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;;; Prime numbers used for factoring
(defconstant some-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))
(defun square-numeric (my-int) (* my-int my-int))
(defconstant some-prime-squares (mapcar #'square-numeric some-primes))
;;; Factoring
(defun count-factors-aux (my-int)
"Return the number of factors in the given integer that's greater than one."
(let ((result 0) (my-res my-int) (divisors some-primes) (divsqrs some-prime-squares))
(do ((stop-flag nil)) (stop-flag)
(if (or (= my-res 1) (null divisors))
(setf stop-flag t)
(let ((divisor (pop divisors)) (divsqr (pop divsqrs)))
(if (> divsqr my-res)
(progn
(incf result)
(setf stop-flag t))
(do () ((plusp (mod my-res divisor)))
(setf my-res (/ my-res divisor))
(incf result))))))
result))
(defun count-factors (my-int)
"Return the number of factors in the given integer."
(if (< my-int 2) 0 (count-factors-aux my-int)))
(defun factor-count-bottom-bit (my-int)
"Return the bottom bit of the factor count of the given integer."
(mod (count-factors my-int) 2))
;;; Hash codes: bit length and constructor
(defconstant hash-code-bit-limit 64)
(defun mk-hash () (make-array hash-code-bit-limit :element-type 'bit :initial-element 0))
(defun clone-hash (my-hash)
"Return a clone of the given hash."
(copy-seq my-hash))
(defun calc-nth-hash-code (my-ord)
"Calculate and return the nth hash code."
(let ((result (mk-hash)) (ordinal (* my-ord hash-code-bit-limit)))
(dotimes (index hash-code-bit-limit)
(setf (sbit result index) (factor-count-bottom-bit ordinal))
(incf ordinal))
result))