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1 272 jeremybenn 
/* Copyright (C) 2007, 2009  Free Software Foundation, Inc.
2 
 
3 
This file is part of GCC.
4 
 
5 
GCC is free software; you can redistribute it and/or modify it under
6 
the terms of the GNU General Public License as published by the Free
7 
Software Foundation; either version 3, or (at your option) any later
8 
version.
9 
 
10 
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
11 
WARRANTY; without even the implied warranty of MERCHANTABILITY or
12 
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
13 
for more details.
14 
 
15 
Under Section 7 of GPL version 3, you are granted additional
16 
permissions described in the GCC Runtime Library Exception, version
17 
3.1, as published by the Free Software Foundation.
18 
 
19 
You should have received a copy of the GNU General Public License and
20 
a copy of the GCC Runtime Library Exception along with this program;
21 
see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
22 
<http://www.gnu.org/licenses/>.  */
23 
 
24 
#define BID_128RES
25 
 
26 
#include "bid_internal.h"
27 
 
28 
/*****************************************************************************
29 
 *  BID128_round_integral_exact
30 
 ****************************************************************************/
31 
 
32 
BID128_FUNCTION_ARG1 (bid128_round_integral_exact, x)
33 
 
34 
     UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull}
35 
     };
36 
UINT64 x_sign;
37 
UINT64 x_exp;
38 
int exp;                        // unbiased exponent
39 
  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
40 
UINT64 tmp64;
41 
BID_UI64DOUBLE tmp1;
42 
unsigned int x_nr_bits;
43 
int q, ind, shift;
44 
UINT128 C1;
45 
UINT256 fstar;
46 
UINT256 P256;
47 
 
48 
  // check for NaN or Infinity
49 
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
50 
  // x is special
51 
  if ((x.w[1] & MASK_NAN) == MASK_NAN) {        // x is NAN
52 
    // if x = NaN, then res = Q (x)
53 
    // check first for non-canonical NaN payload
54 
    if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
55 
        (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
56 
         (x.w[0] > 0x38c15b09ffffffffull))) {
57 
      x.w[1] = x.w[1] & 0xffffc00000000000ull;
58 
      x.w[0] = 0x0ull;
59 
    }
60 
    if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {    // x is SNAN
61 
      // set invalid flag
62 
      *pfpsf |= INVALID_EXCEPTION;
63 
      // return quiet (x)
64 
      res.w[1] = x.w[1] & 0xfc003fffffffffffull;        // clear out also G[6]-G[16]
65 
      res.w[0] = x.w[0];
66 
    } else {    // x is QNaN
67 
      // return x
68 
      res.w[1] = x.w[1] & 0xfc003fffffffffffull;        // clear out G[6]-G[16]
69 
      res.w[0] = x.w[0];
70 
    }
71 
    BID_RETURN (res)
72 
  } else {      // x is not a NaN, so it must be infinity
73 
    if ((x.w[1] & MASK_SIGN) == 0x0ull) {       // x is +inf
74 
      // return +inf
75 
      res.w[1] = 0x7800000000000000ull;
76 
      res.w[0] = 0x0000000000000000ull;
77 
    } else {    // x is -inf
78 
      // return -inf
79 
      res.w[1] = 0xf800000000000000ull;
80 
      res.w[0] = 0x0000000000000000ull;
81 
    }
82 
    BID_RETURN (res);
83 
  }
84 
}
85 
  // unpack x
86 
x_sign = x.w[1] & MASK_SIGN;    // 0 for positive, MASK_SIGN for negative
87 
C1.w[1] = x.w[1] & MASK_COEFF;
88 
C1.w[0] = x.w[0];
89 
 
90 
  // check for non-canonical values (treated as zero)
91 
if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {        // G0_G1=11
92 
  // non-canonical
93 
  x_exp = (x.w[1] << 2) & MASK_EXP;     // biased and shifted left 49 bits
94 
  C1.w[1] = 0;   // significand high
95 
  C1.w[0] = 0;    // significand low
96 
} else {        // G0_G1 != 11
97 
  x_exp = x.w[1] & MASK_EXP;    // biased and shifted left 49 bits
98 
  if (C1.w[1] > 0x0001ed09bead87c0ull ||
99 
      (C1.w[1] == 0x0001ed09bead87c0ull
100 
       && C1.w[0] > 0x378d8e63ffffffffull)) {
101 
    // x is non-canonical if coefficient is larger than 10^34 -1
102 
    C1.w[1] = 0;
103 
    C1.w[0] = 0;
104 
  } else {      // canonical
105 
    ;
106 
  }
107 
}
108 
 
109 
  // test for input equal to zero
110 
if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
111 
  // x is 0
112 
  // return 0 preserving the sign bit and the preferred exponent
113 
  // of MAX(Q(x), 0)
114 
  if (x_exp <= (0x1820ull << 49)) {
115 
    res.w[1] = (x.w[1] & 0x8000000000000000ull) | 0x3040000000000000ull;
116 
  } else {
117 
    res.w[1] = x_sign | x_exp;
118 
  }
119 
  res.w[0] = 0x0000000000000000ull;
120 
  BID_RETURN (res);
121 
}
122 
  // x is not special and is not zero
123 
 
124 
switch (rnd_mode) {
125 
case ROUNDING_TO_NEAREST:
126 
case ROUNDING_TIES_AWAY:
127 
  // if (exp <= -(p+1)) return 0.0
128 
  if (x_exp <= 0x2ffa000000000000ull) { // 0x2ffa000000000000ull == -35
129 
    res.w[1] = x_sign | 0x3040000000000000ull;
130 
    res.w[0] = 0x0000000000000000ull;
131 
    *pfpsf |= INEXACT_EXCEPTION;
132 
    BID_RETURN (res);
133 
  }
134 
  break;
135 
case ROUNDING_DOWN:
136 
  // if (exp <= -p) return -1.0 or +0.0
137 
  if (x_exp <= 0x2ffc000000000000ull) { // 0x2ffa000000000000ull == -34
138 
    if (x_sign) {
139 
      // if negative, return negative 1, because we know coefficient
140 
      // is non-zero (would have been caught above)
141 
      res.w[1] = 0xb040000000000000ull;
142 
      res.w[0] = 0x0000000000000001ull;
143 
    } else {
144 
      // if positive, return positive 0, because we know coefficient is
145 
      // non-zero (would have been caught above)
146 
      res.w[1] = 0x3040000000000000ull;
147 
      res.w[0] = 0x0000000000000000ull;
148 
    }
149 
    *pfpsf |= INEXACT_EXCEPTION;
150 
    BID_RETURN (res);
151 
  }
152 
  break;
153 
case ROUNDING_UP:
154 
  // if (exp <= -p) return -0.0 or +1.0
155 
  if (x_exp <= 0x2ffc000000000000ull) { // 0x2ffc000000000000ull == -34
156 
    if (x_sign) {
157 
      // if negative, return negative 0, because we know the coefficient
158 
      // is non-zero (would have been caught above)
159 
      res.w[1] = 0xb040000000000000ull;
160 
      res.w[0] = 0x0000000000000000ull;
161 
    } else {
162 
      // if positive, return positive 1, because we know coefficient is
163 
      // non-zero (would have been caught above)
164 
      res.w[1] = 0x3040000000000000ull;
165 
      res.w[0] = 0x0000000000000001ull;
166 
    }
167 
    *pfpsf |= INEXACT_EXCEPTION;
168 
    BID_RETURN (res);
169 
  }
170 
  break;
171 
case ROUNDING_TO_ZERO:
172 
  // if (exp <= -p) return -0.0 or +0.0
173 
  if (x_exp <= 0x2ffc000000000000ull) { // 0x2ffc000000000000ull == -34
174 
    res.w[1] = x_sign | 0x3040000000000000ull;
175 
    res.w[0] = 0x0000000000000000ull;
176 
    *pfpsf |= INEXACT_EXCEPTION;
177 
    BID_RETURN (res);
178 
  }
179 
  break;
180 
}
181 
 
182 
  // q = nr. of decimal digits in x
183 
  //  determine first the nr. of bits in x
184 
if (C1.w[1] == 0) {
185 
  if (C1.w[0] >= 0x0020000000000000ull) {        // x >= 2^53
186 
    // split the 64-bit value in two 32-bit halves to avoid rounding errors
187 
    if (C1.w[0] >= 0x0000000100000000ull) {      // x >= 2^32
188 
      tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
189 
      x_nr_bits =
190 
        33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
191 
    } else {    // x < 2^32
192 
      tmp1.d = (double) (C1.w[0]);       // exact conversion
193 
      x_nr_bits =
194 
        1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
195 
    }
196 
  } else {      // if x < 2^53
197 
    tmp1.d = (double) C1.w[0];   // exact conversion
198 
    x_nr_bits =
199 
      1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
200 
  }
201 
} else {        // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
202 
  tmp1.d = (double) C1.w[1];    // exact conversion
203 
  x_nr_bits =
204 
    65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
205 
}
206 
 
207 
q = nr_digits[x_nr_bits - 1].digits;
208 
if (q == 0) {
209 
  q = nr_digits[x_nr_bits - 1].digits1;
210 
  if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi ||
211 
      (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi &&
212 
       C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
213 
    q++;
214 
}
215 
exp = (x_exp >> 49) - 6176;
216 
if (exp >= 0) {  // -exp <= 0
217 
  // the argument is an integer already
218 
  res.w[1] = x.w[1];
219 
  res.w[0] = x.w[0];
220 
  BID_RETURN (res);
221 
}
222 
  // exp < 0
223 
switch (rnd_mode) {
224 
case ROUNDING_TO_NEAREST:
225 
  if ((q + exp) >= 0) {  // exp < 0 and 1 <= -exp <= q
226 
    // need to shift right -exp digits from the coefficient; exp will be 0
227 
    ind = -exp; // 1 <= ind <= 34; ind is a synonym for 'x'
228 
    // chop off ind digits from the lower part of C1
229 
    // C1 = C1 + 1/2 * 10^x where the result C1 fits in 127 bits
230 
    tmp64 = C1.w[0];
231 
    if (ind <= 19) {
232 
      C1.w[0] = C1.w[0] + midpoint64[ind - 1];
233 
    } else {
234 
      C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
235 
      C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
236 
    }
237 
    if (C1.w[0] < tmp64)
238 
      C1.w[1]++;
239 
    // calculate C* and f*
240 
    // C* is actually floor(C*) in this case
241 
    // C* and f* need shifting and masking, as shown by
242 
    // shiftright128[] and maskhigh128[]
243 
    // 1 <= x <= 34
244 
    // kx = 10^(-x) = ten2mk128[ind - 1]
245 
    // C* = (C1 + 1/2 * 10^x) * 10^(-x)
246 
    // the approximation of 10^(-x) was rounded up to 118 bits
247 
    __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
248 
    // determine the value of res and fstar
249 
 
250 
    // determine inexactness of the rounding of C*
251 
    // if (0 < f* - 1/2 < 10^(-x)) then
252 
    //   the result is exact
253 
    // else // if (f* - 1/2 > T*) then
254 
    //   the result is inexact
255 
    // Note: we are going to use ten2mk128[] instead of ten2mk128trunc[]
256 
 
257 
    if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
258 
      // redundant shift = shiftright128[ind - 1]; // shift = 0
259 
      res.w[1] = P256.w[3];
260 
      res.w[0] = P256.w[2];
261 
      // redundant fstar.w[3] = 0;
262 
      // redundant fstar.w[2] = 0;
263 
      fstar.w[1] = P256.w[1];
264 
      fstar.w[0] = P256.w[0];
265 
      // fraction f* < 10^(-x) <=> midpoint
266 
      // f* is in the right position to be compared with
267 
      // 10^(-x) from ten2mk128[]
268 
      // if 0 < fstar < 10^(-x), subtract 1 if odd (for rounding to even)
269 
      if ((res.w[0] & 0x0000000000000001ull) &&  // is result odd?
270 
          ((fstar.w[1] < (ten2mk128[ind - 1].w[1]))
271 
           || ((fstar.w[1] == ten2mk128[ind - 1].w[1])
272 
               && (fstar.w[0] < ten2mk128[ind - 1].w[0])))) {
273 
        // subract 1 to make even
274 
        if (res.w[0]-- == 0) {
275 
          res.w[1]--;
276 
        }
277 
      }
278 
      if (fstar.w[1] > 0x8000000000000000ull ||
279 
          (fstar.w[1] == 0x8000000000000000ull
280 
           && fstar.w[0] > 0x0ull)) {
281 
        // f* > 1/2 and the result may be exact
282 
        tmp64 = fstar.w[1] - 0x8000000000000000ull;     // f* - 1/2
283 
        if (tmp64 > ten2mk128[ind - 1].w[1] ||
284 
            (tmp64 == ten2mk128[ind - 1].w[1] &&
285 
             fstar.w[0] >= ten2mk128[ind - 1].w[0])) {
286 
          // set the inexact flag
287 
          *pfpsf |= INEXACT_EXCEPTION;
288 
        }       // else the result is exact
289 
      } else {  // the result is inexact; f2* <= 1/2
290 
        // set the inexact flag
291 
        *pfpsf |= INEXACT_EXCEPTION;
292 
      }
293 
    } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
294 
      shift = shiftright128[ind - 1];   // 3 <= shift <= 63
295 
      res.w[1] = (P256.w[3] >> shift);
296 
      res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift);
297 
      // redundant fstar.w[3] = 0;
298 
      fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
299 
      fstar.w[1] = P256.w[1];
300 
      fstar.w[0] = P256.w[0];
301 
      // fraction f* < 10^(-x) <=> midpoint
302 
      // f* is in the right position to be compared with
303 
      // 10^(-x) from ten2mk128[]
304 
      if ((res.w[0] & 0x0000000000000001ull) &&  // is result odd?
305 
          fstar.w[2] == 0 && (fstar.w[1] < ten2mk128[ind - 1].w[1] ||
306 
                              (fstar.w[1] == ten2mk128[ind - 1].w[1] &&
307 
                               fstar.w[0] < ten2mk128[ind - 1].w[0]))) {
308 
        // subract 1 to make even
309 
        if (res.w[0]-- == 0) {
310 
          res.w[1]--;
311 
        }
312 
      }
313 
      if (fstar.w[2] > onehalf128[ind - 1] ||
314 
          (fstar.w[2] == onehalf128[ind - 1]
315 
           && (fstar.w[1] || fstar.w[0]))) {
316 
        // f2* > 1/2 and the result may be exact
317 
        // Calculate f2* - 1/2
318 
        tmp64 = fstar.w[2] - onehalf128[ind - 1];
319 
        if (tmp64 || fstar.w[1] > ten2mk128[ind - 1].w[1] ||
320 
            (fstar.w[1] == ten2mk128[ind - 1].w[1] &&
321 
             fstar.w[0] >= ten2mk128[ind - 1].w[0])) {
322 
          // set the inexact flag
323 
          *pfpsf |= INEXACT_EXCEPTION;
324 
        }       // else the result is exact
325 
      } else {  // the result is inexact; f2* <= 1/2
326 
        // set the inexact flag
327 
        *pfpsf |= INEXACT_EXCEPTION;
328 
      }
329 
    } else {    // 22 <= ind - 1 <= 33
330 
      shift = shiftright128[ind - 1] - 64;      // 2 <= shift <= 38
331 
      res.w[1] = 0;
332 
      res.w[0] = P256.w[3] >> shift;
333 
      fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
334 
      fstar.w[2] = P256.w[2];
335 
      fstar.w[1] = P256.w[1];
336 
      fstar.w[0] = P256.w[0];
337 
      // fraction f* < 10^(-x) <=> midpoint
338 
      // f* is in the right position to be compared with
339 
      // 10^(-x) from ten2mk128[]
340 
      if ((res.w[0] & 0x0000000000000001ull) &&  // is result odd?
341 
          fstar.w[3] == 0 && fstar.w[2] == 0 &&
342 
          (fstar.w[1] < ten2mk128[ind - 1].w[1] ||
343 
           (fstar.w[1] == ten2mk128[ind - 1].w[1] &&
344 
            fstar.w[0] < ten2mk128[ind - 1].w[0]))) {
345 
        // subract 1 to make even
346 
        if (res.w[0]-- == 0) {
347 
          res.w[1]--;
348 
        }
349 
      }
350 
      if (fstar.w[3] > onehalf128[ind - 1] ||
351 
          (fstar.w[3] == onehalf128[ind - 1] &&
352 
           (fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
353 
        // f2* > 1/2 and the result may be exact
354 
        // Calculate f2* - 1/2
355 
        tmp64 = fstar.w[3] - onehalf128[ind - 1];
356 
        if (tmp64 || fstar.w[2] || fstar.w[1] > ten2mk128[ind - 1].w[1]
357 
            || (fstar.w[1] == ten2mk128[ind - 1].w[1]
358 
                && fstar.w[0] >= ten2mk128[ind - 1].w[0])) {
359 
          // set the inexact flag
360 
          *pfpsf |= INEXACT_EXCEPTION;
361 
        }       // else the result is exact
362 
      } else {  // the result is inexact; f2* <= 1/2
363 
        // set the inexact flag
364 
        *pfpsf |= INEXACT_EXCEPTION;
365 
      }
366 
    }
367 
    res.w[1] = x_sign | 0x3040000000000000ull | res.w[1];
368 
    BID_RETURN (res);
369 
  } else {      // if ((q + exp) < 0) <=> q < -exp
370 
    // the result is +0 or -0
371 
    res.w[1] = x_sign | 0x3040000000000000ull;
372 
    res.w[0] = 0x0000000000000000ull;
373 
    *pfpsf |= INEXACT_EXCEPTION;
374 
    BID_RETURN (res);
375 
  }
376 
  break;
377 
case ROUNDING_TIES_AWAY:
378 
  if ((q + exp) >= 0) {  // exp < 0 and 1 <= -exp <= q
379 
    // need to shift right -exp digits from the coefficient; exp will be 0
380 
    ind = -exp; // 1 <= ind <= 34; ind is a synonym for 'x'
381 
    // chop off ind digits from the lower part of C1
382 
    // C1 = C1 + 1/2 * 10^x where the result C1 fits in 127 bits
383 
    tmp64 = C1.w[0];
384 
    if (ind <= 19) {
385 
      C1.w[0] = C1.w[0] + midpoint64[ind - 1];
386 
    } else {
387 
      C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
388 
      C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
389 
    }
390 
    if (C1.w[0] < tmp64)
391 
      C1.w[1]++;
392 
    // calculate C* and f*
393 
    // C* is actually floor(C*) in this case
394 
    // C* and f* need shifting and masking, as shown by
395 
    // shiftright128[] and maskhigh128[]
396 
    // 1 <= x <= 34
397 
    // kx = 10^(-x) = ten2mk128[ind - 1]
398 
    // C* = (C1 + 1/2 * 10^x) * 10^(-x)
399 
    // the approximation of 10^(-x) was rounded up to 118 bits
400 
    __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
401 
    // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
402 
    // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
403 
    // if (0 < f* < 10^(-x)) then the result is a midpoint
404 
    //   if floor(C*) is even then C* = floor(C*) - logical right
405 
    //       shift; C* has p decimal digits, correct by Prop. 1)
406 
    //   else if floor(C*) is odd C* = floor(C*)-1 (logical right
407 
    //       shift; C* has p decimal digits, correct by Pr. 1)
408 
    // else
409 
    //   C* = floor(C*) (logical right shift; C has p decimal digits,
410 
    //       correct by Property 1)
411 
    // n = C* * 10^(e+x)
412 
 
413 
    // determine also the inexactness of the rounding of C*
414 
    // if (0 < f* - 1/2 < 10^(-x)) then
415 
    //   the result is exact
416 
    // else // if (f* - 1/2 > T*) then
417 
    //   the result is inexact
418 
    // Note: we are going to use ten2mk128[] instead of ten2mk128trunc[]
419 
    // shift right C* by Ex-128 = shiftright128[ind]
420 
    if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
421 
      // redundant shift = shiftright128[ind - 1]; // shift = 0
422 
      res.w[1] = P256.w[3];
423 
      res.w[0] = P256.w[2];
424 
      // redundant fstar.w[3] = 0;
425 
      // redundant fstar.w[2] = 0;
426 
      fstar.w[1] = P256.w[1];
427 
      fstar.w[0] = P256.w[0];
428 
      if (fstar.w[1] > 0x8000000000000000ull ||
429 
          (fstar.w[1] == 0x8000000000000000ull
430 
           && fstar.w[0] > 0x0ull)) {
431 
        // f* > 1/2 and the result may be exact
432 
        tmp64 = fstar.w[1] - 0x8000000000000000ull;     // f* - 1/2
433 
        if ((tmp64 > ten2mk128[ind - 1].w[1] ||
434 
             (tmp64 == ten2mk128[ind - 1].w[1] &&
435 
              fstar.w[0] >= ten2mk128[ind - 1].w[0]))) {
436 
          // set the inexact flag
437 
          *pfpsf |= INEXACT_EXCEPTION;
438 
        }       // else the result is exact
439 
      } else {  // the result is inexact; f2* <= 1/2
440 
        // set the inexact flag
441 
        *pfpsf |= INEXACT_EXCEPTION;
442 
      }
443 
    } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
444 
      shift = shiftright128[ind - 1];   // 3 <= shift <= 63
445 
      res.w[1] = (P256.w[3] >> shift);
446 
      res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift);
447 
      // redundant fstar.w[3] = 0;
448 
      fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
449 
      fstar.w[1] = P256.w[1];
450 
      fstar.w[0] = P256.w[0];
451 
      if (fstar.w[2] > onehalf128[ind - 1] ||
452 
          (fstar.w[2] == onehalf128[ind - 1]
453 
           && (fstar.w[1] || fstar.w[0]))) {
454 
        // f2* > 1/2 and the result may be exact
455 
        // Calculate f2* - 1/2
456 
        tmp64 = fstar.w[2] - onehalf128[ind - 1];
457 
        if (tmp64 || fstar.w[1] > ten2mk128[ind - 1].w[1] ||
458 
            (fstar.w[1] == ten2mk128[ind - 1].w[1] &&
459 
             fstar.w[0] >= ten2mk128[ind - 1].w[0])) {
460 
          // set the inexact flag
461 
          *pfpsf |= INEXACT_EXCEPTION;
462 
        }       // else the result is exact
463 
      } else {  // the result is inexact; f2* <= 1/2
464 
        // set the inexact flag
465 
        *pfpsf |= INEXACT_EXCEPTION;
466 
      }
467 
    } else {    // 22 <= ind - 1 <= 33
468 
      shift = shiftright128[ind - 1] - 64;      // 2 <= shift <= 38
469 
      res.w[1] = 0;
470 
      res.w[0] = P256.w[3] >> shift;
471 
      fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
472 
      fstar.w[2] = P256.w[2];
473 
      fstar.w[1] = P256.w[1];
474 
      fstar.w[0] = P256.w[0];
475 
      if (fstar.w[3] > onehalf128[ind - 1] ||
476 
          (fstar.w[3] == onehalf128[ind - 1] &&
477 
           (fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
478 
        // f2* > 1/2 and the result may be exact
479 
        // Calculate f2* - 1/2
480 
        tmp64 = fstar.w[3] - onehalf128[ind - 1];
481 
        if (tmp64 || fstar.w[2] || fstar.w[1] > ten2mk128[ind - 1].w[1]
482 
            || (fstar.w[1] == ten2mk128[ind - 1].w[1]
483 
                && fstar.w[0] >= ten2mk128[ind - 1].w[0])) {
484 
          // set the inexact flag
485 
          *pfpsf |= INEXACT_EXCEPTION;
486 
        }       // else the result is exact
487 
      } else {  // the result is inexact; f2* <= 1/2
488 
        // set the inexact flag
489 
        *pfpsf |= INEXACT_EXCEPTION;
490 
      }
491 
    }
492 
    // if the result was a midpoint, it was already rounded away from zero
493 
    res.w[1] |= x_sign | 0x3040000000000000ull;
494 
    BID_RETURN (res);
495 
  } else {      // if ((q + exp) < 0) <=> q < -exp
496 
    // the result is +0 or -0
497 
    res.w[1] = x_sign | 0x3040000000000000ull;
498 
    res.w[0] = 0x0000000000000000ull;
499 
    *pfpsf |= INEXACT_EXCEPTION;
500 
    BID_RETURN (res);
501 
  }
502 
  break;
503 
case ROUNDING_DOWN:
504 
  if ((q + exp) > 0) {   // exp < 0 and 1 <= -exp < q
505 
    // need to shift right -exp digits from the coefficient; exp will be 0
506 
    ind = -exp; // 1 <= ind <= 34; ind is a synonym for 'x'
507 
    // (number of digits to be chopped off)
508 
    // chop off ind digits from the lower part of C1
509 
    // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate
510 
    // FOR ROUND_TO_ZERO, WE DON'T NEED TO ADD 1/2 ULP
511 
    // FOR ROUND_TO_POSITIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF POSITIVE
512 
    // FOR ROUND_TO_NEGATIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF NEGATIVE
513 
    // tmp64 = C1.w[0];
514 
    // if (ind <= 19) {
515 
    //   C1.w[0] = C1.w[0] + midpoint64[ind - 1];
516 
    // } else {
517 
    //   C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
518 
    //   C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
519 
    // }
520 
    // if (C1.w[0] < tmp64) C1.w[1]++;
521 
    // if carry-out from C1.w[0], increment C1.w[1]
522 
    // calculate C* and f*
523 
    // C* is actually floor(C*) in this case
524 
    // C* and f* need shifting and masking, as shown by
525 
    // shiftright128[] and maskhigh128[]
526 
    // 1 <= x <= 34
527 
    // kx = 10^(-x) = ten2mk128[ind - 1]
528 
    // C* = (C1 + 1/2 * 10^x) * 10^(-x)
529 
    // the approximation of 10^(-x) was rounded up to 118 bits
530 
    __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
531 
    if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
532 
      res.w[1] = P256.w[3];
533 
      res.w[0] = P256.w[2];
534 
      // redundant fstar.w[3] = 0;
535 
      // redundant fstar.w[2] = 0;
536 
      // redundant fstar.w[1] = P256.w[1];
537 
      // redundant fstar.w[0] = P256.w[0];
538 
      // fraction f* > 10^(-x) <=> inexact
539 
      // f* is in the right position to be compared with
540 
      // 10^(-x) from ten2mk128[]
541 
      if ((P256.w[1] > ten2mk128[ind - 1].w[1])
542 
          || (P256.w[1] == ten2mk128[ind - 1].w[1]
543 
              && (P256.w[0] >= ten2mk128[ind - 1].w[0]))) {
544 
        *pfpsf |= INEXACT_EXCEPTION;
545 
        // if positive, the truncated value is already the correct result
546 
        if (x_sign) {   // if negative
547 
          if (++res.w[0] == 0) {
548 
            res.w[1]++;
549 
          }
550 
        }
551 
      }
552 
    } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
553 
      shift = shiftright128[ind - 1];   // 0 <= shift <= 102
554 
      res.w[1] = (P256.w[3] >> shift);
555 
      res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift);
556 
      // redundant fstar.w[3] = 0;
557 
      fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
558 
      fstar.w[1] = P256.w[1];
559 
      fstar.w[0] = P256.w[0];
560 
      // fraction f* > 10^(-x) <=> inexact
561 
      // f* is in the right position to be compared with
562 
      // 10^(-x) from ten2mk128[]
563 
      if (fstar.w[2] || fstar.w[1] > ten2mk128[ind - 1].w[1] ||
564 
          (fstar.w[1] == ten2mk128[ind - 1].w[1] &&
565 
           fstar.w[0] >= ten2mk128[ind - 1].w[0])) {
566 
        *pfpsf |= INEXACT_EXCEPTION;
567 
        // if positive, the truncated value is already the correct result
568 
        if (x_sign) {   // if negative
569 
          if (++res.w[0] == 0) {
570 
            res.w[1]++;
571 
          }
572 
        }
573 
      }
574 
    } else {    // 22 <= ind - 1 <= 33
575 
      shift = shiftright128[ind - 1] - 64;      // 2 <= shift <= 38
576 
      res.w[1] = 0;
577 
      res.w[0] = P256.w[3] >> shift;
578 
      fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
579 
      fstar.w[2] = P256.w[2];
580 
      fstar.w[1] = P256.w[1];
581 
      fstar.w[0] = P256.w[0];
582 
      // fraction f* > 10^(-x) <=> inexact
583 
      // f* is in the right position to be compared with
584 
      // 10^(-x) from ten2mk128[]
585 
      if (fstar.w[3] || fstar.w[2]
586 
          || fstar.w[1] > ten2mk128[ind - 1].w[1]
587 
          || (fstar.w[1] == ten2mk128[ind - 1].w[1]
588 
              && fstar.w[0] >= ten2mk128[ind - 1].w[0])) {
589 
        *pfpsf |= INEXACT_EXCEPTION;
590 
        // if positive, the truncated value is already the correct result
591 
        if (x_sign) {   // if negative
592 
          if (++res.w[0] == 0) {
593 
            res.w[1]++;
594 
          }
595 
        }
596 
      }
597 
    }
598 
    res.w[1] = x_sign | 0x3040000000000000ull | res.w[1];
599 
    BID_RETURN (res);
600 
  } else {      // if exp < 0 and q + exp <= 0
601 
    if (x_sign) {       // negative rounds down to -1.0
602 
      res.w[1] = 0xb040000000000000ull;
603 
      res.w[0] = 0x0000000000000001ull;
604 
    } else {    // positive rpunds down to +0.0
605 
      res.w[1] = 0x3040000000000000ull;
606 
      res.w[0] = 0x0000000000000000ull;
607 
    }
608 
    *pfpsf |= INEXACT_EXCEPTION;
609 
    BID_RETURN (res);
610 
  }
611 
  break;
612 
case ROUNDING_UP:
613 
  if ((q + exp) > 0) {   // exp < 0 and 1 <= -exp < q
614 
    // need to shift right -exp digits from the coefficient; exp will be 0
615 
    ind = -exp; // 1 <= ind <= 34; ind is a synonym for 'x'
616 
    // (number of digits to be chopped off)
617 
    // chop off ind digits from the lower part of C1
618 
    // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate
619 
    // FOR ROUND_TO_ZERO, WE DON'T NEED TO ADD 1/2 ULP
620 
    // FOR ROUND_TO_POSITIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF POSITIVE
621 
    // FOR ROUND_TO_NEGATIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF NEGATIVE
622 
    // tmp64 = C1.w[0];
623 
    // if (ind <= 19) {
624 
    //   C1.w[0] = C1.w[0] + midpoint64[ind - 1];
625 
    // } else {
626 
    //   C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
627 
    //   C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
628 
    // }
629 
    // if (C1.w[0] < tmp64) C1.w[1]++;
630 
    // if carry-out from C1.w[0], increment C1.w[1]
631 
    // calculate C* and f*
632 
    // C* is actually floor(C*) in this case
633 
    // C* and f* need shifting and masking, as shown by
634 
    // shiftright128[] and maskhigh128[]
635 
    // 1 <= x <= 34
636 
    // kx = 10^(-x) = ten2mk128[ind - 1]
637 
    // C* = C1 * 10^(-x)
638 
    // the approximation of 10^(-x) was rounded up to 118 bits
639 
    __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
640 
    if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
641 
      res.w[1] = P256.w[3];
642 
      res.w[0] = P256.w[2];
643 
      // redundant fstar.w[3] = 0;
644 
      // redundant fstar.w[2] = 0;
645 
      // redundant fstar.w[1] = P256.w[1];
646 
      // redundant fstar.w[0] = P256.w[0];
647 
      // fraction f* > 10^(-x) <=> inexact
648 
      // f* is in the right position to be compared with
649 
      // 10^(-x) from ten2mk128[]
650 
      if ((P256.w[1] > ten2mk128[ind - 1].w[1])
651 
          || (P256.w[1] == ten2mk128[ind - 1].w[1]
652 
              && (P256.w[0] >= ten2mk128[ind - 1].w[0]))) {
653 
        *pfpsf |= INEXACT_EXCEPTION;
654 
        // if negative, the truncated value is already the correct result
655 
        if (!x_sign) {  // if positive
656 
          if (++res.w[0] == 0) {
657 
            res.w[1]++;
658 
          }
659 
        }
660 
      }
661 
    } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
662 
      shift = shiftright128[ind - 1];   // 3 <= shift <= 63
663 
      res.w[1] = (P256.w[3] >> shift);
664 
      res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift);
665 
      // redundant fstar.w[3] = 0;
666 
      fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
667 
      fstar.w[1] = P256.w[1];
668 
      fstar.w[0] = P256.w[0];
669 
      // fraction f* > 10^(-x) <=> inexact
670 
      // f* is in the right position to be compared with
671 
      // 10^(-x) from ten2mk128[]
672 
      if (fstar.w[2] || fstar.w[1] > ten2mk128[ind - 1].w[1] ||
673 
          (fstar.w[1] == ten2mk128[ind - 1].w[1] &&
674 
           fstar.w[0] >= ten2mk128[ind - 1].w[0])) {
675 
        *pfpsf |= INEXACT_EXCEPTION;
676 
        // if negative, the truncated value is already the correct result
677 
        if (!x_sign) {  // if positive
678 
          if (++res.w[0] == 0) {
679 
            res.w[1]++;
680 
          }
681 
        }
682 
      }
683 
    } else {    // 22 <= ind - 1 <= 33
684 
      shift = shiftright128[ind - 1] - 64;      // 2 <= shift <= 38
685 
      res.w[1] = 0;
686 
      res.w[0] = P256.w[3] >> shift;
687 
      fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
688 
      fstar.w[2] = P256.w[2];
689 
      fstar.w[1] = P256.w[1];
690 
      fstar.w[0] = P256.w[0];
691 
      // fraction f* > 10^(-x) <=> inexact
692 
      // f* is in the right position to be compared with
693 
      // 10^(-x) from ten2mk128[]
694 
      if (fstar.w[3] || fstar.w[2]
695 
          || fstar.w[1] > ten2mk128[ind - 1].w[1]
696 
          || (fstar.w[1] == ten2mk128[ind - 1].w[1]
697 
              && fstar.w[0] >= ten2mk128[ind - 1].w[0])) {
698 
        *pfpsf |= INEXACT_EXCEPTION;
699 
        // if negative, the truncated value is already the correct result
700 
        if (!x_sign) {  // if positive
701 
          if (++res.w[0] == 0) {
702 
            res.w[1]++;
703 
          }
704 
        }
705 
      }
706 
    }
707 
    res.w[1] = x_sign | 0x3040000000000000ull | res.w[1];
708 
    BID_RETURN (res);
709 
  } else {      // if exp < 0 and q + exp <= 0
710 
    if (x_sign) {       // negative rounds up to -0.0
711 
      res.w[1] = 0xb040000000000000ull;
712 
      res.w[0] = 0x0000000000000000ull;
713 
    } else {    // positive rpunds up to +1.0
714 
      res.w[1] = 0x3040000000000000ull;
715 
      res.w[0] = 0x0000000000000001ull;
716 
    }
717 
    *pfpsf |= INEXACT_EXCEPTION;
718 
    BID_RETURN (res);
719 
  }
720 
  break;
721 
case ROUNDING_TO_ZERO:
722 
  if ((q + exp) > 0) {   // exp < 0 and 1 <= -exp < q
723 
    // need to shift right -exp digits from the coefficient; exp will be 0
724 
    ind = -exp; // 1 <= ind <= 34; ind is a synonym for 'x'
725 
    // (number of digits to be chopped off)
726 
    // chop off ind digits from the lower part of C1
727 
    // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate
728 
    // FOR ROUND_TO_ZERO, WE DON'T NEED TO ADD 1/2 ULP
729 
    // FOR ROUND_TO_POSITIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF POSITIVE
730 
    // FOR ROUND_TO_NEGATIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF NEGATIVE
731 
    //tmp64 = C1.w[0];
732 
    // if (ind <= 19) {
733 
    //   C1.w[0] = C1.w[0] + midpoint64[ind - 1];
734 
    // } else {
735 
    //   C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
736 
    //   C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
737 
    // }
738 
    // if (C1.w[0] < tmp64) C1.w[1]++;
739 
    // if carry-out from C1.w[0], increment C1.w[1]
740 
    // calculate C* and f*
741 
    // C* is actually floor(C*) in this case
742 
    // C* and f* need shifting and masking, as shown by
743 
    // shiftright128[] and maskhigh128[]
744 
    // 1 <= x <= 34
745 
    // kx = 10^(-x) = ten2mk128[ind - 1]
746 
    // C* = (C1 + 1/2 * 10^x) * 10^(-x)
747 
    // the approximation of 10^(-x) was rounded up to 118 bits
748 
    __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
749 
    if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
750 
      res.w[1] = P256.w[3];
751 
      res.w[0] = P256.w[2];
752 
      // redundant fstar.w[3] = 0;
753 
      // redundant fstar.w[2] = 0;
754 
      // redundant fstar.w[1] = P256.w[1];
755 
      // redundant fstar.w[0] = P256.w[0];
756 
      // fraction f* > 10^(-x) <=> inexact
757 
      // f* is in the right position to be compared with
758 
      // 10^(-x) from ten2mk128[]
759 
      if ((P256.w[1] > ten2mk128[ind - 1].w[1])
760 
          || (P256.w[1] == ten2mk128[ind - 1].w[1]
761 
              && (P256.w[0] >= ten2mk128[ind - 1].w[0]))) {
762 
        *pfpsf |= INEXACT_EXCEPTION;
763 
      }
764 
    } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
765 
      shift = shiftright128[ind - 1];   // 3 <= shift <= 63
766 
      res.w[1] = (P256.w[3] >> shift);
767 
      res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift);
768 
      // redundant fstar.w[3] = 0;
769 
      fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
770 
      fstar.w[1] = P256.w[1];
771 
      fstar.w[0] = P256.w[0];
772 
      // fraction f* > 10^(-x) <=> inexact
773 
      // f* is in the right position to be compared with
774 
      // 10^(-x) from ten2mk128[]
775 
      if (fstar.w[2] || fstar.w[1] > ten2mk128[ind - 1].w[1] ||
776 
          (fstar.w[1] == ten2mk128[ind - 1].w[1] &&
777 
           fstar.w[0] >= ten2mk128[ind - 1].w[0])) {
778 
        *pfpsf |= INEXACT_EXCEPTION;
779 
      }
780 
    } else {    // 22 <= ind - 1 <= 33
781 
      shift = shiftright128[ind - 1] - 64;      // 2 <= shift <= 38
782 
      res.w[1] = 0;
783 
      res.w[0] = P256.w[3] >> shift;
784 
      fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
785 
      fstar.w[2] = P256.w[2];
786 
      fstar.w[1] = P256.w[1];
787 
      fstar.w[0] = P256.w[0];
788 
      // fraction f* > 10^(-x) <=> inexact
789 
      // f* is in the right position to be compared with
790 
      // 10^(-x) from ten2mk128[]
791 
      if (fstar.w[3] || fstar.w[2]
792 
          || fstar.w[1] > ten2mk128[ind - 1].w[1]
793 
          || (fstar.w[1] == ten2mk128[ind - 1].w[1]
794 
              && fstar.w[0] >= ten2mk128[ind - 1].w[0])) {
795 
        *pfpsf |= INEXACT_EXCEPTION;
796 
      }
797 
    }
798 
    res.w[1] = x_sign | 0x3040000000000000ull | res.w[1];
799 
    BID_RETURN (res);
800 
  } else {      // if exp < 0 and q + exp <= 0 the result is +0 or -0
801 
    res.w[1] = x_sign | 0x3040000000000000ull;
802 
    res.w[0] = 0x0000000000000000ull;
803 
    *pfpsf |= INEXACT_EXCEPTION;
804 
    BID_RETURN (res);
805 
  }
806 
  break;
807 
}
808 
 
809 
BID_RETURN (res);
810 
}
811 
 
812 
/*****************************************************************************
813 
 *  BID128_round_integral_nearest_even
814 
 ****************************************************************************/
815 
 
816 
BID128_FUNCTION_ARG1_NORND (bid128_round_integral_nearest_even, x)
817 
 
818 
     UINT128 res;
819 
     UINT64 x_sign;
820 
     UINT64 x_exp;
821 
     int exp;                   // unbiased exponent
822 
  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
823 
     UINT64 tmp64;
824 
     BID_UI64DOUBLE tmp1;
825 
     unsigned int x_nr_bits;
826 
     int q, ind, shift;
827 
     UINT128 C1;
828 
  // UINT128 res is C* at first - represents up to 34 decimal digits ~ 113 bits
829 
     UINT256 fstar;
830 
     UINT256 P256;
831 
 
832 
  // check for NaN or Infinity
833 
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
834 
    // x is special
835 
if ((x.w[1] & MASK_NAN) == MASK_NAN) {  // x is NAN
836 
  // if x = NaN, then res = Q (x)
837 
  // check first for non-canonical NaN payload
838 
  if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
839 
      (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
840 
       (x.w[0] > 0x38c15b09ffffffffull))) {
841 
    x.w[1] = x.w[1] & 0xffffc00000000000ull;
842 
    x.w[0] = 0x0ull;
843 
  }
844 
  if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {      // x is SNAN
845 
    // set invalid flag
846 
    *pfpsf |= INVALID_EXCEPTION;
847 
    // return quiet (x)
848 
    res.w[1] = x.w[1] & 0xfc003fffffffffffull;  // clear out also G[6]-G[16]
849 
    res.w[0] = x.w[0];
850 
  } else {      // x is QNaN
851 
    // return x
852 
    res.w[1] = x.w[1] & 0xfc003fffffffffffull;  // clear out G[6]-G[16]
853 
    res.w[0] = x.w[0];
854 
  }
855 
  BID_RETURN (res)
856 
} else {        // x is not a NaN, so it must be infinity
857 
  if ((x.w[1] & MASK_SIGN) == 0x0ull) { // x is +inf
858 
    // return +inf
859 
    res.w[1] = 0x7800000000000000ull;
860 
    res.w[0] = 0x0000000000000000ull;
861 
  } else {      // x is -inf
862 
    // return -inf
863 
    res.w[1] = 0xf800000000000000ull;
864 
    res.w[0] = 0x0000000000000000ull;
865 
  }
866 
  BID_RETURN (res);
867 
}
868 
}
869 
  // unpack x
870 
x_sign = x.w[1] & MASK_SIGN;    // 0 for positive, MASK_SIGN for negative
871 
C1.w[1] = x.w[1] & MASK_COEFF;
872 
C1.w[0] = x.w[0];
873 
 
874 
  // check for non-canonical values (treated as zero)
875 
if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {        // G0_G1=11
876 
  // non-canonical
877 
  x_exp = (x.w[1] << 2) & MASK_EXP;     // biased and shifted left 49 bits
878 
  C1.w[1] = 0;   // significand high
879 
  C1.w[0] = 0;    // significand low
880 
} else {        // G0_G1 != 11
881 
  x_exp = x.w[1] & MASK_EXP;    // biased and shifted left 49 bits
882 
  if (C1.w[1] > 0x0001ed09bead87c0ull ||
883 
      (C1.w[1] == 0x0001ed09bead87c0ull
884 
       && C1.w[0] > 0x378d8e63ffffffffull)) {
885 
    // x is non-canonical if coefficient is larger than 10^34 -1
886 
    C1.w[1] = 0;
887 
    C1.w[0] = 0;
888 
  } else {      // canonical
889 
    ;
890 
  }
891 
}
892 
 
893 
  // test for input equal to zero
894 
if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
895 
  // x is 0
896 
  // return 0 preserving the sign bit and the preferred exponent
897 
  // of MAX(Q(x), 0)
898 
  if (x_exp <= (0x1820ull << 49)) {
899 
    res.w[1] = (x.w[1] & 0x8000000000000000ull) | 0x3040000000000000ull;
900 
  } else {
901 
    res.w[1] = x_sign | x_exp;
902 
  }
903 
  res.w[0] = 0x0000000000000000ull;
904 
  BID_RETURN (res);
905 
}
906 
  // x is not special and is not zero
907 
 
908 
  // if (exp <= -(p+1)) return 0
909 
if (x_exp <= 0x2ffa000000000000ull) {   // 0x2ffa000000000000ull == -35
910 
  res.w[1] = x_sign | 0x3040000000000000ull;
911 
  res.w[0] = 0x0000000000000000ull;
912 
  BID_RETURN (res);
913 
}
914 
  // q = nr. of decimal digits in x
915 
  //  determine first the nr. of bits in x
916 
if (C1.w[1] == 0) {
917 
  if (C1.w[0] >= 0x0020000000000000ull) {        // x >= 2^53
918 
    // split the 64-bit value in two 32-bit halves to avoid rounding errors
919 
    if (C1.w[0] >= 0x0000000100000000ull) {      // x >= 2^32
920 
      tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
921 
      x_nr_bits =
922 
        33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
923 
    } else {    // x < 2^32
924 
      tmp1.d = (double) (C1.w[0]);       // exact conversion
925 
      x_nr_bits =
926 
        1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
927 
    }
928 
  } else {      // if x < 2^53
929 
    tmp1.d = (double) C1.w[0];   // exact conversion
930 
    x_nr_bits =
931 
      1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
932 
  }
933 
} else {        // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
934 
  tmp1.d = (double) C1.w[1];    // exact conversion
935 
  x_nr_bits =
936 
    65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
937 
}
938 
 
939 
q = nr_digits[x_nr_bits - 1].digits;
940 
if (q == 0) {
941 
  q = nr_digits[x_nr_bits - 1].digits1;
942 
  if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
943 
      || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi &&
944 
          C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
945 
    q++;
946 
}
947 
exp = (x_exp >> 49) - 6176;
948 
if (exp >= 0) {  // -exp <= 0
949 
  // the argument is an integer already
950 
  res.w[1] = x.w[1];
951 
  res.w[0] = x.w[0];
952 
  BID_RETURN (res);
953 
} else if ((q + exp) >= 0) {     // exp < 0 and 1 <= -exp <= q
954 
  // need to shift right -exp digits from the coefficient; the exp will be 0
955 
  ind = -exp;   // 1 <= ind <= 34; ind is a synonym for 'x'
956 
  // chop off ind digits from the lower part of C1
957 
  // C1 = C1 + 1/2 * 10^x where the result C1 fits in 127 bits
958 
  tmp64 = C1.w[0];
959 
  if (ind <= 19) {
960 
    C1.w[0] = C1.w[0] + midpoint64[ind - 1];
961 
  } else {
962 
    C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
963 
    C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
964 
  }
965 
  if (C1.w[0] < tmp64)
966 
    C1.w[1]++;
967 
  // calculate C* and f*
968 
  // C* is actually floor(C*) in this case
969 
  // C* and f* need shifting and masking, as shown by
970 
  // shiftright128[] and maskhigh128[]
971 
  // 1 <= x <= 34
972 
  // kx = 10^(-x) = ten2mk128[ind - 1]
973 
  // C* = (C1 + 1/2 * 10^x) * 10^(-x)
974 
  // the approximation of 10^(-x) was rounded up to 118 bits
975 
  __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
976 
  // determine the value of res and fstar
977 
  if (ind - 1 <= 2) {   // 0 <= ind - 1 <= 2 => shift = 0
978 
    // redundant shift = shiftright128[ind - 1]; // shift = 0
979 
    res.w[1] = P256.w[3];
980 
    res.w[0] = P256.w[2];
981 
    // redundant fstar.w[3] = 0;
982 
    // redundant fstar.w[2] = 0;
983 
    // redundant fstar.w[1] = P256.w[1];
984 
    // redundant fstar.w[0] = P256.w[0];
985 
    // fraction f* < 10^(-x) <=> midpoint
986 
    // f* is in the right position to be compared with
987 
    // 10^(-x) from ten2mk128[]
988 
    // if 0 < fstar < 10^(-x), subtract 1 if odd (for rounding to even)
989 
    if ((res.w[0] & 0x0000000000000001ull) &&    // is result odd?
990 
        ((P256.w[1] < (ten2mk128[ind - 1].w[1]))
991 
         || ((P256.w[1] == ten2mk128[ind - 1].w[1])
992 
             && (P256.w[0] < ten2mk128[ind - 1].w[0])))) {
993 
      // subract 1 to make even
994 
      if (res.w[0]-- == 0) {
995 
        res.w[1]--;
996 
      }
997 
    }
998 
  } else if (ind - 1 <= 21) {   // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
999 
    shift = shiftright128[ind - 1];     // 3 <= shift <= 63
1000 
    res.w[1] = (P256.w[3] >> shift);
1001 
    res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift);
1002 
    // redundant fstar.w[3] = 0;
1003 
    fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
1004 
    fstar.w[1] = P256.w[1];
1005 
    fstar.w[0] = P256.w[0];
1006 
    // fraction f* < 10^(-x) <=> midpoint
1007 
    // f* is in the right position to be compared with
1008 
    // 10^(-x) from ten2mk128[]
1009 
    if ((res.w[0] & 0x0000000000000001ull) &&    // is result odd?
1010 
        fstar.w[2] == 0 && (fstar.w[1] < ten2mk128[ind - 1].w[1] ||
1011 
                            (fstar.w[1] == ten2mk128[ind - 1].w[1] &&
1012 
                             fstar.w[0] < ten2mk128[ind - 1].w[0]))) {
1013 
      // subract 1 to make even
1014 
      if (res.w[0]-- == 0) {
1015 
        res.w[1]--;
1016 
      }
1017 
    }
1018 
  } else {      // 22 <= ind - 1 <= 33
1019 
    shift = shiftright128[ind - 1] - 64;        // 2 <= shift <= 38
1020 
    res.w[1] = 0;
1021 
    res.w[0] = P256.w[3] >> shift;
1022 
    fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
1023 
    fstar.w[2] = P256.w[2];
1024 
    fstar.w[1] = P256.w[1];
1025 
    fstar.w[0] = P256.w[0];
1026 
    // fraction f* < 10^(-x) <=> midpoint
1027 
    // f* is in the right position to be compared with
1028 
    // 10^(-x) from ten2mk128[]
1029 
    if ((res.w[0] & 0x0000000000000001ull) &&    // is result odd?
1030 
        fstar.w[3] == 0 && fstar.w[2] == 0
1031 
        && (fstar.w[1] < ten2mk128[ind - 1].w[1]
1032 
            || (fstar.w[1] == ten2mk128[ind - 1].w[1]
1033 
                && fstar.w[0] < ten2mk128[ind - 1].w[0]))) {
1034 
      // subract 1 to make even
1035 
      if (res.w[0]-- == 0) {
1036 
        res.w[1]--;
1037 
      }
1038 
    }
1039 
  }
1040 
  res.w[1] = x_sign | 0x3040000000000000ull | res.w[1];
1041 
  BID_RETURN (res);
1042 
} else {        // if ((q + exp) < 0) <=> q < -exp
1043 
  // the result is +0 or -0
1044 
  res.w[1] = x_sign | 0x3040000000000000ull;
1045 
  res.w[0] = 0x0000000000000000ull;
1046 
  BID_RETURN (res);
1047 
}
1048 
}
1049 
 
1050 
/*****************************************************************************
1051 
 *  BID128_round_integral_negative
1052 
 ****************************************************************************/
1053 
 
1054 
BID128_FUNCTION_ARG1_NORND (bid128_round_integral_negative, x)
1055 
 
1056 
     UINT128 res;
1057 
     UINT64 x_sign;
1058 
     UINT64 x_exp;
1059 
     int exp;                   // unbiased exponent
1060 
  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo
1061 
  // (all are UINT64)
1062 
     BID_UI64DOUBLE tmp1;
1063 
     unsigned int x_nr_bits;
1064 
     int q, ind, shift;
1065 
     UINT128 C1;
1066 
  // UINT128 res is C* at first - represents up to 34 decimal digits ~
1067 
  // 113 bits
1068 
     UINT256 fstar;
1069 
     UINT256 P256;
1070 
 
1071 
  // check for NaN or Infinity
1072 
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
1073 
    // x is special
1074 
if ((x.w[1] & MASK_NAN) == MASK_NAN) {  // x is NAN
1075 
  // if x = NaN, then res = Q (x)
1076 
  // check first for non-canonical NaN payload
1077 
  if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
1078 
      (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
1079 
       (x.w[0] > 0x38c15b09ffffffffull))) {
1080 
    x.w[1] = x.w[1] & 0xffffc00000000000ull;
1081 
    x.w[0] = 0x0ull;
1082 
  }
1083 
  if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {      // x is SNAN
1084 
    // set invalid flag
1085 
    *pfpsf |= INVALID_EXCEPTION;
1086 
    // return quiet (x)
1087 
    res.w[1] = x.w[1] & 0xfc003fffffffffffull;  // clear out also G[6]-G[16]
1088 
    res.w[0] = x.w[0];
1089 
  } else {      // x is QNaN
1090 
    // return x
1091 
    res.w[1] = x.w[1] & 0xfc003fffffffffffull;  // clear out G[6]-G[16]
1092 
    res.w[0] = x.w[0];
1093 
  }
1094 
  BID_RETURN (res)
1095 
} else {        // x is not a NaN, so it must be infinity
1096 
  if ((x.w[1] & MASK_SIGN) == 0x0ull) { // x is +inf
1097 
    // return +inf
1098 
    res.w[1] = 0x7800000000000000ull;
1099 
    res.w[0] = 0x0000000000000000ull;
1100 
  } else {      // x is -inf
1101 
    // return -inf
1102 
    res.w[1] = 0xf800000000000000ull;
1103 
    res.w[0] = 0x0000000000000000ull;
1104 
  }
1105 
  BID_RETURN (res);
1106 
}
1107 
}
1108 
  // unpack x
1109 
x_sign = x.w[1] & MASK_SIGN;    // 0 for positive, MASK_SIGN for negative
1110 
C1.w[1] = x.w[1] & MASK_COEFF;
1111 
C1.w[0] = x.w[0];
1112 
 
1113 
  // check for non-canonical values (treated as zero)
1114 
if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {        // G0_G1=11
1115 
  // non-canonical
1116 
  x_exp = (x.w[1] << 2) & MASK_EXP;     // biased and shifted left 49 bits
1117 
  C1.w[1] = 0;   // significand high
1118 
  C1.w[0] = 0;    // significand low
1119 
} else {        // G0_G1 != 11
1120 
  x_exp = x.w[1] & MASK_EXP;    // biased and shifted left 49 bits
1121 
  if (C1.w[1] > 0x0001ed09bead87c0ull ||
1122 
      (C1.w[1] == 0x0001ed09bead87c0ull
1123 
       && C1.w[0] > 0x378d8e63ffffffffull)) {
1124 
    // x is non-canonical if coefficient is larger than 10^34 -1
1125 
    C1.w[1] = 0;
1126 
    C1.w[0] = 0;
1127 
  } else {      // canonical
1128 
    ;
1129 
  }
1130 
}
1131 
 
1132 
  // test for input equal to zero
1133 
if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
1134 
  // x is 0
1135 
  // return 0 preserving the sign bit and the preferred exponent
1136 
  // of MAX(Q(x), 0)
1137 
  if (x_exp <= (0x1820ull << 49)) {
1138 
    res.w[1] = (x.w[1] & 0x8000000000000000ull) | 0x3040000000000000ull;
1139 
  } else {
1140 
    res.w[1] = x_sign | x_exp;
1141 
  }
1142 
  res.w[0] = 0x0000000000000000ull;
1143 
  BID_RETURN (res);
1144 
}
1145 
  // x is not special and is not zero
1146 
 
1147 
  // if (exp <= -p) return -1.0 or +0.0
1148 
if (x_exp <= 0x2ffc000000000000ull) {   // 0x2ffc000000000000ull == -34
1149 
  if (x_sign) {
1150 
    // if negative, return negative 1, because we know the coefficient
1151 
    // is non-zero (would have been caught above)
1152 
    res.w[1] = 0xb040000000000000ull;
1153 
    res.w[0] = 0x0000000000000001ull;
1154 
  } else {
1155 
    // if positive, return positive 0, because we know coefficient is
1156 
    // non-zero (would have been caught above)
1157 
    res.w[1] = 0x3040000000000000ull;
1158 
    res.w[0] = 0x0000000000000000ull;
1159 
  }
1160 
  BID_RETURN (res);
1161 
}
1162 
  // q = nr. of decimal digits in x
1163 
  // determine first the nr. of bits in x
1164 
if (C1.w[1] == 0) {
1165 
  if (C1.w[0] >= 0x0020000000000000ull) {        // x >= 2^53
1166 
    // split the 64-bit value in two 32-bit halves to avoid rounding errors
1167 
    if (C1.w[0] >= 0x0000000100000000ull) {      // x >= 2^32
1168 
      tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
1169 
      x_nr_bits =
1170 
        33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
1171 
    } else {    // x < 2^32
1172 
      tmp1.d = (double) (C1.w[0]);       // exact conversion
1173 
      x_nr_bits =
1174 
        1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
1175 
    }
1176 
  } else {      // if x < 2^53
1177 
    tmp1.d = (double) C1.w[0];   // exact conversion
1178 
    x_nr_bits =
1179 
      1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
1180 
  }
1181 
} else {        // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
1182 
  tmp1.d = (double) C1.w[1];    // exact conversion
1183 
  x_nr_bits =
1184 
    65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
1185 
}
1186 
 
1187 
q = nr_digits[x_nr_bits - 1].digits;
1188 
if (q == 0) {
1189 
  q = nr_digits[x_nr_bits - 1].digits1;
1190 
  if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi ||
1191 
      (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi &&
1192 
       C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
1193 
    q++;
1194 
}
1195 
exp = (x_exp >> 49) - 6176;
1196 
if (exp >= 0) {  // -exp <= 0
1197 
  // the argument is an integer already
1198 
  res.w[1] = x.w[1];
1199 
  res.w[0] = x.w[0];
1200 
  BID_RETURN (res);
1201 
} else if ((q + exp) > 0) {      // exp < 0 and 1 <= -exp < q
1202 
  // need to shift right -exp digits from the coefficient; the exp will be 0
1203 
  ind = -exp;   // 1 <= ind <= 34; ind is a synonym for 'x'
1204 
  // (number of digits to be chopped off)
1205 
  // chop off ind digits from the lower part of C1
1206 
  // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate
1207 
  // FOR ROUND_TO_ZERO, WE DON'T NEED TO ADD 1/2 ULP
1208 
  // FOR ROUND_TO_POSITIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF POSITIVE
1209 
  // FOR ROUND_TO_NEGATIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF NEGATIVE
1210 
  //tmp64 = C1.w[0];
1211 
  // if (ind <= 19) {
1212 
  //   C1.w[0] = C1.w[0] + midpoint64[ind - 1];
1213 
  // } else {
1214 
  //   C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
1215 
  //   C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
1216 
  // }
1217 
  // if (C1.w[0] < tmp64) C1.w[1]++;
1218 
  // if carry-out from C1.w[0], increment C1.w[1]
1219 
  // calculate C* and f*
1220 
  // C* is actually floor(C*) in this case
1221 
  // C* and f* need shifting and masking, as shown by
1222 
  // shiftright128[] and maskhigh128[]
1223 
  // 1 <= x <= 34
1224 
  // kx = 10^(-x) = ten2mk128[ind - 1]
1225 
  // C* = (C1 + 1/2 * 10^x) * 10^(-x)
1226 
  // the approximation of 10^(-x) was rounded up to 118 bits
1227 
  __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
1228 
  if (ind - 1 <= 2) {   // 0 <= ind - 1 <= 2 => shift = 0
1229 
    res.w[1] = P256.w[3];
1230 
    res.w[0] = P256.w[2];
1231 
    // if positive, the truncated value is already the correct result
1232 
    if (x_sign) {       // if negative
1233 
      // redundant fstar.w[3] = 0;
1234 
      // redundant fstar.w[2] = 0;
1235 
      // redundant fstar.w[1] = P256.w[1];
1236 
      // redundant fstar.w[0] = P256.w[0];
1237 
      // fraction f* > 10^(-x) <=> inexact
1238 
      // f* is in the right position to be compared with
1239 
      // 10^(-x) from ten2mk128[]
1240 
      if ((P256.w[1] > ten2mk128[ind - 1].w[1])
1241 
          || (P256.w[1] == ten2mk128[ind - 1].w[1]
1242 
              && (P256.w[0] >= ten2mk128[ind - 1].w[0]))) {
1243 
        if (++res.w[0] == 0) {
1244 
          res.w[1]++;
1245 
        }
1246 
      }
1247 
    }
1248 
  } else if (ind - 1 <= 21) {   // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
1249 
    shift = shiftright128[ind - 1];     // 0 <= shift <= 102
1250 
    res.w[1] = (P256.w[3] >> shift);
1251 
    res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift);
1252 
    // if positive, the truncated value is already the correct result
1253 
    if (x_sign) {       // if negative
1254 
      // redundant fstar.w[3] = 0;
1255 
      fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
1256 
      fstar.w[1] = P256.w[1];
1257 
      fstar.w[0] = P256.w[0];
1258 
      // fraction f* > 10^(-x) <=> inexact
1259 
      // f* is in the right position to be compared with
1260 
      // 10^(-x) from ten2mk128[]
1261 
      if (fstar.w[2] || fstar.w[1] > ten2mk128[ind - 1].w[1] ||
1262 
          (fstar.w[1] == ten2mk128[ind - 1].w[1] &&
1263 
           fstar.w[0] >= ten2mk128[ind - 1].w[0])) {
1264 
        if (++res.w[0] == 0) {
1265 
          res.w[1]++;
1266 
        }
1267 
      }
1268 
    }
1269 
  } else {      // 22 <= ind - 1 <= 33
1270 
    shift = shiftright128[ind - 1] - 64;        // 2 <= shift <= 38
1271 
    res.w[1] = 0;
1272 
    res.w[0] = P256.w[3] >> shift;
1273 
    // if positive, the truncated value is already the correct result
1274 
    if (x_sign) {       // if negative
1275 
      fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
1276 
      fstar.w[2] = P256.w[2];
1277 
      fstar.w[1] = P256.w[1];
1278 
      fstar.w[0] = P256.w[0];
1279 
      // fraction f* > 10^(-x) <=> inexact
1280 
      // f* is in the right position to be compared with
1281 
      // 10^(-x) from ten2mk128[]
1282 
      if (fstar.w[3] || fstar.w[2]
1283 
          || fstar.w[1] > ten2mk128[ind - 1].w[1]
1284 
          || (fstar.w[1] == ten2mk128[ind - 1].w[1]
1285 
              && fstar.w[0] >= ten2mk128[ind - 1].w[0])) {
1286 
        if (++res.w[0] == 0) {
1287 
          res.w[1]++;
1288 
        }
1289 
      }
1290 
    }
1291 
  }
1292 
  res.w[1] = x_sign | 0x3040000000000000ull | res.w[1];
1293 
  BID_RETURN (res);
1294 
} else {        // if exp < 0 and q + exp <= 0
1295 
  if (x_sign) { // negative rounds down to -1.0
1296 
    res.w[1] = 0xb040000000000000ull;
1297 
    res.w[0] = 0x0000000000000001ull;
1298 
  } else {      // positive rpunds down to +0.0
1299 
    res.w[1] = 0x3040000000000000ull;
1300 
    res.w[0] = 0x0000000000000000ull;
1301 
  }
1302 
  BID_RETURN (res);
1303 
}
1304 
}
1305 
 
1306 
/*****************************************************************************
1307 
 *  BID128_round_integral_positive
1308 
 ****************************************************************************/
1309 
 
1310 
BID128_FUNCTION_ARG1_NORND (bid128_round_integral_positive, x)
1311 
 
1312 
     UINT128 res;
1313 
     UINT64 x_sign;
1314 
     UINT64 x_exp;
1315 
     int exp;                   // unbiased exponent
1316 
  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo
1317 
  // (all are UINT64)
1318 
     BID_UI64DOUBLE tmp1;
1319 
     unsigned int x_nr_bits;
1320 
     int q, ind, shift;
1321 
     UINT128 C1;
1322 
  // UINT128 res is C* at first - represents up to 34 decimal digits ~
1323 
  // 113 bits
1324 
     UINT256 fstar;
1325 
     UINT256 P256;
1326 
 
1327 
  // check for NaN or Infinity
1328 
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
1329 
    // x is special
1330 
if ((x.w[1] & MASK_NAN) == MASK_NAN) {  // x is NAN
1331 
  // if x = NaN, then res = Q (x)
1332 
  // check first for non-canonical NaN payload
1333 
  if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
1334 
      (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
1335 
       (x.w[0] > 0x38c15b09ffffffffull))) {
1336 
    x.w[1] = x.w[1] & 0xffffc00000000000ull;
1337 
    x.w[0] = 0x0ull;
1338 
  }
1339 
  if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {      // x is SNAN
1340 
    // set invalid flag
1341 
    *pfpsf |= INVALID_EXCEPTION;
1342 
    // return quiet (x)
1343 
    res.w[1] = x.w[1] & 0xfc003fffffffffffull;  // clear out also G[6]-G[16]
1344 
    res.w[0] = x.w[0];
1345 
  } else {      // x is QNaN
1346 
    // return x
1347 
    res.w[1] = x.w[1] & 0xfc003fffffffffffull;  // clear out G[6]-G[16]
1348 
    res.w[0] = x.w[0];
1349 
  }
1350 
  BID_RETURN (res)
1351 
} else {        // x is not a NaN, so it must be infinity
1352 
  if ((x.w[1] & MASK_SIGN) == 0x0ull) { // x is +inf
1353 
    // return +inf
1354 
    res.w[1] = 0x7800000000000000ull;
1355 
    res.w[0] = 0x0000000000000000ull;
1356 
  } else {      // x is -inf
1357 
    // return -inf
1358 
    res.w[1] = 0xf800000000000000ull;
1359 
    res.w[0] = 0x0000000000000000ull;
1360 
  }
1361 
  BID_RETURN (res);
1362 
}
1363 
}
1364 
  // unpack x
1365 
x_sign = x.w[1] & MASK_SIGN;    // 0 for positive, MASK_SIGN for negative
1366 
C1.w[1] = x.w[1] & MASK_COEFF;
1367 
C1.w[0] = x.w[0];
1368 
 
1369 
  // check for non-canonical values (treated as zero)
1370 
if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {        // G0_G1=11
1371 
  // non-canonical
1372 
  x_exp = (x.w[1] << 2) & MASK_EXP;     // biased and shifted left 49 bits
1373 
  C1.w[1] = 0;   // significand high
1374 
  C1.w[0] = 0;    // significand low
1375 
} else {        // G0_G1 != 11
1376 
  x_exp = x.w[1] & MASK_EXP;    // biased and shifted left 49 bits
1377 
  if (C1.w[1] > 0x0001ed09bead87c0ull ||
1378 
      (C1.w[1] == 0x0001ed09bead87c0ull
1379 
       && C1.w[0] > 0x378d8e63ffffffffull)) {
1380 
    // x is non-canonical if coefficient is larger than 10^34 -1
1381 
    C1.w[1] = 0;
1382 
    C1.w[0] = 0;
1383 
  } else {      // canonical
1384 
    ;
1385 
  }
1386 
}
1387 
 
1388 
  // test for input equal to zero
1389 
if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
1390 
  // x is 0
1391 
  // return 0 preserving the sign bit and the preferred exponent
1392 
  // of MAX(Q(x), 0)
1393 
  if (x_exp <= (0x1820ull << 49)) {
1394 
    res.w[1] = (x.w[1] & 0x8000000000000000ull) | 0x3040000000000000ull;
1395 
  } else {
1396 
    res.w[1] = x_sign | x_exp;
1397 
  }
1398 
  res.w[0] = 0x0000000000000000ull;
1399 
  BID_RETURN (res);
1400 
}
1401 
  // x is not special and is not zero
1402 
 
1403 
  // if (exp <= -p) return -0.0 or +1.0
1404 
if (x_exp <= 0x2ffc000000000000ull) {   // 0x2ffc000000000000ull == -34
1405 
  if (x_sign) {
1406 
    // if negative, return negative 0, because we know the coefficient
1407 
    // is non-zero (would have been caught above)
1408 
    res.w[1] = 0xb040000000000000ull;
1409 
    res.w[0] = 0x0000000000000000ull;
1410 
  } else {
1411 
    // if positive, return positive 1, because we know coefficient is
1412 
    // non-zero (would have been caught above)
1413 
    res.w[1] = 0x3040000000000000ull;
1414 
    res.w[0] = 0x0000000000000001ull;
1415 
  }
1416 
  BID_RETURN (res);
1417 
}
1418 
  // q = nr. of decimal digits in x
1419 
  // determine first the nr. of bits in x
1420 
if (C1.w[1] == 0) {
1421 
  if (C1.w[0] >= 0x0020000000000000ull) {        // x >= 2^53
1422 
    // split 64-bit value in two 32-bit halves to avoid rounding errors
1423 
    if (C1.w[0] >= 0x0000000100000000ull) {      // x >= 2^32
1424 
      tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
1425 
      x_nr_bits =
1426 
        33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
1427 
    } else {    // x < 2^32
1428 
      tmp1.d = (double) (C1.w[0]);       // exact conversion
1429 
      x_nr_bits =
1430 
        1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
1431 
    }
1432 
  } else {      // if x < 2^53
1433 
    tmp1.d = (double) C1.w[0];   // exact conversion
1434 
    x_nr_bits =
1435 
      1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
1436 
  }
1437 
} else {        // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
1438 
  tmp1.d = (double) C1.w[1];    // exact conversion
1439 
  x_nr_bits =
1440 
    65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
1441 
}
1442 
 
1443 
q = nr_digits[x_nr_bits - 1].digits;
1444 
if (q == 0) {
1445 
  q = nr_digits[x_nr_bits - 1].digits1;
1446 
  if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi ||
1447 
      (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi &&
1448 
       C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
1449 
    q++;
1450 
}
1451 
exp = (x_exp >> 49) - 6176;
1452 
if (exp >= 0) {  // -exp <= 0
1453 
  // the argument is an integer already
1454 
  res.w[1] = x.w[1];
1455 
  res.w[0] = x.w[0];
1456 
  BID_RETURN (res);
1457 
} else if ((q + exp) > 0) {      // exp < 0 and 1 <= -exp < q
1458 
  // need to shift right -exp digits from the coefficient; exp will be 0
1459 
  ind = -exp;   // 1 <= ind <= 34; ind is a synonym for 'x'
1460 
  // (number of digits to be chopped off)
1461 
  // chop off ind digits from the lower part of C1
1462 
  // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate
1463 
  // FOR ROUND_TO_ZERO, WE DON'T NEED TO ADD 1/2 ULP
1464 
  // FOR ROUND_TO_POSITIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF POSITIVE
1465 
  // FOR ROUND_TO_NEGATIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF NEGATIVE
1466 
  // tmp64 = C1.w[0];
1467 
  // if (ind <= 19) {
1468 
  //   C1.w[0] = C1.w[0] + midpoint64[ind - 1];
1469 
  // } else {
1470 
  //   C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
1471 
  //   C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
1472 
  // }
1473 
  // if (C1.w[0] < tmp64) C1.w[1]++;
1474 
  // if carry-out from C1.w[0], increment C1.w[1]
1475 
  // calculate C* and f*
1476 
  // C* is actually floor(C*) in this case
1477 
  // C* and f* need shifting and masking, as shown by
1478 
  // shiftright128[] and maskhigh128[]
1479 
  // 1 <= x <= 34
1480 
  // kx = 10^(-x) = ten2mk128[ind - 1]
1481 
  // C* = C1 * 10^(-x)
1482 
  // the approximation of 10^(-x) was rounded up to 118 bits
1483 
  __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
1484 
  if (ind - 1 <= 2) {   // 0 <= ind - 1 <= 2 => shift = 0
1485 
    res.w[1] = P256.w[3];
1486 
    res.w[0] = P256.w[2];
1487 
    // if negative, the truncated value is already the correct result
1488 
    if (!x_sign) {      // if positive
1489 
      // redundant fstar.w[3] = 0;
1490 
      // redundant fstar.w[2] = 0;
1491 
      // redundant fstar.w[1] = P256.w[1];
1492 
      // redundant fstar.w[0] = P256.w[0];
1493 
      // fraction f* > 10^(-x) <=> inexact
1494 
      // f* is in the right position to be compared with
1495 
      // 10^(-x) from ten2mk128[]
1496 
      if ((P256.w[1] > ten2mk128[ind - 1].w[1])
1497 
          || (P256.w[1] == ten2mk128[ind - 1].w[1]
1498 
              && (P256.w[0] >= ten2mk128[ind - 1].w[0]))) {
1499 
        if (++res.w[0] == 0) {
1500 
          res.w[1]++;
1501 
        }
1502 
      }
1503 
    }
1504 
  } else if (ind - 1 <= 21) {   // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
1505 
    shift = shiftright128[ind - 1];     // 3 <= shift <= 63
1506 
    res.w[1] = (P256.w[3] >> shift);
1507 
    res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift);
1508 
    // if negative, the truncated value is already the correct result
1509 
    if (!x_sign) {      // if positive
1510 
      // redundant fstar.w[3] = 0;
1511 
      fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
1512 
      fstar.w[1] = P256.w[1];
1513 
      fstar.w[0] = P256.w[0];
1514 
      // fraction f* > 10^(-x) <=> inexact
1515 
      // f* is in the right position to be compared with
1516 
      // 10^(-x) from ten2mk128[]
1517 
      if (fstar.w[2] || fstar.w[1] > ten2mk128[ind - 1].w[1] ||
1518 
          (fstar.w[1] == ten2mk128[ind - 1].w[1] &&
1519 
           fstar.w[0] >= ten2mk128[ind - 1].w[0])) {
1520 
        if (++res.w[0] == 0) {
1521 
          res.w[1]++;
1522 
        }
1523 
      }
1524 
    }
1525 
  } else {      // 22 <= ind - 1 <= 33
1526 
    shift = shiftright128[ind - 1] - 64;        // 2 <= shift <= 38
1527 
    res.w[1] = 0;
1528 
    res.w[0] = P256.w[3] >> shift;
1529 
    // if negative, the truncated value is already the correct result
1530 
    if (!x_sign) {      // if positive
1531 
      fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
1532 
      fstar.w[2] = P256.w[2];
1533 
      fstar.w[1] = P256.w[1];
1534 
      fstar.w[0] = P256.w[0];
1535 
      // fraction f* > 10^(-x) <=> inexact
1536 
      // f* is in the right position to be compared with
1537 
      // 10^(-x) from ten2mk128[]
1538 
      if (fstar.w[3] || fstar.w[2]
1539 
          || fstar.w[1] > ten2mk128[ind - 1].w[1]
1540 
          || (fstar.w[1] == ten2mk128[ind - 1].w[1]
1541 
              && fstar.w[0] >= ten2mk128[ind - 1].w[0])) {
1542 
        if (++res.w[0] == 0) {
1543 
          res.w[1]++;
1544 
        }
1545 
      }
1546 
    }
1547 
  }
1548 
  res.w[1] = x_sign | 0x3040000000000000ull | res.w[1];
1549 
  BID_RETURN (res);
1550 
} else {        // if exp < 0 and q + exp <= 0
1551 
  if (x_sign) { // negative rounds up to -0.0
1552 
    res.w[1] = 0xb040000000000000ull;
1553 
    res.w[0] = 0x0000000000000000ull;
1554 
  } else {      // positive rpunds up to +1.0
1555 
    res.w[1] = 0x3040000000000000ull;
1556 
    res.w[0] = 0x0000000000000001ull;
1557 
  }
1558 
  BID_RETURN (res);
1559 
}
1560 
}
1561 
 
1562 
/*****************************************************************************
1563 
 *  BID128_round_integral_zero
1564 
 ****************************************************************************/
1565 
 
1566 
BID128_FUNCTION_ARG1_NORND (bid128_round_integral_zero, x)
1567 
 
1568 
     UINT128 res;
1569 
     UINT64 x_sign;
1570 
     UINT64 x_exp;
1571 
     int exp;                   // unbiased exponent
1572 
  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo
1573 
  // (all are UINT64)
1574 
     BID_UI64DOUBLE tmp1;
1575 
     unsigned int x_nr_bits;
1576 
     int q, ind, shift;
1577 
     UINT128 C1;
1578 
  // UINT128 res is C* at first - represents up to 34 decimal digits ~
1579 
  // 113 bits
1580 
     UINT256 P256;
1581 
 
1582 
  // check for NaN or Infinity
1583 
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
1584 
    // x is special
1585 
if ((x.w[1] & MASK_NAN) == MASK_NAN) {  // x is NAN
1586 
  // if x = NaN, then res = Q (x)
1587 
  // check first for non-canonical NaN payload
1588 
  if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
1589 
      (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
1590 
       (x.w[0] > 0x38c15b09ffffffffull))) {
1591 
    x.w[1] = x.w[1] & 0xffffc00000000000ull;
1592 
    x.w[0] = 0x0ull;
1593 
  }
1594 
  if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {      // x is SNAN
1595 
    // set invalid flag
1596 
    *pfpsf |= INVALID_EXCEPTION;
1597 
    // return quiet (x)
1598 
    res.w[1] = x.w[1] & 0xfc003fffffffffffull;  // clear out also G[6]-G[16]
1599 
    res.w[0] = x.w[0];
1600 
  } else {      // x is QNaN
1601 
    // return x
1602 
    res.w[1] = x.w[1] & 0xfc003fffffffffffull;  // clear out G[6]-G[16]
1603 
    res.w[0] = x.w[0];
1604 
  }
1605 
  BID_RETURN (res)
1606 
} else {        // x is not a NaN, so it must be infinity
1607 
  if ((x.w[1] & MASK_SIGN) == 0x0ull) { // x is +inf
1608 
    // return +inf
1609 
    res.w[1] = 0x7800000000000000ull;
1610 
    res.w[0] = 0x0000000000000000ull;
1611 
  } else {      // x is -inf
1612 
    // return -inf
1613 
    res.w[1] = 0xf800000000000000ull;
1614 
    res.w[0] = 0x0000000000000000ull;
1615 
  }
1616 
  BID_RETURN (res);
1617 
}
1618 
}
1619 
  // unpack x
1620 
x_sign = x.w[1] & MASK_SIGN;    // 0 for positive, MASK_SIGN for negative
1621 
C1.w[1] = x.w[1] & MASK_COEFF;
1622 
C1.w[0] = x.w[0];
1623 
 
1624 
  // check for non-canonical values (treated as zero)
1625 
if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {        // G0_G1=11
1626 
  // non-canonical
1627 
  x_exp = (x.w[1] << 2) & MASK_EXP;     // biased and shifted left 49 bits
1628 
  C1.w[1] = 0;   // significand high
1629 
  C1.w[0] = 0;    // significand low
1630 
} else {        // G0_G1 != 11
1631 
  x_exp = x.w[1] & MASK_EXP;    // biased and shifted left 49 bits
1632 
  if (C1.w[1] > 0x0001ed09bead87c0ull ||
1633 
      (C1.w[1] == 0x0001ed09bead87c0ull
1634 
       && C1.w[0] > 0x378d8e63ffffffffull)) {
1635 
    // x is non-canonical if coefficient is larger than 10^34 -1
1636 
    C1.w[1] = 0;
1637 
    C1.w[0] = 0;
1638 
  } else {      // canonical
1639 
    ;
1640 
  }
1641 
}
1642 
 
1643 
  // test for input equal to zero
1644 
if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
1645 
  // x is 0
1646 
  // return 0 preserving the sign bit and the preferred exponent
1647 
  // of MAX(Q(x), 0)
1648 
  if (x_exp <= (0x1820ull << 49)) {
1649 
    res.w[1] = (x.w[1] & 0x8000000000000000ull) | 0x3040000000000000ull;
1650 
  } else {
1651 
    res.w[1] = x_sign | x_exp;
1652 
  }
1653 
  res.w[0] = 0x0000000000000000ull;
1654 
  BID_RETURN (res);
1655 
}
1656 
  // x is not special and is not zero
1657 
 
1658 
  // if (exp <= -p) return -0.0 or +0.0
1659 
if (x_exp <= 0x2ffc000000000000ull) {   // 0x2ffc000000000000ull == -34
1660 
  res.w[1] = x_sign | 0x3040000000000000ull;
1661 
  res.w[0] = 0x0000000000000000ull;
1662 
  BID_RETURN (res);
1663 
}
1664 
  // q = nr. of decimal digits in x
1665 
  // determine first the nr. of bits in x
1666 
if (C1.w[1] == 0) {
1667 
  if (C1.w[0] >= 0x0020000000000000ull) {        // x >= 2^53
1668 
    // split the 64-bit value in two 32-bit halves to avoid rounding errors
1669 
    if (C1.w[0] >= 0x0000000100000000ull) {      // x >= 2^32
1670 
      tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
1671 
      x_nr_bits =
1672 
        33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
1673 
    } else {    // x < 2^32
1674 
      tmp1.d = (double) (C1.w[0]);       // exact conversion
1675 
      x_nr_bits =
1676 
        1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
1677 
    }
1678 
  } else {      // if x < 2^53
1679 
    tmp1.d = (double) C1.w[0];   // exact conversion
1680 
    x_nr_bits =
1681 
      1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
1682 
  }
1683 
} else {        // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
1684 
  tmp1.d = (double) C1.w[1];    // exact conversion
1685 
  x_nr_bits =
1686 
    65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
1687 
}
1688 
 
1689 
q = nr_digits[x_nr_bits - 1].digits;
1690 
if (q == 0) {
1691 
  q = nr_digits[x_nr_bits - 1].digits1;
1692 
  if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi ||
1693 
      (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi &&
1694 
       C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
1695 
    q++;
1696 
}
1697 
exp = (x_exp >> 49) - 6176;
1698 
if (exp >= 0) {  // -exp <= 0
1699 
  // the argument is an integer already
1700 
  res.w[1] = x.w[1];
1701 
  res.w[0] = x.w[0];
1702 
  BID_RETURN (res);
1703 
} else if ((q + exp) > 0) {      // exp < 0 and 1 <= -exp < q
1704 
  // need to shift right -exp digits from the coefficient; the exp will be 0
1705 
  ind = -exp;   // 1 <= ind <= 34; ind is a synonym for 'x'
1706 
  // (number of digits to be chopped off)
1707 
  // chop off ind digits from the lower part of C1
1708 
  // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate
1709 
  // FOR ROUND_TO_ZERO, WE DON'T NEED TO ADD 1/2 ULP
1710 
  // FOR ROUND_TO_POSITIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF POSITIVE
1711 
  // FOR ROUND_TO_NEGATIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF NEGATIVE
1712 
  //tmp64 = C1.w[0];
1713 
  // if (ind <= 19) {
1714 
  //   C1.w[0] = C1.w[0] + midpoint64[ind - 1];
1715 
  // } else {
1716 
  //   C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
1717 
  //   C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
1718 
  // }
1719 
  // if (C1.w[0] < tmp64) C1.w[1]++;
1720 
  // if carry-out from C1.w[0], increment C1.w[1]
1721 
  // calculate C* and f*
1722 
  // C* is actually floor(C*) in this case
1723 
  // C* and f* need shifting and masking, as shown by
1724 
  // shiftright128[] and maskhigh128[]
1725 
  // 1 <= x <= 34
1726 
  // kx = 10^(-x) = ten2mk128[ind - 1]
1727 
  // C* = (C1 + 1/2 * 10^x) * 10^(-x)
1728 
  // the approximation of 10^(-x) was rounded up to 118 bits
1729 
  __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
1730 
  if (ind - 1 <= 2) {   // 0 <= ind - 1 <= 2 => shift = 0
1731 
    res.w[1] = P256.w[3];
1732 
    res.w[0] = P256.w[2];
1733 
  } else if (ind - 1 <= 21) {   // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
1734 
    shift = shiftright128[ind - 1];     // 3 <= shift <= 63
1735 
    res.w[1] = (P256.w[3] >> shift);
1736 
    res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift);
1737 
  } else {      // 22 <= ind - 1 <= 33
1738 
    shift = shiftright128[ind - 1] - 64;        // 2 <= shift <= 38
1739 
    res.w[1] = 0;
1740 
    res.w[0] = P256.w[3] >> shift;
1741 
  }
1742 
  res.w[1] = x_sign | 0x3040000000000000ull | res.w[1];
1743 
  BID_RETURN (res);
1744 
} else {        // if exp < 0 and q + exp <= 0 the result is +0 or -0
1745 
  res.w[1] = x_sign | 0x3040000000000000ull;
1746 
  res.w[0] = 0x0000000000000000ull;
1747 
  BID_RETURN (res);
1748 
}
1749 
}
1750 
 
1751 
/*****************************************************************************
1752 
 *  BID128_round_integral_nearest_away
1753 
 ****************************************************************************/
1754 
 
1755 
BID128_FUNCTION_ARG1_NORND (bid128_round_integral_nearest_away, x)
1756 
 
1757 
     UINT128 res;
1758 
     UINT64 x_sign;
1759 
     UINT64 x_exp;
1760 
     int exp;                   // unbiased exponent
1761 
  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo
1762 
  // (all are UINT64)
1763 
     UINT64 tmp64;
1764 
     BID_UI64DOUBLE tmp1;
1765 
     unsigned int x_nr_bits;
1766 
     int q, ind, shift;
1767 
     UINT128 C1;
1768 
  // UINT128 res is C* at first - represents up to 34 decimal digits ~
1769 
  // 113 bits
1770 
  // UINT256 fstar;
1771 
     UINT256 P256;
1772 
 
1773 
  // check for NaN or Infinity
1774 
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
1775 
    // x is special
1776 
if ((x.w[1] & MASK_NAN) == MASK_NAN) {  // x is NAN
1777 
  // if x = NaN, then res = Q (x)
1778 
  // check first for non-canonical NaN payload
1779 
  if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
1780 
      (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
1781 
       (x.w[0] > 0x38c15b09ffffffffull))) {
1782 
    x.w[1] = x.w[1] & 0xffffc00000000000ull;
1783 
    x.w[0] = 0x0ull;
1784 
  }
1785 
  if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {      // x is SNAN
1786 
    // set invalid flag
1787 
    *pfpsf |= INVALID_EXCEPTION;
1788 
    // return quiet (x)
1789 
    res.w[1] = x.w[1] & 0xfc003fffffffffffull;  // clear out also G[6]-G[16]
1790 
    res.w[0] = x.w[0];
1791 
  } else {      // x is QNaN
1792 
    // return x
1793 
    res.w[1] = x.w[1] & 0xfc003fffffffffffull;  // clear out G[6]-G[16]
1794 
    res.w[0] = x.w[0];
1795 
  }
1796 
  BID_RETURN (res)
1797 
} else {        // x is not a NaN, so it must be infinity
1798 
  if ((x.w[1] & MASK_SIGN) == 0x0ull) { // x is +inf
1799 
    // return +inf
1800 
    res.w[1] = 0x7800000000000000ull;
1801 
    res.w[0] = 0x0000000000000000ull;
1802 
  } else {      // x is -inf
1803 
    // return -inf
1804 
    res.w[1] = 0xf800000000000000ull;
1805 
    res.w[0] = 0x0000000000000000ull;
1806 
  }
1807 
  BID_RETURN (res);
1808 
}
1809 
}
1810 
  // unpack x
1811 
x_sign = x.w[1] & MASK_SIGN;    // 0 for positive, MASK_SIGN for negative
1812 
C1.w[1] = x.w[1] & MASK_COEFF;
1813 
C1.w[0] = x.w[0];
1814 
 
1815 
  // check for non-canonical values (treated as zero)
1816 
if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {        // G0_G1=11
1817 
  // non-canonical
1818 
  x_exp = (x.w[1] << 2) & MASK_EXP;     // biased and shifted left 49 bits
1819 
  C1.w[1] = 0;   // significand high
1820 
  C1.w[0] = 0;    // significand low
1821 
} else {        // G0_G1 != 11
1822 
  x_exp = x.w[1] & MASK_EXP;    // biased and shifted left 49 bits
1823 
  if (C1.w[1] > 0x0001ed09bead87c0ull ||
1824 
      (C1.w[1] == 0x0001ed09bead87c0ull
1825 
       && C1.w[0] > 0x378d8e63ffffffffull)) {
1826 
    // x is non-canonical if coefficient is larger than 10^34 -1
1827 
    C1.w[1] = 0;
1828 
    C1.w[0] = 0;
1829 
  } else {      // canonical
1830 
    ;
1831 
  }
1832 
}
1833 
 
1834 
  // test for input equal to zero
1835 
if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
1836 
  // x is 0
1837 
  // return 0 preserving the sign bit and the preferred exponent
1838 
  // of MAX(Q(x), 0)
1839 
  if (x_exp <= (0x1820ull << 49)) {
1840 
    res.w[1] = (x.w[1] & 0x8000000000000000ull) | 0x3040000000000000ull;
1841 
  } else {
1842 
    res.w[1] = x_sign | x_exp;
1843 
  }
1844 
  res.w[0] = 0x0000000000000000ull;
1845 
  BID_RETURN (res);
1846 
}
1847 
  // x is not special and is not zero
1848 
 
1849 
  // if (exp <= -(p+1)) return 0.0
1850 
if (x_exp <= 0x2ffa000000000000ull) {   // 0x2ffa000000000000ull == -35
1851 
  res.w[1] = x_sign | 0x3040000000000000ull;
1852 
  res.w[0] = 0x0000000000000000ull;
1853 
  BID_RETURN (res);
1854 
}
1855 
  // q = nr. of decimal digits in x
1856 
  //  determine first the nr. of bits in x
1857 
if (C1.w[1] == 0) {
1858 
  if (C1.w[0] >= 0x0020000000000000ull) {        // x >= 2^53
1859 
    // split the 64-bit value in two 32-bit halves to avoid rounding errors
1860 
    if (C1.w[0] >= 0x0000000100000000ull) {      // x >= 2^32
1861 
      tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
1862 
      x_nr_bits =
1863 
        33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
1864 
    } else {    // x < 2^32
1865 
      tmp1.d = (double) (C1.w[0]);       // exact conversion
1866 
      x_nr_bits =
1867 
        1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
1868 
    }
1869 
  } else {      // if x < 2^53
1870 
    tmp1.d = (double) C1.w[0];   // exact conversion
1871 
    x_nr_bits =
1872 
      1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
1873 
  }
1874 
} else {        // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
1875 
  tmp1.d = (double) C1.w[1];    // exact conversion
1876 
  x_nr_bits =
1877 
    65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
1878 
}
1879 
 
1880 
q = nr_digits[x_nr_bits - 1].digits;
1881 
if (q == 0) {
1882 
  q = nr_digits[x_nr_bits - 1].digits1;
1883 
  if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi ||
1884 
      (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi &&
1885 
       C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
1886 
    q++;
1887 
}
1888 
exp = (x_exp >> 49) - 6176;
1889 
if (exp >= 0) {  // -exp <= 0
1890 
  // the argument is an integer already
1891 
  res.w[1] = x.w[1];
1892 
  res.w[0] = x.w[0];
1893 
  BID_RETURN (res);
1894 
} else if ((q + exp) >= 0) {     // exp < 0 and 1 <= -exp <= q
1895 
  // need to shift right -exp digits from the coefficient; the exp will be 0
1896 
  ind = -exp;   // 1 <= ind <= 34; ind is a synonym for 'x'
1897 
  // chop off ind digits from the lower part of C1
1898 
  // C1 = C1 + 1/2 * 10^x where the result C1 fits in 127 bits
1899 
  tmp64 = C1.w[0];
1900 
  if (ind <= 19) {
1901 
    C1.w[0] = C1.w[0] + midpoint64[ind - 1];
1902 
  } else {
1903 
    C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
1904 
    C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
1905 
  }
1906 
  if (C1.w[0] < tmp64)
1907 
    C1.w[1]++;
1908 
  // calculate C* and f*
1909 
  // C* is actually floor(C*) in this case
1910 
  // C* and f* need shifting and masking, as shown by
1911 
  // shiftright128[] and maskhigh128[]
1912 
  // 1 <= x <= 34
1913 
  // kx = 10^(-x) = ten2mk128[ind - 1]
1914 
  // C* = (C1 + 1/2 * 10^x) * 10^(-x)
1915 
  // the approximation of 10^(-x) was rounded up to 118 bits
1916 
  __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
1917 
  // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
1918 
  // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
1919 
  // if (0 < f* < 10^(-x)) then the result is a midpoint
1920 
  //   if floor(C*) is even then C* = floor(C*) - logical right
1921 
  //       shift; C* has p decimal digits, correct by Prop. 1)
1922 
  //   else if floor(C*) is odd C* = floor(C*)-1 (logical right
1923 
  //       shift; C* has p decimal digits, correct by Pr. 1)
1924 
  // else
1925 
  //   C* = floor(C*) (logical right shift; C has p decimal digits,
1926 
  //       correct by Property 1)
1927 
  // n = C* * 10^(e+x)
1928 
 
1929 
  // shift right C* by Ex-128 = shiftright128[ind]
1930 
  if (ind - 1 <= 2) {   // 0 <= ind - 1 <= 2 => shift = 0
1931 
    res.w[1] = P256.w[3];
1932 
    res.w[0] = P256.w[2];
1933 
  } else if (ind - 1 <= 21) {   // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
1934 
    shift = shiftright128[ind - 1];     // 3 <= shift <= 63
1935 
    res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift);
1936 
    res.w[1] = (P256.w[3] >> shift);
1937 
  } else {      // 22 <= ind - 1 <= 33
1938 
    shift = shiftright128[ind - 1];     // 2 <= shift <= 38
1939 
    res.w[1] = 0;
1940 
    res.w[0] = (P256.w[3] >> (shift - 64));      // 2 <= shift - 64 <= 38
1941 
  }
1942 
  // if the result was a midpoint, it was already rounded away from zero
1943 
  res.w[1] |= x_sign | 0x3040000000000000ull;
1944 
  BID_RETURN (res);
1945 
} else {        // if ((q + exp) < 0) <=> q < -exp
1946 
  // the result is +0 or -0
1947 
  res.w[1] = x_sign | 0x3040000000000000ull;
1948 
  res.w[0] = 0x0000000000000000ull;
1949 
  BID_RETURN (res);
1950 
}
1951 
}

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