Solved that issue but getting SEGVs in the math library:
0 rt_bitXratio
1 Fmult
2 floor_ceil_trunc_round1
). Here's a more complete code chunk. Entry point is (get-prime bits). Called from OBJC as (get-prime 1024)
#-mocl (declaim (declaration call-in))
;(rt:enable-objc-reader)
(declaim (call-in get-prime))
(defvar *small-primes*
#(2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103
107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199
211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313
317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433
439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563
569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673
677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811
821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941
947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051
1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163
1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279
1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399
1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489
1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601
1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 1709
1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 1831
1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951
1973 1979 1987 1993 1997)
"All prime numbers < 2000")
(defun randBytes (n)
"retrieve n bytes from /dev/urandom"
(with-open-file (urandom "/dev/urandom" :element-type 'unsigned-byte)
(do ((count n (decf count))
(r 0 (+ (ash r 8) (read-byte urandom))))
((= 0 count) r)
())))
(defun modexp (a x n)
"a^x mod n"
(do ((r 1 (if (= (mod x 2) 1)
(mod (* r a) n)
r))
(x x (floor (/ x 2)))
(a a (mod (* a a) n)))
((<= x 0) r)))
(defun random-number-less-than (n)
"generate an evenly distributed random number less than n"
(mod (randBytes (+ 1 (floor (/ (log n 2) 8)))) n))
(defvar *rabin-miller-cycles* 5
"The number of times to apply the rabin miller test to a prime number candidate")
(defun decompose (x)
(do* ((q 1 (+ q 1))
(m (/ x (expt 2 q)) (/ x (expt 2 q))))
((and (integerp m) (oddp m)) (values q m))))
(defun rabin-miller-round (n a b m)
(let ((init (modexp a m n)))
(or (= init 1)
(= init (- n 1))
(do ((z init (modexp z 2 n))
(j 0 (+ j 1)))
((or (= j b) (= z (- n 1)))
(= z (- n 1)))))))
(defun rabin-miller (n)
"applies the rabin-miller test to n"
(if (evenp n) nil
(multiple-value-bind (b m) (decompose (- n 1))
(dotimes (x *rabin-miller-cycles*)
(when (not (rabin-miller-round n (random-number-less-than n) b m))
(return-from rabin-miller nil)))
t)))
(defun probably-prime-p (n)
"Determine if N is likely to be prime."
;; Performs a couple of quick tests which eliminate a majority of
;; composite numbers, then passes the work off to the Rabin-Miller
;; probabalistic test
(let ((primes-count (length *small-primes*)))
(do ((x 0 (+ x 1)))
((>= x primes-count) (rabin-miller n))
(cond ((= n (aref *small-primes* x)) (return t))
((= (mod n (aref *small-primes* x)) 0) (return nil))))))
(defun generate-prime (bytes)
"probabalisticaly generates a prime number of bytes size"
(do ((candidate (logior
(randbytes bytes)
1 (ash 1 (- (* 8 bytes) 1))) (+ candidate 2)))
((probably-prime-p candidate) candidate)))
(defun get-prime (bits)
(write-to-string (generate-prime (/ bits 8))))
- tom, 1962 days ago
OK, I've reproduced the issue and I'm working on a fix.
- Wukix, 1962 days ago
Hey Tom,
I've got good news and bad news.
The good: I think I fixed the issue - https://wukix.com/support/dist/mocl-140904-osx.tar.gz
The bad: (get-prime 1024) seems pretty slow in the iPhone simulator. FYI, this is almost entirely due to lots of bignum arithmetic (and mocl's non-super-optimized implementation thereof), particularly mod/division and multiplication. I'm hoping you can live with that in your app. If not, let's talk further.
Let me know if that works.
- Wukix, 1961 days ago
Yes, this fixes the bug. Probably is too slow for practical purposes. I can precompute the prime ahead of time and just hard wire it with very little downside.
I will open up an enhancement to optimize this library. Here's the (time) from sbcl to generate a 1024 bit prime:
Evaluation took:
0.083 seconds of real time
0.082610 seconds of total run time (0.074113 user, 0.008497 system)
[ Run times consist of 0.013 seconds GC time, and 0.070 seconds non-GC time. ]
100.00% CPU
189,998,046 processor cycles
38,851,216 bytes consed
103484157528739217420052248015933486213158849701477904349804822894095843447406589045024323582700348079755545209052223207997729901139791186018100474400617812859753826270776954400423215411800390211638888811565719628699618079695517133879170197730107651441010637014978999277734651858209796633210458417000654793959
Solved that issue but getting SEGVs in the math library: 0 rt_bitXratio 1 Fmult 2 floor_ceil_trunc_round1 ). Here's a more complete code chunk. Entry point is (get-prime bits). Called from OBJC as (get-prime 1024) #-mocl (declaim (declaration call-in)) ;(rt:enable-objc-reader) (declaim (call-in get-prime)) (defvar *small-primes* #(2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997) "All prime numbers < 2000") (defun randBytes (n) "retrieve n bytes from /dev/urandom" (with-open-file (urandom "/dev/urandom" :element-type 'unsigned-byte) (do ((count n (decf count)) (r 0 (+ (ash r 8) (read-byte urandom)))) ((= 0 count) r) ()))) (defun modexp (a x n) "a^x mod n" (do ((r 1 (if (= (mod x 2) 1) (mod (* r a) n) r)) (x x (floor (/ x 2))) (a a (mod (* a a) n))) ((<= x 0) r))) (defun random-number-less-than (n) "generate an evenly distributed random number less than n" (mod (randBytes (+ 1 (floor (/ (log n 2) 8)))) n)) (defvar *rabin-miller-cycles* 5 "The number of times to apply the rabin miller test to a prime number candidate") (defun decompose (x) (do* ((q 1 (+ q 1)) (m (/ x (expt 2 q)) (/ x (expt 2 q)))) ((and (integerp m) (oddp m)) (values q m)))) (defun rabin-miller-round (n a b m) (let ((init (modexp a m n))) (or (= init 1) (= init (- n 1)) (do ((z init (modexp z 2 n)) (j 0 (+ j 1))) ((or (= j b) (= z (- n 1))) (= z (- n 1))))))) (defun rabin-miller (n) "applies the rabin-miller test to n" (if (evenp n) nil (multiple-value-bind (b m) (decompose (- n 1)) (dotimes (x *rabin-miller-cycles*) (when (not (rabin-miller-round n (random-number-less-than n) b m)) (return-from rabin-miller nil))) t))) (defun probably-prime-p (n) "Determine if N is likely to be prime." ;; Performs a couple of quick tests which eliminate a majority of ;; composite numbers, then passes the work off to the Rabin-Miller ;; probabalistic test (let ((primes-count (length *small-primes*))) (do ((x 0 (+ x 1))) ((>= x primes-count) (rabin-miller n)) (cond ((= n (aref *small-primes* x)) (return t)) ((= (mod n (aref *small-primes* x)) 0) (return nil)))))) (defun generate-prime (bytes) "probabalisticaly generates a prime number of bytes size" (do ((candidate (logior (randbytes bytes) 1 (ash 1 (- (* 8 bytes) 1))) (+ candidate 2))) ((probably-prime-p candidate) candidate))) (defun get-prime (bits) (write-to-string (generate-prime (/ bits 8))))