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

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