Training courses

Kernel and Embedded Linux

Bootlin training courses

Embedded Linux, kernel,
Yocto Project, Buildroot, real-time,
graphics, boot time, debugging...

Bootlin logo

Elixir Cross Referencer

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
/*******************************************************************
** m a t h 6 4 . c
** Forth Inspired Command Language - 64 bit math support routines
** Author: John Sadler (john_sadler@alum.mit.edu)
** Created: 25 January 1998
** Rev 2.03: Support for 128 bit DP math. This file really ouught to
** be renamed!
** $Id: math64.c,v 1.9 2001/12/05 07:21:34 jsadler Exp $
*******************************************************************/
/*
** Copyright (c) 1997-2001 John Sadler (john_sadler@alum.mit.edu)
** All rights reserved.
**
** Get the latest Ficl release at http://ficl.sourceforge.net
**
** I am interested in hearing from anyone who uses ficl. If you have
** a problem, a success story, a defect, an enhancement request, or
** if you would like to contribute to the ficl release, please
** contact me by email at the address above.
**
** L I C E N S E  and  D I S C L A I M E R
** 
** Redistribution and use in source and binary forms, with or without
** modification, are permitted provided that the following conditions
** are met:
** 1. Redistributions of source code must retain the above copyright
**    notice, this list of conditions and the following disclaimer.
** 2. Redistributions in binary form must reproduce the above copyright
**    notice, this list of conditions and the following disclaimer in the
**    documentation and/or other materials provided with the distribution.
**
** THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
** ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
** IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
** ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
** FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
** DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
** OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
** HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
** OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
** SUCH DAMAGE.
*/

/* $FreeBSD$ */

#include "ficl.h"
#include "math64.h"


/**************************************************************************
                        m 6 4 A b s
** Returns the absolute value of an DPINT
**************************************************************************/
DPINT m64Abs(DPINT x)
{
    if (m64IsNegative(x))
        x = m64Negate(x);

    return x;
}


/**************************************************************************
                        m 6 4 F l o o r e d D i v I
** 
** FROM THE FORTH ANS...
** Floored division is integer division in which the remainder carries
** the sign of the divisor or is zero, and the quotient is rounded to
** its arithmetic floor. Symmetric division is integer division in which
** the remainder carries the sign of the dividend or is zero and the
** quotient is the mathematical quotient rounded towards zero or
** truncated. Examples of each are shown in tables 3.3 and 3.4. 
** 
** Table 3.3 - Floored Division Example
** Dividend        Divisor Remainder       Quotient
** --------        ------- ---------       --------
**  10                7       3                1
** -10                7       4               -2
**  10               -7      -4               -2
** -10               -7      -3                1
** 
** 
** Table 3.4 - Symmetric Division Example
** Dividend        Divisor Remainder       Quotient
** --------        ------- ---------       --------
**  10                7       3                1
** -10                7      -3               -1
**  10               -7       3               -1
** -10               -7      -3                1
**************************************************************************/
INTQR m64FlooredDivI(DPINT num, FICL_INT den)
{
    INTQR qr;
    UNSQR uqr;
    int signRem = 1;
    int signQuot = 1;

    if (m64IsNegative(num))
    {
        num = m64Negate(num);
        signQuot = -signQuot;
    }

    if (den < 0)
    {
        den      = -den;
        signRem  = -signRem;
        signQuot = -signQuot;
    }

    uqr = ficlLongDiv(m64CastIU(num), (FICL_UNS)den);
    qr = m64CastQRUI(uqr);
    if (signQuot < 0)
    {
        qr.quot = -qr.quot;
        if (qr.rem != 0)
        {
            qr.quot--;
            qr.rem = den - qr.rem;
        }
    }

    if (signRem < 0)
        qr.rem = -qr.rem;

    return qr;
}


/**************************************************************************
                        m 6 4 I s N e g a t i v e
** Returns TRUE if the specified DPINT has its sign bit set.
**************************************************************************/
int m64IsNegative(DPINT x)
{
    return (x.hi < 0);
}


/**************************************************************************
                        m 6 4 M a c
** Mixed precision multiply and accumulate primitive for number building.
** Multiplies DPUNS u by FICL_UNS mul and adds FICL_UNS add. Mul is typically
** the numeric base, and add represents a digit to be appended to the 
** growing number. 
** Returns the result of the operation
**************************************************************************/
DPUNS m64Mac(DPUNS u, FICL_UNS mul, FICL_UNS add)
{
    DPUNS resultLo = ficlLongMul(u.lo, mul);
    DPUNS resultHi = ficlLongMul(u.hi, mul);
    resultLo.hi += resultHi.lo;
    resultHi.lo = resultLo.lo + add;

    if (resultHi.lo < resultLo.lo)
        resultLo.hi++;

    resultLo.lo = resultHi.lo;

    return resultLo;
}


/**************************************************************************
                        m 6 4 M u l I
** Multiplies a pair of FICL_INTs and returns an DPINT result.
**************************************************************************/
DPINT m64MulI(FICL_INT x, FICL_INT y)
{
    DPUNS prod;
    int sign = 1;

    if (x < 0)
    {
        sign = -sign;
        x = -x;
    }

    if (y < 0)
    {
        sign = -sign;
        y = -y;
    }

    prod = ficlLongMul(x, y);
    if (sign > 0)
        return m64CastUI(prod);
    else
        return m64Negate(m64CastUI(prod));
}


/**************************************************************************
                        m 6 4 N e g a t e
** Negates an DPINT by complementing and incrementing.
**************************************************************************/
DPINT m64Negate(DPINT x)
{
    x.hi = ~x.hi;
    x.lo = ~x.lo;
    x.lo ++;
    if (x.lo == 0)
        x.hi++;

    return x;
}


/**************************************************************************
                        m 6 4 P u s h
** Push an DPINT onto the specified stack in the order required
** by ANS Forth (most significant cell on top)
** These should probably be macros...
**************************************************************************/
void  i64Push(FICL_STACK *pStack, DPINT i64)
{
    stackPushINT(pStack, i64.lo);
    stackPushINT(pStack, i64.hi);
    return;
}

void  u64Push(FICL_STACK *pStack, DPUNS u64)
{
    stackPushINT(pStack, u64.lo);
    stackPushINT(pStack, u64.hi);
    return;
}


/**************************************************************************
                        m 6 4 P o p
** Pops an DPINT off the stack in the order required by ANS Forth
** (most significant cell on top)
** These should probably be macros...
**************************************************************************/
DPINT i64Pop(FICL_STACK *pStack)
{
    DPINT ret;
    ret.hi = stackPopINT(pStack);
    ret.lo = stackPopINT(pStack);
    return ret;
}

DPUNS u64Pop(FICL_STACK *pStack)
{
    DPUNS ret;
    ret.hi = stackPopINT(pStack);
    ret.lo = stackPopINT(pStack);
    return ret;
}


/**************************************************************************
                        m 6 4 S y m m e t r i c D i v
** Divide an DPINT by a FICL_INT and return a FICL_INT quotient and a
** FICL_INT remainder. The absolute values of quotient and remainder are not
** affected by the signs of the numerator and denominator (the operation
** is symmetric on the number line)
**************************************************************************/
INTQR m64SymmetricDivI(DPINT num, FICL_INT den)
{
    INTQR qr;
    UNSQR uqr;
    int signRem = 1;
    int signQuot = 1;

    if (m64IsNegative(num))
    {
        num = m64Negate(num);
        signRem  = -signRem;
        signQuot = -signQuot;
    }

    if (den < 0)
    {
        den      = -den;
        signQuot = -signQuot;
    }

    uqr = ficlLongDiv(m64CastIU(num), (FICL_UNS)den);
    qr = m64CastQRUI(uqr);
    if (signRem < 0)
        qr.rem = -qr.rem;

    if (signQuot < 0)
        qr.quot = -qr.quot;

    return qr;
}


/**************************************************************************
                        m 6 4 U M o d
** Divides a DPUNS by base (an UNS16) and returns an UNS16 remainder.
** Writes the quotient back to the original DPUNS as a side effect.
** This operation is typically used to convert an DPUNS to a text string
** in any base. See words.c:numberSignS, for example.
** Mechanics: performs 4 ficlLongDivs, each of which produces 16 bits
** of the quotient. C does not provide a way to divide an FICL_UNS by an
** UNS16 and get an FICL_UNS quotient (ldiv is closest, but it's signed,
** unfortunately), so I've used ficlLongDiv.
**************************************************************************/
#if (BITS_PER_CELL == 32)

#define UMOD_SHIFT 16
#define UMOD_MASK 0x0000ffff

#elif (BITS_PER_CELL == 64)

#define UMOD_SHIFT 32
#define UMOD_MASK 0x00000000ffffffff

#endif

UNS16 m64UMod(DPUNS *pUD, UNS16 base)
{
    DPUNS ud;
    UNSQR qr;
    DPUNS result;

    result.hi = result.lo = 0;

    ud.hi = 0;
    ud.lo = pUD->hi >> UMOD_SHIFT;
    qr = ficlLongDiv(ud, (FICL_UNS)base);
    result.hi = qr.quot << UMOD_SHIFT;

    ud.lo = (qr.rem << UMOD_SHIFT) | (pUD->hi & UMOD_MASK);
    qr = ficlLongDiv(ud, (FICL_UNS)base);
    result.hi |= qr.quot & UMOD_MASK;

    ud.lo = (qr.rem << UMOD_SHIFT) | (pUD->lo >> UMOD_SHIFT);
    qr = ficlLongDiv(ud, (FICL_UNS)base);
    result.lo = qr.quot << UMOD_SHIFT;

    ud.lo = (qr.rem << UMOD_SHIFT) | (pUD->lo & UMOD_MASK);
    qr = ficlLongDiv(ud, (FICL_UNS)base);
    result.lo |= qr.quot & UMOD_MASK;

    *pUD = result;

    return (UNS16)(qr.rem);
}


/**************************************************************************
** Contributed by
** Michael A. Gauland   gaulandm@mdhost.cse.tek.com  
**************************************************************************/
#if PORTABLE_LONGMULDIV != 0
/**************************************************************************
                        m 6 4 A d d
** 
**************************************************************************/
DPUNS m64Add(DPUNS x, DPUNS y)
{
    DPUNS result;
    int carry;
    
    result.hi = x.hi + y.hi;
    result.lo = x.lo + y.lo;


    carry  = ((x.lo | y.lo) & CELL_HI_BIT) && !(result.lo & CELL_HI_BIT);
    carry |= ((x.lo & y.lo) & CELL_HI_BIT);

    if (carry)
    {
        result.hi++;
    }

    return result;
}


/**************************************************************************
                        m 6 4 S u b
** 
**************************************************************************/
DPUNS m64Sub(DPUNS x, DPUNS y)
{
    DPUNS result;
    
    result.hi = x.hi - y.hi;
    result.lo = x.lo - y.lo;

    if (x.lo < y.lo) 
    {
        result.hi--;
    }

    return result;
}


/**************************************************************************
                        m 6 4 A S L
** 64 bit left shift
**************************************************************************/
DPUNS m64ASL( DPUNS x )
{
    DPUNS result;
    
    result.hi = x.hi << 1;
    if (x.lo & CELL_HI_BIT) 
    {
        result.hi++;
    }

    result.lo = x.lo << 1;

    return result;
}


/**************************************************************************
                        m 6 4 A S R
** 64 bit right shift (unsigned - no sign extend)
**************************************************************************/
DPUNS m64ASR( DPUNS x )
{
    DPUNS result;
    
    result.lo = x.lo >> 1;
    if (x.hi & 1) 
    {
        result.lo |= CELL_HI_BIT;
    }

    result.hi = x.hi >> 1;
    return result;
}


/**************************************************************************
                        m 6 4 O r
** 64 bit bitwise OR
**************************************************************************/
DPUNS m64Or( DPUNS x, DPUNS y )
{
    DPUNS result;
    
    result.hi = x.hi | y.hi;
    result.lo = x.lo | y.lo;
    
    return result;
}


/**************************************************************************
                        m 6 4 C o m p a r e
** Return -1 if x < y; 0 if x==y, and 1 if x > y.
**************************************************************************/
int m64Compare(DPUNS x, DPUNS y)
{
    int result;
    
    if (x.hi > y.hi) 
    {
        result = +1;
    } 
    else if (x.hi < y.hi) 
    {
        result = -1;
    } 
    else 
    {
        /* High parts are equal */
        if (x.lo > y.lo) 
        {
            result = +1;
        } 
        else if (x.lo < y.lo) 
        {
            result = -1;
        } 
        else 
        {
            result = 0;
        }
    }
    
    return result;
}


/**************************************************************************
                        f i c l L o n g M u l
** Portable versions of ficlLongMul and ficlLongDiv in C
** Contributed by:
** Michael A. Gauland   gaulandm@mdhost.cse.tek.com  
**************************************************************************/
DPUNS ficlLongMul(FICL_UNS x, FICL_UNS y)
{
    DPUNS result = { 0, 0 };
    DPUNS addend;
    
    addend.lo = y;
    addend.hi = 0; /* No sign extension--arguments are unsigned */
    
    while (x != 0) 
    {
        if ( x & 1) 
        {
            result = m64Add(result, addend);
        }
        x >>= 1;
        addend = m64ASL(addend);
    }
    return result;
}


/**************************************************************************
                        f i c l L o n g D i v
** Portable versions of ficlLongMul and ficlLongDiv in C
** Contributed by:
** Michael A. Gauland   gaulandm@mdhost.cse.tek.com  
**************************************************************************/
UNSQR ficlLongDiv(DPUNS q, FICL_UNS y)
{
    UNSQR result;
    DPUNS quotient;
    DPUNS subtrahend;
    DPUNS mask;

    quotient.lo = 0;
    quotient.hi = 0;
    
    subtrahend.lo = y;
    subtrahend.hi = 0;
    
    mask.lo = 1;
    mask.hi = 0;
    
    while ((m64Compare(subtrahend, q) < 0) &&
           (subtrahend.hi & CELL_HI_BIT) == 0)
    {
        mask = m64ASL(mask);
        subtrahend = m64ASL(subtrahend);
    }
    
    while (mask.lo != 0 || mask.hi != 0) 
    {
        if (m64Compare(subtrahend, q) <= 0) 
        {
            q = m64Sub( q, subtrahend);
            quotient = m64Or(quotient, mask);
        }
        mask = m64ASR(mask);
        subtrahend = m64ASR(subtrahend);
    }
    
    result.quot = quotient.lo;
    result.rem = q.lo;
    return result;
}

#endif