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8d9254fc 1/* Copyright (C) 2007-2020 Free Software Foundation, Inc.
200359e8
L		 2
3This file is part of GCC.
4
5GCC is free software; you can redistribute it and/or modify it under
6the terms of the GNU General Public License as published by the Free
748086b7 7Software Foundation; either version 3, or (at your option) any later
200359e8
L		 8version.
9
200359e8
L		 10GCC is distributed in the hope that it will be useful, but WITHOUT ANY
11WARRANTY; without even the implied warranty of MERCHANTABILITY or
12FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
13for more details.
14
748086b7
JJ		 15Under Section 7 of GPL version 3, you are granted additional
16permissions described in the GCC Runtime Library Exception, version
173.1, as published by the Free Software Foundation.
18
19You should have received a copy of the GNU General Public License and
20a copy of the GCC Runtime Library Exception along with this program;
21see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
22<http://www.gnu.org/licenses/>. */
200359e8
L		 23
24#define BID_128RES
25#include "bid_internal.h"
26
27/*****************************************************************************
28 * BID128 minimum number
29 *****************************************************************************/
30
31#if DECIMAL_CALL_BY_REFERENCE
32void
b2a00c89
L		 33bid128_minnum (UINT128 * pres, UINT128 * px,
34 UINT128 * py _EXC_FLAGS_PARAM) {
200359e8
L		 35 UINT128 x = *px;
36 UINT128 y = *py;
37#else
38UINT128
b2a00c89 39bid128_minnum (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) {
200359e8
L		 40#endif
41
42 UINT128 res;
43 int exp_x, exp_y;
44 int diff;
45 UINT128 sig_x, sig_y;
46 UINT192 sig_n_prime192;
47 UINT256 sig_n_prime256;
b2a00c89 48 char x_is_zero = 0, y_is_zero = 0;
200359e8 49
b2a00c89
L		 50 BID_SWAP128 (x);
51 BID_SWAP128 (y);
52
53 // check for non-canonical x
54 if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
55 x.w[1] = x.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
56 // check for non-canonical NaN payload
57 if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
58 (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
59 (x.w[0] > 0x38c15b09ffffffffull))) {
60 x.w[1] = x.w[1] & 0xffffc00000000000ull;
61 x.w[0] = 0x0ull;
200359e8 62 }
b2a00c89
L		 63 } else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf
64 x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
65 x.w[0] = 0x0ull;
66 } else { // x is not special
67 // check for non-canonical values - treated as zero
68 if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
69 // non-canonical
70 x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP);
71 x.w[0] = 0x0ull;
72 } else { // G0_G1 != 11
73 if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
74 ((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
75 && x.w[0] > 0x378d8e63ffffffffull)) {
76 // x is non-canonical if coefficient is larger than 10^34 -1
77 x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP);
78 x.w[0] = 0x0ull;
79 } else { // canonical
80 ;
81 }
200359e8 82 }
200359e8 83 }
b2a00c89
L		 84 // check for non-canonical y
85 if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
86 y.w[1] = y.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
87 // check for non-canonical NaN payload
88 if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
89 (((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
90 (y.w[0] > 0x38c15b09ffffffffull))) {
91 y.w[1] = y.w[1] & 0xffffc00000000000ull;
92 y.w[0] = 0x0ull;
93 }
94 } else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
95 y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
96 y.w[0] = 0x0ull;
97 } else { // y is not special
98 // check for non-canonical values - treated as zero
99 if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
100 // non-canonical
101 y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP);
102 y.w[0] = 0x0ull;
103 } else { // G0_G1 != 11
104 if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
105 ((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
106 && y.w[0] > 0x378d8e63ffffffffull)) {
107 // y is non-canonical if coefficient is larger than 10^34 -1
108 y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP);
109 y.w[0] = 0x0ull;
110 } else { // canonical
111 ;
112 }
113 }
114 }
115
116 // NaN (CASE1)
117 if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
118 if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNaN
119 // if x is SNAN, then return quiet (x)
120 *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
121 x.w[1] = x.w[1] & 0xfdffffffffffffffull; // quietize x
122 res = x;
123 } else { // x is QNaN
124 if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
125 if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
126 *pfpsf |= INVALID_EXCEPTION; // set invalid flag
127 }
128 res = x;
129 } else {
130 res = y;
131 }
132 }
133 BID_RETURN (res);
134 } else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
135 if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
136 *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
137 y.w[1] = y.w[1] & 0xfdffffffffffffffull; // quietize y
138 res = y;
139 } else {
140 // will return x (which is not NaN)
141 res = x;
200359e8 142 }
200359e8
L		 143 BID_RETURN (res);
144 }
145 // SIMPLE (CASE2)
146 // if all the bits are the same, these numbers are equal (not Greater).
147 if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
148 res = x;
149 BID_RETURN (res);
150 }
151 // INFINITY (CASE3)
152 if ((x.w[1] & MASK_INF) == MASK_INF) {
153 // if x is neg infinity, there is no way it is greater than y, return 0
154 res = (((x.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y;
155 BID_RETURN (res);
156 } else if ((y.w[1] & MASK_INF) == MASK_INF) {
157 // x is finite, so if y is positive infinity, then x is less, return 0
158 // if y is negative infinity, then x is greater, return 1
159 res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
160 BID_RETURN (res);
161 }
162 // CONVERT X
163 sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
164 sig_x.w[0] = x.w[0];
165 exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
166
200359e8
L		 167 // CONVERT Y
168 exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
169 sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
170 sig_y.w[0] = y.w[0];
171
200359e8
L		 172 // ZERO (CASE4)
173 // some properties:
174 // (+ZERO == -ZERO) => therefore ignore the sign
175 // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => ignore the exponent
176 // field
177 // (Any non-canonical # is considered 0)
b2a00c89 178 if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) {
200359e8
L		 179 x_is_zero = 1;
180 }
b2a00c89 181 if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) {
200359e8
L		 182 y_is_zero = 1;
183 }
184
185 if (x_is_zero && y_is_zero) {
186 // if both numbers are zero, neither is greater => return either number
187 res = x;
188 BID_RETURN (res);
189 } else if (x_is_zero) {
190 // is x is zero, it is greater if Y is negative
191 res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
192 BID_RETURN (res);
193 } else if (y_is_zero) {
194 // is y is zero, X is greater if it is positive
195 res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? y : x;
196 BID_RETURN (res);
197 }
198 // OPPOSITE SIGN (CASE5)
199 // now, if the sign bits differ, x is greater if y is negative
200 if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
201 res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
202 BID_RETURN (res);
203 }
204 // REDUNDANT REPRESENTATIONS (CASE6)
205 // if exponents are the same, then we have a simple comparison of
206 // the significands
207 if (exp_y == exp_x) {
208 res = (((sig_x.w[1] > sig_y.w[1])
b2a00c89
L		 209 || (sig_x.w[1] == sig_y.w[1]
210 && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) ==
211 MASK_SIGN)) ? y : x;
200359e8
L		 212 BID_RETURN (res);
213 }
214 // if both components are either bigger or smaller, it is clear what
215 // needs to be done
216 if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0]
217 && exp_x > exp_y) {
218 res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? y : x;
219 BID_RETURN (res);
220 }
221 if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0]
222 && exp_x < exp_y) {
223 res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
224 BID_RETURN (res);
225 }
226
227 diff = exp_x - exp_y;
228
229 // if |exp_x - exp_y| < 33, it comes down to the compensated significand
b2a00c89 230 if (diff > 0) { // to simplify the loop below,
200359e8
L		 231 // if exp_x is 33 greater than exp_y, no need for compensation
232 if (diff > 33) {
233 // difference cannot be greater than 10^33
234 res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? y : x;
235 BID_RETURN (res);
236 }
b2a00c89
L		 237 if (diff > 19) { //128 by 128 bit multiply -> 256 bits
238 __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
200359e8
L		 239 // if postitive, return whichever significand is larger
240 // (converse if negative)
241 res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
b2a00c89
L		 242 || (sig_n_prime256.w[1] > sig_y.w[1])
243 || (sig_n_prime256.w[1] == sig_y.w[1]
244 && sig_n_prime256.w[0] >
245 sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) ==
246 MASK_SIGN)) ? y : x;
200359e8
L		 247 BID_RETURN (res);
248 }
b2a00c89 249 __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);
200359e8
L		 250 // if postitive, return whichever significand is larger
251 // (converse if negative)
252 res =
253 (((sig_n_prime192.w[2] > 0) || (sig_n_prime192.w[1] > sig_y.w[1])
b2a00c89
L		 254 || (sig_n_prime192.w[1] == sig_y.w[1]
255 && sig_n_prime192.w[0] >
256 sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)) ? y : x;
200359e8
L		 257 BID_RETURN (res);
258 }
259 diff = exp_y - exp_x;
260 // if exp_x is 33 less than exp_y, no need for compensation
261 if (diff > 33) {
262 res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
263 BID_RETURN (res);
264 }
b2a00c89 265 if (diff > 19) { //128 by 128 bit multiply -> 256 bits
200359e8 266 // adjust the y significand upwards
b2a00c89 267 __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
200359e8
L		 268 // if postitive, return whichever significand is larger
269 // (converse if negative)
270 res =
271 ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
b2a00c89
L		 272 || (sig_n_prime256.w[1] > sig_x.w[1]
273 || (sig_n_prime256.w[1] == sig_x.w[1]
274 && sig_n_prime256.w[0] >
275 sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) ==
276 MASK_SIGN)) ? x : y;
200359e8
L		 277 BID_RETURN (res);
278 }
279 // adjust the y significand upwards
b2a00c89 280 __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y);
200359e8 281 // if postitive, return whichever significand is larger (converse if negative)
b2a00c89
L		 282 res =
283 ((sig_n_prime192.w[2] != 0
284 || (sig_n_prime192.w[1] > sig_x.w[1]
285 || (sig_n_prime192.w[1] == sig_x.w[1]
286 && sig_n_prime192.w[0] > sig_x.w[0])))
287 ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y;
200359e8
L		 288 BID_RETURN (res);
289}
290
291/*****************************************************************************
292 * BID128 minimum magnitude function - returns greater of two numbers
293 *****************************************************************************/
294
295#if DECIMAL_CALL_BY_REFERENCE
296void
b2a00c89
L		 297bid128_minnum_mag (UINT128 * pres, UINT128 * px,
298 UINT128 * py _EXC_FLAGS_PARAM) {
200359e8
L		 299 UINT128 x = *px;
300 UINT128 y = *py;
301#else
302UINT128
b2a00c89 303bid128_minnum_mag (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) {
200359e8
L		 304#endif
305
306 UINT128 res;
307 int exp_x, exp_y;
308 int diff;
309 UINT128 sig_x, sig_y;
310 UINT192 sig_n_prime192;
311 UINT256 sig_n_prime256;
200359e8 312
b2a00c89
L		 313 BID_SWAP128 (x);
314 BID_SWAP128 (y);
315
316 // check for non-canonical x
317 if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
318 x.w[1] = x.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
319 // check for non-canonical NaN payload
320 if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
321 (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
322 (x.w[0] > 0x38c15b09ffffffffull))) {
323 x.w[1] = x.w[1] & 0xffffc00000000000ull;
324 x.w[0] = 0x0ull;
200359e8 325 }
b2a00c89
L		 326 } else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf
327 x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
328 x.w[0] = 0x0ull;
329 } else { // x is not special
330 // check for non-canonical values - treated as zero
331 if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
332 // non-canonical
333 x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP);
334 x.w[0] = 0x0ull;
335 } else { // G0_G1 != 11
336 if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
337 ((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
338 && x.w[0] > 0x378d8e63ffffffffull)) {
339 // x is non-canonical if coefficient is larger than 10^34 -1
340 x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP);
341 x.w[0] = 0x0ull;
342 } else { // canonical
343 ;
344 }
345 }
346 }
347 // check for non-canonical y
348 if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
349 y.w[1] = y.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
350 // check for non-canonical NaN payload
351 if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
352 (((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
353 (y.w[0] > 0x38c15b09ffffffffull))) {
354 y.w[1] = y.w[1] & 0xffffc00000000000ull;
355 y.w[0] = 0x0ull;
356 }
357 } else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
358 y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
359 y.w[0] = 0x0ull;
360 } else { // y is not special
361 // check for non-canonical values - treated as zero
362 if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
363 // non-canonical
364 y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP);
365 y.w[0] = 0x0ull;
366 } else { // G0_G1 != 11
367 if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
368 ((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
369 && y.w[0] > 0x378d8e63ffffffffull)) {
370 // y is non-canonical if coefficient is larger than 10^34 -1
371 y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP);
372 y.w[0] = 0x0ull;
373 } else { // canonical
374 ;
375 }
376 }
377 }
378
379 // NaN (CASE1)
380 if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
381 if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNaN
382 // if x is SNAN, then return quiet (x)
383 *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
384 x.w[1] = x.w[1] & 0xfdffffffffffffffull; // quietize x
385 res = x;
386 } else { // x is QNaN
387 if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
388 if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
389 *pfpsf |= INVALID_EXCEPTION; // set invalid flag
390 }
391 res = x;
392 } else {
393 res = y;
394 }
200359e8 395 }
200359e8 396 BID_RETURN (res);
b2a00c89
L		 397 } else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
398 if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
399 *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
400 y.w[1] = y.w[1] & 0xfdffffffffffffffull; // quietize y
401 res = y;
402 } else {
403 // will return x (which is not NaN)
404 res = x;
200359e8 405 }
200359e8
L		 406 BID_RETURN (res);
407 }
408 // SIMPLE (CASE2)
409 // if all the bits are the same, these numbers are equal (not Greater).
410 if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
411 res = y;
412 BID_RETURN (res);
413 }
414 // INFINITY (CASE3)
415 if ((x.w[1] & MASK_INF) == MASK_INF) {
416 // if x infinity, it has maximum magnitude.
417 // Check if magnitudes are equal. If x is negative, return it.
418 res = ((x.w[1] & MASK_SIGN) == MASK_SIGN
b2a00c89 419 && (y.w[1] & MASK_INF) == MASK_INF) ? x : y;
200359e8
L		 420 BID_RETURN (res);
421 } else if ((y.w[1] & MASK_INF) == MASK_INF) {
422 // x is finite, so if y is infinity, then x is less in magnitude
423 res = x;
424 BID_RETURN (res);
425 }
426 // CONVERT X
427 sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
428 sig_x.w[0] = x.w[0];
429 exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
430
200359e8
L		 431 // CONVERT Y
432 exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
433 sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
434 sig_y.w[0] = y.w[0];
435
200359e8
L		 436 // ZERO (CASE4)
437 // some properties:
438 // (+ZERO == -ZERO) => therefore ignore the sign
439 // (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
440 // therefore ignore the exponent field
441 // (Any non-canonical # is considered 0)
b2a00c89 442 if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) {
200359e8
L		 443 res = x;
444 BID_RETURN (res);
445 }
b2a00c89 446 if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) {
200359e8
L		 447 res = y;
448 BID_RETURN (res);
449 }
450 // REDUNDANT REPRESENTATIONS (CASE6)
451 // check if exponents are the same and significands are the same
452 if (exp_y == exp_x && sig_x.w[1] == sig_y.w[1]
453 && sig_x.w[0] == sig_y.w[0]) {
b2a00c89 454 if (x.w[1] & 0x8000000000000000ull) { // x is negative
200359e8
L		 455 res = x;
456 BID_RETURN (res);
457 } else {
458 res = y;
459 BID_RETURN (res);
460 }
461 } else if (((sig_x.w[1] > sig_y.w[1] || (sig_x.w[1] == sig_y.w[1]
b2a00c89
L		 462 && sig_x.w[0] > sig_y.w[0]))
463 && exp_x == exp_y)
464 || ((sig_x.w[1] > sig_y.w[1]
465 || (sig_x.w[1] == sig_y.w[1]
466 && sig_x.w[0] >= sig_y.w[0]))
467 && exp_x > exp_y)) {
200359e8
L		 468 // if both components are either bigger or smaller, it is clear what
469 // needs to be done; also if the magnitudes are equal
470 res = y;
471 BID_RETURN (res);
472 } else if (((sig_y.w[1] > sig_x.w[1] || (sig_y.w[1] == sig_x.w[1]
b2a00c89
L		 473 && sig_y.w[0] > sig_x.w[0]))
474 && exp_y == exp_x)
475 || ((sig_y.w[1] > sig_x.w[1]
476 || (sig_y.w[1] == sig_x.w[1]
477 && sig_y.w[0] >= sig_x.w[0]))
478 && exp_y > exp_x)) {
200359e8
L		 479 res = x;
480 BID_RETURN (res);
481 } else {
b2a00c89 482 ; // continue
200359e8
L		 483 }
484 diff = exp_x - exp_y;
485 // if |exp_x - exp_y| < 33, it comes down to the compensated significand
b2a00c89 486 if (diff > 0) { // to simplify the loop below,
200359e8
L		 487 // if exp_x is 33 greater than exp_y, no need for compensation
488 if (diff > 33) {
b2a00c89 489 res = y; // difference cannot be greater than 10^33
200359e8
L		 490 BID_RETURN (res);
491 }
b2a00c89
L		 492 if (diff > 19) { //128 by 128 bit multiply -> 256 bits
493 __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
200359e8
L		 494 // if positive, return whichever significand is larger
495 // (converse if negative)
496 if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
b2a00c89
L		 497 && sig_n_prime256.w[1] == sig_y.w[1]
498 && (sig_n_prime256.w[0] == sig_y.w[0])) {
499 res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x; // if equal
500 BID_RETURN (res);
200359e8
L		 501 }
502 res = (((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
b2a00c89
L		 503 || (sig_n_prime256.w[1] > sig_y.w[1])
504 || (sig_n_prime256.w[1] == sig_y.w[1]
505 && sig_n_prime256.w[0] > sig_y.w[0])) ? y : x;
200359e8
L		 506 BID_RETURN (res);
507 }
b2a00c89 508 __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);
200359e8
L		 509 // if positive, return whichever significand is larger
510 // (converse if negative)
511 if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
b2a00c89 512 && (sig_n_prime192.w[0] == sig_y.w[0])) {
200359e8
L		 513 // if = in magnitude, return +, (if possible)
514 res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
515 BID_RETURN (res);
516 }
517 res = ((sig_n_prime192.w[2] > 0)
b2a00c89
L		 518 || (sig_n_prime192.w[1] > sig_y.w[1])
519 || (sig_n_prime192.w[1] == sig_y.w[1]
520 && sig_n_prime192.w[0] > sig_y.w[0])) ? y : x;
200359e8
L		 521 BID_RETURN (res);
522 }
523 diff = exp_y - exp_x;
524 // if exp_x is 33 less than exp_y, no need for compensation
525 if (diff > 33) {
526 res = x;
527 BID_RETURN (res);
528 }
b2a00c89 529 if (diff > 19) { //128 by 128 bit multiply -> 256 bits
200359e8 530 // adjust the y significand upwards
b2a00c89 531 __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
200359e8
L		 532 // if positive, return whichever significand is larger
533 // (converse if negative)
534 if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
b2a00c89
L		 535 && sig_n_prime256.w[1] == sig_x.w[1]
536 && (sig_n_prime256.w[0] == sig_x.w[0])) {
200359e8
L		 537 // if = in magnitude, return +, (if possible)
538 res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
539 BID_RETURN (res);
540 }
541 res = (sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0
b2a00c89
L		 542 && (sig_n_prime256.w[1] < sig_x.w[1]
543 || (sig_n_prime256.w[1] == sig_x.w[1]
544 && sig_n_prime256.w[0] < sig_x.w[0]))) ? y : x;
200359e8
L		 545 BID_RETURN (res);
546 }
547 // adjust the y significand upwards
b2a00c89 548 __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y);
200359e8
L		 549 // if positive, return whichever significand is larger (converse if negative)
550 if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
551 && (sig_n_prime192.w[0] == sig_x.w[0])) {
552 // if = in magnitude, return +, if possible)
553 res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
554 BID_RETURN (res);
555 }
b2a00c89
L		 556 res = (sig_n_prime192.w[2] == 0
557 && (sig_n_prime192.w[1] < sig_x.w[1]
558 || (sig_n_prime192.w[1] == sig_x.w[1]
559 && sig_n_prime192.w[0] < sig_x.w[0]))) ? y : x;
200359e8
L		 560 BID_RETURN (res);
561}
562
563/*****************************************************************************
564 * BID128 maximum function - returns greater of two numbers
565 *****************************************************************************/
566
567#if DECIMAL_CALL_BY_REFERENCE
568void
b2a00c89
L		 569bid128_maxnum (UINT128 * pres, UINT128 * px,
570 UINT128 * py _EXC_FLAGS_PARAM) {
200359e8
L		 571 UINT128 x = *px;
572 UINT128 y = *py;
573#else
574UINT128
b2a00c89 575bid128_maxnum (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) {
200359e8
L		 576#endif
577
578 UINT128 res;
579 int exp_x, exp_y;
580 int diff;
581 UINT128 sig_x, sig_y;
582 UINT192 sig_n_prime192;
583 UINT256 sig_n_prime256;
b2a00c89 584 char x_is_zero = 0, y_is_zero = 0;
200359e8 585
b2a00c89
L		 586 BID_SWAP128 (x);
587 BID_SWAP128 (y);
588
589 // check for non-canonical x
590 if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
591 x.w[1] = x.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
592 // check for non-canonical NaN payload
593 if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
594 (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
595 (x.w[0] > 0x38c15b09ffffffffull))) {
596 x.w[1] = x.w[1] & 0xffffc00000000000ull;
597 x.w[0] = 0x0ull;
200359e8 598 }
b2a00c89
L		 599 } else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf
600 x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
601 x.w[0] = 0x0ull;
602 } else { // x is not special
603 // check for non-canonical values - treated as zero
604 if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
605 // non-canonical
606 x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP);
607 x.w[0] = 0x0ull;
608 } else { // G0_G1 != 11
609 if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
610 ((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
611 && x.w[0] > 0x378d8e63ffffffffull)) {
612 // x is non-canonical if coefficient is larger than 10^34 -1
613 x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP);
614 x.w[0] = 0x0ull;
615 } else { // canonical
616 ;
617 }
618 }
619 }
620 // check for non-canonical y
621 if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
622 y.w[1] = y.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
623 // check for non-canonical NaN payload
624 if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
625 (((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
626 (y.w[0] > 0x38c15b09ffffffffull))) {
627 y.w[1] = y.w[1] & 0xffffc00000000000ull;
628 y.w[0] = 0x0ull;
629 }
630 } else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
631 y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
632 y.w[0] = 0x0ull;
633 } else { // y is not special
634 // check for non-canonical values - treated as zero
635 if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
636 // non-canonical
637 y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP);
638 y.w[0] = 0x0ull;
639 } else { // G0_G1 != 11
640 if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
641 ((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
642 && y.w[0] > 0x378d8e63ffffffffull)) {
643 // y is non-canonical if coefficient is larger than 10^34 -1
644 y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP);
645 y.w[0] = 0x0ull;
646 } else { // canonical
647 ;
648 }
649 }
650 }
651
652 // NaN (CASE1)
653 if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
654 if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNaN
655 // if x is SNAN, then return quiet (x)
656 *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
657 x.w[1] = x.w[1] & 0xfdffffffffffffffull; // quietize x
658 res = x;
659 } else { // x is QNaN
660 if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
661 if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
662 *pfpsf |= INVALID_EXCEPTION; // set invalid flag
663 }
664 res = x;
665 } else {
666 res = y;
667 }
200359e8 668 }
200359e8 669 BID_RETURN (res);
b2a00c89
L		 670 } else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
671 if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
672 *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
673 y.w[1] = y.w[1] & 0xfdffffffffffffffull; // quietize y
674 res = y;
675 } else {
676 // will return x (which is not NaN)
677 res = x;
200359e8 678 }
200359e8
L		 679 BID_RETURN (res);
680 }
681 // SIMPLE (CASE2)
682 // if all the bits are the same, these numbers are equal (not Greater).
683 if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
684 res = x;
685 BID_RETURN (res);
686 }
687 // INFINITY (CASE3)
688 if ((x.w[1] & MASK_INF) == MASK_INF) {
689 res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
690 BID_RETURN (res);
691 } else if ((y.w[1] & MASK_INF) == MASK_INF) {
692 // x is finite, so if y is positive infinity, then x is less, return 0
693 // if y is negative infinity, then x is greater, return 1
694 res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
695 BID_RETURN (res);
696 }
697 // CONVERT X
698 sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
699 sig_x.w[0] = x.w[0];
700 exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
701
200359e8
L		 702 // CONVERT Y
703 exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
704 sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
705 sig_y.w[0] = y.w[0];
706
200359e8
L		 707 // ZERO (CASE4)
708 // some properties:
709 // (+ZERO == -ZERO) => therefore ignore the sign
710 // (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
711 // therefore ignore the exponent field
712 // (Any non-canonical # is considered 0)
b2a00c89 713 if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) {
200359e8
L		 714 x_is_zero = 1;
715 }
b2a00c89 716 if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) {
200359e8
L		 717 y_is_zero = 1;
718 }
719
720 if (x_is_zero && y_is_zero) {
721 // if both numbers are zero, neither is greater => return either number
722 res = x;
723 BID_RETURN (res);
724 } else if (x_is_zero) {
725 // is x is zero, it is greater if Y is negative
726 res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
727 BID_RETURN (res);
728 } else if (y_is_zero) {
729 // is y is zero, X is greater if it is positive
730 res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? x : y;
731 BID_RETURN (res);
732 }
733 // OPPOSITE SIGN (CASE5)
734 // now, if the sign bits differ, x is greater if y is negative
735 if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
736 res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
737 BID_RETURN (res);
738 }
739 // REDUNDANT REPRESENTATIONS (CASE6)
740 // if exponents are the same, then we have a simple comparison of
741 // the significands
742 if (exp_y == exp_x) {
b2a00c89
L		 743 res = (((sig_x.w[1] > sig_y.w[1]) || (sig_x.w[1] == sig_y.w[1] &&
744 sig_x.w[0] >= sig_y.w[0])) ^
745 ((x.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y;
200359e8
L		 746 BID_RETURN (res);
747 }
748 // if both components are either bigger or smaller, it is clear what
749 // needs to be done
750 if ((sig_x.w[1] > sig_y.w[1]
751 || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
752 && exp_x >= exp_y) {
753 res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? x : y;
754 BID_RETURN (res);
755 }
756 if ((sig_x.w[1] < sig_y.w[1]
757 || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
758 && exp_x <= exp_y) {
759 res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
760 BID_RETURN (res);
761 }
762 diff = exp_x - exp_y;
763 // if |exp_x - exp_y| < 33, it comes down to the compensated significand
b2a00c89 764 if (diff > 0) { // to simplify the loop below,
200359e8
L		 765 // if exp_x is 33 greater than exp_y, no need for compensation
766 if (diff > 33) {
767 // difference cannot be greater than 10^33
768 res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? x : y;
769 BID_RETURN (res);
770 }
b2a00c89
L		 771 if (diff > 19) { //128 by 128 bit multiply -> 256 bits
772 __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
200359e8
L		 773 // if postitive, return whichever significand is larger
774 // (converse if negative)
775 res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
b2a00c89
L		 776 || (sig_n_prime256.w[1] > sig_y.w[1])
777 || (sig_n_prime256.w[1] == sig_y.w[1]
778 && sig_n_prime256.w[0] >
779 sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) ==
780 MASK_SIGN)) ? x : y;
200359e8
L		 781 BID_RETURN (res);
782 }
b2a00c89 783 __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);
200359e8
L		 784 // if postitive, return whichever significand is larger
785 // (converse if negative)
786 res =
787 (((sig_n_prime192.w[2] > 0) || (sig_n_prime192.w[1] > sig_y.w[1])
b2a00c89
L		 788 || (sig_n_prime192.w[1] == sig_y.w[1]
789 && sig_n_prime192.w[0] >
790 sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y;
200359e8
L		 791 BID_RETURN (res);
792 }
793 diff = exp_y - exp_x;
794 // if exp_x is 33 less than exp_y, no need for compensation
795 if (diff > 33) {
796 res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
797 BID_RETURN (res);
798 }
b2a00c89 799 if (diff > 19) { //128 by 128 bit multiply -> 256 bits
200359e8 800 // adjust the y significand upwards
b2a00c89 801 __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
200359e8
L		 802 // if postitive, return whichever significand is larger
803 // (converse if negative)
804 res =
805 ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
b2a00c89
L		 806 || (sig_n_prime256.w[1] > sig_x.w[1]
807 || (sig_n_prime256.w[1] == sig_x.w[1]
808 && sig_n_prime256.w[0] >
809 sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) !=
810 MASK_SIGN)) ? x : y;
200359e8
L		 811 BID_RETURN (res);
812 }
813 // adjust the y significand upwards
b2a00c89 814 __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y);
200359e8 815 // if postitive, return whichever significand is larger (converse if negative)
b2a00c89
L		 816 res =
817 ((sig_n_prime192.w[2] != 0
818 || (sig_n_prime192.w[1] > sig_x.w[1]
819 || (sig_n_prime192.w[1] == sig_x.w[1]
820 && sig_n_prime192.w[0] >
821 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) !=
822 MASK_SIGN)) ? x : y;
200359e8
L		 823 BID_RETURN (res);
824}
825
826/*****************************************************************************
827 * BID128 maximum magnitude function - returns greater of two numbers
828 *****************************************************************************/
829
830#if DECIMAL_CALL_BY_REFERENCE
831void
b2a00c89
L		 832bid128_maxnum_mag (UINT128 * pres, UINT128 * px,
833 UINT128 * py _EXC_FLAGS_PARAM) {
200359e8
L		 834 UINT128 x = *px;
835 UINT128 y = *py;
836#else
837UINT128
b2a00c89 838bid128_maxnum_mag (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) {
200359e8
L		 839#endif
840
841 UINT128 res;
842 int exp_x, exp_y;
843 int diff;
844 UINT128 sig_x, sig_y;
845 UINT192 sig_n_prime192;
846 UINT256 sig_n_prime256;
200359e8 847
b2a00c89
L		 848 BID_SWAP128 (x);
849 BID_SWAP128 (y);
850
851 // check for non-canonical x
852 if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
853 x.w[1] = x.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
854 // check for non-canonical NaN payload
855 if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
856 (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
857 (x.w[0] > 0x38c15b09ffffffffull))) {
858 x.w[1] = x.w[1] & 0xffffc00000000000ull;
859 x.w[0] = 0x0ull;
200359e8 860 }
b2a00c89
L		 861 } else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf
862 x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
863 x.w[0] = 0x0ull;
864 } else { // x is not special
865 // check for non-canonical values - treated as zero
866 if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
867 // non-canonical
868 x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP);
869 x.w[0] = 0x0ull;
870 } else { // G0_G1 != 11
871 if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
872 ((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
873 && x.w[0] > 0x378d8e63ffffffffull)) {
874 // x is non-canonical if coefficient is larger than 10^34 -1
875 x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP);
876 x.w[0] = 0x0ull;
877 } else { // canonical
878 ;
879 }
880 }
881 }
882 // check for non-canonical y
883 if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
884 y.w[1] = y.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
885 // check for non-canonical NaN payload
886 if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
887 (((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
888 (y.w[0] > 0x38c15b09ffffffffull))) {
889 y.w[1] = y.w[1] & 0xffffc00000000000ull;
890 y.w[0] = 0x0ull;
891 }
892 } else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
893 y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
894 y.w[0] = 0x0ull;
895 } else { // y is not special
896 // check for non-canonical values - treated as zero
897 if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
898 // non-canonical
899 y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP);
900 y.w[0] = 0x0ull;
901 } else { // G0_G1 != 11
902 if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
903 ((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull &&
904 y.w[0] > 0x378d8e63ffffffffull)) {
905 // y is non-canonical if coefficient is larger than 10^34 -1
906 y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP);
907 y.w[0] = 0x0ull;
908 } else { // canonical
909 ;
910 }
911 }
912 }
913
914 // NaN (CASE1)
915 if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
916 if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNaN
917 // if x is SNAN, then return quiet (x)
918 *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
919 x.w[1] = x.w[1] & 0xfdffffffffffffffull; // quietize x
920 res = x;
921 } else { // x is QNaN
922 if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
923 if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
924 *pfpsf |= INVALID_EXCEPTION; // set invalid flag
925 }
926 res = x;
927 } else {
928 res = y;
929 }
200359e8 930 }
200359e8 931 BID_RETURN (res);
b2a00c89
L		 932 } else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
933 if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
934 *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
935 y.w[1] = y.w[1] & 0xfdffffffffffffffull; // quietize y
936 res = y;
937 } else {
938 // will return x (which is not NaN)
939 res = x;
200359e8 940 }
200359e8
L		 941 BID_RETURN (res);
942 }
943 // SIMPLE (CASE2)
944 // if all the bits are the same, these numbers are equal (not Greater).
945 if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
946 res = y;
947 BID_RETURN (res);
948 }
949 // INFINITY (CASE3)
950 if ((x.w[1] & MASK_INF) == MASK_INF) {
951 // if x infinity, it has maximum magnitude
952 res = ((x.w[1] & MASK_SIGN) == MASK_SIGN
b2a00c89 953 && (y.w[1] & MASK_INF) == MASK_INF) ? y : x;
200359e8
L		 954 BID_RETURN (res);
955 } else if ((y.w[1] & MASK_INF) == MASK_INF) {
956 // x is finite, so if y is positive infinity, then x is less, return 0
957 // if y is negative infinity, then x is greater, return 1
958 res = y;
959 BID_RETURN (res);
960 }
961 // CONVERT X
962 sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
963 sig_x.w[0] = x.w[0];
964 exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
965
200359e8
L		 966 // CONVERT Y
967 exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
968 sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
969 sig_y.w[0] = y.w[0];
970
200359e8
L		 971 // ZERO (CASE4)
972 // some properties:
973 // (+ZERO == -ZERO) => therefore ignore the sign
974 // (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
975 // therefore ignore the exponent field
976 // (Any non-canonical # is considered 0)
b2a00c89 977 if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) {
200359e8
L		 978 res = y;
979 BID_RETURN (res);
980 }
b2a00c89 981 if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) {
200359e8
L		 982 res = x;
983 BID_RETURN (res);
984 }
985 // REDUNDANT REPRESENTATIONS (CASE6)
986 if (exp_y == exp_x && sig_x.w[1] == sig_y.w[1]
987 && sig_x.w[0] == sig_y.w[0]) {
988 // check if exponents are the same and significands are the same
b2a00c89 989 if (x.w[1] & 0x8000000000000000ull) { // x is negative
200359e8
L		 990 res = y;
991 BID_RETURN (res);
992 } else {
993 res = x;
994 BID_RETURN (res);
995 }
996 } else if (((sig_x.w[1] > sig_y.w[1] || (sig_x.w[1] == sig_y.w[1]
b2a00c89
L		 997 && sig_x.w[0] > sig_y.w[0]))
998 && exp_x == exp_y)
999 || ((sig_x.w[1] > sig_y.w[1]
1000 || (sig_x.w[1] == sig_y.w[1]
1001 && sig_x.w[0] >= sig_y.w[0]))
1002 && exp_x > exp_y)) {
200359e8
L		 1003 // if both components are either bigger or smaller, it is clear what
1004 // needs to be done; also if the magnitudes are equal
1005 res = x;
1006 BID_RETURN (res);
1007 } else if (((sig_y.w[1] > sig_x.w[1] || (sig_y.w[1] == sig_x.w[1]
b2a00c89
L		 1008 && sig_y.w[0] > sig_x.w[0]))
1009 && exp_y == exp_x)
1010 || ((sig_y.w[1] > sig_x.w[1]
1011 || (sig_y.w[1] == sig_x.w[1]
1012 && sig_y.w[0] >= sig_x.w[0]))
1013 && exp_y > exp_x)) {
200359e8
L		 1014 res = y;
1015 BID_RETURN (res);
1016 } else {
b2a00c89 1017 ; // continue
200359e8
L		 1018 }
1019 diff = exp_x - exp_y;
1020 // if |exp_x - exp_y| < 33, it comes down to the compensated significand
b2a00c89 1021 if (diff > 0) { // to simplify the loop below,
200359e8
L		 1022 // if exp_x is 33 greater than exp_y, no need for compensation
1023 if (diff > 33) {
b2a00c89 1024 res = x; // difference cannot be greater than 10^33
200359e8
L		 1025 BID_RETURN (res);
1026 }
b2a00c89
L		 1027 if (diff > 19) { //128 by 128 bit multiply -> 256 bits
1028 __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
200359e8
L		 1029 // if postitive, return whichever significand is larger
1030 // (converse if negative)
1031 if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
b2a00c89
L		 1032 && sig_n_prime256.w[1] == sig_y.w[1]
1033 && (sig_n_prime256.w[0] == sig_y.w[0])) {
1034 res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y; // if equal
1035 BID_RETURN (res);
200359e8
L		 1036 }
1037 res = (((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
b2a00c89
L		 1038 || (sig_n_prime256.w[1] > sig_y.w[1])
1039 || (sig_n_prime256.w[1] == sig_y.w[1]
1040 && sig_n_prime256.w[0] > sig_y.w[0])) ? x : y;
200359e8
L		 1041 BID_RETURN (res);
1042 }
b2a00c89 1043 __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);
200359e8
L		 1044 // if postitive, return whichever significand is larger (converse if negative)
1045 if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
b2a00c89 1046 && (sig_n_prime192.w[0] == sig_y.w[0])) {
200359e8
L		 1047 // if equal, return positive magnitude
1048 res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
1049 BID_RETURN (res);
1050 }
1051 res = ((sig_n_prime192.w[2] > 0)
b2a00c89
L		 1052 || (sig_n_prime192.w[1] > sig_y.w[1])
1053 || (sig_n_prime192.w[1] == sig_y.w[1]
1054 && sig_n_prime192.w[0] > sig_y.w[0])) ? x : y;
200359e8
L		 1055 BID_RETURN (res);
1056 }
1057 diff = exp_y - exp_x;
1058 // if exp_x is 33 less than exp_y, no need for compensation
1059 if (diff > 33) {
1060 res = y;
1061 BID_RETURN (res);
1062 }
b2a00c89 1063 if (diff > 19) { //128 by 128 bit multiply -> 256 bits
200359e8 1064 // adjust the y significand upwards
b2a00c89 1065 __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
200359e8
L		 1066 // if postitive, return whichever significand is larger
1067 // (converse if negative)
1068 if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
b2a00c89
L		 1069 && sig_n_prime256.w[1] == sig_x.w[1]
1070 && (sig_n_prime256.w[0] == sig_x.w[0])) {
200359e8
L		 1071 // if equal, return positive (if possible)
1072 res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
1073 BID_RETURN (res);
1074 }
1075 res = (sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0
b2a00c89
L		 1076 && (sig_n_prime256.w[1] < sig_x.w[1]
1077 || (sig_n_prime256.w[1] == sig_x.w[1]
1078 && sig_n_prime256.w[0] < sig_x.w[0]))) ? x : y;
200359e8
L		 1079 BID_RETURN (res);
1080 }
1081 // adjust the y significand upwards
b2a00c89 1082 __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y);
200359e8
L		 1083 // if postitive, return whichever significand is larger (converse if negative)
1084 if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
1085 && (sig_n_prime192.w[0] == sig_x.w[0])) {
1086 // if equal, return positive (if possible)
1087 res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
1088 BID_RETURN (res);
1089 }
b2a00c89
L		 1090 res = (sig_n_prime192.w[2] == 0
1091 && (sig_n_prime192.w[1] < sig_x.w[1]
1092 || (sig_n_prime192.w[1] == sig_x.w[1]
1093 && sig_n_prime192.w[0] < sig_x.w[0]))) ? x : y;
200359e8
L		 1094 BID_RETURN (res);
1095}
Mirror of https://gcc.gnu.org/git/gcc.git