1 /* Copyright (C) 2007-2023 Free Software Foundation, Inc.
2
3 This file is part of GCC.
4
5 GCC is free software; you can redistribute it and/or modify it under
6 the terms of the GNU General Public License as published by the Free
7 Software Foundation; either version 3, or (at your option) any later
8 version.
9
10 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
11 WARRANTY; without even the implied warranty of MERCHANTABILITY or
12 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
13 for more details.
14
15 Under Section 7 of GPL version 3, you are granted additional
16 permissions described in the GCC Runtime Library Exception, version
17 3.1, as published by the Free Software Foundation.
18
19 You should have received a copy of the GNU General Public License and
20 a copy of the GCC Runtime Library Exception along with this program;
21 see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
22 <http://www.gnu.org/licenses/>. */
23
24 #include "bid_internal.h"
25
26 /*****************************************************************************
27 *
28 * BID128 non-computational functions:
29 * - bid128_isSigned
30 * - bid128_isNormal
31 * - bid128_isSubnormal
32 * - bid128_isFinite
33 * - bid128_isZero
34 * - bid128_isInf
35 * - bid128_isSignaling
36 * - bid128_isCanonical
37 * - bid128_isNaN
38 * - bid128_copy
39 * - bid128_negate
40 * - bid128_abs
41 * - bid128_copySign
42 * - bid128_class
43 * - bid128_totalOrder
44 * - bid128_totalOrderMag
45 * - bid128_sameQuantum
46 * - bid128_radix
47 ****************************************************************************/
48
49 #if DECIMAL_CALL_BY_REFERENCE
50 void
51 bid128_isSigned (int *pres,
52 UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
53 UINT128 x = *px;
54 #else
55 int
56 bid128_isSigned (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
57 #endif
58 int res;
59
60 res = ((x.w[HIGH_128W] & MASK_SIGN) == MASK_SIGN);
61 BID_RETURN (res);
62 }
63
64 // return 1 iff x is not zero, nor NaN nor subnormal nor infinity
65 #if DECIMAL_CALL_BY_REFERENCE
66 void
67 bid128_isNormal (int *pres,
68 UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
69 UINT128 x = *px;
70 #else
71 int
72 bid128_isNormal (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
73 #endif
74 int res;
75 UINT64 x_exp, C1_hi, C1_lo;
76 BID_UI64DOUBLE tmp1;
77 int exp, q, x_nr_bits;
78
79 BID_SWAP128 (x);
80 // test for special values - infinity or NaN
81 if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
82 // x is special
83 res = 0;
84 BID_RETURN (res);
85 }
86 // unpack x
87 x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
88 C1_hi = x.w[1] & MASK_COEFF;
89 C1_lo = x.w[0];
90 // test for zero
91 if (C1_hi == 0 && C1_lo == 0) {
92 res = 0;
93 BID_RETURN (res);
94 }
95 // test for non-canonical values of the argument x
96 if ((((C1_hi > 0x0001ed09bead87c0ull)
97 || ((C1_hi == 0x0001ed09bead87c0ull)
98 && (C1_lo > 0x378d8e63ffffffffull)))
99 && ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull))
100 || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
101 res = 0;
102 BID_RETURN (res);
103 }
104 // x is subnormal or normal
105 // determine the number of digits q in the significand
106 // q = nr. of decimal digits in x
107 // determine first the nr. of bits in x
108 if (C1_hi == 0) {
109 if (C1_lo >= 0x0020000000000000ull) { // x >= 2^53
110 // split the 64-bit value in two 32-bit halves to avoid rounding errors
111 if (C1_lo >= 0x0000000100000000ull) { // x >= 2^32
112 tmp1.d = (double) (C1_lo >> 32); // exact conversion
113 x_nr_bits =
114 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
115 } else { // x < 2^32
116 tmp1.d = (double) (C1_lo); // exact conversion
117 x_nr_bits =
118 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
119 }
120 } else { // if x < 2^53
121 tmp1.d = (double) C1_lo; // exact conversion
122 x_nr_bits =
123 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
124 }
125 } else { // C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi)
126 tmp1.d = (double) C1_hi; // exact conversion
127 x_nr_bits =
128 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
129 }
130 q = nr_digits[x_nr_bits - 1].digits;
131 if (q == 0) {
132 q = nr_digits[x_nr_bits - 1].digits1;
133 if (C1_hi > nr_digits[x_nr_bits - 1].threshold_hi ||
134 (C1_hi == nr_digits[x_nr_bits - 1].threshold_hi &&
135 C1_lo >= nr_digits[x_nr_bits - 1].threshold_lo))
136 q++;
137 }
138 exp = (int) (x_exp >> 49) - 6176;
139 // test for subnormal values of x
140 if (exp + q <= -6143) {
141 res = 0;
142 BID_RETURN (res);
143 } else {
144 res = 1;
145 BID_RETURN (res);
146 }
147 }
148
149 // return 1 iff x is not zero, nor NaN nor normal nor infinity
150 #if DECIMAL_CALL_BY_REFERENCE
151 void
152 bid128_isSubnormal (int *pres,
153 UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
154 UINT128 x = *px;
155 #else
156 int
157 bid128_isSubnormal (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
158 #endif
159 int res;
160 UINT64 x_exp, C1_hi, C1_lo;
161 BID_UI64DOUBLE tmp1;
162 int exp, q, x_nr_bits;
163
164 BID_SWAP128 (x);
165 // test for special values - infinity or NaN
166 if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
167 // x is special
168 res = 0;
169 BID_RETURN (res);
170 }
171 // unpack x
172 x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
173 C1_hi = x.w[1] & MASK_COEFF;
174 C1_lo = x.w[0];
175 // test for zero
176 if (C1_hi == 0 && C1_lo == 0) {
177 res = 0;
178 BID_RETURN (res);
179 }
180 // test for non-canonical values of the argument x
181 if ((((C1_hi > 0x0001ed09bead87c0ull)
182 || ((C1_hi == 0x0001ed09bead87c0ull)
183 && (C1_lo > 0x378d8e63ffffffffull)))
184 && ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull))
185 || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
186 res = 0;
187 BID_RETURN (res);
188 }
189 // x is subnormal or normal
190 // determine the number of digits q in the significand
191 // q = nr. of decimal digits in x
192 // determine first the nr. of bits in x
193 if (C1_hi == 0) {
194 if (C1_lo >= 0x0020000000000000ull) { // x >= 2^53
195 // split the 64-bit value in two 32-bit halves to avoid rounding errors
196 if (C1_lo >= 0x0000000100000000ull) { // x >= 2^32
197 tmp1.d = (double) (C1_lo >> 32); // exact conversion
198 x_nr_bits =
199 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
200 } else { // x < 2^32
201 tmp1.d = (double) (C1_lo); // exact conversion
202 x_nr_bits =
203 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
204 }
205 } else { // if x < 2^53
206 tmp1.d = (double) C1_lo; // exact conversion
207 x_nr_bits =
208 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
209 }
210 } else { // C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi)
211 tmp1.d = (double) C1_hi; // exact conversion
212 x_nr_bits =
213 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
214 }
215 q = nr_digits[x_nr_bits - 1].digits;
216 if (q == 0) {
217 q = nr_digits[x_nr_bits - 1].digits1;
218 if (C1_hi > nr_digits[x_nr_bits - 1].threshold_hi ||
219 (C1_hi == nr_digits[x_nr_bits - 1].threshold_hi &&
220 C1_lo >= nr_digits[x_nr_bits - 1].threshold_lo))
221 q++;
222 }
223 exp = (int) (x_exp >> 49) - 6176;
224 // test for subnormal values of x
225 if (exp + q <= -6143) {
226 res = 1;
227 } else {
228 res = 0;
229 }
230 BID_RETURN (res);
231 }
232
233 #if DECIMAL_CALL_BY_REFERENCE
234 void
235 bid128_isFinite (int *pres,
236 UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
237 UINT128 x = *px;
238 #else
239 int
240 bid128_isFinite (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
241 #endif
242 int res;
243 res = ((x.w[HIGH_128W] & MASK_INF) != MASK_INF);
244 BID_RETURN (res);
245 }
246
247 #if DECIMAL_CALL_BY_REFERENCE
248 void
249 bid128_isZero (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
250 UINT128 x = *px;
251 #else
252 int
253 bid128_isZero (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
254 #endif
255 int res;
256 UINT128 sig_x;
257
258 BID_SWAP128 (x);
259 if ((x.w[1] & MASK_INF) == MASK_INF) {
260 res = 0;
261 BID_RETURN (res);
262 }
263 sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
264 sig_x.w[0] = x.w[0];
265 if ((sig_x.w[1] > 0x0001ed09bead87c0ull) || // significand is non-canonical
266 ((sig_x.w[1] == 0x0001ed09bead87c0ull) && (sig_x.w[0] > 0x378d8e63ffffffffull)) || // significand is non-canonical
267 ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull && (x.w[1] & MASK_INF) != MASK_INF) || // significand is non-canonical
268 (sig_x.w[1] == 0 && sig_x.w[0] == 0)) { // significand is 0
269 res = 1;
270 BID_RETURN (res);
271 }
272 res = 0;
273 BID_RETURN (res);
274 }
275
276 #if DECIMAL_CALL_BY_REFERENCE
277 void
278 bid128_isInf (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
279 UINT128 x = *px;
280 #else
281 int
282 bid128_isInf (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
283 #endif
284 int res;
285 res = ((x.w[HIGH_128W] & MASK_INF) == MASK_INF)
286 && ((x.w[HIGH_128W] & MASK_NAN) != MASK_NAN);
287 BID_RETURN (res);
288 }
289
290 #if DECIMAL_CALL_BY_REFERENCE
291 void
292 bid128_isSignaling (int *pres,
293 UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
294 UINT128 x = *px;
295 #else
296 int
297 bid128_isSignaling (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
298 #endif
299 int res;
300
301 res = ((x.w[HIGH_128W] & MASK_SNAN) == MASK_SNAN);
302 BID_RETURN (res);
303 }
304
305 // return 1 iff x is a canonical number ,infinity, or NaN.
306 #if DECIMAL_CALL_BY_REFERENCE
307 void
308 bid128_isCanonical (int *pres,
309 UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
310 UINT128 x = *px;
311 #else
312 int
313 bid128_isCanonical (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
314 #endif
315 int res;
316 UINT128 sig_x;
317
318 BID_SWAP128 (x);
319 if ((x.w[1] & MASK_NAN) == MASK_NAN) { // NaN
320 if (x.w[1] & 0x01ffc00000000000ull) {
321 res = 0;
322 BID_RETURN (res);
323 }
324 sig_x.w[1] = x.w[1] & 0x00003fffffffffffull; // 46 bits
325 sig_x.w[0] = x.w[0]; // 64 bits
326 // payload must be < 10^33 = 0x0000314dc6448d93_38c15b0a00000000
327 if (sig_x.w[1] < 0x0000314dc6448d93ull
328 || (sig_x.w[1] == 0x0000314dc6448d93ull
329 && sig_x.w[0] < 0x38c15b0a00000000ull)) {
330 res = 1;
331 } else {
332 res = 0;
333 }
334 BID_RETURN (res);
335 } else if ((x.w[1] & MASK_INF) == MASK_INF) { // infinity
336 if ((x.w[1] & 0x03ffffffffffffffull) || x.w[0]) {
337 res = 0;
338 } else {
339 res = 1;
340 }
341 BID_RETURN (res);
342 }
343 // not NaN or infinity; extract significand to ensure it is canonical
344 sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
345 sig_x.w[0] = x.w[0];
346 // a canonical number has a coefficient < 10^34
347 // (0x0001ed09_bead87c0_378d8e64_00000000)
348 if ((sig_x.w[1] > 0x0001ed09bead87c0ull) || // significand is non-canonical
349 ((sig_x.w[1] == 0x0001ed09bead87c0ull) && (sig_x.w[0] > 0x378d8e63ffffffffull)) || // significand is non-canonical
350 ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
351 res = 0;
352 } else {
353 res = 1;
354 }
355 BID_RETURN (res);
356 }
357
358 #if DECIMAL_CALL_BY_REFERENCE
359 void
360 bid128_isNaN (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
361 UINT128 x = *px;
362 #else
363 int
364 bid128_isNaN (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
365 #endif
366 int res;
367
368 res = ((x.w[HIGH_128W] & MASK_NAN) == MASK_NAN);
369 BID_RETURN (res);
370 }
371
372 // copies a floating-point operand x to destination y, with no change
373 #if DECIMAL_CALL_BY_REFERENCE
374 void
375 bid128_copy (UINT128 * pres,
376 UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
377 UINT128 x = *px;
378 #else
379 UINT128
380 bid128_copy (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
381 #endif
382 UINT128 res;
383
384 res = x;
385 BID_RETURN (res);
386 }
387
388 // copies a floating-point operand x to destination y, reversing the sign
389 #if DECIMAL_CALL_BY_REFERENCE
390 void
391 bid128_negate (UINT128 * pres,
392 UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
393 UINT128 x = *px;
394 #else
395 UINT128
396 bid128_negate (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
397 #endif
398 UINT128 res;
399
400 x.w[HIGH_128W] ^= MASK_SIGN;
401 res = x;
402 BID_RETURN (res);
403 }
404
405 // copies a floating-point operand x to destination y, changing the sign to positive
406 #if DECIMAL_CALL_BY_REFERENCE
407 void
408 bid128_abs (UINT128 * pres,
409 UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
410 UINT128 x = *px;
411 #else
412 UINT128
413 bid128_abs (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
414 #endif
415 UINT128 res;
416
417 x.w[HIGH_128W] &= ~MASK_SIGN;
418 res = x;
419 BID_RETURN (res);
420 }
421
422 // copies operand x to destination in the same format as x, but with the sign of y
423 #if DECIMAL_CALL_BY_REFERENCE
424 void
425 bid128_copySign (UINT128 * pres, UINT128 * px,
426 UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
427 UINT128 x = *px;
428 UINT128 y = *py;
429 #else
430 UINT128
431 bid128_copySign (UINT128 x, UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
432 #endif
433 UINT128 res;
434
435 x.w[HIGH_128W] =
436 (x.w[HIGH_128W] & ~MASK_SIGN) | (y.w[HIGH_128W] & MASK_SIGN);
437 res = x;
438 BID_RETURN (res);
439 }
440
441 #if DECIMAL_CALL_BY_REFERENCE
442 void
443 bid128_class (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
444 UINT128 x = *px;
445 #else
446 int
447 bid128_class (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
448 #endif
449 int res;
450 UINT256 sig_x_prime256;
451 UINT192 sig_x_prime192;
452 UINT128 sig_x;
453 int exp_x;
454
455 BID_SWAP128 (x);
456 if ((x.w[1] & MASK_NAN) == MASK_NAN) {
457 if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {
458 res = signalingNaN;
459 } else {
460 res = quietNaN;
461 }
462 BID_RETURN (res);
463 }
464 if ((x.w[1] & MASK_INF) == MASK_INF) {
465 if ((x.w[1] & MASK_SIGN) == MASK_SIGN) {
466 res = negativeInfinity;
467 } else {
468 res = positiveInfinity;
469 }
470 BID_RETURN (res);
471 }
472 // decode number into exponent and significand
473 sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
474 sig_x.w[0] = x.w[0];
475 // check for zero or non-canonical
476 if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
477 || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
478 && (sig_x.w[0] > 0x378d8e63ffffffffull))
479 || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)
480 || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
481 if ((x.w[1] & MASK_SIGN) == MASK_SIGN) {
482 res = negativeZero;
483 } else {
484 res = positiveZero;
485 }
486 BID_RETURN (res);
487 }
488 exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
489 // if exponent is less than -6176, the number may be subnormal
490 // (less than the smallest normal value)
491 // the smallest normal value is 1 x 10^-6143 = 10^33 x 10^-6176
492 // if (exp_x - 6176 < -6143)
493 if (exp_x < 33) { // sig_x * 10^exp_x
494 if (exp_x > 19) {
495 __mul_128x128_to_256 (sig_x_prime256, sig_x,
496 ten2k128[exp_x - 20]);
497 // 10^33 = 0x0000314dc6448d93_38c15b0a00000000
498 if ((sig_x_prime256.w[3] == 0) && (sig_x_prime256.w[2] == 0)
499 && ((sig_x_prime256.w[1] < 0x0000314dc6448d93ull)
500 || ((sig_x_prime256.w[1] == 0x0000314dc6448d93ull)
501 && (sig_x_prime256.w[0] < 0x38c15b0a00000000ull)))) {
502 res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? negativeSubnormal :
503 positiveSubnormal;
504 BID_RETURN (res);
505 }
506 } else {
507 __mul_64x128_to_192 (sig_x_prime192, ten2k64[exp_x], sig_x);
508 // 10^33 = 0x0000314dc6448d93_38c15b0a00000000
509 if ((sig_x_prime192.w[2] == 0)
510 && ((sig_x_prime192.w[1] < 0x0000314dc6448d93ull)
511 || ((sig_x_prime192.w[1] == 0x0000314dc6448d93ull)
512 && (sig_x_prime192.w[0] < 0x38c15b0a00000000ull)))) {
513 res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? negativeSubnormal :
514 positiveSubnormal;
515 BID_RETURN (res);
516 }
517 }
518 }
519 // otherwise, normal number, determine the sign
520 res =
521 ((x.w[1] & MASK_SIGN) ==
522 MASK_SIGN) ? negativeNormal : positiveNormal;
523 BID_RETURN (res);
524 }
525
526 // true if the exponents of x and y are the same, false otherwise.
527 // The special cases of sameQuantum(NaN, NaN) and sameQuantum(Inf, Inf) are true
528 // If exactly one operand is infinite or exactly one operand is NaN, then false
529 #if DECIMAL_CALL_BY_REFERENCE
530 void
531 bid128_sameQuantum (int *pres, UINT128 * px,
532 UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
533 UINT128 x = *px;
534 UINT128 y = *py;
535 #else
536 int
537 bid128_sameQuantum (UINT128 x,
538 UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
539 #endif
540 int res;
541 UINT64 x_exp, y_exp;
542
543 BID_SWAP128 (x);
544 BID_SWAP128 (y);
545 // if both operands are NaN, return true
546 if ((x.w[1] & MASK_NAN) == MASK_NAN
547 || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
548 res = ((x.w[1] & MASK_NAN) == MASK_NAN
549 && (y.w[1] & MASK_NAN) == MASK_NAN);
550 BID_RETURN (res);
551 }
552 // if both operands are INF, return true
553 if ((x.w[1] & MASK_INF) == MASK_INF
554 || (y.w[1] & MASK_INF) == MASK_INF) {
555 res = ((x.w[1] & MASK_INF) == MASK_INF)
556 && ((y.w[1] & MASK_INF) == MASK_INF);
557 BID_RETURN (res);
558 }
559 // decode exponents for both numbers, and return true if they match
560 if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11
561 x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits
562 } else { // G0_G1 != 11
563 x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits
564 }
565 if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11
566 y_exp = (y.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits
567 } else { // G0_G1 != 11
568 y_exp = y.w[1] & MASK_EXP; // biased and shifted left 49 bits
569 }
570 res = (x_exp == y_exp);
571 BID_RETURN (res);
572 }
573
574 #if DECIMAL_CALL_BY_REFERENCE
575 void
576 bid128_totalOrder (int *pres, UINT128 * px,
577 UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
578 UINT128 x = *px;
579 UINT128 y = *py;
580 #else
581 int
582 bid128_totalOrder (UINT128 x,
583 UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
584 #endif
585 int res;
586 int exp_x, exp_y;
587 UINT128 sig_x, sig_y, pyld_y, pyld_x;
588 UINT192 sig_n_prime192;
589 UINT256 sig_n_prime256;
590 char x_is_zero = 0, y_is_zero = 0;
591
592 BID_SWAP128 (x);
593 BID_SWAP128 (y);
594 // NaN (CASE 1)
595 // if x and y are unordered numerically because either operand is NaN
596 // (1) totalOrder(-NaN, number) is true
597 // (2) totalOrder(number, +NaN) is true
598 // (3) if x and y are both NaN:
599 // i) negative sign bit < positive sign bit
600 // ii) signaling < quiet for +NaN, reverse for -NaN
601 // iii) lesser payload < greater payload for +NaN (reverse for -NaN)
602 // iv) else if bitwise identical (in canonical form), return 1
603 if ((x.w[1] & MASK_NAN) == MASK_NAN) {
604 // if x is -NaN
605 if ((x.w[1] & MASK_SIGN) == MASK_SIGN) {
606 // return true, unless y is -NaN also
607 if ((y.w[1] & MASK_NAN) != MASK_NAN
608 || (y.w[1] & MASK_SIGN) != MASK_SIGN) {
609 res = 1; // y is a number, return 1
610 BID_RETURN (res);
611 } else { // if y and x are both -NaN
612 pyld_x.w[1] = x.w[1] & 0x00003fffffffffffull;
613 pyld_x.w[0] = x.w[0];
614 pyld_y.w[1] = y.w[1] & 0x00003fffffffffffull;
615 pyld_y.w[0] = y.w[0];
616 if ((pyld_x.w[1] > 0x0000314dc6448d93ull)
617 || ((pyld_x.w[1] == 0x0000314dc6448d93ull)
618 && (pyld_x.w[0] > 0x38c15b09ffffffffull))) {
619 pyld_x.w[1] = 0;
620 pyld_x.w[0] = 0;
621 }
622 if ((pyld_y.w[1] > 0x0000314dc6448d93ull)
623 || ((pyld_y.w[1] == 0x0000314dc6448d93ull)
624 && (pyld_y.w[0] > 0x38c15b09ffffffffull))) {
625 pyld_y.w[1] = 0;
626 pyld_y.w[0] = 0;
627 }
628 // if x and y are both -SNaN or both -QNaN, we have to compare payloads
629 // this statement evaluates to true if both are SNaN or QNaN
630 if (!
631 (((y.w[1] & MASK_SNAN) == MASK_SNAN) ^
632 ((x.w[1] & MASK_SNAN) == MASK_SNAN))) {
633 // it comes down to the payload. we want to return true if x has a
634 // larger payload, or if the payloads are equal (canonical forms
635 // are bitwise identical)
636 if ((pyld_x.w[1] > pyld_y.w[1]) ||
637 ((pyld_x.w[1] == pyld_y.w[1])
638 && (pyld_x.w[0] >= pyld_y.w[0])))
639 res = 1;
640 else
641 res = 0;
642 BID_RETURN (res);
643 } else {
644 // either x = -SNaN and y = -QNaN or x = -QNaN and y = -SNaN
645 res = ((y.w[1] & MASK_SNAN) == MASK_SNAN);
646 // totalOrder (-QNaN, -SNaN) == 1
647 BID_RETURN (res);
648 }
649 }
650 } else { // x is +NaN
651 // return false, unless y is +NaN also
652 if ((y.w[1] & MASK_NAN) != MASK_NAN
653 || (y.w[1] & MASK_SIGN) == MASK_SIGN) {
654 res = 0; // y is a number, return 1
655 BID_RETURN (res);
656 } else {
657 // x and y are both +NaN;
658 pyld_x.w[1] = x.w[1] & 0x00003fffffffffffull;
659 pyld_x.w[0] = x.w[0];
660 pyld_y.w[1] = y.w[1] & 0x00003fffffffffffull;
661 pyld_y.w[0] = y.w[0];
662 if ((pyld_x.w[1] > 0x0000314dc6448d93ull)
663 || ((pyld_x.w[1] == 0x0000314dc6448d93ull)
664 && (pyld_x.w[0] > 0x38c15b09ffffffffull))) {
665 pyld_x.w[1] = 0;
666 pyld_x.w[0] = 0;
667 }
668 if ((pyld_y.w[1] > 0x0000314dc6448d93ull)
669 || ((pyld_y.w[1] == 0x0000314dc6448d93ull)
670 && (pyld_y.w[0] > 0x38c15b09ffffffffull))) {
671 pyld_y.w[1] = 0;
672 pyld_y.w[0] = 0;
673 }
674 // if x and y are both +SNaN or both +QNaN, we have to compare payloads
675 // this statement evaluates to true if both are SNaN or QNaN
676 if (!
677 (((y.w[1] & MASK_SNAN) == MASK_SNAN) ^
678 ((x.w[1] & MASK_SNAN) == MASK_SNAN))) {
679 // it comes down to the payload. we want to return true if x has a
680 // smaller payload, or if the payloads are equal (canonical forms
681 // are bitwise identical)
682 if ((pyld_x.w[1] < pyld_y.w[1]) ||
683 ((pyld_x.w[1] == pyld_y.w[1])
684 && (pyld_x.w[0] <= pyld_y.w[0])))
685 res = 1;
686 else
687 res = 0;
688 BID_RETURN (res);
689 } else {
690 // either x = SNaN and y = QNaN or x = QNaN and y = SNaN
691 res = ((x.w[1] & MASK_SNAN) == MASK_SNAN);
692 // totalOrder (-QNaN, -SNaN) == 1
693 BID_RETURN (res);
694 }
695 }
696 }
697 } else if ((y.w[1] & MASK_NAN) == MASK_NAN) {
698 // x is certainly not NAN in this case.
699 // return true if y is positive
700 res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
701 BID_RETURN (res);
702 }
703 // SIMPLE (CASE 2)
704 // if all the bits are the same, the numbers are equal.
705 if ((x.w[1] == y.w[1]) && (x.w[0] == y.w[0])) {
706 res = 1;
707 BID_RETURN (res);
708 }
709 // OPPOSITE SIGNS (CASE 3)
710 // if signs are opposite, return 1 if x is negative
711 // (if x < y, totalOrder is true)
712 if (((x.w[1] & MASK_SIGN) == MASK_SIGN) ^ ((y.w[1] & MASK_SIGN) ==
713 MASK_SIGN)) {
714 res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
715 BID_RETURN (res);
716 }
717 // INFINITY (CASE 4)
718 if ((x.w[1] & MASK_INF) == MASK_INF) {
719 // if x == neg_inf, return (y == neg_inf);
720 if ((x.w[1] & MASK_SIGN) == MASK_SIGN) {
721 res = 1;
722 BID_RETURN (res);
723 } else {
724 // x is positive infinity, only return1 if y is positive infinity as well
725 res = ((y.w[1] & MASK_INF) == MASK_INF);
726 BID_RETURN (res);
727 // && (y & MASK_SIGN) != MASK_SIGN); (we know y has same sign as x)
728 }
729 } else if ((y.w[1] & MASK_INF) == MASK_INF) {
730 // x is finite, so:
731 // if y is +inf, x<y
732 // if y is -inf, x>y
733 res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
734 BID_RETURN (res);
735 }
736 // CONVERT x
737 sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
738 sig_x.w[0] = x.w[0];
739 exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
740
741 // CHECK IF x IS CANONICAL
742 // 9999999999999999999999999999999999 (decimal) =
743 // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
744 // [0, 10^34) is the 754r supported canonical range.
745 // If the value exceeds that, it is interpreted as 0.
746 if ((((sig_x.w[1] > 0x0001ed09bead87c0ull) ||
747 ((sig_x.w[1] == 0x0001ed09bead87c0ull) &&
748 (sig_x.w[0] > 0x378d8e63ffffffffull))) &&
749 ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) ||
750 ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) ||
751 ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
752 x_is_zero = 1;
753 // check for the case where the exponent is shifted right by 2 bits!
754 if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {
755 exp_x = (x.w[1] >> 47) & 0x000000000003fffull;
756 }
757 }
758 // CONVERT y
759 exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
760 sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
761 sig_y.w[0] = y.w[0];
762
763 // CHECK IF y IS CANONICAL
764 // 9999999999999999999999999999999999(decimal) =
765 // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
766 // [0, 10^34) is the 754r supported canonical range.
767 // If the value exceeds that, it is interpreted as 0.
768 if ((((sig_y.w[1] > 0x0001ed09bead87c0ull) ||
769 ((sig_y.w[1] == 0x0001ed09bead87c0ull) &&
770 (sig_y.w[0] > 0x378d8e63ffffffffull))) &&
771 ((y.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) ||
772 ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) ||
773 ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
774 y_is_zero = 1;
775 // check for the case where the exponent is shifted right by 2 bits!
776 if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {
777 exp_y = (y.w[1] >> 47) & 0x000000000003fffull;
778 }
779 }
780 // ZERO (CASE 5)
781 // if x and y represent the same entities, and both are negative
782 // return true iff exp_x <= exp_y
783 if (x_is_zero && y_is_zero) {
784 // we know that signs must be the same because we would have caught it
785 // in case3 if signs were different
786 // totalOrder(x,y) iff exp_x >= exp_y for negative numbers
787 // totalOrder(x,y) iff exp_x <= exp_y for positive numbers
788 if (exp_x == exp_y) {
789 res = 1;
790 BID_RETURN (res);
791 }
792 res = ((exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
793 BID_RETURN (res);
794 }
795 // if x is zero and y isn't, clearly x has the smaller payload
796 if (x_is_zero) {
797 res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
798 BID_RETURN (res);
799 }
800 // if y is zero, and x isn't, clearly y has the smaller payload
801 if (y_is_zero) {
802 res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
803 BID_RETURN (res);
804 }
805 // REDUNDANT REPRESENTATIONS (CASE 6)
806 // if both components are either bigger or smaller
807 if (((sig_x.w[1] > sig_y.w[1])
808 || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
809 && exp_x >= exp_y) {
810 res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
811 BID_RETURN (res);
812 }
813 if (((sig_x.w[1] < sig_y.w[1])
814 || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
815 && exp_x <= exp_y) {
816 res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
817 BID_RETURN (res);
818 }
819 // if |exp_x - exp_y| < 33, it comes down to the compensated significand
820 if (exp_x > exp_y) {
821 // if exp_x is 33 greater than exp_y, it is definitely larger,
822 // so no need for compensation
823 if (exp_x - exp_y > 33) {
824 res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
825 BID_RETURN (res);
826 // difference cannot be greater than 10^33
827 }
828 // otherwise adjust the x significand upwards
829 if (exp_x - exp_y > 19) {
830 __mul_128x128_to_256 (sig_n_prime256, sig_x,
831 ten2k128[exp_x - exp_y - 20]);
832 // the compensated significands are equal (ie "x and y represent the same
833 // entities") return 1 if (negative && expx > expy) ||
834 // (positive && expx < expy)
835 if ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0)
836 && (sig_n_prime256.w[1] == sig_y.w[1])
837 && (sig_n_prime256.w[0] == sig_y.w[0])) {
838 // the case exp_x == exp_y cannot occur, because all bits must be
839 // the same - would have been caught if (x == y)
840 res = ((exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
841 BID_RETURN (res);
842 }
843 // if positive, return 1 if adjusted x is smaller than y
844 res = (((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0)
845 && ((sig_n_prime256.w[1] < sig_y.w[1])
846 || (sig_n_prime256.w[1] == sig_y.w[1]
847 && sig_n_prime256.w[0] <
848 sig_y.w[0]))) ^ ((x.w[1] & MASK_SIGN) ==
849 MASK_SIGN));
850 BID_RETURN (res);
851 }
852 __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_x - exp_y], sig_x);
853 // if positive, return whichever significand is larger
854 // (converse if negative)
855 if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
856 && (sig_n_prime192.w[0] == sig_y.w[0])) {
857 res = ((exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
858 BID_RETURN (res);
859 }
860 res = (((sig_n_prime192.w[2] == 0)
861 && ((sig_n_prime192.w[1] < sig_y.w[1])
862 || (sig_n_prime192.w[1] == sig_y.w[1]
863 && sig_n_prime192.w[0] <
864 sig_y.w[0]))) ^ ((x.w[1] & MASK_SIGN) ==
865 MASK_SIGN));
866 BID_RETURN (res);
867 }
868 // if exp_x is 33 less than exp_y, it is definitely smaller,
869 // no need for compensation
870 if (exp_y - exp_x > 33) {
871 res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
872 BID_RETURN (res);
873 }
874 if (exp_y - exp_x > 19) {
875 // adjust the y significand upwards
876 __mul_128x128_to_256 (sig_n_prime256, sig_y,
877 ten2k128[exp_y - exp_x - 20]);
878 // if x and y represent the same entities and both are negative
879 // return true iff exp_x <= exp_y
880 if ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0)
881 && (sig_n_prime256.w[1] == sig_x.w[1])
882 && (sig_n_prime256.w[0] == sig_x.w[0])) {
883 res = (exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN);
884 BID_RETURN (res);
885 }
886 // values are not equal, for positive numbers return 1 if x is less than y
887 // and 0 otherwise
888 res = (((sig_n_prime256.w[3] != 0) ||
889 // if upper128 bits of compensated y are non-zero, y is bigger
890 (sig_n_prime256.w[2] != 0) ||
891 // if upper128 bits of compensated y are non-zero, y is bigger
892 (sig_n_prime256.w[1] > sig_x.w[1]) ||
893 // if compensated y is bigger, y is bigger
894 (sig_n_prime256.w[1] == sig_x.w[1]
895 && sig_n_prime256.w[0] >
896 sig_x.w[0])) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
897 BID_RETURN (res);
898 }
899 __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y);
900 if ((sig_n_prime192.w[2] == 0) && (sig_n_prime192.w[1] == sig_x.w[1])
901 && (sig_n_prime192.w[0] == sig_x.w[0])) {
902 res = (exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN);
903 BID_RETURN (res);
904 }
905 res = (((sig_n_prime192.w[2] != 0) ||
906 // if upper128 bits of compensated y are non-zero, y is bigger
907 (sig_n_prime192.w[1] > sig_x.w[1]) ||
908 // if compensated y is bigger, y is bigger
909 (sig_n_prime192.w[1] == sig_x.w[1]
910 && sig_n_prime192.w[0] >
911 sig_x.w[0])) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
912 BID_RETURN (res);
913 }
914
915 #if DECIMAL_CALL_BY_REFERENCE
916 void
917 bid128_totalOrderMag (int *pres, UINT128 * px,
918 UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
919 UINT128 x = *px;
920 UINT128 y = *py;
921 #else
922 int
923 bid128_totalOrderMag (UINT128 x,
924 UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
925 #endif
926 int res;
927 int exp_x, exp_y;
928 UINT128 sig_x, sig_y, pyld_y, pyld_x;
929 UINT192 sig_n_prime192;
930 UINT256 sig_n_prime256;
931 char x_is_zero = 0, y_is_zero = 0;
932
933 BID_SWAP128 (x);
934 BID_SWAP128 (y);
935 x.w[1] = x.w[1] & 0x7fffffffffffffffull;
936 y.w[1] = y.w[1] & 0x7fffffffffffffffull;
937
938 // NaN (CASE 1)
939 // if x and y are unordered numerically because either operand is NaN
940 // (1) totalOrder(number, +NaN) is true
941 // (2) if x and y are both NaN:
942 // i) signaling < quiet for +NaN
943 // ii) lesser payload < greater payload for +NaN
944 // iii) else if bitwise identical (in canonical form), return 1
945 if ((x.w[1] & MASK_NAN) == MASK_NAN) {
946 // x is +NaN
947 // return false, unless y is +NaN also
948 if ((y.w[1] & MASK_NAN) != MASK_NAN) {
949 res = 0; // y is a number, return 0
950 BID_RETURN (res);
951 } else {
952 // x and y are both +NaN;
953 pyld_x.w[1] = x.w[1] & 0x00003fffffffffffull;
954 pyld_x.w[0] = x.w[0];
955 pyld_y.w[1] = y.w[1] & 0x00003fffffffffffull;
956 pyld_y.w[0] = y.w[0];
957 if ((pyld_x.w[1] > 0x0000314dc6448d93ull)
958 || ((pyld_x.w[1] == 0x0000314dc6448d93ull)
959 && (pyld_x.w[0] > 0x38c15b09ffffffffull))) {
960 pyld_x.w[1] = 0;
961 pyld_x.w[0] = 0;
962 }
963 if ((pyld_y.w[1] > 0x0000314dc6448d93ull)
964 || ((pyld_y.w[1] == 0x0000314dc6448d93ull)
965 && (pyld_y.w[0] > 0x38c15b09ffffffffull))) {
966 pyld_y.w[1] = 0;
967 pyld_y.w[0] = 0;
968 }
969 // if x and y are both +SNaN or both +QNaN, we have to compare payloads
970 // this statement evaluates to true if both are SNaN or QNaN
971 if (!
972 (((y.w[1] & MASK_SNAN) == MASK_SNAN) ^
973 ((x.w[1] & MASK_SNAN) == MASK_SNAN))) {
974 // it comes down to the payload. we want to return true if x has a
975 // smaller payload, or if the payloads are equal (canonical forms
976 // are bitwise identical)
977 if ((pyld_x.w[1] < pyld_y.w[1]) ||
978 ((pyld_x.w[1] == pyld_y.w[1])
979 && (pyld_x.w[0] <= pyld_y.w[0]))) {
980 res = 1;
981 } else {
982 res = 0;
983 }
984 BID_RETURN (res);
985 } else {
986 // either x = SNaN and y = QNaN or x = QNaN and y = SNaN
987 res = ((x.w[1] & MASK_SNAN) == MASK_SNAN);
988 // totalOrder (-QNaN, -SNaN) == 1
989 BID_RETURN (res);
990 }
991 }
992 } else if ((y.w[1] & MASK_NAN) == MASK_NAN) {
993 // x is certainly not NAN in this case.
994 // return true because y is positive
995 res = 1;
996 BID_RETURN (res);
997 }
998 // SIMPLE (CASE 2)
999 // if all the bits are the same, the numbers are equal.
1000 if ((x.w[1] == y.w[1]) && (x.w[0] == y.w[0])) {
1001 res = 1;
1002 BID_RETURN (res);
1003 }
1004 // INFINITY (CASE 3)
1005 if ((x.w[1] & MASK_INF) == MASK_INF) {
1006 // x is positive infinity, only return 1 if y is positive infinity as well
1007 res = ((y.w[1] & MASK_INF) == MASK_INF);
1008 BID_RETURN (res);
1009 // (we know y has same sign as x)
1010 } else if ((y.w[1] & MASK_INF) == MASK_INF) {
1011 // x is finite, so:
1012 // since y is +inf, x<y
1013 res = 1;
1014 BID_RETURN (res);
1015 } else {
1016 ; // continue
1017 }
1018
1019 // CONVERT x
1020 sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
1021 sig_x.w[0] = x.w[0];
1022 exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
1023
1024 // CHECK IF x IS CANONICAL
1025 // 9999999999999999999999999999999999 (decimal) =
1026 // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
1027 // [0, 10^34) is the 754r supported canonical range.
1028 // If the value exceeds that, it is interpreted as 0.
1029 if ((((sig_x.w[1] > 0x0001ed09bead87c0ull) ||
1030 ((sig_x.w[1] == 0x0001ed09bead87c0ull) &&
1031 (sig_x.w[0] > 0x378d8e63ffffffffull))) &&
1032 ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) ||
1033 ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) ||
1034 ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
1035 x_is_zero = 1;
1036 // check for the case where the exponent is shifted right by 2 bits!
1037 if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {
1038 exp_x = (x.w[1] >> 47) & 0x000000000003fffull;
1039 }
1040 }
1041 // CONVERT y
1042 exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
1043 sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
1044 sig_y.w[0] = y.w[0];
1045
1046 // CHECK IF y IS CANONICAL
1047 // 9999999999999999999999999999999999(decimal) =
1048 // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
1049 // [0, 10^34) is the 754r supported canonical range.
1050 // If the value exceeds that, it is interpreted as 0.
1051 if ((((sig_y.w[1] > 0x0001ed09bead87c0ull) ||
1052 ((sig_y.w[1] == 0x0001ed09bead87c0ull) &&
1053 (sig_y.w[0] > 0x378d8e63ffffffffull))) &&
1054 ((y.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) ||
1055 ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) ||
1056 ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
1057 y_is_zero = 1;
1058 // check for the case where the exponent is shifted right by 2 bits!
1059 if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {
1060 exp_y = (y.w[1] >> 47) & 0x000000000003fffull;
1061 }
1062 }
1063 // ZERO (CASE 4)
1064 if (x_is_zero && y_is_zero) {
1065 // we know that signs must be the same because we would have caught it
1066 // in case3 if signs were different
1067 // totalOrder(x,y) iff exp_x <= exp_y for positive numbers
1068 if (exp_x == exp_y) {
1069 res = 1;
1070 BID_RETURN (res);
1071 }
1072 res = (exp_x <= exp_y);
1073 BID_RETURN (res);
1074 }
1075 // if x is zero and y isn't, clearly x has the smaller payload
1076 if (x_is_zero) {
1077 res = 1;
1078 BID_RETURN (res);
1079 }
1080 // if y is zero, and x isn't, clearly y has the smaller payload
1081 if (y_is_zero) {
1082 res = 0;
1083 BID_RETURN (res);
1084 }
1085 // REDUNDANT REPRESENTATIONS (CASE 5)
1086 // if both components are either bigger or smaller
1087 if (((sig_x.w[1] > sig_y.w[1])
1088 || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
1089 && exp_x >= exp_y) {
1090 res = 0;
1091 BID_RETURN (res);
1092 }
1093 if (((sig_x.w[1] < sig_y.w[1])
1094 || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
1095 && exp_x <= exp_y) {
1096 res = 1;
1097 BID_RETURN (res);
1098 }
1099 // if |exp_x - exp_y| < 33, it comes down to the compensated significand
1100 if (exp_x > exp_y) {
1101 // if exp_x is 33 greater than exp_y, it is definitely larger,
1102 // so no need for compensation
1103 if (exp_x - exp_y > 33) {
1104 res = 0; // difference cannot be greater than 10^33
1105 BID_RETURN (res);
1106 }
1107 // otherwise adjust the x significand upwards
1108 if (exp_x - exp_y > 19) {
1109 __mul_128x128_to_256 (sig_n_prime256, sig_x,
1110 ten2k128[exp_x - exp_y - 20]);
1111 // the compensated significands are equal (ie "x and y represent the same
1112 // entities") return 1 if (negative && expx > expy) ||
1113 // (positive && expx < expy)
1114 if ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0)
1115 && (sig_n_prime256.w[1] == sig_y.w[1])
1116 && (sig_n_prime256.w[0] == sig_y.w[0])) {
1117 // the case (exp_x == exp_y) cannot occur, because all bits must be
1118 // the same - would have been caught if (x == y)
1119 res = (exp_x <= exp_y);
1120 BID_RETURN (res);
1121 }
1122 // since positive, return 1 if adjusted x is smaller than y
1123 res = ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0)
1124 && ((sig_n_prime256.w[1] < sig_y.w[1])
1125 || (sig_n_prime256.w[1] == sig_y.w[1]
1126 && sig_n_prime256.w[0] < sig_y.w[0])));
1127 BID_RETURN (res);
1128 }
1129 __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_x - exp_y], sig_x);
1130 // if positive, return whichever significand is larger
1131 // (converse if negative)
1132 if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
1133 && (sig_n_prime192.w[0] == sig_y.w[0])) {
1134 res = (exp_x <= exp_y);
1135 BID_RETURN (res);
1136 }
1137 res = ((sig_n_prime192.w[2] == 0)
1138 && ((sig_n_prime192.w[1] < sig_y.w[1])
1139 || (sig_n_prime192.w[1] == sig_y.w[1]
1140 && sig_n_prime192.w[0] < sig_y.w[0])));
1141 BID_RETURN (res);
1142 }
1143 // if exp_x is 33 less than exp_y, it is definitely smaller,
1144 // no need for compensation
1145 if (exp_y - exp_x > 33) {
1146 res = 1;
1147 BID_RETURN (res);
1148 }
1149 if (exp_y - exp_x > 19) {
1150 // adjust the y significand upwards
1151 __mul_128x128_to_256 (sig_n_prime256, sig_y,
1152 ten2k128[exp_y - exp_x - 20]);
1153 if ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0)
1154 && (sig_n_prime256.w[1] == sig_x.w[1])
1155 && (sig_n_prime256.w[0] == sig_x.w[0])) {
1156 res = (exp_x <= exp_y);
1157 BID_RETURN (res);
1158 }
1159 // values are not equal, for positive numbers return 1 if x is less than y
1160 // and 0 otherwise
1161 res = ((sig_n_prime256.w[3] != 0) ||
1162 // if upper128 bits of compensated y are non-zero, y is bigger
1163 (sig_n_prime256.w[2] != 0) ||
1164 // if upper128 bits of compensated y are non-zero, y is bigger
1165 (sig_n_prime256.w[1] > sig_x.w[1]) ||
1166 // if compensated y is bigger, y is bigger
1167 (sig_n_prime256.w[1] == sig_x.w[1]
1168 && sig_n_prime256.w[0] > sig_x.w[0]));
1169 BID_RETURN (res);
1170 }
1171 __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y);
1172 if ((sig_n_prime192.w[2] == 0) && (sig_n_prime192.w[1] == sig_x.w[1])
1173 && (sig_n_prime192.w[0] == sig_x.w[0])) {
1174 res = (exp_x <= exp_y);
1175 BID_RETURN (res);
1176 }
1177 res = ((sig_n_prime192.w[2] != 0) ||
1178 // if upper128 bits of compensated y are non-zero, y is bigger
1179 (sig_n_prime192.w[1] > sig_x.w[1]) ||
1180 // if compensated y is bigger, y is bigger
1181 (sig_n_prime192.w[1] == sig_x.w[1]
1182 && sig_n_prime192.w[0] > sig_x.w[0]));
1183 BID_RETURN (res);
1184 }
1185
1186 #if DECIMAL_CALL_BY_REFERENCE
1187 void
1188 bid128_radix (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
1189 UINT128 x = *px;
1190 #else
1191 int
1192 bid128_radix (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
1193 #endif
1194 int res;
1195 if (x.w[LOW_128W]) // dummy test
1196 res = 10;
1197 else
1198 res = 10;
1199 BID_RETURN (res);
1200 }