Annotation of sys/lib/libkern/softfloat-macros.h, Revision 1.1.1.1
1.1 nbrk 1: /* $OpenBSD: softfloat-macros.h,v 1.1 2002/04/28 20:55:14 pvalchev Exp $ */
2: /* $NetBSD: softfloat-macros.h,v 1.1 2001/04/26 03:10:47 ross Exp $ */
3:
4: /*
5: ===============================================================================
6:
7: This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
8: Arithmetic Package, Release 2a.
9:
10: Written by John R. Hauser. This work was made possible in part by the
11: International Computer Science Institute, located at Suite 600, 1947 Center
12: Street, Berkeley, California 94704. Funding was partially provided by the
13: National Science Foundation under grant MIP-9311980. The original version
14: of this code was written as part of a project to build a fixed-point vector
15: processor in collaboration with the University of California at Berkeley,
16: overseen by Profs. Nelson Morgan and John Wawrzynek. More information
17: is available through the Web page `http://HTTP.CS.Berkeley.EDU/~jhauser/
18: arithmetic/SoftFloat.html'.
19:
20: THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable
21: effort has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT
22: WILL AT TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS
23: RESTRICTED TO PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL
24: RESPONSIBILITY FOR ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM
25: THEIR OWN USE OF THE SOFTWARE, AND WHO ALSO EFFECTIVELY INDEMNIFY
26: (possibly via similar legal warning) JOHN HAUSER AND THE INTERNATIONAL
27: COMPUTER SCIENCE INSTITUTE AGAINST ALL LOSSES, COSTS, OR OTHER PROBLEMS
28: ARISING FROM THE USE OF THE SOFTWARE BY THEIR CUSTOMERS AND CLIENTS.
29:
30: Derivative works are acceptable, even for commercial purposes, so long as
31: (1) they include prominent notice that the work is derivative, and (2) they
32: include prominent notice akin to these four paragraphs for those parts of
33: this code that are retained.
34:
35: ===============================================================================
36: */
37:
38: #ifndef NO_IEEE
39:
40: /*
41: -------------------------------------------------------------------------------
42: Shifts `a' right by the number of bits given in `count'. If any nonzero
43: bits are shifted off, they are ``jammed'' into the least significant bit of
44: the result by setting the least significant bit to 1. The value of `count'
45: can be arbitrarily large; in particular, if `count' is greater than 32, the
46: result will be either 0 or 1, depending on whether `a' is zero or nonzero.
47: The result is stored in the location pointed to by `zPtr'.
48: -------------------------------------------------------------------------------
49: */
50: INLINE void shift32RightJamming( bits32 a, int16 count, bits32 *zPtr )
51: {
52: bits32 z;
53:
54: if ( count == 0 ) {
55: z = a;
56: }
57: else if ( count < 32 ) {
58: z = ( a>>count ) | ( ( a<<( ( - count ) & 31 ) ) != 0 );
59: }
60: else {
61: z = ( a != 0 );
62: }
63: *zPtr = z;
64:
65: }
66:
67: /*
68: -------------------------------------------------------------------------------
69: Shifts `a' right by the number of bits given in `count'. If any nonzero
70: bits are shifted off, they are ``jammed'' into the least significant bit of
71: the result by setting the least significant bit to 1. The value of `count'
72: can be arbitrarily large; in particular, if `count' is greater than 64, the
73: result will be either 0 or 1, depending on whether `a' is zero or nonzero.
74: The result is stored in the location pointed to by `zPtr'.
75: -------------------------------------------------------------------------------
76: */
77: INLINE void shift64RightJamming( bits64 a, int16 count, bits64 *zPtr )
78: {
79: bits64 z;
80:
81: if ( count == 0 ) {
82: z = a;
83: }
84: else if ( count < 64 ) {
85: z = ( a>>count ) | ( ( a<<( ( - count ) & 63 ) ) != 0 );
86: }
87: else {
88: z = ( a != 0 );
89: }
90: *zPtr = z;
91:
92: }
93:
94: /*
95: -------------------------------------------------------------------------------
96: Shifts the 128-bit value formed by concatenating `a0' and `a1' right by 64
97: _plus_ the number of bits given in `count'. The shifted result is at most
98: 64 nonzero bits; this is stored at the location pointed to by `z0Ptr'. The
99: bits shifted off form a second 64-bit result as follows: The _last_ bit
100: shifted off is the most-significant bit of the extra result, and the other
101: 63 bits of the extra result are all zero if and only if _all_but_the_last_
102: bits shifted off were all zero. This extra result is stored in the location
103: pointed to by `z1Ptr'. The value of `count' can be arbitrarily large.
104: (This routine makes more sense if `a0' and `a1' are considered to form a
105: fixed-point value with binary point between `a0' and `a1'. This fixed-point
106: value is shifted right by the number of bits given in `count', and the
107: integer part of the result is returned at the location pointed to by
108: `z0Ptr'. The fractional part of the result may be slightly corrupted as
109: described above, and is returned at the location pointed to by `z1Ptr'.)
110: -------------------------------------------------------------------------------
111: */
112: INLINE void
113: shift64ExtraRightJamming(
114: bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
115: {
116: bits64 z0, z1;
117: int8 negCount = ( - count ) & 63;
118:
119: if ( count == 0 ) {
120: z1 = a1;
121: z0 = a0;
122: }
123: else if ( count < 64 ) {
124: z1 = ( a0<<negCount ) | ( a1 != 0 );
125: z0 = a0>>count;
126: }
127: else {
128: if ( count == 64 ) {
129: z1 = a0 | ( a1 != 0 );
130: }
131: else {
132: z1 = ( ( a0 | a1 ) != 0 );
133: }
134: z0 = 0;
135: }
136: *z1Ptr = z1;
137: *z0Ptr = z0;
138:
139: }
140:
141: /*
142: -------------------------------------------------------------------------------
143: Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
144: number of bits given in `count'. Any bits shifted off are lost. The value
145: of `count' can be arbitrarily large; in particular, if `count' is greater
146: than 128, the result will be 0. The result is broken into two 64-bit pieces
147: which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
148: -------------------------------------------------------------------------------
149: */
150: INLINE void
151: shift128Right(
152: bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
153: {
154: bits64 z0, z1;
155: int8 negCount = ( - count ) & 63;
156:
157: if ( count == 0 ) {
158: z1 = a1;
159: z0 = a0;
160: }
161: else if ( count < 64 ) {
162: z1 = ( a0<<negCount ) | ( a1>>count );
163: z0 = a0>>count;
164: }
165: else {
166: z1 = ( count < 64 ) ? ( a0>>( count & 63 ) ) : 0;
167: z0 = 0;
168: }
169: *z1Ptr = z1;
170: *z0Ptr = z0;
171:
172: }
173:
174: /*
175: -------------------------------------------------------------------------------
176: Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
177: number of bits given in `count'. If any nonzero bits are shifted off, they
178: are ``jammed'' into the least significant bit of the result by setting the
179: least significant bit to 1. The value of `count' can be arbitrarily large;
180: in particular, if `count' is greater than 128, the result will be either
181: 0 or 1, depending on whether the concatenation of `a0' and `a1' is zero or
182: nonzero. The result is broken into two 64-bit pieces which are stored at
183: the locations pointed to by `z0Ptr' and `z1Ptr'.
184: -------------------------------------------------------------------------------
185: */
186: INLINE void
187: shift128RightJamming(
188: bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
189: {
190: bits64 z0, z1;
191: int8 negCount = ( - count ) & 63;
192:
193: if ( count == 0 ) {
194: z1 = a1;
195: z0 = a0;
196: }
197: else if ( count < 64 ) {
198: z1 = ( a0<<negCount ) | ( a1>>count ) | ( ( a1<<negCount ) != 0 );
199: z0 = a0>>count;
200: }
201: else {
202: if ( count == 64 ) {
203: z1 = a0 | ( a1 != 0 );
204: }
205: else if ( count < 128 ) {
206: z1 = ( a0>>( count & 63 ) ) | ( ( ( a0<<negCount ) | a1 ) != 0 );
207: }
208: else {
209: z1 = ( ( a0 | a1 ) != 0 );
210: }
211: z0 = 0;
212: }
213: *z1Ptr = z1;
214: *z0Ptr = z0;
215:
216: }
217:
218: /*
219: -------------------------------------------------------------------------------
220: Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' right
221: by 64 _plus_ the number of bits given in `count'. The shifted result is
222: at most 128 nonzero bits; these are broken into two 64-bit pieces which are
223: stored at the locations pointed to by `z0Ptr' and `z1Ptr'. The bits shifted
224: off form a third 64-bit result as follows: The _last_ bit shifted off is
225: the most-significant bit of the extra result, and the other 63 bits of the
226: extra result are all zero if and only if _all_but_the_last_ bits shifted off
227: were all zero. This extra result is stored in the location pointed to by
228: `z2Ptr'. The value of `count' can be arbitrarily large.
229: (This routine makes more sense if `a0', `a1', and `a2' are considered
230: to form a fixed-point value with binary point between `a1' and `a2'. This
231: fixed-point value is shifted right by the number of bits given in `count',
232: and the integer part of the result is returned at the locations pointed to
233: by `z0Ptr' and `z1Ptr'. The fractional part of the result may be slightly
234: corrupted as described above, and is returned at the location pointed to by
235: `z2Ptr'.)
236: -------------------------------------------------------------------------------
237: */
238: INLINE void
239: shift128ExtraRightJamming(
240: bits64 a0,
241: bits64 a1,
242: bits64 a2,
243: int16 count,
244: bits64 *z0Ptr,
245: bits64 *z1Ptr,
246: bits64 *z2Ptr
247: )
248: {
249: bits64 z0, z1, z2;
250: int8 negCount = ( - count ) & 63;
251:
252: if ( count == 0 ) {
253: z2 = a2;
254: z1 = a1;
255: z0 = a0;
256: }
257: else {
258: if ( count < 64 ) {
259: z2 = a1<<negCount;
260: z1 = ( a0<<negCount ) | ( a1>>count );
261: z0 = a0>>count;
262: }
263: else {
264: if ( count == 64 ) {
265: z2 = a1;
266: z1 = a0;
267: }
268: else {
269: a2 |= a1;
270: if ( count < 128 ) {
271: z2 = a0<<negCount;
272: z1 = a0>>( count & 63 );
273: }
274: else {
275: z2 = ( count == 128 ) ? a0 : ( a0 != 0 );
276: z1 = 0;
277: }
278: }
279: z0 = 0;
280: }
281: z2 |= ( a2 != 0 );
282: }
283: *z2Ptr = z2;
284: *z1Ptr = z1;
285: *z0Ptr = z0;
286:
287: }
288:
289: /*
290: -------------------------------------------------------------------------------
291: Shifts the 128-bit value formed by concatenating `a0' and `a1' left by the
292: number of bits given in `count'. Any bits shifted off are lost. The value
293: of `count' must be less than 64. The result is broken into two 64-bit
294: pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
295: -------------------------------------------------------------------------------
296: */
297: INLINE void
298: shortShift128Left(
299: bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
300: {
301:
302: *z1Ptr = a1<<count;
303: *z0Ptr =
304: ( count == 0 ) ? a0 : ( a0<<count ) | ( a1>>( ( - count ) & 63 ) );
305:
306: }
307:
308: /*
309: -------------------------------------------------------------------------------
310: Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' left
311: by the number of bits given in `count'. Any bits shifted off are lost.
312: The value of `count' must be less than 64. The result is broken into three
313: 64-bit pieces which are stored at the locations pointed to by `z0Ptr',
314: `z1Ptr', and `z2Ptr'.
315: -------------------------------------------------------------------------------
316: */
317: INLINE void
318: shortShift192Left(
319: bits64 a0,
320: bits64 a1,
321: bits64 a2,
322: int16 count,
323: bits64 *z0Ptr,
324: bits64 *z1Ptr,
325: bits64 *z2Ptr
326: )
327: {
328: bits64 z0, z1, z2;
329: int8 negCount;
330:
331: z2 = a2<<count;
332: z1 = a1<<count;
333: z0 = a0<<count;
334: if ( 0 < count ) {
335: negCount = ( ( - count ) & 63 );
336: z1 |= a2>>negCount;
337: z0 |= a1>>negCount;
338: }
339: *z2Ptr = z2;
340: *z1Ptr = z1;
341: *z0Ptr = z0;
342:
343: }
344:
345: /*
346: -------------------------------------------------------------------------------
347: Adds the 128-bit value formed by concatenating `a0' and `a1' to the 128-bit
348: value formed by concatenating `b0' and `b1'. Addition is modulo 2^128, so
349: any carry out is lost. The result is broken into two 64-bit pieces which
350: are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
351: -------------------------------------------------------------------------------
352: */
353: INLINE void
354: add128(
355: bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *z1Ptr )
356: {
357: bits64 z1;
358:
359: z1 = a1 + b1;
360: *z1Ptr = z1;
361: *z0Ptr = a0 + b0 + ( z1 < a1 );
362:
363: }
364:
365: /*
366: -------------------------------------------------------------------------------
367: Adds the 192-bit value formed by concatenating `a0', `a1', and `a2' to the
368: 192-bit value formed by concatenating `b0', `b1', and `b2'. Addition is
369: modulo 2^192, so any carry out is lost. The result is broken into three
370: 64-bit pieces which are stored at the locations pointed to by `z0Ptr',
371: `z1Ptr', and `z2Ptr'.
372: -------------------------------------------------------------------------------
373: */
374: INLINE void
375: add192(
376: bits64 a0,
377: bits64 a1,
378: bits64 a2,
379: bits64 b0,
380: bits64 b1,
381: bits64 b2,
382: bits64 *z0Ptr,
383: bits64 *z1Ptr,
384: bits64 *z2Ptr
385: )
386: {
387: bits64 z0, z1, z2;
388: int8 carry0, carry1;
389:
390: z2 = a2 + b2;
391: carry1 = ( z2 < a2 );
392: z1 = a1 + b1;
393: carry0 = ( z1 < a1 );
394: z0 = a0 + b0;
395: z1 += carry1;
396: z0 += ( z1 < carry1 );
397: z0 += carry0;
398: *z2Ptr = z2;
399: *z1Ptr = z1;
400: *z0Ptr = z0;
401:
402: }
403:
404: /*
405: -------------------------------------------------------------------------------
406: Subtracts the 128-bit value formed by concatenating `b0' and `b1' from the
407: 128-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo
408: 2^128, so any borrow out (carry out) is lost. The result is broken into two
409: 64-bit pieces which are stored at the locations pointed to by `z0Ptr' and
410: `z1Ptr'.
411: -------------------------------------------------------------------------------
412: */
413: INLINE void
414: sub128(
415: bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *z1Ptr )
416: {
417:
418: *z1Ptr = a1 - b1;
419: *z0Ptr = a0 - b0 - ( a1 < b1 );
420:
421: }
422:
423: /*
424: -------------------------------------------------------------------------------
425: Subtracts the 192-bit value formed by concatenating `b0', `b1', and `b2'
426: from the 192-bit value formed by concatenating `a0', `a1', and `a2'.
427: Subtraction is modulo 2^192, so any borrow out (carry out) is lost. The
428: result is broken into three 64-bit pieces which are stored at the locations
429: pointed to by `z0Ptr', `z1Ptr', and `z2Ptr'.
430: -------------------------------------------------------------------------------
431: */
432: INLINE void
433: sub192(
434: bits64 a0,
435: bits64 a1,
436: bits64 a2,
437: bits64 b0,
438: bits64 b1,
439: bits64 b2,
440: bits64 *z0Ptr,
441: bits64 *z1Ptr,
442: bits64 *z2Ptr
443: )
444: {
445: bits64 z0, z1, z2;
446: int8 borrow0, borrow1;
447:
448: z2 = a2 - b2;
449: borrow1 = ( a2 < b2 );
450: z1 = a1 - b1;
451: borrow0 = ( a1 < b1 );
452: z0 = a0 - b0;
453: z0 -= ( z1 < borrow1 );
454: z1 -= borrow1;
455: z0 -= borrow0;
456: *z2Ptr = z2;
457: *z1Ptr = z1;
458: *z0Ptr = z0;
459:
460: }
461:
462: /*
463: -------------------------------------------------------------------------------
464: Multiplies `a' by `b' to obtain a 128-bit product. The product is broken
465: into two 64-bit pieces which are stored at the locations pointed to by
466: `z0Ptr' and `z1Ptr'.
467: -------------------------------------------------------------------------------
468: */
469: INLINE void mul64To128( bits64 a, bits64 b, bits64 *z0Ptr, bits64 *z1Ptr )
470: {
471: bits32 aHigh, aLow, bHigh, bLow;
472: bits64 z0, zMiddleA, zMiddleB, z1;
473:
474: aLow = a;
475: aHigh = a>>32;
476: bLow = b;
477: bHigh = b>>32;
478: z1 = ( (bits64) aLow ) * bLow;
479: zMiddleA = ( (bits64) aLow ) * bHigh;
480: zMiddleB = ( (bits64) aHigh ) * bLow;
481: z0 = ( (bits64) aHigh ) * bHigh;
482: zMiddleA += zMiddleB;
483: z0 += ( ( (bits64) ( zMiddleA < zMiddleB ) )<<32 ) + ( zMiddleA>>32 );
484: zMiddleA <<= 32;
485: z1 += zMiddleA;
486: z0 += ( z1 < zMiddleA );
487: *z1Ptr = z1;
488: *z0Ptr = z0;
489:
490: }
491:
492: /*
493: -------------------------------------------------------------------------------
494: Multiplies the 128-bit value formed by concatenating `a0' and `a1' by
495: `b' to obtain a 192-bit product. The product is broken into three 64-bit
496: pieces which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and
497: `z2Ptr'.
498: -------------------------------------------------------------------------------
499: */
500: INLINE void
501: mul128By64To192(
502: bits64 a0,
503: bits64 a1,
504: bits64 b,
505: bits64 *z0Ptr,
506: bits64 *z1Ptr,
507: bits64 *z2Ptr
508: )
509: {
510: bits64 z0, z1, z2, more1;
511:
512: mul64To128( a1, b, &z1, &z2 );
513: mul64To128( a0, b, &z0, &more1 );
514: add128( z0, more1, 0, z1, &z0, &z1 );
515: *z2Ptr = z2;
516: *z1Ptr = z1;
517: *z0Ptr = z0;
518:
519: }
520:
521: /*
522: -------------------------------------------------------------------------------
523: Multiplies the 128-bit value formed by concatenating `a0' and `a1' to the
524: 128-bit value formed by concatenating `b0' and `b1' to obtain a 256-bit
525: product. The product is broken into four 64-bit pieces which are stored at
526: the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'.
527: -------------------------------------------------------------------------------
528: */
529: INLINE void
530: mul128To256(
531: bits64 a0,
532: bits64 a1,
533: bits64 b0,
534: bits64 b1,
535: bits64 *z0Ptr,
536: bits64 *z1Ptr,
537: bits64 *z2Ptr,
538: bits64 *z3Ptr
539: )
540: {
541: bits64 z0, z1, z2, z3;
542: bits64 more1, more2;
543:
544: mul64To128( a1, b1, &z2, &z3 );
545: mul64To128( a1, b0, &z1, &more2 );
546: add128( z1, more2, 0, z2, &z1, &z2 );
547: mul64To128( a0, b0, &z0, &more1 );
548: add128( z0, more1, 0, z1, &z0, &z1 );
549: mul64To128( a0, b1, &more1, &more2 );
550: add128( more1, more2, 0, z2, &more1, &z2 );
551: add128( z0, z1, 0, more1, &z0, &z1 );
552: *z3Ptr = z3;
553: *z2Ptr = z2;
554: *z1Ptr = z1;
555: *z0Ptr = z0;
556:
557: }
558:
559: /*
560: -------------------------------------------------------------------------------
561: Returns an approximation to the 64-bit integer quotient obtained by dividing
562: `b' into the 128-bit value formed by concatenating `a0' and `a1'. The
563: divisor `b' must be at least 2^63. If q is the exact quotient truncated
564: toward zero, the approximation returned lies between q and q + 2 inclusive.
565: If the exact quotient q is larger than 64 bits, the maximum positive 64-bit
566: unsigned integer is returned.
567: -------------------------------------------------------------------------------
568: */
569: static bits64 estimateDiv128To64( bits64 a0, bits64 a1, bits64 b )
570: {
571: bits64 b0, b1;
572: bits64 rem0, rem1, term0, term1;
573: bits64 z;
574:
575: if ( b <= a0 ) return LIT64( 0xFFFFFFFFFFFFFFFF );
576: b0 = b>>32;
577: z = ( b0<<32 <= a0 ) ? LIT64( 0xFFFFFFFF00000000 ) : ( a0 / b0 )<<32;
578: mul64To128( b, z, &term0, &term1 );
579: sub128( a0, a1, term0, term1, &rem0, &rem1 );
580: while ( ( (sbits64) rem0 ) < 0 ) {
581: z -= LIT64( 0x100000000 );
582: b1 = b<<32;
583: add128( rem0, rem1, b0, b1, &rem0, &rem1 );
584: }
585: rem0 = ( rem0<<32 ) | ( rem1>>32 );
586: z |= ( b0<<32 <= rem0 ) ? 0xFFFFFFFF : rem0 / b0;
587: return z;
588:
589: }
590:
591: #ifndef SOFTFLOAT_FOR_GCC /* Not used */
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:
616: index = ( a>>27 ) & 15;
617: if ( aExp & 1 ) {
618: z = 0x4000 + ( a>>17 ) - sqrtOddAdjustments[ index ];
619: z = ( ( a / z )<<14 ) + ( z<<15 );
620: a >>= 1;
621: }
622: else {
623: z = 0x8000 + ( a>>17 ) - sqrtEvenAdjustments[ index ];
624: z = a / z + z;
625: z = ( 0x20000 <= z ) ? 0xFFFF8000 : ( z<<15 );
626: if ( z <= a ) return (bits32) ( ( (sbits32) a )>>1 );
627: }
628: return ( (bits32) ( ( ( (bits64) a )<<31 ) / z ) ) + ( z>>1 );
629:
630: }
631: #endif
632:
633: /*
634: -------------------------------------------------------------------------------
635: Returns the number of leading 0 bits before the most-significant 1 bit of
636: `a'. If `a' is zero, 32 is returned.
637: -------------------------------------------------------------------------------
638: */
639: static int8 countLeadingZeros32( bits32 a )
640: {
641: static const int8 countLeadingZerosHigh[] = {
642: 8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4,
643: 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
644: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
645: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
646: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
647: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
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: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
651: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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: };
659: int8 shiftCount;
660:
661: shiftCount = 0;
662: if ( a < 0x10000 ) {
663: shiftCount += 16;
664: a <<= 16;
665: }
666: if ( a < 0x1000000 ) {
667: shiftCount += 8;
668: a <<= 8;
669: }
670: shiftCount += countLeadingZerosHigh[ a>>24 ];
671: return shiftCount;
672:
673: }
674:
675: /*
676: -------------------------------------------------------------------------------
677: Returns the number of leading 0 bits before the most-significant 1 bit of
678: `a'. If `a' is zero, 64 is returned.
679: -------------------------------------------------------------------------------
680: */
681: static int8 countLeadingZeros64( bits64 a )
682: {
683: int8 shiftCount;
684:
685: shiftCount = 0;
686: if ( a < ( (bits64) 1 )<<32 ) {
687: shiftCount += 32;
688: }
689: else {
690: a >>= 32;
691: }
692: shiftCount += countLeadingZeros32( a );
693: return shiftCount;
694:
695: }
696:
697: /*
698: -------------------------------------------------------------------------------
699: Returns 1 if the 128-bit value formed by concatenating `a0' and `a1'
700: is equal to the 128-bit value formed by concatenating `b0' and `b1'.
701: Otherwise, returns 0.
702: -------------------------------------------------------------------------------
703: */
704: INLINE flag eq128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 )
705: {
706:
707: return ( a0 == b0 ) && ( a1 == b1 );
708:
709: }
710:
711: /*
712: -------------------------------------------------------------------------------
713: Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
714: than or equal to the 128-bit value formed by concatenating `b0' and `b1'.
715: Otherwise, returns 0.
716: -------------------------------------------------------------------------------
717: */
718: INLINE flag le128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 )
719: {
720:
721: return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 <= b1 ) );
722:
723: }
724:
725: /*
726: -------------------------------------------------------------------------------
727: Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
728: than the 128-bit value formed by concatenating `b0' and `b1'. Otherwise,
729: returns 0.
730: -------------------------------------------------------------------------------
731: */
732: INLINE flag lt128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 )
733: {
734:
735: return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 < b1 ) );
736:
737: }
738:
739: /*
740: -------------------------------------------------------------------------------
741: Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is
742: not equal to the 128-bit value formed by concatenating `b0' and `b1'.
743: Otherwise, returns 0.
744: -------------------------------------------------------------------------------
745: */
746: INLINE flag ne128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 )
747: {
748:
749: return ( a0 != b0 ) || ( a1 != b1 );
750:
751: }
752:
753: #endif /* !NO_IEEE */
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