--- /home/greg/TDevel/cvs/axiom/src/algebra/sf.spad.pamphlet	2006-04-17 08:28:41.000000000 +0200
+++ src/algebra/sf.spad.pamphlet	2007-02-14 12:17:59.000000000 +0100
@@ -846,7 +846,7 @@
          ++ (that is, \spad{|(r-f)/f| < b**(-n)}).
 
  == add
-   format: String := "~G"
+   format: String := "~A"
    MER ==> Record(MANTISSA:Integer,EXPONENT:Integer)
 
    manexp: % -> MER
@@ -914,7 +914,8 @@
    exp1()           == FLOAT(534625820200,MOST_-POSITIVE_-LONG_-FLOAT$Lisp)$Lisp / FLOAT(196677847971,MOST_-POSITIVE_-LONG_-FLOAT$Lisp)$Lisp
    pi()             == PI$Lisp
    coerce(x:%):OutputForm == 
-     outputForm(FORMAT(NIL$Lisp,format,x)$Lisp pretend DoubleFloat)
+     x >= 0 => message(FORMAT(NIL$Lisp,format,x)$Lisp pretend String)
+     - (message(FORMAT(NIL$Lisp,format,-x)$Lisp pretend String))
    convert(x:%):InputForm == convert(x pretend DoubleFloat)$InputForm
    x < y            == (x<y)$Lisp
    - x              == (-x)$Lisp
@@ -1085,273 +1086,277 @@
 
 <<DFLOAT.lsp BOOTSTRAP>>=
 
-(|/VERSIONCHECK| 2) 
 
-(DEFUN |DFLOAT;OMwrite;$S;1| (|x| |$|) (PROG (|sp| |dev| |s|) (RETURN (SEQ (LETT |s| "" |DFLOAT;OMwrite;$S;1|) (LETT |sp| (|OM-STRINGTOSTRINGPTR| |s|) |DFLOAT;OMwrite;$S;1|) (LETT |dev| (SPADCALL |sp| (SPADCALL (QREFELT |$| 7)) (QREFELT |$| 10)) |DFLOAT;OMwrite;$S;1|) (SPADCALL |dev| (QREFELT |$| 12)) (SPADCALL |dev| |x| (QREFELT |$| 14)) (SPADCALL |dev| (QREFELT |$| 15)) (SPADCALL |dev| (QREFELT |$| 16)) (LETT |s| (|OM-STRINGPTRTOSTRING| |sp|) |DFLOAT;OMwrite;$S;1|) (EXIT |s|))))) 
+(/VERSIONCHECK 2) 
 
-(DEFUN |DFLOAT;OMwrite;$BS;2| (|x| |wholeObj| |$|) (PROG (|sp| |dev| |s|) (RETURN (SEQ (LETT |s| "" |DFLOAT;OMwrite;$BS;2|) (LETT |sp| (|OM-STRINGTOSTRINGPTR| |s|) |DFLOAT;OMwrite;$BS;2|) (LETT |dev| (SPADCALL |sp| (SPADCALL (QREFELT |$| 7)) (QREFELT |$| 10)) |DFLOAT;OMwrite;$BS;2|) (COND (|wholeObj| (SPADCALL |dev| (QREFELT |$| 12)))) (SPADCALL |dev| |x| (QREFELT |$| 14)) (COND (|wholeObj| (SPADCALL |dev| (QREFELT |$| 15)))) (SPADCALL |dev| (QREFELT |$| 16)) (LETT |s| (|OM-STRINGPTRTOSTRING| |sp|) |DFLOAT;OMwrite;$BS;2|) (EXIT |s|))))) 
+(DEFUN |DFLOAT;doubleFloatFormat;2S;1| (|s| $) (PROG (|ss|) (RETURN (SEQ (LETT |ss| (QREFELT $ 6) |DFLOAT;doubleFloatFormat;2S;1|) (SETELT $ 6 |s|) (EXIT |ss|))))) 
 
-(DEFUN |DFLOAT;OMwrite;Omd$V;3| (|dev| |x| |$|) (SEQ (SPADCALL |dev| (QREFELT |$| 12)) (SPADCALL |dev| |x| (QREFELT |$| 14)) (EXIT (SPADCALL |dev| (QREFELT |$| 15))))) 
+(DEFUN |DFLOAT;OMwrite;$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 (QREFELT $ 10)) (QREFELT $ 12)) |DFLOAT;OMwrite;$S;2|) (SPADCALL |dev| (QREFELT $ 14)) (SPADCALL |dev| |x| (QREFELT $ 16)) (SPADCALL |dev| (QREFELT $ 17)) (SPADCALL |dev| (QREFELT $ 18)) (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |DFLOAT;OMwrite;$S;2|) (EXIT |s|))))) 
 
-(DEFUN |DFLOAT;OMwrite;Omd$BV;4| (|dev| |x| |wholeObj| |$|) (SEQ (COND (|wholeObj| (SPADCALL |dev| (QREFELT |$| 12)))) (SPADCALL |dev| |x| (QREFELT |$| 14)) (EXIT (COND (|wholeObj| (SPADCALL |dev| (QREFELT |$| 15))))))) 
+(DEFUN |DFLOAT;OMwrite;$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 (QREFELT $ 10)) (QREFELT $ 12)) |DFLOAT;OMwrite;$BS;3|) (COND (|wholeObj| (SPADCALL |dev| (QREFELT $ 14)))) (SPADCALL |dev| |x| (QREFELT $ 16)) (COND (|wholeObj| (SPADCALL |dev| (QREFELT $ 17)))) (SPADCALL |dev| (QREFELT $ 18)) (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |DFLOAT;OMwrite;$BS;3|) (EXIT |s|))))) 
 
-(PUT (QUOTE |DFLOAT;checkComplex|) (QUOTE |SPADreplace|) (QUOTE |C-TO-R|)) 
+(DEFUN |DFLOAT;OMwrite;Omd$V;4| (|dev| |x| $) (SEQ (SPADCALL |dev| (QREFELT $ 14)) (SPADCALL |dev| |x| (QREFELT $ 16)) (EXIT (SPADCALL |dev| (QREFELT $ 17))))) 
 
-(DEFUN |DFLOAT;checkComplex| (|x| |$|) (|C-TO-R| |x|)) 
+(DEFUN |DFLOAT;OMwrite;Omd$BV;5| (|dev| |x| |wholeObj| $) (SEQ (COND (|wholeObj| (SPADCALL |dev| (QREFELT $ 14)))) (SPADCALL |dev| |x| (QREFELT $ 16)) (EXIT (COND (|wholeObj| (SPADCALL |dev| (QREFELT $ 17))))))) 
 
-(PUT (QUOTE |DFLOAT;base;Pi;6|) (QUOTE |SPADreplace|) (QUOTE (XLAM NIL (|FLOAT-RADIX| 0.0)))) 
+(PUT (QUOTE |DFLOAT;checkComplex|) (QUOTE |SPADreplace|) (QUOTE C-TO-R)) 
 
-(DEFUN |DFLOAT;base;Pi;6| (|$|) (|FLOAT-RADIX| 0.0)) 
+(DEFUN |DFLOAT;checkComplex| (|x| $) (C-TO-R |x|)) 
 
-(DEFUN |DFLOAT;mantissa;$I;7| (|x| |$|) (QCAR (|DFLOAT;manexp| |x| |$|))) 
+(PUT (QUOTE |DFLOAT;base;Pi;7|) (QUOTE |SPADreplace|) (QUOTE (XLAM NIL (FLOAT-RADIX 0.0)))) 
 
-(DEFUN |DFLOAT;exponent;$I;8| (|x| |$|) (QCDR (|DFLOAT;manexp| |x| |$|))) 
+(DEFUN |DFLOAT;base;Pi;7| ($) (FLOAT-RADIX 0.0)) 
 
-(PUT (QUOTE |DFLOAT;precision;Pi;9|) (QUOTE |SPADreplace|) (QUOTE (XLAM NIL (|FLOAT-DIGITS| 0.0)))) 
+(DEFUN |DFLOAT;mantissa;$I;8| (|x| $) (QCAR (|DFLOAT;manexp| |x| $))) 
 
-(DEFUN |DFLOAT;precision;Pi;9| (|$|) (|FLOAT-DIGITS| 0.0)) 
+(DEFUN |DFLOAT;exponent;$I;9| (|x| $) (QCDR (|DFLOAT;manexp| |x| $))) 
 
-(DEFUN |DFLOAT;bits;Pi;10| (|$|) (PROG (#1=#:G105705) (RETURN (COND ((EQL (|FLOAT-RADIX| 0.0) 2) (|FLOAT-DIGITS| 0.0)) ((EQL (|FLOAT-RADIX| 0.0) 16) (|*| 4 (|FLOAT-DIGITS| 0.0))) ((QUOTE T) (PROG1 (LETT #1# (FIX (SPADCALL (|FLOAT-DIGITS| 0.0) (SPADCALL (FLOAT (|FLOAT-RADIX| 0.0) |MOST-POSITIVE-LONG-FLOAT|) (QREFELT |$| 28)) (QREFELT |$| 29))) |DFLOAT;bits;Pi;10|) (|check-subtype| (|>| #1# 0) (QUOTE (|PositiveInteger|)) #1#))))))) 
+(PUT (QUOTE |DFLOAT;precision;Pi;10|) (QUOTE |SPADreplace|) (QUOTE (XLAM NIL (FLOAT-DIGITS 0.0)))) 
 
-(PUT (QUOTE |DFLOAT;max;$;11|) (QUOTE |SPADreplace|) (QUOTE (XLAM NIL |MOST-POSITIVE-LONG-FLOAT|))) 
+(DEFUN |DFLOAT;precision;Pi;10| ($) (FLOAT-DIGITS 0.0)) 
 
-(DEFUN |DFLOAT;max;$;11| (|$|) |MOST-POSITIVE-LONG-FLOAT|) 
+(DEFUN |DFLOAT;bits;Pi;11| ($) (PROG (#0=#:G1444) (RETURN (COND ((EQL (FLOAT-RADIX 0.0) 2) (FLOAT-DIGITS 0.0)) ((EQL (FLOAT-RADIX 0.0) 16) (* 4 (FLOAT-DIGITS 0.0))) ((QUOTE T) (PROG1 (LETT #0# (FIX (SPADCALL (FLOAT-DIGITS 0.0) (SPADCALL (FLOAT (FLOAT-RADIX 0.0) MOST-POSITIVE-LONG-FLOAT) (QREFELT $ 30)) (QREFELT $ 31))) |DFLOAT;bits;Pi;11|) (|check-subtype| (> #0# 0) (QUOTE (|PositiveInteger|)) #0#))))))) 
 
-(PUT (QUOTE |DFLOAT;min;$;12|) (QUOTE |SPADreplace|) (QUOTE (XLAM NIL |MOST-NEGATIVE-LONG-FLOAT|))) 
+(PUT (QUOTE |DFLOAT;max;$;12|) (QUOTE |SPADreplace|) (QUOTE (XLAM NIL MOST-POSITIVE-LONG-FLOAT))) 
 
-(DEFUN |DFLOAT;min;$;12| (|$|) |MOST-NEGATIVE-LONG-FLOAT|) 
+(DEFUN |DFLOAT;max;$;12| ($) MOST-POSITIVE-LONG-FLOAT) 
 
-(DEFUN |DFLOAT;order;$I;13| (|a| |$|) (|-| (|+| (|FLOAT-DIGITS| 0.0) (SPADCALL |a| (QREFELT |$| 26))) 1)) 
+(PUT (QUOTE |DFLOAT;min;$;13|) (QUOTE |SPADreplace|) (QUOTE (XLAM NIL MOST-NEGATIVE-LONG-FLOAT))) 
 
-(PUT (QUOTE |DFLOAT;Zero;$;14|) (QUOTE |SPADreplace|) (QUOTE (XLAM NIL (FLOAT 0 |MOST-POSITIVE-LONG-FLOAT|)))) 
+(DEFUN |DFLOAT;min;$;13| ($) MOST-NEGATIVE-LONG-FLOAT) 
 
-(DEFUN |DFLOAT;Zero;$;14| (|$|) (FLOAT 0 |MOST-POSITIVE-LONG-FLOAT|)) 
+(DEFUN |DFLOAT;order;$I;14| (|a| $) (- (+ (FLOAT-DIGITS 0.0) (SPADCALL |a| (QREFELT $ 28))) 1)) 
 
-(PUT (QUOTE |DFLOAT;One;$;15|) (QUOTE |SPADreplace|) (QUOTE (XLAM NIL (FLOAT 1 |MOST-POSITIVE-LONG-FLOAT|)))) 
+(PUT (QUOTE |DFLOAT;Zero;$;15|) (QUOTE |SPADreplace|) (QUOTE (XLAM NIL (FLOAT 0 MOST-POSITIVE-LONG-FLOAT)))) 
 
-(DEFUN |DFLOAT;One;$;15| (|$|) (FLOAT 1 |MOST-POSITIVE-LONG-FLOAT|)) 
+(DEFUN |DFLOAT;Zero;$;15| ($) (FLOAT 0 MOST-POSITIVE-LONG-FLOAT)) 
 
-(DEFUN |DFLOAT;exp1;$;16| (|$|) (|/| (FLOAT 534625820200 |MOST-POSITIVE-LONG-FLOAT|) (FLOAT 196677847971 |MOST-POSITIVE-LONG-FLOAT|))) 
+(PUT (QUOTE |DFLOAT;One;$;16|) (QUOTE |SPADreplace|) (QUOTE (XLAM NIL (FLOAT 1 MOST-POSITIVE-LONG-FLOAT)))) 
 
-(PUT (QUOTE |DFLOAT;pi;$;17|) (QUOTE |SPADreplace|) (QUOTE (XLAM NIL PI))) 
+(DEFUN |DFLOAT;One;$;16| ($) (FLOAT 1 MOST-POSITIVE-LONG-FLOAT)) 
 
-(DEFUN |DFLOAT;pi;$;17| (|$|) PI) 
+(DEFUN |DFLOAT;exp1;$;17| ($) (/ (FLOAT 534625820200 MOST-POSITIVE-LONG-FLOAT) (FLOAT 196677847971 MOST-POSITIVE-LONG-FLOAT))) 
 
-(DEFUN |DFLOAT;coerce;$Of;18| (|x| |$|) (SPADCALL |x| (QREFELT |$| 39))) 
+(PUT (QUOTE |DFLOAT;pi;$;18|) (QUOTE |SPADreplace|) (QUOTE (XLAM NIL PI))) 
 
-(DEFUN |DFLOAT;convert;$If;19| (|x| |$|) (SPADCALL |x| (QREFELT |$| 42))) 
+(DEFUN |DFLOAT;pi;$;18| ($) PI) 
 
-(PUT (QUOTE |DFLOAT;<;2$B;20|) (QUOTE |SPADreplace|) (QUOTE |<|)) 
+(DEFUN |DFLOAT;coerce;$Of;19| (|x| $) (COND ((< |x| 0.0) (SPADCALL (SPADCALL (FORMAT NIL (QREFELT $ 6) (- |x|)) (QREFELT $ 41)) (QREFELT $ 42))) ((QUOTE T) (SPADCALL (FORMAT NIL (QREFELT $ 6) |x|) (QREFELT $ 41))))) 
 
-(DEFUN |DFLOAT;<;2$B;20| (|x| |y| |$|) (|<| |x| |y|)) 
+(DEFUN |DFLOAT;convert;$If;20| (|x| $) (SPADCALL |x| (QREFELT $ 45))) 
 
-(PUT (QUOTE |DFLOAT;-;2$;21|) (QUOTE |SPADreplace|) (QUOTE |-|)) 
+(PUT (QUOTE |DFLOAT;<;2$B;21|) (QUOTE |SPADreplace|) (QUOTE <)) 
 
-(DEFUN |DFLOAT;-;2$;21| (|x| |$|) (|-| |x|)) 
+(DEFUN |DFLOAT;<;2$B;21| (|x| |y| $) (< |x| |y|)) 
 
-(PUT (QUOTE |DFLOAT;+;3$;22|) (QUOTE |SPADreplace|) (QUOTE |+|)) 
+(PUT (QUOTE |DFLOAT;-;2$;22|) (QUOTE |SPADreplace|) (QUOTE -)) 
 
-(DEFUN |DFLOAT;+;3$;22| (|x| |y| |$|) (|+| |x| |y|)) 
+(DEFUN |DFLOAT;-;2$;22| (|x| $) (- |x|)) 
 
-(PUT (QUOTE |DFLOAT;-;3$;23|) (QUOTE |SPADreplace|) (QUOTE |-|)) 
+(PUT (QUOTE |DFLOAT;+;3$;23|) (QUOTE |SPADreplace|) (QUOTE +)) 
 
-(DEFUN |DFLOAT;-;3$;23| (|x| |y| |$|) (|-| |x| |y|)) 
+(DEFUN |DFLOAT;+;3$;23| (|x| |y| $) (+ |x| |y|)) 
 
-(PUT (QUOTE |DFLOAT;*;3$;24|) (QUOTE |SPADreplace|) (QUOTE |*|)) 
+(PUT (QUOTE |DFLOAT;-;3$;24|) (QUOTE |SPADreplace|) (QUOTE -)) 
 
-(DEFUN |DFLOAT;*;3$;24| (|x| |y| |$|) (|*| |x| |y|)) 
+(DEFUN |DFLOAT;-;3$;24| (|x| |y| $) (- |x| |y|)) 
 
-(PUT (QUOTE |DFLOAT;*;I2$;25|) (QUOTE |SPADreplace|) (QUOTE |*|)) 
+(PUT (QUOTE |DFLOAT;*;3$;25|) (QUOTE |SPADreplace|) (QUOTE *)) 
 
-(DEFUN |DFLOAT;*;I2$;25| (|i| |x| |$|) (|*| |i| |x|)) 
+(DEFUN |DFLOAT;*;3$;25| (|x| |y| $) (* |x| |y|)) 
 
-(PUT (QUOTE |DFLOAT;max;3$;26|) (QUOTE |SPADreplace|) (QUOTE MAX)) 
+(PUT (QUOTE |DFLOAT;*;I2$;26|) (QUOTE |SPADreplace|) (QUOTE *)) 
 
-(DEFUN |DFLOAT;max;3$;26| (|x| |y| |$|) (MAX |x| |y|)) 
+(DEFUN |DFLOAT;*;I2$;26| (|i| |x| $) (* |i| |x|)) 
 
-(PUT (QUOTE |DFLOAT;min;3$;27|) (QUOTE |SPADreplace|) (QUOTE MIN)) 
+(PUT (QUOTE |DFLOAT;max;3$;27|) (QUOTE |SPADreplace|) (QUOTE MAX)) 
 
-(DEFUN |DFLOAT;min;3$;27| (|x| |y| |$|) (MIN |x| |y|)) 
+(DEFUN |DFLOAT;max;3$;27| (|x| |y| $) (MAX |x| |y|)) 
 
-(PUT (QUOTE |DFLOAT;=;2$B;28|) (QUOTE |SPADreplace|) (QUOTE |=|)) 
+(PUT (QUOTE |DFLOAT;min;3$;28|) (QUOTE |SPADreplace|) (QUOTE MIN)) 
 
-(DEFUN |DFLOAT;=;2$B;28| (|x| |y| |$|) (|=| |x| |y|)) 
+(DEFUN |DFLOAT;min;3$;28| (|x| |y| $) (MIN |x| |y|)) 
 
-(PUT (QUOTE |DFLOAT;/;$I$;29|) (QUOTE |SPADreplace|) (QUOTE |/|)) 
+(PUT (QUOTE |DFLOAT;=;2$B;29|) (QUOTE |SPADreplace|) (QUOTE =)) 
 
-(DEFUN |DFLOAT;/;$I$;29| (|x| |i| |$|) (|/| |x| |i|)) 
+(DEFUN |DFLOAT;=;2$B;29| (|x| |y| $) (= |x| |y|)) 
 
-(DEFUN |DFLOAT;sqrt;2$;30| (|x| |$|) (|DFLOAT;checkComplex| (SQRT |x|) |$|)) 
+(PUT (QUOTE |DFLOAT;/;$I$;30|) (QUOTE |SPADreplace|) (QUOTE /)) 
 
-(DEFUN |DFLOAT;log10;2$;31| (|x| |$|) (|DFLOAT;checkComplex| (|log| |x|) |$|)) 
+(DEFUN |DFLOAT;/;$I$;30| (|x| |i| $) (/ |x| |i|)) 
 
-(PUT (QUOTE |DFLOAT;**;$I$;32|) (QUOTE |SPADreplace|) (QUOTE EXPT)) 
+(DEFUN |DFLOAT;sqrt;2$;31| (|x| $) (|DFLOAT;checkComplex| (SQRT |x|) $)) 
 
-(DEFUN |DFLOAT;**;$I$;32| (|x| |i| |$|) (EXPT |x| |i|)) 
+(DEFUN |DFLOAT;log10;2$;32| (|x| $) (|DFLOAT;checkComplex| (|log| |x|) $)) 
 
-(DEFUN |DFLOAT;**;3$;33| (|x| |y| |$|) (|DFLOAT;checkComplex| (EXPT |x| |y|) |$|)) 
+(PUT (QUOTE |DFLOAT;**;$I$;33|) (QUOTE |SPADreplace|) (QUOTE EXPT)) 
 
-(PUT (QUOTE |DFLOAT;coerce;I$;34|) (QUOTE |SPADreplace|) (QUOTE (XLAM (|i|) (FLOAT |i| |MOST-POSITIVE-LONG-FLOAT|)))) 
+(DEFUN |DFLOAT;**;$I$;33| (|x| |i| $) (EXPT |x| |i|)) 
 
-(DEFUN |DFLOAT;coerce;I$;34| (|i| |$|) (FLOAT |i| |MOST-POSITIVE-LONG-FLOAT|)) 
+(DEFUN |DFLOAT;**;3$;34| (|x| |y| $) (|DFLOAT;checkComplex| (EXPT |x| |y|) $)) 
 
-(PUT (QUOTE |DFLOAT;exp;2$;35|) (QUOTE |SPADreplace|) (QUOTE EXP)) 
+(PUT (QUOTE |DFLOAT;coerce;I$;35|) (QUOTE |SPADreplace|) (QUOTE (XLAM (|i|) (FLOAT |i| MOST-POSITIVE-LONG-FLOAT)))) 
 
-(DEFUN |DFLOAT;exp;2$;35| (|x| |$|) (EXP |x|)) 
+(DEFUN |DFLOAT;coerce;I$;35| (|i| $) (FLOAT |i| MOST-POSITIVE-LONG-FLOAT)) 
 
-(DEFUN |DFLOAT;log;2$;36| (|x| |$|) (|DFLOAT;checkComplex| (LN |x|) |$|)) 
+(PUT (QUOTE |DFLOAT;exp;2$;36|) (QUOTE |SPADreplace|) (QUOTE EXP)) 
 
-(DEFUN |DFLOAT;log2;2$;37| (|x| |$|) (|DFLOAT;checkComplex| (LOG2 |x|) |$|)) 
+(DEFUN |DFLOAT;exp;2$;36| (|x| $) (EXP |x|)) 
 
-(PUT (QUOTE |DFLOAT;sin;2$;38|) (QUOTE |SPADreplace|) (QUOTE SIN)) 
+(DEFUN |DFLOAT;log;2$;37| (|x| $) (|DFLOAT;checkComplex| (LN |x|) $)) 
 
-(DEFUN |DFLOAT;sin;2$;38| (|x| |$|) (SIN |x|)) 
+(DEFUN |DFLOAT;log2;2$;38| (|x| $) (|DFLOAT;checkComplex| (LOG2 |x|) $)) 
 
-(PUT (QUOTE |DFLOAT;cos;2$;39|) (QUOTE |SPADreplace|) (QUOTE COS)) 
+(PUT (QUOTE |DFLOAT;sin;2$;39|) (QUOTE |SPADreplace|) (QUOTE SIN)) 
 
-(DEFUN |DFLOAT;cos;2$;39| (|x| |$|) (COS |x|)) 
+(DEFUN |DFLOAT;sin;2$;39| (|x| $) (SIN |x|)) 
 
-(PUT (QUOTE |DFLOAT;tan;2$;40|) (QUOTE |SPADreplace|) (QUOTE TAN)) 
+(PUT (QUOTE |DFLOAT;cos;2$;40|) (QUOTE |SPADreplace|) (QUOTE COS)) 
 
-(DEFUN |DFLOAT;tan;2$;40| (|x| |$|) (TAN |x|)) 
+(DEFUN |DFLOAT;cos;2$;40| (|x| $) (COS |x|)) 
 
-(PUT (QUOTE |DFLOAT;cot;2$;41|) (QUOTE |SPADreplace|) (QUOTE COT)) 
+(PUT (QUOTE |DFLOAT;tan;2$;41|) (QUOTE |SPADreplace|) (QUOTE TAN)) 
 
-(DEFUN |DFLOAT;cot;2$;41| (|x| |$|) (COT |x|)) 
+(DEFUN |DFLOAT;tan;2$;41| (|x| $) (TAN |x|)) 
 
-(PUT (QUOTE |DFLOAT;sec;2$;42|) (QUOTE |SPADreplace|) (QUOTE SEC)) 
+(PUT (QUOTE |DFLOAT;cot;2$;42|) (QUOTE |SPADreplace|) (QUOTE COT)) 
 
-(DEFUN |DFLOAT;sec;2$;42| (|x| |$|) (SEC |x|)) 
+(DEFUN |DFLOAT;cot;2$;42| (|x| $) (COT |x|)) 
 
-(PUT (QUOTE |DFLOAT;csc;2$;43|) (QUOTE |SPADreplace|) (QUOTE CSC)) 
+(PUT (QUOTE |DFLOAT;sec;2$;43|) (QUOTE |SPADreplace|) (QUOTE SEC)) 
 
-(DEFUN |DFLOAT;csc;2$;43| (|x| |$|) (CSC |x|)) 
+(DEFUN |DFLOAT;sec;2$;43| (|x| $) (SEC |x|)) 
 
-(DEFUN |DFLOAT;asin;2$;44| (|x| |$|) (|DFLOAT;checkComplex| (ASIN |x|) |$|)) 
+(PUT (QUOTE |DFLOAT;csc;2$;44|) (QUOTE |SPADreplace|) (QUOTE CSC)) 
 
-(DEFUN |DFLOAT;acos;2$;45| (|x| |$|) (|DFLOAT;checkComplex| (ACOS |x|) |$|)) 
+(DEFUN |DFLOAT;csc;2$;44| (|x| $) (CSC |x|)) 
 
-(PUT (QUOTE |DFLOAT;atan;2$;46|) (QUOTE |SPADreplace|) (QUOTE ATAN)) 
+(DEFUN |DFLOAT;asin;2$;45| (|x| $) (|DFLOAT;checkComplex| (ASIN |x|) $)) 
 
-(DEFUN |DFLOAT;atan;2$;46| (|x| |$|) (ATAN |x|)) 
+(DEFUN |DFLOAT;acos;2$;46| (|x| $) (|DFLOAT;checkComplex| (ACOS |x|) $)) 
 
-(DEFUN |DFLOAT;acsc;2$;47| (|x| |$|) (|DFLOAT;checkComplex| (ACSC |x|) |$|)) 
+(PUT (QUOTE |DFLOAT;atan;2$;47|) (QUOTE |SPADreplace|) (QUOTE ATAN)) 
 
-(PUT (QUOTE |DFLOAT;acot;2$;48|) (QUOTE |SPADreplace|) (QUOTE ACOT)) 
+(DEFUN |DFLOAT;atan;2$;47| (|x| $) (ATAN |x|)) 
 
-(DEFUN |DFLOAT;acot;2$;48| (|x| |$|) (ACOT |x|)) 
+(DEFUN |DFLOAT;acsc;2$;48| (|x| $) (|DFLOAT;checkComplex| (ACSC |x|) $)) 
 
-(DEFUN |DFLOAT;asec;2$;49| (|x| |$|) (|DFLOAT;checkComplex| (ASEC |x|) |$|)) 
+(PUT (QUOTE |DFLOAT;acot;2$;49|) (QUOTE |SPADreplace|) (QUOTE ACOT)) 
 
-(PUT (QUOTE |DFLOAT;sinh;2$;50|) (QUOTE |SPADreplace|) (QUOTE SINH)) 
+(DEFUN |DFLOAT;acot;2$;49| (|x| $) (ACOT |x|)) 
 
-(DEFUN |DFLOAT;sinh;2$;50| (|x| |$|) (SINH |x|)) 
+(DEFUN |DFLOAT;asec;2$;50| (|x| $) (|DFLOAT;checkComplex| (ASEC |x|) $)) 
 
-(PUT (QUOTE |DFLOAT;cosh;2$;51|) (QUOTE |SPADreplace|) (QUOTE COSH)) 
+(PUT (QUOTE |DFLOAT;sinh;2$;51|) (QUOTE |SPADreplace|) (QUOTE SINH)) 
 
-(DEFUN |DFLOAT;cosh;2$;51| (|x| |$|) (COSH |x|)) 
+(DEFUN |DFLOAT;sinh;2$;51| (|x| $) (SINH |x|)) 
 
-(PUT (QUOTE |DFLOAT;tanh;2$;52|) (QUOTE |SPADreplace|) (QUOTE TANH)) 
+(PUT (QUOTE |DFLOAT;cosh;2$;52|) (QUOTE |SPADreplace|) (QUOTE COSH)) 
 
-(DEFUN |DFLOAT;tanh;2$;52| (|x| |$|) (TANH |x|)) 
+(DEFUN |DFLOAT;cosh;2$;52| (|x| $) (COSH |x|)) 
 
-(PUT (QUOTE |DFLOAT;csch;2$;53|) (QUOTE |SPADreplace|) (QUOTE CSCH)) 
+(PUT (QUOTE |DFLOAT;tanh;2$;53|) (QUOTE |SPADreplace|) (QUOTE TANH)) 
 
-(DEFUN |DFLOAT;csch;2$;53| (|x| |$|) (CSCH |x|)) 
+(DEFUN |DFLOAT;tanh;2$;53| (|x| $) (TANH |x|)) 
 
-(PUT (QUOTE |DFLOAT;coth;2$;54|) (QUOTE |SPADreplace|) (QUOTE COTH)) 
+(PUT (QUOTE |DFLOAT;csch;2$;54|) (QUOTE |SPADreplace|) (QUOTE CSCH)) 
 
-(DEFUN |DFLOAT;coth;2$;54| (|x| |$|) (COTH |x|)) 
+(DEFUN |DFLOAT;csch;2$;54| (|x| $) (CSCH |x|)) 
 
-(PUT (QUOTE |DFLOAT;sech;2$;55|) (QUOTE |SPADreplace|) (QUOTE SECH)) 
+(PUT (QUOTE |DFLOAT;coth;2$;55|) (QUOTE |SPADreplace|) (QUOTE COTH)) 
 
-(DEFUN |DFLOAT;sech;2$;55| (|x| |$|) (SECH |x|)) 
+(DEFUN |DFLOAT;coth;2$;55| (|x| $) (COTH |x|)) 
 
-(PUT (QUOTE |DFLOAT;asinh;2$;56|) (QUOTE |SPADreplace|) (QUOTE ASINH)) 
+(PUT (QUOTE |DFLOAT;sech;2$;56|) (QUOTE |SPADreplace|) (QUOTE SECH)) 
 
-(DEFUN |DFLOAT;asinh;2$;56| (|x| |$|) (ASINH |x|)) 
+(DEFUN |DFLOAT;sech;2$;56| (|x| $) (SECH |x|)) 
 
-(DEFUN |DFLOAT;acosh;2$;57| (|x| |$|) (|DFLOAT;checkComplex| (ACOSH |x|) |$|)) 
+(PUT (QUOTE |DFLOAT;asinh;2$;57|) (QUOTE |SPADreplace|) (QUOTE ASINH)) 
 
-(DEFUN |DFLOAT;atanh;2$;58| (|x| |$|) (|DFLOAT;checkComplex| (ATANH |x|) |$|)) 
+(DEFUN |DFLOAT;asinh;2$;57| (|x| $) (ASINH |x|)) 
 
-(PUT (QUOTE |DFLOAT;acsch;2$;59|) (QUOTE |SPADreplace|) (QUOTE ACSCH)) 
+(DEFUN |DFLOAT;acosh;2$;58| (|x| $) (|DFLOAT;checkComplex| (ACOSH |x|) $)) 
 
-(DEFUN |DFLOAT;acsch;2$;59| (|x| |$|) (ACSCH |x|)) 
+(DEFUN |DFLOAT;atanh;2$;59| (|x| $) (|DFLOAT;checkComplex| (ATANH |x|) $)) 
 
-(DEFUN |DFLOAT;acoth;2$;60| (|x| |$|) (|DFLOAT;checkComplex| (ACOTH |x|) |$|)) 
+(PUT (QUOTE |DFLOAT;acsch;2$;60|) (QUOTE |SPADreplace|) (QUOTE ACSCH)) 
 
-(DEFUN |DFLOAT;asech;2$;61| (|x| |$|) (|DFLOAT;checkComplex| (ASECH |x|) |$|)) 
+(DEFUN |DFLOAT;acsch;2$;60| (|x| $) (ACSCH |x|)) 
 
-(PUT (QUOTE |DFLOAT;/;3$;62|) (QUOTE |SPADreplace|) (QUOTE |/|)) 
+(DEFUN |DFLOAT;acoth;2$;61| (|x| $) (|DFLOAT;checkComplex| (ACOTH |x|) $)) 
 
-(DEFUN |DFLOAT;/;3$;62| (|x| |y| |$|) (|/| |x| |y|)) 
+(DEFUN |DFLOAT;asech;2$;62| (|x| $) (|DFLOAT;checkComplex| (ASECH |x|) $)) 
 
-(PUT (QUOTE |DFLOAT;negative?;$B;63|) (QUOTE |SPADreplace|) (QUOTE MINUSP)) 
+(PUT (QUOTE |DFLOAT;/;3$;63|) (QUOTE |SPADreplace|) (QUOTE /)) 
 
-(DEFUN |DFLOAT;negative?;$B;63| (|x| |$|) (MINUSP |x|)) 
+(DEFUN |DFLOAT;/;3$;63| (|x| |y| $) (/ |x| |y|)) 
 
-(PUT (QUOTE |DFLOAT;zero?;$B;64|) (QUOTE |SPADreplace|) (QUOTE ZEROP)) 
+(PUT (QUOTE |DFLOAT;negative?;$B;64|) (QUOTE |SPADreplace|) (QUOTE MINUSP)) 
 
-(DEFUN |DFLOAT;zero?;$B;64| (|x| |$|) (ZEROP |x|)) 
+(DEFUN |DFLOAT;negative?;$B;64| (|x| $) (MINUSP |x|)) 
 
-(PUT (QUOTE |DFLOAT;hash;$I;65|) (QUOTE |SPADreplace|) (QUOTE HASHEQ)) 
+(PUT (QUOTE |DFLOAT;zero?;$B;65|) (QUOTE |SPADreplace|) (QUOTE ZEROP)) 
 
-(DEFUN |DFLOAT;hash;$I;65| (|x| |$|) (HASHEQ |x|)) 
+(DEFUN |DFLOAT;zero?;$B;65| (|x| $) (ZEROP |x|)) 
 
-(DEFUN |DFLOAT;recip;$U;66| (|x| |$|) (COND ((ZEROP |x|) (CONS 1 "failed")) ((QUOTE T) (CONS 0 (|/| 1.0 |x|))))) 
+(PUT (QUOTE |DFLOAT;hash;$I;66|) (QUOTE |SPADreplace|) (QUOTE HASHEQ)) 
 
-(PUT (QUOTE |DFLOAT;differentiate;2$;67|) (QUOTE |SPADreplace|) (QUOTE (XLAM (|x|) 0.0))) 
+(DEFUN |DFLOAT;hash;$I;66| (|x| $) (HASHEQ |x|)) 
 
-(DEFUN |DFLOAT;differentiate;2$;67| (|x| |$|) 0.0) 
+(DEFUN |DFLOAT;recip;$U;67| (|x| $) (COND ((ZEROP |x|) (CONS 1 "failed")) ((QUOTE T) (CONS 0 (/ 1.0 |x|))))) 
 
-(DEFUN |DFLOAT;Gamma;2$;68| (|x| |$|) (SPADCALL |x| (QREFELT |$| 93))) 
+(PUT (QUOTE |DFLOAT;differentiate;2$;68|) (QUOTE |SPADreplace|) (QUOTE (XLAM (|x|) 0.0))) 
 
-(DEFUN |DFLOAT;Beta;3$;69| (|x| |y| |$|) (SPADCALL |x| |y| (QREFELT |$| 95))) 
+(DEFUN |DFLOAT;differentiate;2$;68| (|x| $) 0.0) 
 
-(PUT (QUOTE |DFLOAT;wholePart;$I;70|) (QUOTE |SPADreplace|) (QUOTE FIX)) 
+(DEFUN |DFLOAT;Gamma;2$;69| (|x| $) (SPADCALL |x| (QREFELT $ 96))) 
 
-(DEFUN |DFLOAT;wholePart;$I;70| (|x| |$|) (FIX |x|)) 
+(DEFUN |DFLOAT;Beta;3$;70| (|x| |y| $) (SPADCALL |x| |y| (QREFELT $ 98))) 
 
-(DEFUN |DFLOAT;float;2IPi$;71| (|ma| |ex| |b| |$|) (|*| |ma| (EXPT (FLOAT |b| |MOST-POSITIVE-LONG-FLOAT|) |ex|))) 
+(PUT (QUOTE |DFLOAT;wholePart;$I;71|) (QUOTE |SPADreplace|) (QUOTE FIX)) 
 
-(PUT (QUOTE |DFLOAT;convert;2$;72|) (QUOTE |SPADreplace|) (QUOTE (XLAM (|x|) |x|))) 
+(DEFUN |DFLOAT;wholePart;$I;71| (|x| $) (FIX |x|)) 
 
-(DEFUN |DFLOAT;convert;2$;72| (|x| |$|) |x|) 
+(DEFUN |DFLOAT;float;2IPi$;72| (|ma| |ex| |b| $) (* |ma| (EXPT (FLOAT |b| MOST-POSITIVE-LONG-FLOAT) |ex|))) 
 
-(DEFUN |DFLOAT;convert;$F;73| (|x| |$|) (SPADCALL |x| (QREFELT |$| 101))) 
+(PUT (QUOTE |DFLOAT;convert;2$;73|) (QUOTE |SPADreplace|) (QUOTE (XLAM (|x|) |x|))) 
 
-(DEFUN |DFLOAT;rationalApproximation;$NniF;74| (|x| |d| |$|) (SPADCALL |x| |d| 10 (QREFELT |$| 105))) 
+(DEFUN |DFLOAT;convert;2$;73| (|x| $) |x|) 
 
-(DEFUN |DFLOAT;atan;3$;75| (|x| |y| |$|) (PROG (|theta|) (RETURN (SEQ (COND ((|=| |x| 0.0) (COND ((|<| 0.0 |y|) (|/| PI 2)) ((|<| |y| 0.0) (|-| (|/| PI 2))) ((QUOTE T) 0.0))) ((QUOTE T) (SEQ (LETT |theta| (ATAN (|FLOAT-SIGN| 1.0 (|/| |y| |x|))) |DFLOAT;atan;3$;75|) (COND ((|<| |x| 0.0) (LETT |theta| (|-| PI |theta|) |DFLOAT;atan;3$;75|))) (COND ((|<| |y| 0.0) (LETT |theta| (|-| |theta|) |DFLOAT;atan;3$;75|))) (EXIT |theta|)))))))) 
+(DEFUN |DFLOAT;convert;$F;74| (|x| $) (SPADCALL |x| (QREFELT $ 104))) 
 
-(DEFUN |DFLOAT;retract;$F;76| (|x| |$|) (PROG (#1=#:G105780) (RETURN (SPADCALL |x| (PROG1 (LETT #1# (|-| (|FLOAT-DIGITS| 0.0) 1) |DFLOAT;retract;$F;76|) (|check-subtype| (|>=| #1# 0) (QUOTE (|NonNegativeInteger|)) #1#)) (|FLOAT-RADIX| 0.0) (QREFELT |$| 105))))) 
+(DEFUN |DFLOAT;rationalApproximation;$NniF;75| (|x| |d| $) (SPADCALL |x| |d| 10 (QREFELT $ 108))) 
 
-(DEFUN |DFLOAT;retractIfCan;$U;77| (|x| |$|) (PROG (#1=#:G105785) (RETURN (CONS 0 (SPADCALL |x| (PROG1 (LETT #1# (|-| (|FLOAT-DIGITS| 0.0) 1) |DFLOAT;retractIfCan;$U;77|) (|check-subtype| (|>=| #1# 0) (QUOTE (|NonNegativeInteger|)) #1#)) (|FLOAT-RADIX| 0.0) (QREFELT |$| 105)))))) 
+(DEFUN |DFLOAT;atan;3$;76| (|x| |y| $) (PROG (|theta|) (RETURN (SEQ (COND ((= |x| 0.0) (COND ((< 0.0 |y|) (/ PI 2)) ((< |y| 0.0) (- (/ PI 2))) ((QUOTE T) 0.0))) ((QUOTE T) (SEQ (LETT |theta| (ATAN (FLOAT-SIGN 1.0 (/ |y| |x|))) |DFLOAT;atan;3$;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;$I;78| (|x| |$|) (PROG (|n|) (RETURN (SEQ (LETT |n| (FIX |x|) |DFLOAT;retract;$I;78|) (EXIT (COND ((|=| |x| (FLOAT |n| |MOST-POSITIVE-LONG-FLOAT|)) |n|) ((QUOTE T) (|error| "Not an integer")))))))) 
+(DEFUN |DFLOAT;retract;$F;77| (|x| $) (PROG (#0=#:G1519) (RETURN (SPADCALL |x| (PROG1 (LETT #0# (- (FLOAT-DIGITS 0.0) 1) |DFLOAT;retract;$F;77|) (|check-subtype| (>= #0# 0) (QUOTE (|NonNegativeInteger|)) #0#)) (FLOAT-RADIX 0.0) (QREFELT $ 108))))) 
 
-(DEFUN |DFLOAT;retractIfCan;$U;79| (|x| |$|) (PROG (|n|) (RETURN (SEQ (LETT |n| (FIX |x|) |DFLOAT;retractIfCan;$U;79|) (EXIT (COND ((|=| |x| (FLOAT |n| |MOST-POSITIVE-LONG-FLOAT|)) (CONS 0 |n|)) ((QUOTE T) (CONS 1 "failed")))))))) 
+(DEFUN |DFLOAT;retractIfCan;$U;78| (|x| $) (PROG (#0=#:G1524) (RETURN (CONS 0 (SPADCALL |x| (PROG1 (LETT #0# (- (FLOAT-DIGITS 0.0) 1) |DFLOAT;retractIfCan;$U;78|) (|check-subtype| (>= #0# 0) (QUOTE (|NonNegativeInteger|)) #0#)) (FLOAT-RADIX 0.0) (QREFELT $ 108)))))) 
 
-(DEFUN |DFLOAT;sign;$I;80| (|x| |$|) (SPADCALL (|FLOAT-SIGN| |x| 1.0) (QREFELT |$| 111))) 
+(DEFUN |DFLOAT;retract;$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|) ((QUOTE T) (|error| "Not an integer")))))))) 
 
-(PUT (QUOTE |DFLOAT;abs;2$;81|) (QUOTE |SPADreplace|) (QUOTE (XLAM (|x|) (|FLOAT-SIGN| 1.0 |x|)))) 
+(DEFUN |DFLOAT;retractIfCan;$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|)) ((QUOTE T) (CONS 1 "failed")))))))) 
 
-(DEFUN |DFLOAT;abs;2$;81| (|x| |$|) (|FLOAT-SIGN| 1.0 |x|)) 
+(DEFUN |DFLOAT;sign;$I;81| (|x| $) (SPADCALL (FLOAT-SIGN |x| 1.0) (QREFELT $ 114))) 
 
-(DEFUN |DFLOAT;manexp| (|x| |$|) (PROG (|s| #1=#:G105806 |me| |two53|) (RETURN (SEQ (EXIT (COND ((ZEROP |x|) (CONS 0 0)) ((QUOTE T) (SEQ (LETT |s| (SPADCALL |x| (QREFELT |$| 114)) |DFLOAT;manexp|) (LETT |x| (|FLOAT-SIGN| 1.0 |x|) |DFLOAT;manexp|) (COND ((|<| |MOST-POSITIVE-LONG-FLOAT| |x|) (PROGN (LETT #1# (CONS (|+| (|*| |s| (SPADCALL |MOST-POSITIVE-LONG-FLOAT| (QREFELT |$| 25))) 1) (SPADCALL |MOST-POSITIVE-LONG-FLOAT| (QREFELT |$| 26))) |DFLOAT;manexp|) (GO #1#)))) (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)))))))) #1# (EXIT #1#))))) 
+(PUT (QUOTE |DFLOAT;abs;2$;82|) (QUOTE |SPADreplace|) (QUOTE (XLAM (|x|) (FLOAT-SIGN 1.0 |x|)))) 
 
-(DEFUN |DFLOAT;rationalApproximation;$2NniF;83| (|f| |d| |b| |$|) (PROG (|#G102| |nu| |ex| BASE #1=#:G105809 |de| |tol| |#G103| |q| |r| |p2| |q2| #2=#:G105827 |#G104| |#G105| |p0| |p1| |#G106| |#G107| |q0| |q1| |#G108| |#G109| |s| |t| #3=#:G105825) (RETURN (SEQ (EXIT (SEQ (PROGN (LETT |#G102| (|DFLOAT;manexp| |f| |$|) |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |nu| (QCAR |#G102|) |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |ex| (QCDR |#G102|) |DFLOAT;rationalApproximation;$2NniF;83|) |#G102|) (LETT BASE (|FLOAT-RADIX| 0.0) |DFLOAT;rationalApproximation;$2NniF;83|) (EXIT (COND ((|<| |ex| 0) (SEQ (LETT |de| (EXPT BASE (PROG1 (LETT #1# (|-| |ex|) |DFLOAT;rationalApproximation;$2NniF;83|) (|check-subtype| (|>=| #1# 0) (QUOTE (|NonNegativeInteger|)) #1#))) |DFLOAT;rationalApproximation;$2NniF;83|) (EXIT (COND ((|<| |b| 2) (|error| "base must be > 1")) ((QUOTE T) (SEQ (LETT |tol| (EXPT |b| |d|) |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |s| |nu| |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |t| |de| |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |p0| 0 |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |p1| 1 |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |q0| 1 |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |q1| 0 |DFLOAT;rationalApproximation;$2NniF;83|) (EXIT (SEQ G190 NIL (SEQ (PROGN (LETT |#G103| (DIVIDE2 |s| |t|) |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |q| (QCAR |#G103|) |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |r| (QCDR |#G103|) |DFLOAT;rationalApproximation;$2NniF;83|) |#G103|) (LETT |p2| (|+| (|*| |q| |p1|) |p0|) |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |q2| (|+| (|*| |q| |q1|) |q0|) |DFLOAT;rationalApproximation;$2NniF;83|) (COND ((OR (EQL |r| 0) (|<| (SPADCALL |tol| (ABS (|-| (|*| |nu| |q2|) (|*| |de| |p2|))) (QREFELT |$| 118)) (|*| |de| (ABS |p2|)))) (EXIT (PROGN (LETT #2# (SPADCALL |p2| |q2| (QREFELT |$| 117)) |DFLOAT;rationalApproximation;$2NniF;83|) (GO #2#))))) (PROGN (LETT |#G104| |p1| |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |#G105| |p2| |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |p0| |#G104| |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |p1| |#G105| |DFLOAT;rationalApproximation;$2NniF;83|)) (PROGN (LETT |#G106| |q1| |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |#G107| |q2| |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |q0| |#G106| |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |q1| |#G107| |DFLOAT;rationalApproximation;$2NniF;83|)) (EXIT (PROGN (LETT |#G108| |t| |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |#G109| |r| |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |s| |#G108| |DFLOAT;rationalApproximation;$2NniF;83|) (LETT |t| |#G109| |DFLOAT;rationalApproximation;$2NniF;83|)))) NIL (GO G190) G191 (EXIT NIL))))))))) ((QUOTE T) (SPADCALL (|*| |nu| (EXPT BASE (PROG1 (LETT #3# |ex| |DFLOAT;rationalApproximation;$2NniF;83|) (|check-subtype| (|>=| #3# 0) (QUOTE (|NonNegativeInteger|)) #3#)))) (QREFELT |$| 119))))))) #2# (EXIT #2#))))) 
+(DEFUN |DFLOAT;abs;2$;82| (|x| $) (FLOAT-SIGN 1.0 |x|)) 
 
-(DEFUN |DFLOAT;**;$F$;84| (|x| |r| |$|) (PROG (|n| |d| #1=#:G105837) (RETURN (SEQ (EXIT (COND ((ZEROP |x|) (COND ((SPADCALL |r| (QREFELT |$| 120)) (|error| "0**0 is undefined")) ((SPADCALL |r| (QREFELT |$| 121)) (|error| "division by 0")) ((QUOTE T) 0.0))) ((OR (SPADCALL |r| (QREFELT |$| 120)) (SPADCALL |x| (QREFELT |$| 122))) 1.0) ((QUOTE T) (COND ((SPADCALL |r| (QREFELT |$| 123)) |x|) ((QUOTE T) (SEQ (LETT |n| (SPADCALL |r| (QREFELT |$| 124)) |DFLOAT;**;$F$;84|) (LETT |d| (SPADCALL |r| (QREFELT |$| 125)) |DFLOAT;**;$F$;84|) (EXIT (COND ((MINUSP |x|) (COND ((ODDP |d|) (COND ((ODDP |n|) (PROGN (LETT #1# (|-| (SPADCALL (|-| |x|) |r| (QREFELT |$| 126))) |DFLOAT;**;$F$;84|) (GO #1#))) ((QUOTE T) (PROGN (LETT #1# (SPADCALL (|-| |x|) |r| (QREFELT |$| 126)) |DFLOAT;**;$F$;84|) (GO #1#))))) ((QUOTE T) (|error| "negative root")))) ((EQL |d| 2) (EXPT (SPADCALL |x| (QREFELT |$| 54)) |n|)) ((QUOTE T) (SPADCALL |x| (|/| (FLOAT |n| |MOST-POSITIVE-LONG-FLOAT|) (FLOAT |d| |MOST-POSITIVE-LONG-FLOAT|)) (QREFELT |$| 57))))))))))) #1# (EXIT #1#))))) 
+(DEFUN |DFLOAT;manexp| (|x| $) (PROG (|s| #0=#:G1545 |me| |two53|) (RETURN (SEQ (EXIT (COND ((ZEROP |x|) (CONS 0 0)) ((QUOTE T) (SEQ (LETT |s| (SPADCALL |x| (QREFELT $ 117)) |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 (QREFELT $ 27))) 1) (SPADCALL MOST-POSITIVE-LONG-FLOAT (QREFELT $ 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 |DoubleFloat| NIL (PROG NIL (RETURN (PROG (#1=#:G105850) (RETURN (COND ((LETT #1# (HGET |$ConstructorCache| (QUOTE |DoubleFloat|)) |DoubleFloat|) (|CDRwithIncrement| (CDAR #1#))) ((QUOTE T) (|UNWIND-PROTECT| (PROG1 (CDDAR (HPUT |$ConstructorCache| (QUOTE |DoubleFloat|) (LIST (CONS NIL (CONS 1 (|DoubleFloat;|)))))) (LETT #1# T |DoubleFloat|)) (COND ((NOT #1#) (HREM |$ConstructorCache| (QUOTE |DoubleFloat|)))))))))))) 
+(DEFUN |DFLOAT;rationalApproximation;$2NniF;84| (|f| |d| |b| $) (PROG (|#G103| |nu| |ex| BASE #0=#:G1548 |de| |tol| |#G104| |q| |r| |p2| |q2| #1=#:G1566 |#G105| |#G106| |p0| |p1| |#G107| |#G108| |q0| |q1| |#G109| |#G110| |s| |t| #2=#:G1564) (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) (QUOTE (|NonNegativeInteger|)) #0#))) |DFLOAT;rationalApproximation;$2NniF;84|) (EXIT (COND ((< |b| 2) (|error| "base must be > 1")) ((QUOTE 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|))) (QREFELT $ 121)) (* |de| (ABS |p2|)))) (EXIT (PROGN (LETT #1# (SPADCALL |p2| |q2| (QREFELT $ 120)) |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))))))))) ((QUOTE T) (SPADCALL (* |nu| (EXPT BASE (PROG1 (LETT #2# |ex| |DFLOAT;rationalApproximation;$2NniF;84|) (|check-subtype| (>= #2# 0) (QUOTE (|NonNegativeInteger|)) #2#)))) (QREFELT $ 122))))))) #1# (EXIT #1#))))) 
 
-(DEFUN |DoubleFloat;| NIL (PROG (|dv$| |$| |pv$|) (RETURN (PROGN (LETT |dv$| (QUOTE (|DoubleFloat|)) . #1=(|DoubleFloat|)) (LETT |$| (GETREFV 140) . #1#) (QSETREFV |$| 0 |dv$|) (QSETREFV |$| 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #1#)) (|haddProp| |$ConstructorCache| (QUOTE |DoubleFloat|) NIL (CONS 1 |$|)) (|stuffDomainSlots| |$|) |$|)))) 
+(DEFUN |DFLOAT;**;$F$;85| (|x| |r| $) (PROG (|n| |d| #0=#:G1575) (RETURN (SEQ (EXIT (COND ((ZEROP |x|) (COND ((SPADCALL |r| (QREFELT $ 123)) (|error| "0**0 is undefined")) ((SPADCALL |r| (QREFELT $ 124)) (|error| "division by 0")) ((QUOTE T) 0.0))) ((OR (SPADCALL |r| (QREFELT $ 123)) (= |x| 1.0)) 1.0) ((QUOTE T) (COND ((SPADCALL |r| (|spadConstant| $ 125) (QREFELT $ 126)) |x|) ((QUOTE T) (SEQ (LETT |n| (SPADCALL |r| (QREFELT $ 127)) |DFLOAT;**;$F$;85|) (LETT |d| (SPADCALL |r| (QREFELT $ 128)) |DFLOAT;**;$F$;85|) (EXIT (COND ((MINUSP |x|) (COND ((ODDP |d|) (COND ((ODDP |n|) (PROGN (LETT #0# (- (SPADCALL (- |x|) |r| (QREFELT $ 129))) |DFLOAT;**;$F$;85|) (GO #0#))) ((QUOTE T) (PROGN (LETT #0# (SPADCALL (- |x|) |r| (QREFELT $ 129)) |DFLOAT;**;$F$;85|) (GO #0#))))) ((QUOTE T) (|error| "negative root")))) ((EQL |d| 2) (EXPT (SPADCALL |x| (QREFELT $ 57)) |n|)) ((QUOTE T) (SPADCALL |x| (/ (FLOAT |n| MOST-POSITIVE-LONG-FLOAT) (FLOAT |d| MOST-POSITIVE-LONG-FLOAT)) (QREFELT $ 60))))))))))) #0# (EXIT #0#))))) 
 
-(MAKEPROP (QUOTE |DoubleFloat|) (QUOTE |infovec|) (LIST (QUOTE #(NIL NIL NIL NIL NIL NIL (|OpenMathEncoding|) (0 . |OMencodingXML|) (|String|) (|OpenMathDevice|) (4 . |OMopenString|) (|Void|) (10 . |OMputObject|) (|DoubleFloat|) (15 . |OMputFloat|) (21 . |OMputEndObject|) (26 . |OMclose|) |DFLOAT;OMwrite;$S;1| (|Boolean|) |DFLOAT;OMwrite;$BS;2| |DFLOAT;OMwrite;Omd$V;3| |DFLOAT;OMwrite;Omd$BV;4| (|PositiveInteger|) |DFLOAT;base;Pi;6| (|Integer|) |DFLOAT;mantissa;$I;7| |DFLOAT;exponent;$I;8| |DFLOAT;precision;Pi;9| |DFLOAT;log2;2$;37| (31 . |*|) |DFLOAT;bits;Pi;10| |DFLOAT;max;$;11| |DFLOAT;min;$;12| |DFLOAT;order;$I;13| (CONS IDENTITY (FUNCALL (|dispatchFunction| |DFLOAT;Zero;$;14|) |$|)) (CONS IDENTITY (FUNCALL (|dispatchFunction| |DFLOAT;One;$;15|) |$|)) |DFLOAT;exp1;$;16| |DFLOAT;pi;$;17| (|OutputForm|) (37 . |outputForm|) |DFLOAT;coerce;$Of;18| (|InputForm|) (42 . |convert|) |DFLOAT;convert;$If;19| |DFLOAT;<;2$B;20| |DFLOAT;-;2$;21| |DFLOAT;+;3$;22| |DFLOAT;-;3$;23| |DFLOAT;*;3$;24| |DFLOAT;*;I2$;25| |DFLOAT;max;3$;26| |DFLOAT;min;3$;27| |DFLOAT;=;2$B;28| |DFLOAT;/;$I$;29| |DFLOAT;sqrt;2$;30| |DFLOAT;log10;2$;31| |DFLOAT;**;$I$;32| |DFLOAT;**;3$;33| |DFLOAT;coerce;I$;34| |DFLOAT;exp;2$;35| |DFLOAT;log;2$;36| |DFLOAT;sin;2$;38| |DFLOAT;cos;2$;39| |DFLOAT;tan;2$;40| |DFLOAT;cot;2$;41| |DFLOAT;sec;2$;42| |DFLOAT;csc;2$;43| |DFLOAT;asin;2$;44| |DFLOAT;acos;2$;45| |DFLOAT;atan;2$;46| |DFLOAT;acsc;2$;47| |DFLOAT;acot;2$;48| |DFLOAT;asec;2$;49| |DFLOAT;sinh;2$;50| |DFLOAT;cosh;2$;51| |DFLOAT;tanh;2$;52| |DFLOAT;csch;2$;53| |DFLOAT;coth;2$;54| |DFLOAT;sech;2$;55| |DFLOAT;asinh;2$;56| |DFLOAT;acosh;2$;57| |DFLOAT;atanh;2$;58| |DFLOAT;acsch;2$;59| |DFLOAT;acoth;2$;60| |DFLOAT;asech;2$;61| |DFLOAT;/;3$;62| |DFLOAT;negative?;$B;63| |DFLOAT;zero?;$B;64| |DFLOAT;hash;$I;65| (|Union| |$| (QUOTE "failed")) |DFLOAT;recip;$U;66| |DFLOAT;differentiate;2$;67| (|DoubleFloatSpecialFunctions|) (47 . |Gamma|) |DFLOAT;Gamma;2$;68| (52 . |Beta|) |DFLOAT;Beta;3$;69| |DFLOAT;wholePart;$I;70| |DFLOAT;float;2IPi$;71| |DFLOAT;convert;2$;72| (|Float|) (58 . |convert|) |DFLOAT;convert;$F;73| (|Fraction| 24) (|NonNegativeInteger|) |DFLOAT;rationalApproximation;$2NniF;83| |DFLOAT;rationalApproximation;$NniF;74| |DFLOAT;atan;3$;75| |DFLOAT;retract;$F;76| (|Union| 103 (QUOTE "failed")) |DFLOAT;retractIfCan;$U;77| |DFLOAT;retract;$I;78| (|Union| 24 (QUOTE "failed")) |DFLOAT;retractIfCan;$U;79| |DFLOAT;sign;$I;80| |DFLOAT;abs;2$;81| (63 . |Zero|) (67 . |/|) (73 . |*|) (79 . |coerce|) (84 . |zero?|) (89 . |negative?|) (94 . |one?|) (99 . |one?|) (104 . |numer|) (109 . |denom|) |DFLOAT;**;$F$;84| (|Pattern| 100) (|PatternMatchResult| 100 |$|) (|Factored| |$|) (|Union| 131 (QUOTE "failed")) (|List| |$|) (|Record| (|:| |coef1| |$|) (|:| |coef2| |$|) (|:| |generator| |$|)) (|Record| (|:| |coef1| |$|) (|:| |coef2| |$|)) (|Union| 133 (QUOTE "failed")) (|Record| (|:| |quotient| |$|) (|:| |remainder| |$|)) (|Record| (|:| |coef| 131) (|:| |generator| |$|)) (|SparseUnivariatePolynomial| |$|) (|Record| (|:| |unit| |$|) (|:| |canonical| |$|) (|:| |associate| |$|)) (|SingleInteger|))) (QUOTE #(|~=| 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 |divide| 493 |digits| 499 |differentiate| 503 |csch| 514 |csc| 519 |coth| 524 |cot| 529 |cosh| 534 |cos| 539 |convert| 544 |coerce| 564 |characteristic| 594 |ceiling| 598 |bits| 603 |base| 607 |atanh| 611 |atan| 616 |associates?| 627 |asinh| 633 |asin| 638 |asech| 643 |asec| 648 |acsch| 653 |acsc| 658 |acoth| 663 |acot| 668 |acosh| 673 |acos| 678 |abs| 683 |^| 688 |Zero| 706 |One| 710 |OMwrite| 714 |Gamma| 738 D 743 |Beta| 754 |>=| 760 |>| 766 |=| 772 |<=| 778 |<| 784 |/| 790 |-| 802 |+| 813 |**| 819 |*| 849)) (QUOTE ((|approximate| . 0) (|canonicalsClosed| . 0) (|canonicalUnitNormal| . 0) (|noZeroDivisors| . 0) ((|commutative| "*") . 0) (|rightUnitary| . 0) (|leftUnitary| . 0) (|unitsKnown| . 0))) (CONS (|makeByteWordVec2| 1 (QUOTE (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 (QUOTE #(|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 (QUOTE #((|FloatingPointSystem|) (|RealNumberSystem|) (|Field|) (|EuclideanDomain|) (|PrincipalIdealDomain|) (|UniqueFactorizationDomain|) (|GcdDomain|) (|DivisionRing|) (|IntegralDomain|) (|Algebra| 103) (|Algebra| |$$|) (|DifferentialRing|) (|CharacteristicZero|) (|OrderedRing|) (|Module| 103) (|EntireRing|) (|CommutativeRing|) (|Module| |$$|) (|OrderedAbelianGroup|) (|BiModule| 103 103) (|BiModule| |$$| |$$|) (|Ring|) (|OrderedCancellationAbelianMonoid|) (|RightModule| 103) (|LeftModule| 103) (|LeftModule| |$$|) (|Rng|) (|RightModule| |$$|) (|OrderedAbelianMonoid|) (|AbelianGroup|) (|OrderedAbelianSemiGroup|) (|CancellationAbelianMonoid|) (|AbelianMonoid|) (|Monoid|) (|PatternMatchable| 100) (|OrderedSet|) (|AbelianSemiGroup|) (|SemiGroup|) (|TranscendentalFunctionCategory|) (|RealConstant|) (|SetCategory|) (|ConvertibleTo| 41) (|ElementaryFunctionCategory|) (|ArcHyperbolicFunctionCategory|) (|HyperbolicFunctionCategory|) (|ArcTrigonometricFunctionCategory|) (|TrigonometricFunctionCategory|) (|OpenMath|) (|ConvertibleTo| 127) (|RadicalCategory|) (|RetractableTo| 103) (|RetractableTo| 24) (|ConvertibleTo| 100) (|ConvertibleTo| 13) (|BasicType|) (|CoercibleTo| 38))) (|makeByteWordVec2| 139 (QUOTE (0 6 0 7 2 9 0 8 6 10 1 9 11 0 12 2 9 11 0 13 14 1 9 11 0 15 1 9 11 0 16 2 0 0 22 0 29 1 38 0 13 39 1 41 0 13 42 1 92 13 13 93 2 92 13 13 13 95 1 100 0 13 101 0 103 0 116 2 103 0 24 24 117 2 24 0 104 0 118 1 103 0 24 119 1 103 18 0 120 1 103 18 0 121 1 0 18 0 122 1 103 18 0 123 1 103 24 0 124 1 103 24 0 125 2 0 18 0 0 1 1 0 18 0 87 1 0 24 0 97 1 0 138 0 1 1 0 0 0 1 1 0 18 0 1 1 0 0 0 1 1 0 0 0 75 1 0 0 0 63 2 0 89 0 0 1 1 0 0 0 1 1 0 129 0 1 1 0 0 0 54 2 0 18 0 0 1 1 0 0 0 73 1 0 0 0 61 1 0 24 0 114 1 0 0 0 78 1 0 0 0 65 0 0 0 1 1 0 0 0 1 1 0 109 0 110 1 0 112 0 113 1 0 103 0 108 1 0 24 0 111 2 0 0 0 0 1 1 0 89 0 90 2 0 103 0 104 106 3 0 103 0 104 104 105 2 0 0 0 0 1 1 0 136 131 1 1 0 18 0 1 0 0 22 27 1 0 18 0 1 0 0 0 37 3 0 128 0 127 128 1 1 0 24 0 33 1 0 18 0 122 2 0 0 0 24 1 1 0 0 0 1 1 0 18 0 86 2 0 130 131 0 1 0 0 0 32 2 0 0 0 0 51 0 0 0 31 2 0 0 0 0 50 1 0 24 0 25 1 0 0 0 28 1 0 0 0 55 1 0 0 0 60 1 0 0 131 1 2 0 0 0 0 1 1 0 8 0 1 1 0 0 0 1 1 0 24 0 88 1 0 139 0 1 2 0 137 137 137 1 1 0 0 131 1 2 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 3 0 0 24 24 22 98 2 0 0 24 24 1 1 0 129 0 1 2 0 132 0 0 1 3 0 134 0 0 0 1 2 0 89 0 0 1 2 0 130 131 0 1 1 0 24 0 26 0 0 0 36 1 0 0 0 59 1 0 104 0 1 2 0 135 0 0 1 0 0 22 1 1 0 0 0 91 2 0 0 0 104 1 1 0 0 0 76 1 0 0 0 66 1 0 0 0 77 1 0 0 0 64 1 0 0 0 74 1 0 0 0 62 1 0 41 0 43 1 0 127 0 1 1 0 13 0 99 1 0 100 0 102 1 0 0 103 1 1 0 0 24 58 1 0 0 103 1 1 0 0 24 58 1 0 0 0 1 1 0 38 0 40 0 0 104 1 1 0 0 0 1 0 0 22 30 0 0 22 23 1 0 0 0 81 2 0 0 0 0 107 1 0 0 0 69 2 0 18 0 0 1 1 0 0 0 79 1 0 0 0 67 1 0 0 0 84 1 0 0 0 72 1 0 0 0 82 1 0 0 0 70 1 0 0 0 83 1 0 0 0 71 1 0 0 0 80 1 0 0 0 68 1 0 0 0 115 2 0 0 0 24 1 2 0 0 0 104 1 2 0 0 0 22 1 0 0 0 34 0 0 0 35 2 0 11 9 0 20 3 0 11 9 0 18 21 1 0 8 0 17 2 0 8 0 18 19 1 0 0 0 94 1 0 0 0 1 2 0 0 0 104 1 2 0 0 0 0 96 2 0 18 0 0 1 2 0 18 0 0 1 2 0 18 0 0 52 2 0 18 0 0 1 2 0 18 0 0 44 2 0 0 0 24 53 2 0 0 0 0 85 2 0 0 0 0 47 1 0 0 0 45 2 0 0 0 0 46 2 0 0 0 0 57 2 0 0 0 103 126 2 0 0 0 24 56 2 0 0 0 104 1 2 0 0 0 22 1 2 0 0 0 103 1 2 0 0 103 0 1 2 0 0 0 0 48 2 0 0 24 0 49 2 0 0 104 0 1 2 0 0 22 0 29)))))) (QUOTE |lookupComplete|))) 
+(DEFUN |DoubleFloat| NIL (PROG NIL (RETURN (PROG (#0=#:G1588) (RETURN (COND ((LETT #0# (HGET |$ConstructorCache| (QUOTE |DoubleFloat|)) |DoubleFloat|) (|CDRwithIncrement| (CDAR #0#))) ((QUOTE T) (UNWIND-PROTECT (PROG1 (CDDAR (HPUT |$ConstructorCache| (QUOTE |DoubleFloat|) (LIST (CONS NIL (CONS 1 (|DoubleFloat;|)))))) (LETT #0# T |DoubleFloat|)) (COND ((NOT #0#) (HREM |$ConstructorCache| (QUOTE |DoubleFloat|)))))))))))) 
+
+(DEFUN |DoubleFloat;| NIL (PROG (|dv$| $ |pv$|) (RETURN (PROGN (LETT |dv$| (QUOTE (|DoubleFloat|)) . #0=(|DoubleFloat|)) (LETT $ (GETREFV 143) . #0#) (QSETREFV $ 0 |dv$|) (QSETREFV $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) (|haddProp| |$ConstructorCache| (QUOTE |DoubleFloat|) NIL (CONS 1 $)) (|stuffDomainSlots| $) (QSETREFV $ 6 "~A") $)))) 
+
+(MAKEPROP (QUOTE |DoubleFloat|) (QUOTE |infovec|) (LIST (QUOTE #(NIL NIL NIL NIL NIL NIL (QUOTE |format|) (|String|) |DFLOAT;doubleFloatFormat;2S;1| (|OpenMathEncoding|) (0 . |OMencodingXML|) (|OpenMathDevice|) (4 . |OMopenString|) (|Void|) (10 . |OMputObject|) (|DoubleFloat|) (15 . |OMputFloat|) (21 . |OMputEndObject|) (26 . |OMclose|) |DFLOAT;OMwrite;$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;$;18| (|OutputForm|) (37 . |message|) (42 . -) |DFLOAT;coerce;$Of;19| (|InputForm|) (47 . |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| $ (QUOTE "failed")) |DFLOAT;recip;$U;67| |DFLOAT;differentiate;2$;68| (|DoubleFloatSpecialFunctions|) (52 . |Gamma|) |DFLOAT;Gamma;2$;69| (57 . |Beta|) |DFLOAT;Beta;3$;70| |DFLOAT;wholePart;$I;71| |DFLOAT;float;2IPi$;72| |DFLOAT;convert;2$;73| (|Float|) (63 . |convert|) |DFLOAT;convert;$F;74| (|Fraction| 26) (|NonNegativeInteger|) |DFLOAT;rationalApproximation;$2NniF;84| |DFLOAT;rationalApproximation;$NniF;75| |DFLOAT;atan;3$;76| |DFLOAT;retract;$F;77| (|Union| 106 (QUOTE "failed")) |DFLOAT;retractIfCan;$U;78| |DFLOAT;retract;$I;79| (|Union| 26 (QUOTE "failed")) |DFLOAT;retractIfCan;$U;80| |DFLOAT;sign;$I;81| |DFLOAT;abs;2$;82| (68 . |Zero|) (72 . /) (78 . *) (84 . |coerce|) (89 . |zero?|) (94 . |negative?|) (99 . |One|) (103 . =) (109 . |numer|) (114 . |denom|) |DFLOAT;**;$F$;85| (|PatternMatchResult| 103 $) (|Pattern| 103) (|Factored| $) (|Union| 134 (QUOTE "failed")) (|List| $) (|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) (|Record| (|:| |coef1| $) (|:| |coef2| $)) (|Union| 136 (QUOTE "failed")) (|Record| (|:| |quotient| $) (|:| |remainder| $)) (|Record| (|:| |coef| 134) (|:| |generator| $)) (|SparseUnivariatePolynomial| $) (|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) (|SingleInteger|))) (QUOTE #(~= 119 |zero?| 125 |wholePart| 130 |unitNormal| 135 |unitCanonical| 140 |unit?| 145 |truncate| 150 |tanh| 155 |tan| 160 |subtractIfCan| 165 |squareFreePart| 171 |squareFree| 176 |sqrt| 181 |sizeLess?| 186 |sinh| 192 |sin| 197 |sign| 202 |sech| 207 |sec| 212 |sample| 217 |round| 221 |retractIfCan| 226 |retract| 236 |rem| 246 |recip| 252 |rationalApproximation| 257 |quo| 270 |principalIdeal| 276 |prime?| 281 |precision| 286 |positive?| 290 |pi| 295 |patternMatch| 299 |order| 306 |one?| 311 |nthRoot| 316 |norm| 322 |negative?| 327 |multiEuclidean| 332 |min| 338 |max| 348 |mantissa| 358 |log2| 363 |log10| 368 |log| 373 |lcm| 378 |latex| 389 |inv| 394 |hash| 399 |gcdPolynomial| 409 |gcd| 415 |fractionPart| 426 |floor| 431 |float| 436 |factor| 449 |extendedEuclidean| 454 |exquo| 467 |expressIdealMember| 473 |exponent| 479 |exp1| 484 |exp| 488 |euclideanSize| 493 |doubleFloatFormat| 498 |divide| 503 |digits| 509 |differentiate| 513 |csch| 524 |csc| 529 |coth| 534 |cot| 539 |cosh| 544 |cos| 549 |convert| 554 |coerce| 574 |characteristic| 604 |ceiling| 608 |bits| 613 |base| 617 |atanh| 621 |atan| 626 |associates?| 637 |asinh| 643 |asin| 648 |asech| 653 |asec| 658 |acsch| 663 |acsc| 668 |acoth| 673 |acot| 678 |acosh| 683 |acos| 688 |abs| 693 ^ 698 |Zero| 716 |One| 720 |OMwrite| 724 |Gamma| 748 D 753 |Beta| 764 >= 770 > 776 = 782 <= 788 < 794 / 800 - 812 + 823 ** 829 * 859)) (QUOTE ((|approximate| . 0) (|canonicalsClosed| . 0) (|canonicalUnitNormal| . 0) (|noZeroDivisors| . 0) ((|commutative| "*") . 0) (|rightUnitary| . 0) (|leftUnitary| . 0) (|unitsKnown| . 0))) (CONS (|makeByteWordVec2| 1 (QUOTE (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 (QUOTE #(|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 (QUOTE #((|FloatingPointSystem|) (|RealNumberSystem|) (|Field|) (|EuclideanDomain|) (|PrincipalIdealDomain|) (|UniqueFactorizationDomain|) (|GcdDomain|) (|DivisionRing|) (|IntegralDomain|) (|Algebra| 106) (|Algebra| $$) (|DifferentialRing|) (|CharacteristicZero|) (|OrderedRing|) (|Module| 106) (|EntireRing|) (|CommutativeRing|) (|Module| $$) (|OrderedAbelianGroup|) (|BiModule| 106 106) (|BiModule| $$ $$) (|Ring|) (|OrderedCancellationAbelianMonoid|) (|RightModule| 106) (|LeftModule| 106) (|LeftModule| $$) (|Rng|) (|RightModule| $$) (|OrderedAbelianMonoid|) (|AbelianGroup|) (|OrderedAbelianSemiGroup|) (|CancellationAbelianMonoid|) (|AbelianMonoid|) (|Monoid|) (|PatternMatchable| 103) (|OrderedSet|) (|AbelianSemiGroup|) (|SemiGroup|) (|TranscendentalFunctionCategory|) (|RealConstant|) (|SetCategory|) (|ConvertibleTo| 44) (|ElementaryFunctionCategory|) (|ArcHyperbolicFunctionCategory|) (|HyperbolicFunctionCategory|) (|ArcTrigonometricFunctionCategory|) (|TrigonometricFunctionCategory|) (|OpenMath|) (|ConvertibleTo| 131) (|RadicalCategory|) (|RetractableTo| 106) (|RetractableTo| 26) (|ConvertibleTo| 103) (|ConvertibleTo| 15) (|BasicType|) (|CoercibleTo| 40))) (|makeByteWordVec2| 142 (QUOTE (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 7 41 1 40 0 0 42 1 44 0 15 45 1 95 15 15 96 2 95 15 15 15 98 1 103 0 15 104 0 106 0 119 2 106 0 26 26 120 2 26 0 107 0 121 1 106 0 26 122 1 106 20 0 123 1 106 20 0 124 0 106 0 125 2 106 20 0 0 126 1 106 26 0 127 1 106 26 0 128 2 0 20 0 0 1 1 0 20 0 90 1 0 26 0 100 1 0 141 0 1 1 0 0 0 1 1 0 20 0 1 1 0 0 0 1 1 0 0 0 78 1 0 0 0 66 2 0 92 0 0 1 1 0 0 0 1 1 0 132 0 1 1 0 0 0 57 2 0 20 0 0 1 1 0 0 0 76 1 0 0 0 64 1 0 26 0 117 1 0 0 0 81 1 0 0 0 68 0 0 0 1 1 0 0 0 1 1 0 112 0 113 1 0 115 0 116 1 0 106 0 111 1 0 26 0 114 2 0 0 0 0 1 1 0 92 0 93 2 0 106 0 107 109 3 0 106 0 107 107 108 2 0 0 0 0 1 1 0 139 134 1 1 0 20 0 1 0 0 24 29 1 0 20 0 1 0 0 0 39 3 0 130 0 131 130 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 89 2 0 133 134 0 1 0 0 0 34 2 0 0 0 0 54 0 0 0 33 2 0 0 0 0 53 1 0 26 0 27 1 0 0 0 30 1 0 0 0 58 1 0 0 0 63 1 0 0 134 1 2 0 0 0 0 1 1 0 7 0 1 1 0 0 0 1 1 0 26 0 91 1 0 142 0 1 2 0 140 140 140 1 1 0 0 134 1 2 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 3 0 0 26 26 24 101 2 0 0 26 26 1 1 0 132 0 1 2 0 135 0 0 1 3 0 137 0 0 0 1 2 0 92 0 0 1 2 0 133 134 0 1 1 0 26 0 28 0 0 0 38 1 0 0 0 62 1 0 107 0 1 1 0 7 7 8 2 0 138 0 0 1 0 0 24 1 1 0 0 0 94 2 0 0 0 107 1 1 0 0 0 79 1 0 0 0 69 1 0 0 0 80 1 0 0 0 67 1 0 0 0 77 1 0 0 0 65 1 0 44 0 46 1 0 131 0 1 1 0 103 0 105 1 0 15 0 102 1 0 0 106 1 1 0 0 26 61 1 0 0 106 1 1 0 0 26 61 1 0 0 0 1 1 0 40 0 43 0 0 107 1 1 0 0 0 1 0 0 24 32 0 0 24 25 1 0 0 0 84 2 0 0 0 0 110 1 0 0 0 72 2 0 20 0 0 1 1 0 0 0 82 1 0 0 0 70 1 0 0 0 87 1 0 0 0 75 1 0 0 0 85 1 0 0 0 73 1 0 0 0 86 1 0 0 0 74 1 0 0 0 83 1 0 0 0 71 1 0 0 0 118 2 0 0 0 26 1 2 0 0 0 107 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 97 1 0 0 0 1 2 0 0 0 107 1 2 0 0 0 0 99 2 0 20 0 0 1 2 0 20 0 0 1 2 0 20 0 0 55 2 0 20 0 0 1 2 0 20 0 0 47 2 0 0 0 26 56 2 0 0 0 0 88 2 0 0 0 0 50 1 0 0 0 48 2 0 0 0 0 49 2 0 0 0 0 60 2 0 0 0 106 129 2 0 0 0 26 59 2 0 0 0 107 1 2 0 0 0 24 1 2 0 0 0 106 1 2 0 0 106 0 1 2 0 0 0 0 51 2 0 0 26 0 52 2 0 0 107 0 1 2 0 0 24 0 31)))))) (QUOTE |lookupComplete|))) 
 
 (MAKEPROP (QUOTE |DoubleFloat|) (QUOTE NILADIC) T) 
+
 @
 \section{License}
 <<license>>=