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1 272 jeremybenn 
/* Copyright (C) 2007, 2009  Free Software Foundation, Inc.
2 
 
3 
This file is part of GCC.
4 
 
5 
GCC is free software; you can redistribute it and/or modify it under
6 
the terms of the GNU General Public License as published by the Free
7 
Software Foundation; either version 3, or (at your option) any later
8 
version.
9 
 
10 
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
11 
WARRANTY; without even the implied warranty of MERCHANTABILITY or
12 
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
13 
for more details.
14 
 
15 
Under Section 7 of GPL version 3, you are granted additional
16 
permissions described in the GCC Runtime Library Exception, version
17 
3.1, as published by the Free Software Foundation.
18 
 
19 
You should have received a copy of the GNU General Public License and
20 
a copy of the GCC Runtime Library Exception along with this program;
21 
see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
22 
<http://www.gnu.org/licenses/>.  */
23 
 
24 
#include "bid_internal.h"
25 
 
26 
/*****************************************************************************
27 
 *  BID64 minimum function - returns greater of two numbers
28 
 *****************************************************************************/
29 
 
30 
static const UINT64 mult_factor[16] = {
31 
  1ull, 10ull, 100ull, 1000ull,
32 
  10000ull, 100000ull, 1000000ull, 10000000ull,
33 
  100000000ull, 1000000000ull, 10000000000ull, 100000000000ull,
34 
  1000000000000ull, 10000000000000ull,
35 
  100000000000000ull, 1000000000000000ull
36 
};
37 
 
38 
#if DECIMAL_CALL_BY_REFERENCE
39 
void
40 
bid64_minnum (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM) {
41 
  UINT64 x = *px;
42 
  UINT64 y = *py;
43 
#else
44 
UINT64
45 
bid64_minnum (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) {
46 
#endif
47 
 
48 
  UINT64 res;
49 
  int exp_x, exp_y;
50 
  UINT64 sig_x, sig_y;
51 
  UINT128 sig_n_prime;
52 
  char x_is_zero = 0, y_is_zero = 0;
53 
 
54 
  // check for non-canonical x
55 
  if ((x & MASK_NAN) == MASK_NAN) {     // x is NaN
56 
    x = x & 0xfe03ffffffffffffull;      // clear G6-G12
57 
    if ((x & 0x0003ffffffffffffull) > 999999999999999ull) {
58 
      x = x & 0xfe00000000000000ull;    // clear G6-G12 and the payload bits
59 
    }
60 
  } else if ((x & MASK_INF) == MASK_INF) {      // check for Infinity
61 
    x = x & (MASK_SIGN | MASK_INF);
62 
  } else {      // x is not special
63 
    // check for non-canonical values - treated as zero
64 
    if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
65 
      // if the steering bits are 11, then the exponent is G[0:w+1]
66 
      if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
67 
          9999999999999999ull) {
68 
        // non-canonical
69 
        x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2);
70 
      } // else canonical
71 
    }   // else canonical
72 
  }
73 
 
74 
  // check for non-canonical y
75 
  if ((y & MASK_NAN) == MASK_NAN) {     // y is NaN
76 
    y = y & 0xfe03ffffffffffffull;      // clear G6-G12
77 
    if ((y & 0x0003ffffffffffffull) > 999999999999999ull) {
78 
      y = y & 0xfe00000000000000ull;    // clear G6-G12 and the payload bits
79 
    }
80 
  } else if ((y & MASK_INF) == MASK_INF) {      // check for Infinity
81 
    y = y & (MASK_SIGN | MASK_INF);
82 
  } else {      // y is not special
83 
    // check for non-canonical values - treated as zero
84 
    if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
85 
      // if the steering bits are 11, then the exponent is G[0:w+1]
86 
      if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
87 
          9999999999999999ull) {
88 
        // non-canonical
89 
        y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2);
90 
      } // else canonical
91 
    }   // else canonical
92 
  }
93 
 
94 
  // NaN (CASE1)
95 
  if ((x & MASK_NAN) == MASK_NAN) {     // x is NAN
96 
    if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN
97 
      // if x is SNAN, then return quiet (x)
98 
      *pfpsf |= INVALID_EXCEPTION;      // set exception if SNaN
99 
      x = x & 0xfdffffffffffffffull;    // quietize x
100 
      res = x;
101 
    } else {    // x is QNaN
102 
      if ((y & MASK_NAN) == MASK_NAN) { // y is NAN
103 
        if ((y & MASK_SNAN) == MASK_SNAN) {     // y is SNAN
104 
          *pfpsf |= INVALID_EXCEPTION;  // set invalid flag
105 
        }
106 
        res = x;
107 
      } else {
108 
        res = y;
109 
      }
110 
    }
111 
    BID_RETURN (res);
112 
  } else if ((y & MASK_NAN) == MASK_NAN) {      // y is NaN, but x is not
113 
    if ((y & MASK_SNAN) == MASK_SNAN) {
114 
      *pfpsf |= INVALID_EXCEPTION;      // set exception if SNaN
115 
      y = y & 0xfdffffffffffffffull;    // quietize y
116 
      res = y;
117 
    } else {
118 
      // will return x (which is not NaN)
119 
      res = x;
120 
    }
121 
    BID_RETURN (res);
122 
  }
123 
  // SIMPLE (CASE2)
124 
  // if all the bits are the same, these numbers are equal, return either number
125 
  if (x == y) {
126 
    res = x;
127 
    BID_RETURN (res);
128 
  }
129 
  // INFINITY (CASE3)
130 
  if ((x & MASK_INF) == MASK_INF) {
131 
    // if x is neg infinity, there is no way it is greater than y, return x
132 
    if (((x & MASK_SIGN) == MASK_SIGN)) {
133 
      res = x;
134 
      BID_RETURN (res);
135 
    }
136 
    // x is pos infinity, return y
137 
    else {
138 
      res = y;
139 
      BID_RETURN (res);
140 
    }
141 
  } else if ((y & MASK_INF) == MASK_INF) {
142 
    // x is finite, so if y is positive infinity, then x is less, return y
143 
    //                 if y is negative infinity, then x is greater, return x
144 
    res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x;
145 
    BID_RETURN (res);
146 
  }
147 
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
148 
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
149 
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
150 
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
151 
  } else {
152 
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
153 
    sig_x = (x & MASK_BINARY_SIG1);
154 
  }
155 
 
156 
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
157 
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
158 
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
159 
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
160 
  } else {
161 
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
162 
    sig_y = (y & MASK_BINARY_SIG1);
163 
  }
164 
 
165 
  // ZERO (CASE4)
166 
  // some properties:
167 
  //    (+ZERO == -ZERO) => therefore
168 
  //        ignore the sign, and neither number is greater
169 
  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
170 
  //        ignore the exponent field
171 
  //    (Any non-canonical # is considered 0)
172 
  if (sig_x == 0) {
173 
    x_is_zero = 1;
174 
  }
175 
  if (sig_y == 0) {
176 
    y_is_zero = 1;
177 
  }
178 
 
179 
  if (x_is_zero && y_is_zero) {
180 
    // if both numbers are zero, neither is greater => return either
181 
    res = y;
182 
    BID_RETURN (res);
183 
  } else if (x_is_zero) {
184 
    // is x is zero, it is greater if Y is negative
185 
    res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x;
186 
    BID_RETURN (res);
187 
  } else if (y_is_zero) {
188 
    // is y is zero, X is greater if it is positive
189 
    res = ((x & MASK_SIGN) != MASK_SIGN) ? y : x;;
190 
    BID_RETURN (res);
191 
  }
192 
  // OPPOSITE SIGN (CASE5)
193 
  // now, if the sign bits differ, x is greater if y is negative
194 
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
195 
    res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x;
196 
    BID_RETURN (res);
197 
  }
198 
  // REDUNDANT REPRESENTATIONS (CASE6)
199 
 
200 
  // if both components are either bigger or smaller,
201 
  // it is clear what needs to be done
202 
  if (sig_x > sig_y && exp_x >= exp_y) {
203 
    res = ((x & MASK_SIGN) != MASK_SIGN) ? y : x;
204 
    BID_RETURN (res);
205 
  }
206 
  if (sig_x < sig_y && exp_x <= exp_y) {
207 
    res = ((x & MASK_SIGN) == MASK_SIGN) ? y : x;
208 
    BID_RETURN (res);
209 
  }
210 
  // if exp_x is 15 greater than exp_y, no need for compensation
211 
  if (exp_x - exp_y > 15) {
212 
    res = ((x & MASK_SIGN) != MASK_SIGN) ? y : x;       // difference cannot be >10^15
213 
    BID_RETURN (res);
214 
  }
215 
  // if exp_x is 15 less than exp_y, no need for compensation
216 
  if (exp_y - exp_x > 15) {
217 
    res = ((x & MASK_SIGN) == MASK_SIGN) ? y : x;
218 
    BID_RETURN (res);
219 
  }
220 
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
221 
  if (exp_x > exp_y) {  // to simplify the loop below,
222 
 
223 
    // otherwise adjust the x significand upwards
224 
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
225 
                            mult_factor[exp_x - exp_y]);
226 
    // if postitive, return whichever significand is larger
227 
    // (converse if negative)
228 
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
229 
      res = y;
230 
      BID_RETURN (res);
231 
    }
232 
 
233 
    res = (((sig_n_prime.w[1] > 0)
234 
            || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
235 
                                            MASK_SIGN)) ? y : x;
236 
    BID_RETURN (res);
237 
  }
238 
  // adjust the y significand upwards
239 
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
240 
                          mult_factor[exp_y - exp_x]);
241 
 
242 
  // if postitive, return whichever significand is larger (converse if negative)
243 
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
244 
    res = y;
245 
    BID_RETURN (res);
246 
  }
247 
  res = (((sig_n_prime.w[1] == 0)
248 
          && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
249 
                                            MASK_SIGN)) ? y : x;
250 
  BID_RETURN (res);
251 
}
252 
 
253 
/*****************************************************************************
254 
 *  BID64 minimum magnitude function - returns greater of two numbers
255 
 *****************************************************************************/
256 
 
257 
#if DECIMAL_CALL_BY_REFERENCE
258 
void
259 
bid64_minnum_mag (UINT64 * pres, UINT64 * px,
260 
                  UINT64 * py _EXC_FLAGS_PARAM) {
261 
  UINT64 x = *px;
262 
  UINT64 y = *py;
263 
#else
264 
UINT64
265 
bid64_minnum_mag (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) {
266 
#endif
267 
 
268 
  UINT64 res;
269 
  int exp_x, exp_y;
270 
  UINT64 sig_x, sig_y;
271 
  UINT128 sig_n_prime;
272 
 
273 
  // check for non-canonical x
274 
  if ((x & MASK_NAN) == MASK_NAN) {     // x is NaN
275 
    x = x & 0xfe03ffffffffffffull;      // clear G6-G12
276 
    if ((x & 0x0003ffffffffffffull) > 999999999999999ull) {
277 
      x = x & 0xfe00000000000000ull;    // clear G6-G12 and the payload bits
278 
    }
279 
  } else if ((x & MASK_INF) == MASK_INF) {      // check for Infinity
280 
    x = x & (MASK_SIGN | MASK_INF);
281 
  } else {      // x is not special
282 
    // check for non-canonical values - treated as zero
283 
    if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
284 
      // if the steering bits are 11, then the exponent is G[0:w+1]
285 
      if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
286 
          9999999999999999ull) {
287 
        // non-canonical
288 
        x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2);
289 
      } // else canonical
290 
    }   // else canonical
291 
  }
292 
 
293 
  // check for non-canonical y
294 
  if ((y & MASK_NAN) == MASK_NAN) {     // y is NaN
295 
    y = y & 0xfe03ffffffffffffull;      // clear G6-G12
296 
    if ((y & 0x0003ffffffffffffull) > 999999999999999ull) {
297 
      y = y & 0xfe00000000000000ull;    // clear G6-G12 and the payload bits
298 
    }
299 
  } else if ((y & MASK_INF) == MASK_INF) {      // check for Infinity
300 
    y = y & (MASK_SIGN | MASK_INF);
301 
  } else {      // y is not special
302 
    // check for non-canonical values - treated as zero
303 
    if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
304 
      // if the steering bits are 11, then the exponent is G[0:w+1]
305 
      if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
306 
          9999999999999999ull) {
307 
        // non-canonical
308 
        y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2);
309 
      } // else canonical
310 
    }   // else canonical
311 
  }
312 
 
313 
  // NaN (CASE1)
314 
  if ((x & MASK_NAN) == MASK_NAN) {     // x is NAN
315 
    if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN
316 
      // if x is SNAN, then return quiet (x)
317 
      *pfpsf |= INVALID_EXCEPTION;      // set exception if SNaN
318 
      x = x & 0xfdffffffffffffffull;    // quietize x
319 
      res = x;
320 
    } else {    // x is QNaN
321 
      if ((y & MASK_NAN) == MASK_NAN) { // y is NAN
322 
        if ((y & MASK_SNAN) == MASK_SNAN) {     // y is SNAN
323 
          *pfpsf |= INVALID_EXCEPTION;  // set invalid flag
324 
        }
325 
        res = x;
326 
      } else {
327 
        res = y;
328 
      }
329 
    }
330 
    BID_RETURN (res);
331 
  } else if ((y & MASK_NAN) == MASK_NAN) {      // y is NaN, but x is not
332 
    if ((y & MASK_SNAN) == MASK_SNAN) {
333 
      *pfpsf |= INVALID_EXCEPTION;      // set exception if SNaN
334 
      y = y & 0xfdffffffffffffffull;    // quietize y
335 
      res = y;
336 
    } else {
337 
      // will return x (which is not NaN)
338 
      res = x;
339 
    }
340 
    BID_RETURN (res);
341 
  }
342 
  // SIMPLE (CASE2)
343 
  // if all the bits are the same, these numbers are equal, return either number
344 
  if (x == y) {
345 
    res = x;
346 
    BID_RETURN (res);
347 
  }
348 
  // INFINITY (CASE3)
349 
  if ((x & MASK_INF) == MASK_INF) {
350 
    // x is infinity, its magnitude is greater than or equal to y
351 
    // return x only if y is infinity and x is negative
352 
    res = ((x & MASK_SIGN) == MASK_SIGN
353 
           && (y & MASK_INF) == MASK_INF) ? x : y;
354 
    BID_RETURN (res);
355 
  } else if ((y & MASK_INF) == MASK_INF) {
356 
    // y is infinity, then it must be greater in magnitude, return x
357 
    res = x;
358 
    BID_RETURN (res);
359 
  }
360 
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
361 
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
362 
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
363 
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
364 
  } else {
365 
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
366 
    sig_x = (x & MASK_BINARY_SIG1);
367 
  }
368 
 
369 
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
370 
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
371 
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
372 
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
373 
  } else {
374 
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
375 
    sig_y = (y & MASK_BINARY_SIG1);
376 
  }
377 
 
378 
  // ZERO (CASE4)
379 
  // some properties:
380 
  //    (+ZERO == -ZERO) => therefore
381 
  //        ignore the sign, and neither number is greater
382 
  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
383 
  //        ignore the exponent field
384 
  //    (Any non-canonical # is considered 0)
385 
  if (sig_x == 0) {
386 
    res = x;    // x_is_zero, its magnitude must be smaller than y
387 
    BID_RETURN (res);
388 
  }
389 
  if (sig_y == 0) {
390 
    res = y;    // y_is_zero, its magnitude must be smaller than x
391 
    BID_RETURN (res);
392 
  }
393 
  // REDUNDANT REPRESENTATIONS (CASE6)
394 
  // if both components are either bigger or smaller,
395 
  // it is clear what needs to be done
396 
  if (sig_x > sig_y && exp_x >= exp_y) {
397 
    res = y;
398 
    BID_RETURN (res);
399 
  }
400 
  if (sig_x < sig_y && exp_x <= exp_y) {
401 
    res = x;
402 
    BID_RETURN (res);
403 
  }
404 
  // if exp_x is 15 greater than exp_y, no need for compensation
405 
  if (exp_x - exp_y > 15) {
406 
    res = y;    // difference cannot be greater than 10^15
407 
    BID_RETURN (res);
408 
  }
409 
  // if exp_x is 15 less than exp_y, no need for compensation
410 
  if (exp_y - exp_x > 15) {
411 
    res = x;
412 
    BID_RETURN (res);
413 
  }
414 
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
415 
  if (exp_x > exp_y) {  // to simplify the loop below,
416 
    // otherwise adjust the x significand upwards
417 
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
418 
                            mult_factor[exp_x - exp_y]);
419 
    // now, sig_n_prime has: sig_x * 10^(exp_x-exp_y), this is
420 
    // the compensated signif.
421 
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
422 
      // two numbers are equal, return minNum(x,y)
423 
      res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x;
424 
      BID_RETURN (res);
425 
    }
426 
    // now, if compensated_x (sig_n_prime) is greater than y, return y,
427 
    // otherwise return x
428 
    res = ((sig_n_prime.w[1] != 0) || sig_n_prime.w[0] > sig_y) ? y : x;
429 
    BID_RETURN (res);
430 
  }
431 
  // exp_y must be greater than exp_x, thus adjust the y significand upwards
432 
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
433 
                          mult_factor[exp_y - exp_x]);
434 
 
435 
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
436 
    res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x;
437 
    // two numbers are equal, return either
438 
    BID_RETURN (res);
439 
  }
440 
 
441 
  res = ((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ? y : x;
442 
  BID_RETURN (res);
443 
}
444 
 
445 
/*****************************************************************************
446 
 *  BID64 maximum function - returns greater of two numbers
447 
 *****************************************************************************/
448 
 
449 
#if DECIMAL_CALL_BY_REFERENCE
450 
void
451 
bid64_maxnum (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM) {
452 
  UINT64 x = *px;
453 
  UINT64 y = *py;
454 
#else
455 
UINT64
456 
bid64_maxnum (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) {
457 
#endif
458 
 
459 
  UINT64 res;
460 
  int exp_x, exp_y;
461 
  UINT64 sig_x, sig_y;
462 
  UINT128 sig_n_prime;
463 
  char x_is_zero = 0, y_is_zero = 0;
464 
 
465 
  // check for non-canonical x
466 
  if ((x & MASK_NAN) == MASK_NAN) {     // x is NaN
467 
    x = x & 0xfe03ffffffffffffull;      // clear G6-G12
468 
    if ((x & 0x0003ffffffffffffull) > 999999999999999ull) {
469 
      x = x & 0xfe00000000000000ull;    // clear G6-G12 and the payload bits
470 
    }
471 
  } else if ((x & MASK_INF) == MASK_INF) {      // check for Infinity
472 
    x = x & (MASK_SIGN | MASK_INF);
473 
  } else {      // x is not special
474 
    // check for non-canonical values - treated as zero
475 
    if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
476 
      // if the steering bits are 11, then the exponent is G[0:w+1]
477 
      if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
478 
          9999999999999999ull) {
479 
        // non-canonical
480 
        x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2);
481 
      } // else canonical
482 
    }   // else canonical
483 
  }
484 
 
485 
  // check for non-canonical y
486 
  if ((y & MASK_NAN) == MASK_NAN) {     // y is NaN
487 
    y = y & 0xfe03ffffffffffffull;      // clear G6-G12
488 
    if ((y & 0x0003ffffffffffffull) > 999999999999999ull) {
489 
      y = y & 0xfe00000000000000ull;    // clear G6-G12 and the payload bits
490 
    }
491 
  } else if ((y & MASK_INF) == MASK_INF) {      // check for Infinity
492 
    y = y & (MASK_SIGN | MASK_INF);
493 
  } else {      // y is not special
494 
    // check for non-canonical values - treated as zero
495 
    if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
496 
      // if the steering bits are 11, then the exponent is G[0:w+1]
497 
      if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
498 
          9999999999999999ull) {
499 
        // non-canonical
500 
        y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2);
501 
      } // else canonical
502 
    }   // else canonical
503 
  }
504 
 
505 
  // NaN (CASE1)
506 
  if ((x & MASK_NAN) == MASK_NAN) {     // x is NAN
507 
    if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN
508 
      // if x is SNAN, then return quiet (x)
509 
      *pfpsf |= INVALID_EXCEPTION;      // set exception if SNaN
510 
      x = x & 0xfdffffffffffffffull;    // quietize x
511 
      res = x;
512 
    } else {    // x is QNaN
513 
      if ((y & MASK_NAN) == MASK_NAN) { // y is NAN
514 
        if ((y & MASK_SNAN) == MASK_SNAN) {     // y is SNAN
515 
          *pfpsf |= INVALID_EXCEPTION;  // set invalid flag
516 
        }
517 
        res = x;
518 
      } else {
519 
        res = y;
520 
      }
521 
    }
522 
    BID_RETURN (res);
523 
  } else if ((y & MASK_NAN) == MASK_NAN) {      // y is NaN, but x is not
524 
    if ((y & MASK_SNAN) == MASK_SNAN) {
525 
      *pfpsf |= INVALID_EXCEPTION;      // set exception if SNaN
526 
      y = y & 0xfdffffffffffffffull;    // quietize y
527 
      res = y;
528 
    } else {
529 
      // will return x (which is not NaN)
530 
      res = x;
531 
    }
532 
    BID_RETURN (res);
533 
  }
534 
  // SIMPLE (CASE2)
535 
  // if all the bits are the same, these numbers are equal (not Greater).
536 
  if (x == y) {
537 
    res = x;
538 
    BID_RETURN (res);
539 
  }
540 
  // INFINITY (CASE3)
541 
  if ((x & MASK_INF) == MASK_INF) {
542 
    // if x is neg infinity, there is no way it is greater than y, return y
543 
    // x is pos infinity, it is greater, unless y is positive infinity =>
544 
    // return y!=pos_infinity
545 
    if (((x & MASK_SIGN) == MASK_SIGN)) {
546 
      res = y;
547 
      BID_RETURN (res);
548 
    } else {
549 
      res = (((y & MASK_INF) != MASK_INF)
550 
             || ((y & MASK_SIGN) == MASK_SIGN)) ? x : y;
551 
      BID_RETURN (res);
552 
    }
553 
  } else if ((y & MASK_INF) == MASK_INF) {
554 
    // x is finite, so if y is positive infinity, then x is less, return y
555 
    //                 if y is negative infinity, then x is greater, return x
556 
    res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y;
557 
    BID_RETURN (res);
558 
  }
559 
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
560 
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
561 
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
562 
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
563 
  } else {
564 
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
565 
    sig_x = (x & MASK_BINARY_SIG1);
566 
  }
567 
 
568 
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
569 
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
570 
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
571 
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
572 
  } else {
573 
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
574 
    sig_y = (y & MASK_BINARY_SIG1);
575 
  }
576 
 
577 
  // ZERO (CASE4)
578 
  // some properties:
579 
  //    (+ZERO == -ZERO) => therefore
580 
  //        ignore the sign, and neither number is greater
581 
  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
582 
  //        ignore the exponent field
583 
  //    (Any non-canonical # is considered 0)
584 
  if (sig_x == 0) {
585 
    x_is_zero = 1;
586 
  }
587 
  if (sig_y == 0) {
588 
    y_is_zero = 1;
589 
  }
590 
 
591 
  if (x_is_zero && y_is_zero) {
592 
    // if both numbers are zero, neither is greater => return NOTGREATERTHAN
593 
    res = y;
594 
    BID_RETURN (res);
595 
  } else if (x_is_zero) {
596 
    // is x is zero, it is greater if Y is negative
597 
    res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y;
598 
    BID_RETURN (res);
599 
  } else if (y_is_zero) {
600 
    // is y is zero, X is greater if it is positive
601 
    res = ((x & MASK_SIGN) != MASK_SIGN) ? x : y;;
602 
    BID_RETURN (res);
603 
  }
604 
  // OPPOSITE SIGN (CASE5)
605 
  // now, if the sign bits differ, x is greater if y is negative
606 
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
607 
    res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y;
608 
    BID_RETURN (res);
609 
  }
610 
  // REDUNDANT REPRESENTATIONS (CASE6)
611 
 
612 
  // if both components are either bigger or smaller,
613 
  //     it is clear what needs to be done
614 
  if (sig_x > sig_y && exp_x >= exp_y) {
615 
    res = ((x & MASK_SIGN) != MASK_SIGN) ? x : y;
616 
    BID_RETURN (res);
617 
  }
618 
  if (sig_x < sig_y && exp_x <= exp_y) {
619 
    res = ((x & MASK_SIGN) == MASK_SIGN) ? x : y;
620 
    BID_RETURN (res);
621 
  }
622 
  // if exp_x is 15 greater than exp_y, no need for compensation
623 
  if (exp_x - exp_y > 15) {
624 
    res = ((x & MASK_SIGN) != MASK_SIGN) ? x : y;
625 
    // difference cannot be > 10^15
626 
    BID_RETURN (res);
627 
  }
628 
  // if exp_x is 15 less than exp_y, no need for compensation
629 
  if (exp_y - exp_x > 15) {
630 
    res = ((x & MASK_SIGN) == MASK_SIGN) ? x : y;
631 
    BID_RETURN (res);
632 
  }
633 
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
634 
  if (exp_x > exp_y) {  // to simplify the loop below,
635 
    // otherwise adjust the x significand upwards
636 
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
637 
                            mult_factor[exp_x - exp_y]);
638 
    // if postitive, return whichever significand is larger
639 
    // (converse if negative)
640 
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
641 
      res = y;
642 
      BID_RETURN (res);
643 
    }
644 
    res = (((sig_n_prime.w[1] > 0)
645 
            || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
646 
                                            MASK_SIGN)) ? x : y;
647 
    BID_RETURN (res);
648 
  }
649 
  // adjust the y significand upwards
650 
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
651 
                          mult_factor[exp_y - exp_x]);
652 
 
653 
  // if postitive, return whichever significand is larger (converse if negative)
654 
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
655 
    res = y;
656 
    BID_RETURN (res);
657 
  }
658 
  res = (((sig_n_prime.w[1] == 0)
659 
          && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
660 
                                            MASK_SIGN)) ? x : y;
661 
  BID_RETURN (res);
662 
}
663 
 
664 
/*****************************************************************************
665 
 *  BID64 maximum magnitude function - returns greater of two numbers
666 
 *****************************************************************************/
667 
 
668 
#if DECIMAL_CALL_BY_REFERENCE
669 
void
670 
bid64_maxnum_mag (UINT64 * pres, UINT64 * px,
671 
                  UINT64 * py _EXC_FLAGS_PARAM) {
672 
  UINT64 x = *px;
673 
  UINT64 y = *py;
674 
#else
675 
UINT64
676 
bid64_maxnum_mag (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) {
677 
#endif
678 
 
679 
  UINT64 res;
680 
  int exp_x, exp_y;
681 
  UINT64 sig_x, sig_y;
682 
  UINT128 sig_n_prime;
683 
 
684 
  // check for non-canonical x
685 
  if ((x & MASK_NAN) == MASK_NAN) {     // x is NaN
686 
    x = x & 0xfe03ffffffffffffull;      // clear G6-G12
687 
    if ((x & 0x0003ffffffffffffull) > 999999999999999ull) {
688 
      x = x & 0xfe00000000000000ull;    // clear G6-G12 and the payload bits
689 
    }
690 
  } else if ((x & MASK_INF) == MASK_INF) {      // check for Infinity
691 
    x = x & (MASK_SIGN | MASK_INF);
692 
  } else {      // x is not special
693 
    // check for non-canonical values - treated as zero
694 
    if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
695 
      // if the steering bits are 11, then the exponent is G[0:w+1]
696 
      if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
697 
          9999999999999999ull) {
698 
        // non-canonical
699 
        x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2);
700 
      } // else canonical
701 
    }   // else canonical
702 
  }
703 
 
704 
  // check for non-canonical y
705 
  if ((y & MASK_NAN) == MASK_NAN) {     // y is NaN
706 
    y = y & 0xfe03ffffffffffffull;      // clear G6-G12
707 
    if ((y & 0x0003ffffffffffffull) > 999999999999999ull) {
708 
      y = y & 0xfe00000000000000ull;    // clear G6-G12 and the payload bits
709 
    }
710 
  } else if ((y & MASK_INF) == MASK_INF) {      // check for Infinity
711 
    y = y & (MASK_SIGN | MASK_INF);
712 
  } else {      // y is not special
713 
    // check for non-canonical values - treated as zero
714 
    if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
715 
      // if the steering bits are 11, then the exponent is G[0:w+1]
716 
      if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
717 
          9999999999999999ull) {
718 
        // non-canonical
719 
        y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2);
720 
      } // else canonical
721 
    }   // else canonical
722 
  }
723 
 
724 
  // NaN (CASE1)
725 
  if ((x & MASK_NAN) == MASK_NAN) {     // x is NAN
726 
    if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN
727 
      // if x is SNAN, then return quiet (x)
728 
      *pfpsf |= INVALID_EXCEPTION;      // set exception if SNaN
729 
      x = x & 0xfdffffffffffffffull;    // quietize x
730 
      res = x;
731 
    } else {    // x is QNaN
732 
      if ((y & MASK_NAN) == MASK_NAN) { // y is NAN
733 
        if ((y & MASK_SNAN) == MASK_SNAN) {     // y is SNAN
734 
          *pfpsf |= INVALID_EXCEPTION;  // set invalid flag
735 
        }
736 
        res = x;
737 
      } else {
738 
        res = y;
739 
      }
740 
    }
741 
    BID_RETURN (res);
742 
  } else if ((y & MASK_NAN) == MASK_NAN) {      // y is NaN, but x is not
743 
    if ((y & MASK_SNAN) == MASK_SNAN) {
744 
      *pfpsf |= INVALID_EXCEPTION;      // set exception if SNaN
745 
      y = y & 0xfdffffffffffffffull;    // quietize y
746 
      res = y;
747 
    } else {
748 
      // will return x (which is not NaN)
749 
      res = x;
750 
    }
751 
    BID_RETURN (res);
752 
  }
753 
  // SIMPLE (CASE2)
754 
  // if all the bits are the same, these numbers are equal, return either number
755 
  if (x == y) {
756 
    res = x;
757 
    BID_RETURN (res);
758 
  }
759 
  // INFINITY (CASE3)
760 
  if ((x & MASK_INF) == MASK_INF) {
761 
    // x is infinity, its magnitude is greater than or equal to y
762 
    // return y as long as x isn't negative infinity
763 
    res = ((x & MASK_SIGN) == MASK_SIGN
764 
           && (y & MASK_INF) == MASK_INF) ? y : x;
765 
    BID_RETURN (res);
766 
  } else if ((y & MASK_INF) == MASK_INF) {
767 
    // y is infinity, then it must be greater in magnitude
768 
    res = y;
769 
    BID_RETURN (res);
770 
  }
771 
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
772 
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
773 
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
774 
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
775 
  } else {
776 
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
777 
    sig_x = (x & MASK_BINARY_SIG1);
778 
  }
779 
 
780 
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
781 
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
782 
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
783 
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
784 
  } else {
785 
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
786 
    sig_y = (y & MASK_BINARY_SIG1);
787 
  }
788 
 
789 
  // ZERO (CASE4)
790 
  // some properties:
791 
  //    (+ZERO == -ZERO) => therefore
792 
  //        ignore the sign, and neither number is greater
793 
  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
794 
  //        ignore the exponent field
795 
  //    (Any non-canonical # is considered 0)
796 
  if (sig_x == 0) {
797 
    res = y;    // x_is_zero, its magnitude must be smaller than y
798 
    BID_RETURN (res);
799 
  }
800 
  if (sig_y == 0) {
801 
    res = x;    // y_is_zero, its magnitude must be smaller than x
802 
    BID_RETURN (res);
803 
  }
804 
  // REDUNDANT REPRESENTATIONS (CASE6)
805 
  // if both components are either bigger or smaller,
806 
  // it is clear what needs to be done
807 
  if (sig_x > sig_y && exp_x >= exp_y) {
808 
    res = x;
809 
    BID_RETURN (res);
810 
  }
811 
  if (sig_x < sig_y && exp_x <= exp_y) {
812 
    res = y;
813 
    BID_RETURN (res);
814 
  }
815 
  // if exp_x is 15 greater than exp_y, no need for compensation
816 
  if (exp_x - exp_y > 15) {
817 
    res = x;    // difference cannot be greater than 10^15
818 
    BID_RETURN (res);
819 
  }
820 
  // if exp_x is 15 less than exp_y, no need for compensation
821 
  if (exp_y - exp_x > 15) {
822 
    res = y;
823 
    BID_RETURN (res);
824 
  }
825 
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
826 
  if (exp_x > exp_y) {  // to simplify the loop below,
827 
    // otherwise adjust the x significand upwards
828 
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
829 
                            mult_factor[exp_x - exp_y]);
830 
    // now, sig_n_prime has: sig_x * 10^(exp_x-exp_y),
831 
    // this is the compensated signif.
832 
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
833 
      // two numbers are equal, return maxNum(x,y)
834 
      res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y;
835 
      BID_RETURN (res);
836 
    }
837 
    // now, if compensated_x (sig_n_prime) is greater than y return y,
838 
    // otherwise return x
839 
    res = ((sig_n_prime.w[1] != 0) || sig_n_prime.w[0] > sig_y) ? x : y;
840 
    BID_RETURN (res);
841 
  }
842 
  // exp_y must be greater than exp_x, thus adjust the y significand upwards
843 
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
844 
                          mult_factor[exp_y - exp_x]);
845 
 
846 
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
847 
    res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y;
848 
    // two numbers are equal, return either
849 
    BID_RETURN (res);
850 
  }
851 
 
852 
  res = ((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ? x : y;
853 
  BID_RETURN (res);
854 
}

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