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1.1 root 1: /*
2: * QEMU float support macros
3: *
4: * The code in this source file is derived from release 2a of the SoftFloat
5: * IEC/IEEE Floating-point Arithmetic Package. Those parts of the code (and
6: * some later contributions) are provided under that license, as detailed below.
7: * It has subsequently been modified by contributors to the QEMU Project,
8: * so some portions are provided under:
9: * the SoftFloat-2a license
10: * the BSD license
11: * GPL-v2-or-later
12: *
13: * Any future contributions to this file after December 1st 2014 will be
14: * taken to be licensed under the Softfloat-2a license unless specifically
15: * indicated otherwise.
16: */
17:
18: /*
19: ===============================================================================
20: This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
21: Arithmetic Package, Release 2a.
22:
23: Written by John R. Hauser. This work was made possible in part by the
24: International Computer Science Institute, located at Suite 600, 1947 Center
25: Street, Berkeley, California 94704. Funding was partially provided by the
26: National Science Foundation under grant MIP-9311980. The original version
27: of this code was written as part of a project to build a fixed-point vector
28: processor in collaboration with the University of California at Berkeley,
29: overseen by Profs. Nelson Morgan and John Wawrzynek. More information
30: is available through the Web page `http://HTTP.CS.Berkeley.EDU/~jhauser/
31: arithmetic/SoftFloat.html'.
32:
33: THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort
34: has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
35: TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO
36: PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
37: AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
38:
39: Derivative works are acceptable, even for commercial purposes, so long as
40: (1) they include prominent notice that the work is derivative, and (2) they
41: include prominent notice akin to these four paragraphs for those parts of
42: this code that are retained.
43:
44: ===============================================================================
45: */
46:
47: /* BSD licensing:
48: * Copyright (c) 2006, Fabrice Bellard
49: * All rights reserved.
50: *
51: * Redistribution and use in source and binary forms, with or without
52: * modification, are permitted provided that the following conditions are met:
53: *
54: * 1. Redistributions of source code must retain the above copyright notice,
55: * this list of conditions and the following disclaimer.
56: *
57: * 2. Redistributions in binary form must reproduce the above copyright notice,
58: * this list of conditions and the following disclaimer in the documentation
59: * and/or other materials provided with the distribution.
60: *
61: * 3. Neither the name of the copyright holder nor the names of its contributors
62: * may be used to endorse or promote products derived from this software without
63: * specific prior written permission.
64: *
65: * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
66: * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
67: * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
68: * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
69: * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
70: * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
71: * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
72: * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
73: * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
74: * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
75: * THE POSSIBILITY OF SUCH DAMAGE.
76: */
77:
78: /* Portions of this work are licensed under the terms of the GNU GPL,
79: * version 2 or later. See the COPYING file in the top-level directory.
80: */
81:
82: /*----------------------------------------------------------------------------
83: | This macro tests for minimum version of the GNU C compiler.
84: *----------------------------------------------------------------------------*/
85: #if defined(__GNUC__) && defined(__GNUC_MINOR__)
86: # define SOFTFLOAT_GNUC_PREREQ(maj, min) \
87: ((__GNUC__ << 16) + __GNUC_MINOR__ >= ((maj) << 16) + (min))
88: #else
89: # define SOFTFLOAT_GNUC_PREREQ(maj, min) 0
90: #endif
91:
92:
93: /*----------------------------------------------------------------------------
94: | Shifts `a' right by the number of bits given in `count'. If any nonzero
95: | bits are shifted off, they are ``jammed'' into the least significant bit of
96: | the result by setting the least significant bit to 1. The value of `count'
97: | can be arbitrarily large; in particular, if `count' is greater than 32, the
98: | result will be either 0 or 1, depending on whether `a' is zero or nonzero.
99: | The result is stored in the location pointed to by `zPtr'.
100: *----------------------------------------------------------------------------*/
101:
102: static inline void shift32RightJamming(uint32_t a, int count, uint32_t *zPtr)
103: {
104: uint32_t z;
105:
106: if ( count == 0 ) {
107: z = a;
108: }
109: else if ( count < 32 ) {
110: z = ( a>>count ) | ( ( a<<( ( - count ) & 31 ) ) != 0 );
111: }
112: else {
113: z = ( a != 0 );
114: }
115: *zPtr = z;
116:
117: }
118:
119: /*----------------------------------------------------------------------------
120: | Shifts `a' right by the number of bits given in `count'. If any nonzero
121: | bits are shifted off, they are ``jammed'' into the least significant bit of
122: | the result by setting the least significant bit to 1. The value of `count'
123: | can be arbitrarily large; in particular, if `count' is greater than 64, the
124: | result will be either 0 or 1, depending on whether `a' is zero or nonzero.
125: | The result is stored in the location pointed to by `zPtr'.
126: *----------------------------------------------------------------------------*/
127:
128: static inline void shift64RightJamming(uint64_t a, int count, uint64_t *zPtr)
129: {
130: uint64_t z;
131:
132: if ( count == 0 ) {
133: z = a;
134: }
135: else if ( count < 64 ) {
136: z = ( a>>count ) | ( ( a<<( ( - count ) & 63 ) ) != 0 );
137: }
138: else {
139: z = ( a != 0 );
140: }
141: *zPtr = z;
142:
143: }
144:
145: /*----------------------------------------------------------------------------
146: | Shifts the 128-bit value formed by concatenating `a0' and `a1' right by 64
147: | _plus_ the number of bits given in `count'. The shifted result is at most
148: | 64 nonzero bits; this is stored at the location pointed to by `z0Ptr'. The
149: | bits shifted off form a second 64-bit result as follows: The _last_ bit
150: | shifted off is the most-significant bit of the extra result, and the other
151: | 63 bits of the extra result are all zero if and only if _all_but_the_last_
152: | bits shifted off were all zero. This extra result is stored in the location
153: | pointed to by `z1Ptr'. The value of `count' can be arbitrarily large.
154: | (This routine makes more sense if `a0' and `a1' are considered to form a
155: | fixed-point value with binary point between `a0' and `a1'. This fixed-point
156: | value is shifted right by the number of bits given in `count', and the
157: | integer part of the result is returned at the location pointed to by
158: | `z0Ptr'. The fractional part of the result may be slightly corrupted as
159: | described above, and is returned at the location pointed to by `z1Ptr'.)
160: *----------------------------------------------------------------------------*/
161:
162: static inline void
163: shift64ExtraRightJamming(
164: uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr)
165: {
166: uint64_t z0, z1;
167: int8_t negCount = ( - count ) & 63;
168:
169: if ( count == 0 ) {
170: z1 = a1;
171: z0 = a0;
172: }
173: else if ( count < 64 ) {
174: z1 = ( a0<<negCount ) | ( a1 != 0 );
175: z0 = a0>>count;
176: }
177: else {
178: if ( count == 64 ) {
179: z1 = a0 | ( a1 != 0 );
180: }
181: else {
182: z1 = ( ( a0 | a1 ) != 0 );
183: }
184: z0 = 0;
185: }
186: *z1Ptr = z1;
187: *z0Ptr = z0;
188:
189: }
190:
191: /*----------------------------------------------------------------------------
192: | Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
193: | number of bits given in `count'. Any bits shifted off are lost. The value
194: | of `count' can be arbitrarily large; in particular, if `count' is greater
195: | than 128, the result will be 0. The result is broken into two 64-bit pieces
196: | which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
197: *----------------------------------------------------------------------------*/
198:
199: static inline void
200: shift128Right(
201: uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr)
202: {
203: uint64_t z0, z1;
204: int8_t negCount = ( - count ) & 63;
205:
206: if ( count == 0 ) {
207: z1 = a1;
208: z0 = a0;
209: }
210: else if ( count < 64 ) {
211: z1 = ( a0<<negCount ) | ( a1>>count );
212: z0 = a0>>count;
213: }
214: else {
215: z1 = (count < 128) ? (a0 >> (count & 63)) : 0;
216: z0 = 0;
217: }
218: *z1Ptr = z1;
219: *z0Ptr = z0;
220:
221: }
222:
223: /*----------------------------------------------------------------------------
224: | Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
225: | number of bits given in `count'. If any nonzero bits are shifted off, they
226: | are ``jammed'' into the least significant bit of the result by setting the
227: | least significant bit to 1. The value of `count' can be arbitrarily large;
228: | in particular, if `count' is greater than 128, the result will be either
229: | 0 or 1, depending on whether the concatenation of `a0' and `a1' is zero or
230: | nonzero. The result is broken into two 64-bit pieces which are stored at
231: | the locations pointed to by `z0Ptr' and `z1Ptr'.
232: *----------------------------------------------------------------------------*/
233:
234: static inline void
235: shift128RightJamming(
236: uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr)
237: {
238: uint64_t z0, z1;
239: int8_t negCount = ( - count ) & 63;
240:
241: if ( count == 0 ) {
242: z1 = a1;
243: z0 = a0;
244: }
245: else if ( count < 64 ) {
246: z1 = ( a0<<negCount ) | ( a1>>count ) | ( ( a1<<negCount ) != 0 );
247: z0 = a0>>count;
248: }
249: else {
250: if ( count == 64 ) {
251: z1 = a0 | ( a1 != 0 );
252: }
253: else if ( count < 128 ) {
254: z1 = ( a0>>( count & 63 ) ) | ( ( ( a0<<negCount ) | a1 ) != 0 );
255: }
256: else {
257: z1 = ( ( a0 | a1 ) != 0 );
258: }
259: z0 = 0;
260: }
261: *z1Ptr = z1;
262: *z0Ptr = z0;
263:
264: }
265:
266: /*----------------------------------------------------------------------------
267: | Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' right
268: | by 64 _plus_ the number of bits given in `count'. The shifted result is
269: | at most 128 nonzero bits; these are broken into two 64-bit pieces which are
270: | stored at the locations pointed to by `z0Ptr' and `z1Ptr'. The bits shifted
271: | off form a third 64-bit result as follows: The _last_ bit shifted off is
272: | the most-significant bit of the extra result, and the other 63 bits of the
273: | extra result are all zero if and only if _all_but_the_last_ bits shifted off
274: | were all zero. This extra result is stored in the location pointed to by
275: | `z2Ptr'. The value of `count' can be arbitrarily large.
276: | (This routine makes more sense if `a0', `a1', and `a2' are considered
277: | to form a fixed-point value with binary point between `a1' and `a2'. This
278: | fixed-point value is shifted right by the number of bits given in `count',
279: | and the integer part of the result is returned at the locations pointed to
280: | by `z0Ptr' and `z1Ptr'. The fractional part of the result may be slightly
281: | corrupted as described above, and is returned at the location pointed to by
282: | `z2Ptr'.)
283: *----------------------------------------------------------------------------*/
284:
285: static inline void
286: shift128ExtraRightJamming(
287: uint64_t a0,
288: uint64_t a1,
289: uint64_t a2,
290: int count,
291: uint64_t *z0Ptr,
292: uint64_t *z1Ptr,
293: uint64_t *z2Ptr
294: )
295: {
296: uint64_t z0, z1, z2;
297: int8_t negCount = ( - count ) & 63;
298:
299: if ( count == 0 ) {
300: z2 = a2;
301: z1 = a1;
302: z0 = a0;
303: }
304: else {
305: if ( count < 64 ) {
306: z2 = a1<<negCount;
307: z1 = ( a0<<negCount ) | ( a1>>count );
308: z0 = a0>>count;
309: }
310: else {
311: if ( count == 64 ) {
312: z2 = a1;
313: z1 = a0;
314: }
315: else {
316: a2 |= a1;
317: if ( count < 128 ) {
318: z2 = a0<<negCount;
319: z1 = a0>>( count & 63 );
320: }
321: else {
322: z2 = ( count == 128 ) ? a0 : ( a0 != 0 );
323: z1 = 0;
324: }
325: }
326: z0 = 0;
327: }
328: z2 |= ( a2 != 0 );
329: }
330: *z2Ptr = z2;
331: *z1Ptr = z1;
332: *z0Ptr = z0;
333:
334: }
335:
336: /*----------------------------------------------------------------------------
337: | Shifts the 128-bit value formed by concatenating `a0' and `a1' left by the
338: | number of bits given in `count'. Any bits shifted off are lost. The value
339: | of `count' must be less than 64. The result is broken into two 64-bit
340: | pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
341: *----------------------------------------------------------------------------*/
342:
343: static inline void
344: shortShift128Left(
345: uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr)
346: {
347:
348: *z1Ptr = a1<<count;
349: *z0Ptr =
350: ( count == 0 ) ? a0 : ( a0<<count ) | ( a1>>( ( - count ) & 63 ) );
351:
352: }
353:
354: /*----------------------------------------------------------------------------
355: | Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' left
356: | by the number of bits given in `count'. Any bits shifted off are lost.
357: | The value of `count' must be less than 64. The result is broken into three
358: | 64-bit pieces which are stored at the locations pointed to by `z0Ptr',
359: | `z1Ptr', and `z2Ptr'.
360: *----------------------------------------------------------------------------*/
361:
362: static inline void
363: shortShift192Left(
364: uint64_t a0,
365: uint64_t a1,
366: uint64_t a2,
367: int count,
368: uint64_t *z0Ptr,
369: uint64_t *z1Ptr,
370: uint64_t *z2Ptr
371: )
372: {
373: uint64_t z0, z1, z2;
374: int8_t negCount;
375:
376: z2 = a2<<count;
377: z1 = a1<<count;
378: z0 = a0<<count;
379: if ( 0 < count ) {
380: negCount = ( ( - count ) & 63 );
381: z1 |= a2>>negCount;
382: z0 |= a1>>negCount;
383: }
384: *z2Ptr = z2;
385: *z1Ptr = z1;
386: *z0Ptr = z0;
387:
388: }
389:
390: /*----------------------------------------------------------------------------
391: | Adds the 128-bit value formed by concatenating `a0' and `a1' to the 128-bit
392: | value formed by concatenating `b0' and `b1'. Addition is modulo 2^128, so
393: | any carry out is lost. The result is broken into two 64-bit pieces which
394: | are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
395: *----------------------------------------------------------------------------*/
396:
397: static inline void
398: add128(
399: uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1, uint64_t *z0Ptr, uint64_t *z1Ptr )
400: {
401: uint64_t z1;
402:
403: z1 = a1 + b1;
404: *z1Ptr = z1;
405: *z0Ptr = a0 + b0 + ( z1 < a1 );
406:
407: }
408:
409: /*----------------------------------------------------------------------------
410: | Adds the 192-bit value formed by concatenating `a0', `a1', and `a2' to the
411: | 192-bit value formed by concatenating `b0', `b1', and `b2'. Addition is
412: | modulo 2^192, so any carry out is lost. The result is broken into three
413: | 64-bit pieces which are stored at the locations pointed to by `z0Ptr',
414: | `z1Ptr', and `z2Ptr'.
415: *----------------------------------------------------------------------------*/
416:
417: static inline void
418: add192(
419: uint64_t a0,
420: uint64_t a1,
421: uint64_t a2,
422: uint64_t b0,
423: uint64_t b1,
424: uint64_t b2,
425: uint64_t *z0Ptr,
426: uint64_t *z1Ptr,
427: uint64_t *z2Ptr
428: )
429: {
430: uint64_t z0, z1, z2;
431: uint8_t carry0, carry1;
432:
433: z2 = a2 + b2;
434: carry1 = ( z2 < a2 );
435: z1 = a1 + b1;
436: carry0 = ( z1 < a1 );
437: z0 = a0 + b0;
438: z1 += carry1;
439: z0 += ( z1 < carry1 );
440: z0 += carry0;
441: *z2Ptr = z2;
442: *z1Ptr = z1;
443: *z0Ptr = z0;
444:
445: }
446:
447: /*----------------------------------------------------------------------------
448: | Subtracts the 128-bit value formed by concatenating `b0' and `b1' from the
449: | 128-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo
450: | 2^128, so any borrow out (carry out) is lost. The result is broken into two
451: | 64-bit pieces which are stored at the locations pointed to by `z0Ptr' and
452: | `z1Ptr'.
453: *----------------------------------------------------------------------------*/
454:
455: static inline void
456: sub128(
457: uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1, uint64_t *z0Ptr, uint64_t *z1Ptr )
458: {
459:
460: *z1Ptr = a1 - b1;
461: *z0Ptr = a0 - b0 - ( a1 < b1 );
462:
463: }
464:
465: /*----------------------------------------------------------------------------
466: | Subtracts the 192-bit value formed by concatenating `b0', `b1', and `b2'
467: | from the 192-bit value formed by concatenating `a0', `a1', and `a2'.
468: | Subtraction is modulo 2^192, so any borrow out (carry out) is lost. The
469: | result is broken into three 64-bit pieces which are stored at the locations
470: | pointed to by `z0Ptr', `z1Ptr', and `z2Ptr'.
471: *----------------------------------------------------------------------------*/
472:
473: static inline void
474: sub192(
475: uint64_t a0,
476: uint64_t a1,
477: uint64_t a2,
478: uint64_t b0,
479: uint64_t b1,
480: uint64_t b2,
481: uint64_t *z0Ptr,
482: uint64_t *z1Ptr,
483: uint64_t *z2Ptr
484: )
485: {
486: uint64_t z0, z1, z2;
487: uint8_t borrow0, borrow1;
488:
489: z2 = a2 - b2;
490: borrow1 = ( a2 < b2 );
491: z1 = a1 - b1;
492: borrow0 = ( a1 < b1 );
493: z0 = a0 - b0;
494: z0 -= ( z1 < borrow1 );
495: z1 -= borrow1;
496: z0 -= borrow0;
497: *z2Ptr = z2;
498: *z1Ptr = z1;
499: *z0Ptr = z0;
500:
501: }
502:
503: /*----------------------------------------------------------------------------
504: | Multiplies `a' by `b' to obtain a 128-bit product. The product is broken
505: | into two 64-bit pieces which are stored at the locations pointed to by
506: | `z0Ptr' and `z1Ptr'.
507: *----------------------------------------------------------------------------*/
508:
509: static inline void mul64To128( uint64_t a, uint64_t b, uint64_t *z0Ptr, uint64_t *z1Ptr )
510: {
511: uint32_t aHigh, aLow, bHigh, bLow;
512: uint64_t z0, zMiddleA, zMiddleB, z1;
513:
514: aLow = a;
515: aHigh = a>>32;
516: bLow = b;
517: bHigh = b>>32;
518: z1 = ( (uint64_t) aLow ) * bLow;
519: zMiddleA = ( (uint64_t) aLow ) * bHigh;
520: zMiddleB = ( (uint64_t) aHigh ) * bLow;
521: z0 = ( (uint64_t) aHigh ) * bHigh;
522: zMiddleA += zMiddleB;
523: z0 += ( ( (uint64_t) ( zMiddleA < zMiddleB ) )<<32 ) + ( zMiddleA>>32 );
524: zMiddleA <<= 32;
525: z1 += zMiddleA;
526: z0 += ( z1 < zMiddleA );
527: *z1Ptr = z1;
528: *z0Ptr = z0;
529:
530: }
531:
532: /*----------------------------------------------------------------------------
533: | Multiplies the 128-bit value formed by concatenating `a0' and `a1' by
534: | `b' to obtain a 192-bit product. The product is broken into three 64-bit
535: | pieces which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and
536: | `z2Ptr'.
537: *----------------------------------------------------------------------------*/
538:
539: static inline void
540: mul128By64To192(
541: uint64_t a0,
542: uint64_t a1,
543: uint64_t b,
544: uint64_t *z0Ptr,
545: uint64_t *z1Ptr,
546: uint64_t *z2Ptr
547: )
548: {
549: uint64_t z0, z1, z2, more1;
550:
551: mul64To128( a1, b, &z1, &z2 );
552: mul64To128( a0, b, &z0, &more1 );
553: add128( z0, more1, 0, z1, &z0, &z1 );
554: *z2Ptr = z2;
555: *z1Ptr = z1;
556: *z0Ptr = z0;
557:
558: }
559:
560: /*----------------------------------------------------------------------------
561: | Multiplies the 128-bit value formed by concatenating `a0' and `a1' to the
562: | 128-bit value formed by concatenating `b0' and `b1' to obtain a 256-bit
563: | product. The product is broken into four 64-bit pieces which are stored at
564: | the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'.
565: *----------------------------------------------------------------------------*/
566:
567: static inline void
568: mul128To256(
569: uint64_t a0,
570: uint64_t a1,
571: uint64_t b0,
572: uint64_t b1,
573: uint64_t *z0Ptr,
574: uint64_t *z1Ptr,
575: uint64_t *z2Ptr,
576: uint64_t *z3Ptr
577: )
578: {
579: uint64_t z0, z1, z2, z3;
580: uint64_t more1, more2;
581:
582: mul64To128( a1, b1, &z2, &z3 );
583: mul64To128( a1, b0, &z1, &more2 );
584: add128( z1, more2, 0, z2, &z1, &z2 );
585: mul64To128( a0, b0, &z0, &more1 );
586: add128( z0, more1, 0, z1, &z0, &z1 );
587: mul64To128( a0, b1, &more1, &more2 );
588: add128( more1, more2, 0, z2, &more1, &z2 );
589: add128( z0, z1, 0, more1, &z0, &z1 );
590: *z3Ptr = z3;
591: *z2Ptr = z2;
592: *z1Ptr = z1;
593: *z0Ptr = z0;
594:
595: }
596:
597: /*----------------------------------------------------------------------------
598: | Returns an approximation to the 64-bit integer quotient obtained by dividing
599: | `b' into the 128-bit value formed by concatenating `a0' and `a1'. The
600: | divisor `b' must be at least 2^63. If q is the exact quotient truncated
601: | toward zero, the approximation returned lies between q and q + 2 inclusive.
602: | If the exact quotient q is larger than 64 bits, the maximum positive 64-bit
603: | unsigned integer is returned.
604: *----------------------------------------------------------------------------*/
605:
606: static inline uint64_t estimateDiv128To64( uint64_t a0, uint64_t a1, uint64_t b )
607: {
608: uint64_t b0, b1;
609: uint64_t rem0, rem1, term0, term1;
610: uint64_t z;
611:
612: if ( b <= a0 ) return LIT64( 0xFFFFFFFFFFFFFFFF );
613: b0 = b>>32;
614: z = ( b0<<32 <= a0 ) ? LIT64( 0xFFFFFFFF00000000 ) : ( a0 / b0 )<<32;
615: mul64To128( b, z, &term0, &term1 );
616: sub128( a0, a1, term0, term1, &rem0, &rem1 );
617: while ( ( (int64_t) rem0 ) < 0 ) {
618: z -= LIT64( 0x100000000 );
619: b1 = b<<32;
620: add128( rem0, rem1, b0, b1, &rem0, &rem1 );
621: }
622: rem0 = ( rem0<<32 ) | ( rem1>>32 );
623: z |= ( b0<<32 <= rem0 ) ? 0xFFFFFFFF : rem0 / b0;
624: return z;
625:
626: }
627:
628: /*----------------------------------------------------------------------------
629: | Returns an approximation to the square root of the 32-bit significand given
630: | by `a'. Considered as an integer, `a' must be at least 2^31. If bit 0 of
631: | `aExp' (the least significant bit) is 1, the integer returned approximates
632: | 2^31*sqrt(`a'/2^31), where `a' is considered an integer. If bit 0 of `aExp'
633: | is 0, the integer returned approximates 2^31*sqrt(`a'/2^30). In either
634: | case, the approximation returned lies strictly within +/-2 of the exact
635: | value.
636: *----------------------------------------------------------------------------*/
637:
638: static inline uint32_t estimateSqrt32(int aExp, uint32_t a)
639: {
640: static const uint16_t sqrtOddAdjustments[] = {
641: 0x0004, 0x0022, 0x005D, 0x00B1, 0x011D, 0x019F, 0x0236, 0x02E0,
642: 0x039C, 0x0468, 0x0545, 0x0631, 0x072B, 0x0832, 0x0946, 0x0A67
643: };
644: static const uint16_t sqrtEvenAdjustments[] = {
645: 0x0A2D, 0x08AF, 0x075A, 0x0629, 0x051A, 0x0429, 0x0356, 0x029E,
646: 0x0200, 0x0179, 0x0109, 0x00AF, 0x0068, 0x0034, 0x0012, 0x0002
647: };
648: int8_t index;
649: uint32_t z;
650:
651: index = ( a>>27 ) & 15;
652: if ( aExp & 1 ) {
653: z = 0x4000 + ( a>>17 ) - sqrtOddAdjustments[ (int)index ];
654: z = ( ( a / z )<<14 ) + ( z<<15 );
655: a >>= 1;
656: }
657: else {
658: z = 0x8000 + ( a>>17 ) - sqrtEvenAdjustments[ (int)index ];
659: z = a / z + z;
660: z = ( 0x20000 <= z ) ? 0xFFFF8000 : ( z<<15 );
661: if ( z <= a ) return (uint32_t) ( ( (int32_t) a )>>1 );
662: }
663: return ( (uint32_t) ( ( ( (uint64_t) a )<<31 ) / z ) ) + ( z>>1 );
664:
665: }
666:
667: /*----------------------------------------------------------------------------
668: | Returns the number of leading 0 bits before the most-significant 1 bit of
669: | `a'. If `a' is zero, 32 is returned.
670: *----------------------------------------------------------------------------*/
671:
672: static inline int8_t countLeadingZeros32( uint32_t a )
673: {
674: #if SOFTFLOAT_GNUC_PREREQ(3, 4)
675: if (a) {
676: return __builtin_clz(a);
677: } else {
678: return 32;
679: }
680: #else
681: static const int8_t countLeadingZerosHigh[] = {
682: 8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4,
683: 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
684: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
685: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
686: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
687: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
688: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
689: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
690: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
691: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
692: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
693: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
694: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
695: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
696: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
697: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
698: };
699: int8_t shiftCount;
700:
701: shiftCount = 0;
702: if ( a < 0x10000 ) {
703: shiftCount += 16;
704: a <<= 16;
705: }
706: if ( a < 0x1000000 ) {
707: shiftCount += 8;
708: a <<= 8;
709: }
710: shiftCount += countLeadingZerosHigh[ a>>24 ];
711: return shiftCount;
712: #endif
713: }
714:
715: /*----------------------------------------------------------------------------
716: | Returns the number of leading 0 bits before the most-significant 1 bit of
717: | `a'. If `a' is zero, 64 is returned.
718: *----------------------------------------------------------------------------*/
719:
720: static inline int8_t countLeadingZeros64( uint64_t a )
721: {
722: #if SOFTFLOAT_GNUC_PREREQ(3, 4)
723: if (a) {
724: return __builtin_clzll(a);
725: } else {
726: return 64;
727: }
728: #else
729: int8_t shiftCount;
730:
731: shiftCount = 0;
732: if ( a < ( (uint64_t) 1 )<<32 ) {
733: shiftCount += 32;
734: }
735: else {
736: a >>= 32;
737: }
738: shiftCount += countLeadingZeros32( a );
739: return shiftCount;
740: #endif
741: }
742:
743: /*----------------------------------------------------------------------------
744: | Returns 1 if the 128-bit value formed by concatenating `a0' and `a1'
745: | is equal to the 128-bit value formed by concatenating `b0' and `b1'.
746: | Otherwise, returns 0.
747: *----------------------------------------------------------------------------*/
748:
749: static inline flag eq128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 )
750: {
751:
752: return ( a0 == b0 ) && ( a1 == b1 );
753:
754: }
755:
756: /*----------------------------------------------------------------------------
757: | Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
758: | than or equal to the 128-bit value formed by concatenating `b0' and `b1'.
759: | Otherwise, returns 0.
760: *----------------------------------------------------------------------------*/
761:
762: static inline flag le128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 )
763: {
764:
765: return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 <= b1 ) );
766:
767: }
768:
769: /*----------------------------------------------------------------------------
770: | Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
771: | than the 128-bit value formed by concatenating `b0' and `b1'. Otherwise,
772: | returns 0.
773: *----------------------------------------------------------------------------*/
774:
775: static inline flag lt128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 )
776: {
777:
778: return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 < b1 ) );
779:
780: }
781:
782: /*----------------------------------------------------------------------------
783: | Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is
784: | not equal to the 128-bit value formed by concatenating `b0' and `b1'.
785: | Otherwise, returns 0.
786: *----------------------------------------------------------------------------*/
787:
788: static inline flag ne128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 )
789: {
790:
791: return ( a0 != b0 ) || ( a1 != b1 );
792:
793: }
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