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