[1656e5]: contrib / sb-gmp / gmp.lisp  Maximize  Restore  History

Download this file

910 lines (802 with data), 31.9 kB

  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
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
(defpackage "SB-GMP"
(:use "COMMON-LISP" "SB-ALIEN" "SB-BIGNUM")
;; we need a few very internal symbols
(:import-from "SB-BIGNUM"
"%BIGNUM-0-OR-PLUSP" "%NORMALIZE-BIGNUM"
"NEGATE-BIGNUM-IN-PLACE")
(:export
;; bignum integer operations
#:mpz-add
#:mpz-sub
#:mpz-mul
#:mpz-mod
#:mpz-cdiv
#:mpz-fdiv
#:mpz-tdiv
#:mpz-powm
#:mpz-pow
#:mpz-gcd
#:mpz-lcm
#:mpz-sqrt
#:mpz-probably-prime-p
#:mpz-nextprime
#:mpz-fac
;; Following three are GMP >= 5.1 only
#:mpz-2fac
#:mpz-mfac
#:mpz-primorial
#:mpz-bin
#:mpz-fib2
;; random number generation
#:make-gmp-rstate
#:make-gmp-rstate-lc
#:rand-seed
#:random-bitcount
#:random-int
;; ratio arithmetic
#:mpq-add
#:mpq-sub
#:mpq-mul
#:mpq-div
;; (un)installer functions
; these insert/remove the runtime patch in SBCL's runtime
#:install-gmp-funs
#:uninstall-gmp-funs
; these also load/unload the shared library and setup/clear
; hooks to handle core saves
#:load-gmp
#:unload-gmp
;; special variables
#:*gmp-version*
#:*gmp-disabled*
))
(in-package "SB-GMP")
(defvar *gmp-disabled* nil)
(defconstant +bignum-raw-area-offset+
(- (* sb-vm:bignum-digits-offset sb-vm:n-word-bytes)
sb-vm:other-pointer-lowtag))
(declaim (inline bignum-data-sap))
(defun bignum-data-sap (x)
(declare (type bignum x))
(sb-sys:sap+ (sb-sys:int-sap (sb-kernel:get-lisp-obj-address x))
+bignum-raw-area-offset+))
(defun %load-gmp ()
(handler-case
(load-shared-object #-(or win32 darwin) "libgmp.so"
#+darwin "libgmp.dylib"
#+win32 "libgmp-10.dll"
:dont-save t)
(error (e)
(warn "GMP not loaded (~a)" e)
(return-from %load-gmp nil)))
t)
(defvar *gmp-features* nil)
(defvar *gmp-version* nil)
;; We load only the library right now to avoid undefined alien
;; style warnings
(%load-gmp)
;;; types and initialization
(define-alien-type nil
(struct gmpint
(mp_alloc int)
(mp_size int)
(mp_d (* unsigned-long))))
;; Section 3.6 "Memory Management" of the GMP manual states: "mpz_t
;; and mpq_t variables never reduce their allocated space. Normally
;; this is the best policy, since it avoids frequent
;; reallocation. Applications that need to return memory to the heap
;; at some particular point can use mpz_realloc2, or clear variables
;; no longer needed."
;;
;; We can therefore allocate a bignum of sufficiant size and use the
;; space for GMP computations without the need for memory transfer
;; from C to Lisp space.
(declaim (inline z-to-bignum z-to-bignum-neg))
(defun z-to-bignum (b count)
"Convert GMP integer in the buffer of a pre-allocated bignum."
(declare (optimize (speed 3) (space 3) (safety 0))
(type bignum-type b)
(type bignum-index count))
(if (zerop count)
0
(the unsigned-byte (%normalize-bignum b count))))
(defun z-to-bignum-neg (b count)
"Convert to twos complement int the buffer of a pre-allocated
bignum."
(declare (optimize (speed 3) (space 3) (safety 0))
(type bignum-type b)
(type bignum-index count))
(negate-bignum-in-place b)
(the (integer * 0) (%normalize-bignum b count)))
;;; conversion functions that also copy from GMP to SBCL bignum space
(declaim (inline gmp-z-to-bignum gmp-z-to-bignum-neg))
(defun gmp-z-to-bignum (z b count)
"Convert and copy a positive GMP integer into the buffer of a
pre-allocated bignum. The allocated bignum-length must be (1+ COUNT)."
(declare (optimize (speed 3) (space 3) (safety 0))
(type (alien (* unsigned-long)) z)
(type bignum-type b)
(type bignum-index count))
(dotimes (i count (%normalize-bignum b count))
(%bignum-set b i (deref z i))))
(defun gmp-z-to-bignum-neg (z b count)
"Convert to twos complement and copy a negative GMP integer into the
buffer of a pre-allocated bignum. The allocated bignum-length must
be (1+ COUNT)."
(declare (optimize (speed 3) (space 3) (safety 0))
(type (alien (* unsigned-long)) z)
(type bignum-type b)
(type bignum-index count))
(let ((carry 0)
(add 1))
(declare (type (mod 2) carry add))
(dotimes (i count b)
(multiple-value-bind (value carry-tmp)
(%add-with-carry
(%lognot (deref z i)) add carry)
(%bignum-set b i value)
(setf carry carry-tmp
add 0)))))
(declaim (inline blength bassert)
(ftype (function (integer) (values bignum-index &optional)) blength)
(ftype (function (integer) (values bignum &optional)) bassert))
(defun blength (a)
(declare (optimize (speed 3) (space 3) (safety 0)))
(etypecase a
(fixnum 1)
(t (%bignum-length a))))
(defun bassert (a)
(declare (optimize (speed 3) (space 3) (safety 0)))
(etypecase a
(fixnum (make-small-bignum a))
(t a)))
;;;; rationals
(define-alien-type nil
(struct gmprat
(mp_num (struct gmpint))
(mp_den (struct gmpint))))
;;; memory initialization functions to support non-alloced results
;;; since an upper bound cannot always correctly predetermined
;;; (e.g. the memory required for the fib function exceed the number
;;; of limbs that are be determined through the infamous Phi-relation
;;; resulting in a memory access error.
;; use these for non-prealloced bignum values, but only when
;; ultimately necessary since copying back into bignum space a the end
;; of the operation is about three times slower than the shared buffer
;; approach.
(declaim (inline __gmpz_init __gmpz_clear))
(define-alien-routine __gmpz_init void
(x (* (struct gmpint))))
(define-alien-routine __gmpz_clear void
(x (* (struct gmpint))))
;;; integer interface functions
(defmacro define-twoarg-mpz-funs (funs)
(loop for i in funs collect `(define-alien-routine ,i void
(r (* (struct gmpint)))
(a (* (struct gmpint))))
into defines
finally (return `(progn
(declaim (inline ,@funs))
,@defines))))
(defmacro define-threearg-mpz-funs (funs)
(loop for i in funs collect `(define-alien-routine ,i void
(r (* (struct gmpint)))
(a (* (struct gmpint)))
(b (* (struct gmpint))))
into defines
finally (return `(progn
(declaim (inline ,@funs))
,@defines))))
(defmacro define-fourarg-mpz-funs (funs)
(loop for i in funs collect `(define-alien-routine ,i void
(r (* (struct gmpint)))
(a (* (struct gmpint)))
(b (* (struct gmpint)))
(c (* (struct gmpint))))
into defines
finally (return `(progn
(declaim (inline ,@funs))
,@defines))))
(define-twoarg-mpz-funs (__gmpz_sqrt
__gmpz_nextprime))
(define-threearg-mpz-funs (__gmpz_add
__gmpz_sub
__gmpz_mul
__gmpz_mod
__gmpz_gcd
__gmpz_lcm))
(define-fourarg-mpz-funs (__gmpz_cdiv_qr
__gmpz_fdiv_qr
__gmpz_tdiv_qr
__gmpz_powm))
(declaim (inline __gmpz_pow_ui
__gmpz_probab_prime_p
__gmpz_fac_ui
__gmpz_2fac_ui
__gmpz_mfac_uiui
__gmpz_primorial_ui
__gmpz_bin_ui
__gmpz_fib2_ui))
(define-alien-routine __gmpz_pow_ui void
(r (* (struct gmpint)))
(b (* (struct gmpint)))
(e unsigned-long))
(define-alien-routine __gmpz_probab_prime_p int
(n (* (struct gmpint)))
(reps int))
(define-alien-routine __gmpz_fac_ui void
(r (* (struct gmpint)))
(a unsigned-long))
(define-alien-routine __gmpz_2fac_ui void
(r (* (struct gmpint)))
(a unsigned-long))
(define-alien-routine __gmpz_mfac_uiui void
(r (* (struct gmpint)))
(n unsigned-long)
(m unsigned-long))
(define-alien-routine __gmpz_primorial_ui void
(r (* (struct gmpint)))
(n unsigned-long))
(define-alien-routine __gmpz_bin_ui void
(r (* (struct gmpint)))
(n (* (struct gmpint)))
(k unsigned-long))
(define-alien-routine __gmpz_fib2_ui void
(r (* (struct gmpint)))
(a (* (struct gmpint)))
(b unsigned-long))
;; ratio functions
(defmacro define-threearg-mpq-funs (funs)
(loop for i in funs collect `(define-alien-routine ,i void
(r (* (struct gmprat)))
(a (* (struct gmprat)))
(b (* (struct gmprat))))
into defines
finally (return `(progn
(declaim (inline ,@funs))
,@defines))))
(define-threearg-mpq-funs (__gmpq_add
__gmpq_sub
__gmpq_mul
__gmpq_div))
;;;; SBCL interface
;;; utility macros for GMP mpz variable and result declaration and
;;; incarnation of associated SBCL bignums
(defmacro with-mpz-results (pairs &body body)
(loop for (gres size) in pairs
for res = (gensym "RESULT")
collect `(,gres (struct gmpint)) into declares
collect `(,res (%allocate-bignum ,size))
into resinits
collect `(setf (slot ,gres 'mp_alloc) (%bignum-length ,res)
(slot ,gres 'mp_size) 0
(slot ,gres 'mp_d) (bignum-data-sap ,res))
into inits
collect `(if (minusp (slot ,gres 'mp_size)) ; check for negative result
(z-to-bignum-neg ,res ,size)
(z-to-bignum ,res ,size))
into normlimbs
collect res into results
finally (return
`(let ,resinits
(sb-sys:with-pinned-objects ,results
(with-alien ,declares
,@inits
,@body
(values ,@normlimbs)))))))
(defmacro with-mpz-vars (pairs &body body)
(loop for (a ga) in pairs
for length = (gensym "LENGTH")
for plusp = (gensym "PLUSP")
for barg = (gensym "BARG")
for arg = (gensym "ARG")
collect `(,ga (struct gmpint)) into declares
collect `(,barg (bassert ,a)) into gmpinits
collect `(,plusp (%bignum-0-or-plusp ,barg (%bignum-length ,barg))) into gmpinits
collect `(,arg (if ,plusp ,barg (negate-bignum ,barg nil))) into gmpinits
collect `(,length (%bignum-length ,arg)) into gmpinits
collect arg into vars
collect `(setf (slot ,ga 'mp_alloc) ,length
(slot ,ga 'mp_size)
(progn ;; handle twos complements/ulong limbs mismatch
(when (zerop (%bignum-ref ,arg (1- ,length)))
(decf ,length))
(if ,plusp ,length (- ,length)))
(slot ,ga 'mp_d) (bignum-data-sap ,arg))
into gmpvarssetup
finally (return
`(with-alien ,declares
(let* ,gmpinits
(sb-sys:with-pinned-objects ,vars
,@gmpvarssetup
,@body))))))
(defmacro with-gmp-mpz-results (resultvars &body body)
(loop for gres in resultvars
for res = (gensym "RESULT")
for size = (gensym "SIZE")
collect size into sizes
collect `(,gres (struct gmpint)) into declares
collect `(__gmpz_init (addr ,gres)) into inits
collect `(,size (1+ (abs (slot ,gres 'mp_size))))
into resinits
collect `(,res (%allocate-bignum ,size))
into resinits
collect `(setf ,res (if (minusp (slot ,gres 'mp_size)) ; check for negative result
(gmp-z-to-bignum-neg (slot ,gres 'mp_d) ,res ,size)
(gmp-z-to-bignum (slot ,gres 'mp_d) ,res ,size)))
into copylimbs
collect `(__gmpz_clear (addr ,gres)) into clears
collect res into results
finally (return
`(with-alien ,declares
,@inits
,@body
(let* ,resinits
(declare (type bignum-index ,@sizes))
;; copy GMP limbs into result bignum
(sb-sys:with-pinned-objects ,results
,@copylimbs)
,@clears
(values ,@results))))))
;;; function definition and foreign function relationships
(defmacro defgmpfun (name args &body body)
`(progn
(declaim (sb-ext:maybe-inline ,name))
(defun ,name ,args
(declare (optimize (speed 3) (space 3) (safety 0))
(type integer ,@args))
,@body)))
;; SBCL/GMP functions
(defgmpfun mpz-add (a b)
(with-mpz-results ((result (1+ (max (blength a)
(blength b)))))
(with-mpz-vars ((a ga) (b gb))
(__gmpz_add (addr result) (addr ga) (addr gb)))))
(defgmpfun mpz-sub (a b)
(with-mpz-results ((result (1+ (max (blength a)
(blength b)))))
(with-mpz-vars ((a ga) (b gb))
(__gmpz_sub (addr result) (addr ga) (addr gb)))))
(defgmpfun mpz-mul (a b)
(with-mpz-results ((result (+ (blength a)
(blength b))))
(with-mpz-vars ((a ga) (b gb))
(__gmpz_mul (addr result) (addr ga) (addr gb)))))
(defgmpfun mpz-mod (a b)
(with-mpz-results ((result (1+ (max (blength a)
(blength b)))))
(with-mpz-vars ((a ga) (b gb))
(__gmpz_mod (addr result) (addr ga) (addr gb))
(when (and (minusp (slot gb 'mp_size))
(/= 0 (slot result 'mp_size)))
(__gmpz_add (addr result) (addr result) (addr gb))))))
(defgmpfun mpz-cdiv (n d)
(let ((size (1+ (max (blength n)
(blength d)))))
(with-mpz-results ((quot size)
(rem size))
(with-mpz-vars ((n gn) (d gd))
(__gmpz_cdiv_qr (addr quot) (addr rem) (addr gn) (addr gd))))))
(defgmpfun mpz-fdiv (n d)
(let ((size (1+ (max (blength n)
(blength d)))))
(with-mpz-results ((quot size)
(rem size))
(with-mpz-vars ((n gn) (d gd))
(__gmpz_fdiv_qr (addr quot) (addr rem) (addr gn) (addr gd))))))
(defgmpfun mpz-tdiv (n d)
(let ((size (max (blength n)
(blength d))))
(with-mpz-results ((quot size)
(rem size))
(with-mpz-vars ((n gn) (d gd))
(__gmpz_tdiv_qr (addr quot) (addr rem) (addr gn) (addr gd))))))
(defun mpz-pow (base exp)
(declare (optimize (speed 3) (space 3) (safety 0))
(type bignum-type base))
(check-type exp (unsigned-byte #.sb-vm:n-word-bits))
(with-gmp-mpz-results (rop)
(with-mpz-vars ((base gbase))
(__gmpz_pow_ui (addr rop) (addr gbase) exp))))
(defgmpfun mpz-powm (base exp mod)
(with-mpz-results ((rop (1+ (blength mod))))
(with-mpz-vars ((base gbase) (exp gexp) (mod gmod))
(__gmpz_powm (addr rop) (addr gbase) (addr gexp) (addr gmod)))))
(defgmpfun mpz-gcd (a b)
(with-mpz-results ((result (min (blength a)
(blength b))))
(with-mpz-vars ((a ga) (b gb))
(__gmpz_gcd (addr result) (addr ga) (addr gb)))))
(defgmpfun mpz-lcm (a b)
(with-mpz-results ((result (+ (blength a)
(blength b))))
(with-mpz-vars ((a ga) (b gb))
(__gmpz_lcm (addr result) (addr ga) (addr gb)))))
(defgmpfun mpz-sqrt (a)
(with-mpz-results ((result (1+ (ceiling (blength a) 2))))
(with-mpz-vars ((a ga))
(__gmpz_sqrt (addr result) (addr ga)))))
;;; Functions that use GMP-side allocated integers and copy the result
;;; into a SBCL bignum at the end of the computation when the required
;;; bignum length is known.
(defun mpz-probably-prime-p (n &optional (reps 25))
(declare (optimize (speed 3) (space 3) (safety 0)))
(check-type reps fixnum)
(with-mpz-vars ((n gn))
(__gmpz_probab_prime_p (addr gn) reps)))
(defun mpz-nextprime (a)
(declare (optimize (speed 3) (space 3) (safety 0)))
(with-gmp-mpz-results (prime)
(with-mpz-vars ((a ga))
(__gmpz_nextprime (addr prime) (addr ga)))))
(defun mpz-fac (n)
(declare (optimize (speed 3) (space 3) (safety 0)))
(check-type n (unsigned-byte #.sb-vm:n-word-bits))
(with-gmp-mpz-results (fac)
(__gmpz_fac_ui (addr fac) n)))
(defun %mpz-2fac (n)
(declare (optimize (speed 3) (space 3) (safety 0)))
(check-type n (unsigned-byte #.sb-vm:n-word-bits))
(with-gmp-mpz-results (fac)
(__gmpz_2fac_ui (addr fac) n)))
(defun %mpz-mfac (n m)
(declare (optimize (speed 3) (space 3) (safety 0)))
(check-type n (unsigned-byte #.sb-vm:n-word-bits))
(check-type m (unsigned-byte #.sb-vm:n-word-bits))
(with-gmp-mpz-results (fac)
(__gmpz_mfac_uiui (addr fac) n m)))
(defun %mpz-primorial (n)
(declare (optimize (speed 3) (space 3) (safety 0)))
(check-type n (unsigned-byte #.sb-vm:n-word-bits))
(with-gmp-mpz-results (r)
(__gmpz_primorial_ui (addr r) n)))
(defun setup-5.1-stubs ()
(macrolet ((stubify (name implementation &rest arguments)
`(setf (fdefinition ',name)
(if (member :sb-gmp-5.1 *gmp-features*)
(fdefinition ',implementation)
(lambda ,arguments
(declare (ignore ,@arguments))
(error "~S is only available in GMP >= 5.1"
',name))))))
(stubify mpz-2fac %mpz-2fac n)
(stubify mpz-mfac %mpz-mfac n m)
(stubify mpz-primorial %mpz-primorial n)))
(defun mpz-bin (n k)
(declare (optimize (speed 3) (space 3) (safety 0)))
(check-type k (unsigned-byte #.sb-vm:n-word-bits))
(with-gmp-mpz-results (r)
(with-mpz-vars ((n gn))
(__gmpz_bin_ui (addr r) (addr gn) k))))
(defun mpz-fib2 (n)
(declare (optimize (speed 3) (space 3) (safety 0)))
;; (let ((size (1+ (ceiling (* n (log 1.618034 2)) 64)))))
;; fibonacci number magnitude in bits is assymptotic to n(log_2 phi)
;; This is correct for the result but appears not to be enough for GMP
;; during computation (memory access error), so use GMP-side allocation.
(check-type n (unsigned-byte #.sb-vm:n-word-bits))
(with-gmp-mpz-results (fibn fibn-1)
(__gmpz_fib2_ui (addr fibn) (addr fibn-1) n)))
;;;; Random bignum (mpz) generation
;; we do not actually use the gestalt of the struct but need its size
;; for allocation purposes
(define-alien-type nil
(struct gmprandstate
(mp_seed (struct gmpint))
(mp_alg int)
(mp_algdata (* t))))
(declaim (inline __gmp_randinit_mt
__gmp_randinit_lc_2exp
__gmp_randseed
__gmp_randseed_ui
__gmpz_urandomb
__gmpz_urandomm))
(define-alien-routine __gmp_randinit_mt void
(s (* (struct gmprandstate))))
(define-alien-routine __gmp_randinit_lc_2exp void
(s (* (struct gmprandstate)))
(a (* (struct gmpint)))
(c unsigned-long)
(exp unsigned-long))
(define-alien-routine __gmp_randseed void
(s (* (struct gmprandstate)))
(sd (* (struct gmpint))))
(define-alien-routine __gmp_randseed_ui void
(s (* (struct gmprandstate)))
(sd unsigned-long))
(define-alien-routine __gmpz_urandomb void
(r (* (struct gmpint)))
(s (* (struct gmprandstate)))
(bcnt unsigned-long))
(define-alien-routine __gmpz_urandomm void
(r (* (struct gmpint)))
(s (* (struct gmprandstate)))
(n (* (struct gmpint))))
(defstruct (gmp-rstate (:constructor %make-gmp-rstate))
(ref (make-alien (struct gmprandstate))
:type (alien (* (struct gmprandstate))) :read-only t))
(defun make-gmp-rstate ()
"Instantiate a state for the GMP Mersenne-Twister random number generator."
(declare (optimize (speed 3) (space 3)))
(let* ((state (%make-gmp-rstate))
(ref (gmp-rstate-ref state)))
(__gmp_randinit_mt ref)
(sb-ext:finalize state (lambda () (free-alien ref)))
state))
(defun make-gmp-rstate-lc (a c m2exp)
"Instantiate a state for the GMP linear congruential random number generator."
(declare (optimize (speed 3) (space 3) (safety 0)))
(check-type c (unsigned-byte #.sb-vm:n-word-bits))
(check-type m2exp (unsigned-byte #.sb-vm:n-word-bits))
(let* ((state (%make-gmp-rstate))
(ref (gmp-rstate-ref state)))
(with-mpz-vars ((a ga))
(__gmp_randinit_lc_2exp ref (addr ga) c m2exp))
(sb-ext:finalize state (lambda () (free-alien ref)))
state))
(defun rand-seed (state seed)
"Initialize a random STATE with SEED."
(declare (optimize (speed 3) (space 3) (safety 0)))
(check-type state gmp-rstate)
(let ((ref (gmp-rstate-ref state)))
(cond
((typep seed '(unsigned-byte #.sb-vm:n-word-bits))
(__gmp_randseed_ui ref seed))
((typep seed '(integer 0 *))
(with-mpz-vars ((seed gseed))
(__gmp_randseed ref (addr gseed))))
(t
(error "SEED must be a positive integer")))))
(defun random-bitcount (state bitcount)
"Return a random integer in the range 0..(2^bitcount - 1)."
(declare (optimize (speed 3) (space 3) (safety 0)))
(check-type state gmp-rstate)
(check-type bitcount (unsigned-byte #.sb-vm:n-word-bits))
(let ((ref (gmp-rstate-ref state)))
(with-mpz-results ((result (+ (ceiling bitcount sb-vm:n-word-bits) 2)))
(__gmpz_urandomb (addr result) ref bitcount))))
(defun random-int (state boundary)
"Return a random integer in the range 0..(boundary - 1)."
(declare (optimize (speed 3) (space 3) (safety 0)))
(check-type state gmp-rstate)
(let ((b (bassert boundary))
(ref (gmp-rstate-ref state)))
(with-mpz-results ((result (1+ (%bignum-length b))))
(with-mpz-vars ((b gb))
(__gmpz_urandomm (addr result) ref (addr gb))))))
;;; Rational functions
(declaim (inline %lsize))
(defun %lsize (minusp n)
(declare (optimize (speed 3) (space 3) (safety 0)))
"n must be a (potentially denormalized) bignum"
(let ((length (%bignum-length n)))
(when (zerop (%bignum-ref n (1- length)))
(decf length))
(if minusp (- length) length)))
(defmacro defmpqfun (name gmpfun)
`(progn
(declaim (sb-ext:maybe-inline ,name))
(defun ,name (a b)
(declare (optimize (speed 3) (space 3) (safety 0)))
(let ((size (+ (max (blength (numerator a))
(blength (denominator a)))
(max (blength (numerator b))
(blength (denominator b)))
3)))
(with-alien ((r (struct gmprat)))
(let ((num (%allocate-bignum size))
(den (%allocate-bignum size)))
(sb-sys:with-pinned-objects (num den)
(setf (slot (slot r 'mp_num) 'mp_size) 0
(slot (slot r 'mp_num) 'mp_alloc) size
(slot (slot r 'mp_num) 'mp_d) (bignum-data-sap num))
(setf (slot (slot r 'mp_den) 'mp_size) 0
(slot (slot r 'mp_den) 'mp_alloc) size
(slot (slot r 'mp_den) 'mp_d) (bignum-data-sap den))
(let* ((an (bassert (numerator a)))
(ad (bassert (denominator a)))
(asign (not (%bignum-0-or-plusp an (%bignum-length an))))
(bn (bassert (numerator b)))
(bd (bassert (denominator b)))
(bsign (not (%bignum-0-or-plusp bn (%bignum-length bn)))))
(when asign
(setf an (negate-bignum an nil)))
(when bsign
(setf bn (negate-bignum bn nil)))
(let* ((anlen (%lsize asign an))
(adlen (%lsize NIL ad))
(bnlen (%lsize bsign bn))
(bdlen (%lsize NIL bd)))
(with-alien ((arga (struct gmprat))
(argb (struct gmprat)))
(sb-sys:with-pinned-objects (an ad bn bd)
(setf (slot (slot arga 'mp_num) 'mp_size) anlen
(slot (slot arga 'mp_num) 'mp_alloc) (abs anlen)
(slot (slot arga 'mp_num) 'mp_d)
(bignum-data-sap an))
(setf (slot (slot arga 'mp_den) 'mp_size) adlen
(slot (slot arga 'mp_den) 'mp_alloc) (abs adlen)
(slot (slot arga 'mp_den) 'mp_d)
(bignum-data-sap ad))
(setf (slot (slot argb 'mp_num) 'mp_size) bnlen
(slot (slot argb 'mp_num) 'mp_alloc) (abs bnlen)
(slot (slot argb 'mp_num) 'mp_d)
(bignum-data-sap bn))
(setf (slot (slot argb 'mp_den) 'mp_size) bdlen
(slot (slot argb 'mp_den) 'mp_alloc) (abs bdlen)
(slot (slot argb 'mp_den) 'mp_d)
(bignum-data-sap bd))
(,gmpfun (addr r) (addr arga) (addr argb)))))
(locally (declare (optimize (speed 1)))
(sb-kernel::build-ratio (if (minusp (slot (slot r 'mp_num) 'mp_size))
(z-to-bignum-neg num size)
(z-to-bignum num size))
(z-to-bignum den size)))))))))))
(defmpqfun mpq-add __gmpq_add)
(defmpqfun mpq-sub __gmpq_sub)
(defmpqfun mpq-mul __gmpq_mul)
(defmpqfun mpq-div __gmpq_div)
;;;; SBCL interface and integration installation
(macrolet ((def (name original)
(let ((special (intern (format nil "*~A-FUNCTION*" name))))
`(progn
(declaim (type function ,special)
(inline ,name))
(defvar ,special (symbol-function ',original))
(defun ,name (&rest args)
(apply (load-time-value ,special t) args))))))
(def orig-mul multiply-bignums)
(def orig-truncate bignum-truncate)
(def orig-gcd bignum-gcd)
(def orig-lcm sb-kernel:two-arg-lcm)
(def orig-isqrt isqrt)
(def orig-two-arg-+ sb-kernel:two-arg-+)
(def orig-two-arg-- sb-kernel:two-arg--)
(def orig-two-arg-* sb-kernel:two-arg-*)
(def orig-two-arg-/ sb-kernel:two-arg-/))
;;; integers
(defun gmp-mul (a b)
(declare (optimize (speed 3) (space 3))
(type bignum-type a b)
(inline mpz-mul))
(if (or (< (min (%bignum-length a)
(%bignum-length b))
6)
*gmp-disabled*)
(orig-mul a b)
(mpz-mul a b)))
(defun gmp-truncate (a b)
(declare (optimize (speed 3) (space 3))
(type bignum-type a b)
(inline mpz-tdiv))
(if (or (< (min (%bignum-length a)
(%bignum-length b))
3)
*gmp-disabled*)
(orig-truncate a b)
(mpz-tdiv a b)))
(defun gmp-lcm (a b)
(declare (optimize (speed 3) (space 3))
(type integer a b)
(inline mpz-lcm))
(if (or (and (typep a 'fixnum)
(typep b 'fixnum))
*gmp-disabled*)
(orig-lcm a b)
(mpz-lcm a b)))
(defun gmp-isqrt (n)
(declare (optimize (speed 3) (space 3))
(type unsigned-byte n)
(inline mpz-sqrt))
(if (or (typep n 'fixnum)
*gmp-disabled*)
(orig-isqrt n)
(mpz-sqrt n)))
;;; rationals
(defun gmp-two-arg-+ (x y)
(declare (optimize (speed 3) (space 3))
(inline mpq-add))
(if (and (or (typep x 'ratio)
(typep y 'ratio))
(rationalp y)
(rationalp x)
(not *gmp-disabled*))
(mpq-add x y)
(orig-two-arg-+ x y)))
(defun gmp-two-arg-- (x y)
(declare (optimize (speed 3) (space 3))
(inline mpq-sub))
(if (and (or (typep x 'ratio)
(typep y 'ratio))
(rationalp y)
(rationalp x)
(not *gmp-disabled*))
(mpq-sub x y)
(orig-two-arg-- x y)))
(defun gmp-two-arg-* (x y)
(declare (optimize (speed 3) (space 3))
(inline mpq-mul))
(if (and (or (typep x 'ratio)
(typep y 'ratio))
(rationalp y)
(rationalp x)
(not *gmp-disabled*))
(mpq-mul x y)
(orig-two-arg-* x y)))
(defun gmp-two-arg-/ (x y)
(declare (optimize (speed 3) (space 3))
(inline mpq-div))
(if (and (rationalp x)
(rationalp y)
(not (eql y 0))
(not *gmp-disabled*))
(mpq-div x y)
(orig-two-arg-/ x y)))
;;; installation
(defmacro with-package-locks-ignored (&body body)
`(handler-bind ((sb-ext:package-lock-violation
(lambda (condition)
(declare (ignore condition))
(invoke-restart :ignore-all))))
,@body))
(defun install-gmp-funs ()
(with-package-locks-ignored
(macrolet ((def (destination source)
`(setf (fdefinition ',destination)
(fdefinition ',source))))
(def multiply-bignums gmp-mul)
(def bignum-truncate gmp-truncate)
(def bignum-gcd mpz-gcd)
(def sb-kernel:two-arg-lcm gmp-lcm)
(def sb-kernel:two-arg-+ gmp-two-arg-+)
(def sb-kernel:two-arg-- gmp-two-arg--)
(def sb-kernel:two-arg-* gmp-two-arg-*)
(def sb-kernel:two-arg-/ gmp-two-arg-/)
(def isqrt gmp-isqrt)))
(values))
(defun uninstall-gmp-funs ()
(with-package-locks-ignored
(macrolet ((def (destination source)
`(setf (fdefinition ',destination)
,(intern (format nil "*~A-FUNCTION*" source)))))
(def multiply-bignums orig-mul)
(def bignum-truncate orig-truncate)
(def bignum-gcd orig-gcd)
(def sb-kernel:two-arg-lcm orig-lcm)
(def sb-kernel:two-arg-+ orig-two-arg-+)
(def sb-kernel:two-arg-- orig-two-arg--)
(def sb-kernel:two-arg-* orig-two-arg-*)
(def sb-kernel:two-arg-/ orig-two-arg-/)
(def isqrt orig-isqrt)))
(values))
(defun load-gmp (&key (persistently t))
(setf *gmp-features* nil
*gmp-version* nil
*features* (set-difference *features* '(:sb-gmp :sb-gmp-5.0 :sb-gmp-5.1)))
(when persistently
(pushnew 'load-gmp sb-ext:*init-hooks*)
(pushnew 'uninstall-gmp-funs sb-ext:*save-hooks*))
(let ((success (%load-gmp)))
(when success
(setf *gmp-version* (extern-alien "__gmp_version" c-string)))
(cond ((null *gmp-version*))
((string<= *gmp-version* "5.")
(warn "SB-GMP requires at least GMP version 5.0")
(setf success nil))
(t
(pushnew :sb-gmp *gmp-features*)
(pushnew :sb-gmp-5.0 *gmp-features*)
(when (string>= *gmp-version* "5.1")
(pushnew :sb-gmp-5.1 *gmp-features*))
(setf *features* (union *features* *gmp-features*))))
(if success
(install-gmp-funs)
(uninstall-gmp-funs))
(setup-5.1-stubs)
success))
(defun unload-gmp ()
(setf sb-ext:*init-hooks* (remove 'load-gmp sb-ext:*init-hooks*))
(uninstall-gmp-funs)
(setf sb-ext:*save-hooks* (remove 'uninstall-gmp-funs sb-ext:*save-hooks*))
(values))
(load-gmp)

Get latest updates about Open Source Projects, Conferences and News.

Sign up for the SourceForge newsletter:





No, thanks