| 6515 |
serge |
1 |
/* Copyright (C) 2007-2015 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 |
. */ |
|
|
23 |
|
|
|
24 |
#include "bid_internal.h" |
|
|
25 |
|
|
|
26 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_equal, x, y) |
|
|
27 |
|
|
|
28 |
int res; |
|
|
29 |
int exp_x, exp_y, exp_t; |
|
|
30 |
UINT128 sig_x, sig_y, sig_t; |
|
|
31 |
UINT192 sig_n_prime192; |
|
|
32 |
UINT256 sig_n_prime256; |
|
|
33 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
34 |
|
|
|
35 |
// NaN (CASE1) |
|
|
36 |
// if either number is NAN, the comparison is unordered, |
|
|
37 |
// rather than equal : return 0 |
|
|
38 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
39 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
40 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN |
|
|
41 |
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) { |
|
|
42 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
43 |
} |
|
|
44 |
{ |
|
|
45 |
res = 0; |
|
|
46 |
BID_RETURN (res); |
|
|
47 |
} |
|
|
48 |
} |
|
|
49 |
// SIMPLE (CASE2) |
|
|
50 |
// if all the bits are the same, these numbers are equivalent. |
|
|
51 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
52 |
res = 1; |
|
|
53 |
BID_RETURN (res); |
|
|
54 |
} |
|
|
55 |
// INFINITY (CASE3) |
|
|
56 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
57 |
if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
58 |
res = (((x.w[1] ^ y.w[1]) & MASK_SIGN) != MASK_SIGN); |
|
|
59 |
BID_RETURN (res); |
|
|
60 |
} else { |
|
|
61 |
res = 0; |
|
|
62 |
BID_RETURN (res); |
|
|
63 |
} |
|
|
64 |
} |
|
|
65 |
if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
66 |
res = 0; |
|
|
67 |
BID_RETURN (res); |
|
|
68 |
} |
|
|
69 |
// CONVERT X |
|
|
70 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
71 |
sig_x.w[0] = x.w[0]; |
|
|
72 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
73 |
|
|
|
74 |
// CHECK IF X IS CANONICAL |
|
|
75 |
// 9999999999999999999999999999999999(decimal) = |
|
|
76 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
77 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
78 |
// If the value exceeds that, it is interpreted as 0. |
|
|
79 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
80 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
81 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
82 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
83 |
non_canon_x = 1; |
|
|
84 |
else |
|
|
85 |
non_canon_x = 0; |
|
|
86 |
|
|
|
87 |
// CONVERT Y |
|
|
88 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
89 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
90 |
sig_y.w[0] = y.w[0]; |
|
|
91 |
|
|
|
92 |
// CHECK IF Y IS CANONICAL |
|
|
93 |
// 9999999999999999999999999999999999(decimal) = |
|
|
94 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
95 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
96 |
// If the value exceeds that, it is interpreted as 0. |
|
|
97 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
98 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
99 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
100 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
101 |
non_canon_y = 1; |
|
|
102 |
else |
|
|
103 |
non_canon_y = 0; |
|
|
104 |
|
|
|
105 |
// some properties: |
|
|
106 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
107 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
108 |
// ignore the exponent field |
|
|
109 |
// (Any non-canonical # is considered 0) |
|
|
110 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
111 |
x_is_zero = 1; |
|
|
112 |
} |
|
|
113 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
114 |
y_is_zero = 1; |
|
|
115 |
} |
|
|
116 |
|
|
|
117 |
if (x_is_zero && y_is_zero) { |
|
|
118 |
res = 1; |
|
|
119 |
BID_RETURN (res); |
|
|
120 |
} else if ((x_is_zero && !y_is_zero) || (!x_is_zero && y_is_zero)) { |
|
|
121 |
res = 0; |
|
|
122 |
BID_RETURN (res); |
|
|
123 |
} |
|
|
124 |
// OPPOSITE SIGN (CASE5) |
|
|
125 |
// now, if the sign bits differ => not equal : return 0 |
|
|
126 |
if ((x.w[1] ^ y.w[1]) & MASK_SIGN) { |
|
|
127 |
res = 0; |
|
|
128 |
BID_RETURN (res); |
|
|
129 |
} |
|
|
130 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
131 |
if (exp_x > exp_y) { // to simplify the loop below, |
|
|
132 |
SWAP (exp_x, exp_y, exp_t); // put the larger exp in y, |
|
|
133 |
SWAP (sig_x.w[1], sig_y.w[1], sig_t.w[1]); // and the smaller exp in x |
|
|
134 |
SWAP (sig_x.w[0], sig_y.w[0], sig_t.w[0]); // and the smaller exp in x |
|
|
135 |
} |
|
|
136 |
|
|
|
137 |
|
|
|
138 |
if (exp_y - exp_x > 33) { |
|
|
139 |
res = 0; |
|
|
140 |
BID_RETURN (res); |
|
|
141 |
} // difference cannot be greater than 10^33 |
|
|
142 |
|
|
|
143 |
if (exp_y - exp_x > 19) { |
|
|
144 |
// recalculate y's significand upwards |
|
|
145 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, |
|
|
146 |
ten2k128[exp_y - exp_x - 20]); |
|
|
147 |
{ |
|
|
148 |
res = ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0) |
|
|
149 |
&& (sig_n_prime256.w[1] == sig_x.w[1]) |
|
|
150 |
&& (sig_n_prime256.w[0] == sig_x.w[0])); |
|
|
151 |
BID_RETURN (res); |
|
|
152 |
} |
|
|
153 |
|
|
|
154 |
} |
|
|
155 |
//else{ |
|
|
156 |
// recalculate y's significand upwards |
|
|
157 |
__mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y); |
|
|
158 |
{ |
|
|
159 |
res = ((sig_n_prime192.w[2] == 0) |
|
|
160 |
&& (sig_n_prime192.w[1] == sig_x.w[1]) |
|
|
161 |
&& (sig_n_prime192.w[0] == sig_x.w[0])); |
|
|
162 |
BID_RETURN (res); |
|
|
163 |
} |
|
|
164 |
} |
|
|
165 |
|
|
|
166 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_greater, x, |
|
|
167 |
y) |
|
|
168 |
|
|
|
169 |
int res; |
|
|
170 |
int exp_x, exp_y; |
|
|
171 |
int diff; |
|
|
172 |
UINT128 sig_x, sig_y; |
|
|
173 |
UINT192 sig_n_prime192; |
|
|
174 |
UINT256 sig_n_prime256; |
|
|
175 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
176 |
|
|
|
177 |
// NaN (CASE1) |
|
|
178 |
// if either number is NAN, the comparison is unordered, rather than |
|
|
179 |
// equal : return 0 |
|
|
180 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
181 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
182 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN |
|
|
183 |
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) { |
|
|
184 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
185 |
} |
|
|
186 |
{ |
|
|
187 |
res = 0; |
|
|
188 |
BID_RETURN (res); |
|
|
189 |
} |
|
|
190 |
} |
|
|
191 |
// SIMPLE (CASE2) |
|
|
192 |
// if all the bits are the same, these numbers are equal (not Greater). |
|
|
193 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
194 |
res = 0; |
|
|
195 |
BID_RETURN (res); |
|
|
196 |
} |
|
|
197 |
// INFINITY (CASE3) |
|
|
198 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
199 |
// if x is neg infinity, there is no way it is greater than y, return 0 |
|
|
200 |
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) { |
|
|
201 |
res = 0; |
|
|
202 |
BID_RETURN (res); |
|
|
203 |
} |
|
|
204 |
// x is pos infinity, it is greater, unless y is positive infinity => |
|
|
205 |
// return y!=pos_infinity |
|
|
206 |
else { |
|
|
207 |
res = (((y.w[1] & MASK_INF) != MASK_INF) |
|
|
208 |
|| ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
209 |
BID_RETURN (res); |
|
|
210 |
} |
|
|
211 |
} else if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
212 |
// x is finite, so if y is positive infinity, then x is less, return 0 |
|
|
213 |
// if y is negative infinity, then x is greater, return 1 |
|
|
214 |
{ |
|
|
215 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
216 |
BID_RETURN (res); |
|
|
217 |
} |
|
|
218 |
} |
|
|
219 |
// CONVERT X |
|
|
220 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
221 |
sig_x.w[0] = x.w[0]; |
|
|
222 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
223 |
|
|
|
224 |
// CHECK IF X IS CANONICAL |
|
|
225 |
// 9999999999999999999999999999999999(decimal) = |
|
|
226 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
227 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
228 |
// If the value exceeds that, it is interpreted as 0. |
|
|
229 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
230 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
231 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
232 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
233 |
non_canon_x = 1; |
|
|
234 |
else |
|
|
235 |
non_canon_x = 0; |
|
|
236 |
|
|
|
237 |
// CONVERT Y |
|
|
238 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
239 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
240 |
sig_y.w[0] = y.w[0]; |
|
|
241 |
|
|
|
242 |
// CHECK IF Y IS CANONICAL |
|
|
243 |
// 9999999999999999999999999999999999(decimal) = |
|
|
244 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
245 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
246 |
// If the value exceeds that, it is interpreted as 0. |
|
|
247 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
248 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
249 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
250 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
251 |
non_canon_y = 1; |
|
|
252 |
else |
|
|
253 |
non_canon_y = 0; |
|
|
254 |
|
|
|
255 |
// ZERO (CASE4) |
|
|
256 |
// some properties: |
|
|
257 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
258 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
259 |
// ignore the exponent field |
|
|
260 |
// (Any non-canonical # is considered 0) |
|
|
261 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
262 |
x_is_zero = 1; |
|
|
263 |
} |
|
|
264 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
265 |
y_is_zero = 1; |
|
|
266 |
} |
|
|
267 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
268 |
if (x_is_zero && y_is_zero) { |
|
|
269 |
res = 0; |
|
|
270 |
BID_RETURN (res); |
|
|
271 |
} |
|
|
272 |
// is x is zero, it is greater if Y is negative |
|
|
273 |
else if (x_is_zero) { |
|
|
274 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
275 |
BID_RETURN (res); |
|
|
276 |
} |
|
|
277 |
// is y is zero, X is greater if it is positive |
|
|
278 |
else if (y_is_zero) { |
|
|
279 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
280 |
BID_RETURN (res); |
|
|
281 |
} |
|
|
282 |
// OPPOSITE SIGN (CASE5) |
|
|
283 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
284 |
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { |
|
|
285 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
286 |
BID_RETURN (res); |
|
|
287 |
} |
|
|
288 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
289 |
// if exponents are the same, then we have a simple comparison |
|
|
290 |
// of the significands |
|
|
291 |
if (exp_y == exp_x) { |
|
|
292 |
res = (((sig_x.w[1] > sig_y.w[1]) |
|
|
293 |
|| (sig_x.w[1] == sig_y.w[1] |
|
|
294 |
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == |
|
|
295 |
MASK_SIGN)); |
|
|
296 |
BID_RETURN (res); |
|
|
297 |
} |
|
|
298 |
// if both components are either bigger or smaller, |
|
|
299 |
// it is clear what needs to be done |
|
|
300 |
if ((sig_x.w[1] > sig_y.w[1] |
|
|
301 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) |
|
|
302 |
&& exp_x >= exp_y) { |
|
|
303 |
{ |
|
|
304 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
305 |
BID_RETURN (res); |
|
|
306 |
} |
|
|
307 |
} |
|
|
308 |
if ((sig_x.w[1] < sig_y.w[1] |
|
|
309 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) |
|
|
310 |
&& exp_x <= exp_y) { |
|
|
311 |
{ |
|
|
312 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
313 |
BID_RETURN (res); |
|
|
314 |
} |
|
|
315 |
} |
|
|
316 |
|
|
|
317 |
diff = exp_x - exp_y; |
|
|
318 |
|
|
|
319 |
// if |exp_x - exp_y| < 33, it comes down to the compensated significand |
|
|
320 |
if (diff > 0) { // to simplify the loop below, |
|
|
321 |
|
|
|
322 |
// if exp_x is 33 greater than exp_y, no need for compensation |
|
|
323 |
if (diff > 33) { |
|
|
324 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
325 |
BID_RETURN (res); |
|
|
326 |
} // difference cannot be greater than 10^33 |
|
|
327 |
|
|
|
328 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
329 |
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); |
|
|
330 |
|
|
|
331 |
// if postitive, return whichever significand is larger |
|
|
332 |
// (converse if negative) |
|
|
333 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
334 |
&& sig_n_prime256.w[1] == sig_y.w[1] |
|
|
335 |
&& (sig_n_prime256.w[0] == sig_y.w[0])) { |
|
|
336 |
res = 0; |
|
|
337 |
BID_RETURN (res); |
|
|
338 |
} // if equal, return 0 |
|
|
339 |
{ |
|
|
340 |
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) |
|
|
341 |
|| (sig_n_prime256.w[1] > sig_y.w[1]) |
|
|
342 |
|| (sig_n_prime256.w[1] == sig_y.w[1] |
|
|
343 |
&& sig_n_prime256.w[0] > |
|
|
344 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
345 |
BID_RETURN (res); |
|
|
346 |
} |
|
|
347 |
} |
|
|
348 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
349 |
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x); |
|
|
350 |
|
|
|
351 |
// if postitive, return whichever significand is larger |
|
|
352 |
// (converse if negative) |
|
|
353 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] |
|
|
354 |
&& (sig_n_prime192.w[0] == sig_y.w[0])) { |
|
|
355 |
res = 0; |
|
|
356 |
BID_RETURN (res); |
|
|
357 |
} // if equal, return 0 |
|
|
358 |
{ |
|
|
359 |
res = (((sig_n_prime192.w[2] > 0) || |
|
|
360 |
(sig_n_prime192.w[1] > sig_y.w[1]) || |
|
|
361 |
(sig_n_prime192.w[1] == sig_y.w[1] && |
|
|
362 |
sig_n_prime192.w[0] > sig_y.w[0])) ^ |
|
|
363 |
((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
364 |
BID_RETURN (res); |
|
|
365 |
} |
|
|
366 |
} |
|
|
367 |
|
|
|
368 |
diff = exp_y - exp_x; |
|
|
369 |
|
|
|
370 |
// if exp_x is 33 less than exp_y, no need for compensation |
|
|
371 |
if (diff > 33) { |
|
|
372 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
373 |
BID_RETURN (res); |
|
|
374 |
} |
|
|
375 |
|
|
|
376 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
377 |
// adjust the y significand upwards |
|
|
378 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); |
|
|
379 |
|
|
|
380 |
// if postitive, return whichever significand is larger |
|
|
381 |
// (converse if negative) |
|
|
382 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
383 |
&& sig_n_prime256.w[1] == sig_x.w[1] |
|
|
384 |
&& (sig_n_prime256.w[0] == sig_x.w[0])) { |
|
|
385 |
res = 0; |
|
|
386 |
BID_RETURN (res); |
|
|
387 |
} // if equal, return 0 |
|
|
388 |
{ |
|
|
389 |
res = ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 || |
|
|
390 |
(sig_n_prime256.w[1] > sig_x.w[1] || |
|
|
391 |
(sig_n_prime256.w[1] == sig_x.w[1] && |
|
|
392 |
sig_n_prime256.w[0] > sig_x.w[0]))) ^ |
|
|
393 |
((x.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
394 |
BID_RETURN (res); |
|
|
395 |
} |
|
|
396 |
} |
|
|
397 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
398 |
// adjust the y significand upwards |
|
|
399 |
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y); |
|
|
400 |
|
|
|
401 |
// if postitive, return whichever significand is larger |
|
|
402 |
// (converse if negative) |
|
|
403 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] |
|
|
404 |
&& (sig_n_prime192.w[0] == sig_x.w[0])) { |
|
|
405 |
res = 0; |
|
|
406 |
BID_RETURN (res); |
|
|
407 |
} // if equal, return 0 |
|
|
408 |
{ |
|
|
409 |
res = (sig_n_prime192.w[2] != 0 |
|
|
410 |
|| (sig_n_prime192.w[1] > sig_x.w[1] |
|
|
411 |
|| (sig_n_prime192.w[1] == sig_x.w[1] |
|
|
412 |
&& sig_n_prime192.w[0] > |
|
|
413 |
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
414 |
BID_RETURN (res); |
|
|
415 |
} |
|
|
416 |
} |
|
|
417 |
|
|
|
418 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, |
|
|
419 |
bid128_quiet_greater_equal, x, |
|
|
420 |
y) |
|
|
421 |
|
|
|
422 |
int res; |
|
|
423 |
int exp_x, exp_y; |
|
|
424 |
int diff; |
|
|
425 |
UINT128 sig_x, sig_y; |
|
|
426 |
UINT192 sig_n_prime192; |
|
|
427 |
UINT256 sig_n_prime256; |
|
|
428 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
429 |
|
|
|
430 |
// NaN (CASE1) |
|
|
431 |
// if either number is NAN, the comparison is unordered, |
|
|
432 |
// rather than equal : return 1 |
|
|
433 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
434 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
435 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN |
|
|
436 |
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) { |
|
|
437 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
438 |
} |
|
|
439 |
{ |
|
|
440 |
res = 0; |
|
|
441 |
BID_RETURN (res); |
|
|
442 |
} |
|
|
443 |
} |
|
|
444 |
// SIMPLE (CASE2) |
|
|
445 |
// if all the bits are the same, these numbers are equal (not Greater). |
|
|
446 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
447 |
res = 1; |
|
|
448 |
BID_RETURN (res); |
|
|
449 |
} |
|
|
450 |
// INFINITY (CASE3) |
|
|
451 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
452 |
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } |
|
|
453 |
if ((x.w[1] & MASK_SIGN) == MASK_SIGN) |
|
|
454 |
// x is -inf, so it is less than y unless y is -inf |
|
|
455 |
{ |
|
|
456 |
res = (((y.w[1] & MASK_INF) == MASK_INF) |
|
|
457 |
&& (y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
458 |
BID_RETURN (res); |
|
|
459 |
} else |
|
|
460 |
// x is pos_inf, no way for it to be less than y |
|
|
461 |
{ |
|
|
462 |
res = 1; |
|
|
463 |
BID_RETURN (res); |
|
|
464 |
} |
|
|
465 |
} else if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
466 |
// x is finite, so if y is positive infinity, then x is less, return 0 |
|
|
467 |
// if y is negative infinity, then x is greater, return 1 |
|
|
468 |
{ |
|
|
469 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
470 |
BID_RETURN (res); |
|
|
471 |
} |
|
|
472 |
} |
|
|
473 |
// CONVERT X |
|
|
474 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
475 |
sig_x.w[0] = x.w[0]; |
|
|
476 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
477 |
|
|
|
478 |
// CHECK IF X IS CANONICAL |
|
|
479 |
// 9999999999999999999999999999999999(decimal) = |
|
|
480 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
481 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
482 |
// If the value exceeds that, it is interpreted as 0. |
|
|
483 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
484 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
485 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
486 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
487 |
non_canon_x = 1; |
|
|
488 |
else |
|
|
489 |
non_canon_x = 0; |
|
|
490 |
|
|
|
491 |
// CONVERT Y |
|
|
492 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
493 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
494 |
sig_y.w[0] = y.w[0]; |
|
|
495 |
|
|
|
496 |
// CHECK IF Y IS CANONICAL |
|
|
497 |
// 9999999999999999999999999999999999(decimal) = |
|
|
498 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
499 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
500 |
// If the value exceeds that, it is interpreted as 0. |
|
|
501 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
502 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
503 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
504 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
505 |
non_canon_y = 1; |
|
|
506 |
else |
|
|
507 |
non_canon_y = 0; |
|
|
508 |
|
|
|
509 |
// ZERO (CASE4) |
|
|
510 |
// some properties: |
|
|
511 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
512 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
513 |
// ignore the exponent field |
|
|
514 |
// (Any non-canonical # is considered 0) |
|
|
515 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
516 |
x_is_zero = 1; |
|
|
517 |
} |
|
|
518 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
519 |
y_is_zero = 1; |
|
|
520 |
} |
|
|
521 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
522 |
if (x_is_zero && y_is_zero) { |
|
|
523 |
res = 1; |
|
|
524 |
BID_RETURN (res); |
|
|
525 |
} |
|
|
526 |
// is x is zero, it is greater if Y is negative |
|
|
527 |
else if (x_is_zero) { |
|
|
528 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
529 |
BID_RETURN (res); |
|
|
530 |
} |
|
|
531 |
// is y is zero, X is greater if it is positive |
|
|
532 |
else if (y_is_zero) { |
|
|
533 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
534 |
BID_RETURN (res); |
|
|
535 |
} |
|
|
536 |
// OPPOSITE SIGN (CASE5) |
|
|
537 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
538 |
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { |
|
|
539 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
540 |
BID_RETURN (res); |
|
|
541 |
} |
|
|
542 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
543 |
// if exponents are the same, then we have a simple comparison of the |
|
|
544 |
// significands |
|
|
545 |
if (exp_y == exp_x) { |
|
|
546 |
res = (((sig_x.w[1] > sig_y.w[1]) |
|
|
547 |
|| (sig_x.w[1] == sig_y.w[1] |
|
|
548 |
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == |
|
|
549 |
MASK_SIGN)); |
|
|
550 |
BID_RETURN (res); |
|
|
551 |
} |
|
|
552 |
// if both components are either bigger or smaller, |
|
|
553 |
// it is clear what needs to be done |
|
|
554 |
if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0] |
|
|
555 |
&& exp_x > exp_y) { |
|
|
556 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
557 |
BID_RETURN (res); |
|
|
558 |
} |
|
|
559 |
if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0] |
|
|
560 |
&& exp_x < exp_y) { |
|
|
561 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
562 |
BID_RETURN (res); |
|
|
563 |
} |
|
|
564 |
|
|
|
565 |
diff = exp_x - exp_y; |
|
|
566 |
|
|
|
567 |
// if |exp_x - exp_y| < 33, it comes down to the compensated significand |
|
|
568 |
if (diff > 0) { // to simplify the loop below, |
|
|
569 |
|
|
|
570 |
// if exp_x is 33 greater than exp_y, no need for compensation |
|
|
571 |
if (diff > 33) { |
|
|
572 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
573 |
BID_RETURN (res); |
|
|
574 |
} // difference cannot be greater than 10^33 |
|
|
575 |
|
|
|
576 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
577 |
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); |
|
|
578 |
|
|
|
579 |
|
|
|
580 |
// if postitive, return whichever significand is larger |
|
|
581 |
// (converse if negative) |
|
|
582 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
583 |
&& sig_n_prime256.w[1] == sig_y.w[1] |
|
|
584 |
&& (sig_n_prime256.w[0] == sig_y.w[0])) { |
|
|
585 |
res = 1; |
|
|
586 |
BID_RETURN (res); |
|
|
587 |
} // if equal, return 1 |
|
|
588 |
{ |
|
|
589 |
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) |
|
|
590 |
|| (sig_n_prime256.w[1] > sig_y.w[1]) |
|
|
591 |
|| (sig_n_prime256.w[1] == sig_y.w[1] |
|
|
592 |
&& sig_n_prime256.w[0] > |
|
|
593 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
594 |
BID_RETURN (res); |
|
|
595 |
} |
|
|
596 |
} |
|
|
597 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
598 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); |
|
|
599 |
|
|
|
600 |
// if postitive, return whichever significand is larger |
|
|
601 |
// (converse if negative) |
|
|
602 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] |
|
|
603 |
&& (sig_n_prime192.w[0] == sig_y.w[0])) { |
|
|
604 |
res = 1; |
|
|
605 |
BID_RETURN (res); |
|
|
606 |
} // if equal, return 1 |
|
|
607 |
{ |
|
|
608 |
res = (((sig_n_prime192.w[2] > 0) |
|
|
609 |
|| (sig_n_prime192.w[1] > sig_y.w[1]) |
|
|
610 |
|| (sig_n_prime192.w[1] == sig_y.w[1] |
|
|
611 |
&& sig_n_prime192.w[0] > |
|
|
612 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
613 |
BID_RETURN (res); |
|
|
614 |
} |
|
|
615 |
} |
|
|
616 |
|
|
|
617 |
diff = exp_y - exp_x; |
|
|
618 |
|
|
|
619 |
// if exp_x is 33 less than exp_y, no need for compensation |
|
|
620 |
if (diff > 33) { |
|
|
621 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
622 |
BID_RETURN (res); |
|
|
623 |
} |
|
|
624 |
|
|
|
625 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
626 |
// adjust the y significand upwards |
|
|
627 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); |
|
|
628 |
|
|
|
629 |
|
|
|
630 |
// if postitive, return whichever significand is larger |
|
|
631 |
// (converse if negative) |
|
|
632 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
633 |
&& sig_n_prime256.w[1] == sig_x.w[1] |
|
|
634 |
&& (sig_n_prime256.w[0] == sig_x.w[0])) { |
|
|
635 |
res = 1; |
|
|
636 |
BID_RETURN (res); |
|
|
637 |
} // if equal, return 1 |
|
|
638 |
{ |
|
|
639 |
res = ((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0 |
|
|
640 |
&& (sig_n_prime256.w[1] < sig_x.w[1] |
|
|
641 |
|| (sig_n_prime256.w[1] == sig_x.w[1] |
|
|
642 |
&& sig_n_prime256.w[0] < |
|
|
643 |
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == |
|
|
644 |
MASK_SIGN)); |
|
|
645 |
BID_RETURN (res); |
|
|
646 |
} |
|
|
647 |
} |
|
|
648 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
649 |
// adjust the y significand upwards |
|
|
650 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); |
|
|
651 |
|
|
|
652 |
// if postitive, return whichever significand is larger |
|
|
653 |
// (converse if negative) |
|
|
654 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] |
|
|
655 |
&& (sig_n_prime192.w[0] == sig_x.w[0])) { |
|
|
656 |
res = 1; |
|
|
657 |
BID_RETURN (res); |
|
|
658 |
} // if equal, return 1 |
|
|
659 |
{ |
|
|
660 |
res = (sig_n_prime192.w[2] == 0 |
|
|
661 |
&& (sig_n_prime192.w[1] < sig_x.w[1] |
|
|
662 |
|| (sig_n_prime192.w[1] == sig_x.w[1] |
|
|
663 |
&& sig_n_prime192.w[0] < |
|
|
664 |
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
665 |
BID_RETURN (res); |
|
|
666 |
} |
|
|
667 |
} |
|
|
668 |
|
|
|
669 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, |
|
|
670 |
bid128_quiet_greater_unordered, |
|
|
671 |
x, y) |
|
|
672 |
|
|
|
673 |
int res; |
|
|
674 |
int exp_x, exp_y; |
|
|
675 |
int diff; |
|
|
676 |
UINT128 sig_x, sig_y; |
|
|
677 |
UINT192 sig_n_prime192; |
|
|
678 |
UINT256 sig_n_prime256; |
|
|
679 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
680 |
|
|
|
681 |
// NaN (CASE1) |
|
|
682 |
// if either number is NAN, the comparison is unordered, |
|
|
683 |
// rather than |
|
|
684 |
// equal : return 1 |
|
|
685 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
686 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
687 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN |
|
|
688 |
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) { |
|
|
689 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
690 |
} |
|
|
691 |
{ |
|
|
692 |
res = 1; |
|
|
693 |
BID_RETURN (res); |
|
|
694 |
} |
|
|
695 |
} |
|
|
696 |
// SIMPLE (CASE2) |
|
|
697 |
// if all the bits are the same, these numbers are equal (not Greater). |
|
|
698 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
699 |
res = 0; |
|
|
700 |
BID_RETURN (res); |
|
|
701 |
} |
|
|
702 |
// INFINITY (CASE3) |
|
|
703 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
704 |
// if x is neg infinity, there is no way it is greater than y, return 0 |
|
|
705 |
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) { |
|
|
706 |
res = 0; |
|
|
707 |
BID_RETURN (res); |
|
|
708 |
} |
|
|
709 |
// x is pos infinity, it is greater, unless y is positive infinity => |
|
|
710 |
// return y!=pos_infinity |
|
|
711 |
else { |
|
|
712 |
res = (((y.w[1] & MASK_INF) != MASK_INF) |
|
|
713 |
|| ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
714 |
BID_RETURN (res); |
|
|
715 |
} |
|
|
716 |
} else if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
717 |
// x is finite, so if y is positive infinity, then x is less, return 0 |
|
|
718 |
// if y is negative infinity, then x is greater, return 1 |
|
|
719 |
{ |
|
|
720 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
721 |
BID_RETURN (res); |
|
|
722 |
} |
|
|
723 |
} |
|
|
724 |
// CONVERT X |
|
|
725 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
726 |
sig_x.w[0] = x.w[0]; |
|
|
727 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
728 |
|
|
|
729 |
// CHECK IF X IS CANONICAL |
|
|
730 |
// 9999999999999999999999999999999999(decimal) = |
|
|
731 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
732 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
733 |
// If the value exceeds that, it is interpreted as 0. |
|
|
734 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
735 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
736 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
737 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
738 |
non_canon_x = 1; |
|
|
739 |
else |
|
|
740 |
non_canon_x = 0; |
|
|
741 |
|
|
|
742 |
// CONVERT Y |
|
|
743 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
744 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
745 |
sig_y.w[0] = y.w[0]; |
|
|
746 |
|
|
|
747 |
// CHECK IF Y IS CANONICAL |
|
|
748 |
// 9999999999999999999999999999999999(decimal) = |
|
|
749 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
750 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
751 |
// If the value exceeds that, it is interpreted as 0. |
|
|
752 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
753 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
754 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
755 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
756 |
non_canon_y = 1; |
|
|
757 |
else |
|
|
758 |
non_canon_y = 0; |
|
|
759 |
|
|
|
760 |
// ZERO (CASE4) |
|
|
761 |
// some properties: |
|
|
762 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
763 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
764 |
// ignore the exponent field |
|
|
765 |
// (Any non-canonical # is considered 0) |
|
|
766 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
767 |
x_is_zero = 1; |
|
|
768 |
} |
|
|
769 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
770 |
y_is_zero = 1; |
|
|
771 |
} |
|
|
772 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
773 |
if (x_is_zero && y_is_zero) { |
|
|
774 |
res = 0; |
|
|
775 |
BID_RETURN (res); |
|
|
776 |
} |
|
|
777 |
// is x is zero, it is greater if Y is negative |
|
|
778 |
else if (x_is_zero) { |
|
|
779 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
780 |
BID_RETURN (res); |
|
|
781 |
} |
|
|
782 |
// is y is zero, X is greater if it is positive |
|
|
783 |
else if (y_is_zero) { |
|
|
784 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
785 |
BID_RETURN (res); |
|
|
786 |
} |
|
|
787 |
// OPPOSITE SIGN (CASE5) |
|
|
788 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
789 |
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { |
|
|
790 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
791 |
BID_RETURN (res); |
|
|
792 |
} |
|
|
793 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
794 |
// if exponents are the same, then we have a simple comparison of the |
|
|
795 |
// significands |
|
|
796 |
if (exp_y == exp_x) { |
|
|
797 |
res = (((sig_x.w[1] > sig_y.w[1]) |
|
|
798 |
|| (sig_x.w[1] == sig_y.w[1] |
|
|
799 |
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == |
|
|
800 |
MASK_SIGN)); |
|
|
801 |
BID_RETURN (res); |
|
|
802 |
} |
|
|
803 |
// if both components are either bigger or smaller, |
|
|
804 |
// it is clear what needs to be done |
|
|
805 |
if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0] |
|
|
806 |
&& exp_x > exp_y) { |
|
|
807 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
808 |
BID_RETURN (res); |
|
|
809 |
} |
|
|
810 |
if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0] |
|
|
811 |
&& exp_x < exp_y) { |
|
|
812 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
813 |
BID_RETURN (res); |
|
|
814 |
} |
|
|
815 |
|
|
|
816 |
diff = exp_x - exp_y; |
|
|
817 |
|
|
|
818 |
// if |exp_x - exp_y| < 33, it comes down to the compensated significand |
|
|
819 |
if (diff > 0) { // to simplify the loop below, |
|
|
820 |
|
|
|
821 |
// if exp_x is 33 greater than exp_y, no need for compensation |
|
|
822 |
if (diff > 33) { |
|
|
823 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
824 |
BID_RETURN (res); |
|
|
825 |
} // difference cannot be greater than 10^33 |
|
|
826 |
|
|
|
827 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
828 |
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); |
|
|
829 |
|
|
|
830 |
|
|
|
831 |
// if postitive, return whichever significand is larger |
|
|
832 |
// (converse if negative) |
|
|
833 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
834 |
&& sig_n_prime256.w[1] == sig_y.w[1] |
|
|
835 |
&& (sig_n_prime256.w[0] == sig_y.w[0])) { |
|
|
836 |
res = 0; |
|
|
837 |
BID_RETURN (res); |
|
|
838 |
} // if equal, return 0 |
|
|
839 |
{ |
|
|
840 |
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) |
|
|
841 |
|| (sig_n_prime256.w[1] > sig_y.w[1]) |
|
|
842 |
|| (sig_n_prime256.w[1] == sig_y.w[1] |
|
|
843 |
&& sig_n_prime256.w[0] > |
|
|
844 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
845 |
BID_RETURN (res); |
|
|
846 |
} |
|
|
847 |
} |
|
|
848 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
849 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); |
|
|
850 |
|
|
|
851 |
// if postitive, return whichever significand is larger |
|
|
852 |
// (converse if negative) |
|
|
853 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] |
|
|
854 |
&& (sig_n_prime192.w[0] == sig_y.w[0])) { |
|
|
855 |
res = 0; |
|
|
856 |
BID_RETURN (res); |
|
|
857 |
} // if equal, return 0 |
|
|
858 |
{ |
|
|
859 |
res = (((sig_n_prime192.w[2] > 0) |
|
|
860 |
|| (sig_n_prime192.w[1] > sig_y.w[1]) |
|
|
861 |
|| (sig_n_prime192.w[1] == sig_y.w[1] |
|
|
862 |
&& sig_n_prime192.w[0] > |
|
|
863 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
864 |
BID_RETURN (res); |
|
|
865 |
} |
|
|
866 |
} |
|
|
867 |
|
|
|
868 |
diff = exp_y - exp_x; |
|
|
869 |
|
|
|
870 |
// if exp_x is 33 less than exp_y, no need for compensation |
|
|
871 |
if (diff > 33) { |
|
|
872 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
873 |
BID_RETURN (res); |
|
|
874 |
} |
|
|
875 |
|
|
|
876 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
877 |
// adjust the y significand upwards |
|
|
878 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); |
|
|
879 |
|
|
|
880 |
|
|
|
881 |
// if postitive, return whichever significand is larger |
|
|
882 |
// (converse if negative) |
|
|
883 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
884 |
&& sig_n_prime256.w[1] == sig_x.w[1] |
|
|
885 |
&& (sig_n_prime256.w[0] == sig_x.w[0])) { |
|
|
886 |
res = 0; |
|
|
887 |
BID_RETURN (res); |
|
|
888 |
} // if equal, return 0 |
|
|
889 |
{ |
|
|
890 |
res = ((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0 |
|
|
891 |
&& (sig_n_prime256.w[1] < sig_x.w[1] |
|
|
892 |
|| (sig_n_prime256.w[1] == sig_x.w[1] |
|
|
893 |
&& sig_n_prime256.w[0] < |
|
|
894 |
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == |
|
|
895 |
MASK_SIGN)); |
|
|
896 |
BID_RETURN (res); |
|
|
897 |
} |
|
|
898 |
} |
|
|
899 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
900 |
// adjust the y significand upwards |
|
|
901 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); |
|
|
902 |
|
|
|
903 |
// if postitive, return whichever significand is larger |
|
|
904 |
// (converse if negative) |
|
|
905 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] |
|
|
906 |
&& (sig_n_prime192.w[0] == sig_x.w[0])) { |
|
|
907 |
res = 0; |
|
|
908 |
BID_RETURN (res); |
|
|
909 |
} // if equal, return 0 |
|
|
910 |
{ |
|
|
911 |
res = (sig_n_prime192.w[2] == 0 |
|
|
912 |
&& (sig_n_prime192.w[1] < sig_x.w[1] |
|
|
913 |
|| (sig_n_prime192.w[1] == sig_x.w[1] |
|
|
914 |
&& sig_n_prime192.w[0] < |
|
|
915 |
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
916 |
BID_RETURN (res); |
|
|
917 |
} |
|
|
918 |
} |
|
|
919 |
|
|
|
920 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_less, x, y) |
|
|
921 |
|
|
|
922 |
int res; |
|
|
923 |
int exp_x, exp_y; |
|
|
924 |
int diff; |
|
|
925 |
UINT128 sig_x, sig_y; |
|
|
926 |
UINT192 sig_n_prime192; |
|
|
927 |
UINT256 sig_n_prime256; |
|
|
928 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
929 |
|
|
|
930 |
// NaN (CASE1) |
|
|
931 |
// if either number is NAN, the comparison is unordered, |
|
|
932 |
// rather than equal : return 0 |
|
|
933 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
934 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
935 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN |
|
|
936 |
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) { |
|
|
937 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
938 |
} |
|
|
939 |
{ |
|
|
940 |
res = 0; |
|
|
941 |
BID_RETURN (res); |
|
|
942 |
} |
|
|
943 |
} |
|
|
944 |
// SIMPLE (CASE2) |
|
|
945 |
// if all the bits are the same, these numbers are equal. |
|
|
946 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
947 |
res = 0; |
|
|
948 |
BID_RETURN (res); |
|
|
949 |
} |
|
|
950 |
// INFINITY (CASE3) |
|
|
951 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
952 |
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } |
|
|
953 |
if ((x.w[1] & MASK_SIGN) == MASK_SIGN) |
|
|
954 |
// x is -inf, so it is less than y unless y is -inf |
|
|
955 |
{ |
|
|
956 |
res = (((y.w[1] & MASK_INF) != MASK_INF) |
|
|
957 |
|| (y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
958 |
BID_RETURN (res); |
|
|
959 |
} else |
|
|
960 |
// x is pos_inf, no way for it to be less than y |
|
|
961 |
{ |
|
|
962 |
res = 0; |
|
|
963 |
BID_RETURN (res); |
|
|
964 |
} |
|
|
965 |
} else if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
966 |
// x is finite, so if y is positive infinity, then x is less, return 0 |
|
|
967 |
// if y is negative infinity, then x is greater, return 1 |
|
|
968 |
{ |
|
|
969 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
970 |
BID_RETURN (res); |
|
|
971 |
} |
|
|
972 |
} |
|
|
973 |
// CONVERT X |
|
|
974 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
975 |
sig_x.w[0] = x.w[0]; |
|
|
976 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
977 |
|
|
|
978 |
// CHECK IF X IS CANONICAL |
|
|
979 |
// 9999999999999999999999999999999999(decimal) = |
|
|
980 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
981 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
982 |
// If the value exceeds that, it is interpreted as 0. |
|
|
983 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
984 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
985 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
986 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
987 |
non_canon_x = 1; |
|
|
988 |
else |
|
|
989 |
non_canon_x = 0; |
|
|
990 |
|
|
|
991 |
// CONVERT Y |
|
|
992 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
993 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
994 |
sig_y.w[0] = y.w[0]; |
|
|
995 |
|
|
|
996 |
// CHECK IF Y IS CANONICAL |
|
|
997 |
// 9999999999999999999999999999999999(decimal) = |
|
|
998 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
999 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
1000 |
// If the value exceeds that, it is interpreted as 0. |
|
|
1001 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
1002 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
1003 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
1004 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
1005 |
non_canon_y = 1; |
|
|
1006 |
else |
|
|
1007 |
non_canon_y = 0; |
|
|
1008 |
|
|
|
1009 |
// ZERO (CASE4) |
|
|
1010 |
// some properties: |
|
|
1011 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
1012 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
1013 |
// ignore the exponent field |
|
|
1014 |
// (Any non-canonical # is considered 0) |
|
|
1015 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
1016 |
x_is_zero = 1; |
|
|
1017 |
} |
|
|
1018 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
1019 |
y_is_zero = 1; |
|
|
1020 |
} |
|
|
1021 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
1022 |
if (x_is_zero && y_is_zero) { |
|
|
1023 |
res = 0; |
|
|
1024 |
BID_RETURN (res); |
|
|
1025 |
} |
|
|
1026 |
// is x is zero, it is greater if Y is negative |
|
|
1027 |
else if (x_is_zero) { |
|
|
1028 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1029 |
BID_RETURN (res); |
|
|
1030 |
} |
|
|
1031 |
// is y is zero, X is greater if it is positive |
|
|
1032 |
else if (y_is_zero) { |
|
|
1033 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
1034 |
BID_RETURN (res); |
|
|
1035 |
} |
|
|
1036 |
// OPPOSITE SIGN (CASE5) |
|
|
1037 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
1038 |
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { |
|
|
1039 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1040 |
BID_RETURN (res); |
|
|
1041 |
} |
|
|
1042 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
1043 |
// if exponents are the same, then we have a simple comparison of the |
|
|
1044 |
// significands |
|
|
1045 |
if (exp_y == exp_x) { |
|
|
1046 |
res = (((sig_x.w[1] > sig_y.w[1]) |
|
|
1047 |
|| (sig_x.w[1] == sig_y.w[1] |
|
|
1048 |
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) != |
|
|
1049 |
MASK_SIGN)); |
|
|
1050 |
BID_RETURN (res); |
|
|
1051 |
} |
|
|
1052 |
// if both components are either bigger or smaller, |
|
|
1053 |
// it is clear what needs to be done |
|
|
1054 |
if ((sig_x.w[1] > sig_y.w[1] |
|
|
1055 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) |
|
|
1056 |
&& exp_x >= exp_y) { |
|
|
1057 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
1058 |
BID_RETURN (res); |
|
|
1059 |
} |
|
|
1060 |
if ((sig_x.w[1] < sig_y.w[1] |
|
|
1061 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) |
|
|
1062 |
&& exp_x <= exp_y) { |
|
|
1063 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1064 |
BID_RETURN (res); |
|
|
1065 |
} |
|
|
1066 |
|
|
|
1067 |
diff = exp_x - exp_y; |
|
|
1068 |
|
|
|
1069 |
// if |exp_x - exp_y| < 33, it comes down to the compensated significand |
|
|
1070 |
if (diff > 0) { // to simplify the loop below, |
|
|
1071 |
|
|
|
1072 |
// if exp_x is 33 greater than exp_y, no need for compensation |
|
|
1073 |
if (diff > 33) { |
|
|
1074 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
1075 |
BID_RETURN (res); |
|
|
1076 |
} // difference cannot be greater than 10^33 |
|
|
1077 |
|
|
|
1078 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
1079 |
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); |
|
|
1080 |
|
|
|
1081 |
|
|
|
1082 |
// if postitive, return whichever significand is larger |
|
|
1083 |
// (converse if negative) |
|
|
1084 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
1085 |
&& sig_n_prime256.w[1] == sig_y.w[1] |
|
|
1086 |
&& (sig_n_prime256.w[0] == sig_y.w[0])) { |
|
|
1087 |
res = 0; |
|
|
1088 |
BID_RETURN (res); |
|
|
1089 |
} // if equal, return 0 |
|
|
1090 |
{ |
|
|
1091 |
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) |
|
|
1092 |
|| (sig_n_prime256.w[1] > sig_y.w[1]) |
|
|
1093 |
|| (sig_n_prime256.w[1] == sig_y.w[1] |
|
|
1094 |
&& sig_n_prime256.w[0] > |
|
|
1095 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
1096 |
BID_RETURN (res); |
|
|
1097 |
} |
|
|
1098 |
} |
|
|
1099 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
1100 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); |
|
|
1101 |
|
|
|
1102 |
// if postitive, return whichever significand is larger |
|
|
1103 |
// (converse if negative) |
|
|
1104 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] |
|
|
1105 |
&& (sig_n_prime192.w[0] == sig_y.w[0])) { |
|
|
1106 |
res = 0; |
|
|
1107 |
BID_RETURN (res); |
|
|
1108 |
} // if equal, return 0 |
|
|
1109 |
{ |
|
|
1110 |
res = (((sig_n_prime192.w[2] > 0) |
|
|
1111 |
|| (sig_n_prime192.w[1] > sig_y.w[1]) |
|
|
1112 |
|| (sig_n_prime192.w[1] == sig_y.w[1] |
|
|
1113 |
&& sig_n_prime192.w[0] > |
|
|
1114 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
1115 |
BID_RETURN (res); |
|
|
1116 |
} |
|
|
1117 |
} |
|
|
1118 |
|
|
|
1119 |
diff = exp_y - exp_x; |
|
|
1120 |
|
|
|
1121 |
// if exp_x is 33 less than exp_y, no need for compensation |
|
|
1122 |
if (diff > 33) { |
|
|
1123 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1124 |
BID_RETURN (res); |
|
|
1125 |
} |
|
|
1126 |
|
|
|
1127 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
1128 |
// adjust the y significand upwards |
|
|
1129 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); |
|
|
1130 |
|
|
|
1131 |
// if postitive, return whichever significand is larger |
|
|
1132 |
// (converse if negative) |
|
|
1133 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
1134 |
&& sig_n_prime256.w[1] == sig_x.w[1] |
|
|
1135 |
&& (sig_n_prime256.w[0] == sig_x.w[0])) { |
|
|
1136 |
res = 0; |
|
|
1137 |
BID_RETURN (res); |
|
|
1138 |
} // if equal, return 1 |
|
|
1139 |
{ |
|
|
1140 |
res = ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 |
|
|
1141 |
|| (sig_n_prime256.w[1] > sig_x.w[1] |
|
|
1142 |
|| (sig_n_prime256.w[1] == sig_x.w[1] |
|
|
1143 |
&& sig_n_prime256.w[0] > |
|
|
1144 |
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == |
|
|
1145 |
MASK_SIGN)); |
|
|
1146 |
BID_RETURN (res); |
|
|
1147 |
} |
|
|
1148 |
} |
|
|
1149 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
1150 |
// adjust the y significand upwards |
|
|
1151 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); |
|
|
1152 |
|
|
|
1153 |
// if postitive, return whichever significand is larger |
|
|
1154 |
// (converse if negative) |
|
|
1155 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] |
|
|
1156 |
&& (sig_n_prime192.w[0] == sig_x.w[0])) { |
|
|
1157 |
res = 0; |
|
|
1158 |
BID_RETURN (res); |
|
|
1159 |
} // if equal, return 0 |
|
|
1160 |
{ |
|
|
1161 |
res = (sig_n_prime192.w[2] != 0 |
|
|
1162 |
|| (sig_n_prime192.w[1] > sig_x.w[1] |
|
|
1163 |
|| (sig_n_prime192.w[1] == sig_x.w[1] |
|
|
1164 |
&& sig_n_prime192.w[0] > |
|
|
1165 |
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
1166 |
BID_RETURN (res); |
|
|
1167 |
} |
|
|
1168 |
} |
|
|
1169 |
|
|
|
1170 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_less_equal, |
|
|
1171 |
x, y) |
|
|
1172 |
|
|
|
1173 |
int res; |
|
|
1174 |
int exp_x, exp_y; |
|
|
1175 |
int diff; |
|
|
1176 |
UINT128 sig_x, sig_y; |
|
|
1177 |
UINT192 sig_n_prime192; |
|
|
1178 |
UINT256 sig_n_prime256; |
|
|
1179 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
1180 |
|
|
|
1181 |
// NaN (CASE1) |
|
|
1182 |
// if either number is NAN, the comparison is unordered, |
|
|
1183 |
// rather than equal : return 0 |
|
|
1184 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
1185 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
1186 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN |
|
|
1187 |
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) { |
|
|
1188 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1189 |
} |
|
|
1190 |
{ |
|
|
1191 |
res = 0; |
|
|
1192 |
BID_RETURN (res); |
|
|
1193 |
} |
|
|
1194 |
} |
|
|
1195 |
// SIMPLE (CASE2) |
|
|
1196 |
// if all the bits are the same, these numbers are equal (not Greater). |
|
|
1197 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
1198 |
res = 1; |
|
|
1199 |
BID_RETURN (res); |
|
|
1200 |
} |
|
|
1201 |
// INFINITY (CASE3) |
|
|
1202 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
1203 |
// if x is neg infinity, there is no way it is greater than y, return 1 |
|
|
1204 |
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) { |
|
|
1205 |
res = 1; |
|
|
1206 |
BID_RETURN (res); |
|
|
1207 |
} |
|
|
1208 |
// x is pos infinity, it is greater, unless y is positive infinity => |
|
|
1209 |
// return y!=pos_infinity |
|
|
1210 |
else { |
|
|
1211 |
res = (((y.w[1] & MASK_INF) == MASK_INF) |
|
|
1212 |
&& ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
1213 |
BID_RETURN (res); |
|
|
1214 |
} |
|
|
1215 |
} else if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
1216 |
// x is finite, so if y is positive infinity, then x is less, return 0 |
|
|
1217 |
// if y is negative infinity, then x is greater, return 1 |
|
|
1218 |
{ |
|
|
1219 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1220 |
BID_RETURN (res); |
|
|
1221 |
} |
|
|
1222 |
} |
|
|
1223 |
// CONVERT X |
|
|
1224 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
1225 |
sig_x.w[0] = x.w[0]; |
|
|
1226 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
1227 |
|
|
|
1228 |
// CHECK IF X IS CANONICAL |
|
|
1229 |
// 9999999999999999999999999999999999(decimal) = |
|
|
1230 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
1231 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
1232 |
// If the value exceeds that, it is interpreted as 0. |
|
|
1233 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
1234 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
1235 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
1236 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
1237 |
non_canon_x = 1; |
|
|
1238 |
else |
|
|
1239 |
non_canon_x = 0; |
|
|
1240 |
|
|
|
1241 |
// CONVERT Y |
|
|
1242 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
1243 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
1244 |
sig_y.w[0] = y.w[0]; |
|
|
1245 |
|
|
|
1246 |
// CHECK IF Y IS CANONICAL |
|
|
1247 |
// 9999999999999999999999999999999999(decimal) = |
|
|
1248 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
1249 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
1250 |
// If the value exceeds that, it is interpreted as 0. |
|
|
1251 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
1252 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
1253 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
1254 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
1255 |
non_canon_y = 1; |
|
|
1256 |
else |
|
|
1257 |
non_canon_y = 0; |
|
|
1258 |
|
|
|
1259 |
// ZERO (CASE4) |
|
|
1260 |
// some properties: |
|
|
1261 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
1262 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
1263 |
// ignore the exponent field |
|
|
1264 |
// (Any non-canonical # is considered 0) |
|
|
1265 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
1266 |
x_is_zero = 1; |
|
|
1267 |
} |
|
|
1268 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
1269 |
y_is_zero = 1; |
|
|
1270 |
} |
|
|
1271 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
1272 |
if (x_is_zero && y_is_zero) { |
|
|
1273 |
res = 1; |
|
|
1274 |
BID_RETURN (res); |
|
|
1275 |
} |
|
|
1276 |
// is x is zero, it is greater if Y is negative |
|
|
1277 |
else if (x_is_zero) { |
|
|
1278 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1279 |
BID_RETURN (res); |
|
|
1280 |
} |
|
|
1281 |
// is y is zero, X is greater if it is positive |
|
|
1282 |
else if (y_is_zero) { |
|
|
1283 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
1284 |
BID_RETURN (res); |
|
|
1285 |
} |
|
|
1286 |
// OPPOSITE SIGN (CASE5) |
|
|
1287 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
1288 |
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { |
|
|
1289 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1290 |
BID_RETURN (res); |
|
|
1291 |
} |
|
|
1292 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
1293 |
// if exponents are the same, then we have a simple comparison of the |
|
|
1294 |
// significands |
|
|
1295 |
if (exp_y == exp_x) { |
|
|
1296 |
res = (((sig_x.w[1] > sig_y.w[1]) || (sig_x.w[1] == sig_y.w[1] && |
|
|
1297 |
sig_x.w[0] >= |
|
|
1298 |
sig_y.w[0])) ^ ((x. |
|
|
1299 |
w[1] & |
|
|
1300 |
MASK_SIGN) != |
|
|
1301 |
MASK_SIGN)); |
|
|
1302 |
BID_RETURN (res); |
|
|
1303 |
} |
|
|
1304 |
// if both components are either bigger or smaller, |
|
|
1305 |
// it is clear what needs to be done |
|
|
1306 |
if ((sig_x.w[1] > sig_y.w[1] |
|
|
1307 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) |
|
|
1308 |
&& exp_x >= exp_y) { |
|
|
1309 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
1310 |
BID_RETURN (res); |
|
|
1311 |
} |
|
|
1312 |
if ((sig_x.w[1] < sig_y.w[1] |
|
|
1313 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) |
|
|
1314 |
&& exp_x <= exp_y) { |
|
|
1315 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1316 |
BID_RETURN (res); |
|
|
1317 |
} |
|
|
1318 |
|
|
|
1319 |
diff = exp_x - exp_y; |
|
|
1320 |
|
|
|
1321 |
// if |exp_x - exp_y| < 33, it comes down to the compensated significand |
|
|
1322 |
if (diff > 0) { // to simplify the loop below, |
|
|
1323 |
|
|
|
1324 |
// if exp_x is 33 greater than exp_y, no need for compensation |
|
|
1325 |
if (diff > 33) { |
|
|
1326 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
1327 |
BID_RETURN (res); |
|
|
1328 |
} // difference cannot be greater than 10^33 |
|
|
1329 |
|
|
|
1330 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
1331 |
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); |
|
|
1332 |
|
|
|
1333 |
|
|
|
1334 |
// if postitive, return whichever significand is larger |
|
|
1335 |
// (converse if negative) |
|
|
1336 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
1337 |
&& sig_n_prime256.w[1] == sig_y.w[1] |
|
|
1338 |
&& (sig_n_prime256.w[0] == sig_y.w[0])) { |
|
|
1339 |
res = 1; |
|
|
1340 |
BID_RETURN (res); |
|
|
1341 |
} // if equal, return 0 |
|
|
1342 |
{ |
|
|
1343 |
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) |
|
|
1344 |
|| (sig_n_prime256.w[1] > sig_y.w[1]) |
|
|
1345 |
|| (sig_n_prime256.w[1] == sig_y.w[1] |
|
|
1346 |
&& sig_n_prime256.w[0] > |
|
|
1347 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
1348 |
BID_RETURN (res); |
|
|
1349 |
} |
|
|
1350 |
} |
|
|
1351 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
1352 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); |
|
|
1353 |
|
|
|
1354 |
// if postitive, return whichever significand is larger |
|
|
1355 |
// (converse if negative) |
|
|
1356 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] |
|
|
1357 |
&& (sig_n_prime192.w[0] == sig_y.w[0])) { |
|
|
1358 |
res = 1; |
|
|
1359 |
BID_RETURN (res); |
|
|
1360 |
} // if equal, return 0 |
|
|
1361 |
{ |
|
|
1362 |
res = (((sig_n_prime192.w[2] > 0) |
|
|
1363 |
|| (sig_n_prime192.w[1] > sig_y.w[1]) |
|
|
1364 |
|| (sig_n_prime192.w[1] == sig_y.w[1] |
|
|
1365 |
&& sig_n_prime192.w[0] > |
|
|
1366 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
1367 |
BID_RETURN (res); |
|
|
1368 |
} |
|
|
1369 |
} |
|
|
1370 |
|
|
|
1371 |
diff = exp_y - exp_x; |
|
|
1372 |
|
|
|
1373 |
// if exp_x is 33 less than exp_y, no need for compensation |
|
|
1374 |
if (diff > 33) { |
|
|
1375 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1376 |
BID_RETURN (res); |
|
|
1377 |
} |
|
|
1378 |
|
|
|
1379 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
1380 |
// adjust the y significand upwards |
|
|
1381 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); |
|
|
1382 |
|
|
|
1383 |
|
|
|
1384 |
// if postitive, return whichever significand is larger |
|
|
1385 |
// (converse if negative) |
|
|
1386 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
1387 |
&& sig_n_prime256.w[1] == sig_x.w[1] |
|
|
1388 |
&& (sig_n_prime256.w[0] == sig_x.w[0])) { |
|
|
1389 |
res = 1; |
|
|
1390 |
BID_RETURN (res); |
|
|
1391 |
} // if equal, return 0 |
|
|
1392 |
{ |
|
|
1393 |
res = |
|
|
1394 |
((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 |
|
|
1395 |
|| (sig_n_prime256.w[1] > sig_x.w[1] |
|
|
1396 |
|| (sig_n_prime256.w[1] == sig_x.w[1] |
|
|
1397 |
&& sig_n_prime256.w[0] > |
|
|
1398 |
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
1399 |
BID_RETURN (res); |
|
|
1400 |
} |
|
|
1401 |
} |
|
|
1402 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
1403 |
// adjust the y significand upwards |
|
|
1404 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); |
|
|
1405 |
|
|
|
1406 |
// if postitive, return whichever significand is larger |
|
|
1407 |
// (converse if negative) |
|
|
1408 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] |
|
|
1409 |
&& (sig_n_prime192.w[0] == sig_x.w[0])) { |
|
|
1410 |
res = 1; |
|
|
1411 |
BID_RETURN (res); |
|
|
1412 |
} // if equal, return 0 |
|
|
1413 |
{ |
|
|
1414 |
res = (sig_n_prime192.w[2] != 0 |
|
|
1415 |
|| (sig_n_prime192.w[1] > sig_x.w[1] |
|
|
1416 |
|| (sig_n_prime192.w[1] == sig_x.w[1] |
|
|
1417 |
&& sig_n_prime192.w[0] > |
|
|
1418 |
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
1419 |
BID_RETURN (res); |
|
|
1420 |
} |
|
|
1421 |
} |
|
|
1422 |
|
|
|
1423 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, |
|
|
1424 |
bid128_quiet_less_unordered, |
|
|
1425 |
x, y) |
|
|
1426 |
|
|
|
1427 |
int res; |
|
|
1428 |
int exp_x, exp_y; |
|
|
1429 |
int diff; |
|
|
1430 |
UINT128 sig_x, sig_y; |
|
|
1431 |
UINT192 sig_n_prime192; |
|
|
1432 |
UINT256 sig_n_prime256; |
|
|
1433 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
1434 |
|
|
|
1435 |
// NaN (CASE1) |
|
|
1436 |
// if either number is NAN, the comparison is unordered |
|
|
1437 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
1438 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
1439 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN |
|
|
1440 |
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) { |
|
|
1441 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1442 |
} |
|
|
1443 |
{ |
|
|
1444 |
res = 1; |
|
|
1445 |
BID_RETURN (res); |
|
|
1446 |
} |
|
|
1447 |
} |
|
|
1448 |
// SIMPLE (CASE2) |
|
|
1449 |
// if all the bits are the same, these numbers are equal. |
|
|
1450 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
1451 |
res = 0; |
|
|
1452 |
BID_RETURN (res); |
|
|
1453 |
} |
|
|
1454 |
// INFINITY (CASE3) |
|
|
1455 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
1456 |
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } |
|
|
1457 |
if ((x.w[1] & MASK_SIGN) == MASK_SIGN) |
|
|
1458 |
// x is -inf, so it is less than y unless y is -inf |
|
|
1459 |
{ |
|
|
1460 |
res = (((y.w[1] & MASK_INF) != MASK_INF) |
|
|
1461 |
|| (y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1462 |
BID_RETURN (res); |
|
|
1463 |
} else |
|
|
1464 |
// x is pos_inf, no way for it to be less than y |
|
|
1465 |
{ |
|
|
1466 |
res = 0; |
|
|
1467 |
BID_RETURN (res); |
|
|
1468 |
} |
|
|
1469 |
} else if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
1470 |
// x is finite, so if y is positive infinity, then x is less, return 0 |
|
|
1471 |
// if y is negative infinity, then x is greater, return 1 |
|
|
1472 |
{ |
|
|
1473 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1474 |
BID_RETURN (res); |
|
|
1475 |
} |
|
|
1476 |
} |
|
|
1477 |
// CONVERT X |
|
|
1478 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
1479 |
sig_x.w[0] = x.w[0]; |
|
|
1480 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
1481 |
|
|
|
1482 |
// CHECK IF X IS CANONICAL |
|
|
1483 |
// 9999999999999999999999999999999999(decimal) = |
|
|
1484 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
1485 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
1486 |
// If the value exceeds that, it is interpreted as 0. |
|
|
1487 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
1488 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
1489 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
1490 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
1491 |
non_canon_x = 1; |
|
|
1492 |
else |
|
|
1493 |
non_canon_x = 0; |
|
|
1494 |
|
|
|
1495 |
// CONVERT Y |
|
|
1496 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
1497 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
1498 |
sig_y.w[0] = y.w[0]; |
|
|
1499 |
|
|
|
1500 |
// CHECK IF Y IS CANONICAL |
|
|
1501 |
// 9999999999999999999999999999999999(decimal) = |
|
|
1502 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
1503 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
1504 |
// If the value exceeds that, it is interpreted as 0. |
|
|
1505 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
1506 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
1507 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
1508 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
1509 |
non_canon_y = 1; |
|
|
1510 |
else |
|
|
1511 |
non_canon_y = 0; |
|
|
1512 |
|
|
|
1513 |
// ZERO (CASE4) |
|
|
1514 |
// some properties: |
|
|
1515 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
1516 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
1517 |
// ignore the exponent field |
|
|
1518 |
// (Any non-canonical # is considered 0) |
|
|
1519 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
1520 |
x_is_zero = 1; |
|
|
1521 |
} |
|
|
1522 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
1523 |
y_is_zero = 1; |
|
|
1524 |
} |
|
|
1525 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
1526 |
if (x_is_zero && y_is_zero) { |
|
|
1527 |
res = 0; |
|
|
1528 |
BID_RETURN (res); |
|
|
1529 |
} |
|
|
1530 |
// is x is zero, it is greater if Y is negative |
|
|
1531 |
else if (x_is_zero) { |
|
|
1532 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1533 |
BID_RETURN (res); |
|
|
1534 |
} |
|
|
1535 |
// is y is zero, X is greater if it is positive |
|
|
1536 |
else if (y_is_zero) { |
|
|
1537 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
1538 |
BID_RETURN (res); |
|
|
1539 |
} |
|
|
1540 |
// OPPOSITE SIGN (CASE5) |
|
|
1541 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
1542 |
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { |
|
|
1543 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1544 |
BID_RETURN (res); |
|
|
1545 |
} |
|
|
1546 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
1547 |
// if exponents are the same, then we have a simple comparison |
|
|
1548 |
// of the significands |
|
|
1549 |
if (exp_y == exp_x) { |
|
|
1550 |
res = (((sig_x.w[1] > sig_y.w[1]) |
|
|
1551 |
|| (sig_x.w[1] == sig_y.w[1] |
|
|
1552 |
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) != |
|
|
1553 |
MASK_SIGN)); |
|
|
1554 |
BID_RETURN (res); |
|
|
1555 |
} |
|
|
1556 |
// if both components are either bigger or smaller, |
|
|
1557 |
// it is clear what needs to be done |
|
|
1558 |
if ((sig_x.w[1] > sig_y.w[1] |
|
|
1559 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) |
|
|
1560 |
&& exp_x >= exp_y) { |
|
|
1561 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
1562 |
BID_RETURN (res); |
|
|
1563 |
} |
|
|
1564 |
if ((sig_x.w[1] < sig_y.w[1] |
|
|
1565 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) |
|
|
1566 |
&& exp_x <= exp_y) { |
|
|
1567 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1568 |
BID_RETURN (res); |
|
|
1569 |
} |
|
|
1570 |
|
|
|
1571 |
diff = exp_x - exp_y; |
|
|
1572 |
|
|
|
1573 |
// if |exp_x - exp_y| < 33, it comes down to the compensated significand |
|
|
1574 |
if (diff > 0) { // to simplify the loop below, |
|
|
1575 |
|
|
|
1576 |
// if exp_x is 33 greater than exp_y, no need for compensation |
|
|
1577 |
if (diff > 33) { |
|
|
1578 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
1579 |
BID_RETURN (res); |
|
|
1580 |
} // difference cannot be greater than 10^33 |
|
|
1581 |
|
|
|
1582 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
1583 |
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); |
|
|
1584 |
|
|
|
1585 |
|
|
|
1586 |
// if postitive, return whichever significand is larger |
|
|
1587 |
// (converse if negative) |
|
|
1588 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
1589 |
&& sig_n_prime256.w[1] == sig_y.w[1] |
|
|
1590 |
&& (sig_n_prime256.w[0] == sig_y.w[0])) { |
|
|
1591 |
res = 0; |
|
|
1592 |
BID_RETURN (res); |
|
|
1593 |
} // if equal, return 0 |
|
|
1594 |
{ |
|
|
1595 |
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) |
|
|
1596 |
|| (sig_n_prime256.w[1] > sig_y.w[1]) |
|
|
1597 |
|| (sig_n_prime256.w[1] == sig_y.w[1] |
|
|
1598 |
&& sig_n_prime256.w[0] > |
|
|
1599 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
1600 |
BID_RETURN (res); |
|
|
1601 |
} |
|
|
1602 |
} |
|
|
1603 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
1604 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); |
|
|
1605 |
|
|
|
1606 |
// if postitive, return whichever significand is larger |
|
|
1607 |
// (converse if negative) |
|
|
1608 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] |
|
|
1609 |
&& (sig_n_prime192.w[0] == sig_y.w[0])) { |
|
|
1610 |
res = 0; |
|
|
1611 |
BID_RETURN (res); |
|
|
1612 |
} // if equal, return 0 |
|
|
1613 |
{ |
|
|
1614 |
res = (((sig_n_prime192.w[2] > 0) |
|
|
1615 |
|| (sig_n_prime192.w[1] > sig_y.w[1]) |
|
|
1616 |
|| (sig_n_prime192.w[1] == sig_y.w[1] |
|
|
1617 |
&& sig_n_prime192.w[0] > |
|
|
1618 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
1619 |
BID_RETURN (res); |
|
|
1620 |
} |
|
|
1621 |
} |
|
|
1622 |
|
|
|
1623 |
diff = exp_y - exp_x; |
|
|
1624 |
|
|
|
1625 |
// if exp_x is 33 less than exp_y, no need for compensation |
|
|
1626 |
if (diff > 33) { |
|
|
1627 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1628 |
BID_RETURN (res); |
|
|
1629 |
} |
|
|
1630 |
|
|
|
1631 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
1632 |
// adjust the y significand upwards |
|
|
1633 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); |
|
|
1634 |
|
|
|
1635 |
|
|
|
1636 |
// if postitive, return whichever significand is larger |
|
|
1637 |
// (converse if negative) |
|
|
1638 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
1639 |
&& sig_n_prime256.w[1] == sig_x.w[1] |
|
|
1640 |
&& (sig_n_prime256.w[0] == sig_x.w[0])) { |
|
|
1641 |
res = 0; |
|
|
1642 |
BID_RETURN (res); |
|
|
1643 |
} // if equal, return 1 |
|
|
1644 |
{ |
|
|
1645 |
res = |
|
|
1646 |
((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 |
|
|
1647 |
|| (sig_n_prime256.w[1] > sig_x.w[1] |
|
|
1648 |
|| (sig_n_prime256.w[1] == sig_x.w[1] |
|
|
1649 |
&& sig_n_prime256.w[0] > |
|
|
1650 |
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
1651 |
BID_RETURN (res); |
|
|
1652 |
} |
|
|
1653 |
} |
|
|
1654 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
1655 |
// adjust the y significand upwards |
|
|
1656 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); |
|
|
1657 |
|
|
|
1658 |
// if postitive, return whichever significand is larger |
|
|
1659 |
// (converse if negative) |
|
|
1660 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] |
|
|
1661 |
&& (sig_n_prime192.w[0] == sig_x.w[0])) { |
|
|
1662 |
res = 0; |
|
|
1663 |
BID_RETURN (res); |
|
|
1664 |
} // if equal, return 0 |
|
|
1665 |
{ |
|
|
1666 |
res = (sig_n_prime192.w[2] != 0 |
|
|
1667 |
|| (sig_n_prime192.w[1] > sig_x.w[1] |
|
|
1668 |
|| (sig_n_prime192.w[1] == sig_x.w[1] |
|
|
1669 |
&& sig_n_prime192.w[0] > |
|
|
1670 |
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
1671 |
BID_RETURN (res); |
|
|
1672 |
} |
|
|
1673 |
} |
|
|
1674 |
|
|
|
1675 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_not_equal, |
|
|
1676 |
x, y) |
|
|
1677 |
|
|
|
1678 |
int res; |
|
|
1679 |
int exp_x, exp_y, exp_t; |
|
|
1680 |
UINT128 sig_x, sig_y, sig_t; |
|
|
1681 |
UINT192 sig_n_prime192; |
|
|
1682 |
UINT256 sig_n_prime256; |
|
|
1683 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
1684 |
|
|
|
1685 |
// NaN (CASE1) |
|
|
1686 |
// if either number is NAN, the comparison is unordered, |
|
|
1687 |
// rather than equal : return 0 |
|
|
1688 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
1689 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
1690 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN |
|
|
1691 |
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) { |
|
|
1692 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1693 |
} |
|
|
1694 |
{ |
|
|
1695 |
res = 1; |
|
|
1696 |
BID_RETURN (res); |
|
|
1697 |
} |
|
|
1698 |
} |
|
|
1699 |
// SIMPLE (CASE2) |
|
|
1700 |
// if all the bits are the same, these numbers are equivalent. |
|
|
1701 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
1702 |
res = 0; |
|
|
1703 |
BID_RETURN (res); |
|
|
1704 |
} |
|
|
1705 |
// INFINITY (CASE3) |
|
|
1706 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
1707 |
if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
1708 |
res = (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN); |
|
|
1709 |
BID_RETURN (res); |
|
|
1710 |
} else { |
|
|
1711 |
res = 1; |
|
|
1712 |
BID_RETURN (res); |
|
|
1713 |
} |
|
|
1714 |
} |
|
|
1715 |
if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
1716 |
res = 1; |
|
|
1717 |
BID_RETURN (res); |
|
|
1718 |
} |
|
|
1719 |
// CONVERT X |
|
|
1720 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
1721 |
sig_x.w[0] = x.w[0]; |
|
|
1722 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
1723 |
|
|
|
1724 |
// CHECK IF X IS CANONICAL |
|
|
1725 |
// 9999999999999999999999999999999999(decimal) = |
|
|
1726 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
1727 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
1728 |
// If the value exceeds that, it is interpreted as 0. |
|
|
1729 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
1730 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
1731 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
1732 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
1733 |
non_canon_x = 1; |
|
|
1734 |
else |
|
|
1735 |
non_canon_x = 0; |
|
|
1736 |
|
|
|
1737 |
// CONVERT Y |
|
|
1738 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
1739 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
1740 |
sig_y.w[0] = y.w[0]; |
|
|
1741 |
|
|
|
1742 |
// CHECK IF Y IS CANONICAL |
|
|
1743 |
// 9999999999999999999999999999999999(decimal) = |
|
|
1744 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
1745 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
1746 |
// If the value exceeds that, it is interpreted as 0. |
|
|
1747 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
1748 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
1749 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
1750 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
1751 |
non_canon_y = 1; |
|
|
1752 |
else |
|
|
1753 |
non_canon_y = 0; |
|
|
1754 |
|
|
|
1755 |
// some properties: |
|
|
1756 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
1757 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
1758 |
// ignore the exponent field |
|
|
1759 |
// (Any non-canonical # is considered 0) |
|
|
1760 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
1761 |
x_is_zero = 1; |
|
|
1762 |
} |
|
|
1763 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
1764 |
y_is_zero = 1; |
|
|
1765 |
} |
|
|
1766 |
|
|
|
1767 |
if (x_is_zero && y_is_zero) { |
|
|
1768 |
res = 0; |
|
|
1769 |
BID_RETURN (res); |
|
|
1770 |
} else if ((x_is_zero && !y_is_zero) || (!x_is_zero && y_is_zero)) { |
|
|
1771 |
res = 1; |
|
|
1772 |
BID_RETURN (res); |
|
|
1773 |
} |
|
|
1774 |
// OPPOSITE SIGN (CASE5) |
|
|
1775 |
// now, if the sign bits differ => not equal : return 0 |
|
|
1776 |
if ((x.w[1] ^ y.w[1]) & MASK_SIGN) { |
|
|
1777 |
res = 1; |
|
|
1778 |
BID_RETURN (res); |
|
|
1779 |
} |
|
|
1780 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
1781 |
if (exp_x > exp_y) { // to simplify the loop below, |
|
|
1782 |
SWAP (exp_x, exp_y, exp_t); // put the larger exp in y, |
|
|
1783 |
SWAP (sig_x.w[1], sig_y.w[1], sig_t.w[1]); // and the smaller exp in x |
|
|
1784 |
SWAP (sig_x.w[0], sig_y.w[0], sig_t.w[0]); // and the smaller exp in x |
|
|
1785 |
} |
|
|
1786 |
|
|
|
1787 |
|
|
|
1788 |
if (exp_y - exp_x > 33) { |
|
|
1789 |
res = 1; |
|
|
1790 |
BID_RETURN (res); |
|
|
1791 |
} // difference cannot be greater than 10^33 |
|
|
1792 |
|
|
|
1793 |
if (exp_y - exp_x > 19) { |
|
|
1794 |
// recalculate y's significand upwards |
|
|
1795 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, |
|
|
1796 |
ten2k128[exp_y - exp_x - 20]); |
|
|
1797 |
{ |
|
|
1798 |
res = ((sig_n_prime256.w[3] != 0) || (sig_n_prime256.w[2] != 0) |
|
|
1799 |
|| (sig_n_prime256.w[1] != sig_x.w[1]) |
|
|
1800 |
|| (sig_n_prime256.w[0] != sig_x.w[0])); |
|
|
1801 |
BID_RETURN (res); |
|
|
1802 |
} |
|
|
1803 |
|
|
|
1804 |
} |
|
|
1805 |
//else{ |
|
|
1806 |
// recalculate y's significand upwards |
|
|
1807 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y); |
|
|
1808 |
{ |
|
|
1809 |
res = ((sig_n_prime192.w[2] != 0) |
|
|
1810 |
|| (sig_n_prime192.w[1] != sig_x.w[1]) |
|
|
1811 |
|| (sig_n_prime192.w[0] != sig_x.w[0])); |
|
|
1812 |
BID_RETURN (res); |
|
|
1813 |
} |
|
|
1814 |
} |
|
|
1815 |
|
|
|
1816 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_not_greater, |
|
|
1817 |
x, y) |
|
|
1818 |
|
|
|
1819 |
int res; |
|
|
1820 |
int exp_x, exp_y; |
|
|
1821 |
int diff; |
|
|
1822 |
UINT128 sig_x, sig_y; |
|
|
1823 |
UINT192 sig_n_prime192; |
|
|
1824 |
UINT256 sig_n_prime256; |
|
|
1825 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
1826 |
|
|
|
1827 |
// NaN (CASE1) |
|
|
1828 |
// if either number is NAN, the comparison is unordered, |
|
|
1829 |
// rather than equal : return 0 |
|
|
1830 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
1831 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
1832 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN |
|
|
1833 |
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) { |
|
|
1834 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1835 |
} |
|
|
1836 |
{ |
|
|
1837 |
res = 1; |
|
|
1838 |
BID_RETURN (res); |
|
|
1839 |
} |
|
|
1840 |
} |
|
|
1841 |
// SIMPLE (CASE2) |
|
|
1842 |
// if all the bits are the same, these numbers are equal (not Greater). |
|
|
1843 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
1844 |
res = 1; |
|
|
1845 |
BID_RETURN (res); |
|
|
1846 |
} |
|
|
1847 |
// INFINITY (CASE3) |
|
|
1848 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
1849 |
// if x is neg infinity, there is no way it is greater than y, return 1 |
|
|
1850 |
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) { |
|
|
1851 |
res = 1; |
|
|
1852 |
BID_RETURN (res); |
|
|
1853 |
} |
|
|
1854 |
// x is pos infinity, it is greater, unless y is positive infinity => return y!=pos_infinity |
|
|
1855 |
else { |
|
|
1856 |
res = (((y.w[1] & MASK_INF) == MASK_INF) |
|
|
1857 |
&& ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
1858 |
BID_RETURN (res); |
|
|
1859 |
} |
|
|
1860 |
} else if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
1861 |
// x is finite, so if y is positive infinity, then x is less, return 0 |
|
|
1862 |
// if y is negative infinity, then x is greater, return 1 |
|
|
1863 |
{ |
|
|
1864 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1865 |
BID_RETURN (res); |
|
|
1866 |
} |
|
|
1867 |
} |
|
|
1868 |
// CONVERT X |
|
|
1869 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
1870 |
sig_x.w[0] = x.w[0]; |
|
|
1871 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
1872 |
|
|
|
1873 |
// CHECK IF X IS CANONICAL |
|
|
1874 |
// 9999999999999999999999999999999999(decimal) = |
|
|
1875 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
1876 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
1877 |
// If the value exceeds that, it is interpreted as 0. |
|
|
1878 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
1879 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
1880 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
1881 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
1882 |
non_canon_x = 1; |
|
|
1883 |
else |
|
|
1884 |
non_canon_x = 0; |
|
|
1885 |
|
|
|
1886 |
// CONVERT Y |
|
|
1887 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
1888 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
1889 |
sig_y.w[0] = y.w[0]; |
|
|
1890 |
|
|
|
1891 |
// CHECK IF Y IS CANONICAL |
|
|
1892 |
// 9999999999999999999999999999999999(decimal) = |
|
|
1893 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
1894 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
1895 |
// If the value exceeds that, it is interpreted as 0. |
|
|
1896 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
1897 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
1898 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
1899 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
1900 |
non_canon_y = 1; |
|
|
1901 |
else |
|
|
1902 |
non_canon_y = 0; |
|
|
1903 |
|
|
|
1904 |
// ZERO (CASE4) |
|
|
1905 |
// some properties: |
|
|
1906 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
1907 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
1908 |
// ignore the exponent field |
|
|
1909 |
// (Any non-canonical # is considered 0) |
|
|
1910 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
1911 |
x_is_zero = 1; |
|
|
1912 |
} |
|
|
1913 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
1914 |
y_is_zero = 1; |
|
|
1915 |
} |
|
|
1916 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
1917 |
if (x_is_zero && y_is_zero) { |
|
|
1918 |
res = 1; |
|
|
1919 |
BID_RETURN (res); |
|
|
1920 |
} |
|
|
1921 |
// is x is zero, it is greater if Y is negative |
|
|
1922 |
else if (x_is_zero) { |
|
|
1923 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1924 |
BID_RETURN (res); |
|
|
1925 |
} |
|
|
1926 |
// is y is zero, X is greater if it is positive |
|
|
1927 |
else if (y_is_zero) { |
|
|
1928 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
1929 |
BID_RETURN (res); |
|
|
1930 |
} |
|
|
1931 |
// OPPOSITE SIGN (CASE5) |
|
|
1932 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
1933 |
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { |
|
|
1934 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1935 |
BID_RETURN (res); |
|
|
1936 |
} |
|
|
1937 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
1938 |
// if exponents are the same, then we have a simple comparison |
|
|
1939 |
// of the significands |
|
|
1940 |
if (exp_y == exp_x) { |
|
|
1941 |
res = (((sig_x.w[1] > sig_y.w[1]) |
|
|
1942 |
|| (sig_x.w[1] == sig_y.w[1] |
|
|
1943 |
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) != |
|
|
1944 |
MASK_SIGN)); |
|
|
1945 |
BID_RETURN (res); |
|
|
1946 |
} |
|
|
1947 |
// if both components are either bigger or smaller, |
|
|
1948 |
// it is clear what needs to be done |
|
|
1949 |
if ((sig_x.w[1] > sig_y.w[1] |
|
|
1950 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) |
|
|
1951 |
&& exp_x >= exp_y) { |
|
|
1952 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
1953 |
BID_RETURN (res); |
|
|
1954 |
} |
|
|
1955 |
if ((sig_x.w[1] < sig_y.w[1] |
|
|
1956 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) |
|
|
1957 |
&& exp_x <= exp_y) { |
|
|
1958 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
1959 |
BID_RETURN (res); |
|
|
1960 |
} |
|
|
1961 |
|
|
|
1962 |
diff = exp_x - exp_y; |
|
|
1963 |
|
|
|
1964 |
// if |exp_x - exp_y| < 33, it comes down to the compensated significand |
|
|
1965 |
if (diff > 0) { // to simplify the loop below, |
|
|
1966 |
|
|
|
1967 |
// if exp_x is 33 greater than exp_y, no need for compensation |
|
|
1968 |
if (diff > 33) { |
|
|
1969 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
1970 |
BID_RETURN (res); |
|
|
1971 |
} // difference cannot be greater than 10^33 |
|
|
1972 |
|
|
|
1973 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
1974 |
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); |
|
|
1975 |
|
|
|
1976 |
|
|
|
1977 |
// if postitive, return whichever significand is larger |
|
|
1978 |
// (converse if negative) |
|
|
1979 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
1980 |
&& sig_n_prime256.w[1] == sig_y.w[1] |
|
|
1981 |
&& (sig_n_prime256.w[0] == sig_y.w[0])) { |
|
|
1982 |
res = 1; |
|
|
1983 |
BID_RETURN (res); |
|
|
1984 |
} // if equal, return 0 |
|
|
1985 |
{ |
|
|
1986 |
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) |
|
|
1987 |
|| (sig_n_prime256.w[1] > sig_y.w[1]) |
|
|
1988 |
|| (sig_n_prime256.w[1] == sig_y.w[1] |
|
|
1989 |
&& sig_n_prime256.w[0] > |
|
|
1990 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
1991 |
BID_RETURN (res); |
|
|
1992 |
} |
|
|
1993 |
} |
|
|
1994 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
1995 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); |
|
|
1996 |
|
|
|
1997 |
// if postitive, return whichever significand is larger |
|
|
1998 |
// (converse if negative) |
|
|
1999 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] |
|
|
2000 |
&& (sig_n_prime192.w[0] == sig_y.w[0])) { |
|
|
2001 |
res = 1; |
|
|
2002 |
BID_RETURN (res); |
|
|
2003 |
} // if equal, return 0 |
|
|
2004 |
{ |
|
|
2005 |
res = (((sig_n_prime192.w[2] > 0) |
|
|
2006 |
|| (sig_n_prime192.w[1] > sig_y.w[1]) |
|
|
2007 |
|| (sig_n_prime192.w[1] == sig_y.w[1] |
|
|
2008 |
&& sig_n_prime192.w[0] > |
|
|
2009 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
2010 |
BID_RETURN (res); |
|
|
2011 |
} |
|
|
2012 |
} |
|
|
2013 |
|
|
|
2014 |
diff = exp_y - exp_x; |
|
|
2015 |
|
|
|
2016 |
// if exp_x is 33 less than exp_y, no need for compensation |
|
|
2017 |
if (diff > 33) { |
|
|
2018 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
2019 |
BID_RETURN (res); |
|
|
2020 |
} |
|
|
2021 |
|
|
|
2022 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
2023 |
// adjust the y significand upwards |
|
|
2024 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); |
|
|
2025 |
|
|
|
2026 |
|
|
|
2027 |
// if postitive, return whichever significand is larger |
|
|
2028 |
// (converse if negative) |
|
|
2029 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
2030 |
&& sig_n_prime256.w[1] == sig_x.w[1] |
|
|
2031 |
&& (sig_n_prime256.w[0] == sig_x.w[0])) { |
|
|
2032 |
res = 1; |
|
|
2033 |
BID_RETURN (res); |
|
|
2034 |
} // if equal, return 0 |
|
|
2035 |
{ |
|
|
2036 |
res = |
|
|
2037 |
((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 |
|
|
2038 |
|| (sig_n_prime256.w[1] > sig_x.w[1] |
|
|
2039 |
|| (sig_n_prime256.w[1] == sig_x.w[1] |
|
|
2040 |
&& sig_n_prime256.w[0] > |
|
|
2041 |
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
2042 |
BID_RETURN (res); |
|
|
2043 |
} |
|
|
2044 |
} |
|
|
2045 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
2046 |
// adjust the y significand upwards |
|
|
2047 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); |
|
|
2048 |
|
|
|
2049 |
// if postitive, return whichever significand is larger |
|
|
2050 |
// (converse if negative) |
|
|
2051 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] |
|
|
2052 |
&& (sig_n_prime192.w[0] == sig_x.w[0])) { |
|
|
2053 |
res = 1; |
|
|
2054 |
BID_RETURN (res); |
|
|
2055 |
} // if equal, return 0 |
|
|
2056 |
{ |
|
|
2057 |
res = (sig_n_prime192.w[2] != 0 |
|
|
2058 |
|| (sig_n_prime192.w[1] > sig_x.w[1] |
|
|
2059 |
|| (sig_n_prime192.w[1] == sig_x.w[1] |
|
|
2060 |
&& sig_n_prime192.w[0] > |
|
|
2061 |
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2062 |
BID_RETURN (res); |
|
|
2063 |
} |
|
|
2064 |
} |
|
|
2065 |
|
|
|
2066 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_not_less, x, |
|
|
2067 |
y) |
|
|
2068 |
|
|
|
2069 |
int res; |
|
|
2070 |
int exp_x, exp_y; |
|
|
2071 |
int diff; |
|
|
2072 |
UINT128 sig_x, sig_y; |
|
|
2073 |
UINT192 sig_n_prime192; |
|
|
2074 |
UINT256 sig_n_prime256; |
|
|
2075 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
2076 |
|
|
|
2077 |
// NaN (CASE1) |
|
|
2078 |
// if either number is NAN, the comparison is unordered, |
|
|
2079 |
// rather than equal : return 1 |
|
|
2080 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
2081 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
2082 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN |
|
|
2083 |
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) { |
|
|
2084 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2085 |
} |
|
|
2086 |
{ |
|
|
2087 |
res = 1; |
|
|
2088 |
BID_RETURN (res); |
|
|
2089 |
} |
|
|
2090 |
} |
|
|
2091 |
// SIMPLE (CASE2) |
|
|
2092 |
// if all the bits are the same, these numbers are equal (not Greater). |
|
|
2093 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
2094 |
res = 1; |
|
|
2095 |
BID_RETURN (res); |
|
|
2096 |
} |
|
|
2097 |
// INFINITY (CASE3) |
|
|
2098 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
2099 |
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } |
|
|
2100 |
if ((x.w[1] & MASK_SIGN) == MASK_SIGN) |
|
|
2101 |
// x is -inf, so it is less than y unless y is -inf |
|
|
2102 |
{ |
|
|
2103 |
res = (((y.w[1] & MASK_INF) == MASK_INF) |
|
|
2104 |
&& (y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2105 |
BID_RETURN (res); |
|
|
2106 |
} else |
|
|
2107 |
// x is pos_inf, no way for it to be less than y |
|
|
2108 |
{ |
|
|
2109 |
res = 1; |
|
|
2110 |
BID_RETURN (res); |
|
|
2111 |
} |
|
|
2112 |
} else if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
2113 |
// x is finite, so if y is positive infinity, then x is less, return 0 |
|
|
2114 |
// if y is negative infinity, then x is greater, return 1 |
|
|
2115 |
{ |
|
|
2116 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2117 |
BID_RETURN (res); |
|
|
2118 |
} |
|
|
2119 |
} |
|
|
2120 |
// CONVERT X |
|
|
2121 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
2122 |
sig_x.w[0] = x.w[0]; |
|
|
2123 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
2124 |
|
|
|
2125 |
// CHECK IF X IS CANONICAL |
|
|
2126 |
// 9999999999999999999999999999999999(decimal) = |
|
|
2127 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
2128 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
2129 |
// If the value exceeds that, it is interpreted as 0. |
|
|
2130 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
2131 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
2132 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
2133 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
2134 |
non_canon_x = 1; |
|
|
2135 |
else |
|
|
2136 |
non_canon_x = 0; |
|
|
2137 |
|
|
|
2138 |
// CONVERT Y |
|
|
2139 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
2140 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
2141 |
sig_y.w[0] = y.w[0]; |
|
|
2142 |
|
|
|
2143 |
// CHECK IF Y IS CANONICAL |
|
|
2144 |
// 9999999999999999999999999999999999(decimal) = |
|
|
2145 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
2146 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
2147 |
// If the value exceeds that, it is interpreted as 0. |
|
|
2148 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
2149 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
2150 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
2151 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
2152 |
non_canon_y = 1; |
|
|
2153 |
else |
|
|
2154 |
non_canon_y = 0; |
|
|
2155 |
|
|
|
2156 |
// ZERO (CASE4) |
|
|
2157 |
// some properties: |
|
|
2158 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
2159 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
2160 |
// ignore the exponent field |
|
|
2161 |
// (Any non-canonical # is considered 0) |
|
|
2162 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
2163 |
x_is_zero = 1; |
|
|
2164 |
} |
|
|
2165 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
2166 |
y_is_zero = 1; |
|
|
2167 |
} |
|
|
2168 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
2169 |
if (x_is_zero && y_is_zero) { |
|
|
2170 |
res = 1; |
|
|
2171 |
BID_RETURN (res); |
|
|
2172 |
} |
|
|
2173 |
// is x is zero, it is greater if Y is negative |
|
|
2174 |
else if (x_is_zero) { |
|
|
2175 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2176 |
BID_RETURN (res); |
|
|
2177 |
} |
|
|
2178 |
// is y is zero, X is greater if it is positive |
|
|
2179 |
else if (y_is_zero) { |
|
|
2180 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
2181 |
BID_RETURN (res); |
|
|
2182 |
} |
|
|
2183 |
// OPPOSITE SIGN (CASE5) |
|
|
2184 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
2185 |
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { |
|
|
2186 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2187 |
BID_RETURN (res); |
|
|
2188 |
} |
|
|
2189 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
2190 |
|
|
|
2191 |
// if exponents are the same, then we have a simple comparison |
|
|
2192 |
// of the significands |
|
|
2193 |
if (exp_y == exp_x) { |
|
|
2194 |
res = (((sig_x.w[1] > sig_y.w[1]) |
|
|
2195 |
|| (sig_x.w[1] == sig_y.w[1] |
|
|
2196 |
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == |
|
|
2197 |
MASK_SIGN)); |
|
|
2198 |
BID_RETURN (res); |
|
|
2199 |
} |
|
|
2200 |
// if both components are either bigger or smaller, |
|
|
2201 |
// it is clear what needs to be done |
|
|
2202 |
if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0] |
|
|
2203 |
&& exp_x > exp_y) { |
|
|
2204 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
2205 |
BID_RETURN (res); |
|
|
2206 |
} |
|
|
2207 |
if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0] |
|
|
2208 |
&& exp_x < exp_y) { |
|
|
2209 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2210 |
BID_RETURN (res); |
|
|
2211 |
} |
|
|
2212 |
|
|
|
2213 |
diff = exp_x - exp_y; |
|
|
2214 |
|
|
|
2215 |
// if |exp_x - exp_y| < 33, it comes down to the compensated significand |
|
|
2216 |
if (diff > 0) { // to simplify the loop below, |
|
|
2217 |
|
|
|
2218 |
// if exp_x is 33 greater than exp_y, no need for compensation |
|
|
2219 |
if (diff > 33) { |
|
|
2220 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
2221 |
BID_RETURN (res); |
|
|
2222 |
} // difference cannot be greater than 10^33 |
|
|
2223 |
|
|
|
2224 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
2225 |
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); |
|
|
2226 |
|
|
|
2227 |
|
|
|
2228 |
// if postitive, return whichever significand is larger |
|
|
2229 |
// (converse if negative) |
|
|
2230 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
2231 |
&& sig_n_prime256.w[1] == sig_y.w[1] |
|
|
2232 |
&& (sig_n_prime256.w[0] == sig_y.w[0])) { |
|
|
2233 |
res = 1; |
|
|
2234 |
BID_RETURN (res); |
|
|
2235 |
} // if equal, return 1 |
|
|
2236 |
{ |
|
|
2237 |
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) |
|
|
2238 |
|| (sig_n_prime256.w[1] > sig_y.w[1]) |
|
|
2239 |
|| (sig_n_prime256.w[1] == sig_y.w[1] |
|
|
2240 |
&& sig_n_prime256.w[0] > |
|
|
2241 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
2242 |
BID_RETURN (res); |
|
|
2243 |
} |
|
|
2244 |
} |
|
|
2245 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
2246 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); |
|
|
2247 |
|
|
|
2248 |
// if postitive, return whichever significand is larger |
|
|
2249 |
// (converse if negative) |
|
|
2250 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] |
|
|
2251 |
&& (sig_n_prime192.w[0] == sig_y.w[0])) { |
|
|
2252 |
res = 1; |
|
|
2253 |
BID_RETURN (res); |
|
|
2254 |
} // if equal, return 1 |
|
|
2255 |
{ |
|
|
2256 |
res = (((sig_n_prime192.w[2] > 0) |
|
|
2257 |
|| (sig_n_prime192.w[1] > sig_y.w[1]) |
|
|
2258 |
|| (sig_n_prime192.w[1] == sig_y.w[1] |
|
|
2259 |
&& sig_n_prime192.w[0] > |
|
|
2260 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
2261 |
BID_RETURN (res); |
|
|
2262 |
} |
|
|
2263 |
} |
|
|
2264 |
|
|
|
2265 |
diff = exp_y - exp_x; |
|
|
2266 |
|
|
|
2267 |
// if exp_x is 33 less than exp_y, no need for compensation |
|
|
2268 |
if (diff > 33) { |
|
|
2269 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2270 |
BID_RETURN (res); |
|
|
2271 |
} |
|
|
2272 |
|
|
|
2273 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
2274 |
// adjust the y significand upwards |
|
|
2275 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); |
|
|
2276 |
|
|
|
2277 |
|
|
|
2278 |
// if postitive, return whichever significand is larger |
|
|
2279 |
// (converse if negative) |
|
|
2280 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
2281 |
&& sig_n_prime256.w[1] == sig_x.w[1] |
|
|
2282 |
&& (sig_n_prime256.w[0] == sig_x.w[0])) { |
|
|
2283 |
res = 1; |
|
|
2284 |
BID_RETURN (res); |
|
|
2285 |
} // if equal, return 1 |
|
|
2286 |
{ |
|
|
2287 |
res = |
|
|
2288 |
((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0 |
|
|
2289 |
&& (sig_n_prime256.w[1] < sig_x.w[1] |
|
|
2290 |
|| (sig_n_prime256.w[1] == sig_x.w[1] |
|
|
2291 |
&& sig_n_prime256.w[0] < |
|
|
2292 |
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
2293 |
BID_RETURN (res); |
|
|
2294 |
} |
|
|
2295 |
} |
|
|
2296 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
2297 |
// adjust the y significand upwards |
|
|
2298 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); |
|
|
2299 |
|
|
|
2300 |
// if postitive, return whichever significand is larger |
|
|
2301 |
// (converse if negative) |
|
|
2302 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] |
|
|
2303 |
&& (sig_n_prime192.w[0] == sig_x.w[0])) { |
|
|
2304 |
res = 1; |
|
|
2305 |
BID_RETURN (res); |
|
|
2306 |
} // if equal, return 1 |
|
|
2307 |
{ |
|
|
2308 |
res = (sig_n_prime192.w[2] == 0 |
|
|
2309 |
&& (sig_n_prime192.w[1] < sig_x.w[1] |
|
|
2310 |
|| (sig_n_prime192.w[1] == sig_x.w[1] |
|
|
2311 |
&& sig_n_prime192.w[0] < |
|
|
2312 |
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2313 |
BID_RETURN (res); |
|
|
2314 |
} |
|
|
2315 |
} |
|
|
2316 |
|
|
|
2317 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_ordered, x, |
|
|
2318 |
y) |
|
|
2319 |
|
|
|
2320 |
int res; |
|
|
2321 |
|
|
|
2322 |
// NaN (CASE1) |
|
|
2323 |
// if either number is NAN, the comparison is ordered : return 1 |
|
|
2324 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
2325 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
2326 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN |
|
|
2327 |
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) { |
|
|
2328 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2329 |
} |
|
|
2330 |
{ |
|
|
2331 |
res = 0; |
|
|
2332 |
BID_RETURN (res); |
|
|
2333 |
} |
|
|
2334 |
} |
|
|
2335 |
{ |
|
|
2336 |
res = 1; |
|
|
2337 |
BID_RETURN (res); |
|
|
2338 |
} |
|
|
2339 |
} |
|
|
2340 |
|
|
|
2341 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_unordered, |
|
|
2342 |
x, y) |
|
|
2343 |
|
|
|
2344 |
int res; |
|
|
2345 |
|
|
|
2346 |
// NaN (CASE1) |
|
|
2347 |
// if either number is NAN, the comparison is unordered : return 1 |
|
|
2348 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
2349 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
2350 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN |
|
|
2351 |
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) { |
|
|
2352 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2353 |
} |
|
|
2354 |
{ |
|
|
2355 |
res = 1; |
|
|
2356 |
BID_RETURN (res); |
|
|
2357 |
} |
|
|
2358 |
} |
|
|
2359 |
{ |
|
|
2360 |
res = 0; |
|
|
2361 |
BID_RETURN (res); |
|
|
2362 |
} |
|
|
2363 |
} |
|
|
2364 |
|
|
|
2365 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_signaling_greater, |
|
|
2366 |
x, y) |
|
|
2367 |
|
|
|
2368 |
int res; |
|
|
2369 |
int exp_x, exp_y; |
|
|
2370 |
int diff; |
|
|
2371 |
UINT128 sig_x, sig_y; |
|
|
2372 |
UINT192 sig_n_prime192; |
|
|
2373 |
UINT256 sig_n_prime256; |
|
|
2374 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
2375 |
|
|
|
2376 |
// NaN (CASE1) |
|
|
2377 |
// if either number is NAN, the comparison is unordered, |
|
|
2378 |
// rather than equal : return 0 |
|
|
2379 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
2380 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
2381 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2382 |
{ |
|
|
2383 |
res = 0; |
|
|
2384 |
BID_RETURN (res); |
|
|
2385 |
} |
|
|
2386 |
} |
|
|
2387 |
// SIMPLE (CASE2) |
|
|
2388 |
// if all the bits are the same, these numbers are equal (not Greater). |
|
|
2389 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
2390 |
res = 0; |
|
|
2391 |
BID_RETURN (res); |
|
|
2392 |
} |
|
|
2393 |
// INFINITY (CASE3) |
|
|
2394 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
2395 |
// if x is neg infinity, there is no way it is greater than y, return 0 |
|
|
2396 |
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) { |
|
|
2397 |
res = 0; |
|
|
2398 |
BID_RETURN (res); |
|
|
2399 |
} |
|
|
2400 |
// x is pos infinity, it is greater, unless y is positive infinity => return y!=pos_infinity |
|
|
2401 |
else { |
|
|
2402 |
res = (((y.w[1] & MASK_INF) != MASK_INF) |
|
|
2403 |
|| ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
2404 |
BID_RETURN (res); |
|
|
2405 |
} |
|
|
2406 |
} else if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
2407 |
// x is finite, so if y is positive infinity, then x is less, return 0 |
|
|
2408 |
// if y is negative infinity, then x is greater, return 1 |
|
|
2409 |
{ |
|
|
2410 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2411 |
BID_RETURN (res); |
|
|
2412 |
} |
|
|
2413 |
} |
|
|
2414 |
// CONVERT X |
|
|
2415 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
2416 |
sig_x.w[0] = x.w[0]; |
|
|
2417 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
2418 |
|
|
|
2419 |
// CHECK IF X IS CANONICAL |
|
|
2420 |
// 9999999999999999999999999999999999(decimal) = |
|
|
2421 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
2422 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
2423 |
// If the value exceeds that, it is interpreted as 0. |
|
|
2424 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
2425 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
2426 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
2427 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
2428 |
non_canon_x = 1; |
|
|
2429 |
else |
|
|
2430 |
non_canon_x = 0; |
|
|
2431 |
|
|
|
2432 |
// CONVERT Y |
|
|
2433 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
2434 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
2435 |
sig_y.w[0] = y.w[0]; |
|
|
2436 |
|
|
|
2437 |
// CHECK IF Y IS CANONICAL |
|
|
2438 |
// 9999999999999999999999999999999999(decimal) = |
|
|
2439 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
2440 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
2441 |
// If the value exceeds that, it is interpreted as 0. |
|
|
2442 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
2443 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
2444 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
2445 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
2446 |
non_canon_y = 1; |
|
|
2447 |
else |
|
|
2448 |
non_canon_y = 0; |
|
|
2449 |
|
|
|
2450 |
// ZERO (CASE4) |
|
|
2451 |
// some properties: |
|
|
2452 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
2453 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
2454 |
// ignore the exponent field |
|
|
2455 |
// (Any non-canonical # is considered 0) |
|
|
2456 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
2457 |
x_is_zero = 1; |
|
|
2458 |
} |
|
|
2459 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
2460 |
y_is_zero = 1; |
|
|
2461 |
} |
|
|
2462 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
2463 |
if (x_is_zero && y_is_zero) { |
|
|
2464 |
res = 0; |
|
|
2465 |
BID_RETURN (res); |
|
|
2466 |
} |
|
|
2467 |
// is x is zero, it is greater if Y is negative |
|
|
2468 |
else if (x_is_zero) { |
|
|
2469 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2470 |
BID_RETURN (res); |
|
|
2471 |
} |
|
|
2472 |
// is y is zero, X is greater if it is positive |
|
|
2473 |
else if (y_is_zero) { |
|
|
2474 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
2475 |
BID_RETURN (res); |
|
|
2476 |
} |
|
|
2477 |
// OPPOSITE SIGN (CASE5) |
|
|
2478 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
2479 |
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { |
|
|
2480 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2481 |
BID_RETURN (res); |
|
|
2482 |
} |
|
|
2483 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
2484 |
// if exponents are the same, then we have a simple comparison |
|
|
2485 |
// of the significands |
|
|
2486 |
if (exp_y == exp_x) { |
|
|
2487 |
res = (((sig_x.w[1] > sig_y.w[1]) |
|
|
2488 |
|| (sig_x.w[1] == sig_y.w[1] |
|
|
2489 |
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == |
|
|
2490 |
MASK_SIGN)); |
|
|
2491 |
BID_RETURN (res); |
|
|
2492 |
} |
|
|
2493 |
// if both components are either bigger or smaller, |
|
|
2494 |
// it is clear what needs to be done |
|
|
2495 |
if ((sig_x.w[1] > sig_y.w[1] |
|
|
2496 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) |
|
|
2497 |
&& exp_x >= exp_y) { |
|
|
2498 |
{ |
|
|
2499 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
2500 |
BID_RETURN (res); |
|
|
2501 |
} |
|
|
2502 |
} |
|
|
2503 |
if ((sig_x.w[1] < sig_y.w[1] |
|
|
2504 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) |
|
|
2505 |
&& exp_x <= exp_y) { |
|
|
2506 |
{ |
|
|
2507 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2508 |
BID_RETURN (res); |
|
|
2509 |
} |
|
|
2510 |
} |
|
|
2511 |
|
|
|
2512 |
diff = exp_x - exp_y; |
|
|
2513 |
|
|
|
2514 |
// if |exp_x - exp_y| < 33, it comes down to the compensated significand |
|
|
2515 |
if (diff > 0) { // to simplify the loop below, |
|
|
2516 |
|
|
|
2517 |
// if exp_x is 33 greater than exp_y, no need for compensation |
|
|
2518 |
if (diff > 33) { |
|
|
2519 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
2520 |
BID_RETURN (res); |
|
|
2521 |
} // difference cannot be greater than 10^33 |
|
|
2522 |
|
|
|
2523 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
2524 |
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); |
|
|
2525 |
|
|
|
2526 |
// if postitive, return whichever significand is larger |
|
|
2527 |
// (converse if negative) |
|
|
2528 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
2529 |
&& sig_n_prime256.w[1] == sig_y.w[1] |
|
|
2530 |
&& (sig_n_prime256.w[0] == sig_y.w[0])) { |
|
|
2531 |
res = 0; |
|
|
2532 |
BID_RETURN (res); |
|
|
2533 |
} // if equal, return 0 |
|
|
2534 |
{ |
|
|
2535 |
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) |
|
|
2536 |
|| (sig_n_prime256.w[1] > sig_y.w[1]) |
|
|
2537 |
|| (sig_n_prime256.w[1] == sig_y.w[1] |
|
|
2538 |
&& sig_n_prime256.w[0] > |
|
|
2539 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
2540 |
BID_RETURN (res); |
|
|
2541 |
} |
|
|
2542 |
} |
|
|
2543 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
2544 |
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x); |
|
|
2545 |
|
|
|
2546 |
// if postitive, return whichever significand is larger |
|
|
2547 |
// (converse if negative) |
|
|
2548 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] |
|
|
2549 |
&& (sig_n_prime192.w[0] == sig_y.w[0])) { |
|
|
2550 |
res = 0; |
|
|
2551 |
BID_RETURN (res); |
|
|
2552 |
} // if equal, return 0 |
|
|
2553 |
{ |
|
|
2554 |
res = (((sig_n_prime192.w[2] > 0) |
|
|
2555 |
|| (sig_n_prime192.w[1] > sig_y.w[1]) |
|
|
2556 |
|| (sig_n_prime192.w[1] == sig_y.w[1] |
|
|
2557 |
&& sig_n_prime192.w[0] > |
|
|
2558 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
2559 |
BID_RETURN (res); |
|
|
2560 |
} |
|
|
2561 |
} |
|
|
2562 |
|
|
|
2563 |
diff = exp_y - exp_x; |
|
|
2564 |
|
|
|
2565 |
// if exp_x is 33 less than exp_y, no need for compensation |
|
|
2566 |
if (diff > 33) { |
|
|
2567 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2568 |
BID_RETURN (res); |
|
|
2569 |
} |
|
|
2570 |
|
|
|
2571 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
2572 |
// adjust the y significand upwards |
|
|
2573 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); |
|
|
2574 |
|
|
|
2575 |
// if postitive, return whichever significand is larger |
|
|
2576 |
// (converse if negative) |
|
|
2577 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
2578 |
&& sig_n_prime256.w[1] == sig_x.w[1] |
|
|
2579 |
&& (sig_n_prime256.w[0] == sig_x.w[0])) { |
|
|
2580 |
res = 0; |
|
|
2581 |
BID_RETURN (res); |
|
|
2582 |
} // if equal, return 0 |
|
|
2583 |
{ |
|
|
2584 |
res = |
|
|
2585 |
((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 |
|
|
2586 |
|| (sig_n_prime256.w[1] > sig_x.w[1] |
|
|
2587 |
|| (sig_n_prime256.w[1] == sig_x.w[1] |
|
|
2588 |
&& sig_n_prime256.w[0] > |
|
|
2589 |
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
2590 |
BID_RETURN (res); |
|
|
2591 |
} |
|
|
2592 |
} |
|
|
2593 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
2594 |
// adjust the y significand upwards |
|
|
2595 |
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y); |
|
|
2596 |
|
|
|
2597 |
// if postitive, return whichever significand is larger |
|
|
2598 |
// (converse if negative) |
|
|
2599 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] |
|
|
2600 |
&& (sig_n_prime192.w[0] == sig_x.w[0])) { |
|
|
2601 |
res = 0; |
|
|
2602 |
BID_RETURN (res); |
|
|
2603 |
} // if equal, return 0 |
|
|
2604 |
{ |
|
|
2605 |
res = (sig_n_prime192.w[2] != 0 |
|
|
2606 |
|| (sig_n_prime192.w[1] > sig_x.w[1] |
|
|
2607 |
|| (sig_n_prime192.w[1] == sig_x.w[1] |
|
|
2608 |
&& sig_n_prime192.w[0] > |
|
|
2609 |
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
2610 |
BID_RETURN (res); |
|
|
2611 |
} |
|
|
2612 |
} |
|
|
2613 |
|
|
|
2614 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, |
|
|
2615 |
bid128_signaling_greater_equal, |
|
|
2616 |
x, y) |
|
|
2617 |
|
|
|
2618 |
int res; |
|
|
2619 |
int exp_x, exp_y; |
|
|
2620 |
int diff; |
|
|
2621 |
UINT128 sig_x, sig_y; |
|
|
2622 |
UINT192 sig_n_prime192; |
|
|
2623 |
UINT256 sig_n_prime256; |
|
|
2624 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
2625 |
|
|
|
2626 |
// NaN (CASE1) |
|
|
2627 |
// if either number is NAN, the comparison is unordered, |
|
|
2628 |
// rather than equal : return 1 |
|
|
2629 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
2630 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
2631 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2632 |
{ |
|
|
2633 |
res = 0; |
|
|
2634 |
BID_RETURN (res); |
|
|
2635 |
} |
|
|
2636 |
} |
|
|
2637 |
// SIMPLE (CASE2) |
|
|
2638 |
// if all the bits are the same, these numbers are equal (not Greater). |
|
|
2639 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
2640 |
res = 1; |
|
|
2641 |
BID_RETURN (res); |
|
|
2642 |
} |
|
|
2643 |
// INFINITY (CASE3) |
|
|
2644 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
2645 |
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } |
|
|
2646 |
if ((x.w[1] & MASK_SIGN) == MASK_SIGN) |
|
|
2647 |
// x is -inf, so it is less than y unless y is -inf |
|
|
2648 |
{ |
|
|
2649 |
res = (((y.w[1] & MASK_INF) == MASK_INF) |
|
|
2650 |
&& (y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2651 |
BID_RETURN (res); |
|
|
2652 |
} else |
|
|
2653 |
// x is pos_inf, no way for it to be less than y |
|
|
2654 |
{ |
|
|
2655 |
res = 1; |
|
|
2656 |
BID_RETURN (res); |
|
|
2657 |
} |
|
|
2658 |
} else if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
2659 |
// x is finite, so if y is positive infinity, then x is less, return 0 |
|
|
2660 |
// if y is negative infinity, then x is greater, return 1 |
|
|
2661 |
{ |
|
|
2662 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2663 |
BID_RETURN (res); |
|
|
2664 |
} |
|
|
2665 |
} |
|
|
2666 |
// CONVERT X |
|
|
2667 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
2668 |
sig_x.w[0] = x.w[0]; |
|
|
2669 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
2670 |
|
|
|
2671 |
// CHECK IF X IS CANONICAL |
|
|
2672 |
// 9999999999999999999999999999999999(decimal) = |
|
|
2673 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
2674 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
2675 |
// If the value exceeds that, it is interpreted as 0. |
|
|
2676 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
2677 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
2678 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
2679 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
2680 |
non_canon_x = 1; |
|
|
2681 |
else |
|
|
2682 |
non_canon_x = 0; |
|
|
2683 |
|
|
|
2684 |
// CONVERT Y |
|
|
2685 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
2686 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
2687 |
sig_y.w[0] = y.w[0]; |
|
|
2688 |
|
|
|
2689 |
// CHECK IF Y IS CANONICAL |
|
|
2690 |
// 9999999999999999999999999999999999(decimal) = |
|
|
2691 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
2692 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
2693 |
// If the value exceeds that, it is interpreted as 0. |
|
|
2694 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
2695 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
2696 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
2697 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
2698 |
non_canon_y = 1; |
|
|
2699 |
else |
|
|
2700 |
non_canon_y = 0; |
|
|
2701 |
|
|
|
2702 |
// ZERO (CASE4) |
|
|
2703 |
// some properties: |
|
|
2704 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
2705 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
2706 |
// ignore the exponent field |
|
|
2707 |
// (Any non-canonical # is considered 0) |
|
|
2708 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
2709 |
x_is_zero = 1; |
|
|
2710 |
} |
|
|
2711 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
2712 |
y_is_zero = 1; |
|
|
2713 |
} |
|
|
2714 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
2715 |
if (x_is_zero && y_is_zero) { |
|
|
2716 |
res = 1; |
|
|
2717 |
BID_RETURN (res); |
|
|
2718 |
} |
|
|
2719 |
// is x is zero, it is greater if Y is negative |
|
|
2720 |
else if (x_is_zero) { |
|
|
2721 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2722 |
BID_RETURN (res); |
|
|
2723 |
} |
|
|
2724 |
// is y is zero, X is greater if it is positive |
|
|
2725 |
else if (y_is_zero) { |
|
|
2726 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
2727 |
BID_RETURN (res); |
|
|
2728 |
} |
|
|
2729 |
// OPPOSITE SIGN (CASE5) |
|
|
2730 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
2731 |
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { |
|
|
2732 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2733 |
BID_RETURN (res); |
|
|
2734 |
} |
|
|
2735 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
2736 |
// if exponents are the same, then we have a simple comparison |
|
|
2737 |
// of the significands |
|
|
2738 |
if (exp_y == exp_x) { |
|
|
2739 |
res = (((sig_x.w[1] > sig_y.w[1]) |
|
|
2740 |
|| (sig_x.w[1] == sig_y.w[1] |
|
|
2741 |
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == |
|
|
2742 |
MASK_SIGN)); |
|
|
2743 |
BID_RETURN (res); |
|
|
2744 |
} |
|
|
2745 |
// if both components are either bigger or smaller, |
|
|
2746 |
// it is clear what needs to be done |
|
|
2747 |
if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0] |
|
|
2748 |
&& exp_x > exp_y) { |
|
|
2749 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
2750 |
BID_RETURN (res); |
|
|
2751 |
} |
|
|
2752 |
if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0] |
|
|
2753 |
&& exp_x < exp_y) { |
|
|
2754 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2755 |
BID_RETURN (res); |
|
|
2756 |
} |
|
|
2757 |
|
|
|
2758 |
diff = exp_x - exp_y; |
|
|
2759 |
|
|
|
2760 |
// if |exp_x - exp_y| < 33, it comes down to the compensated significand |
|
|
2761 |
if (diff > 0) { // to simplify the loop below, |
|
|
2762 |
|
|
|
2763 |
// if exp_x is 33 greater than exp_y, no need for compensation |
|
|
2764 |
if (diff > 33) { |
|
|
2765 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
2766 |
BID_RETURN (res); |
|
|
2767 |
} // difference cannot be greater than 10^33 |
|
|
2768 |
|
|
|
2769 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
2770 |
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); |
|
|
2771 |
|
|
|
2772 |
|
|
|
2773 |
// if postitive, return whichever significand is larger |
|
|
2774 |
// (converse if negative) |
|
|
2775 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
2776 |
&& sig_n_prime256.w[1] == sig_y.w[1] |
|
|
2777 |
&& (sig_n_prime256.w[0] == sig_y.w[0])) { |
|
|
2778 |
res = 1; |
|
|
2779 |
BID_RETURN (res); |
|
|
2780 |
} // if equal, return 1 |
|
|
2781 |
{ |
|
|
2782 |
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) |
|
|
2783 |
|| (sig_n_prime256.w[1] > sig_y.w[1]) |
|
|
2784 |
|| (sig_n_prime256.w[1] == sig_y.w[1] |
|
|
2785 |
&& sig_n_prime256.w[0] > |
|
|
2786 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
2787 |
BID_RETURN (res); |
|
|
2788 |
} |
|
|
2789 |
} |
|
|
2790 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
2791 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); |
|
|
2792 |
|
|
|
2793 |
// if postitive, return whichever significand is larger |
|
|
2794 |
// (converse if negative) |
|
|
2795 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] |
|
|
2796 |
&& (sig_n_prime192.w[0] == sig_y.w[0])) { |
|
|
2797 |
res = 1; |
|
|
2798 |
BID_RETURN (res); |
|
|
2799 |
} // if equal, return 1 |
|
|
2800 |
{ |
|
|
2801 |
res = (((sig_n_prime192.w[2] > 0) |
|
|
2802 |
|| (sig_n_prime192.w[1] > sig_y.w[1]) |
|
|
2803 |
|| (sig_n_prime192.w[1] == sig_y.w[1] |
|
|
2804 |
&& sig_n_prime192.w[0] > |
|
|
2805 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
2806 |
BID_RETURN (res); |
|
|
2807 |
} |
|
|
2808 |
} |
|
|
2809 |
|
|
|
2810 |
diff = exp_y - exp_x; |
|
|
2811 |
|
|
|
2812 |
// if exp_x is 33 less than exp_y, no need for compensation |
|
|
2813 |
if (diff > 33) { |
|
|
2814 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2815 |
BID_RETURN (res); |
|
|
2816 |
} |
|
|
2817 |
|
|
|
2818 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
2819 |
// adjust the y significand upwards |
|
|
2820 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); |
|
|
2821 |
|
|
|
2822 |
|
|
|
2823 |
// if postitive, return whichever significand is larger |
|
|
2824 |
// (converse if negative) |
|
|
2825 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
2826 |
&& sig_n_prime256.w[1] == sig_x.w[1] |
|
|
2827 |
&& (sig_n_prime256.w[0] == sig_x.w[0])) { |
|
|
2828 |
res = 1; |
|
|
2829 |
BID_RETURN (res); |
|
|
2830 |
} // if equal, return 1 |
|
|
2831 |
{ |
|
|
2832 |
res = |
|
|
2833 |
((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0 |
|
|
2834 |
&& (sig_n_prime256.w[1] < sig_x.w[1] |
|
|
2835 |
|| (sig_n_prime256.w[1] == sig_x.w[1] |
|
|
2836 |
&& sig_n_prime256.w[0] < |
|
|
2837 |
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
2838 |
BID_RETURN (res); |
|
|
2839 |
} |
|
|
2840 |
} |
|
|
2841 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
2842 |
// adjust the y significand upwards |
|
|
2843 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); |
|
|
2844 |
|
|
|
2845 |
// if postitive, return whichever significand is larger |
|
|
2846 |
// (converse if negative) |
|
|
2847 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] |
|
|
2848 |
&& (sig_n_prime192.w[0] == sig_x.w[0])) { |
|
|
2849 |
res = 1; |
|
|
2850 |
BID_RETURN (res); |
|
|
2851 |
} // if equal, return 1 |
|
|
2852 |
{ |
|
|
2853 |
res = (sig_n_prime192.w[2] == 0 |
|
|
2854 |
&& (sig_n_prime192.w[1] < sig_x.w[1] |
|
|
2855 |
|| (sig_n_prime192.w[1] == sig_x.w[1] |
|
|
2856 |
&& sig_n_prime192.w[0] < |
|
|
2857 |
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2858 |
BID_RETURN (res); |
|
|
2859 |
} |
|
|
2860 |
} |
|
|
2861 |
|
|
|
2862 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, |
|
|
2863 |
bid128_signaling_greater_unordered, |
|
|
2864 |
x, y) |
|
|
2865 |
|
|
|
2866 |
int res; |
|
|
2867 |
int exp_x, exp_y; |
|
|
2868 |
int diff; |
|
|
2869 |
UINT128 sig_x, sig_y; |
|
|
2870 |
UINT192 sig_n_prime192; |
|
|
2871 |
UINT256 sig_n_prime256; |
|
|
2872 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
2873 |
|
|
|
2874 |
// NaN (CASE1) |
|
|
2875 |
// if either number is NAN, the comparison is unordered, |
|
|
2876 |
// rather than equal : return 1 |
|
|
2877 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
2878 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
2879 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2880 |
{ |
|
|
2881 |
res = 1; |
|
|
2882 |
BID_RETURN (res); |
|
|
2883 |
} |
|
|
2884 |
} |
|
|
2885 |
// SIMPLE (CASE2) |
|
|
2886 |
// if all the bits are the same, these numbers are equal (not Greater). |
|
|
2887 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
2888 |
res = 0; |
|
|
2889 |
BID_RETURN (res); |
|
|
2890 |
} |
|
|
2891 |
// INFINITY (CASE3) |
|
|
2892 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
2893 |
// if x is neg infinity, there is no way it is greater than y, return 0 |
|
|
2894 |
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) { |
|
|
2895 |
res = 0; |
|
|
2896 |
BID_RETURN (res); |
|
|
2897 |
} |
|
|
2898 |
// x is pos infinity, it is greater, unless y is positive infinity => return y!=pos_infinity |
|
|
2899 |
else { |
|
|
2900 |
res = (((y.w[1] & MASK_INF) != MASK_INF) |
|
|
2901 |
|| ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
2902 |
BID_RETURN (res); |
|
|
2903 |
} |
|
|
2904 |
} else if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
2905 |
// x is finite, so if y is positive infinity, then x is less, return 0 |
|
|
2906 |
// if y is negative infinity, then x is greater, return 1 |
|
|
2907 |
{ |
|
|
2908 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2909 |
BID_RETURN (res); |
|
|
2910 |
} |
|
|
2911 |
} |
|
|
2912 |
// CONVERT X |
|
|
2913 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
2914 |
sig_x.w[0] = x.w[0]; |
|
|
2915 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
2916 |
|
|
|
2917 |
// CHECK IF X IS CANONICAL |
|
|
2918 |
// 9999999999999999999999999999999999(decimal) = |
|
|
2919 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
2920 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
2921 |
// If the value exceeds that, it is interpreted as 0. |
|
|
2922 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
2923 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
2924 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
2925 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
2926 |
non_canon_x = 1; |
|
|
2927 |
else |
|
|
2928 |
non_canon_x = 0; |
|
|
2929 |
|
|
|
2930 |
// CONVERT Y |
|
|
2931 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
2932 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
2933 |
sig_y.w[0] = y.w[0]; |
|
|
2934 |
|
|
|
2935 |
// CHECK IF Y IS CANONICAL |
|
|
2936 |
// 9999999999999999999999999999999999(decimal) = |
|
|
2937 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
2938 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
2939 |
// If the value exceeds that, it is interpreted as 0. |
|
|
2940 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
2941 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
2942 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
2943 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
2944 |
non_canon_y = 1; |
|
|
2945 |
else |
|
|
2946 |
non_canon_y = 0; |
|
|
2947 |
|
|
|
2948 |
// ZERO (CASE4) |
|
|
2949 |
// some properties: |
|
|
2950 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
2951 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
2952 |
// ignore the exponent field |
|
|
2953 |
// (Any non-canonical # is considered 0) |
|
|
2954 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
2955 |
x_is_zero = 1; |
|
|
2956 |
} |
|
|
2957 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
2958 |
y_is_zero = 1; |
|
|
2959 |
} |
|
|
2960 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
2961 |
if (x_is_zero && y_is_zero) { |
|
|
2962 |
res = 0; |
|
|
2963 |
BID_RETURN (res); |
|
|
2964 |
} |
|
|
2965 |
// is x is zero, it is greater if Y is negative |
|
|
2966 |
else if (x_is_zero) { |
|
|
2967 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2968 |
BID_RETURN (res); |
|
|
2969 |
} |
|
|
2970 |
// is y is zero, X is greater if it is positive |
|
|
2971 |
else if (y_is_zero) { |
|
|
2972 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
2973 |
BID_RETURN (res); |
|
|
2974 |
} |
|
|
2975 |
// OPPOSITE SIGN (CASE5) |
|
|
2976 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
2977 |
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { |
|
|
2978 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
2979 |
BID_RETURN (res); |
|
|
2980 |
} |
|
|
2981 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
2982 |
// if exponents are the same, then we have a simple comparison |
|
|
2983 |
// of the significands |
|
|
2984 |
if (exp_y == exp_x) { |
|
|
2985 |
res = (((sig_x.w[1] > sig_y.w[1]) |
|
|
2986 |
|| (sig_x.w[1] == sig_y.w[1] |
|
|
2987 |
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == |
|
|
2988 |
MASK_SIGN)); |
|
|
2989 |
BID_RETURN (res); |
|
|
2990 |
} |
|
|
2991 |
// if both components are either bigger or smaller, |
|
|
2992 |
// it is clear what needs to be done |
|
|
2993 |
if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0] |
|
|
2994 |
&& exp_x > exp_y) { |
|
|
2995 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
2996 |
BID_RETURN (res); |
|
|
2997 |
} |
|
|
2998 |
if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0] |
|
|
2999 |
&& exp_x < exp_y) { |
|
|
3000 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3001 |
BID_RETURN (res); |
|
|
3002 |
} |
|
|
3003 |
|
|
|
3004 |
diff = exp_x - exp_y; |
|
|
3005 |
|
|
|
3006 |
// if |exp_x - exp_y| < 33, it comes down to the compensated significand |
|
|
3007 |
if (diff > 0) { // to simplify the loop below, |
|
|
3008 |
|
|
|
3009 |
// if exp_x is 33 greater than exp_y, no need for compensation |
|
|
3010 |
if (diff > 33) { |
|
|
3011 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3012 |
BID_RETURN (res); |
|
|
3013 |
} // difference cannot be greater than 10^33 |
|
|
3014 |
|
|
|
3015 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
3016 |
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); |
|
|
3017 |
|
|
|
3018 |
|
|
|
3019 |
// if postitive, return whichever significand is larger |
|
|
3020 |
// (converse if negative) |
|
|
3021 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
3022 |
&& sig_n_prime256.w[1] == sig_y.w[1] |
|
|
3023 |
&& (sig_n_prime256.w[0] == sig_y.w[0])) { |
|
|
3024 |
res = 0; |
|
|
3025 |
BID_RETURN (res); |
|
|
3026 |
} // if equal, return 0 |
|
|
3027 |
{ |
|
|
3028 |
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) |
|
|
3029 |
|| (sig_n_prime256.w[1] > sig_y.w[1]) |
|
|
3030 |
|| (sig_n_prime256.w[1] == sig_y.w[1] |
|
|
3031 |
&& sig_n_prime256.w[0] > |
|
|
3032 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
3033 |
BID_RETURN (res); |
|
|
3034 |
} |
|
|
3035 |
} |
|
|
3036 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
3037 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); |
|
|
3038 |
|
|
|
3039 |
// if postitive, return whichever significand is larger |
|
|
3040 |
// (converse if negative) |
|
|
3041 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] |
|
|
3042 |
&& (sig_n_prime192.w[0] == sig_y.w[0])) { |
|
|
3043 |
res = 0; |
|
|
3044 |
BID_RETURN (res); |
|
|
3045 |
} // if equal, return 0 |
|
|
3046 |
{ |
|
|
3047 |
res = (((sig_n_prime192.w[2] > 0) |
|
|
3048 |
|| (sig_n_prime192.w[1] > sig_y.w[1]) |
|
|
3049 |
|| (sig_n_prime192.w[1] == sig_y.w[1] |
|
|
3050 |
&& sig_n_prime192.w[0] > |
|
|
3051 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
3052 |
BID_RETURN (res); |
|
|
3053 |
} |
|
|
3054 |
} |
|
|
3055 |
|
|
|
3056 |
diff = exp_y - exp_x; |
|
|
3057 |
|
|
|
3058 |
// if exp_x is 33 less than exp_y, no need for compensation |
|
|
3059 |
if (diff > 33) { |
|
|
3060 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3061 |
BID_RETURN (res); |
|
|
3062 |
} |
|
|
3063 |
|
|
|
3064 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
3065 |
// adjust the y significand upwards |
|
|
3066 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); |
|
|
3067 |
|
|
|
3068 |
|
|
|
3069 |
// if postitive, return whichever significand is larger |
|
|
3070 |
// (converse if negative) |
|
|
3071 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
3072 |
&& sig_n_prime256.w[1] == sig_x.w[1] |
|
|
3073 |
&& (sig_n_prime256.w[0] == sig_x.w[0])) { |
|
|
3074 |
res = 0; |
|
|
3075 |
BID_RETURN (res); |
|
|
3076 |
} // if equal, return 0 |
|
|
3077 |
{ |
|
|
3078 |
res = |
|
|
3079 |
((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0 |
|
|
3080 |
&& (sig_n_prime256.w[1] < sig_x.w[1] |
|
|
3081 |
|| (sig_n_prime256.w[1] == sig_x.w[1] |
|
|
3082 |
&& sig_n_prime256.w[0] < |
|
|
3083 |
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
3084 |
BID_RETURN (res); |
|
|
3085 |
} |
|
|
3086 |
} |
|
|
3087 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
3088 |
// adjust the y significand upwards |
|
|
3089 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); |
|
|
3090 |
|
|
|
3091 |
// if postitive, return whichever significand is larger |
|
|
3092 |
// (converse if negative) |
|
|
3093 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] |
|
|
3094 |
&& (sig_n_prime192.w[0] == sig_x.w[0])) { |
|
|
3095 |
res = 0; |
|
|
3096 |
BID_RETURN (res); |
|
|
3097 |
} // if equal, return 0 |
|
|
3098 |
{ |
|
|
3099 |
res = (sig_n_prime192.w[2] == 0 |
|
|
3100 |
&& (sig_n_prime192.w[1] < sig_x.w[1] |
|
|
3101 |
|| (sig_n_prime192.w[1] == sig_x.w[1] |
|
|
3102 |
&& sig_n_prime192.w[0] < |
|
|
3103 |
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3104 |
BID_RETURN (res); |
|
|
3105 |
} |
|
|
3106 |
} |
|
|
3107 |
|
|
|
3108 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_signaling_less, x, |
|
|
3109 |
y) |
|
|
3110 |
|
|
|
3111 |
int res; |
|
|
3112 |
int exp_x, exp_y; |
|
|
3113 |
int diff; |
|
|
3114 |
UINT128 sig_x, sig_y; |
|
|
3115 |
UINT192 sig_n_prime192; |
|
|
3116 |
UINT256 sig_n_prime256; |
|
|
3117 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
3118 |
|
|
|
3119 |
// NaN (CASE1) |
|
|
3120 |
// if either number is NAN, the comparison is unordered, |
|
|
3121 |
// rather than equal : return 0 |
|
|
3122 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
3123 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
3124 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3125 |
{ |
|
|
3126 |
res = 0; |
|
|
3127 |
BID_RETURN (res); |
|
|
3128 |
} |
|
|
3129 |
} |
|
|
3130 |
// SIMPLE (CASE2) |
|
|
3131 |
// if all the bits are the same, these numbers are equal. |
|
|
3132 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
3133 |
res = 0; |
|
|
3134 |
BID_RETURN (res); |
|
|
3135 |
} |
|
|
3136 |
// INFINITY (CASE3) |
|
|
3137 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
3138 |
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } |
|
|
3139 |
if ((x.w[1] & MASK_SIGN) == MASK_SIGN) |
|
|
3140 |
// x is -inf, so it is less than y unless y is -inf |
|
|
3141 |
{ |
|
|
3142 |
res = (((y.w[1] & MASK_INF) != MASK_INF) |
|
|
3143 |
|| (y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3144 |
BID_RETURN (res); |
|
|
3145 |
} else |
|
|
3146 |
// x is pos_inf, no way for it to be less than y |
|
|
3147 |
{ |
|
|
3148 |
res = 0; |
|
|
3149 |
BID_RETURN (res); |
|
|
3150 |
} |
|
|
3151 |
} else if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
3152 |
// x is finite, so if y is positive infinity, then x is less, return 0 |
|
|
3153 |
// if y is negative infinity, then x is greater, return 1 |
|
|
3154 |
{ |
|
|
3155 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3156 |
BID_RETURN (res); |
|
|
3157 |
} |
|
|
3158 |
} |
|
|
3159 |
// CONVERT X |
|
|
3160 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
3161 |
sig_x.w[0] = x.w[0]; |
|
|
3162 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
3163 |
|
|
|
3164 |
// CHECK IF X IS CANONICAL |
|
|
3165 |
// 9999999999999999999999999999999999(decimal) = |
|
|
3166 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
3167 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
3168 |
// If the value exceeds that, it is interpreted as 0. |
|
|
3169 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
3170 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
3171 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
3172 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
3173 |
non_canon_x = 1; |
|
|
3174 |
else |
|
|
3175 |
non_canon_x = 0; |
|
|
3176 |
|
|
|
3177 |
// CONVERT Y |
|
|
3178 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
3179 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
3180 |
sig_y.w[0] = y.w[0]; |
|
|
3181 |
|
|
|
3182 |
// CHECK IF Y IS CANONICAL |
|
|
3183 |
// 9999999999999999999999999999999999(decimal) = |
|
|
3184 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
3185 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
3186 |
// If the value exceeds that, it is interpreted as 0. |
|
|
3187 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
3188 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
3189 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
3190 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
3191 |
non_canon_y = 1; |
|
|
3192 |
else |
|
|
3193 |
non_canon_y = 0; |
|
|
3194 |
|
|
|
3195 |
// ZERO (CASE4) |
|
|
3196 |
// some properties: |
|
|
3197 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
3198 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
3199 |
// ignore the exponent field |
|
|
3200 |
// (Any non-canonical # is considered 0) |
|
|
3201 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
3202 |
x_is_zero = 1; |
|
|
3203 |
} |
|
|
3204 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
3205 |
y_is_zero = 1; |
|
|
3206 |
} |
|
|
3207 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
3208 |
if (x_is_zero && y_is_zero) { |
|
|
3209 |
res = 0; |
|
|
3210 |
BID_RETURN (res); |
|
|
3211 |
} |
|
|
3212 |
// is x is zero, it is greater if Y is negative |
|
|
3213 |
else if (x_is_zero) { |
|
|
3214 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3215 |
BID_RETURN (res); |
|
|
3216 |
} |
|
|
3217 |
// is y is zero, X is greater if it is positive |
|
|
3218 |
else if (y_is_zero) { |
|
|
3219 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3220 |
BID_RETURN (res); |
|
|
3221 |
} |
|
|
3222 |
// OPPOSITE SIGN (CASE5) |
|
|
3223 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
3224 |
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { |
|
|
3225 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3226 |
BID_RETURN (res); |
|
|
3227 |
} |
|
|
3228 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
3229 |
// if exponents are the same, then we have a simple comparison |
|
|
3230 |
// of the significands |
|
|
3231 |
if (exp_y == exp_x) { |
|
|
3232 |
res = (((sig_x.w[1] > sig_y.w[1]) |
|
|
3233 |
|| (sig_x.w[1] == sig_y.w[1] |
|
|
3234 |
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) != |
|
|
3235 |
MASK_SIGN)); |
|
|
3236 |
BID_RETURN (res); |
|
|
3237 |
} |
|
|
3238 |
// if both components are either bigger or smaller, |
|
|
3239 |
// it is clear what needs to be done |
|
|
3240 |
if ((sig_x.w[1] > sig_y.w[1] |
|
|
3241 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) |
|
|
3242 |
&& exp_x >= exp_y) { |
|
|
3243 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3244 |
BID_RETURN (res); |
|
|
3245 |
} |
|
|
3246 |
if ((sig_x.w[1] < sig_y.w[1] |
|
|
3247 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) |
|
|
3248 |
&& exp_x <= exp_y) { |
|
|
3249 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3250 |
BID_RETURN (res); |
|
|
3251 |
} |
|
|
3252 |
|
|
|
3253 |
diff = exp_x - exp_y; |
|
|
3254 |
|
|
|
3255 |
// if |exp_x - exp_y| < 33, it comes down to the compensated significand |
|
|
3256 |
if (diff > 0) { // to simplify the loop below, |
|
|
3257 |
|
|
|
3258 |
// if exp_x is 33 greater than exp_y, no need for compensation |
|
|
3259 |
if (diff > 33) { |
|
|
3260 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3261 |
BID_RETURN (res); |
|
|
3262 |
} // difference cannot be greater than 10^33 |
|
|
3263 |
|
|
|
3264 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
3265 |
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); |
|
|
3266 |
|
|
|
3267 |
|
|
|
3268 |
// if postitive, return whichever significand is larger |
|
|
3269 |
// (converse if negative) |
|
|
3270 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
3271 |
&& sig_n_prime256.w[1] == sig_y.w[1] |
|
|
3272 |
&& (sig_n_prime256.w[0] == sig_y.w[0])) { |
|
|
3273 |
res = 0; |
|
|
3274 |
BID_RETURN (res); |
|
|
3275 |
} // if equal, return 0 |
|
|
3276 |
{ |
|
|
3277 |
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) |
|
|
3278 |
|| (sig_n_prime256.w[1] > sig_y.w[1]) |
|
|
3279 |
|| (sig_n_prime256.w[1] == sig_y.w[1] |
|
|
3280 |
&& sig_n_prime256.w[0] > |
|
|
3281 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
3282 |
BID_RETURN (res); |
|
|
3283 |
} |
|
|
3284 |
} |
|
|
3285 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
3286 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); |
|
|
3287 |
|
|
|
3288 |
// if postitive, return whichever significand is larger |
|
|
3289 |
// (converse if negative) |
|
|
3290 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] |
|
|
3291 |
&& (sig_n_prime192.w[0] == sig_y.w[0])) { |
|
|
3292 |
res = 0; |
|
|
3293 |
BID_RETURN (res); |
|
|
3294 |
} // if equal, return 0 |
|
|
3295 |
{ |
|
|
3296 |
res = (((sig_n_prime192.w[2] > 0) |
|
|
3297 |
|| (sig_n_prime192.w[1] > sig_y.w[1]) |
|
|
3298 |
|| (sig_n_prime192.w[1] == sig_y.w[1] |
|
|
3299 |
&& sig_n_prime192.w[0] > |
|
|
3300 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
3301 |
BID_RETURN (res); |
|
|
3302 |
} |
|
|
3303 |
} |
|
|
3304 |
|
|
|
3305 |
diff = exp_y - exp_x; |
|
|
3306 |
|
|
|
3307 |
// if exp_x is 33 less than exp_y, |x| < |y|, return 1 if positive |
|
|
3308 |
if (diff > 33) { |
|
|
3309 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3310 |
BID_RETURN (res); |
|
|
3311 |
} |
|
|
3312 |
|
|
|
3313 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
3314 |
// adjust the y significand upwards |
|
|
3315 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); |
|
|
3316 |
|
|
|
3317 |
|
|
|
3318 |
// if postitive, return whichever significand is larger |
|
|
3319 |
// (converse if negative) |
|
|
3320 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
3321 |
&& sig_n_prime256.w[1] == sig_x.w[1] |
|
|
3322 |
&& (sig_n_prime256.w[0] == sig_x.w[0])) { |
|
|
3323 |
res = 0; |
|
|
3324 |
BID_RETURN (res); |
|
|
3325 |
} // if equal, return 1 |
|
|
3326 |
{ |
|
|
3327 |
res = |
|
|
3328 |
((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 |
|
|
3329 |
|| (sig_n_prime256.w[1] > sig_x.w[1] |
|
|
3330 |
|| (sig_n_prime256.w[1] == sig_x.w[1] |
|
|
3331 |
&& sig_n_prime256.w[0] > |
|
|
3332 |
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
3333 |
BID_RETURN (res); |
|
|
3334 |
} |
|
|
3335 |
} |
|
|
3336 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
3337 |
// adjust the y significand upwards |
|
|
3338 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); |
|
|
3339 |
|
|
|
3340 |
// if postitive, return whichever significand is larger |
|
|
3341 |
// (converse if negative) |
|
|
3342 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] |
|
|
3343 |
&& (sig_n_prime192.w[0] == sig_x.w[0])) { |
|
|
3344 |
res = 0; |
|
|
3345 |
BID_RETURN (res); |
|
|
3346 |
} // if equal, return 0 |
|
|
3347 |
{ |
|
|
3348 |
res = (sig_n_prime192.w[2] != 0 |
|
|
3349 |
|| (sig_n_prime192.w[1] > sig_x.w[1] |
|
|
3350 |
|| (sig_n_prime192.w[1] == sig_x.w[1] |
|
|
3351 |
&& sig_n_prime192.w[0] > |
|
|
3352 |
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3353 |
BID_RETURN (res); |
|
|
3354 |
} |
|
|
3355 |
} |
|
|
3356 |
|
|
|
3357 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, |
|
|
3358 |
bid128_signaling_less_equal, |
|
|
3359 |
x, y) |
|
|
3360 |
|
|
|
3361 |
int res; |
|
|
3362 |
int exp_x, exp_y; |
|
|
3363 |
int diff; |
|
|
3364 |
UINT128 sig_x, sig_y; |
|
|
3365 |
UINT192 sig_n_prime192; |
|
|
3366 |
UINT256 sig_n_prime256; |
|
|
3367 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
3368 |
|
|
|
3369 |
// NaN (CASE1) |
|
|
3370 |
// if either number is NAN, the comparison is unordered, |
|
|
3371 |
// rather than equal : return 0 |
|
|
3372 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
3373 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
3374 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3375 |
{ |
|
|
3376 |
res = 0; |
|
|
3377 |
BID_RETURN (res); |
|
|
3378 |
} |
|
|
3379 |
} |
|
|
3380 |
// SIMPLE (CASE2) |
|
|
3381 |
// if all the bits are the same, these numbers are equal (not Greater). |
|
|
3382 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
3383 |
res = 1; |
|
|
3384 |
BID_RETURN (res); |
|
|
3385 |
} |
|
|
3386 |
// INFINITY (CASE3) |
|
|
3387 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
3388 |
// if x is neg infinity, there is no way it is greater than y, return 1 |
|
|
3389 |
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) { |
|
|
3390 |
res = 1; |
|
|
3391 |
BID_RETURN (res); |
|
|
3392 |
} |
|
|
3393 |
// x is pos infinity, it is greater, unless y is positive infinity => return y!=pos_infinity |
|
|
3394 |
else { |
|
|
3395 |
res = (((y.w[1] & MASK_INF) == MASK_INF) |
|
|
3396 |
&& ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
3397 |
BID_RETURN (res); |
|
|
3398 |
} |
|
|
3399 |
} else if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
3400 |
// x is finite, so if y is positive infinity, then x is less, return 0 |
|
|
3401 |
// if y is negative infinity, then x is greater, return 1 |
|
|
3402 |
{ |
|
|
3403 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3404 |
BID_RETURN (res); |
|
|
3405 |
} |
|
|
3406 |
} |
|
|
3407 |
// CONVERT X |
|
|
3408 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
3409 |
sig_x.w[0] = x.w[0]; |
|
|
3410 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
3411 |
|
|
|
3412 |
// CHECK IF X IS CANONICAL |
|
|
3413 |
// 9999999999999999999999999999999999(decimal) = |
|
|
3414 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
3415 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
3416 |
// If the value exceeds that, it is interpreted as 0. |
|
|
3417 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
3418 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
3419 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
3420 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
3421 |
non_canon_x = 1; |
|
|
3422 |
else |
|
|
3423 |
non_canon_x = 0; |
|
|
3424 |
|
|
|
3425 |
// CONVERT Y |
|
|
3426 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
3427 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
3428 |
sig_y.w[0] = y.w[0]; |
|
|
3429 |
|
|
|
3430 |
// CHECK IF Y IS CANONICAL |
|
|
3431 |
// 9999999999999999999999999999999999(decimal) = |
|
|
3432 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
3433 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
3434 |
// If the value exceeds that, it is interpreted as 0. |
|
|
3435 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
3436 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
3437 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
3438 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
3439 |
non_canon_y = 1; |
|
|
3440 |
else |
|
|
3441 |
non_canon_y = 0; |
|
|
3442 |
|
|
|
3443 |
// ZERO (CASE4) |
|
|
3444 |
// some properties: |
|
|
3445 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
3446 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
3447 |
// ignore the exponent field |
|
|
3448 |
// (Any non-canonical # is considered 0) |
|
|
3449 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
3450 |
x_is_zero = 1; |
|
|
3451 |
} |
|
|
3452 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
3453 |
y_is_zero = 1; |
|
|
3454 |
} |
|
|
3455 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
3456 |
if (x_is_zero && y_is_zero) { |
|
|
3457 |
res = 1; |
|
|
3458 |
BID_RETURN (res); |
|
|
3459 |
} |
|
|
3460 |
// is x is zero, it is greater if Y is negative |
|
|
3461 |
else if (x_is_zero) { |
|
|
3462 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3463 |
BID_RETURN (res); |
|
|
3464 |
} |
|
|
3465 |
// is y is zero, X is greater if it is positive |
|
|
3466 |
else if (y_is_zero) { |
|
|
3467 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3468 |
BID_RETURN (res); |
|
|
3469 |
} |
|
|
3470 |
// OPPOSITE SIGN (CASE5) |
|
|
3471 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
3472 |
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { |
|
|
3473 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3474 |
BID_RETURN (res); |
|
|
3475 |
} |
|
|
3476 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
3477 |
// if exponents are the same, then we have a simple comparison |
|
|
3478 |
// of the significands |
|
|
3479 |
if (exp_y == exp_x) { |
|
|
3480 |
res = (((sig_x.w[1] > sig_y.w[1]) |
|
|
3481 |
|| (sig_x.w[1] == sig_y.w[1] |
|
|
3482 |
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) != |
|
|
3483 |
MASK_SIGN)); |
|
|
3484 |
BID_RETURN (res); |
|
|
3485 |
} |
|
|
3486 |
// if both components are either bigger or smaller, |
|
|
3487 |
// it is clear what needs to be done |
|
|
3488 |
if ((sig_x.w[1] > sig_y.w[1] |
|
|
3489 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) |
|
|
3490 |
&& exp_x >= exp_y) { |
|
|
3491 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3492 |
BID_RETURN (res); |
|
|
3493 |
} |
|
|
3494 |
if ((sig_x.w[1] < sig_y.w[1] |
|
|
3495 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) |
|
|
3496 |
&& exp_x <= exp_y) { |
|
|
3497 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3498 |
BID_RETURN (res); |
|
|
3499 |
} |
|
|
3500 |
|
|
|
3501 |
diff = exp_x - exp_y; |
|
|
3502 |
|
|
|
3503 |
// if |exp_x - exp_y| < 33, it comes down to the compensated significand |
|
|
3504 |
if (diff > 0) { // to simplify the loop below, |
|
|
3505 |
|
|
|
3506 |
// if exp_x is 33 greater than exp_y, no need for compensation |
|
|
3507 |
if (diff > 33) { |
|
|
3508 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3509 |
BID_RETURN (res); |
|
|
3510 |
} // difference cannot be greater than 10^33 |
|
|
3511 |
|
|
|
3512 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
3513 |
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); |
|
|
3514 |
|
|
|
3515 |
|
|
|
3516 |
// if postitive, return whichever significand is larger |
|
|
3517 |
// (converse if negative) |
|
|
3518 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
3519 |
&& sig_n_prime256.w[1] == sig_y.w[1] |
|
|
3520 |
&& (sig_n_prime256.w[0] == sig_y.w[0])) { |
|
|
3521 |
res = 1; |
|
|
3522 |
BID_RETURN (res); |
|
|
3523 |
} // if equal, return 0 |
|
|
3524 |
{ |
|
|
3525 |
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) |
|
|
3526 |
|| (sig_n_prime256.w[1] > sig_y.w[1]) |
|
|
3527 |
|| (sig_n_prime256.w[1] == sig_y.w[1] |
|
|
3528 |
&& sig_n_prime256.w[0] > |
|
|
3529 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
3530 |
BID_RETURN (res); |
|
|
3531 |
} |
|
|
3532 |
} |
|
|
3533 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
3534 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); |
|
|
3535 |
|
|
|
3536 |
// if postitive, return whichever significand is larger |
|
|
3537 |
// (converse if negative) |
|
|
3538 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] |
|
|
3539 |
&& (sig_n_prime192.w[0] == sig_y.w[0])) { |
|
|
3540 |
res = 1; |
|
|
3541 |
BID_RETURN (res); |
|
|
3542 |
} // if equal, return 0 |
|
|
3543 |
{ |
|
|
3544 |
res = (((sig_n_prime192.w[2] > 0) |
|
|
3545 |
|| (sig_n_prime192.w[1] > sig_y.w[1]) |
|
|
3546 |
|| (sig_n_prime192.w[1] == sig_y.w[1] |
|
|
3547 |
&& sig_n_prime192.w[0] > |
|
|
3548 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
3549 |
BID_RETURN (res); |
|
|
3550 |
} |
|
|
3551 |
} |
|
|
3552 |
|
|
|
3553 |
diff = exp_y - exp_x; |
|
|
3554 |
|
|
|
3555 |
// if exp_x is 33 less than exp_y, no need for compensation |
|
|
3556 |
if (diff > 33) { |
|
|
3557 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3558 |
BID_RETURN (res); |
|
|
3559 |
} |
|
|
3560 |
|
|
|
3561 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
3562 |
// adjust the y significand upwards |
|
|
3563 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); |
|
|
3564 |
|
|
|
3565 |
|
|
|
3566 |
// if postitive, return whichever significand is larger |
|
|
3567 |
// (converse if negative) |
|
|
3568 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
3569 |
&& sig_n_prime256.w[1] == sig_x.w[1] |
|
|
3570 |
&& (sig_n_prime256.w[0] == sig_x.w[0])) { |
|
|
3571 |
res = 1; |
|
|
3572 |
BID_RETURN (res); |
|
|
3573 |
} // if equal, return 0 |
|
|
3574 |
{ |
|
|
3575 |
res = |
|
|
3576 |
((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 |
|
|
3577 |
|| (sig_n_prime256.w[1] > sig_x.w[1] |
|
|
3578 |
|| (sig_n_prime256.w[1] == sig_x.w[1] |
|
|
3579 |
&& sig_n_prime256.w[0] > |
|
|
3580 |
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
3581 |
BID_RETURN (res); |
|
|
3582 |
} |
|
|
3583 |
} |
|
|
3584 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
3585 |
// adjust the y significand upwards |
|
|
3586 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); |
|
|
3587 |
|
|
|
3588 |
// if postitive, return whichever significand is larger |
|
|
3589 |
// (converse if negative) |
|
|
3590 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] |
|
|
3591 |
&& (sig_n_prime192.w[0] == sig_x.w[0])) { |
|
|
3592 |
res = 1; |
|
|
3593 |
BID_RETURN (res); |
|
|
3594 |
} // if equal, return 0 |
|
|
3595 |
{ |
|
|
3596 |
res = (sig_n_prime192.w[2] != 0 |
|
|
3597 |
|| (sig_n_prime192.w[1] > sig_x.w[1] |
|
|
3598 |
|| (sig_n_prime192.w[1] == sig_x.w[1] |
|
|
3599 |
&& sig_n_prime192.w[0] > |
|
|
3600 |
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3601 |
BID_RETURN (res); |
|
|
3602 |
} |
|
|
3603 |
} |
|
|
3604 |
|
|
|
3605 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, |
|
|
3606 |
bid128_signaling_less_unordered, |
|
|
3607 |
x, y) |
|
|
3608 |
|
|
|
3609 |
int res; |
|
|
3610 |
int exp_x, exp_y; |
|
|
3611 |
int diff; |
|
|
3612 |
UINT128 sig_x, sig_y; |
|
|
3613 |
UINT192 sig_n_prime192; |
|
|
3614 |
UINT256 sig_n_prime256; |
|
|
3615 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
3616 |
|
|
|
3617 |
// NaN (CASE1) |
|
|
3618 |
// if either number is NAN, the comparison is unordered |
|
|
3619 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
3620 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
3621 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3622 |
{ |
|
|
3623 |
res = 1; |
|
|
3624 |
BID_RETURN (res); |
|
|
3625 |
} |
|
|
3626 |
} |
|
|
3627 |
// SIMPLE (CASE2) |
|
|
3628 |
// if all the bits are the same, these numbers are equal. |
|
|
3629 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
3630 |
res = 0; |
|
|
3631 |
BID_RETURN (res); |
|
|
3632 |
} |
|
|
3633 |
// INFINITY (CASE3) |
|
|
3634 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
3635 |
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } |
|
|
3636 |
if ((x.w[1] & MASK_SIGN) == MASK_SIGN) |
|
|
3637 |
// x is -inf, so it is less than y unless y is -inf |
|
|
3638 |
{ |
|
|
3639 |
res = (((y.w[1] & MASK_INF) != MASK_INF) |
|
|
3640 |
|| (y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3641 |
BID_RETURN (res); |
|
|
3642 |
} else |
|
|
3643 |
// x is pos_inf, no way for it to be less than y |
|
|
3644 |
{ |
|
|
3645 |
res = 0; |
|
|
3646 |
BID_RETURN (res); |
|
|
3647 |
} |
|
|
3648 |
} else if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
3649 |
// x is finite, so if y is positive infinity, then x is less, return 0 |
|
|
3650 |
// if y is negative infinity, then x is greater, return 1 |
|
|
3651 |
{ |
|
|
3652 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3653 |
BID_RETURN (res); |
|
|
3654 |
} |
|
|
3655 |
} |
|
|
3656 |
// CONVERT X |
|
|
3657 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
3658 |
sig_x.w[0] = x.w[0]; |
|
|
3659 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
3660 |
|
|
|
3661 |
// CHECK IF X IS CANONICAL |
|
|
3662 |
// 9999999999999999999999999999999999(decimal) = |
|
|
3663 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
3664 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
3665 |
// If the value exceeds that, it is interpreted as 0. |
|
|
3666 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
3667 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
3668 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
3669 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
3670 |
non_canon_x = 1; |
|
|
3671 |
else |
|
|
3672 |
non_canon_x = 0; |
|
|
3673 |
|
|
|
3674 |
// CONVERT Y |
|
|
3675 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
3676 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
3677 |
sig_y.w[0] = y.w[0]; |
|
|
3678 |
|
|
|
3679 |
// CHECK IF Y IS CANONICAL |
|
|
3680 |
// 9999999999999999999999999999999999(decimal) = |
|
|
3681 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
3682 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
3683 |
// If the value exceeds that, it is interpreted as 0. |
|
|
3684 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
3685 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
3686 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
3687 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
3688 |
non_canon_y = 1; |
|
|
3689 |
else |
|
|
3690 |
non_canon_y = 0; |
|
|
3691 |
|
|
|
3692 |
// ZERO (CASE4) |
|
|
3693 |
// some properties: |
|
|
3694 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
3695 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
3696 |
// ignore the exponent field |
|
|
3697 |
// (Any non-canonical # is considered 0) |
|
|
3698 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
3699 |
x_is_zero = 1; |
|
|
3700 |
} |
|
|
3701 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
3702 |
y_is_zero = 1; |
|
|
3703 |
} |
|
|
3704 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
3705 |
if (x_is_zero && y_is_zero) { |
|
|
3706 |
res = 0; |
|
|
3707 |
BID_RETURN (res); |
|
|
3708 |
} |
|
|
3709 |
// is x is zero, it is greater if Y is negative |
|
|
3710 |
else if (x_is_zero) { |
|
|
3711 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3712 |
BID_RETURN (res); |
|
|
3713 |
} |
|
|
3714 |
// is y is zero, X is greater if it is positive |
|
|
3715 |
else if (y_is_zero) { |
|
|
3716 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3717 |
BID_RETURN (res); |
|
|
3718 |
} |
|
|
3719 |
// OPPOSITE SIGN (CASE5) |
|
|
3720 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
3721 |
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { |
|
|
3722 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3723 |
BID_RETURN (res); |
|
|
3724 |
} |
|
|
3725 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
3726 |
// if exponents are the same, then we have a simple comparison |
|
|
3727 |
// of the significands |
|
|
3728 |
if (exp_y == exp_x) { |
|
|
3729 |
res = (((sig_x.w[1] > sig_y.w[1]) |
|
|
3730 |
|| (sig_x.w[1] == sig_y.w[1] |
|
|
3731 |
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) != |
|
|
3732 |
MASK_SIGN)); |
|
|
3733 |
BID_RETURN (res); |
|
|
3734 |
} |
|
|
3735 |
// if both components are either bigger or smaller, |
|
|
3736 |
// it is clear what needs to be done |
|
|
3737 |
if ((sig_x.w[1] > sig_y.w[1] |
|
|
3738 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) |
|
|
3739 |
&& exp_x >= exp_y) { |
|
|
3740 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3741 |
BID_RETURN (res); |
|
|
3742 |
} |
|
|
3743 |
if ((sig_x.w[1] < sig_y.w[1] |
|
|
3744 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) |
|
|
3745 |
&& exp_x <= exp_y) { |
|
|
3746 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3747 |
BID_RETURN (res); |
|
|
3748 |
} |
|
|
3749 |
|
|
|
3750 |
diff = exp_x - exp_y; |
|
|
3751 |
|
|
|
3752 |
// if |exp_x - exp_y| < 33, it comes down to the compensated significand |
|
|
3753 |
if (diff > 0) { // to simplify the loop below, |
|
|
3754 |
|
|
|
3755 |
// if exp_x is 33 greater than exp_y, no need for compensation |
|
|
3756 |
if (diff > 33) { |
|
|
3757 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3758 |
BID_RETURN (res); |
|
|
3759 |
} // difference cannot be greater than 10^33 |
|
|
3760 |
|
|
|
3761 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
3762 |
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); |
|
|
3763 |
|
|
|
3764 |
|
|
|
3765 |
// if postitive, return whichever significand is larger |
|
|
3766 |
// (converse if negative) |
|
|
3767 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
3768 |
&& sig_n_prime256.w[1] == sig_y.w[1] |
|
|
3769 |
&& (sig_n_prime256.w[0] == sig_y.w[0])) { |
|
|
3770 |
res = 0; |
|
|
3771 |
BID_RETURN (res); |
|
|
3772 |
} // if equal, return 0 |
|
|
3773 |
{ |
|
|
3774 |
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) |
|
|
3775 |
|| (sig_n_prime256.w[1] > sig_y.w[1]) |
|
|
3776 |
|| (sig_n_prime256.w[1] == sig_y.w[1] |
|
|
3777 |
&& sig_n_prime256.w[0] > |
|
|
3778 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
3779 |
BID_RETURN (res); |
|
|
3780 |
} |
|
|
3781 |
} |
|
|
3782 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
3783 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); |
|
|
3784 |
|
|
|
3785 |
// if postitive, return whichever significand is larger |
|
|
3786 |
// (converse if negative) |
|
|
3787 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] |
|
|
3788 |
&& (sig_n_prime192.w[0] == sig_y.w[0])) { |
|
|
3789 |
res = 0; |
|
|
3790 |
BID_RETURN (res); |
|
|
3791 |
} // if equal, return 0 |
|
|
3792 |
{ |
|
|
3793 |
res = (((sig_n_prime192.w[2] > 0) |
|
|
3794 |
|| (sig_n_prime192.w[1] > sig_y.w[1]) |
|
|
3795 |
|| (sig_n_prime192.w[1] == sig_y.w[1] |
|
|
3796 |
&& sig_n_prime192.w[0] > |
|
|
3797 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
3798 |
BID_RETURN (res); |
|
|
3799 |
} |
|
|
3800 |
} |
|
|
3801 |
|
|
|
3802 |
diff = exp_y - exp_x; |
|
|
3803 |
|
|
|
3804 |
// if exp_x is 33 less than exp_y, no need for compensation |
|
|
3805 |
if (diff > 33) { |
|
|
3806 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3807 |
BID_RETURN (res); |
|
|
3808 |
} |
|
|
3809 |
|
|
|
3810 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
3811 |
// adjust the y significand upwards |
|
|
3812 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); |
|
|
3813 |
|
|
|
3814 |
|
|
|
3815 |
// if postitive, return whichever significand is larger |
|
|
3816 |
// (converse if negative) |
|
|
3817 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
3818 |
&& sig_n_prime256.w[1] == sig_x.w[1] |
|
|
3819 |
&& (sig_n_prime256.w[0] == sig_x.w[0])) { |
|
|
3820 |
res = 0; |
|
|
3821 |
BID_RETURN (res); |
|
|
3822 |
} // if equal, return 1 |
|
|
3823 |
{ |
|
|
3824 |
res = |
|
|
3825 |
((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 |
|
|
3826 |
|| (sig_n_prime256.w[1] > sig_x.w[1] |
|
|
3827 |
|| (sig_n_prime256.w[1] == sig_x.w[1] |
|
|
3828 |
&& sig_n_prime256.w[0] > |
|
|
3829 |
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
3830 |
BID_RETURN (res); |
|
|
3831 |
} |
|
|
3832 |
} |
|
|
3833 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
3834 |
// adjust the y significand upwards |
|
|
3835 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); |
|
|
3836 |
|
|
|
3837 |
// if postitive, return whichever significand is larger (converse if negative) |
|
|
3838 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] |
|
|
3839 |
&& (sig_n_prime192.w[0] == sig_x.w[0])) { |
|
|
3840 |
res = 0; |
|
|
3841 |
BID_RETURN (res); |
|
|
3842 |
} // if equal, return 0 |
|
|
3843 |
{ |
|
|
3844 |
res = (sig_n_prime192.w[2] != 0 |
|
|
3845 |
|| (sig_n_prime192.w[1] > sig_x.w[1] |
|
|
3846 |
|| (sig_n_prime192.w[1] == sig_x.w[1] |
|
|
3847 |
&& sig_n_prime192.w[0] > |
|
|
3848 |
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3849 |
BID_RETURN (res); |
|
|
3850 |
} |
|
|
3851 |
} |
|
|
3852 |
|
|
|
3853 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, |
|
|
3854 |
bid128_signaling_not_greater, |
|
|
3855 |
x, y) |
|
|
3856 |
|
|
|
3857 |
int res; |
|
|
3858 |
int exp_x, exp_y; |
|
|
3859 |
int diff; |
|
|
3860 |
UINT128 sig_x, sig_y; |
|
|
3861 |
UINT192 sig_n_prime192; |
|
|
3862 |
UINT256 sig_n_prime256; |
|
|
3863 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
3864 |
|
|
|
3865 |
// NaN (CASE1) |
|
|
3866 |
// if either number is NAN, the comparison is unordered, |
|
|
3867 |
// rather than equal : return 0 |
|
|
3868 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
3869 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
3870 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3871 |
{ |
|
|
3872 |
res = 1; |
|
|
3873 |
BID_RETURN (res); |
|
|
3874 |
} |
|
|
3875 |
} |
|
|
3876 |
// SIMPLE (CASE2) |
|
|
3877 |
// if all the bits are the same, these numbers are equal (not Greater). |
|
|
3878 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
3879 |
res = 1; |
|
|
3880 |
BID_RETURN (res); |
|
|
3881 |
} |
|
|
3882 |
// INFINITY (CASE3) |
|
|
3883 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
3884 |
// if x is neg infinity, there is no way it is greater than y, return 1 |
|
|
3885 |
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) { |
|
|
3886 |
res = 1; |
|
|
3887 |
BID_RETURN (res); |
|
|
3888 |
} |
|
|
3889 |
// x is pos infinity, it is greater, unless y is positive infinity => return y!=pos_infinity |
|
|
3890 |
else { |
|
|
3891 |
res = (((y.w[1] & MASK_INF) == MASK_INF) |
|
|
3892 |
&& ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
3893 |
BID_RETURN (res); |
|
|
3894 |
} |
|
|
3895 |
} else if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
3896 |
// x is finite, so if y is positive infinity, then x is less, return 0 |
|
|
3897 |
// if y is negative infinity, then x is greater, return 1 |
|
|
3898 |
{ |
|
|
3899 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3900 |
BID_RETURN (res); |
|
|
3901 |
} |
|
|
3902 |
} |
|
|
3903 |
// CONVERT X |
|
|
3904 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
3905 |
sig_x.w[0] = x.w[0]; |
|
|
3906 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
3907 |
|
|
|
3908 |
// CHECK IF X IS CANONICAL |
|
|
3909 |
// 9999999999999999999999999999999999(decimal) = |
|
|
3910 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
3911 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
3912 |
// If the value exceeds that, it is interpreted as 0. |
|
|
3913 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
3914 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
3915 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
3916 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
3917 |
non_canon_x = 1; |
|
|
3918 |
else |
|
|
3919 |
non_canon_x = 0; |
|
|
3920 |
|
|
|
3921 |
// CONVERT Y |
|
|
3922 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
3923 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
3924 |
sig_y.w[0] = y.w[0]; |
|
|
3925 |
|
|
|
3926 |
// CHECK IF Y IS CANONICAL |
|
|
3927 |
// 9999999999999999999999999999999999(decimal) = |
|
|
3928 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
3929 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
3930 |
// If the value exceeds that, it is interpreted as 0. |
|
|
3931 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
3932 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
3933 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
3934 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
3935 |
non_canon_y = 1; |
|
|
3936 |
else |
|
|
3937 |
non_canon_y = 0; |
|
|
3938 |
|
|
|
3939 |
// ZERO (CASE4) |
|
|
3940 |
// some properties: |
|
|
3941 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
3942 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
3943 |
// ignore the exponent field |
|
|
3944 |
// (Any non-canonical # is considered 0) |
|
|
3945 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
3946 |
x_is_zero = 1; |
|
|
3947 |
} |
|
|
3948 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
3949 |
y_is_zero = 1; |
|
|
3950 |
} |
|
|
3951 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
3952 |
if (x_is_zero && y_is_zero) { |
|
|
3953 |
res = 1; |
|
|
3954 |
BID_RETURN (res); |
|
|
3955 |
} |
|
|
3956 |
// is x is zero, it is greater if Y is negative |
|
|
3957 |
else if (x_is_zero) { |
|
|
3958 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3959 |
BID_RETURN (res); |
|
|
3960 |
} |
|
|
3961 |
// is y is zero, X is greater if it is positive |
|
|
3962 |
else if (y_is_zero) { |
|
|
3963 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3964 |
BID_RETURN (res); |
|
|
3965 |
} |
|
|
3966 |
// OPPOSITE SIGN (CASE5) |
|
|
3967 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
3968 |
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { |
|
|
3969 |
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3970 |
BID_RETURN (res); |
|
|
3971 |
} |
|
|
3972 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
3973 |
// if exponents are the same, then we have a simple comparison |
|
|
3974 |
// of the significands |
|
|
3975 |
if (exp_y == exp_x) { |
|
|
3976 |
res = (((sig_x.w[1] > sig_y.w[1]) |
|
|
3977 |
|| (sig_x.w[1] == sig_y.w[1] |
|
|
3978 |
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) != |
|
|
3979 |
MASK_SIGN)); |
|
|
3980 |
BID_RETURN (res); |
|
|
3981 |
} |
|
|
3982 |
// if both components are either bigger or smaller, |
|
|
3983 |
// it is clear what needs to be done |
|
|
3984 |
if ((sig_x.w[1] > sig_y.w[1] |
|
|
3985 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) |
|
|
3986 |
&& exp_x >= exp_y) { |
|
|
3987 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
3988 |
BID_RETURN (res); |
|
|
3989 |
} |
|
|
3990 |
if ((sig_x.w[1] < sig_y.w[1] |
|
|
3991 |
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) |
|
|
3992 |
&& exp_x <= exp_y) { |
|
|
3993 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
3994 |
BID_RETURN (res); |
|
|
3995 |
} |
|
|
3996 |
|
|
|
3997 |
diff = exp_x - exp_y; |
|
|
3998 |
|
|
|
3999 |
// if |exp_x - exp_y| < 33, it comes down to the compensated significand |
|
|
4000 |
if (diff > 0) { // to simplify the loop below, |
|
|
4001 |
|
|
|
4002 |
// if exp_x is 33 greater than exp_y, no need for compensation |
|
|
4003 |
if (diff > 33) { |
|
|
4004 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
4005 |
BID_RETURN (res); |
|
|
4006 |
} // difference cannot be greater than 10^33 |
|
|
4007 |
|
|
|
4008 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
4009 |
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); |
|
|
4010 |
|
|
|
4011 |
|
|
|
4012 |
// if postitive, return whichever significand is larger |
|
|
4013 |
// (converse if negative) |
|
|
4014 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
4015 |
&& sig_n_prime256.w[1] == sig_y.w[1] |
|
|
4016 |
&& (sig_n_prime256.w[0] == sig_y.w[0])) { |
|
|
4017 |
res = 1; |
|
|
4018 |
BID_RETURN (res); |
|
|
4019 |
} // if equal, return 0 |
|
|
4020 |
{ |
|
|
4021 |
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) |
|
|
4022 |
|| (sig_n_prime256.w[1] > sig_y.w[1]) |
|
|
4023 |
|| (sig_n_prime256.w[1] == sig_y.w[1] |
|
|
4024 |
&& sig_n_prime256.w[0] > |
|
|
4025 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
4026 |
BID_RETURN (res); |
|
|
4027 |
} |
|
|
4028 |
} |
|
|
4029 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
4030 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); |
|
|
4031 |
|
|
|
4032 |
// if postitive, return whichever significand is larger |
|
|
4033 |
// (converse if negative) |
|
|
4034 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] |
|
|
4035 |
&& (sig_n_prime192.w[0] == sig_y.w[0])) { |
|
|
4036 |
res = 1; |
|
|
4037 |
BID_RETURN (res); |
|
|
4038 |
} // if equal, return 0 |
|
|
4039 |
{ |
|
|
4040 |
res = (((sig_n_prime192.w[2] > 0) |
|
|
4041 |
|| (sig_n_prime192.w[1] > sig_y.w[1]) |
|
|
4042 |
|| (sig_n_prime192.w[1] == sig_y.w[1] |
|
|
4043 |
&& sig_n_prime192.w[0] > |
|
|
4044 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); |
|
|
4045 |
BID_RETURN (res); |
|
|
4046 |
} |
|
|
4047 |
} |
|
|
4048 |
|
|
|
4049 |
diff = exp_y - exp_x; |
|
|
4050 |
|
|
|
4051 |
// if exp_x is 33 less than exp_y, no need for compensation |
|
|
4052 |
if (diff > 33) { |
|
|
4053 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
4054 |
BID_RETURN (res); |
|
|
4055 |
} |
|
|
4056 |
|
|
|
4057 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
4058 |
// adjust the y significand upwards |
|
|
4059 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); |
|
|
4060 |
|
|
|
4061 |
// if postitive, return whichever significand is larger |
|
|
4062 |
// (converse if negative) |
|
|
4063 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
4064 |
&& sig_n_prime256.w[1] == sig_x.w[1] |
|
|
4065 |
&& (sig_n_prime256.w[0] == sig_x.w[0])) { |
|
|
4066 |
res = 1; |
|
|
4067 |
BID_RETURN (res); |
|
|
4068 |
} // if equal, return 0 |
|
|
4069 |
{ |
|
|
4070 |
res = |
|
|
4071 |
((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 |
|
|
4072 |
|| (sig_n_prime256.w[1] > sig_x.w[1] |
|
|
4073 |
|| (sig_n_prime256.w[1] == sig_x.w[1] |
|
|
4074 |
&& sig_n_prime256.w[0] > |
|
|
4075 |
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
4076 |
BID_RETURN (res); |
|
|
4077 |
} |
|
|
4078 |
} |
|
|
4079 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
4080 |
// adjust the y significand upwards |
|
|
4081 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); |
|
|
4082 |
|
|
|
4083 |
// if postitive, return whichever significand is larger |
|
|
4084 |
// (converse if negative) |
|
|
4085 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] |
|
|
4086 |
&& (sig_n_prime192.w[0] == sig_x.w[0])) { |
|
|
4087 |
res = 1; |
|
|
4088 |
BID_RETURN (res); |
|
|
4089 |
} // if equal, return 0 |
|
|
4090 |
{ |
|
|
4091 |
res = (sig_n_prime192.w[2] != 0 |
|
|
4092 |
|| (sig_n_prime192.w[1] > sig_x.w[1] |
|
|
4093 |
|| (sig_n_prime192.w[1] == sig_x.w[1] |
|
|
4094 |
&& sig_n_prime192.w[0] > |
|
|
4095 |
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
4096 |
BID_RETURN (res); |
|
|
4097 |
} |
|
|
4098 |
} |
|
|
4099 |
|
|
|
4100 |
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, |
|
|
4101 |
bid128_signaling_not_less, x, |
|
|
4102 |
y) |
|
|
4103 |
|
|
|
4104 |
int res; |
|
|
4105 |
int exp_x, exp_y; |
|
|
4106 |
int diff; |
|
|
4107 |
UINT128 sig_x, sig_y; |
|
|
4108 |
UINT192 sig_n_prime192; |
|
|
4109 |
UINT256 sig_n_prime256; |
|
|
4110 |
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; |
|
|
4111 |
|
|
|
4112 |
// NaN (CASE1) |
|
|
4113 |
// if either number is NAN, the comparison is unordered, |
|
|
4114 |
// rather than equal : return 1 |
|
|
4115 |
if (((x.w[1] & MASK_NAN) == MASK_NAN) |
|
|
4116 |
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) { |
|
|
4117 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
4118 |
{ |
|
|
4119 |
res = 1; |
|
|
4120 |
BID_RETURN (res); |
|
|
4121 |
} |
|
|
4122 |
} |
|
|
4123 |
// SIMPLE (CASE2) |
|
|
4124 |
// if all the bits are the same, these numbers are equal (not Greater). |
|
|
4125 |
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { |
|
|
4126 |
res = 1; |
|
|
4127 |
BID_RETURN (res); |
|
|
4128 |
} |
|
|
4129 |
// INFINITY (CASE3) |
|
|
4130 |
if ((x.w[1] & MASK_INF) == MASK_INF) { |
|
|
4131 |
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } |
|
|
4132 |
if ((x.w[1] & MASK_SIGN) == MASK_SIGN) |
|
|
4133 |
// x is -inf, so it is less than y unless y is -inf |
|
|
4134 |
{ |
|
|
4135 |
res = (((y.w[1] & MASK_INF) == MASK_INF) |
|
|
4136 |
&& (y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
4137 |
BID_RETURN (res); |
|
|
4138 |
} else |
|
|
4139 |
// x is pos_inf, no way for it to be less than y |
|
|
4140 |
{ |
|
|
4141 |
res = 1; |
|
|
4142 |
BID_RETURN (res); |
|
|
4143 |
} |
|
|
4144 |
} else if ((y.w[1] & MASK_INF) == MASK_INF) { |
|
|
4145 |
// x is finite, so if y is positive infinity, then x is less, return 0 |
|
|
4146 |
// if y is negative infinity, then x is greater, return 1 |
|
|
4147 |
{ |
|
|
4148 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
4149 |
BID_RETURN (res); |
|
|
4150 |
} |
|
|
4151 |
} |
|
|
4152 |
// CONVERT X |
|
|
4153 |
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; |
|
|
4154 |
sig_x.w[0] = x.w[0]; |
|
|
4155 |
exp_x = (x.w[1] >> 49) & 0x000000000003fffull; |
|
|
4156 |
|
|
|
4157 |
// CHECK IF X IS CANONICAL |
|
|
4158 |
// 9999999999999999999999999999999999(decimal) = |
|
|
4159 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
4160 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
4161 |
// If the value exceeds that, it is interpreted as 0. |
|
|
4162 |
if ((sig_x.w[1] > 0x0001ed09bead87c0ull) |
|
|
4163 |
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull) |
|
|
4164 |
&& (sig_x.w[0] > 0x378d8e63ffffffffull)) |
|
|
4165 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
4166 |
non_canon_x = 1; |
|
|
4167 |
else |
|
|
4168 |
non_canon_x = 0; |
|
|
4169 |
|
|
|
4170 |
// CONVERT Y |
|
|
4171 |
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; |
|
|
4172 |
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; |
|
|
4173 |
sig_y.w[0] = y.w[0]; |
|
|
4174 |
|
|
|
4175 |
// CHECK IF Y IS CANONICAL |
|
|
4176 |
// 9999999999999999999999999999999999(decimal) = |
|
|
4177 |
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) |
|
|
4178 |
// [0, 10^34) is the 754r supported canonical range. |
|
|
4179 |
// If the value exceeds that, it is interpreted as 0. |
|
|
4180 |
if ((sig_y.w[1] > 0x0001ed09bead87c0ull) |
|
|
4181 |
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull) |
|
|
4182 |
&& (sig_y.w[0] > 0x378d8e63ffffffffull)) |
|
|
4183 |
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) |
|
|
4184 |
non_canon_y = 1; |
|
|
4185 |
else |
|
|
4186 |
non_canon_y = 0; |
|
|
4187 |
|
|
|
4188 |
// ZERO (CASE4) |
|
|
4189 |
// some properties: |
|
|
4190 |
// (+ZERO == -ZERO) => therefore ignore the sign |
|
|
4191 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore |
|
|
4192 |
// ignore the exponent field |
|
|
4193 |
// (Any non-canonical # is considered 0) |
|
|
4194 |
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { |
|
|
4195 |
x_is_zero = 1; |
|
|
4196 |
} |
|
|
4197 |
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { |
|
|
4198 |
y_is_zero = 1; |
|
|
4199 |
} |
|
|
4200 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
4201 |
if (x_is_zero && y_is_zero) { |
|
|
4202 |
res = 1; |
|
|
4203 |
BID_RETURN (res); |
|
|
4204 |
} |
|
|
4205 |
// is x is zero, it is greater if Y is negative |
|
|
4206 |
else if (x_is_zero) { |
|
|
4207 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
4208 |
BID_RETURN (res); |
|
|
4209 |
} |
|
|
4210 |
// is y is zero, X is greater if it is positive |
|
|
4211 |
else if (y_is_zero) { |
|
|
4212 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
4213 |
BID_RETURN (res); |
|
|
4214 |
} |
|
|
4215 |
// OPPOSITE SIGN (CASE5) |
|
|
4216 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
4217 |
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { |
|
|
4218 |
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
4219 |
BID_RETURN (res); |
|
|
4220 |
} |
|
|
4221 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
4222 |
|
|
|
4223 |
// if exponents are the same, then we have a simple comparison |
|
|
4224 |
// of the significands |
|
|
4225 |
if (exp_y == exp_x) { |
|
|
4226 |
res = (((sig_x.w[1] > sig_y.w[1]) |
|
|
4227 |
|| (sig_x.w[1] == sig_y.w[1] |
|
|
4228 |
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == |
|
|
4229 |
MASK_SIGN)); |
|
|
4230 |
BID_RETURN (res); |
|
|
4231 |
} |
|
|
4232 |
// if both components are either bigger or smaller, |
|
|
4233 |
// it is clear what needs to be done |
|
|
4234 |
if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0] |
|
|
4235 |
&& exp_x > exp_y) { |
|
|
4236 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
4237 |
BID_RETURN (res); |
|
|
4238 |
} |
|
|
4239 |
if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0] |
|
|
4240 |
&& exp_x < exp_y) { |
|
|
4241 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
4242 |
BID_RETURN (res); |
|
|
4243 |
} |
|
|
4244 |
|
|
|
4245 |
diff = exp_x - exp_y; |
|
|
4246 |
|
|
|
4247 |
// if |exp_x - exp_y| < 33, it comes down to the compensated significand |
|
|
4248 |
if (diff > 0) { // to simplify the loop below, |
|
|
4249 |
|
|
|
4250 |
// if exp_x is 33 greater than exp_y, no need for compensation |
|
|
4251 |
if (diff > 33) { |
|
|
4252 |
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); |
|
|
4253 |
BID_RETURN (res); |
|
|
4254 |
} // difference cannot be greater than 10^33 |
|
|
4255 |
|
|
|
4256 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
4257 |
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); |
|
|
4258 |
|
|
|
4259 |
|
|
|
4260 |
// if postitive, return whichever significand is larger |
|
|
4261 |
// (converse if negative) |
|
|
4262 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
4263 |
&& sig_n_prime256.w[1] == sig_y.w[1] |
|
|
4264 |
&& (sig_n_prime256.w[0] == sig_y.w[0])) { |
|
|
4265 |
res = 1; |
|
|
4266 |
BID_RETURN (res); |
|
|
4267 |
} // if equal, return 1 |
|
|
4268 |
{ |
|
|
4269 |
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) |
|
|
4270 |
|| (sig_n_prime256.w[1] > sig_y.w[1]) |
|
|
4271 |
|| (sig_n_prime256.w[1] == sig_y.w[1] |
|
|
4272 |
&& sig_n_prime256.w[0] > |
|
|
4273 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
4274 |
BID_RETURN (res); |
|
|
4275 |
} |
|
|
4276 |
} |
|
|
4277 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
4278 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); |
|
|
4279 |
|
|
|
4280 |
// if postitive, return whichever significand is larger |
|
|
4281 |
// (converse if negative) |
|
|
4282 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] |
|
|
4283 |
&& (sig_n_prime192.w[0] == sig_y.w[0])) { |
|
|
4284 |
res = 1; |
|
|
4285 |
BID_RETURN (res); |
|
|
4286 |
} // if equal, return 1 |
|
|
4287 |
{ |
|
|
4288 |
res = (((sig_n_prime192.w[2] > 0) |
|
|
4289 |
|| (sig_n_prime192.w[1] > sig_y.w[1]) |
|
|
4290 |
|| (sig_n_prime192.w[1] == sig_y.w[1] |
|
|
4291 |
&& sig_n_prime192.w[0] > |
|
|
4292 |
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
4293 |
BID_RETURN (res); |
|
|
4294 |
} |
|
|
4295 |
} |
|
|
4296 |
|
|
|
4297 |
diff = exp_y - exp_x; |
|
|
4298 |
|
|
|
4299 |
// if exp_x is 33 less than exp_y, no need for compensation |
|
|
4300 |
if (diff > 33) { |
|
|
4301 |
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
4302 |
BID_RETURN (res); |
|
|
4303 |
} |
|
|
4304 |
|
|
|
4305 |
if (diff > 19) { //128 by 128 bit multiply -> 256 bits |
|
|
4306 |
// adjust the y significand upwards |
|
|
4307 |
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); |
|
|
4308 |
|
|
|
4309 |
|
|
|
4310 |
// if postitive, return whichever significand is larger |
|
|
4311 |
// (converse if negative) |
|
|
4312 |
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) |
|
|
4313 |
&& sig_n_prime256.w[1] == sig_x.w[1] |
|
|
4314 |
&& (sig_n_prime256.w[0] == sig_x.w[0])) { |
|
|
4315 |
res = 1; |
|
|
4316 |
BID_RETURN (res); |
|
|
4317 |
} // if equal, return 1 |
|
|
4318 |
{ |
|
|
4319 |
res = |
|
|
4320 |
((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0 |
|
|
4321 |
&& (sig_n_prime256.w[1] < sig_x.w[1] |
|
|
4322 |
|| (sig_n_prime256.w[1] == sig_x.w[1] |
|
|
4323 |
&& sig_n_prime256.w[0] < |
|
|
4324 |
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); |
|
|
4325 |
BID_RETURN (res); |
|
|
4326 |
} |
|
|
4327 |
} |
|
|
4328 |
//else { //128 by 64 bit multiply -> 192 bits |
|
|
4329 |
// adjust the y significand upwards |
|
|
4330 |
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); |
|
|
4331 |
|
|
|
4332 |
// if postitive, return whichever significand is larger (converse if negative) |
|
|
4333 |
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] |
|
|
4334 |
&& (sig_n_prime192.w[0] == sig_x.w[0])) { |
|
|
4335 |
res = 1; |
|
|
4336 |
BID_RETURN (res); |
|
|
4337 |
} // if equal, return 1 |
|
|
4338 |
{ |
|
|
4339 |
res = (sig_n_prime192.w[2] == 0 |
|
|
4340 |
&& (sig_n_prime192.w[1] < sig_x.w[1] |
|
|
4341 |
|| (sig_n_prime192.w[1] == sig_x.w[1] |
|
|
4342 |
&& sig_n_prime192.w[0] < |
|
|
4343 |
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); |
|
|
4344 |
BID_RETURN (res); |
|
|
4345 |
} |
|
|
4346 |
} |