p += NE; | |
3515 | r += NE; | |
3516 | } | |
3517 | ediv (t, eone, t); | |
3518 | } | |
3519 | isone: | |
3520 | /* Find the first (leading) digit. */ | |
3521 | emovi (t, w); | |
3522 | emovz (w, t); | |
3523 | emovi (y, w); | |
3524 | emovz (w, y); | |
3525 | eiremain (t, y); | |
3526 | digit = equot[NI - 1]; | |
3527 | while ((digit == 0) && (ecmp (y, ezero) != 0)) | |
3528 | { | |
3529 | eshup1 (y); | |
3530 | emovz (y, u); | |
3531 | eshup1 (u); | |
3532 | eshup1 (u); | |
3533 | eaddm (u, y); | |
3534 | eiremain (t, y); | |
3535 | digit = equot[NI - 1]; | |
3536 | expon -= 1; | |
3537 | } | |
3538 | s = wstring; | |
3539 | if (sign) | |
3540 | *s++ = '-'; | |
3541 | else | |
3542 | *s++ = ' '; | |
3543 | *s++ = (char) digit + '0'; | |
3544 | *s++ = '.'; | |
3545 | /* Examine number of digits requested by caller. */ | |
3546 | if (ndigs < 0) | |
3547 | ndigs = 0; | |
3548 | if (ndigs > NDEC) | |
3549 | ndigs = NDEC; | |
3550 | /* Generate digits after the decimal point. */ | |
3551 | for (k = 0; k <= ndigs; k++) | |
3552 | { | |
3553 | /* multiply current number by 10, without normalizing */ | |
3554 | eshup1 (y); | |
3555 | emovz (y, u); | |
3556 | eshup1 (u); | |
3557 | eshup1 (u); | |
3558 | eaddm (u, y); | |
3559 | eiremain (t, y); | |
3560 | *s++ = (char) equot[NI - 1] + '0'; | |
3561 | } | |
3562 | digit = equot[NI - 1]; | |
3563 | --s; | |
3564 | ss = s; | |
3565 | /* round off the ASCII string */ | |
3566 | if (digit > 4) | |
3567 | { | |
3568 | /* Test for critical rounding case in ASCII output. */ | |
3569 | if (digit == 5) | |
3570 | { | |
3571 | emovo (y, t); | |
3572 | if (ecmp (t, ezero) != 0) | |
3573 | goto roun; /* round to nearest */ | |
3574 | if ((*(s - 1) & 1) == 0) | |
3575 | goto doexp; /* round to even */ | |
3576 | } | |
3577 | /* Round up and propagate carry-outs */ | |
3578 | roun: | |
3579 | --s; | |
3580 | k = *s & 0x7f; | |
3581 | /* Carry out to most significant digit? */ | |
3582 | if (k == '.') | |
3583 | { | |
3584 | --s; | |
3585 | k = *s; | |
3586 | k += 1; | |
3587 | *s = (char) k; | |
3588 | /* Most significant digit carries to 10? */ | |
3589 | if (k > '9') | |
3590 | { | |
3591 | expon += 1; | |
3592 | *s = '1'; | |
3593 | } | |
3594 | goto doexp; | |
3595 | } | |
3596 | /* Round up and carry out from less significant digits */ | |
3597 | k += 1; | |
3598 | *s = (char) k; | |
3599 | if (k > '9') | |
3600 | { | |
3601 | *s = '0'; | |
3602 | goto roun; | |
3603 | } | |
3604 | } | |
3605 | doexp: | |
3606 | /* | |
3607 | if (expon >= 0) | |
3608 | sprintf (ss, "e+%d", expon); | |
3609 | else | |
3610 | sprintf (ss, "e%d", expon); | |
3611 | */ | |
3612 | sprintf (ss, "e%d", expon); | |
3613 | bxit: | |
3614 | rndprc = rndsav; | |
3615 | /* copy out the working string */ | |
3616 | s = string; | |
3617 | ss = wstring; | |
3618 | while (*ss == ' ') /* strip possible leading space */ | |
3619 | ++ss; | |
3620 | while ((*s++ = *ss++) != '\0') | |
3621 | ; | |
3622 | } | |
3623 | ||
3624 | ||
3625 | ||
3626 | ||
3627 | /* | |
3628 | ; ASCTOQ | |
3629 | ; ASCTOQ.MAC LATEST REV: 11 JAN 84 | |
3630 | ; SLM, 3 JAN 78 | |
3631 | ; | |
3632 | ; Convert ASCII string to quadruple precision floating point | |
3633 | ; | |
3634 | ; Numeric input is free field decimal number | |
3635 | ; with max of 15 digits with or without | |
3636 | ; decimal point entered as ASCII from teletype. | |
3637 | ; Entering E after the number followed by a second | |
3638 | ; number causes the second number to be interpreted | |
3639 | ; as a power of 10 to be multiplied by the first number | |
3640 | ; (i.e., "scientific" notation). | |
3641 | ; | |
3642 | ; Usage: | |
3643 | ; asctoq (string, q); | |
3644 | */ | |
3645 | ||
3646 | /* ASCII to single */ | |
3647 | void | |
3648 | asctoe24 (s, y) | |
3649 | char *s; | |
3650 | unsigned EMUSHORT *y; | |
3651 | { | |
3652 | asctoeg (s, y, 24); | |
3653 | } | |
3654 | ||
3655 | ||
3656 | /* ASCII to double */ | |
3657 | void | |
3658 | asctoe53 (s, y) | |
3659 | char *s; | |
3660 | unsigned EMUSHORT *y; | |
3661 | { | |
3662 | #ifdef DEC | |
3663 | asctoeg (s, y, 56); | |
3664 | #else | |
3665 | asctoeg (s, y, 53); | |
3666 | #endif | |
3667 | } | |
3668 | ||
3669 | ||
3670 | /* ASCII to long double */ | |
3671 | void | |
3672 | asctoe64 (s, y) | |
3673 | char *s; | |
3674 | unsigned EMUSHORT *y; | |
3675 | { | |
3676 | asctoeg (s, y, 64); | |
3677 | } | |
3678 | ||
3679 | /* ASCII to super double */ | |
3680 | void | |
3681 | asctoe (s, y) | |
3682 | char *s; | |
3683 | unsigned EMUSHORT *y; | |
3684 | { | |
3685 | asctoeg (s, y, NBITS); | |
3686 | } | |
3687 | ||
3688 | /* Space to make a copy of the input string: */ | |
3689 | static char lstr[82]; | |
3690 | ||
3691 | void | |
3692 | asctoeg (ss, y, oprec) | |
3693 | char *ss; | |
3694 | unsigned EMUSHORT *y; | |
3695 | int oprec; | |
3696 | { | |
3697 | unsigned EMUSHORT yy[NI], xt[NI], tt[NI]; | |
3698 | int esign, decflg, sgnflg, nexp, exp, prec, lost; | |
3699 | int k, trail, c, rndsav; | |
3700 | EMULONG lexp; | |
3701 | unsigned EMUSHORT nsign, *p; | |
3702 | char *sp, *s; | |
3703 | ||
3704 | /* Copy the input string. */ | |
3705 | s = ss; | |
3706 | while (*s == ' ') /* skip leading spaces */ | |
3707 | ++s; | |
3708 | sp = lstr; | |
3709 | for (k = 0; k < 79; k++) | |
3710 | { | |
3711 | if ((*sp++ = *s++) == '\0') | |
3712 | break; | |
3713 | } | |
3714 | *sp = '\0'; | |
3715 | s = lstr; | |
3716 | ||
3717 | rndsav = rndprc; | |
3718 | rndprc = NBITS; /* Set to full precision */ | |
3719 | lost = 0; | |
3720 | nsign = 0; | |
3721 | decflg = 0; | |
3722 | sgnflg = 0; | |
3723 | nexp = 0; | |
3724 | exp = 0; | |
3725 | prec = 0; | |
3726 | ecleaz (yy); | |
3727 | trail = 0; | |
3728 | ||
3729 | nxtcom: | |
3730 | k = *s - '0'; | |
3731 | if ((k >= 0) && (k <= 9)) | |
3732 | { | |
3733 | /* Ignore leading zeros */ | |
3734 | if ((prec == 0) && (decflg == 0) && (k == 0)) | |
3735 | goto donchr; | |
3736 | /* Identify and strip trailing zeros after the decimal point. */ | |
3737 | if ((trail == 0) && (decflg != 0)) | |
3738 | { | |
3739 | sp = s; | |
3740 | while ((*sp >= '0') && (*sp <= '9')) | |
3741 | ++sp; | |
3742 | /* Check for syntax error */ | |
3743 | c = *sp & 0x7f; | |
3744 | if ((c != 'e') && (c != 'E') && (c != '\0') | |
3745 | && (c != '\n') && (c != '\r') && (c != ' ') | |
3746 | && (c != ',')) | |
3747 | goto error; | |
3748 | --sp; | |
3749 | while (*sp == '0') | |
3750 | *sp-- = 'z'; | |
3751 | trail = 1; | |
3752 | if (*s == 'z') | |
3753 | goto donchr; | |
3754 | } | |
3755 | /* If enough digits were given to more than fill up the yy register, | |
3756 | * continuing until overflow into the high guard word yy[2] | |
3757 | * guarantees that there will be a roundoff bit at the top | |
3758 | * of the low guard word after normalization. | |
3759 | */ | |
3760 | if (yy[2] == 0) | |
3761 | { | |
3762 | if (decflg) | |
3763 | nexp += 1; /* count digits after decimal point */ | |
3764 | eshup1 (yy); /* multiply current number by 10 */ | |
3765 | emovz (yy, xt); | |
3766 | eshup1 (xt); | |
3767 | eshup1 (xt); | |
3768 | eaddm (xt, yy); | |
3769 | ecleaz (xt); | |
3770 | xt[NI - 2] = (unsigned EMUSHORT) k; | |
3771 | eaddm (xt, yy); | |
3772 | } | |
3773 | else | |
3774 | { | |
3775 | lost |= k; | |
3776 | } | |
3777 | prec += 1; | |
3778 | goto donchr; | |
3779 | } | |
3780 | ||
3781 | switch (*s) | |
3782 | { | |
3783 | case 'z': | |
3784 | break; | |
3785 | case 'E': | |
3786 | case 'e': | |
3787 | goto expnt; | |
3788 | case '.': /* decimal point */ | |
3789 | if (decflg) | |
3790 | goto error; | |
3791 | ++decflg; | |
3792 | break; | |
3793 | case '-': | |
3794 | nsign = 0xffff; | |
3795 | if (sgnflg) | |
3796 | goto error; | |
3797 | ++sgnflg; | |
3798 | break; | |
3799 | case '+': | |
3800 | if (sgnflg) | |
3801 | goto error; | |
3802 | ++sgnflg; | |
3803 | break; | |
3804 | case ',': | |
3805 | case ' ': | |
3806 | case '\0': | |
3807 | case '\n': | |
3808 | case '\r': | |
3809 | goto daldone; | |
3810 | case 'i': | |
3811 | case 'I': | |
3812 | ecleaz (yy); | |
3813 | yy[E] = 0x7fff; /* infinity */ | |
3814 | goto aexit; | |
3815 | default: | |
3816 | error: | |
3817 | mtherr ("asctoe", DOMAIN); | |
3818 | eclear (y); | |
3819 | goto aexit; | |
3820 | } | |
3821 | donchr: | |
3822 | ++s; | |
3823 | goto nxtcom; | |
3824 | ||
3825 | /* Exponent interpretation */ | |
3826 | expnt: | |
3827 | ||
3828 | esign = 1; | |
3829 | exp = 0; | |
3830 | ++s; | |
3831 | /* check for + or - */ | |
3832 | if (*s == '-') | |
3833 | { | |
3834 | esign = -1; | |
3835 | ++s; | |
3836 | } | |
3837 | if (*s == '+') | |
3838 | ++s; | |
3839 | while ((*s >= '0') && (*s <= '9')) | |
3840 | { | |
3841 | exp *= 10; | |
3842 | exp += *s++ - '0'; | |
3843 | } | |
3844 | if (esign < 0) | |
3845 | exp = -exp; | |
3846 | ||
3847 | daldone: | |
3848 | nexp = exp - nexp; | |
3849 | /* Pad trailing zeros to minimize power of 10, per IEEE spec. */ | |
3850 | while ((nexp > 0) && (yy[2] == 0)) | |
3851 | { | |
3852 | emovz (yy, xt); | |
3853 | eshup1 (xt); | |
3854 | eshup1 (xt); | |
3855 | eaddm (yy, xt); | |
3856 | eshup1 (xt); | |
3857 | if (xt[2] != 0) | |
3858 | break; | |
3859 | nexp -= 1; | |
3860 | emovz (xt, yy); | |
3861 | } | |
3862 | if ((k = enormlz (yy)) > NBITS) | |
3863 | { | |
3864 | ecleaz (yy); | |
3865 | goto aexit; | |
3866 | } | |
3867 | lexp = (EXONE - 1 + NBITS) - k; | |
3868 | emdnorm (yy, lost, 0, lexp, 64); | |
3869 | /* convert to external format */ | |
3870 | ||
3871 | ||
3872 | /* Multiply by 10**nexp. If precision is 64 bits, | |
3873 | * the maximum relative error incurred in forming 10**n | |
3874 | * for 0 <= n <= 324 is 8.2e-20, at 10**180. | |
3875 | * For 0 <= n <= 999, the peak relative error is 1.4e-19 at 10**947. | |
3876 | * For 0 >= n >= -999, it is -1.55e-19 at 10**-435. | |
3877 | */ | |
3878 | lexp = yy[E]; | |
3879 | if (nexp == 0) | |
3880 | { | |
3881 | k = 0; | |
3882 | goto expdon; | |
3883 | } | |
3884 | esign = 1; | |
3885 | if (nexp < 0) | |
3886 | { | |
3887 | nexp = -nexp; | |
3888 | esign = -1; | |
3889 | if (nexp > 4096) | |
3890 | { /* Punt. Can't handle this without 2 divides. */ | |
3891 | emovi (etens[0], tt); | |
3892 | lexp -= tt[E]; | |
3893 | k = edivm (tt, yy); | |
3894 | lexp += EXONE; | |
3895 | nexp -= 4096; | |
3896 | } | |
3897 | } | |
3898 | p = &etens[NTEN][0]; | |
3899 | emov (eone, xt); | |
3900 | exp = 1; | |
3901 | do | |
3902 | { | |
3903 | if (exp & nexp) | |
3904 | emul (p, xt, xt); | |
3905 | p -= NE; | |
3906 | exp = exp + exp; | |
3907 | } | |
3908 | while (exp <= MAXP); | |
3909 | ||
3910 | emovi (xt, tt); | |
3911 | if (esign < 0) | |
3912 | { | |
3913 | lexp -= tt[E]; | |
3914 | k = edivm (tt, yy); | |
3915 | lexp += EXONE; | |
3916 | } | |
3917 | else | |
3918 | { | |
3919 | lexp += tt[E]; | |
3920 | k = emulm (tt, yy); | |
3921 | lexp -= EXONE - 1; | |
3922 | } | |
3923 | ||
3924 | expdon: | |
3925 | ||
3926 | /* Round and convert directly to the destination type */ | |
3927 | if (oprec == 53) | |
3928 | lexp -= EXONE - 0x3ff; | |
3929 | else if (oprec == 24) | |
3930 | lexp -= EXONE - 0177; | |
3931 | #ifdef DEC | |
3932 | else if (oprec == 56) | |
3933 | lexp -= EXONE - 0201; | |
3934 | #endif | |
3935 | rndprc = oprec; | |
3936 | emdnorm (yy, k, 0, lexp, 64); | |
3937 | ||
3938 | aexit: | |
3939 | ||
3940 | rndprc = rndsav; | |
3941 | yy[0] = nsign; | |
3942 | switch (oprec) | |
3943 | { | |
3944 | #ifdef DEC | |
3945 | case 56: | |
3946 | todec (yy, y); /* see etodec.c */ | |
3947 | break; | |
3948 | #endif | |
3949 | case 53: | |
3950 | toe53 (yy, y); | |
3951 | break; | |
3952 | case 24: | |
3953 | toe24 (yy, y); | |
3954 | break; | |
3955 | case 64: | |
3956 | toe64 (yy, y); | |
3957 | break; | |
3958 | case NBITS: | |
3959 | emovo (yy, y); | |
3960 | break; | |
3961 | } | |
3962 | } | |
3963 | ||
3964 | ||
3965 | ||
3966 | /* y = largest integer not greater than x | |
3967 | * (truncated toward minus infinity) | |
3968 | * | |
3969 | * unsigned EMUSHORT x[NE], y[NE] | |
3970 | * | |
3971 | * efloor (x, y); | |
3972 | */ | |
3973 | static unsigned EMUSHORT bmask[] = | |
3974 | { | |
3975 | 0xffff, | |
3976 | 0xfffe, | |
3977 | 0xfffc, | |
3978 | 0xfff8, | |
3979 | 0xfff0, | |
3980 | 0xffe0, | |
3981 | 0xffc0, | |
3982 | 0xff80, | |
3983 | 0xff00, | |
3984 | 0xfe00, | |
3985 | 0xfc00, | |
3986 | 0xf800, | |
3987 | 0xf000, | |
3988 | 0xe000, | |
3989 | 0xc000, | |
3990 | 0x8000, | |
3991 | 0x0000, | |
3992 | }; | |
3993 | ||
3994 | void | |
3995 | efloor (x, y) | |
3996 | unsigned EMUSHORT x[], y[]; | |
3997 | { | |
3998 | register unsigned EMUSHORT *p; | |
3999 | int e, expon, i; | |
4000 | unsigned EMUSHORT f[NE]; | |
4001 | ||
4002 | emov (x, f); /* leave in external format */ | |
4003 | expon = (int) f[NE - 1]; | |
4004 | e = (expon & 0x7fff) - (EXONE - 1); | |
4005 | if (e <= 0) | |
4006 | { | |
4007 | eclear (y); | |
4008 | goto isitneg; | |
4009 | } | |
4010 | /* number of bits to clear out */ | |
4011 | e = NBITS - e; | |
4012 | emov (f, y); | |
4013 | if (e <= 0) | |
4014 | return; | |
4015 | ||
4016 | p = &y[0]; | |
4017 | while (e >= 16) | |
4018 | { | |
4019 | *p++ = 0; | |
4020 | e -= 16; | |
4021 | } | |
4022 | /* clear the remaining bits */ | |
4023 | *p &= bmask[e]; | |
4024 | /* truncate negatives toward minus infinity */ | |
4025 | isitneg: | |
4026 | ||
4027 | if ((unsigned EMUSHORT) expon & (unsigned EMUSHORT) 0x8000) | |
4028 | { | |
4029 | for (i = 0; i < NE - 1; i++) | |
4030 | { | |
4031 | if (f[i] != y[i]) | |
4032 | { | |
4033 | esub (eone, y, y); | |
4034 | break; | |
4035 | } | |
4036 | } | |
4037 | } | |
4038 | } | |
4039 | ||
4040 | ||
4041 | /* unsigned EMUSHORT x[], s[]; | |
4042 | * int *exp; | |
4043 | * | |
4044 | * efrexp (x, exp, s); | |
4045 | * | |
4046 | * Returns s and exp such that s * 2**exp = x and .5 <= s < 1. | |
4047 | * For example, 1.1 = 0.55 * 2**1 | |
4048 | * Handles denormalized numbers properly using long integer exp. | |
4049 | */ | |
4050 | void | |
4051 | efrexp (x, exp, s) | |
4052 | unsigned EMUSHORT x[]; | |
4053 | int *exp; | |
4054 | unsigned EMUSHORT s[]; | |
4055 | { | |
4056 | unsigned EMUSHORT xi[NI]; | |
4057 | EMULONG li; | |
4058 | ||
4059 | emovi (x, xi); | |
4060 | li = (EMULONG) ((EMUSHORT) xi[1]); | |
4061 | ||
4062 | if (li == 0) | |
4063 | { | |
4064 | li -= enormlz (xi); | |
4065 | } | |
4066 | xi[1] = 0x3ffe; | |
4067 | emovo (xi, s); | |
4068 | *exp = (int) (li - 0x3ffe); | |
4069 | } | |
4070 | ||
4071 | ||
4072 | ||
4073 | /* unsigned EMUSHORT x[], y[]; | |
4074 | * long pwr2; | |
4075 | * | |
4076 | * eldexp (x, pwr2, y); | |
4077 | * | |
4078 | * Returns y = x * 2**pwr2. | |
4079 | */ | |
4080 | void | |
4081 | eldexp (x, pwr2, y) | |
4082 | unsigned EMUSHORT x[]; | |
4083 | int pwr2; | |
4084 | unsigned EMUSHORT y[]; | |
4085 | { | |
4086 | unsigned EMUSHORT xi[NI]; | |
4087 | EMULONG li; | |
4088 | int i; | |
4089 | ||
4090 | emovi (x, xi); | |
4091 | li = xi[1]; | |
4092 | li += pwr2; | |
4093 | i = 0; | |
4094 | emdnorm (xi, i, i, li, 64); | |
4095 | emovo (xi, y); | |
4096 | } | |
4097 | ||
4098 | ||
4099 | /* c = remainder after dividing b by a | |
4100 | * Least significant integer quotient bits left in equot[]. | |
4101 | */ | |
4102 | void | |
4103 | eremain (a, b, c) | |
4104 | unsigned EMUSHORT a[], b[], c[]; | |
4105 | { | |
4106 | unsigned EMUSHORT den[NI], num[NI]; | |
4107 | ||
4108 | if (ecmp (a, ezero) == 0) | |
4109 | { | |
4110 | mtherr ("eremain", SING); | |
4111 | eclear (c); | |
4112 | return; | |
4113 | } | |
4114 | emovi (a, den); | |
4115 | emovi (b, num); | |
4116 | eiremain (den, num); | |
4117 | /* Sign of remainder = sign of quotient */ | |
4118 | if (a[0] == b[0]) | |
4119 | num[0] = 0; | |
4120 | else | |
4121 | num[0] = 0xffff; | |
4122 | emovo (num, c); | |
4123 | } | |
4124 | ||
4125 | void | |
4126 | eiremain (den, num) | |
4127 | unsigned EMUSHORT den[], num[]; | |
4128 | { | |
4129 | EMULONG ld, ln; | |
4130 | unsigned EMUSHORT j; | |
4131 | ||
4132 | ld = den[E]; | |
4133 | ld -= enormlz (den); | |
4134 | ln = num[E]; | |
4135 | ln -= enormlz (num); | |
4136 | ecleaz (equot); | |
4137 | while (ln >= ld) | |
4138 | { | |
4139 | if (ecmpm (den, num) <= 0) | |
4140 | { | |
4141 | esubm (den, num); | |
4142 | j = 1; | |
4143 | } | |
4144 | else | |
4145 | { | |
4146 | j = 0; | |
4147 | } | |
4148 | eshup1 (equot); | |
4149 | equot[NI - 1] |= j; | |
4150 | eshup1 (num); | |
4151 | ln -= 1; | |
4152 | } | |
4153 | emdnorm (num, 0, 0, ln, 0); | |
4154 | } | |
4155 | ||
4156 | /* mtherr.c | |
4157 | * | |
4158 | * Library common error handling routine | |
4159 | * | |
4160 | * | |
4161 | * | |
4162 | * SYNOPSIS: | |
4163 | * | |
4164 | * char *fctnam; | |
4165 | * int code; | |
4166 | * void mtherr (); | |
4167 | * | |
4168 | * mtherr (fctnam, code); | |
4169 | * | |
4170 | * | |
4171 | * | |
4172 | * DESCRIPTION: | |
4173 | * | |
4174 | * This routine may be called to report one of the following | |
4175 | * error conditions (in the include file mconf.h). | |
4176 | * | |
4177 | * Mnemonic Value Significance | |
4178 | * | |
4179 | * DOMAIN 1 argument domain error | |
4180 | * SING 2 function singularity | |
4181 | * OVERFLOW 3 overflow range error | |
4182 | * UNDERFLOW 4 underflow range error | |
4183 | * TLOSS 5 total loss of precision | |
4184 | * PLOSS 6 partial loss of precision | |
4185 | * EDOM 33 Unix domain error code | |
4186 | * ERANGE 34 Unix range error code | |
4187 | * | |
4188 | * The default version of the file prints the function name, | |
4189 | * passed to it by the pointer fctnam, followed by the | |
4190 | * error condition. The display is directed to the standard | |
4191 | * output device. The routine then returns to the calling | |
4192 | * program. Users may wish to modify the program to abort by | |
4193 | * calling exit under severe error conditions such as domain | |
4194 | * errors. | |
4195 | * | |
4196 | * Since all error conditions pass control to this function, | |
4197 | * the display may be easily changed, eliminated, or directed | |
4198 | * to an error logging device. | |
4199 | * | |
4200 | * SEE ALSO: | |
4201 | * | |
4202 | * mconf.h | |
4203 | * | |
4204 | */ | |
4205 | \f | |
4206 | /* | |
4207 | Cephes Math Library Release 2.0: April, 1987 | |
4208 | Copyright 1984, 1987 by Stephen L. Moshier | |
4209 | Direct inquiries to 30 Frost Street, Cambridge, MA 02140 | |
4210 | */ | |
4211 | ||
4212 | /* include "mconf.h" */ | |
4213 | ||
4214 | /* Notice: the order of appearance of the following | |
4215 | * messages is bound to the error codes defined | |
4216 | * in mconf.h. | |
4217 | */ | |
4218 | static char *ermsg[7] = | |
4219 | { | |
4220 | "unknown", /* error code 0 */ | |
4221 | "domain", /* error code 1 */ | |
4222 | "singularity", /* et seq. */ | |
4223 | "overflow", | |
4224 | "underflow", | |
4225 | "total loss of precision", | |
4226 | "partial loss of precision" | |
4227 | }; | |
4228 | ||
4229 | int merror = 0; | |
4230 | extern int merror; | |
4231 | ||
4232 | void | |
4233 | mtherr (name, code) | |
4234 | char *name; | |
4235 | int code; | |
4236 | { | |
4237 | char errstr[80]; | |
4238 | ||
4239 | /* Display string passed by calling program, | |
4240 | * which is supposed to be the name of the | |
4241 | * function in which the error occurred. | |
4242 | */ | |
4243 | ||
4244 | /* Display error message defined | |
4245 | * by the code argument. | |
4246 | */ | |
4247 | if ((code <= 0) || (code >= 6)) | |
4248 | code = 0; | |
4249 | sprintf (errstr, "\n%s %s error\n", name, ermsg[code]); | |
4250 | pedwarn (errstr); | |
4251 | /* Set global error message word */ | |
4252 | merror = code + 1; | |
4253 | ||
4254 | /* Return to calling | |
4255 | * program | |
4256 | */ | |
4257 | } | |
4258 | ||
4259 | /* Here is etodec.c . | |
4260 | * | |
4261 | */ | |
4262 | ||
4263 | /* | |
4264 | ; convert DEC double precision to e type | |
4265 | ; double d; | |
4266 | ; EMUSHORT e[NE]; | |
4267 | ; dectoe (&d, e); | |
4268 | */ | |
4269 | void | |
4270 | dectoe (d, e) | |
4271 | unsigned EMUSHORT *d; | |
4272 | unsigned EMUSHORT *e; | |
4273 | { | |
4274 | unsigned EMUSHORT y[NI]; | |
4275 | register unsigned EMUSHORT r, *p; | |
4276 | ||
4277 | ecleaz (y); /* start with a zero */ | |
4278 | p = y; /* point to our number */ | |
4279 | r = *d; /* get DEC exponent word */ | |
4280 | if (*d & (unsigned int) 0x8000) | |
4281 | *p = 0xffff; /* fill in our sign */ | |
4282 | ++p; /* bump pointer to our exponent word */ | |
4283 | r &= 0x7fff; /* strip the sign bit */ | |
4284 | if (r == 0) /* answer = 0 if high order DEC word = 0 */ | |
4285 | goto done; | |
4286 | ||
4287 | ||
4288 | r >>= 7; /* shift exponent word down 7 bits */ | |
4289 | r += EXONE - 0201; /* subtract DEC exponent offset */ | |
4290 | /* add our e type exponent offset */ | |
4291 | *p++ = r; /* to form our exponent */ | |
4292 | ||
4293 | r = *d++; /* now do the high order mantissa */ | |
4294 | r &= 0177; /* strip off the DEC exponent and sign bits */ | |
4295 | r |= 0200; /* the DEC understood high order mantissa bit */ | |
4296 | *p++ = r; /* put result in our high guard word */ | |
4297 | ||
4298 | *p++ = *d++; /* fill in the rest of our mantissa */ | |
4299 | *p++ = *d++; | |
4300 | *p = *d; | |
4301 | ||
4302 | eshdn8 (y); /* shift our mantissa down 8 bits */ | |
4303 | done: | |
4304 | emovo (y, e); | |
4305 | } | |
4306 | ||
4307 | ||
4308 | ||
4309 | /* | |
4310 | ; convert e type to DEC double precision | |
4311 | ; double d; | |
4312 | ; EMUSHORT e[NE]; | |
4313 | ; etodec (e, &d); | |
4314 | */ | |
4315 | #if 0 | |
4316 | static unsigned EMUSHORT decbit[NI] = {0, 0, 0, 0, 0, 0, 0200, 0}; | |
4317 | ||
4318 | void | |
4319 | etodec (x, d) | |
4320 | unsigned EMUSHORT *x, *d; | |
4321 | { | |
4322 | unsigned EMUSHORT xi[NI]; | |
4323 | register unsigned EMUSHORT r; | |
4324 | int i, j; | |
4325 | ||
4326 | emovi (x, xi); | |
4327 | *d = 0; | |
4328 | if (xi[0] != 0) | |
4329 | *d = 0100000; | |
4330 | r = xi[E]; | |
4331 | if (r < (EXONE - 128)) | |
4332 | goto zout; | |
4333 | i = xi[M + 4]; | |
4334 | if ((i & 0200) != 0) | |
4335 | { | |
4336 | if ((i & 0377) == 0200) | |
4337 | { | |
4338 | if ((i & 0400) != 0) | |
4339 | { | |
4340 | /* check all less significant bits */ | |
4341 | for (j = M + 5; j < NI; j++) | |
4342 | { | |
4343 | if (xi[j] != 0) | |
4344 | goto yesrnd; | |
4345 | } | |
4346 | } | |
4347 | goto nornd; | |
4348 | } | |
4349 | yesrnd: | |
4350 | eaddm (decbit, xi); | |
4351 | r -= enormlz (xi); | |
4352 | } | |
4353 | ||
4354 | nornd: | |
4355 | ||
4356 | r -= EXONE; | |
4357 | r += 0201; | |
4358 | if (r < 0) | |
4359 | { | |
4360 | zout: | |
4361 | *d++ = 0; | |
4362 | *d++ = 0; | |
4363 | *d++ = 0; | |
4364 | *d++ = 0; | |
4365 | return; | |
4366 | } | |
4367 | if (r >= 0377) | |
4368 | { | |
4369 | *d++ = 077777; | |
4370 | *d++ = -1; | |
4371 | *d++ = -1; | |
4372 | *d++ = -1; | |
4373 | return; | |
4374 | } | |
4375 | r &= 0377; | |
4376 | r <<= 7; | |
4377 | eshup8 (xi); | |
4378 | xi[M] &= 0177; | |
4379 | r |= xi[M]; | |
4380 | *d++ |= r; | |
4381 | *d++ = xi[M + 1]; | |
4382 | *d++ = xi[M + 2]; | |
4383 | *d++ = xi[M + 3]; | |
4384 | } | |
4385 | ||
4386 | #else | |
4387 | ||
4388 | void | |
4389 | etodec (x, d) | |
4390 | unsigned EMUSHORT *x, *d; | |
4391 | { | |
4392 | unsigned EMUSHORT xi[NI]; | |
4393 | EMULONG exp; | |
4394 | int rndsav; | |
4395 | ||
4396 | emovi (x, xi); | |
4397 | exp = (EMULONG) xi[E] - (EXONE - 0201); /* adjust exponent for offsets */ | |
4398 | /* round off to nearest or even */ | |
4399 | rndsav = rndprc; | |
4400 | rndprc = 56; | |
4401 | emdnorm (xi, 0, 0, exp, 64); | |
4402 | rndprc = rndsav; | |
4403 | todec (xi, d); | |
4404 | } | |
4405 | ||
4406 | void | |
4407 | todec (x, y) | |
4408 | unsigned EMUSHORT *x, *y; | |
4409 | { | |
4410 | unsigned EMUSHORT i; | |
4411 | unsigned EMUSHORT *p; | |
4412 | ||
4413 | p = x; | |
4414 | *y = 0; | |
4415 | if (*p++) | |
4416 | *y = 0100000; | |
4417 | i = *p++; | |
4418 | if (i == 0) | |
4419 | { | |
4420 | *y++ = 0; | |
4421 | *y++ = 0; | |
4422 | *y++ = 0; | |
4423 | *y++ = 0; | |
4424 | return; | |
4425 | } | |
4426 | if (i > 0377) | |
4427 | { | |
4428 | *y++ |= 077777; | |
4429 | *y++ = 0xffff; | |
4430 | *y++ = 0xffff; | |
4431 | *y++ = 0xffff; | |
4432 | return; | |
4433 | } | |
4434 | i &= 0377; | |
4435 | i <<= 7; | |
4436 | eshup8 (x); | |
4437 | x[M] &= 0177; | |
4438 | i |= x[M]; | |
4439 | *y++ |= i; | |
4440 | *y++ = x[M + 1]; | |
4441 | *y++ = x[M + 2]; | |
4442 | *y++ = x[M + 3]; | |
4443 | } | |
4444 | ||
4445 | #endif /* not 0 */ | |
4446 | ||
4447 | #endif /* EMU_NON_COMPILE not defined */ |