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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 
#include "bid_internal.h"
25 
 
26 
/*****************************************************************************
27 
 *
28 
 *    BID128 non-computational functions:
29 
 *         - bid128_isSigned
30 
 *         - bid128_isNormal
31 
 *         - bid128_isSubnormal
32 
 *         - bid128_isFinite
33 
 *         - bid128_isZero
34 
 *         - bid128_isInf
35 
 *         - bid128_isSignaling
36 
 *         - bid128_isCanonical
37 
 *         - bid128_isNaN
38 
 *         - bid128_copy
39 
 *         - bid128_negate
40 
 *         - bid128_abs
41 
 *         - bid128_copySign
42 
 *         - bid128_class
43 
 *         - bid128_totalOrder
44 
 *         - bid128_totalOrderMag
45 
 *         - bid128_sameQuantum
46 
 *         - bid128_radix
47 
 ****************************************************************************/
48 
 
49 
#if DECIMAL_CALL_BY_REFERENCE
50 
void
51 
bid128_isSigned (int *pres,
52 
                 UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
53 
  UINT128 x = *px;
54 
#else
55 
int
56 
bid128_isSigned (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
57 
#endif
58 
  int res;
59 
 
60 
  res = ((x.w[HIGH_128W] & MASK_SIGN) == MASK_SIGN);
61 
  BID_RETURN (res);
62 
}
63 
 
64 
// return 1 iff x is not zero, nor NaN nor subnormal nor infinity
65 
#if DECIMAL_CALL_BY_REFERENCE
66 
void
67 
bid128_isNormal (int *pres,
68 
                 UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
69 
  UINT128 x = *px;
70 
#else
71 
int
72 
bid128_isNormal (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
73 
#endif
74 
  int res;
75 
  UINT64 x_exp, C1_hi, C1_lo;
76 
  BID_UI64DOUBLE tmp1;
77 
  int exp, q, x_nr_bits;
78 
 
79 
  BID_SWAP128 (x);
80 
  // test for special values - infinity or NaN
81 
  if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
82 
    // x is special
83 
    res = 0;
84 
    BID_RETURN (res);
85 
  }
86 
  // unpack x
87 
  x_exp = x.w[1] & MASK_EXP;    // biased and shifted left 49 bit positions
88 
  C1_hi = x.w[1] & MASK_COEFF;
89 
  C1_lo = x.w[0];
90 
  // test for zero
91 
  if (C1_hi == 0 && C1_lo == 0) {
92 
    res = 0;
93 
    BID_RETURN (res);
94 
  }
95 
  // test for non-canonical values of the argument x
96 
  if ((((C1_hi > 0x0001ed09bead87c0ull)
97 
        || ((C1_hi == 0x0001ed09bead87c0ull)
98 
            && (C1_lo > 0x378d8e63ffffffffull)))
99 
       && ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull))
100 
      || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
101 
    res = 0;
102 
    BID_RETURN (res);
103 
  }
104 
  // x is subnormal or normal
105 
  // determine the number of digits q in the significand
106 
  // q = nr. of decimal digits in x
107 
  // determine first the nr. of bits in x
108 
  if (C1_hi == 0) {
109 
    if (C1_lo >= 0x0020000000000000ull) {       // x >= 2^53
110 
      // split the 64-bit value in two 32-bit halves to avoid rounding errors
111 
      if (C1_lo >= 0x0000000100000000ull) {     // x >= 2^32
112 
        tmp1.d = (double) (C1_lo >> 32);        // exact conversion
113 
        x_nr_bits =
114 
          33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
115 
      } else {  // x < 2^32
116 
        tmp1.d = (double) (C1_lo);      // exact conversion
117 
        x_nr_bits =
118 
          1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
119 
      }
120 
    } else {    // if x < 2^53
121 
      tmp1.d = (double) C1_lo;  // exact conversion
122 
      x_nr_bits =
123 
        1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
124 
    }
125 
  } else {      // C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi)
126 
    tmp1.d = (double) C1_hi;    // exact conversion
127 
    x_nr_bits =
128 
      65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
129 
  }
130 
  q = nr_digits[x_nr_bits - 1].digits;
131 
  if (q == 0) {
132 
    q = nr_digits[x_nr_bits - 1].digits1;
133 
    if (C1_hi > nr_digits[x_nr_bits - 1].threshold_hi ||
134 
        (C1_hi == nr_digits[x_nr_bits - 1].threshold_hi &&
135 
         C1_lo >= nr_digits[x_nr_bits - 1].threshold_lo))
136 
      q++;
137 
  }
138 
  exp = (int) (x_exp >> 49) - 6176;
139 
  // test for subnormal values of x
140 
  if (exp + q <= -6143) {
141 
    res = 0;
142 
    BID_RETURN (res);
143 
  } else {
144 
    res = 1;
145 
    BID_RETURN (res);
146 
  }
147 
}
148 
 
149 
// return 1 iff x is not zero, nor NaN nor normal nor infinity
150 
#if DECIMAL_CALL_BY_REFERENCE
151 
void
152 
bid128_isSubnormal (int *pres,
153 
                    UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
154 
  UINT128 x = *px;
155 
#else
156 
int
157 
bid128_isSubnormal (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
158 
#endif
159 
  int res;
160 
  UINT64 x_exp, C1_hi, C1_lo;
161 
  BID_UI64DOUBLE tmp1;
162 
  int exp, q, x_nr_bits;
163 
 
164 
  BID_SWAP128 (x);
165 
  // test for special values - infinity or NaN
166 
  if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
167 
    // x is special
168 
    res = 0;
169 
    BID_RETURN (res);
170 
  }
171 
  // unpack x
172 
  x_exp = x.w[1] & MASK_EXP;    // biased and shifted left 49 bit positions
173 
  C1_hi = x.w[1] & MASK_COEFF;
174 
  C1_lo = x.w[0];
175 
  // test for zero
176 
  if (C1_hi == 0 && C1_lo == 0) {
177 
    res = 0;
178 
    BID_RETURN (res);
179 
  }
180 
  // test for non-canonical values of the argument x
181 
  if ((((C1_hi > 0x0001ed09bead87c0ull)
182 
        || ((C1_hi == 0x0001ed09bead87c0ull)
183 
            && (C1_lo > 0x378d8e63ffffffffull)))
184 
       && ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull))
185 
      || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
186 
    res = 0;
187 
    BID_RETURN (res);
188 
  }
189 
  // x is subnormal or normal
190 
  // determine the number of digits q in the significand
191 
  // q = nr. of decimal digits in x
192 
  // determine first the nr. of bits in x
193 
  if (C1_hi == 0) {
194 
    if (C1_lo >= 0x0020000000000000ull) {       // x >= 2^53
195 
      // split the 64-bit value in two 32-bit halves to avoid rounding errors
196 
      if (C1_lo >= 0x0000000100000000ull) {     // x >= 2^32
197 
        tmp1.d = (double) (C1_lo >> 32);        // exact conversion
198 
        x_nr_bits =
199 
          33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
200 
      } else {  // x < 2^32
201 
        tmp1.d = (double) (C1_lo);      // exact conversion
202 
        x_nr_bits =
203 
          1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
204 
      }
205 
    } else {    // if x < 2^53
206 
      tmp1.d = (double) C1_lo;  // exact conversion
207 
      x_nr_bits =
208 
        1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
209 
    }
210 
  } else {      // C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi)
211 
    tmp1.d = (double) C1_hi;    // exact conversion
212 
    x_nr_bits =
213 
      65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
214 
  }
215 
  q = nr_digits[x_nr_bits - 1].digits;
216 
  if (q == 0) {
217 
    q = nr_digits[x_nr_bits - 1].digits1;
218 
    if (C1_hi > nr_digits[x_nr_bits - 1].threshold_hi ||
219 
        (C1_hi == nr_digits[x_nr_bits - 1].threshold_hi &&
220 
         C1_lo >= nr_digits[x_nr_bits - 1].threshold_lo))
221 
      q++;
222 
  }
223 
  exp = (int) (x_exp >> 49) - 6176;
224 
  // test for subnormal values of x
225 
  if (exp + q <= -6143) {
226 
    res = 1;
227 
  } else {
228 
    res = 0;
229 
  }
230 
  BID_RETURN (res);
231 
}
232 
 
233 
#if DECIMAL_CALL_BY_REFERENCE
234 
void
235 
bid128_isFinite (int *pres,
236 
                 UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
237 
  UINT128 x = *px;
238 
#else
239 
int
240 
bid128_isFinite (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
241 
#endif
242 
  int res;
243 
  res = ((x.w[HIGH_128W] & MASK_INF) != MASK_INF);
244 
  BID_RETURN (res);
245 
}
246 
 
247 
#if DECIMAL_CALL_BY_REFERENCE
248 
void
249 
bid128_isZero (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
250 
  UINT128 x = *px;
251 
#else
252 
int
253 
bid128_isZero (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
254 
#endif
255 
  int res;
256 
  UINT128 sig_x;
257 
 
258 
  BID_SWAP128 (x);
259 
  if ((x.w[1] & MASK_INF) == MASK_INF) {
260 
    res = 0;
261 
    BID_RETURN (res);
262 
  }
263 
  sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
264 
  sig_x.w[0] = x.w[0];
265 
  if ((sig_x.w[1] > 0x0001ed09bead87c0ull) ||   // significand is non-canonical
266 
      ((sig_x.w[1] == 0x0001ed09bead87c0ull) && (sig_x.w[0] > 0x378d8e63ffffffffull)) || // significand is non-canonical
267 
      ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull && (x.w[1] & MASK_INF) != MASK_INF) || // significand is non-canonical
268 
      (sig_x.w[1] == 0 && sig_x.w[0] == 0)) {      // significand is 0
269 
    res = 1;
270 
    BID_RETURN (res);
271 
  }
272 
  res = 0;
273 
  BID_RETURN (res);
274 
}
275 
 
276 
#if DECIMAL_CALL_BY_REFERENCE
277 
void
278 
bid128_isInf (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
279 
  UINT128 x = *px;
280 
#else
281 
int
282 
bid128_isInf (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
283 
#endif
284 
  int res;
285 
  res = ((x.w[HIGH_128W] & MASK_INF) == MASK_INF)
286 
    && ((x.w[HIGH_128W] & MASK_NAN) != MASK_NAN);
287 
  BID_RETURN (res);
288 
}
289 
 
290 
#if DECIMAL_CALL_BY_REFERENCE
291 
void
292 
bid128_isSignaling (int *pres,
293 
                    UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
294 
  UINT128 x = *px;
295 
#else
296 
int
297 
bid128_isSignaling (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
298 
#endif
299 
  int res;
300 
 
301 
  res = ((x.w[HIGH_128W] & MASK_SNAN) == MASK_SNAN);
302 
  BID_RETURN (res);
303 
}
304 
 
305 
// return 1 iff x is a canonical number ,infinity, or NaN.
306 
#if DECIMAL_CALL_BY_REFERENCE
307 
void
308 
bid128_isCanonical (int *pres,
309 
                    UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
310 
  UINT128 x = *px;
311 
#else
312 
int
313 
bid128_isCanonical (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
314 
#endif
315 
  int res;
316 
  UINT128 sig_x;
317 
 
318 
  BID_SWAP128 (x);
319 
  if ((x.w[1] & MASK_NAN) == MASK_NAN) {        // NaN
320 
    if (x.w[1] & 0x01ffc00000000000ull) {
321 
      res = 0;
322 
      BID_RETURN (res);
323 
    }
324 
    sig_x.w[1] = x.w[1] & 0x00003fffffffffffull;        // 46 bits
325 
    sig_x.w[0] = x.w[0];  // 64 bits
326 
    // payload must be < 10^33 = 0x0000314dc6448d93_38c15b0a00000000
327 
    if (sig_x.w[1] < 0x0000314dc6448d93ull
328 
        || (sig_x.w[1] == 0x0000314dc6448d93ull
329 
            && sig_x.w[0] < 0x38c15b0a00000000ull)) {
330 
      res = 1;
331 
    } else {
332 
      res = 0;
333 
    }
334 
    BID_RETURN (res);
335 
  } else if ((x.w[1] & MASK_INF) == MASK_INF) { // infinity
336 
    if ((x.w[1] & 0x03ffffffffffffffull) || x.w[0]) {
337 
      res = 0;
338 
    } else {
339 
      res = 1;
340 
    }
341 
    BID_RETURN (res);
342 
  }
343 
  // not NaN or infinity; extract significand to ensure it is canonical
344 
  sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
345 
  sig_x.w[0] = x.w[0];
346 
  // a canonical number has a coefficient < 10^34
347 
  //    (0x0001ed09_bead87c0_378d8e64_00000000)
348 
  if ((sig_x.w[1] > 0x0001ed09bead87c0ull) ||   // significand is non-canonical
349 
      ((sig_x.w[1] == 0x0001ed09bead87c0ull) && (sig_x.w[0] > 0x378d8e63ffffffffull)) || // significand is non-canonical
350 
      ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
351 
    res = 0;
352 
  } else {
353 
    res = 1;
354 
  }
355 
  BID_RETURN (res);
356 
}
357 
 
358 
#if DECIMAL_CALL_BY_REFERENCE
359 
void
360 
bid128_isNaN (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
361 
  UINT128 x = *px;
362 
#else
363 
int
364 
bid128_isNaN (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
365 
#endif
366 
  int res;
367 
 
368 
  res = ((x.w[HIGH_128W] & MASK_NAN) == MASK_NAN);
369 
  BID_RETURN (res);
370 
}
371 
 
372 
// copies a floating-point operand x to destination y, with no change
373 
#if DECIMAL_CALL_BY_REFERENCE
374 
void
375 
bid128_copy (UINT128 * pres,
376 
             UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
377 
  UINT128 x = *px;
378 
#else
379 
UINT128
380 
bid128_copy (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
381 
#endif
382 
  UINT128 res;
383 
 
384 
  res = x;
385 
  BID_RETURN (res);
386 
}
387 
 
388 
// copies a floating-point operand x to destination y, reversing the sign
389 
#if DECIMAL_CALL_BY_REFERENCE
390 
void
391 
bid128_negate (UINT128 * pres,
392 
               UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
393 
  UINT128 x = *px;
394 
#else
395 
UINT128
396 
bid128_negate (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
397 
#endif
398 
  UINT128 res;
399 
 
400 
  x.w[HIGH_128W] ^= MASK_SIGN;
401 
  res = x;
402 
  BID_RETURN (res);
403 
}
404 
 
405 
// copies a floating-point operand x to destination y, changing the sign to positive
406 
#if DECIMAL_CALL_BY_REFERENCE
407 
void
408 
bid128_abs (UINT128 * pres,
409 
            UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
410 
  UINT128 x = *px;
411 
#else
412 
UINT128
413 
bid128_abs (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
414 
#endif
415 
  UINT128 res;
416 
 
417 
  x.w[HIGH_128W] &= ~MASK_SIGN;
418 
  res = x;
419 
  BID_RETURN (res);
420 
}
421 
 
422 
// copies operand x to destination in the same format as x, but with the sign of y
423 
#if DECIMAL_CALL_BY_REFERENCE
424 
void
425 
bid128_copySign (UINT128 * pres, UINT128 * px,
426 
                 UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
427 
  UINT128 x = *px;
428 
  UINT128 y = *py;
429 
#else
430 
UINT128
431 
bid128_copySign (UINT128 x, UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
432 
#endif
433 
  UINT128 res;
434 
 
435 
  x.w[HIGH_128W] =
436 
    (x.w[HIGH_128W] & ~MASK_SIGN) | (y.w[HIGH_128W] & MASK_SIGN);
437 
  res = x;
438 
  BID_RETURN (res);
439 
}
440 
 
441 
#if DECIMAL_CALL_BY_REFERENCE
442 
void
443 
bid128_class (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
444 
  UINT128 x = *px;
445 
#else
446 
int
447 
bid128_class (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
448 
#endif
449 
  int res;
450 
  UINT256 sig_x_prime256;
451 
  UINT192 sig_x_prime192;
452 
  UINT128 sig_x;
453 
  int exp_x;
454 
 
455 
  BID_SWAP128 (x);
456 
  if ((x.w[1] & MASK_NAN) == MASK_NAN) {
457 
    if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {
458 
      res = signalingNaN;
459 
    } else {
460 
      res = quietNaN;
461 
    }
462 
    BID_RETURN (res);
463 
  }
464 
  if ((x.w[1] & MASK_INF) == MASK_INF) {
465 
    if ((x.w[1] & MASK_SIGN) == MASK_SIGN) {
466 
      res = negativeInfinity;
467 
    } else {
468 
      res = positiveInfinity;
469 
    }
470 
    BID_RETURN (res);
471 
  }
472 
  // decode number into exponent and significand
473 
  sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
474 
  sig_x.w[0] = x.w[0];
475 
  // check for zero or non-canonical
476 
  if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
477 
      || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
478 
          && (sig_x.w[0] > 0x378d8e63ffffffffull))
479 
      || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)
480 
      || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
481 
    if ((x.w[1] & MASK_SIGN) == MASK_SIGN) {
482 
      res = negativeZero;
483 
    } else {
484 
      res = positiveZero;
485 
    }
486 
    BID_RETURN (res);
487 
  }
488 
  exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
489 
  // if exponent is less than -6176, the number may be subnormal
490 
  // (less than the smallest normal value)
491 
  //  the smallest normal value is 1 x 10^-6143 = 10^33 x 10^-6176
492 
  //  if (exp_x - 6176 < -6143)
493 
  if (exp_x < 33) {     // sig_x * 10^exp_x
494 
    if (exp_x > 19) {
495 
      __mul_128x128_to_256 (sig_x_prime256, sig_x,
496 
                            ten2k128[exp_x - 20]);
497 
      // 10^33 = 0x0000314dc6448d93_38c15b0a00000000
498 
      if ((sig_x_prime256.w[3] == 0) && (sig_x_prime256.w[2] == 0)
499 
          && ((sig_x_prime256.w[1] < 0x0000314dc6448d93ull)
500 
              || ((sig_x_prime256.w[1] == 0x0000314dc6448d93ull)
501 
                  && (sig_x_prime256.w[0] < 0x38c15b0a00000000ull)))) {
502 
        res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? negativeSubnormal :
503 
          positiveSubnormal;
504 
        BID_RETURN (res);
505 
      }
506 
    } else {
507 
      __mul_64x128_to_192 (sig_x_prime192, ten2k64[exp_x], sig_x);
508 
      // 10^33 = 0x0000314dc6448d93_38c15b0a00000000
509 
      if ((sig_x_prime192.w[2] == 0)
510 
          && ((sig_x_prime192.w[1] < 0x0000314dc6448d93ull)
511 
              || ((sig_x_prime192.w[1] == 0x0000314dc6448d93ull)
512 
                  && (sig_x_prime192.w[0] < 0x38c15b0a00000000ull)))) {
513 
        res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? negativeSubnormal :
514 
          positiveSubnormal;
515 
        BID_RETURN (res);
516 
      }
517 
    }
518 
  }
519 
  // otherwise, normal number, determine the sign
520 
  res =
521 
    ((x.w[1] & MASK_SIGN) ==
522 
     MASK_SIGN) ? negativeNormal : positiveNormal;
523 
  BID_RETURN (res);
524 
}
525 
 
526 
// true if the exponents of x and y are the same, false otherwise.
527 
// The special cases of sameQuantum(NaN, NaN) and sameQuantum(Inf, Inf) are true
528 
// If exactly one operand is infinite or exactly one operand is NaN, then false
529 
#if DECIMAL_CALL_BY_REFERENCE
530 
void
531 
bid128_sameQuantum (int *pres, UINT128 * px,
532 
                    UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
533 
  UINT128 x = *px;
534 
  UINT128 y = *py;
535 
#else
536 
int
537 
bid128_sameQuantum (UINT128 x,
538 
                    UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
539 
#endif
540 
  int res;
541 
  UINT64 x_exp, y_exp;
542 
 
543 
  BID_SWAP128 (x);
544 
  BID_SWAP128 (y);
545 
  // if both operands are NaN, return true
546 
  if ((x.w[1] & MASK_NAN) == MASK_NAN
547 
      || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
548 
    res = ((x.w[1] & MASK_NAN) == MASK_NAN
549 
           && (y.w[1] & MASK_NAN) == MASK_NAN);
550 
    BID_RETURN (res);
551 
  }
552 
  // if both operands are INF, return true
553 
  if ((x.w[1] & MASK_INF) == MASK_INF
554 
      || (y.w[1] & MASK_INF) == MASK_INF) {
555 
    res = ((x.w[1] & MASK_INF) == MASK_INF)
556 
      && ((y.w[1] & MASK_INF) == MASK_INF);
557 
    BID_RETURN (res);
558 
  }
559 
  // decode exponents for both numbers, and return true if they match
560 
  if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {      // G0_G1=11
561 
    x_exp = (x.w[1] << 2) & MASK_EXP;   // biased and shifted left 49 bits
562 
  } else {      // G0_G1 != 11
563 
    x_exp = x.w[1] & MASK_EXP;  // biased and shifted left 49 bits
564 
  }
565 
  if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {      // G0_G1=11
566 
    y_exp = (y.w[1] << 2) & MASK_EXP;   // biased and shifted left 49 bits
567 
  } else {      // G0_G1 != 11
568 
    y_exp = y.w[1] & MASK_EXP;  // biased and shifted left 49 bits
569 
  }
570 
  res = (x_exp == y_exp);
571 
  BID_RETURN (res);
572 
}
573 
 
574 
#if DECIMAL_CALL_BY_REFERENCE
575 
void
576 
bid128_totalOrder (int *pres, UINT128 * px,
577 
                   UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
578 
  UINT128 x = *px;
579 
  UINT128 y = *py;
580 
#else
581 
int
582 
bid128_totalOrder (UINT128 x,
583 
                   UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
584 
#endif
585 
  int res;
586 
  int exp_x, exp_y;
587 
  UINT128 sig_x, sig_y, pyld_y, pyld_x;
588 
  UINT192 sig_n_prime192;
589 
  UINT256 sig_n_prime256;
590 
  char x_is_zero = 0, y_is_zero = 0;
591 
 
592 
  BID_SWAP128 (x);
593 
  BID_SWAP128 (y);
594 
  // NaN (CASE 1)
595 
  // if x and y are unordered numerically because either operand is NaN
596 
  //    (1) totalOrder(-NaN, number) is true
597 
  //    (2) totalOrder(number, +NaN) is true
598 
  //    (3) if x and y are both NaN:
599 
  //       i) negative sign bit < positive sign bit
600 
  //       ii) signaling < quiet for +NaN, reverse for -NaN
601 
  //       iii) lesser payload < greater payload for +NaN (reverse for -NaN)
602 
  //       iv) else if bitwise identical (in canonical form), return 1
603 
  if ((x.w[1] & MASK_NAN) == MASK_NAN) {
604 
    // if x is -NaN
605 
    if ((x.w[1] & MASK_SIGN) == MASK_SIGN) {
606 
      // return true, unless y is -NaN also
607 
      if ((y.w[1] & MASK_NAN) != MASK_NAN
608 
          || (y.w[1] & MASK_SIGN) != MASK_SIGN) {
609 
        res = 1;        // y is a number, return 1
610 
        BID_RETURN (res);
611 
      } else {  // if y and x are both -NaN
612 
        pyld_x.w[1] = x.w[1] & 0x00003fffffffffffull;
613 
        pyld_x.w[0] = x.w[0];
614 
        pyld_y.w[1] = y.w[1] & 0x00003fffffffffffull;
615 
        pyld_y.w[0] = y.w[0];
616 
        if ((pyld_x.w[1] > 0x0000314dc6448d93ull)
617 
            || ((pyld_x.w[1] == 0x0000314dc6448d93ull)
618 
                && (pyld_x.w[0] > 0x38c15b09ffffffffull))) {
619 
          pyld_x.w[1] = 0;
620 
          pyld_x.w[0] = 0;
621 
        }
622 
        if ((pyld_y.w[1] > 0x0000314dc6448d93ull)
623 
            || ((pyld_y.w[1] == 0x0000314dc6448d93ull)
624 
                && (pyld_y.w[0] > 0x38c15b09ffffffffull))) {
625 
          pyld_y.w[1] = 0;
626 
          pyld_y.w[0] = 0;
627 
        }
628 
        // if x and y are both -SNaN or both -QNaN, we have to compare payloads
629 
        // this statement evaluates to true if both are SNaN or QNaN
630 
        if (!
631 
            (((y.w[1] & MASK_SNAN) == MASK_SNAN) ^
632 
             ((x.w[1] & MASK_SNAN) == MASK_SNAN))) {
633 
          // it comes down to the payload.  we want to return true if x has a
634 
          // larger payload, or if the payloads are equal (canonical forms
635 
          // are bitwise identical)
636 
          if ((pyld_x.w[1] > pyld_y.w[1]) ||
637 
              ((pyld_x.w[1] == pyld_y.w[1])
638 
               && (pyld_x.w[0] >= pyld_y.w[0])))
639 
            res = 1;
640 
          else
641 
            res = 0;
642 
          BID_RETURN (res);
643 
        } else {
644 
          // either x = -SNaN and y = -QNaN or x = -QNaN and y = -SNaN
645 
          res = ((y.w[1] & MASK_SNAN) == MASK_SNAN);
646 
          // totalOrder (-QNaN, -SNaN) == 1
647 
          BID_RETURN (res);
648 
        }
649 
      }
650 
    } else {    // x is +NaN
651 
      // return false, unless y is +NaN also
652 
      if ((y.w[1] & MASK_NAN) != MASK_NAN
653 
          || (y.w[1] & MASK_SIGN) == MASK_SIGN) {
654 
        res = 0; // y is a number, return 1
655 
        BID_RETURN (res);
656 
      } else {
657 
        // x and y are both +NaN;
658 
        pyld_x.w[1] = x.w[1] & 0x00003fffffffffffull;
659 
        pyld_x.w[0] = x.w[0];
660 
        pyld_y.w[1] = y.w[1] & 0x00003fffffffffffull;
661 
        pyld_y.w[0] = y.w[0];
662 
        if ((pyld_x.w[1] > 0x0000314dc6448d93ull)
663 
            || ((pyld_x.w[1] == 0x0000314dc6448d93ull)
664 
                && (pyld_x.w[0] > 0x38c15b09ffffffffull))) {
665 
          pyld_x.w[1] = 0;
666 
          pyld_x.w[0] = 0;
667 
        }
668 
        if ((pyld_y.w[1] > 0x0000314dc6448d93ull)
669 
            || ((pyld_y.w[1] == 0x0000314dc6448d93ull)
670 
                && (pyld_y.w[0] > 0x38c15b09ffffffffull))) {
671 
          pyld_y.w[1] = 0;
672 
          pyld_y.w[0] = 0;
673 
        }
674 
        // if x and y are both +SNaN or both +QNaN, we have to compare payloads
675 
        // this statement evaluates to true if both are SNaN or QNaN
676 
        if (!
677 
            (((y.w[1] & MASK_SNAN) == MASK_SNAN) ^
678 
             ((x.w[1] & MASK_SNAN) == MASK_SNAN))) {
679 
          // it comes down to the payload.  we want to return true if x has a
680 
          // smaller payload, or if the payloads are equal (canonical forms
681 
          // are bitwise identical)
682 
          if ((pyld_x.w[1] < pyld_y.w[1]) ||
683 
              ((pyld_x.w[1] == pyld_y.w[1])
684 
               && (pyld_x.w[0] <= pyld_y.w[0])))
685 
            res = 1;
686 
          else
687 
            res = 0;
688 
          BID_RETURN (res);
689 
        } else {
690 
          // either x = SNaN and y = QNaN or x = QNaN and y = SNaN
691 
          res = ((x.w[1] & MASK_SNAN) == MASK_SNAN);
692 
          // totalOrder (-QNaN, -SNaN) == 1
693 
          BID_RETURN (res);
694 
        }
695 
      }
696 
    }
697 
  } else if ((y.w[1] & MASK_NAN) == MASK_NAN) {
698 
    // x is certainly not NAN in this case.
699 
    // return true if y is positive
700 
    res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
701 
    BID_RETURN (res);
702 
  }
703 
  // SIMPLE (CASE 2)
704 
  // if all the bits are the same, the numbers are equal.
705 
  if ((x.w[1] == y.w[1]) && (x.w[0] == y.w[0])) {
706 
    res = 1;
707 
    BID_RETURN (res);
708 
  }
709 
  // OPPOSITE SIGNS (CASE 3)
710 
  // if signs are opposite, return 1 if x is negative
711 
  // (if x < y, totalOrder is true)
712 
  if (((x.w[1] & MASK_SIGN) == MASK_SIGN) ^ ((y.w[1] & MASK_SIGN) ==
713 
                                             MASK_SIGN)) {
714 
    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
715 
    BID_RETURN (res);
716 
  }
717 
  // INFINITY (CASE 4)
718 
  if ((x.w[1] & MASK_INF) == MASK_INF) {
719 
    // if x == neg_inf, return (y == neg_inf);
720 
    if ((x.w[1] & MASK_SIGN) == MASK_SIGN) {
721 
      res = 1;
722 
      BID_RETURN (res);
723 
    } else {
724 
      // x is positive infinity, only return1 if y is positive infinity as well
725 
      res = ((y.w[1] & MASK_INF) == MASK_INF);
726 
      BID_RETURN (res);
727 
      // && (y & MASK_SIGN) != MASK_SIGN); (we know y has same sign as x)
728 
    }
729 
  } else if ((y.w[1] & MASK_INF) == MASK_INF) {
730 
    // x is finite, so:
731 
    //    if y is +inf, x<y
732 
    //    if y is -inf, x>y
733 
    res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
734 
    BID_RETURN (res);
735 
  }
736 
  // CONVERT x
737 
  sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
738 
  sig_x.w[0] = x.w[0];
739 
  exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
740 
 
741 
  // CHECK IF x IS CANONICAL
742 
  // 9999999999999999999999999999999999 (decimal) =
743 
  //     1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
744 
  // [0, 10^34) is the 754r supported canonical range.
745 
  // If the value exceeds that, it is interpreted as 0.
746 
  if ((((sig_x.w[1] > 0x0001ed09bead87c0ull) ||
747 
        ((sig_x.w[1] == 0x0001ed09bead87c0ull) &&
748 
         (sig_x.w[0] > 0x378d8e63ffffffffull))) &&
749 
       ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) ||
750 
      ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) ||
751 
      ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
752 
    x_is_zero = 1;
753 
    // check for the case where the exponent is shifted right by 2 bits!
754 
    if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {
755 
      exp_x = (x.w[1] >> 47) & 0x000000000003fffull;
756 
    }
757 
  }
758 
  // CONVERT y
759 
  exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
760 
  sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
761 
  sig_y.w[0] = y.w[0];
762 
 
763 
  // CHECK IF y IS CANONICAL
764 
  // 9999999999999999999999999999999999(decimal) =
765 
  //     1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
766 
  // [0, 10^34) is the 754r supported canonical range.
767 
  // If the value exceeds that, it is interpreted as 0.
768 
  if ((((sig_y.w[1] > 0x0001ed09bead87c0ull) ||
769 
        ((sig_y.w[1] == 0x0001ed09bead87c0ull) &&
770 
         (sig_y.w[0] > 0x378d8e63ffffffffull))) &&
771 
       ((y.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) ||
772 
      ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) ||
773 
      ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
774 
    y_is_zero = 1;
775 
    // check for the case where the exponent is shifted right by 2 bits!
776 
    if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {
777 
      exp_y = (y.w[1] >> 47) & 0x000000000003fffull;
778 
    }
779 
  }
780 
  // ZERO (CASE 5)
781 
  // if x and y represent the same entities, and both are negative
782 
  // return true iff exp_x <= exp_y
783 
  if (x_is_zero && y_is_zero) {
784 
    // we know that signs must be the same because we would have caught it
785 
    // in case3 if signs were different
786 
    // totalOrder(x,y) iff exp_x >= exp_y for negative numbers
787 
    // totalOrder(x,y) iff exp_x <= exp_y for positive numbers
788 
    if (exp_x == exp_y) {
789 
      res = 1;
790 
      BID_RETURN (res);
791 
    }
792 
    res = ((exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
793 
    BID_RETURN (res);
794 
  }
795 
  // if x is zero and y isn't, clearly x has the smaller payload
796 
  if (x_is_zero) {
797 
    res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
798 
    BID_RETURN (res);
799 
  }
800 
  // if y is zero, and x isn't, clearly y has the smaller payload
801 
  if (y_is_zero) {
802 
    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
803 
    BID_RETURN (res);
804 
  }
805 
  // REDUNDANT REPRESENTATIONS (CASE 6)
806 
  // if both components are either bigger or smaller
807 
  if (((sig_x.w[1] > sig_y.w[1])
808 
       || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
809 
      && exp_x >= exp_y) {
810 
    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
811 
    BID_RETURN (res);
812 
  }
813 
  if (((sig_x.w[1] < sig_y.w[1])
814 
       || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
815 
      && exp_x <= exp_y) {
816 
    res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
817 
    BID_RETURN (res);
818 
  }
819 
  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
820 
  if (exp_x > exp_y) {
821 
    // if exp_x is 33 greater than exp_y, it is definitely larger,
822 
    // so no need for compensation
823 
    if (exp_x - exp_y > 33) {
824 
      res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
825 
      BID_RETURN (res);
826 
      // difference cannot be greater than 10^33
827 
    }
828 
    // otherwise adjust the x significand upwards
829 
    if (exp_x - exp_y > 19) {
830 
      __mul_128x128_to_256 (sig_n_prime256, sig_x,
831 
                            ten2k128[exp_x - exp_y - 20]);
832 
      // the compensated significands are equal (ie "x and y represent the same
833 
      // entities") return 1 if (negative && expx > expy) ||
834 
      // (positive && expx < expy)
835 
      if ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0)
836 
          && (sig_n_prime256.w[1] == sig_y.w[1])
837 
          && (sig_n_prime256.w[0] == sig_y.w[0])) {
838 
        // the case exp_x == exp_y  cannot occur, because all bits must be
839 
        // the same - would have been caught if (x == y)
840 
        res = ((exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
841 
        BID_RETURN (res);
842 
      }
843 
      // if positive, return 1 if adjusted x is smaller than y
844 
      res = (((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0)
845 
              && ((sig_n_prime256.w[1] < sig_y.w[1])
846 
                  || (sig_n_prime256.w[1] == sig_y.w[1]
847 
                      && sig_n_prime256.w[0] <
848 
                      sig_y.w[0]))) ^ ((x.w[1] & MASK_SIGN) ==
849 
                                       MASK_SIGN));
850 
      BID_RETURN (res);
851 
    }
852 
    __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_x - exp_y], sig_x);
853 
    // if positive, return whichever significand is larger
854 
    // (converse if negative)
855 
    if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
856 
        && (sig_n_prime192.w[0] == sig_y.w[0])) {
857 
      res = ((exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
858 
      BID_RETURN (res);
859 
    }
860 
    res = (((sig_n_prime192.w[2] == 0)
861 
            && ((sig_n_prime192.w[1] < sig_y.w[1])
862 
                || (sig_n_prime192.w[1] == sig_y.w[1]
863 
                    && sig_n_prime192.w[0] <
864 
                    sig_y.w[0]))) ^ ((x.w[1] & MASK_SIGN) ==
865 
                                     MASK_SIGN));
866 
    BID_RETURN (res);
867 
  }
868 
  // if exp_x is 33 less than exp_y, it is definitely smaller,
869 
  // no need for compensation
870 
  if (exp_y - exp_x > 33) {
871 
    res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
872 
    BID_RETURN (res);
873 
  }
874 
  if (exp_y - exp_x > 19) {
875 
    // adjust the y significand upwards
876 
    __mul_128x128_to_256 (sig_n_prime256, sig_y,
877 
                          ten2k128[exp_y - exp_x - 20]);
878 
    // if x and y represent the same entities and both are negative
879 
    // return true iff exp_x <= exp_y
880 
    if ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0)
881 
        && (sig_n_prime256.w[1] == sig_x.w[1])
882 
        && (sig_n_prime256.w[0] == sig_x.w[0])) {
883 
      res = (exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN);
884 
      BID_RETURN (res);
885 
    }
886 
    // values are not equal, for positive numbers return 1 if x is less than y
887 
    // and 0 otherwise
888 
    res = (((sig_n_prime256.w[3] != 0) ||
889 
            // if upper128 bits of compensated y are non-zero, y is bigger
890 
            (sig_n_prime256.w[2] != 0) ||
891 
            // if upper128 bits of compensated y are non-zero, y is bigger
892 
            (sig_n_prime256.w[1] > sig_x.w[1]) ||
893 
            // if compensated y is bigger, y is bigger
894 
            (sig_n_prime256.w[1] == sig_x.w[1]
895 
             && sig_n_prime256.w[0] >
896 
             sig_x.w[0])) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
897 
    BID_RETURN (res);
898 
  }
899 
  __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y);
900 
  if ((sig_n_prime192.w[2] == 0) && (sig_n_prime192.w[1] == sig_x.w[1])
901 
      && (sig_n_prime192.w[0] == sig_x.w[0])) {
902 
    res = (exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN);
903 
    BID_RETURN (res);
904 
  }
905 
  res = (((sig_n_prime192.w[2] != 0) ||
906 
          // if upper128 bits of compensated y are non-zero, y is bigger
907 
          (sig_n_prime192.w[1] > sig_x.w[1]) ||
908 
          // if compensated y is bigger, y is bigger
909 
          (sig_n_prime192.w[1] == sig_x.w[1]
910 
           && sig_n_prime192.w[0] >
911 
           sig_x.w[0])) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
912 
  BID_RETURN (res);
913 
}
914 
 
915 
#if DECIMAL_CALL_BY_REFERENCE
916 
void
917 
bid128_totalOrderMag (int *pres, UINT128 * px,
918 
                      UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
919 
  UINT128 x = *px;
920 
  UINT128 y = *py;
921 
#else
922 
int
923 
bid128_totalOrderMag (UINT128 x,
924 
                      UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
925 
#endif
926 
  int res;
927 
  int exp_x, exp_y;
928 
  UINT128 sig_x, sig_y, pyld_y, pyld_x;
929 
  UINT192 sig_n_prime192;
930 
  UINT256 sig_n_prime256;
931 
  char x_is_zero = 0, y_is_zero = 0;
932 
 
933 
  BID_SWAP128 (x);
934 
  BID_SWAP128 (y);
935 
  x.w[1] = x.w[1] & 0x7fffffffffffffffull;
936 
  y.w[1] = y.w[1] & 0x7fffffffffffffffull;
937 
 
938 
  // NaN (CASE 1)
939 
  // if x and y are unordered numerically because either operand is NaN
940 
  //    (1) totalOrder(number, +NaN) is true
941 
  //    (2) if x and y are both NaN:
942 
  //       i) signaling < quiet for +NaN
943 
  //       ii) lesser payload < greater payload for +NaN
944 
  //       iii) else if bitwise identical (in canonical form), return 1
945 
  if ((x.w[1] & MASK_NAN) == MASK_NAN) {
946 
    // x is +NaN
947 
    // return false, unless y is +NaN also
948 
    if ((y.w[1] & MASK_NAN) != MASK_NAN) {
949 
      res = 0;   // y is a number, return 0
950 
      BID_RETURN (res);
951 
    } else {
952 
      // x and y are both +NaN;
953 
      pyld_x.w[1] = x.w[1] & 0x00003fffffffffffull;
954 
      pyld_x.w[0] = x.w[0];
955 
      pyld_y.w[1] = y.w[1] & 0x00003fffffffffffull;
956 
      pyld_y.w[0] = y.w[0];
957 
      if ((pyld_x.w[1] > 0x0000314dc6448d93ull)
958 
          || ((pyld_x.w[1] == 0x0000314dc6448d93ull)
959 
              && (pyld_x.w[0] > 0x38c15b09ffffffffull))) {
960 
        pyld_x.w[1] = 0;
961 
        pyld_x.w[0] = 0;
962 
      }
963 
      if ((pyld_y.w[1] > 0x0000314dc6448d93ull)
964 
          || ((pyld_y.w[1] == 0x0000314dc6448d93ull)
965 
              && (pyld_y.w[0] > 0x38c15b09ffffffffull))) {
966 
        pyld_y.w[1] = 0;
967 
        pyld_y.w[0] = 0;
968 
      }
969 
      // if x and y are both +SNaN or both +QNaN, we have to compare payloads
970 
      // this statement evaluates to true if both are SNaN or QNaN
971 
      if (!
972 
          (((y.w[1] & MASK_SNAN) == MASK_SNAN) ^
973 
           ((x.w[1] & MASK_SNAN) == MASK_SNAN))) {
974 
        // it comes down to the payload.  we want to return true if x has a
975 
        // smaller payload, or if the payloads are equal (canonical forms
976 
        // are bitwise identical)
977 
        if ((pyld_x.w[1] < pyld_y.w[1]) ||
978 
            ((pyld_x.w[1] == pyld_y.w[1])
979 
             && (pyld_x.w[0] <= pyld_y.w[0]))) {
980 
          res = 1;
981 
        } else {
982 
          res = 0;
983 
        }
984 
        BID_RETURN (res);
985 
      } else {
986 
        // either x = SNaN and y = QNaN or x = QNaN and y = SNaN
987 
        res = ((x.w[1] & MASK_SNAN) == MASK_SNAN);
988 
        // totalOrder (-QNaN, -SNaN) == 1
989 
        BID_RETURN (res);
990 
      }
991 
    }
992 
  } else if ((y.w[1] & MASK_NAN) == MASK_NAN) {
993 
    // x is certainly not NAN in this case.
994 
    // return true because y is positive
995 
    res = 1;
996 
    BID_RETURN (res);
997 
  }
998 
  // SIMPLE (CASE 2)
999 
  // if all the bits are the same, the numbers are equal.
1000 
  if ((x.w[1] == y.w[1]) && (x.w[0] == y.w[0])) {
1001 
    res = 1;
1002 
    BID_RETURN (res);
1003 
  }
1004 
  // INFINITY (CASE 3)
1005 
  if ((x.w[1] & MASK_INF) == MASK_INF) {
1006 
    // x is positive infinity, only return 1 if y is positive infinity as well
1007 
    res = ((y.w[1] & MASK_INF) == MASK_INF);
1008 
    BID_RETURN (res);
1009 
    // (we know y has same sign as x)
1010 
  } else if ((y.w[1] & MASK_INF) == MASK_INF) {
1011 
    // x is finite, so:
1012 
    //    since y is +inf, x<y
1013 
    res = 1;
1014 
    BID_RETURN (res);
1015 
  } else {
1016 
    ;   // continue
1017 
  }
1018 
 
1019 
  // CONVERT x
1020 
  sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
1021 
  sig_x.w[0] = x.w[0];
1022 
  exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
1023 
 
1024 
  // CHECK IF x IS CANONICAL
1025 
  // 9999999999999999999999999999999999 (decimal) =
1026 
  //     1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
1027 
  // [0, 10^34) is the 754r supported canonical range.
1028 
  // If the value exceeds that, it is interpreted as 0.
1029 
  if ((((sig_x.w[1] > 0x0001ed09bead87c0ull) ||
1030 
        ((sig_x.w[1] == 0x0001ed09bead87c0ull) &&
1031 
         (sig_x.w[0] > 0x378d8e63ffffffffull))) &&
1032 
       ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) ||
1033 
      ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) ||
1034 
      ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
1035 
    x_is_zero = 1;
1036 
    // check for the case where the exponent is shifted right by 2 bits!
1037 
    if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {
1038 
      exp_x = (x.w[1] >> 47) & 0x000000000003fffull;
1039 
    }
1040 
  }
1041 
  // CONVERT y
1042 
  exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
1043 
  sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
1044 
  sig_y.w[0] = y.w[0];
1045 
 
1046 
  // CHECK IF y IS CANONICAL
1047 
  // 9999999999999999999999999999999999(decimal) =
1048 
  //     1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
1049 
  // [0, 10^34) is the 754r supported canonical range.
1050 
  // If the value exceeds that, it is interpreted as 0.
1051 
  if ((((sig_y.w[1] > 0x0001ed09bead87c0ull) ||
1052 
        ((sig_y.w[1] == 0x0001ed09bead87c0ull) &&
1053 
         (sig_y.w[0] > 0x378d8e63ffffffffull))) &&
1054 
       ((y.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) ||
1055 
      ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) ||
1056 
      ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
1057 
    y_is_zero = 1;
1058 
    // check for the case where the exponent is shifted right by 2 bits!
1059 
    if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {
1060 
      exp_y = (y.w[1] >> 47) & 0x000000000003fffull;
1061 
    }
1062 
  }
1063 
  // ZERO (CASE 4)
1064 
  if (x_is_zero && y_is_zero) {
1065 
    // we know that signs must be the same because we would have caught it
1066 
    // in case3 if signs were different
1067 
    // totalOrder(x,y) iff exp_x <= exp_y for positive numbers
1068 
    if (exp_x == exp_y) {
1069 
      res = 1;
1070 
      BID_RETURN (res);
1071 
    }
1072 
    res = (exp_x <= exp_y);
1073 
    BID_RETURN (res);
1074 
  }
1075 
  // if x is zero and y isn't, clearly x has the smaller payload
1076 
  if (x_is_zero) {
1077 
    res = 1;
1078 
    BID_RETURN (res);
1079 
  }
1080 
  // if y is zero, and x isn't, clearly y has the smaller payload
1081 
  if (y_is_zero) {
1082 
    res = 0;
1083 
    BID_RETURN (res);
1084 
  }
1085 
  // REDUNDANT REPRESENTATIONS (CASE 5)
1086 
  // if both components are either bigger or smaller
1087 
  if (((sig_x.w[1] > sig_y.w[1])
1088 
       || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
1089 
      && exp_x >= exp_y) {
1090 
    res = 0;
1091 
    BID_RETURN (res);
1092 
  }
1093 
  if (((sig_x.w[1] < sig_y.w[1])
1094 
       || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
1095 
      && exp_x <= exp_y) {
1096 
    res = 1;
1097 
    BID_RETURN (res);
1098 
  }
1099 
  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
1100 
  if (exp_x > exp_y) {
1101 
    // if exp_x is 33 greater than exp_y, it is definitely larger,
1102 
    // so no need for compensation
1103 
    if (exp_x - exp_y > 33) {
1104 
      res = 0;   // difference cannot be greater than 10^33
1105 
      BID_RETURN (res);
1106 
    }
1107 
    // otherwise adjust the x significand upwards
1108 
    if (exp_x - exp_y > 19) {
1109 
      __mul_128x128_to_256 (sig_n_prime256, sig_x,
1110 
                            ten2k128[exp_x - exp_y - 20]);
1111 
      // the compensated significands are equal (ie "x and y represent the same
1112 
      // entities") return 1 if (negative && expx > expy) ||
1113 
      // (positive && expx < expy)
1114 
      if ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0)
1115 
          && (sig_n_prime256.w[1] == sig_y.w[1])
1116 
          && (sig_n_prime256.w[0] == sig_y.w[0])) {
1117 
        // the case (exp_x == exp_y) cannot occur, because all bits must be
1118 
        // the same - would have been caught if (x == y)
1119 
        res = (exp_x <= exp_y);
1120 
        BID_RETURN (res);
1121 
      }
1122 
      // since positive, return 1 if adjusted x is smaller than y
1123 
      res = ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0)
1124 
             && ((sig_n_prime256.w[1] < sig_y.w[1])
1125 
                 || (sig_n_prime256.w[1] == sig_y.w[1]
1126 
                     && sig_n_prime256.w[0] < sig_y.w[0])));
1127 
      BID_RETURN (res);
1128 
    }
1129 
    __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_x - exp_y], sig_x);
1130 
    // if positive, return whichever significand is larger
1131 
    // (converse if negative)
1132 
    if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
1133 
        && (sig_n_prime192.w[0] == sig_y.w[0])) {
1134 
      res = (exp_x <= exp_y);
1135 
      BID_RETURN (res);
1136 
    }
1137 
    res = ((sig_n_prime192.w[2] == 0)
1138 
           && ((sig_n_prime192.w[1] < sig_y.w[1])
1139 
               || (sig_n_prime192.w[1] == sig_y.w[1]
1140 
                   && sig_n_prime192.w[0] < sig_y.w[0])));
1141 
    BID_RETURN (res);
1142 
  }
1143 
  // if exp_x is 33 less than exp_y, it is definitely smaller,
1144 
  // no need for compensation
1145 
  if (exp_y - exp_x > 33) {
1146 
    res = 1;
1147 
    BID_RETURN (res);
1148 
  }
1149 
  if (exp_y - exp_x > 19) {
1150 
    // adjust the y significand upwards
1151 
    __mul_128x128_to_256 (sig_n_prime256, sig_y,
1152 
                          ten2k128[exp_y - exp_x - 20]);
1153 
    if ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0)
1154 
        && (sig_n_prime256.w[1] == sig_x.w[1])
1155 
        && (sig_n_prime256.w[0] == sig_x.w[0])) {
1156 
      res = (exp_x <= exp_y);
1157 
      BID_RETURN (res);
1158 
    }
1159 
    // values are not equal, for positive numbers return 1 if x is less than y
1160 
    // and 0 otherwise
1161 
    res = ((sig_n_prime256.w[3] != 0) ||
1162 
           // if upper128 bits of compensated y are non-zero, y is bigger
1163 
           (sig_n_prime256.w[2] != 0) ||
1164 
           // if upper128 bits of compensated y are non-zero, y is bigger
1165 
           (sig_n_prime256.w[1] > sig_x.w[1]) ||
1166 
           // if compensated y is bigger, y is bigger
1167 
           (sig_n_prime256.w[1] == sig_x.w[1]
1168 
            && sig_n_prime256.w[0] > sig_x.w[0]));
1169 
    BID_RETURN (res);
1170 
  }
1171 
  __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y);
1172 
  if ((sig_n_prime192.w[2] == 0) && (sig_n_prime192.w[1] == sig_x.w[1])
1173 
      && (sig_n_prime192.w[0] == sig_x.w[0])) {
1174 
    res = (exp_x <= exp_y);
1175 
    BID_RETURN (res);
1176 
  }
1177 
  res = ((sig_n_prime192.w[2] != 0) ||
1178 
         // if upper128 bits of compensated y are non-zero, y is bigger
1179 
         (sig_n_prime192.w[1] > sig_x.w[1]) ||
1180 
         // if compensated y is bigger, y is bigger
1181 
         (sig_n_prime192.w[1] == sig_x.w[1]
1182 
          && sig_n_prime192.w[0] > sig_x.w[0]));
1183 
  BID_RETURN (res);
1184 
}
1185 
 
1186 
#if DECIMAL_CALL_BY_REFERENCE
1187 
void
1188 
bid128_radix (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
1189 
  UINT128 x = *px;
1190 
#else
1191 
int
1192 
bid128_radix (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
1193 
#endif
1194 
  int res;
1195 
  if (x.w[LOW_128W])    // dummy test
1196 
    res = 10;
1197 
  else
1198 
    res = 10;
1199 
  BID_RETURN (res);
1200 
}

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