path: root/src/algebra/strap/DFLOAT.lsp

(/VERSIONCHECK 2) 

(DEFUN |DFLOAT;doubleFloatFormat;2S;1| (|s| $)
  (PROG (|ss|)
    (RETURN
      (SEQ (LETT |ss| (|getShellEntry| $ 6)
                 |DFLOAT;doubleFloatFormat;2S;1|)
           (SETELT $ 6 |s|) (EXIT |ss|))))) 

(DEFUN |DFLOAT;OMwrite;$S;2| (|x| $)
  (PROG (|sp| |dev| |s|)
    (RETURN
      (SEQ (LETT |s| "" |DFLOAT;OMwrite;$S;2|)
           (LETT |sp| (OM-STRINGTOSTRINGPTR |s|) |DFLOAT;OMwrite;$S;2|)
           (LETT |dev|
                 (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 10))
                     (|getShellEntry| $ 12))
                 |DFLOAT;OMwrite;$S;2|)
           (SPADCALL |dev| (|getShellEntry| $ 14))
           (SPADCALL |dev| |x| (|getShellEntry| $ 16))
           (SPADCALL |dev| (|getShellEntry| $ 17))
           (SPADCALL |dev| (|getShellEntry| $ 18))
           (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |DFLOAT;OMwrite;$S;2|)
           (EXIT |s|))))) 

(DEFUN |DFLOAT;OMwrite;$BS;3| (|x| |wholeObj| $)
  (PROG (|sp| |dev| |s|)
    (RETURN
      (SEQ (LETT |s| "" |DFLOAT;OMwrite;$BS;3|)
           (LETT |sp| (OM-STRINGTOSTRINGPTR |s|)
                 |DFLOAT;OMwrite;$BS;3|)
           (LETT |dev|
                 (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 10))
                     (|getShellEntry| $ 12))
                 |DFLOAT;OMwrite;$BS;3|)
           (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 14))))
           (SPADCALL |dev| |x| (|getShellEntry| $ 16))
           (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 17))))
           (SPADCALL |dev| (|getShellEntry| $ 18))
           (LETT |s| (OM-STRINGPTRTOSTRING |sp|)
                 |DFLOAT;OMwrite;$BS;3|)
           (EXIT |s|))))) 

(DEFUN |DFLOAT;OMwrite;Omd$V;4| (|dev| |x| $)
  (SEQ (SPADCALL |dev| (|getShellEntry| $ 14))
       (SPADCALL |dev| |x| (|getShellEntry| $ 16))
       (EXIT (SPADCALL |dev| (|getShellEntry| $ 17))))) 

(DEFUN |DFLOAT;OMwrite;Omd$BV;5| (|dev| |x| |wholeObj| $)
  (SEQ (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 14))))
       (SPADCALL |dev| |x| (|getShellEntry| $ 16))
       (EXIT (COND
               (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 17))))))) 

(PUT '|DFLOAT;checkComplex| '|SPADreplace| 'C-TO-R) 

(DEFUN |DFLOAT;checkComplex| (|x| $) (C-TO-R |x|)) 

(PUT '|DFLOAT;base;Pi;7| '|SPADreplace| '(XLAM NIL (FLOAT-RADIX 0.0))) 

(DEFUN |DFLOAT;base;Pi;7| ($) (FLOAT-RADIX 0.0)) 

(DEFUN |DFLOAT;mantissa;$I;8| (|x| $) (QCAR (|DFLOAT;manexp| |x| $))) 

(DEFUN |DFLOAT;exponent;$I;9| (|x| $) (QCDR (|DFLOAT;manexp| |x| $))) 

(PUT '|DFLOAT;precision;Pi;10| '|SPADreplace|
     '(XLAM NIL (FLOAT-DIGITS 0.0))) 

(DEFUN |DFLOAT;precision;Pi;10| ($) (FLOAT-DIGITS 0.0)) 

(DEFUN |DFLOAT;bits;Pi;11| ($)
  (PROG (#0=#:G1419)
    (RETURN
      (COND
        ((EQL (FLOAT-RADIX 0.0) 2) (FLOAT-DIGITS 0.0))
        ((EQL (FLOAT-RADIX 0.0) 16) (* 4 (FLOAT-DIGITS 0.0)))
        ('T
         (PROG1 (LETT #0#
                      (FIX (SPADCALL (FLOAT-DIGITS 0.0)
                               (SPADCALL
                                   (FLOAT (FLOAT-RADIX 0.0)
                                    MOST-POSITIVE-LONG-FLOAT)
                                   (|getShellEntry| $ 30))
                               (|getShellEntry| $ 31)))
                      |DFLOAT;bits;Pi;11|)
           (|check-subtype| (> #0# 0) '(|PositiveInteger|) #0#))))))) 

(PUT '|DFLOAT;max;$;12| '|SPADreplace|
     '(XLAM NIL MOST-POSITIVE-LONG-FLOAT)) 

(DEFUN |DFLOAT;max;$;12| ($) MOST-POSITIVE-LONG-FLOAT) 

(PUT '|DFLOAT;min;$;13| '|SPADreplace|
     '(XLAM NIL MOST-NEGATIVE-LONG-FLOAT)) 

(DEFUN |DFLOAT;min;$;13| ($) MOST-NEGATIVE-LONG-FLOAT) 

(DEFUN |DFLOAT;order;$I;14| (|a| $)
  (- (+ (FLOAT-DIGITS 0.0) (SPADCALL |a| (|getShellEntry| $ 28))) 1)) 

(PUT '|DFLOAT;Zero;$;15| '|SPADreplace|
     '(XLAM NIL (FLOAT 0 MOST-POSITIVE-LONG-FLOAT))) 

(DEFUN |DFLOAT;Zero;$;15| ($) (FLOAT 0 MOST-POSITIVE-LONG-FLOAT)) 

(PUT '|DFLOAT;One;$;16| '|SPADreplace|
     '(XLAM NIL (FLOAT 1 MOST-POSITIVE-LONG-FLOAT))) 

(DEFUN |DFLOAT;One;$;16| ($) (FLOAT 1 MOST-POSITIVE-LONG-FLOAT)) 

(DEFUN |DFLOAT;exp1;$;17| ($)
  (/ (FLOAT 534625820200 MOST-POSITIVE-LONG-FLOAT)
     (FLOAT 196677847971 MOST-POSITIVE-LONG-FLOAT))) 

(PUT '|DFLOAT;pi;$;18| '|SPADreplace| '(XLAM NIL PI)) 

(DEFUN |DFLOAT;pi;$;18| ($) PI) 

(DEFUN |DFLOAT;coerce;$Of;19| (|x| $)
  (SPADCALL (FORMAT NIL (|getShellEntry| $ 6) |x|)
      (|getShellEntry| $ 41))) 

(DEFUN |DFLOAT;convert;$If;20| (|x| $)
  (SPADCALL |x| (|getShellEntry| $ 44))) 

(PUT '|DFLOAT;<;2$B;21| '|SPADreplace| '<) 

(DEFUN |DFLOAT;<;2$B;21| (|x| |y| $) (< |x| |y|)) 

(PUT '|DFLOAT;-;2$;22| '|SPADreplace| '-) 

(DEFUN |DFLOAT;-;2$;22| (|x| $) (- |x|)) 

(PUT '|DFLOAT;+;3$;23| '|SPADreplace| '+) 

(DEFUN |DFLOAT;+;3$;23| (|x| |y| $) (+ |x| |y|)) 

(PUT '|DFLOAT;-;3$;24| '|SPADreplace| '-) 

(DEFUN |DFLOAT;-;3$;24| (|x| |y| $) (- |x| |y|)) 

(PUT '|DFLOAT;*;3$;25| '|SPADreplace| '*) 

(DEFUN |DFLOAT;*;3$;25| (|x| |y| $) (* |x| |y|)) 

(PUT '|DFLOAT;*;I2$;26| '|SPADreplace| '*) 

(DEFUN |DFLOAT;*;I2$;26| (|i| |x| $) (* |i| |x|)) 

(PUT '|DFLOAT;max;3$;27| '|SPADreplace| 'MAX) 

(DEFUN |DFLOAT;max;3$;27| (|x| |y| $) (MAX |x| |y|)) 

(PUT '|DFLOAT;min;3$;28| '|SPADreplace| 'MIN) 

(DEFUN |DFLOAT;min;3$;28| (|x| |y| $) (MIN |x| |y|)) 

(PUT '|DFLOAT;=;2$B;29| '|SPADreplace| '=) 

(DEFUN |DFLOAT;=;2$B;29| (|x| |y| $) (= |x| |y|)) 

(PUT '|DFLOAT;/;$I$;30| '|SPADreplace| '/) 

(DEFUN |DFLOAT;/;$I$;30| (|x| |i| $) (/ |x| |i|)) 

(DEFUN |DFLOAT;sqrt;2$;31| (|x| $)
  (|DFLOAT;checkComplex| (SQRT |x|) $)) 

(DEFUN |DFLOAT;log10;2$;32| (|x| $)
  (|DFLOAT;checkComplex| (|log| |x|) $)) 

(PUT '|DFLOAT;**;$I$;33| '|SPADreplace| 'EXPT) 

(DEFUN |DFLOAT;**;$I$;33| (|x| |i| $) (EXPT |x| |i|)) 

(DEFUN |DFLOAT;**;3$;34| (|x| |y| $)
  (|DFLOAT;checkComplex| (EXPT |x| |y|) $)) 

(PUT '|DFLOAT;coerce;I$;35| '|SPADreplace|
     '(XLAM (|i|) (FLOAT |i| MOST-POSITIVE-LONG-FLOAT))) 

(DEFUN |DFLOAT;coerce;I$;35| (|i| $)
  (FLOAT |i| MOST-POSITIVE-LONG-FLOAT)) 

(PUT '|DFLOAT;exp;2$;36| '|SPADreplace| 'EXP) 

(DEFUN |DFLOAT;exp;2$;36| (|x| $) (EXP |x|)) 

(DEFUN |DFLOAT;log;2$;37| (|x| $) (|DFLOAT;checkComplex| (LN |x|) $)) 

(DEFUN |DFLOAT;log2;2$;38| (|x| $)
  (|DFLOAT;checkComplex| (LOG2 |x|) $)) 

(PUT '|DFLOAT;sin;2$;39| '|SPADreplace| 'SIN) 

(DEFUN |DFLOAT;sin;2$;39| (|x| $) (SIN |x|)) 

(PUT '|DFLOAT;cos;2$;40| '|SPADreplace| 'COS) 

(DEFUN |DFLOAT;cos;2$;40| (|x| $) (COS |x|)) 

(PUT '|DFLOAT;tan;2$;41| '|SPADreplace| 'TAN) 

(DEFUN |DFLOAT;tan;2$;41| (|x| $) (TAN |x|)) 

(PUT '|DFLOAT;cot;2$;42| '|SPADreplace| 'COT) 

(DEFUN |DFLOAT;cot;2$;42| (|x| $) (COT |x|)) 

(PUT '|DFLOAT;sec;2$;43| '|SPADreplace| 'SEC) 

(DEFUN |DFLOAT;sec;2$;43| (|x| $) (SEC |x|)) 

(PUT '|DFLOAT;csc;2$;44| '|SPADreplace| 'CSC) 

(DEFUN |DFLOAT;csc;2$;44| (|x| $) (CSC |x|)) 

(DEFUN |DFLOAT;asin;2$;45| (|x| $)
  (|DFLOAT;checkComplex| (ASIN |x|) $)) 

(DEFUN |DFLOAT;acos;2$;46| (|x| $)
  (|DFLOAT;checkComplex| (ACOS |x|) $)) 

(PUT '|DFLOAT;atan;2$;47| '|SPADreplace| 'ATAN) 

(DEFUN |DFLOAT;atan;2$;47| (|x| $) (ATAN |x|)) 

(DEFUN |DFLOAT;acsc;2$;48| (|x| $)
  (|DFLOAT;checkComplex| (ACSC |x|) $)) 

(PUT '|DFLOAT;acot;2$;49| '|SPADreplace| 'ACOT) 

(DEFUN |DFLOAT;acot;2$;49| (|x| $) (ACOT |x|)) 

(DEFUN |DFLOAT;asec;2$;50| (|x| $)
  (|DFLOAT;checkComplex| (ASEC |x|) $)) 

(PUT '|DFLOAT;sinh;2$;51| '|SPADreplace| 'SINH) 

(DEFUN |DFLOAT;sinh;2$;51| (|x| $) (SINH |x|)) 

(PUT '|DFLOAT;cosh;2$;52| '|SPADreplace| 'COSH) 

(DEFUN |DFLOAT;cosh;2$;52| (|x| $) (COSH |x|)) 

(PUT '|DFLOAT;tanh;2$;53| '|SPADreplace| 'TANH) 

(DEFUN |DFLOAT;tanh;2$;53| (|x| $) (TANH |x|)) 

(PUT '|DFLOAT;csch;2$;54| '|SPADreplace| 'CSCH) 

(DEFUN |DFLOAT;csch;2$;54| (|x| $) (CSCH |x|)) 

(PUT '|DFLOAT;coth;2$;55| '|SPADreplace| 'COTH) 

(DEFUN |DFLOAT;coth;2$;55| (|x| $) (COTH |x|)) 

(PUT '|DFLOAT;sech;2$;56| '|SPADreplace| 'SECH) 

(DEFUN |DFLOAT;sech;2$;56| (|x| $) (SECH |x|)) 

(PUT '|DFLOAT;asinh;2$;57| '|SPADreplace| 'ASINH) 

(DEFUN |DFLOAT;asinh;2$;57| (|x| $) (ASINH |x|)) 

(DEFUN |DFLOAT;acosh;2$;58| (|x| $)
  (|DFLOAT;checkComplex| (ACOSH |x|) $)) 

(DEFUN |DFLOAT;atanh;2$;59| (|x| $)
  (|DFLOAT;checkComplex| (ATANH |x|) $)) 

(PUT '|DFLOAT;acsch;2$;60| '|SPADreplace| 'ACSCH) 

(DEFUN |DFLOAT;acsch;2$;60| (|x| $) (ACSCH |x|)) 

(DEFUN |DFLOAT;acoth;2$;61| (|x| $)
  (|DFLOAT;checkComplex| (ACOTH |x|) $)) 

(DEFUN |DFLOAT;asech;2$;62| (|x| $)
  (|DFLOAT;checkComplex| (ASECH |x|) $)) 

(PUT '|DFLOAT;/;3$;63| '|SPADreplace| '/) 

(DEFUN |DFLOAT;/;3$;63| (|x| |y| $) (/ |x| |y|)) 

(PUT '|DFLOAT;negative?;$B;64| '|SPADreplace| 'MINUSP) 

(DEFUN |DFLOAT;negative?;$B;64| (|x| $) (MINUSP |x|)) 

(PUT '|DFLOAT;zero?;$B;65| '|SPADreplace| 'ZEROP) 

(DEFUN |DFLOAT;zero?;$B;65| (|x| $) (ZEROP |x|)) 

(PUT '|DFLOAT;hash;$I;66| '|SPADreplace| 'HASHEQ) 

(DEFUN |DFLOAT;hash;$I;66| (|x| $) (HASHEQ |x|)) 

(DEFUN |DFLOAT;recip;$U;67| (|x| $)
  (COND ((ZEROP |x|) (CONS 1 "failed")) ('T (CONS 0 (/ 1.0 |x|))))) 

(PUT '|DFLOAT;differentiate;2$;68| '|SPADreplace| '(XLAM (|x|) 0.0)) 

(DEFUN |DFLOAT;differentiate;2$;68| (|x| $) 0.0) 

(DEFUN |DFLOAT;Gamma;2$;69| (|x| $)
  (SPADCALL |x| (|getShellEntry| $ 95))) 

(DEFUN |DFLOAT;Beta;3$;70| (|x| |y| $)
  (SPADCALL |x| |y| (|getShellEntry| $ 97))) 

(PUT '|DFLOAT;wholePart;$I;71| '|SPADreplace| 'FIX) 

(DEFUN |DFLOAT;wholePart;$I;71| (|x| $) (FIX |x|)) 

(DEFUN |DFLOAT;float;2IPi$;72| (|ma| |ex| |b| $)
  (* |ma| (EXPT (FLOAT |b| MOST-POSITIVE-LONG-FLOAT) |ex|))) 

(PUT '|DFLOAT;convert;$Df;73| '|SPADreplace| '(XLAM (|x|) |x|)) 

(DEFUN |DFLOAT;convert;$Df;73| (|x| $) |x|) 

(DEFUN |DFLOAT;convert;$F;74| (|x| $)
  (SPADCALL |x| (|getShellEntry| $ 103))) 

(DEFUN |DFLOAT;rationalApproximation;$NniF;75| (|x| |d| $)
  (SPADCALL |x| |d| 10 (|getShellEntry| $ 107))) 

(DEFUN |DFLOAT;atan;3$;76| (|x| |y| $)
  (PROG (|theta|)
    (RETURN
      (SEQ (COND
             ((= |x| 0.0)
              (COND
                ((< 0.0 |y|) (/ PI 2))
                ((< |y| 0.0) (- (/ PI 2)))
                ('T 0.0)))
             ('T
              (SEQ (LETT |theta| (ATAN (FLOAT-SIGN 1.0 (/ |y| |x|)))
                         |DFLOAT;atan;3$;76|)
                   (COND
                     ((< |x| 0.0)
                      (LETT |theta| (- PI |theta|) |DFLOAT;atan;3$;76|)))
                   (COND
                     ((< |y| 0.0)
                      (LETT |theta| (- |theta|) |DFLOAT;atan;3$;76|)))
                   (EXIT |theta|)))))))) 

(DEFUN |DFLOAT;retract;$F;77| (|x| $)
  (PROG (#0=#:G1494)
    (RETURN
      (SPADCALL |x|
          (PROG1 (LETT #0# (- (FLOAT-DIGITS 0.0) 1)
                       |DFLOAT;retract;$F;77|)
            (|check-subtype| (>= #0# 0) '(|NonNegativeInteger|) #0#))
          (FLOAT-RADIX 0.0) (|getShellEntry| $ 107))))) 

(DEFUN |DFLOAT;retractIfCan;$U;78| (|x| $)
  (PROG (#0=#:G1499)
    (RETURN
      (CONS 0
            (SPADCALL |x|
                (PROG1 (LETT #0# (- (FLOAT-DIGITS 0.0) 1)
                             |DFLOAT;retractIfCan;$U;78|)
                  (|check-subtype| (>= #0# 0) '(|NonNegativeInteger|)
                      #0#))
                (FLOAT-RADIX 0.0) (|getShellEntry| $ 107)))))) 

(DEFUN |DFLOAT;retract;$I;79| (|x| $)
  (PROG (|n|)
    (RETURN
      (SEQ (LETT |n| (FIX |x|) |DFLOAT;retract;$I;79|)
           (EXIT (COND
                   ((= |x| (FLOAT |n| MOST-POSITIVE-LONG-FLOAT)) |n|)
                   ('T (|error| "Not an integer")))))))) 

(DEFUN |DFLOAT;retractIfCan;$U;80| (|x| $)
  (PROG (|n|)
    (RETURN
      (SEQ (LETT |n| (FIX |x|) |DFLOAT;retractIfCan;$U;80|)
           (EXIT (COND
                   ((= |x| (FLOAT |n| MOST-POSITIVE-LONG-FLOAT))
                    (CONS 0 |n|))
                   ('T (CONS 1 "failed")))))))) 

(DEFUN |DFLOAT;sign;$I;81| (|x| $)
  (SPADCALL (FLOAT-SIGN |x| 1.0) (|getShellEntry| $ 113))) 

(PUT '|DFLOAT;abs;2$;82| '|SPADreplace|
     '(XLAM (|x|) (FLOAT-SIGN 1.0 |x|))) 

(DEFUN |DFLOAT;abs;2$;82| (|x| $) (FLOAT-SIGN 1.0 |x|)) 

(DEFUN |DFLOAT;manexp| (|x| $)
  (PROG (|s| #0=#:G1520 |me| |two53|)
    (RETURN
      (SEQ (EXIT (COND
                   ((ZEROP |x|) (CONS 0 0))
                   ('T
                    (SEQ (LETT |s|
                               (SPADCALL |x| (|getShellEntry| $ 116))
                               |DFLOAT;manexp|)
                         (LETT |x| (FLOAT-SIGN 1.0 |x|)
                               |DFLOAT;manexp|)
                         (COND
                           ((< MOST-POSITIVE-LONG-FLOAT |x|)
                            (PROGN
                              (LETT #0#
                                    (CONS
                                     (+
                                      (* |s|
                                       (SPADCALL
                                        MOST-POSITIVE-LONG-FLOAT
                                        (|getShellEntry| $ 27)))
                                      1)
                                     (SPADCALL MOST-POSITIVE-LONG-FLOAT
                                      (|getShellEntry| $ 28)))
                                    |DFLOAT;manexp|)
                              (GO #0#))))
                         (LETT |me| (MANEXP |x|) |DFLOAT;manexp|)
                         (LETT |two53|
                               (EXPT (FLOAT-RADIX 0.0)
                                     (FLOAT-DIGITS 0.0))
                               |DFLOAT;manexp|)
                         (EXIT (CONS (* |s|
                                      (FIX (* |two53| (QCAR |me|))))
                                     (- (QCDR |me|) (FLOAT-DIGITS 0.0))))))))
           #0# (EXIT #0#))))) 

(DEFUN |DFLOAT;rationalApproximation;$2NniF;84| (|f| |d| |b| $)
  (PROG (|#G103| |nu| |ex| BASE #0=#:G1523 |de| |tol| |#G104| |q| |r|
                 |p2| |q2| #1=#:G1541 |#G105| |#G106| |p0| |p1| |#G107|
                 |#G108| |q0| |q1| |#G109| |#G110| |s| |t| #2=#:G1539)
    (RETURN
      (SEQ (EXIT (SEQ (PROGN
                        (LETT |#G103| (|DFLOAT;manexp| |f| $)
                              |DFLOAT;rationalApproximation;$2NniF;84|)
                        (LETT |nu| (QCAR |#G103|)
                              |DFLOAT;rationalApproximation;$2NniF;84|)
                        (LETT |ex| (QCDR |#G103|)
                              |DFLOAT;rationalApproximation;$2NniF;84|)
                        |#G103|)
                      (LETT BASE (FLOAT-RADIX 0.0)
                            |DFLOAT;rationalApproximation;$2NniF;84|)
                      (EXIT (COND
                              ((< |ex| 0)
                               (SEQ (LETT |de|
                                     (EXPT BASE
                                      (PROG1
                                       (LETT #0# (- |ex|)
                                        |DFLOAT;rationalApproximation;$2NniF;84|)
                                        (|check-subtype| (>= #0# 0)
                                         '(|NonNegativeInteger|) #0#)))
                                     |DFLOAT;rationalApproximation;$2NniF;84|)
                                    (EXIT
                                     (COND
                                       ((< |b| 2)
                                        (|error| "base must be > 1"))
                                       ('T
                                        (SEQ
                                         (LETT |tol| (EXPT |b| |d|)
                                          |DFLOAT;rationalApproximation;$2NniF;84|)
                                         (LETT |s| |nu|
                                          |DFLOAT;rationalApproximation;$2NniF;84|)
                                         (LETT |t| |de|
                                          |DFLOAT;rationalApproximation;$2NniF;84|)
                                         (LETT |p0| 0
                                          |DFLOAT;rationalApproximation;$2NniF;84|)
                                         (LETT |p1| 1
                                          |DFLOAT;rationalApproximation;$2NniF;84|)
                                         (LETT |q0| 1
                                          |DFLOAT;rationalApproximation;$2NniF;84|)
                                         (LETT |q1| 0
                                          |DFLOAT;rationalApproximation;$2NniF;84|)
                                         (EXIT
                                          (SEQ G190 NIL
                                           (SEQ
                                            (PROGN
                                              (LETT |#G104|
                                               (DIVIDE2 |s| |t|)
                                               |DFLOAT;rationalApproximation;$2NniF;84|)
                                              (LETT |q| (QCAR |#G104|)
                                               |DFLOAT;rationalApproximation;$2NniF;84|)
                                              (LETT |r| (QCDR |#G104|)
                                               |DFLOAT;rationalApproximation;$2NniF;84|)
                                              |#G104|)
                                            (LETT |p2|
                                             (+ (* |q| |p1|) |p0|)
                                             |DFLOAT;rationalApproximation;$2NniF;84|)
                                            (LETT |q2|
                                             (+ (* |q| |q1|) |q0|)
                                             |DFLOAT;rationalApproximation;$2NniF;84|)
                                            (COND
                                              ((OR (EQL |r| 0)
                                                (<
                                                 (SPADCALL |tol|
                                                  (ABS
                                                   (- (* |nu| |q2|)
                                                    (* |de| |p2|)))
                                                  (|getShellEntry| $
                                                   120))
                                                 (* |de| (ABS |p2|))))
                                               (EXIT
                                                (PROGN
                                                  (LETT #1#
                                                   (SPADCALL |p2| |q2|
                                                    (|getShellEntry| $
                                                     119))
                                                   |DFLOAT;rationalApproximation;$2NniF;84|)
                                                  (GO #1#)))))
                                            (PROGN
                                              (LETT |#G105| |p1|
                                               |DFLOAT;rationalApproximation;$2NniF;84|)
                                              (LETT |#G106| |p2|
                                               |DFLOAT;rationalApproximation;$2NniF;84|)
                                              (LETT |p0| |#G105|
                                               |DFLOAT;rationalApproximation;$2NniF;84|)
                                              (LETT |p1| |#G106|
                                               |DFLOAT;rationalApproximation;$2NniF;84|))
                                            (PROGN
                                              (LETT |#G107| |q1|
                                               |DFLOAT;rationalApproximation;$2NniF;84|)
                                              (LETT |#G108| |q2|
                                               |DFLOAT;rationalApproximation;$2NniF;84|)
                                              (LETT |q0| |#G107|
                                               |DFLOAT;rationalApproximation;$2NniF;84|)
                                              (LETT |q1| |#G108|
                                               |DFLOAT;rationalApproximation;$2NniF;84|))
                                            (EXIT
                                             (PROGN
                                               (LETT |#G109| |t|
                                                |DFLOAT;rationalApproximation;$2NniF;84|)
                                               (LETT |#G110| |r|
                                                |DFLOAT;rationalApproximation;$2NniF;84|)
                                               (LETT |s| |#G109|
                                                |DFLOAT;rationalApproximation;$2NniF;84|)
                                               (LETT |t| |#G110|
                                                |DFLOAT;rationalApproximation;$2NniF;84|))))
                                           NIL (GO G190) G191
                                           (EXIT NIL)))))))))
                              ('T
                               (SPADCALL
                                   (* |nu|
                                    (EXPT BASE
                                     (PROG1
                                      (LETT #2# |ex|
                                       |DFLOAT;rationalApproximation;$2NniF;84|)
                                       (|check-subtype| (>= #2# 0)
                                        '(|NonNegativeInteger|) #2#))))
                                   (|getShellEntry| $ 121)))))))
           #1# (EXIT #1#))))) 

(DEFUN |DFLOAT;**;$F$;85| (|x| |r| $)
  (PROG (|n| |d| #0=#:G1550)
    (RETURN
      (SEQ (EXIT (COND
                   ((ZEROP |x|)
                    (COND
                      ((SPADCALL |r| (|getShellEntry| $ 122))
                       (|error| "0**0 is undefined"))
                      ((SPADCALL |r| (|getShellEntry| $ 123))
                       (|error| "division by 0"))
                      ('T 0.0)))
                   ((OR (SPADCALL |r| (|getShellEntry| $ 122))
                        (= |x| 1.0))
                    1.0)
                   ('T
                    (COND
                      ((SPADCALL |r| (|spadConstant| $ 124)
                           (|getShellEntry| $ 125))
                       |x|)
                      ('T
                       (SEQ (LETT |n|
                                  (SPADCALL |r|
                                      (|getShellEntry| $ 126))
                                  |DFLOAT;**;$F$;85|)
                            (LETT |d|
                                  (SPADCALL |r|
                                      (|getShellEntry| $ 127))
                                  |DFLOAT;**;$F$;85|)
                            (EXIT (COND
                                    ((MINUSP |x|)
                                     (COND
                                       ((ODDP |d|)
                                        (COND
                                          ((ODDP |n|)
                                           (PROGN
                                             (LETT #0#
                                              (-
                                               (SPADCALL (- |x|) |r|
                                                (|getShellEntry| $ 128)))
                                              |DFLOAT;**;$F$;85|)
                                             (GO #0#)))
                                          ('T
                                           (PROGN
                                             (LETT #0#
                                              (SPADCALL (- |x|) |r|
                                               (|getShellEntry| $ 128))
                                              |DFLOAT;**;$F$;85|)
                                             (GO #0#)))))
                                       ('T (|error| "negative root"))))
                                    ((EQL |d| 2)
                                     (EXPT
                                      (SPADCALL |x|
                                       (|getShellEntry| $ 56))
                                      |n|))
                                    ('T
                                     (SPADCALL |x|
                                      (/
                                       (FLOAT |n|
                                        MOST-POSITIVE-LONG-FLOAT)
                                       (FLOAT |d|
                                        MOST-POSITIVE-LONG-FLOAT))
                                      (|getShellEntry| $ 59)))))))))))
           #0# (EXIT #0#))))) 

(DEFUN |DoubleFloat| ()
  (PROG ()
    (RETURN
      (PROG (#0=#:G1563)
        (RETURN
          (COND
            ((LETT #0# (HGET |$ConstructorCache| '|DoubleFloat|)
                   |DoubleFloat|)
             (|CDRwithIncrement| (CDAR #0#)))
            ('T
             (UNWIND-PROTECT
               (PROG1 (CDDAR (HPUT |$ConstructorCache| '|DoubleFloat|
                                   (LIST
                                    (CONS NIL
                                     (CONS 1 (|DoubleFloat;|))))))
                 (LETT #0# T |DoubleFloat|))
               (COND
                 ((NOT #0#) (HREM |$ConstructorCache| '|DoubleFloat|))))))))))) 

(DEFUN |DoubleFloat;| ()
  (PROG (|dv$| $ |pv$|)
    (RETURN
      (PROGN
        (LETT |dv$| '(|DoubleFloat|) . #0=(|DoubleFloat|))
        (LETT $ (|newShell| 142) . #0#)
        (|setShellEntry| $ 0 |dv$|)
        (|setShellEntry| $ 3
            (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#))
        (|haddProp| |$ConstructorCache| '|DoubleFloat| NIL (CONS 1 $))
        (|stuffDomainSlots| $)
        (|setShellEntry| $ 6 "~G")
        $)))) 

(MAKEPROP '|DoubleFloat| '|infovec|
    (LIST '#(NIL NIL NIL NIL NIL NIL '|format| (|String|)
             |DFLOAT;doubleFloatFormat;2S;1| (|OpenMathEncoding|)
             (0 . |OMencodingXML|) (|OpenMathDevice|)
             (4 . |OMopenString|) (|Void|) (10 . |OMputObject|)
             (|DoubleFloat|) (15 . |OMputFloat|)
             (21 . |OMputEndObject|) (26 . |OMclose|)
             |DFLOAT;OMwrite;$S;2| (|Boolean|) |DFLOAT;OMwrite;$BS;3|
             |DFLOAT;OMwrite;Omd$V;4| |DFLOAT;OMwrite;Omd$BV;5|
             (|PositiveInteger|) |DFLOAT;base;Pi;7| (|Integer|)
             |DFLOAT;mantissa;$I;8| |DFLOAT;exponent;$I;9|
             |DFLOAT;precision;Pi;10| |DFLOAT;log2;2$;38| (31 . *)
             |DFLOAT;bits;Pi;11| |DFLOAT;max;$;12| |DFLOAT;min;$;13|
             |DFLOAT;order;$I;14|
             (CONS IDENTITY
                   (FUNCALL (|dispatchFunction| |DFLOAT;Zero;$;15|) $))
             (CONS IDENTITY
                   (FUNCALL (|dispatchFunction| |DFLOAT;One;$;16|) $))
             |DFLOAT;exp1;$;17| |DFLOAT;pi;$;18| (|OutputForm|)
             (37 . |outputForm|) |DFLOAT;coerce;$Of;19| (|InputForm|)
             (42 . |convert|) |DFLOAT;convert;$If;20| |DFLOAT;<;2$B;21|
             |DFLOAT;-;2$;22| |DFLOAT;+;3$;23| |DFLOAT;-;3$;24|
             |DFLOAT;*;3$;25| |DFLOAT;*;I2$;26| |DFLOAT;max;3$;27|
             |DFLOAT;min;3$;28| |DFLOAT;=;2$B;29| |DFLOAT;/;$I$;30|
             |DFLOAT;sqrt;2$;31| |DFLOAT;log10;2$;32|
             |DFLOAT;**;$I$;33| |DFLOAT;**;3$;34| |DFLOAT;coerce;I$;35|
             |DFLOAT;exp;2$;36| |DFLOAT;log;2$;37| |DFLOAT;sin;2$;39|
             |DFLOAT;cos;2$;40| |DFLOAT;tan;2$;41| |DFLOAT;cot;2$;42|
             |DFLOAT;sec;2$;43| |DFLOAT;csc;2$;44| |DFLOAT;asin;2$;45|
             |DFLOAT;acos;2$;46| |DFLOAT;atan;2$;47|
             |DFLOAT;acsc;2$;48| |DFLOAT;acot;2$;49|
             |DFLOAT;asec;2$;50| |DFLOAT;sinh;2$;51|
             |DFLOAT;cosh;2$;52| |DFLOAT;tanh;2$;53|
             |DFLOAT;csch;2$;54| |DFLOAT;coth;2$;55|
             |DFLOAT;sech;2$;56| |DFLOAT;asinh;2$;57|
             |DFLOAT;acosh;2$;58| |DFLOAT;atanh;2$;59|
             |DFLOAT;acsch;2$;60| |DFLOAT;acoth;2$;61|
             |DFLOAT;asech;2$;62| |DFLOAT;/;3$;63|
             |DFLOAT;negative?;$B;64| |DFLOAT;zero?;$B;65|
             |DFLOAT;hash;$I;66| (|Union| $ '"failed")
             |DFLOAT;recip;$U;67| |DFLOAT;differentiate;2$;68|
             (|DoubleFloatSpecialFunctions|) (47 . |Gamma|)
             |DFLOAT;Gamma;2$;69| (52 . |Beta|) |DFLOAT;Beta;3$;70|
             |DFLOAT;wholePart;$I;71| |DFLOAT;float;2IPi$;72|
             |DFLOAT;convert;$Df;73| (|Float|) (58 . |convert|)
             |DFLOAT;convert;$F;74| (|Fraction| 26)
             (|NonNegativeInteger|)
             |DFLOAT;rationalApproximation;$2NniF;84|
             |DFLOAT;rationalApproximation;$NniF;75|
             |DFLOAT;atan;3$;76| |DFLOAT;retract;$F;77|
             (|Union| 105 '"failed") |DFLOAT;retractIfCan;$U;78|
             |DFLOAT;retract;$I;79| (|Union| 26 '"failed")
             |DFLOAT;retractIfCan;$U;80| |DFLOAT;sign;$I;81|
             |DFLOAT;abs;2$;82| (63 . |Zero|) (67 . /) (73 . *)
             (79 . |coerce|) (84 . |zero?|) (89 . |negative?|)
             (94 . |One|) (98 . =) (104 . |numer|) (109 . |denom|)
             |DFLOAT;**;$F$;85| (|PatternMatchResult| 102 $)
             (|Pattern| 102) (|Factored| $) (|List| $)
             (|Union| 132 '"failed")
             (|Record| (|:| |coef1| $) (|:| |coef2| $)
                 (|:| |generator| $))
             (|Record| (|:| |coef1| $) (|:| |coef2| $))
             (|Union| 135 '"failed")
             (|Record| (|:| |quotient| $) (|:| |remainder| $))
             (|Record| (|:| |coef| 132) (|:| |generator| $))
             (|SparseUnivariatePolynomial| $)
             (|Record| (|:| |unit| $) (|:| |canonical| $)
                 (|:| |associate| $))
             (|SingleInteger|))
          '#(~= 114 |zero?| 120 |wholePart| 125 |unitNormal| 130
             |unitCanonical| 135 |unit?| 140 |truncate| 145 |tanh| 150
             |tan| 155 |subtractIfCan| 160 |squareFreePart| 166
             |squareFree| 171 |sqrt| 176 |sizeLess?| 181 |sinh| 187
             |sin| 192 |sign| 197 |sech| 202 |sec| 207 |sample| 212
             |round| 216 |retractIfCan| 221 |retract| 231 |rem| 241
             |recip| 247 |rationalApproximation| 252 |quo| 265
             |principalIdeal| 271 |prime?| 276 |precision| 281
             |positive?| 285 |pi| 290 |patternMatch| 294 |order| 301
             |one?| 306 |nthRoot| 311 |norm| 317 |negative?| 322
             |multiEuclidean| 327 |min| 333 |max| 343 |mantissa| 353
             |log2| 358 |log10| 363 |log| 368 |lcm| 373 |latex| 384
             |inv| 389 |hash| 394 |gcdPolynomial| 404 |gcd| 410
             |fractionPart| 421 |floor| 426 |float| 431 |factor| 444
             |extendedEuclidean| 449 |exquo| 462 |expressIdealMember|
             468 |exponent| 474 |exp1| 479 |exp| 483 |euclideanSize|
             488 |doubleFloatFormat| 493 |divide| 498 |digits| 504
             |differentiate| 508 |csch| 519 |csc| 524 |coth| 529 |cot|
             534 |cosh| 539 |cos| 544 |convert| 549 |coerce| 569
             |characteristic| 599 |ceiling| 603 |bits| 608 |base| 612
             |atanh| 616 |atan| 621 |associates?| 632 |asinh| 638
             |asin| 643 |asech| 648 |asec| 653 |acsch| 658 |acsc| 663
             |acoth| 668 |acot| 673 |acosh| 678 |acos| 683 |abs| 688 ^
             693 |Zero| 711 |One| 715 |OMwrite| 719 |Gamma| 743 D 748
             |Beta| 759 >= 765 > 771 = 777 <= 783 < 789 / 795 - 807 +
             818 ** 824 * 854)
          '((|approximate| . 0) (|canonicalsClosed| . 0)
            (|canonicalUnitNormal| . 0) (|noZeroDivisors| . 0)
            ((|commutative| "*") . 0) (|rightUnitary| . 0)
            (|leftUnitary| . 0) (|unitsKnown| . 0))
          (CONS (|makeByteWordVec2| 1
                    '(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
                      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
                      0 0 0 0 0 0))
                (CONS '#(|FloatingPointSystem&| |RealNumberSystem&|
                         |Field&| |EuclideanDomain&| NIL
                         |UniqueFactorizationDomain&| |GcdDomain&|
                         |DivisionRing&| |IntegralDomain&| |Algebra&|
                         |Algebra&| |DifferentialRing&| NIL
                         |OrderedRing&| |Module&| NIL NIL |Module&| NIL
                         NIL NIL |Ring&| NIL NIL NIL NIL NIL NIL NIL
                         |AbelianGroup&| NIL NIL |AbelianMonoid&|
                         |Monoid&| NIL |OrderedSet&|
                         |AbelianSemiGroup&| |SemiGroup&|
                         |TranscendentalFunctionCategory&| NIL
                         |SetCategory&| NIL
                         |ElementaryFunctionCategory&| NIL
                         |HyperbolicFunctionCategory&|
                         |ArcTrigonometricFunctionCategory&|
                         |TrigonometricFunctionCategory&| NIL NIL
                         |RadicalCategory&| |RetractableTo&|
                         |RetractableTo&| NIL NIL |BasicType&| NIL)
                      (CONS '#((|FloatingPointSystem|)
                               (|RealNumberSystem|) (|Field|)
                               (|EuclideanDomain|)
                               (|PrincipalIdealDomain|)
                               (|UniqueFactorizationDomain|)
                               (|GcdDomain|) (|DivisionRing|)
                               (|IntegralDomain|) (|Algebra| 105)
                               (|Algebra| $$) (|DifferentialRing|)
                               (|CharacteristicZero|) (|OrderedRing|)
                               (|Module| 105) (|EntireRing|)
                               (|CommutativeRing|) (|Module| $$)
                               (|OrderedAbelianGroup|)
                               (|BiModule| 105 105) (|BiModule| $$ $$)
                               (|Ring|)
                               (|OrderedCancellationAbelianMonoid|)
                               (|RightModule| 105) (|LeftModule| 105)
                               (|LeftModule| $$) (|Rng|)
                               (|RightModule| $$)
                               (|OrderedAbelianMonoid|)
                               (|AbelianGroup|)
                               (|OrderedAbelianSemiGroup|)
                               (|CancellationAbelianMonoid|)
                               (|AbelianMonoid|) (|Monoid|)
                               (|PatternMatchable| 102) (|OrderedSet|)
                               (|AbelianSemiGroup|) (|SemiGroup|)
                               (|TranscendentalFunctionCategory|)
                               (|RealConstant|) (|SetCategory|)
                               (|ConvertibleTo| 43)
                               (|ElementaryFunctionCategory|)
                               (|ArcHyperbolicFunctionCategory|)
                               (|HyperbolicFunctionCategory|)
                               (|ArcTrigonometricFunctionCategory|)
                               (|TrigonometricFunctionCategory|)
                               (|OpenMath|) (|ConvertibleTo| 130)
                               (|RadicalCategory|)
                               (|RetractableTo| 105)
                               (|RetractableTo| 26)
                               (|ConvertibleTo| 102)
                               (|ConvertibleTo| 15) (|BasicType|)
                               (|CoercibleTo| 40))
                            (|makeByteWordVec2| 141
                                '(0 9 0 10 2 11 0 7 9 12 1 11 13 0 14 2
                                  11 13 0 15 16 1 11 13 0 17 1 11 13 0
                                  18 2 0 0 24 0 31 1 40 0 15 41 1 43 0
                                  15 44 1 94 15 15 95 2 94 15 15 15 97
                                  1 102 0 15 103 0 105 0 118 2 105 0 26
                                  26 119 2 26 0 106 0 120 1 105 0 26
                                  121 1 105 20 0 122 1 105 20 0 123 0
                                  105 0 124 2 105 20 0 0 125 1 105 26 0
                                  126 1 105 26 0 127 2 0 20 0 0 1 1 0
                                  20 0 89 1 0 26 0 99 1 0 140 0 1 1 0 0
                                  0 1 1 0 20 0 1 1 0 0 0 1 1 0 0 0 77 1
                                  0 0 0 65 2 0 91 0 0 1 1 0 0 0 1 1 0
                                  131 0 1 1 0 0 0 56 2 0 20 0 0 1 1 0 0
                                  0 75 1 0 0 0 63 1 0 26 0 116 1 0 0 0
                                  80 1 0 0 0 67 0 0 0 1 1 0 0 0 1 1 0
                                  111 0 112 1 0 114 0 115 1 0 105 0 110
                                  1 0 26 0 113 2 0 0 0 0 1 1 0 91 0 92
                                  2 0 105 0 106 108 3 0 105 0 106 106
                                  107 2 0 0 0 0 1 1 0 138 132 1 1 0 20
                                  0 1 0 0 24 29 1 0 20 0 1 0 0 0 39 3 0
                                  129 0 130 129 1 1 0 26 0 35 1 0 20 0
                                  1 2 0 0 0 26 1 1 0 0 0 1 1 0 20 0 88
                                  2 0 133 132 0 1 0 0 0 34 2 0 0 0 0 53
                                  0 0 0 33 2 0 0 0 0 52 1 0 26 0 27 1 0
                                  0 0 30 1 0 0 0 57 1 0 0 0 62 1 0 0
                                  132 1 2 0 0 0 0 1 1 0 7 0 1 1 0 0 0 1
                                  1 0 26 0 90 1 0 141 0 1 2 0 139 139
                                  139 1 1 0 0 132 1 2 0 0 0 0 1 1 0 0 0
                                  1 1 0 0 0 1 3 0 0 26 26 24 100 2 0 0
                                  26 26 1 1 0 131 0 1 2 0 134 0 0 1 3 0
                                  136 0 0 0 1 2 0 91 0 0 1 2 0 133 132
                                  0 1 1 0 26 0 28 0 0 0 38 1 0 0 0 61 1
                                  0 106 0 1 1 0 7 7 8 2 0 137 0 0 1 0 0
                                  24 1 1 0 0 0 93 2 0 0 0 106 1 1 0 0 0
                                  78 1 0 0 0 68 1 0 0 0 79 1 0 0 0 66 1
                                  0 0 0 76 1 0 0 0 64 1 0 43 0 45 1 0
                                  130 0 1 1 0 102 0 104 1 0 15 0 101 1
                                  0 0 105 1 1 0 0 26 60 1 0 0 105 1 1 0
                                  0 26 60 1 0 0 0 1 1 0 40 0 42 0 0 106
                                  1 1 0 0 0 1 0 0 24 32 0 0 24 25 1 0 0
                                  0 83 2 0 0 0 0 109 1 0 0 0 71 2 0 20
                                  0 0 1 1 0 0 0 81 1 0 0 0 69 1 0 0 0
                                  86 1 0 0 0 74 1 0 0 0 84 1 0 0 0 72 1
                                  0 0 0 85 1 0 0 0 73 1 0 0 0 82 1 0 0
                                  0 70 1 0 0 0 117 2 0 0 0 26 1 2 0 0 0
                                  106 1 2 0 0 0 24 1 0 0 0 36 0 0 0 37
                                  3 0 13 11 0 20 23 2 0 7 0 20 21 2 0
                                  13 11 0 22 1 0 7 0 19 1 0 0 0 96 1 0
                                  0 0 1 2 0 0 0 106 1 2 0 0 0 0 98 2 0
                                  20 0 0 1 2 0 20 0 0 1 2 0 20 0 0 54 2
                                  0 20 0 0 1 2 0 20 0 0 46 2 0 0 0 26
                                  55 2 0 0 0 0 87 2 0 0 0 0 49 1 0 0 0
                                  47 2 0 0 0 0 48 2 0 0 0 0 59 2 0 0 0
                                  105 128 2 0 0 0 26 58 2 0 0 0 106 1 2
                                  0 0 0 24 1 2 0 0 0 105 1 2 0 0 105 0
                                  1 2 0 0 0 0 50 2 0 0 26 0 51 2 0 0
                                  106 0 1 2 0 0 24 0 31)))))
          '|lookupComplete|)) 

(MAKEPROP '|DoubleFloat| 'NILADIC T)