
(/VERSIONCHECK 2) 

(DEFUN |GALUTIL;safeFloor;RI;1| (|x| $)
  (PROG (|shift|)
    (RETURN
      (SEQ (SEQ (LETT |shift|
                      (+ (- (SPADCALL |x| (QREFELT $ 9))
                            (SPADCALL (QREFELT $ 11)))
                         (QREFELT $ 7))
                      . #0=(|GALUTIL;safeFloor;RI;1|))
                (EXIT (COND
                        ((NULL (< |shift| 0))
                         (LETT |x|
                               (SPADCALL |x|
                                   (SPADCALL 1 |shift| (QREFELT $ 14))
                                   (QREFELT $ 15)) . #0#)))))
           (EXIT (SPADCALL (SPADCALL |x| (QREFELT $ 16))
                     (QREFELT $ 17))))))) 

(DEFUN |GALUTIL;safeCeiling;RI;2| (|x| $)
  (PROG (|shift|)
    (RETURN
      (SEQ (SEQ (LETT |shift|
                      (+ (- (SPADCALL |x| (QREFELT $ 9))
                            (SPADCALL (QREFELT $ 11)))
                         (QREFELT $ 7))
                      . #0=(|GALUTIL;safeCeiling;RI;2|))
                (EXIT (COND
                        ((NULL (< |shift| 0))
                         (LETT |x|
                               (SPADCALL |x|
                                   (SPADCALL 1 |shift| (QREFELT $ 14))
                                   (QREFELT $ 15)) . #0#)))))
           (EXIT (SPADCALL (SPADCALL |x| (QREFELT $ 19))
                     (QREFELT $ 17))))))) 

(DEFUN |GALUTIL;safetyMargin;2Nni;3| (|n| $)
  (PROG (|#G6| |#G7|)
    (RETURN
      (SEQ (PROGN
             (LETT |#G6| |n| . #0=(|GALUTIL;safetyMargin;2Nni;3|))
             (LETT |#G7| (QREFELT $ 7) . #0#)
             (SETELT $ 7 |#G6|)
             (LETT |n| |#G7| . #0#))
           (EXIT |n|))))) 

(DEFUN |GALUTIL;safetyMargin;Nni;4| ($) (QREFELT $ 7)) 

(DEFUN |GALUTIL;pascalTriangle;NniIR;5| (|n| |r| $)
  (PROG (|d| |i| |j| #0=#:G1839 #1=#:G1827 #2=#:G1828 |m| |mq|)
    (RETURN
      (SEQ (COND
             ((MINUSP |r|) (|spadConstant| $ 12))
             ('T
              (SEQ (LETT |d| (- |n| |r|)
                         . #3=(|GALUTIL;pascalTriangle;NniIR;5|))
                   (EXIT (COND
                           ((< |d| |r|)
                            (SPADCALL |n| |d| (QREFELT $ 29)))
                           ((ZEROP |r|) (|spadConstant| $ 13))
                           ((EQL |r| 1) (SPADCALL |n| (QREFELT $ 30)))
                           ((< (QREFELT $ 28) |n|)
                            (SPADCALL (SPADCALL |n| |r| (QREFELT $ 32))
                                (QREFELT $ 30)))
                           ((< (QREFELT $ 27) |n|)
                            (SEQ (SEQ (LETT |i|
                                       (+ (QREFELT $ 27) 1) . #3#)
                                      G190
                                      (COND
                                        ((> |i| |n|) #4=(GO G191)))
                                      (SEQ
                                       (SEQ (LETT |j| 2 . #3#)
                                        (LETT #0#
                                         (QUOTIENT2 |i| 2) . #3#)
                                        G190
                                        (COND
                                          ((QSGREATERP |j| #0#) #4#))
                                        (SEQ
                                         (EXIT
                                          (SETELT $ 26
                                           (SPADCALL (QREFELT $ 26)
                                            (SPADCALL
                                             (SPADCALL
                                              (PROG1
                                               (LETT #1#
                                                (- |i| 1) . #3#)
                                                (|check-subtype|
                                                 (>= #1# 0)
                                                 '(|NonNegativeInteger|)
                                                 #1#))
                                              (- |j| 1) (QREFELT $ 29))
                                             (SPADCALL
                                              (PROG1
                                               (LETT #2#
                                                (- |i| 1) . #3#)
                                                (|check-subtype|
                                                 (>= #2# 0)
                                                 '(|NonNegativeInteger|)
                                                 #2#))
                                              |j| (QREFELT $ 29))
                                             (QREFELT $ 15))
                                            (QREFELT $ 33)))))
                                        (LETT |j| (QSADD1 |j|) . #3#)
                                        #5=(GO G190) G191 (EXIT NIL))
                                       (EXIT (SETELT $ 27 |i|)))
                                      (LETT |i| (+ |i| 1) . #3#) #5#
                                      G191 (EXIT NIL))
                                 (EXIT (SPADCALL |n| |r|
                                        (QREFELT $ 29)))))
                           ('T
                            (SEQ (LETT |m| (DIVIDE2 (- |n| 4) 2) . #3#)
                                 (LETT |mq| (QCAR |m|) . #3#)
                                 (EXIT (SPADCALL (QREFELT $ 26)
                                        (-
                                         (+
                                          (* (+ |mq| 1)
                                           (+ |mq| (QCDR |m|)))
                                          |r|)
                                         1)
                                        (QREFELT $ 34)))))))))))))) 

(DEFUN |GALUTIL;rangePascalTriangle;2Nni;6| (|n| $)
  (PROG (|d| |dq| |#G17| |#G18|)
    (RETURN
      (SEQ (COND
             ((< |n| (QREFELT $ 27))
              (COND
                ((< |n| 3)
                 (SEQ (SETELT $ 26
                              (SPADCALL (QREFELT $ 26)
                                  (SPADCALL 1
                                      (SPADCALL (QREFELT $ 26)
                                       (QREFELT $ 35))
                                      (QREFELT $ 37))
                                  (QREFELT $ 38)))
                      (EXIT (SETELT $ 27 3))))
                ('T
                 (SEQ (LETT |d| (DIVIDE2 (- |n| 3) 2)
                            . #0=(|GALUTIL;rangePascalTriangle;2Nni;6|))
                      (LETT |dq| (QCAR |d|) . #0#)
                      (SETELT $ 26
                              (SPADCALL (QREFELT $ 26)
                                  (SPADCALL
                                      (+
                                       (* (+ |dq| 1)
                                        (+ |dq| (QCDR |d|)))
                                       1)
                                      (SPADCALL (QREFELT $ 26)
                                       (QREFELT $ 35))
                                      (QREFELT $ 37))
                                  (QREFELT $ 38)))
                      (EXIT (SETELT $ 27 |n|)))))))
           (PROGN
             (LETT |#G17| |n| . #0#)
             (LETT |#G18| (QREFELT $ 28) . #0#)
             (SETELT $ 28 |#G17|)
             (LETT |n| |#G18| . #0#))
           (EXIT |n|))))) 

(DEFUN |GALUTIL;rangePascalTriangle;Nni;7| ($) (QREFELT $ 28)) 

(DEFUN |GALUTIL;sizePascalTriangle;Nni;8| ($)
  (SPADCALL (QREFELT $ 26) (QREFELT $ 35))) 

(DEFUN |GALUTIL;fillPascalTriangle;V;9| ($)
  (SPADCALL (QREFELT $ 28) 2 (QREFELT $ 29))) 

(DEFUN |GaloisGroupUtilities| (#0=#:G1848)
  (PROG ()
    (RETURN
      (PROG (#1=#:G1849)
        (RETURN
          (COND
            ((LETT #1#
                   (|lassocShiftWithFunction| (LIST (|devaluate| #0#))
                       (HGET |$ConstructorCache|
                             '|GaloisGroupUtilities|)
                       '|domainEqualList|)
                   . #2=(|GaloisGroupUtilities|))
             (|CDRwithIncrement| #1#))
            ('T
             (UNWIND-PROTECT
               (PROG1 (|GaloisGroupUtilities;| #0#)
                 (LETT #1# T . #2#))
               (COND
                 ((NOT #1#)
                  (HREM |$ConstructorCache| '|GaloisGroupUtilities|))))))))))) 

(DEFUN |GaloisGroupUtilities;| (|#1|)
  (PROG (DV$1 |dv$| $ |pv$|)
    (RETURN
      (PROGN
        (LETT DV$1 (|devaluate| |#1|) . #0=(|GaloisGroupUtilities|))
        (LETT |dv$| (LIST '|GaloisGroupUtilities| DV$1) . #0#)
        (LETT $ (GETREFV 44) . #0#)
        (QSETREFV $ 0 |dv$|)
        (QSETREFV $ 3
            (LETT |pv$|
                  (|buildPredVector| 0 0
                      (LIST (|HasCategory| |#1|
                                '(|FloatingPointSystem|)))) . #0#))
        (|haddProp| |$ConstructorCache| '|GaloisGroupUtilities|
            (LIST DV$1) (CONS 1 $))
        (|stuffDomainSlots| $)
        (QSETREFV $ 6 |#1|)
        (COND
          ((|testBitVector| |pv$| 1)
           (PROGN
             (QSETREFV $ 7 6)
             (QSETREFV $ 18
                 (CONS (|dispatchFunction| |GALUTIL;safeFloor;RI;1|) $))
             (QSETREFV $ 20
                 (CONS (|dispatchFunction| |GALUTIL;safeCeiling;RI;2|)
                       $))
             (QSETREFV $ 22
                 (CONS (|dispatchFunction|
                           |GALUTIL;safetyMargin;2Nni;3|)
                       $))
             (QSETREFV $ 23
                 (CONS (|dispatchFunction|
                           |GALUTIL;safetyMargin;Nni;4|)
                       $)))))
        (QSETREFV $ 26 (SPADCALL (QREFELT $ 25)))
        (QSETREFV $ 27 3)
        (QSETREFV $ 28 216)
        $)))) 

(MAKEPROP '|GaloisGroupUtilities| '|infovec|
    (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) '|safetymargin|
             (|Integer|) (0 . |order|) (|PositiveInteger|)
             (5 . |precision|) (9 . |Zero|) (13 . |One|) (17 . |float|)
             (23 . +) (29 . |floor|) (34 . |retract|)
             (39 . |safeFloor|) (44 . |ceiling|) (49 . |safeCeiling|)
             (|NonNegativeInteger|) (54 . |safetyMargin|)
             (59 . |safetyMargin|) (|FlexibleArray| 6) (63 . |empty|)
             '|pascaltriangle| '|ncomputed| '|rangepascaltriangle|
             |GALUTIL;pascalTriangle;NniIR;5| (67 . |coerce|)
             (|IntegerCombinatoricFunctions| 8) (72 . |binomial|)
             (78 . |concat!|) (84 . |elt|) (90 . |#|)
             (|UniversalSegment| 8) (95 . SEGMENT) (101 . |delete!|)
             |GALUTIL;rangePascalTriangle;2Nni;6|
             |GALUTIL;rangePascalTriangle;Nni;7|
             |GALUTIL;sizePascalTriangle;Nni;8| (|Void|)
             |GALUTIL;fillPascalTriangle;V;9|)
          '#(|sizePascalTriangle| 107 |safetyMargin| 111 |safeFloor|
             120 |safeCeiling| 125 |rangePascalTriangle| 130
             |pascalTriangle| 139 |fillPascalTriangle| 145)
          'NIL
          (CONS (|makeByteWordVec2| 1 'NIL)
                (CONS '#()
                      (CONS '#()
                            (|makeByteWordVec2| 43
                                '(1 6 8 0 9 0 6 10 11 0 6 0 12 0 6 0 13
                                  2 6 0 8 8 14 2 6 0 0 0 15 1 6 0 0 16
                                  1 6 8 0 17 1 0 8 6 18 1 6 0 0 19 1 0
                                  8 6 20 1 0 21 21 22 0 0 21 23 0 24 0
                                  25 1 6 0 8 30 2 31 8 8 8 32 2 24 0 0
                                  6 33 2 24 6 0 8 34 1 24 21 0 35 2 36
                                  0 8 8 37 2 24 0 0 36 38 0 0 21 41 0 1
                                  21 23 1 1 21 21 22 1 1 8 6 18 1 1 8 6
                                  20 1 0 21 21 39 0 0 21 40 2 0 6 21 8
                                  29 0 0 42 43)))))
          '|lookupComplete|)) 
