
(PUT '|INS-;characteristic;Nni;1| '|SPADreplace| '(XLAM NIL 0)) 

(SDEFUN |INS-;characteristic;Nni;1| (($ |NonNegativeInteger|)) 0) 

(SDEFUN |INS-;differentiate;2S;2| ((|x| S) ($ S)) (|spadConstant| $ 9)) 

(SDEFUN |INS-;even?;SB;3| ((|x| S) ($ |Boolean|))
        (NULL (SPADCALL |x| (QREFELT $ 12)))) 

(SDEFUN |INS-;positive?;SB;4| ((|x| S) ($ |Boolean|))
        (SPADCALL |x| (|spadConstant| $ 9) (QREFELT $ 14))) 

(PUT '|INS-;copy;2S;5| '|SPADreplace| '(XLAM (|x|) |x|)) 

(SDEFUN |INS-;copy;2S;5| ((|x| S) ($ S)) |x|) 

(SDEFUN |INS-;bit?;2SB;6| ((|x| S) (|i| S) ($ |Boolean|))
        (SPADCALL (SPADCALL |x| (SPADCALL |i| (QREFELT $ 17)) (QREFELT $ 18))
                  (QREFELT $ 12))) 

(SDEFUN |INS-;mask;2S;7| ((|n| S) ($ S))
        (SPADCALL (SPADCALL (|spadConstant| $ 20) |n| (QREFELT $ 18))
                  (QREFELT $ 21))) 

(PUT '|INS-;rational?;SB;8| '|SPADreplace| '(XLAM (|x|) 'T)) 

(SDEFUN |INS-;rational?;SB;8| ((|x| S) ($ |Boolean|)) 'T) 

(SDEFUN |INS-;euclideanSize;SNni;9| ((|x| S) ($ |NonNegativeInteger|))
        (SPROG ((#1=#:G731 NIL) (#2=#:G730 NIL))
               (COND
                ((SPADCALL |x| (|spadConstant| $ 9) (QREFELT $ 24))
                 (|error| "euclideanSize called on zero"))
                ((SPADCALL |x| (|spadConstant| $ 9) (QREFELT $ 25))
                 (PROG1
                     (LETT #2# (- (SPADCALL |x| (QREFELT $ 27)))
                           . #3=(|INS-;euclideanSize;SNni;9|))
                   (|check_subtype2| (>= #2# 0) '(|NonNegativeInteger|)
                                     '(|Integer|) #2#)))
                ('T
                 (PROG1 (LETT #1# (SPADCALL |x| (QREFELT $ 27)) . #3#)
                   (|check_subtype2| (>= #1# 0) '(|NonNegativeInteger|)
                                     '(|Integer|) #1#)))))) 

(SDEFUN |INS-;convert;SF;10| ((|x| S) ($ |Float|))
        (SPADCALL (SPADCALL |x| (QREFELT $ 27)) (QREFELT $ 30))) 

(SDEFUN |INS-;convert;SDf;11| ((|x| S) ($ |DoubleFloat|))
        (FLOAT (SPADCALL |x| (QREFELT $ 27)) MOST-POSITIVE-DOUBLE-FLOAT)) 

(SDEFUN |INS-;convert;SIf;12| ((|x| S) ($ |InputForm|))
        (SPADCALL (SPADCALL |x| (QREFELT $ 27)) (QREFELT $ 35))) 

(SDEFUN |INS-;retract;SI;13| ((|x| S) ($ |Integer|))
        (SPADCALL |x| (QREFELT $ 27))) 

(SDEFUN |INS-;convert;SP;14| ((|x| S) ($ |Pattern| (|Integer|)))
        (SPADCALL (SPADCALL |x| (QREFELT $ 27)) (QREFELT $ 39))) 

(SDEFUN |INS-;factor;SF;15| ((|x| S) ($ |Factored| S))
        (SPADCALL |x| (QREFELT $ 43))) 

(SDEFUN |INS-;squareFree;SF;16| ((|x| S) ($ |Factored| S))
        (SPADCALL |x| (QREFELT $ 46))) 

(SDEFUN |INS-;prime?;SB;17| ((|x| S) ($ |Boolean|))
        (SPADCALL |x| (QREFELT $ 49))) 

(SDEFUN |INS-;factorial;2S;18| ((|x| S) ($ S)) (SPADCALL |x| (QREFELT $ 52))) 

(SDEFUN |INS-;binomial;3S;19| ((|n| S) (|m| S) ($ S))
        (SPADCALL |n| |m| (QREFELT $ 54))) 

(SDEFUN |INS-;permutation;3S;20| ((|n| S) (|m| S) ($ S))
        (SPADCALL |n| |m| (QREFELT $ 56))) 

(SDEFUN |INS-;retractIfCan;SU;21| ((|x| S) ($ |Union| (|Integer|) "failed"))
        (CONS 0 (SPADCALL |x| (QREFELT $ 27)))) 

(SDEFUN |INS-;init;S;22| (($ S)) (|spadConstant| $ 9)) 

(SDEFUN |INS-;nextItem;SU;23| ((|n| S) ($ |Union| S "failed"))
        (COND ((SPADCALL |n| (QREFELT $ 61)) (CONS 0 (|spadConstant| $ 20)))
              ((SPADCALL |n| (|spadConstant| $ 9) (QREFELT $ 14))
               (CONS 0 (SPADCALL |n| (QREFELT $ 17))))
              ('T
               (CONS 0 (SPADCALL (|spadConstant| $ 20) |n| (QREFELT $ 62)))))) 

(SDEFUN |INS-;patternMatch;SP2Pmr;24|
        ((|x| S) (|p| |Pattern| (|Integer|))
         (|l| |PatternMatchResult| (|Integer|) S)
         ($ |PatternMatchResult| (|Integer|) S))
        (SPADCALL |x| |p| |l| (QREFELT $ 67))) 

(SDEFUN |INS-;rational;SF;25| ((|x| S) ($ |Fraction| (|Integer|)))
        (SPADCALL (SPADCALL |x| (QREFELT $ 27)) (QREFELT $ 71))) 

(SDEFUN |INS-;rationalIfCan;SU;26|
        ((|x| S) ($ |Union| (|Fraction| (|Integer|)) "failed"))
        (CONS 0 (SPADCALL (SPADCALL |x| (QREFELT $ 27)) (QREFELT $ 71)))) 

(SDEFUN |INS-;symmetricRemainder;3S;27| ((|x| S) (|n| S) ($ S))
        (SPROG ((|r| (S)))
               (SEQ
                (LETT |r| (SPADCALL |x| |n| (QREFELT $ 75))
                      . #1=(|INS-;symmetricRemainder;3S;27|))
                (EXIT
                 (COND ((SPADCALL |r| (|spadConstant| $ 9) (QREFELT $ 24)) |r|)
                       (#2='T
                        (SEQ
                         (COND
                          ((SPADCALL |n| (|spadConstant| $ 9) (QREFELT $ 25))
                           (LETT |n| (SPADCALL |n| (QREFELT $ 17)) . #1#)))
                         (EXIT
                          (COND
                           ((SPADCALL |r| (|spadConstant| $ 9) (QREFELT $ 14))
                            (COND
                             ((SPADCALL (SPADCALL 2 |r| (QREFELT $ 77)) |n|
                                        (QREFELT $ 14))
                              (SPADCALL |r| |n| (QREFELT $ 62)))
                             (#2# |r|)))
                           ((SPADCALL
                             (SPADCALL (SPADCALL 2 |r| (QREFELT $ 77)) |n|
                                       (QREFELT $ 78))
                             (|spadConstant| $ 9) (QREFELT $ 79))
                            (SPADCALL |r| |n| (QREFELT $ 78)))
                           (#2# |r|)))))))))) 

(SDEFUN |INS-;invmod;3S;28| ((|a| S) (|b| S) ($ S))
        (SPROG
         ((|d1| (S)) (|d| (S)) (|c1| (S)) (|c| (S)) (|r1| (S)) (|r| (S))
          (|q| (S)))
         (SEQ
          (COND
           ((SPADCALL |a| (QREFELT $ 81))
            (LETT |a| (SPADCALL |a| |b| (QREFELT $ 82))
                  . #1=(|INS-;invmod;3S;28|))))
          (LETT |c| |a| . #1#) (LETT |c1| (|spadConstant| $ 20) . #1#)
          (LETT |d| |b| . #1#) (LETT |d1| (|spadConstant| $ 9) . #1#)
          (SEQ G190
               (COND ((NULL (NULL (SPADCALL |d| (QREFELT $ 61)))) (GO G191)))
               (SEQ (LETT |q| (SPADCALL |c| |d| (QREFELT $ 83)) . #1#)
                    (LETT |r|
                          (SPADCALL |c| (SPADCALL |q| |d| (QREFELT $ 84))
                                    (QREFELT $ 62))
                          . #1#)
                    (LETT |r1|
                          (SPADCALL |c1| (SPADCALL |q| |d1| (QREFELT $ 84))
                                    (QREFELT $ 62))
                          . #1#)
                    (LETT |c| |d| . #1#) (LETT |c1| |d1| . #1#)
                    (LETT |d| |r| . #1#) (EXIT (LETT |d1| |r1| . #1#)))
               NIL (GO G190) G191 (EXIT NIL))
          (EXIT
           (COND
            ((SPADCALL |c| (|spadConstant| $ 20) (QREFELT $ 24))
             (COND
              ((SPADCALL |c1| (QREFELT $ 81))
               (SPADCALL |c1| |b| (QREFELT $ 78)))
              (#2='T |c1|)))
            (#2# (|error| "inverse does not exist"))))))) 

(SDEFUN |INS-;powmod;4S;29| ((|x| S) (|n| S) (|p| S) ($ S))
        (SPROG ((|z| (S)) (#1=#:G810 NIL) (|y| (S)))
               (SEQ
                (EXIT
                 (SEQ
                  (COND
                   ((SPADCALL |x| (QREFELT $ 81))
                    (LETT |x| (SPADCALL |x| |p| (QREFELT $ 82))
                          . #2=(|INS-;powmod;4S;29|))))
                  (EXIT
                   (COND ((SPADCALL |x| (QREFELT $ 61)) (|spadConstant| $ 9))
                         ((SPADCALL |n| (QREFELT $ 61)) (|spadConstant| $ 20))
                         ('T
                          (SEQ (LETT |y| (|spadConstant| $ 20) . #2#)
                               (LETT |z| |x| . #2#)
                               (EXIT
                                (SEQ G190 NIL
                                     (SEQ
                                      (COND
                                       ((SPADCALL |n| (QREFELT $ 12))
                                        (LETT |y|
                                              (SPADCALL |y| |z| |p|
                                                        (QREFELT $ 86))
                                              . #2#)))
                                      (EXIT
                                       (COND
                                        ((SPADCALL
                                          (LETT |n|
                                                (SPADCALL |n|
                                                          (SPADCALL
                                                           (|spadConstant| $
                                                                           20)
                                                           (QREFELT $ 17))
                                                          (QREFELT $ 18))
                                                . #2#)
                                          (QREFELT $ 61))
                                         (PROGN
                                          (LETT #1# |y| . #2#)
                                          (GO #3=#:G809)))
                                        ('T
                                         (LETT |z|
                                               (SPADCALL |z| |z| |p|
                                                         (QREFELT $ 86))
                                               . #2#)))))
                                     NIL (GO G190) G191 (EXIT NIL)))))))))
                #3# (EXIT #1#)))) 

(DECLAIM (NOTINLINE |IntegerNumberSystem&;|)) 

(DEFUN |IntegerNumberSystem&| (|#1|)
  (SPROG ((|pv$| NIL) ($ NIL) (|dv$| NIL) (DV$1 NIL))
         (PROGN
          (LETT DV$1 (|devaluate| |#1|) . #1=(|IntegerNumberSystem&|))
          (LETT |dv$| (LIST '|IntegerNumberSystem&| DV$1) . #1#)
          (LETT $ (GETREFV 88) . #1#)
          (QSETREFV $ 0 |dv$|)
          (QSETREFV $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #1#))
          (|stuffDomainSlots| $)
          (QSETREFV $ 6 |#1|)
          (SETF |pv$| (QREFELT $ 3))
          $))) 

(MAKEPROP '|IntegerNumberSystem&| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|NonNegativeInteger|)
              |INS-;characteristic;Nni;1| (0 . |Zero|)
              |INS-;differentiate;2S;2| (|Boolean|) (4 . |odd?|)
              |INS-;even?;SB;3| (9 . >) |INS-;positive?;SB;4| |INS-;copy;2S;5|
              (15 . -) (20 . |shift|) |INS-;bit?;2SB;6| (26 . |One|)
              (30 . |dec|) |INS-;mask;2S;7| |INS-;rational?;SB;8| (35 . =)
              (41 . <) (|Integer|) (47 . |convert|) |INS-;euclideanSize;SNni;9|
              (|Float|) (52 . |coerce|) |INS-;convert;SF;10| (|DoubleFloat|)
              |INS-;convert;SDf;11| (|InputForm|) (57 . |convert|)
              |INS-;convert;SIf;12| |INS-;retract;SI;13| (|Pattern| 26)
              (62 . |coerce|) |INS-;convert;SP;14| (|Factored| 6)
              (|IntegerFactorizationPackage| 6) (67 . |factor|) (|Factored| $)
              |INS-;factor;SF;15| (72 . |squareFree|) |INS-;squareFree;SF;16|
              (|IntegerPrimesPackage| 6) (77 . |prime?|) |INS-;prime?;SB;17|
              (|IntegerCombinatoricFunctions| 6) (82 . |factorial|)
              |INS-;factorial;2S;18| (87 . |binomial|) |INS-;binomial;3S;19|
              (93 . |permutation|) |INS-;permutation;3S;20|
              (|Union| 26 '"failed") |INS-;retractIfCan;SU;21| |INS-;init;S;22|
              (99 . |zero?|) (104 . -) (|Union| $ '"failed")
              |INS-;nextItem;SU;23| (|PatternMatchResult| 26 6)
              (|PatternMatchIntegerNumberSystem| 6) (110 . |patternMatch|)
              (|PatternMatchResult| 26 $) |INS-;patternMatch;SP2Pmr;24|
              (|Fraction| 26) (117 . |coerce|) |INS-;rational;SF;25|
              (|Union| 70 '"failed") |INS-;rationalIfCan;SU;26| (122 . |rem|)
              (|PositiveInteger|) (128 . *) (134 . +) (140 . <=)
              |INS-;symmetricRemainder;3S;27| (146 . |negative?|)
              (151 . |positiveRemainder|) (157 . |quo|) (163 . *)
              |INS-;invmod;3S;28| (169 . |mulmod|) |INS-;powmod;4S;29|)
           '#(|symmetricRemainder| 176 |squareFree| 182 |retractIfCan| 187
              |retract| 192 |rationalIfCan| 197 |rational?| 202 |rational| 207
              |prime?| 212 |powmod| 217 |positive?| 224 |permutation| 229
              |patternMatch| 235 |nextItem| 242 |mask| 247 |invmod| 252 |init|
              258 |factorial| 262 |factor| 267 |even?| 272 |euclideanSize| 277
              |differentiate| 282 |copy| 287 |convert| 292 |characteristic| 312
              |bit?| 316 |binomial| 322)
           'NIL
           (CONS (|makeByteWordVec2| 1 'NIL)
                 (CONS '#()
                       (CONS '#()
                             (|makeByteWordVec2| 87
                                                 '(0 6 0 9 1 6 11 0 12 2 6 11 0
                                                   0 14 1 6 0 0 17 2 6 0 0 0 18
                                                   0 6 0 20 1 6 0 0 21 2 6 11 0
                                                   0 24 2 6 11 0 0 25 1 6 26 0
                                                   27 1 29 0 26 30 1 34 0 26 35
                                                   1 38 0 26 39 1 42 41 6 43 1
                                                   42 41 6 46 1 48 11 6 49 1 51
                                                   6 6 52 2 51 6 6 6 54 2 51 6
                                                   6 6 56 1 6 11 0 61 2 6 0 0 0
                                                   62 3 66 65 6 38 65 67 1 70 0
                                                   26 71 2 6 0 0 0 75 2 6 0 76
                                                   0 77 2 6 0 0 0 78 2 6 11 0 0
                                                   79 1 6 11 0 81 2 6 0 0 0 82
                                                   2 6 0 0 0 83 2 6 0 0 0 84 3
                                                   6 0 0 0 0 86 2 0 0 0 0 80 1
                                                   0 44 0 47 1 0 58 0 59 1 0 26
                                                   0 37 1 0 73 0 74 1 0 11 0 23
                                                   1 0 70 0 72 1 0 11 0 50 3 0
                                                   0 0 0 0 87 1 0 11 0 15 2 0 0
                                                   0 0 57 3 0 68 0 38 68 69 1 0
                                                   63 0 64 1 0 0 0 22 2 0 0 0 0
                                                   85 0 0 0 60 1 0 0 0 53 1 0
                                                   44 0 45 1 0 11 0 13 1 0 7 0
                                                   28 1 0 0 0 10 1 0 0 0 16 1 0
                                                   32 0 33 1 0 29 0 31 1 0 38 0
                                                   40 1 0 34 0 36 0 0 7 8 2 0
                                                   11 0 0 19 2 0 0 0 0 55)))))
           '|lookupComplete|)) 
