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Linux/arch/arm/nwfpe/softfloat-macros

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  1 
  2 /*
  3 ===============================================================================
  4 
  5 This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
  6 Arithmetic Package, Release 2.
  7 
  8 Written by John R. Hauser.  This work was made possible in part by the
  9 International Computer Science Institute, located at Suite 600, 1947 Center
 10 Street, Berkeley, California 94704.  Funding was partially provided by the
 11 National Science Foundation under grant MIP-9311980.  The original version
 12 of this code was written as part of a project to build a fixed-point vector
 13 processor in collaboration with the University of California at Berkeley,
 14 overseen by Profs. Nelson Morgan and John Wawrzynek.  More information
 15 is available through the web page
 16 http://www.jhauser.us/arithmetic/SoftFloat-2b/SoftFloat-source.txt
 17 
 18 THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE.  Although reasonable effort
 19 has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
 20 TIMES RESULT IN INCORRECT BEHAVIOR.  USE OF THIS SOFTWARE IS RESTRICTED TO
 21 PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
 22 AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
 23 
 24 Derivative works are acceptable, even for commercial purposes, so long as
 25 (1) they include prominent notice that the work is derivative, and (2) they
 26 include prominent notice akin to these three paragraphs for those parts of
 27 this code that are retained.
 28 
 29 ===============================================================================
 30 */
 31 
 32 /*
 33 -------------------------------------------------------------------------------
 34 Shifts `a' right by the number of bits given in `count'.  If any nonzero
 35 bits are shifted off, they are ``jammed'' into the least significant bit of
 36 the result by setting the least significant bit to 1.  The value of `count'
 37 can be arbitrarily large; in particular, if `count' is greater than 32, the
 38 result will be either 0 or 1, depending on whether `a' is zero or nonzero.
 39 The result is stored in the location pointed to by `zPtr'.
 40 -------------------------------------------------------------------------------
 41 */
 42 INLINE void shift32RightJamming( bits32 a, int16 count, bits32 *zPtr )
 43 {
 44     bits32 z;
 45     if ( count == 0 ) {
 46         z = a;
 47     }
 48     else if ( count < 32 ) {
 49         z = ( a>>count ) | ( ( a<<( ( - count ) & 31 ) ) != 0 );
 50     }
 51     else {
 52         z = ( a != 0 );
 53     }
 54     *zPtr = z;
 55 }
 56 
 57 /*
 58 -------------------------------------------------------------------------------
 59 Shifts `a' right by the number of bits given in `count'.  If any nonzero
 60 bits are shifted off, they are ``jammed'' into the least significant bit of
 61 the result by setting the least significant bit to 1.  The value of `count'
 62 can be arbitrarily large; in particular, if `count' is greater than 64, the
 63 result will be either 0 or 1, depending on whether `a' is zero or nonzero.
 64 The result is stored in the location pointed to by `zPtr'.
 65 -------------------------------------------------------------------------------
 66 */
 67 INLINE void shift64RightJamming( bits64 a, int16 count, bits64 *zPtr )
 68 {
 69     bits64 z;
 70 
 71  __asm__("@shift64RightJamming -- start");   
 72     if ( count == 0 ) {
 73         z = a;
 74     }
 75     else if ( count < 64 ) {
 76         z = ( a>>count ) | ( ( a<<( ( - count ) & 63 ) ) != 0 );
 77     }
 78     else {
 79         z = ( a != 0 );
 80     }
 81  __asm__("@shift64RightJamming -- end");   
 82     *zPtr = z;
 83 }
 84 
 85 /*
 86 -------------------------------------------------------------------------------
 87 Shifts the 128-bit value formed by concatenating `a0' and `a1' right by 64
 88 _plus_ the number of bits given in `count'.  The shifted result is at most
 89 64 nonzero bits; this is stored at the location pointed to by `z0Ptr'.  The
 90 bits shifted off form a second 64-bit result as follows:  The _last_ bit
 91 shifted off is the most-significant bit of the extra result, and the other
 92 63 bits of the extra result are all zero if and only if _all_but_the_last_
 93 bits shifted off were all zero.  This extra result is stored in the location
 94 pointed to by `z1Ptr'.  The value of `count' can be arbitrarily large.
 95     (This routine makes more sense if `a0' and `a1' are considered to form a
 96 fixed-point value with binary point between `a0' and `a1'.  This fixed-point
 97 value is shifted right by the number of bits given in `count', and the
 98 integer part of the result is returned at the location pointed to by
 99 `z0Ptr'.  The fractional part of the result may be slightly corrupted as
100 described above, and is returned at the location pointed to by `z1Ptr'.)
101 -------------------------------------------------------------------------------
102 */
103 INLINE void
104  shift64ExtraRightJamming(
105      bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
106 {
107     bits64 z0, z1;
108     int8 negCount = ( - count ) & 63;
109 
110     if ( count == 0 ) {
111         z1 = a1;
112         z0 = a0;
113     }
114     else if ( count < 64 ) {
115         z1 = ( a0<<negCount ) | ( a1 != 0 );
116         z0 = a0>>count;
117     }
118     else {
119         if ( count == 64 ) {
120             z1 = a0 | ( a1 != 0 );
121         }
122         else {
123             z1 = ( ( a0 | a1 ) != 0 );
124         }
125         z0 = 0;
126     }
127     *z1Ptr = z1;
128     *z0Ptr = z0;
129 
130 }
131 
132 /*
133 -------------------------------------------------------------------------------
134 Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
135 number of bits given in `count'.  Any bits shifted off are lost.  The value
136 of `count' can be arbitrarily large; in particular, if `count' is greater
137 than 128, the result will be 0.  The result is broken into two 64-bit pieces
138 which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
139 -------------------------------------------------------------------------------
140 */
141 INLINE void
142  shift128Right(
143      bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
144 {
145     bits64 z0, z1;
146     int8 negCount = ( - count ) & 63;
147 
148     if ( count == 0 ) {
149         z1 = a1;
150         z0 = a0;
151     }
152     else if ( count < 64 ) {
153         z1 = ( a0<<negCount ) | ( a1>>count );
154         z0 = a0>>count;
155     }
156     else {
157         z1 = ( count < 64 ) ? ( a0>>( count & 63 ) ) : 0;
158         z0 = 0;
159     }
160     *z1Ptr = z1;
161     *z0Ptr = z0;
162 
163 }
164 
165 /*
166 -------------------------------------------------------------------------------
167 Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
168 number of bits given in `count'.  If any nonzero bits are shifted off, they
169 are ``jammed'' into the least significant bit of the result by setting the
170 least significant bit to 1.  The value of `count' can be arbitrarily large;
171 in particular, if `count' is greater than 128, the result will be either 0
172 or 1, depending on whether the concatenation of `a0' and `a1' is zero or
173 nonzero.  The result is broken into two 64-bit pieces which are stored at
174 the locations pointed to by `z0Ptr' and `z1Ptr'.
175 -------------------------------------------------------------------------------
176 */
177 INLINE void
178  shift128RightJamming(
179      bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
180 {
181     bits64 z0, z1;
182     int8 negCount = ( - count ) & 63;
183 
184     if ( count == 0 ) {
185         z1 = a1;
186         z0 = a0;
187     }
188     else if ( count < 64 ) {
189         z1 = ( a0<<negCount ) | ( a1>>count ) | ( ( a1<<negCount ) != 0 );
190         z0 = a0>>count;
191     }
192     else {
193         if ( count == 64 ) {
194             z1 = a0 | ( a1 != 0 );
195         }
196         else if ( count < 128 ) {
197             z1 = ( a0>>( count & 63 ) ) | ( ( ( a0<<negCount ) | a1 ) != 0 );
198         }
199         else {
200             z1 = ( ( a0 | a1 ) != 0 );
201         }
202         z0 = 0;
203     }
204     *z1Ptr = z1;
205     *z0Ptr = z0;
206 
207 }
208 
209 /*
210 -------------------------------------------------------------------------------
211 Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' right
212 by 64 _plus_ the number of bits given in `count'.  The shifted result is
213 at most 128 nonzero bits; these are broken into two 64-bit pieces which are
214 stored at the locations pointed to by `z0Ptr' and `z1Ptr'.  The bits shifted
215 off form a third 64-bit result as follows:  The _last_ bit shifted off is
216 the most-significant bit of the extra result, and the other 63 bits of the
217 extra result are all zero if and only if _all_but_the_last_ bits shifted off
218 were all zero.  This extra result is stored in the location pointed to by
219 `z2Ptr'.  The value of `count' can be arbitrarily large.
220     (This routine makes more sense if `a0', `a1', and `a2' are considered
221 to form a fixed-point value with binary point between `a1' and `a2'.  This
222 fixed-point value is shifted right by the number of bits given in `count',
223 and the integer part of the result is returned at the locations pointed to
224 by `z0Ptr' and `z1Ptr'.  The fractional part of the result may be slightly
225 corrupted as described above, and is returned at the location pointed to by
226 `z2Ptr'.)
227 -------------------------------------------------------------------------------
228 */
229 INLINE void
230  shift128ExtraRightJamming(
231      bits64 a0,
232      bits64 a1,
233      bits64 a2,
234      int16 count,
235      bits64 *z0Ptr,
236      bits64 *z1Ptr,
237      bits64 *z2Ptr
238  )
239 {
240     bits64 z0, z1, z2;
241     int8 negCount = ( - count ) & 63;
242 
243     if ( count == 0 ) {
244         z2 = a2;
245         z1 = a1;
246         z0 = a0;
247     }
248     else {
249         if ( count < 64 ) {
250             z2 = a1<<negCount;
251             z1 = ( a0<<negCount ) | ( a1>>count );
252             z0 = a0>>count;
253         }
254         else {
255             if ( count == 64 ) {
256                 z2 = a1;
257                 z1 = a0;
258             }
259             else {
260                 a2 |= a1;
261                 if ( count < 128 ) {
262                     z2 = a0<<negCount;
263                     z1 = a0>>( count & 63 );
264                 }
265                 else {
266                     z2 = ( count == 128 ) ? a0 : ( a0 != 0 );
267                     z1 = 0;
268                 }
269             }
270             z0 = 0;
271         }
272         z2 |= ( a2 != 0 );
273     }
274     *z2Ptr = z2;
275     *z1Ptr = z1;
276     *z0Ptr = z0;
277 
278 }
279 
280 /*
281 -------------------------------------------------------------------------------
282 Shifts the 128-bit value formed by concatenating `a0' and `a1' left by the
283 number of bits given in `count'.  Any bits shifted off are lost.  The value
284 of `count' must be less than 64.  The result is broken into two 64-bit
285 pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
286 -------------------------------------------------------------------------------
287 */
288 INLINE void
289  shortShift128Left(
290      bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
291 {
292 
293     *z1Ptr = a1<<count;
294     *z0Ptr =
295         ( count == 0 ) ? a0 : ( a0<<count ) | ( a1>>( ( - count ) & 63 ) );
296 
297 }
298 
299 /*
300 -------------------------------------------------------------------------------
301 Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' left
302 by the number of bits given in `count'.  Any bits shifted off are lost.
303 The value of `count' must be less than 64.  The result is broken into three
304 64-bit pieces which are stored at the locations pointed to by `z0Ptr',
305 `z1Ptr', and `z2Ptr'.
306 -------------------------------------------------------------------------------
307 */
308 INLINE void
309  shortShift192Left(
310      bits64 a0,
311      bits64 a1,
312      bits64 a2,
313      int16 count,
314      bits64 *z0Ptr,
315      bits64 *z1Ptr,
316      bits64 *z2Ptr
317  )
318 {
319     bits64 z0, z1, z2;
320     int8 negCount;
321 
322     z2 = a2<<count;
323     z1 = a1<<count;
324     z0 = a0<<count;
325     if ( 0 < count ) {
326         negCount = ( ( - count ) & 63 );
327         z1 |= a2>>negCount;
328         z0 |= a1>>negCount;
329     }
330     *z2Ptr = z2;
331     *z1Ptr = z1;
332     *z0Ptr = z0;
333 
334 }
335 
336 /*
337 -------------------------------------------------------------------------------
338 Adds the 128-bit value formed by concatenating `a0' and `a1' to the 128-bit
339 value formed by concatenating `b0' and `b1'.  Addition is modulo 2^128, so
340 any carry out is lost.  The result is broken into two 64-bit pieces which
341 are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
342 -------------------------------------------------------------------------------
343 */
344 INLINE void
345  add128(
346      bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *z1Ptr )
347 {
348     bits64 z1;
349 
350     z1 = a1 + b1;
351     *z1Ptr = z1;
352     *z0Ptr = a0 + b0 + ( z1 < a1 );
353 
354 }
355 
356 /*
357 -------------------------------------------------------------------------------
358 Adds the 192-bit value formed by concatenating `a0', `a1', and `a2' to the
359 192-bit value formed by concatenating `b0', `b1', and `b2'.  Addition is
360 modulo 2^192, so any carry out is lost.  The result is broken into three
361 64-bit pieces which are stored at the locations pointed to by `z0Ptr',
362 `z1Ptr', and `z2Ptr'.
363 -------------------------------------------------------------------------------
364 */
365 INLINE void
366  add192(
367      bits64 a0,
368      bits64 a1,
369      bits64 a2,
370      bits64 b0,
371      bits64 b1,
372      bits64 b2,
373      bits64 *z0Ptr,
374      bits64 *z1Ptr,
375      bits64 *z2Ptr
376  )
377 {
378     bits64 z0, z1, z2;
379     int8 carry0, carry1;
380 
381     z2 = a2 + b2;
382     carry1 = ( z2 < a2 );
383     z1 = a1 + b1;
384     carry0 = ( z1 < a1 );
385     z0 = a0 + b0;
386     z1 += carry1;
387     z0 += ( z1 < carry1 );
388     z0 += carry0;
389     *z2Ptr = z2;
390     *z1Ptr = z1;
391     *z0Ptr = z0;
392 
393 }
394 
395 /*
396 -------------------------------------------------------------------------------
397 Subtracts the 128-bit value formed by concatenating `b0' and `b1' from the
398 128-bit value formed by concatenating `a0' and `a1'.  Subtraction is modulo
399 2^128, so any borrow out (carry out) is lost.  The result is broken into two
400 64-bit pieces which are stored at the locations pointed to by `z0Ptr' and
401 `z1Ptr'.
402 -------------------------------------------------------------------------------
403 */
404 INLINE void
405  sub128(
406      bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *z1Ptr )
407 {
408 
409     *z1Ptr = a1 - b1;
410     *z0Ptr = a0 - b0 - ( a1 < b1 );
411 
412 }
413 
414 /*
415 -------------------------------------------------------------------------------
416 Subtracts the 192-bit value formed by concatenating `b0', `b1', and `b2'
417 from the 192-bit value formed by concatenating `a0', `a1', and `a2'.
418 Subtraction is modulo 2^192, so any borrow out (carry out) is lost.  The
419 result is broken into three 64-bit pieces which are stored at the locations
420 pointed to by `z0Ptr', `z1Ptr', and `z2Ptr'.
421 -------------------------------------------------------------------------------
422 */
423 INLINE void
424  sub192(
425      bits64 a0,
426      bits64 a1,
427      bits64 a2,
428      bits64 b0,
429      bits64 b1,
430      bits64 b2,
431      bits64 *z0Ptr,
432      bits64 *z1Ptr,
433      bits64 *z2Ptr
434  )
435 {
436     bits64 z0, z1, z2;
437     int8 borrow0, borrow1;
438 
439     z2 = a2 - b2;
440     borrow1 = ( a2 < b2 );
441     z1 = a1 - b1;
442     borrow0 = ( a1 < b1 );
443     z0 = a0 - b0;
444     z0 -= ( z1 < borrow1 );
445     z1 -= borrow1;
446     z0 -= borrow0;
447     *z2Ptr = z2;
448     *z1Ptr = z1;
449     *z0Ptr = z0;
450 
451 }
452 
453 /*
454 -------------------------------------------------------------------------------
455 Multiplies `a' by `b' to obtain a 128-bit product.  The product is broken
456 into two 64-bit pieces which are stored at the locations pointed to by
457 `z0Ptr' and `z1Ptr'.
458 -------------------------------------------------------------------------------
459 */
460 INLINE void mul64To128( bits64 a, bits64 b, bits64 *z0Ptr, bits64 *z1Ptr )
461 {
462     bits32 aHigh, aLow, bHigh, bLow;
463     bits64 z0, zMiddleA, zMiddleB, z1;
464 
465     aLow = a;
466     aHigh = a>>32;
467     bLow = b;
468     bHigh = b>>32;
469     z1 = ( (bits64) aLow ) * bLow;
470     zMiddleA = ( (bits64) aLow ) * bHigh;
471     zMiddleB = ( (bits64) aHigh ) * bLow;
472     z0 = ( (bits64) aHigh ) * bHigh;
473     zMiddleA += zMiddleB;
474     z0 += ( ( (bits64) ( zMiddleA < zMiddleB ) )<<32 ) + ( zMiddleA>>32 );
475     zMiddleA <<= 32;
476     z1 += zMiddleA;
477     z0 += ( z1 < zMiddleA );
478     *z1Ptr = z1;
479     *z0Ptr = z0;
480 
481 }
482 
483 /*
484 -------------------------------------------------------------------------------
485 Multiplies the 128-bit value formed by concatenating `a0' and `a1' by `b' to
486 obtain a 192-bit product.  The product is broken into three 64-bit pieces
487 which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and
488 `z2Ptr'.
489 -------------------------------------------------------------------------------
490 */
491 INLINE void
492  mul128By64To192(
493      bits64 a0,
494      bits64 a1,
495      bits64 b,
496      bits64 *z0Ptr,
497      bits64 *z1Ptr,
498      bits64 *z2Ptr
499  )
500 {
501     bits64 z0, z1, z2, more1;
502 
503     mul64To128( a1, b, &z1, &z2 );
504     mul64To128( a0, b, &z0, &more1 );
505     add128( z0, more1, 0, z1, &z0, &z1 );
506     *z2Ptr = z2;
507     *z1Ptr = z1;
508     *z0Ptr = z0;
509 
510 }
511 
512 /*
513 -------------------------------------------------------------------------------
514 Multiplies the 128-bit value formed by concatenating `a0' and `a1' to the
515 128-bit value formed by concatenating `b0' and `b1' to obtain a 256-bit
516 product.  The product is broken into four 64-bit pieces which are stored at
517 the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'.
518 -------------------------------------------------------------------------------
519 */
520 INLINE void
521  mul128To256(
522      bits64 a0,
523      bits64 a1,
524      bits64 b0,
525      bits64 b1,
526      bits64 *z0Ptr,
527      bits64 *z1Ptr,
528      bits64 *z2Ptr,
529      bits64 *z3Ptr
530  )
531 {
532     bits64 z0, z1, z2, z3;
533     bits64 more1, more2;
534 
535     mul64To128( a1, b1, &z2, &z3 );
536     mul64To128( a1, b0, &z1, &more2 );
537     add128( z1, more2, 0, z2, &z1, &z2 );
538     mul64To128( a0, b0, &z0, &more1 );
539     add128( z0, more1, 0, z1, &z0, &z1 );
540     mul64To128( a0, b1, &more1, &more2 );
541     add128( more1, more2, 0, z2, &more1, &z2 );
542     add128( z0, z1, 0, more1, &z0, &z1 );
543     *z3Ptr = z3;
544     *z2Ptr = z2;
545     *z1Ptr = z1;
546     *z0Ptr = z0;
547 
548 }
549 
550 /*
551 -------------------------------------------------------------------------------
552 Returns an approximation to the 64-bit integer quotient obtained by dividing
553 `b' into the 128-bit value formed by concatenating `a0' and `a1'.  The
554 divisor `b' must be at least 2^63.  If q is the exact quotient truncated
555 toward zero, the approximation returned lies between q and q + 2 inclusive.
556 If the exact quotient q is larger than 64 bits, the maximum positive 64-bit
557 unsigned integer is returned.
558 -------------------------------------------------------------------------------
559 */
560 static bits64 estimateDiv128To64( bits64 a0, bits64 a1, bits64 b )
561 {
562     bits64 b0, b1;
563     bits64 rem0, rem1, term0, term1;
564     bits64 z;
565     if ( b <= a0 ) return LIT64( 0xFFFFFFFFFFFFFFFF );
566     b0 = b>>32;  /* hence b0 is 32 bits wide now */
567     if ( b0<<32 <= a0 ) {
568         z = LIT64( 0xFFFFFFFF00000000 );
569     }  else {
570         z = a0;
571         do_div( z, b0 );
572         z <<= 32;
573     }
574     mul64To128( b, z, &term0, &term1 );
575     sub128( a0, a1, term0, term1, &rem0, &rem1 );
576     while ( ( (sbits64) rem0 ) < 0 ) {
577         z -= LIT64( 0x100000000 );
578         b1 = b<<32;
579         add128( rem0, rem1, b0, b1, &rem0, &rem1 );
580     }
581     rem0 = ( rem0<<32 ) | ( rem1>>32 );
582     if ( b0<<32 <= rem0 ) {
583         z |= 0xFFFFFFFF;
584     } else {
585         do_div( rem0, b0 );
586         z |= rem0;
587     }
588     return z;
589 
590 }
591 
592 /*
593 -------------------------------------------------------------------------------
594 Returns an approximation to the square root of the 32-bit significand given
595 by `a'.  Considered as an integer, `a' must be at least 2^31.  If bit 0 of
596 `aExp' (the least significant bit) is 1, the integer returned approximates
597 2^31*sqrt(`a'/2^31), where `a' is considered an integer.  If bit 0 of `aExp'
598 is 0, the integer returned approximates 2^31*sqrt(`a'/2^30).  In either
599 case, the approximation returned lies strictly within +/-2 of the exact
600 value.
601 -------------------------------------------------------------------------------
602 */
603 static bits32 estimateSqrt32( int16 aExp, bits32 a )
604 {
605     static const bits16 sqrtOddAdjustments[] = {
606         0x0004, 0x0022, 0x005D, 0x00B1, 0x011D, 0x019F, 0x0236, 0x02E0,
607         0x039C, 0x0468, 0x0545, 0x0631, 0x072B, 0x0832, 0x0946, 0x0A67
608     };
609     static const bits16 sqrtEvenAdjustments[] = {
610         0x0A2D, 0x08AF, 0x075A, 0x0629, 0x051A, 0x0429, 0x0356, 0x029E,
611         0x0200, 0x0179, 0x0109, 0x00AF, 0x0068, 0x0034, 0x0012, 0x0002
612     };
613     int8 index;
614     bits32 z;
615     bits64 A;
616 
617     index = ( a>>27 ) & 15;
618     if ( aExp & 1 ) {
619         z = 0x4000 + ( a>>17 ) - sqrtOddAdjustments[ index ];
620         z = ( ( a / z )<<14 ) + ( z<<15 );
621         a >>= 1;
622     }
623     else {
624         z = 0x8000 + ( a>>17 ) - sqrtEvenAdjustments[ index ];
625         z = a / z + z;
626         z = ( 0x20000 <= z ) ? 0xFFFF8000 : ( z<<15 );
627         if ( z <= a ) return (bits32) ( ( (sbits32) a )>>1 );
628     }
629     A = ( (bits64) a )<<31;
630     do_div( A, z );
631     return ( (bits32) A ) + ( z>>1 );
632 
633 }
634 
635 /*
636 -------------------------------------------------------------------------------
637 Returns the number of leading 0 bits before the most-significant 1 bit
638 of `a'.  If `a' is zero, 32 is returned.
639 -------------------------------------------------------------------------------
640 */
641 static int8 countLeadingZeros32( bits32 a )
642 {
643     static const int8 countLeadingZerosHigh[] = {
644         8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4,
645         3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
646         2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
647         2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
648         1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
649         1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
650         1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
651         1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
652         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
653         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
654         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
655         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
656         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
657         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
658         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
659         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
660     };
661     int8 shiftCount;
662 
663     shiftCount = 0;
664     if ( a < 0x10000 ) {
665         shiftCount += 16;
666         a <<= 16;
667     }
668     if ( a < 0x1000000 ) {
669         shiftCount += 8;
670         a <<= 8;
671     }
672     shiftCount += countLeadingZerosHigh[ a>>24 ];
673     return shiftCount;
674 
675 }
676 
677 /*
678 -------------------------------------------------------------------------------
679 Returns the number of leading 0 bits before the most-significant 1 bit
680 of `a'.  If `a' is zero, 64 is returned.
681 -------------------------------------------------------------------------------
682 */
683 static int8 countLeadingZeros64( bits64 a )
684 {
685     int8 shiftCount;
686 
687     shiftCount = 0;
688     if ( a < ( (bits64) 1 )<<32 ) {
689         shiftCount += 32;
690     }
691     else {
692         a >>= 32;
693     }
694     shiftCount += countLeadingZeros32( a );
695     return shiftCount;
696 
697 }
698 
699 /*
700 -------------------------------------------------------------------------------
701 Returns 1 if the 128-bit value formed by concatenating `a0' and `a1'
702 is equal to the 128-bit value formed by concatenating `b0' and `b1'.
703 Otherwise, returns 0.
704 -------------------------------------------------------------------------------
705 */
706 INLINE flag eq128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 )
707 {
708 
709     return ( a0 == b0 ) && ( a1 == b1 );
710 
711 }
712 
713 /*
714 -------------------------------------------------------------------------------
715 Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
716 than or equal to the 128-bit value formed by concatenating `b0' and `b1'.
717 Otherwise, returns 0.
718 -------------------------------------------------------------------------------
719 */
720 INLINE flag le128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 )
721 {
722 
723     return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 <= b1 ) );
724 
725 }
726 
727 /*
728 -------------------------------------------------------------------------------
729 Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
730 than the 128-bit value formed by concatenating `b0' and `b1'.  Otherwise,
731 returns 0.
732 -------------------------------------------------------------------------------
733 */
734 INLINE flag lt128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 )
735 {
736 
737     return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 < b1 ) );
738 
739 }
740 
741 /*
742 -------------------------------------------------------------------------------
743 Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is
744 not equal to the 128-bit value formed by concatenating `b0' and `b1'.
745 Otherwise, returns 0.
746 -------------------------------------------------------------------------------
747 */
748 INLINE flag ne128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 )
749 {
750 
751     return ( a0 != b0 ) || ( a1 != b1 );
752 
753 }
754 

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