Mercurial > hg > CbC > CbC_gcc
comparison libgcc/config/libbid/bid128_noncomp.c @ 0:a06113de4d67
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author | kent <kent@cr.ie.u-ryukyu.ac.jp> |
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date | Fri, 17 Jul 2009 14:47:48 +0900 |
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children | 04ced10e8804 |
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1 /* Copyright (C) 2007, 2009 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 } |