(FILECREATED "20-Aug-86 20:30:46" ("compiled on " {ERIS}<LISPCORE>LIBRARY>CMLFLOAT.;38) 
"18-Aug-86 12:42:20" "COMPILE-FILEd" in "Xerox Lisp 18-Aug-86 ..." dated "18-Aug-86 13:55:08")
(FILECREATED "20-Aug-86 20:27:43" {ERIS}<LISPCORE>LIBRARY>CMLFLOAT.;38 80964 changes to: (FNS 
%%MAKE-ARRAY %%FLOAT EXP %%EXP-FLOAT %%EXP-COMPLEX CL:EXPT %%EXPT-INTEGER %%EXPT-FLOAT %%EXPT-COMPLEX 
%%EXPT-COMPLEX-POWER CL:LOG %%LOG-FLOAT %%LOG-COMPLEX CL:SQRT %%SQRT-FLOAT %%SQRT-COMPLEX CL:SIN 
%%SIN-FLOAT %%SIN-COMPLEX CL:COS %%COS-COMPLEX CL:TAN %%TAN-FLOAT %%TAN-COMPLEX ASIN %%ASIN-FLOAT 
%%ASIN-COMPLEX ACOS %%ACOS-COMPLEX CL:ATAN %%ATAN-FLOAT1 %%ATAN-FLOAT2 %%ATAN-DOMAIN-CHECK 
%%ATAN-FLOAT %%ATAN-COMPLEX CIS SINH COSH TANH ASINH ACOSH ATANH %%ATANH-DOMAIN-CHECK) (VARS 
CMLFLOATCOMS) previous date: "20-Aug-86 18:40:46" {ERIS}<LISPCORE>LIBRARY>CMLFLOAT.;37)
(RPAQQ CMLFLOATCOMS ((* * CMLFLOAT -- Covering sections %12.5-12.5.3 irrational, transcendental, 
exponential, logarithmic, trigonometric, and hyperbolic functions. Section 12.10, implementation 
parameters. -- By Kelly Roach. *) (DECLARE: EVAL@COMPILE DONTCOPY (FILES (LOADCOMP) LLFLOAT)) (COMS (*
 Section 12.10, implementation parameters. The constants in this COMS are exported to the user. *) (* 
%%FLOAT allows us to recreate FLOATPs in a way that is independent of the ordinairy reading and 
printing FLOATPs to files which involves loss of the last couple bits of accuracy due to rounding 
effects. *) (* Using INITVARS instead of CONSTANTS in various places here because of problems with the
 way BYTECOMPILER stores FLOATPs in DCOM files. *) (FNS %%FLOAT) (CONSTANTS (MOST-POSITIVE-FIXNUM 
65535) (MOST-NEGATIVE-FIXNUM -65536)) (INITVARS (MOST-POSITIVE-SINGLE-FLOAT (%%FLOAT 32639 65535)) (
LEAST-POSITIVE-SINGLE-FLOAT (%%FLOAT 128 0)) (LEAST-NEGATIVE-SINGLE-FLOAT (%%FLOAT 32896 0)) (
MOST-NEGATIVE-SINGLE-FLOAT (%%FLOAT 65407 65535)) (MOST-POSITIVE-SHORT-FLOAT 
MOST-POSITIVE-SINGLE-FLOAT) (LEAST-POSITIVE-SHORT-FLOAT LEAST-POSITIVE-SINGLE-FLOAT) (
LEAST-NEGATIVE-SHORT-FLOAT LEAST-NEGATIVE-SINGLE-FLOAT) (MOST-NEGATIVE-SHORT-FLOAT 
MOST-NEGATIVE-SINGLE-FLOAT) (MOST-POSITIVE-DOUBLE-FLOAT MOST-POSITIVE-SINGLE-FLOAT) (
LEAST-POSITIVE-DOUBLE-FLOAT LEAST-POSITIVE-SINGLE-FLOAT) (LEAST-NEGATIVE-DOUBLE-FLOAT 
LEAST-NEGATIVE-SINGLE-FLOAT) (MOST-NEGATIVE-DOUBLE-FLOAT MOST-NEGATIVE-SINGLE-FLOAT) (
MOST-POSITIVE-LONG-FLOAT MOST-POSITIVE-SINGLE-FLOAT) (LEAST-POSITIVE-LONG-FLOAT 
LEAST-POSITIVE-SINGLE-FLOAT) (LEAST-NEGATIVE-LONG-FLOAT LEAST-NEGATIVE-SINGLE-FLOAT) (
MOST-NEGATIVE-LONG-FLOAT MOST-NEGATIVE-SINGLE-FLOAT)) (* EPSILON is the smallest positive floating 
point number such that (NOT (= (FLOAT 1 EPSILON) (+ (FLOAT 1 EPSILON) EPSILON))) *) (INITVARS (
SINGLE-FLOAT-EPSILON (%%FLOAT 13312 0)) (SHORT-FLOAT-EPSILON SINGLE-FLOAT-EPSILON) (
DOUBLE-FLOAT-EPSILON SINGLE-FLOAT-EPSILON) (LONG-FLOAT-EPSILON SINGLE-FLOAT-EPSILON)) (* 
NEGATIVE-EPSILON is the smallest negative floating point number such that (NOT (= (FLOAT 1 
NEGATIVE-EPSILON) (- (FLOAT 1 NEGATIVE-EPSILON) NEGATIVE-EPSILON))) *) (INITVARS (
SINGLE-FLOAT-NEGATIVE-EPSILON (%%FLOAT 13184 0)) (SHORT-FLOAT-NEGATIVE-EPSILON 
SINGLE-FLOAT-NEGATIVE-EPSILON) (DOUBLE-FLOAT-NEGATIVE-EPSILON SINGLE-FLOAT-NEGATIVE-EPSILON) (
LONG-FLOAT-NEGATIVE-EPSILON SINGLE-FLOAT-NEGATIVE-EPSILON))) (COMS (* Miscellaneous. *) (DECLARE: 
EVAL@COMPILE DONTCOPY (FILES (LOADCOMP) LLFLOAT)) (INITVARS (PI (%%FLOAT 16457 4059))) (* Should be (
DECLARE: EVAL@COMPILE DONTCOPY (CONSTANTS ...)) except that compiler does a poor job of compiling 
FLOATPs. Use an INITVARS to patch around this situation for now. *) (INITVARS (%%E (%%FLOAT 16429 
63572)) (%%2PI (%%FLOAT 16585 4059)) (%%PI (%%FLOAT 16457 4059)) (%%2PI/3 (%%FLOAT 16390 2706)) (
%%PI/2 (%%FLOAT 16329 4059)) (%%-PI/2 (%%FLOAT 49097 4059)) (%%PI/3 (%%FLOAT 16262 2706)) (%%PI/4 (
%%FLOAT 16201 4059)) (%%-PI/4 (%%FLOAT 48969 4059)) (%%PI/6 (%%FLOAT 16134 2706)) (%%2/PI (%%FLOAT 
16162 63875))) (FNS %%MAKE-ARRAY)) (COMS (* EXP *) (COMS (INITVARS (%%LOG-BASE2-E (%%FLOAT 16312 43579
))) (* * %%EXP-POLY contains P and Q coefficients of Harris et al EXPB 1103 rational approximation to 
(EXPT 2 X) in interval (0 .125) %. %%EXP-TABLE contains values of powers (EXPT 2 (/ N 8)) . *) (VARS (
%%EXP-POLY (%%MAKE-ARRAY (LIST (%%FLOAT 15549 17659) (%%FLOAT 16256 0) (%%FLOAT 16801 38273) (%%FLOAT 
17257 7717) (%%FLOAT 17597 11739) (%%FLOAT 17800 30401)))) (%%EXP-TABLE (%%MAKE-ARRAY (LIST (%%FLOAT 
16256 0) (%%FLOAT 16267 38338) (%%FLOAT 16280 14320) (%%FLOAT 16293 65239) (%%FLOAT 16309 1267) (
%%FLOAT 16325 26410) (%%FLOAT 16343 17661) (%%FLOAT 16362 49351)))))) (FNS EXP %%EXP-FLOAT 
%%EXP-COMPLEX)) (COMS (* EXPT *) (FNS CL:EXPT %%EXPT-INTEGER %%EXPT-FLOAT %%EXPT-COMPLEX 
%%EXPT-COMPLEX-POWER)) (COMS (* LOG *) (COMS (INITVARS (%%LOG2 (%%FLOAT 16177 29208)) (%%SQRT2 (
%%FLOAT 16309 1267))) (* * %%LOG-PPOLY and %%LOG-QPOLY contain P and Q coefficients of Harris et al 
LOGE 2707 rational approximation to (LOG X) in interval ((SQRT .5) (SQRT 2)) . *) (VARS (%%LOG-PPOLY (
%%MAKE-ARRAY (LIST (%%FLOAT 16042 22803) (%%FLOAT 49484 23590) (%%FLOAT 17044 17982) (%%FLOAT 49926 
37153) (%%FLOAT 17046 5367)))) (%%LOG-QPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 16256 0) (%%FLOAT 49512 9103)
 (%%FLOAT 16992 42274) (%%FLOAT 49823 38048) (%%FLOAT 16918 5367)))))) (FNS CL:LOG %%LOG-FLOAT 
%%LOG-COMPLEX)) (COMS (* SQRT *) (FNS CL:SQRT %%SQRT-FLOAT %%SQRT-COMPLEX)) (COMS (* SIN *) (COMS (* *
 %%SIN-EPSILON is sufficiently small that (SIN X) = X for X in interval (0 %%SIN-EPSILON) %. It 
suffices to take %%SIN-EPSILON a little bit smaller than (SQRT (CL:* 6 SINGLE-FLOAT-EPSILON)) which we
 get by the Taylor series expansion (SIN X) = (+ X (/ (EXPT X 3) 6) ...) (The relative error caused by
 ommitting (/ (EXPT X 3) 6) isn't observable.) Comparison against %%SIN-EPSILON is used to avoid 
POLYEVAL microcode underflow when computing SIN. *) (INITVARS (%%SIN-EPSILON (%%FLOAT 14720 0))) (* * 
%%SIN-PPOLY and %%SIN-QPOLY contain adapted P and Q coefficients of Harris et al SIN 3374 rational 
approximation to (SIN X) in interval (0 (/ PI 2)) %. The coefficients for %%SIN-PPOLY and %%SIN-QPOLY 
have been computed from Harris using extended precision routines and the relations %%SIN-PPOLY = (
REVERSE (for I from 0 as ENTRY in PS collect (/ (CL:* (EXPT (/ 2 PI) (1+ (CL:* 2 I))) ENTRY) Q0))) and
 %%SIN-QPOLY = (REVERSE (for I from 0 as ENTRY in QS collect (/ (CL:* (EXPT (/ 2 PI) (CL:* 2 I)) ENTRY
) Q0))) *) (VARS (%%SIN-PPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 45236 25611) (%%FLOAT 13589 26148) (%%FLOAT
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%%MAKE-ARRAY (LIST (%%FLOAT 11384 52865) (%%FLOAT 12553 9550) (%%FLOAT 13604 38385) (%%FLOAT 14593 
18841) (%%FLOAT 15489 5549) (%%FLOAT 16256 0)))))) (FNS CL:SIN %%SIN-FLOAT %%SIN-COMPLEX)) (COMS (* 
COS *) (FNS CL:COS %%COS-COMPLEX)) (COMS (* TAN *) (COMS (* * %%TAN-EPSILON is sufficiently small that
 (TAN X) = X for X in interval (0 %%TAN-EPSILON) %. It suffices to take %%TAN-EPSILON a little bit 
smaller than (SQRT (CL:* 3 SINGLE-FLOAT-EPSILON)) which we get by the Taylor series expansion (TAN X) 
= (+ X (/ (EXPT X 3) 3) ...) (The relative error caused by ommitting (/ (EXPT X 3) 3) isn't 
observable.) Comparison against %%TAN-EPSILON is used to avoid POLYEVAL microcode underflow when 
computing TAN. *) (INITVARS (%%TAN-EPSILON (%%FLOAT 14720 0))) (* * %%TAN-PPOLY and %%TAN-QPOLY 
contain adapted P and Q coefficients of Harris et al TAN 4288 rational approximation to (TAN X) in 
interval (-PI/4 PI/4) %. The coefficients for %%TAN-PPOLY and %%TAN-QPOLY have been computed from 
Harris using extended precision routines and the relations %%TAN-PPOLY = (REVERSE (for I from 0 as 
ENTRY in PS collect (/ (CL:* (EXPT (/ 4 PI) (1+ (CL:* 2 I))) ENTRY) Q0))) and %%TAN-QPOLY = (REVERSE (
for I from 0 as ENTRY in QS collect (/ (CL:* (EXPT (/ 4 PI) (CL:* 2 I)) ENTRY) Q0))) *) (VARS (
%%TAN-PPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 13237 21090) (%%FLOAT 47141 15825) (%%FLOAT 15246 8785) (
%%FLOAT 48655 48761) (%%FLOAT 16256 0)))) (%%TAN-QPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 45267 36947) (
%%FLOAT 13848 46875) (%%FLOAT 47612 53738) (%%FLOAT 15596 52854) (%%FLOAT 48882 35303) (%%FLOAT 16256 
0)))))) (FNS CL:TAN %%TAN-FLOAT %%TAN-COMPLEX)) (COMS (* ASIN *) (COMS (* * %%ASIN-EPSILON is 
sufficiently small that (ASIN X) = X for X in interval (0 %%ASIN-EPSILON) %. It suffices to take 
%%ASIN-EPSILON a little bit smaller than (CL:* 2 SINGLE-FLOAT-EPSILON) which we get by the Taylor 
series expansion (ASIN X) = (+ X (/ (EXPT X 3) 6) ...) (The relative error caused by ommitting (/ (
EXPT X 3) 6) isn't observable.) Comparison against %%ASIN-EPSILON is used to avoid POLYEVAL microcode 
underflow when computing SIN. *) (INITVARS (%%ASIN-EPSILON (%%FLOAT 14720 0))) (* * %%ASIN-PPOLY and 
%%ASIN-QPOLY contain P and Q coefficients of Harris et al ARCSN 4671 rational approximation to (ASIN X
) in interval (0 (SQRT .5)) . *) (VARS (%%ASIN-PPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 16007 50045) (
%%FLOAT 49549 8020) (%%FLOAT 17236 15848) (%%FLOAT 50285 63464) (%%FLOAT 17650 31235) (%%FLOAT 50403 
62852) (%%FLOAT 17440 39471)))) (%%ASIN-QPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 16256 0) (%%FLOAT 49672 
25817) (%%FLOAT 17308 55260) (%%FLOAT 50326 38098) (%%FLOAT 17674 22210) (%%FLOAT 50417 22451) (
%%FLOAT 17440 39471)))))) (FNS ASIN %%ASIN-FLOAT %%ASIN-COMPLEX)) (COMS (* ACOS *) (FNS ACOS 
%%ACOS-COMPLEX)) (COMS (* ATAN *) (INITVARS (%%SQRT3 (%%FLOAT 16349 46039)) (%%2-SQRT3 (%%FLOAT 16009 
12451)) (%%INV-2-SQRT3 (%%FLOAT 16494 55788))) (FNS CL:ATAN %%ATAN-FLOAT1 %%ATAN-FLOAT2 
%%ATAN-DOMAIN-CHECK %%ATAN-FLOAT %%ATAN-COMPLEX)) (COMS (* CIS *) (FNS CIS)) (COMS (* SINH COSH TANH *
) (FNS SINH COSH TANH)) (COMS (* ASINH ACOSH ATANH *) (FNS ASINH ACOSH ATANH %%ATANH-DOMAIN-CHECK)) (
PROP FILETYPE CMLFLOAT) (DECLARE: DONTEVAL@LOAD DOEVAL@COMPILE DONTCOPY COMPILERVARS (ADDVARS (NLAMA) 
(NLAML) (LAMA CL:LOG)))))
%%FLOAT D1
(I 1 LOWORD I 0 HIWORD) @A��NIL
NIL
()
(RPAQQ MOST-POSITIVE-FIXNUM 65535)
(RPAQQ MOST-NEGATIVE-FIXNUM -65536)
(CONSTANTS (MOST-POSITIVE-FIXNUM 65535) (MOST-NEGATIVE-FIXNUM -65536))
(RPAQ? MOST-POSITIVE-SINGLE-FLOAT (%%FLOAT 32639 65535))
(RPAQ? LEAST-POSITIVE-SINGLE-FLOAT (%%FLOAT 128 0))
(RPAQ? LEAST-NEGATIVE-SINGLE-FLOAT (%%FLOAT 32896 0))
(RPAQ? MOST-NEGATIVE-SINGLE-FLOAT (%%FLOAT 65407 65535))
(RPAQ? MOST-POSITIVE-SHORT-FLOAT MOST-POSITIVE-SINGLE-FLOAT)
(RPAQ? LEAST-POSITIVE-SHORT-FLOAT LEAST-POSITIVE-SINGLE-FLOAT)
(RPAQ? LEAST-NEGATIVE-SHORT-FLOAT LEAST-NEGATIVE-SINGLE-FLOAT)
(RPAQ? MOST-NEGATIVE-SHORT-FLOAT MOST-NEGATIVE-SINGLE-FLOAT)
(RPAQ? MOST-POSITIVE-DOUBLE-FLOAT MOST-POSITIVE-SINGLE-FLOAT)
(RPAQ? LEAST-POSITIVE-DOUBLE-FLOAT LEAST-POSITIVE-SINGLE-FLOAT)
(RPAQ? LEAST-NEGATIVE-DOUBLE-FLOAT LEAST-NEGATIVE-SINGLE-FLOAT)
(RPAQ? MOST-NEGATIVE-DOUBLE-FLOAT MOST-NEGATIVE-SINGLE-FLOAT)
(RPAQ? MOST-POSITIVE-LONG-FLOAT MOST-POSITIVE-SINGLE-FLOAT)
(RPAQ? LEAST-POSITIVE-LONG-FLOAT LEAST-POSITIVE-SINGLE-FLOAT)
(RPAQ? LEAST-NEGATIVE-LONG-FLOAT LEAST-NEGATIVE-SINGLE-FLOAT)
(RPAQ? MOST-NEGATIVE-LONG-FLOAT MOST-NEGATIVE-SINGLE-FLOAT)
(RPAQ? SINGLE-FLOAT-EPSILON (%%FLOAT 13312 0))
(RPAQ? SHORT-FLOAT-EPSILON SINGLE-FLOAT-EPSILON)
(RPAQ? DOUBLE-FLOAT-EPSILON SINGLE-FLOAT-EPSILON)
(RPAQ? LONG-FLOAT-EPSILON SINGLE-FLOAT-EPSILON)
(RPAQ? SINGLE-FLOAT-NEGATIVE-EPSILON (%%FLOAT 13184 0))
(RPAQ? SHORT-FLOAT-NEGATIVE-EPSILON SINGLE-FLOAT-NEGATIVE-EPSILON)
(RPAQ? DOUBLE-FLOAT-NEGATIVE-EPSILON SINGLE-FLOAT-NEGATIVE-EPSILON)
(RPAQ? LONG-FLOAT-NEGATIVE-EPSILON SINGLE-FLOAT-NEGATIVE-EPSILON)
(RPAQ? PI (%%FLOAT 16457 4059))
(RPAQ? %%E (%%FLOAT 16429 63572))
(RPAQ? %%2PI (%%FLOAT 16585 4059))
(RPAQ? %%PI (%%FLOAT 16457 4059))
(RPAQ? %%2PI/3 (%%FLOAT 16390 2706))
(RPAQ? %%PI/2 (%%FLOAT 16329 4059))
(RPAQ? %%-PI/2 (%%FLOAT 49097 4059))
(RPAQ? %%PI/3 (%%FLOAT 16262 2706))
(RPAQ? %%PI/4 (%%FLOAT 16201 4059))
(RPAQ? %%-PI/4 (%%FLOAT 48969 4059))
(RPAQ? %%PI/6 (%%FLOAT 16134 2706))
(RPAQ? %%2/PI (%%FLOAT 16162 63875))
%%MAKE-ARRAY D1
(P 0 ARRAY I 0 LIST) 1
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(RPAQ %%EXP-POLY (%%MAKE-ARRAY (LIST (%%FLOAT 15549 17659) (%%FLOAT 16256 0) (%%FLOAT 16801 38273) (
%%FLOAT 17257 7717) (%%FLOAT 17597 11739) (%%FLOAT 17800 30401))))
(RPAQ %%EXP-TABLE (%%MAKE-ARRAY (LIST (%%FLOAT 16256 0) (%%FLOAT 16267 38338) (%%FLOAT 16280 14320) (
%%FLOAT 16293 65239) (%%FLOAT 16309 1267) (%%FLOAT 16325 26410) (%%FLOAT 16343 17661) (%%FLOAT 16362 
49351))))
EXP D1
(L (0 NUMBER)) 0

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%%EXP-FLOAT D1
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%%EXP-COMPLEX D1
(L (0 Z)) 
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CL:EXPT D1
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( 155Q "Negative number ~A to non-integral power ~A." 120Q "~A negative number to a complex power ~A."
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%%EXPT-INTEGER D1
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Ak�j�@Iև	��II�X��(170Q \FZEROP 153Q ASH 107Q ASH 100Q %%MAKE-RATIO 75Q %%EXPT-INTEGER 71Q DENOMINATOR 65Q %%EXPT-INTEGER 61Q NUMERATOR 55Q ASH 46Q %%= 24Q RATIONALP 16Q %%/ 13Q %%EXPT-INTEGER)
NIL
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%%EXPT-FLOAT D1
(I 1 Y I 0 X) @o
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%%EXPT-COMPLEX D1
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(L (1 W 0 Z)) A@	�	(10Q EXP 4 CL:LOG)
NIL
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(RPAQ? %%LOG2 (%%FLOAT 16177 29208))
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(RPAQ %%LOG-QPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 16256 0) (%%FLOAT 49512 9103) (%%FLOAT 16992 42274) (
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CL:LOG D1
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(RPAQ %%SIN-PPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 45236 25611) (%%FLOAT 13589 26148) (%%FLOAT 47286 34797
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(RPAQ %%SIN-QPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 11384 52865) (%%FLOAT 12553 9550) (%%FLOAT 13604 38385)
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CL:SIN D1
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( 64Q (OR COMPLEX FLOAT NUMBER))
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CL:COS D1
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%%COS-COMPLEX D1
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(RPAQ? %%TAN-EPSILON (%%FLOAT 14720 0))
(RPAQ %%TAN-PPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 13237 21090) (%%FLOAT 47141 15825) (%%FLOAT 15246 8785)
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(RPAQ %%TAN-QPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 45267 36947) (%%FLOAT 13848 46875) (%%FLOAT 47612 53738
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CL:TAN D1
(L (0 RADIANS)) 0

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( 46Q (OR COMPLEX NUMBER))
%%TAN-FLOAT D1
(P 4 RECIPFLG P 3 SIGN I 0 X F 5 %%PI F 6 %%PI/2 F 7 %%-PI/4 F 10Q %%TAN-EPSILON F 11Q %%-PI/2 F 12Q %%PI/4) �
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( 35Q 1.0 23Q -1.0)
%%TAN-COMPLEX D1
(L (0 Z)) )
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(46Q CL:ERROR 34Q \FZEROP 30Q %%/ 12Q CL:COS 3 CL:SIN)
NIL
( 42Q "~S undefined tangent.")
(RPAQ? %%ASIN-EPSILON (%%FLOAT 14720 0))
(RPAQ %%ASIN-PPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 16007 50045) (%%FLOAT 49549 8020) (%%FLOAT 17236 15848
) (%%FLOAT 50285 63464) (%%FLOAT 17650 31235) (%%FLOAT 50403 62852) (%%FLOAT 17440 39471))))
(RPAQ %%ASIN-QPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 16256 0) (%%FLOAT 49672 25817) (%%FLOAT 17308 55260) (
%%FLOAT 50326 38098) (%%FLOAT 17674 22210) (%%FLOAT 50417 22451) (%%FLOAT 17440 39471))))
ASIN D1
(L (0 NUMBER)) >
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(57Q NUMBER 47Q FLOATP 26Q COMPLEX 11Q FLOATP)
( 64Q (OR FLOAT COMPLEX NUMBER))
%%ASIN-FLOAT D1
(P 4 ANSWER P 3 R2 P 2 R P 1 REDUCED P 0 NEGATIVE I 1 ACOS-FLAG I 0 X F 5 %%PI/2 F 6 %%ASIN-EPSILON) �P@ZoJ�do�oJ
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(150Q ARRAYP 145Q %%ASIN-QPOLY 127Q ARRAYP 124Q %%ASIN-PPOLY)
( 175Q 2.0 75Q .5 67Q 1.0 56Q .5 37Q 0.0 26Q "ARCSIN: arg not in range" 20Q 1.0 10Q -1.0)
%%ASIN-COMPLEX D1
(L (0 Z)) 
@	k@d��	�			(25Q %%COMPLEX-MINUS 22Q %%COMPLEX-TIMESI 17Q CL:LOG 13Q CL:SQRT 3 %%COMPLEX-TIMESI)
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ACOS D1
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(61Q NUMBER 50Q FLOATP 27Q COMPLEX 11Q FLOATP)
( 66Q (OR FLOAT COMPLEX NUMBER))
%%ACOS-COMPLEX D1
(L (0 Z)) 
@k@d��		�			(25Q %%COMPLEX-MINUS 22Q %%COMPLEX-TIMESI 17Q CL:LOG 13Q %%COMPLEX-TIMESI 10Q CL:SQRT)
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(RPAQ? %%SQRT3 (%%FLOAT 16349 46039))
(RPAQ? %%2-SQRT3 (%%FLOAT 16009 12451))
(RPAQ? %%INV-2-SQRT3 (%%FLOAT 16494 55788))
CL:ATAN D1
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NIL
( 55Q "Error in double entry atan both 0." 26Q 0.0)
%%ATAN-COMPLEX D1
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( 50Q "Argument not in domain for atan. ~S" 34Q .5)
CIS D1
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%%ATANH-DOMAIN-CHECK D1
(L (0 Z)) '

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(PUTPROPS CMLFLOAT FILETYPE COMPILE-FILE)
(RPAQQ CMLFLOATCOMS ((* * CMLFLOAT -- Covering sections %12.5-12.5.3 irrational, transcendental, 
exponential, logarithmic, trigonometric, and hyperbolic functions. Section 12.10, implementation 
parameters. -- By Kelly Roach. *) (DECLARE: EVAL@COMPILE DONTCOPY (FILES (LOADCOMP) LLFLOAT)) (COMS (*
 Section 12.10, implementation parameters. The constants in this COMS are exported to the user. *) (* 
%%FLOAT allows us to recreate FLOATPs in a way that is independent of the ordinairy reading and 
printing FLOATPs to files which involves loss of the last couple bits of accuracy due to rounding 
effects. *) (* Using INITVARS instead of CONSTANTS in various places here because of problems with the
 way BYTECOMPILER stores FLOATPs in DCOM files. *) (FNS %%FLOAT) (CONSTANTS (MOST-POSITIVE-FIXNUM 
65535) (MOST-NEGATIVE-FIXNUM -65536)) (INITVARS (MOST-POSITIVE-SINGLE-FLOAT (%%FLOAT 32639 65535)) (
LEAST-POSITIVE-SINGLE-FLOAT (%%FLOAT 128 0)) (LEAST-NEGATIVE-SINGLE-FLOAT (%%FLOAT 32896 0)) (
MOST-NEGATIVE-SINGLE-FLOAT (%%FLOAT 65407 65535)) (MOST-POSITIVE-SHORT-FLOAT 
MOST-POSITIVE-SINGLE-FLOAT) (LEAST-POSITIVE-SHORT-FLOAT LEAST-POSITIVE-SINGLE-FLOAT) (
LEAST-NEGATIVE-SHORT-FLOAT LEAST-NEGATIVE-SINGLE-FLOAT) (MOST-NEGATIVE-SHORT-FLOAT 
MOST-NEGATIVE-SINGLE-FLOAT) (MOST-POSITIVE-DOUBLE-FLOAT MOST-POSITIVE-SINGLE-FLOAT) (
LEAST-POSITIVE-DOUBLE-FLOAT LEAST-POSITIVE-SINGLE-FLOAT) (LEAST-NEGATIVE-DOUBLE-FLOAT 
LEAST-NEGATIVE-SINGLE-FLOAT) (MOST-NEGATIVE-DOUBLE-FLOAT MOST-NEGATIVE-SINGLE-FLOAT) (
MOST-POSITIVE-LONG-FLOAT MOST-POSITIVE-SINGLE-FLOAT) (LEAST-POSITIVE-LONG-FLOAT 
LEAST-POSITIVE-SINGLE-FLOAT) (LEAST-NEGATIVE-LONG-FLOAT LEAST-NEGATIVE-SINGLE-FLOAT) (
MOST-NEGATIVE-LONG-FLOAT MOST-NEGATIVE-SINGLE-FLOAT)) (* EPSILON is the smallest positive floating 
point number such that (NOT (= (FLOAT 1 EPSILON) (+ (FLOAT 1 EPSILON) EPSILON))) *) (INITVARS (
SINGLE-FLOAT-EPSILON (%%FLOAT 13312 0)) (SHORT-FLOAT-EPSILON SINGLE-FLOAT-EPSILON) (
DOUBLE-FLOAT-EPSILON SINGLE-FLOAT-EPSILON) (LONG-FLOAT-EPSILON SINGLE-FLOAT-EPSILON)) (* 
NEGATIVE-EPSILON is the smallest negative floating point number such that (NOT (= (FLOAT 1 
NEGATIVE-EPSILON) (- (FLOAT 1 NEGATIVE-EPSILON) NEGATIVE-EPSILON))) *) (INITVARS (
SINGLE-FLOAT-NEGATIVE-EPSILON (%%FLOAT 13184 0)) (SHORT-FLOAT-NEGATIVE-EPSILON 
SINGLE-FLOAT-NEGATIVE-EPSILON) (DOUBLE-FLOAT-NEGATIVE-EPSILON SINGLE-FLOAT-NEGATIVE-EPSILON) (
LONG-FLOAT-NEGATIVE-EPSILON SINGLE-FLOAT-NEGATIVE-EPSILON))) (COMS (* Miscellaneous. *) (DECLARE: 
EVAL@COMPILE DONTCOPY (FILES (LOADCOMP) LLFLOAT)) (INITVARS (PI (%%FLOAT 16457 4059))) (* Should be (
DECLARE: EVAL@COMPILE DONTCOPY (CONSTANTS ...)) except that compiler does a poor job of compiling 
FLOATPs. Use an INITVARS to patch around this situation for now. *) (INITVARS (%%E (%%FLOAT 16429 
63572)) (%%2PI (%%FLOAT 16585 4059)) (%%PI (%%FLOAT 16457 4059)) (%%2PI/3 (%%FLOAT 16390 2706)) (
%%PI/2 (%%FLOAT 16329 4059)) (%%-PI/2 (%%FLOAT 49097 4059)) (%%PI/3 (%%FLOAT 16262 2706)) (%%PI/4 (
%%FLOAT 16201 4059)) (%%-PI/4 (%%FLOAT 48969 4059)) (%%PI/6 (%%FLOAT 16134 2706)) (%%2/PI (%%FLOAT 
16162 63875))) (FNS %%MAKE-ARRAY)) (COMS (* EXP *) (COMS (INITVARS (%%LOG-BASE2-E (%%FLOAT 16312 43579
))) (* * %%EXP-POLY contains P and Q coefficients of Harris et al EXPB 1103 rational approximation to 
(EXPT 2 X) in interval (0 .125) %. %%EXP-TABLE contains values of powers (EXPT 2 (/ N 8)) . *) (VARS (
%%EXP-POLY (%%MAKE-ARRAY (LIST (%%FLOAT 15549 17659) (%%FLOAT 16256 0) (%%FLOAT 16801 38273) (%%FLOAT 
17257 7717) (%%FLOAT 17597 11739) (%%FLOAT 17800 30401)))) (%%EXP-TABLE (%%MAKE-ARRAY (LIST (%%FLOAT 
16256 0) (%%FLOAT 16267 38338) (%%FLOAT 16280 14320) (%%FLOAT 16293 65239) (%%FLOAT 16309 1267) (
%%FLOAT 16325 26410) (%%FLOAT 16343 17661) (%%FLOAT 16362 49351)))))) (FNS EXP %%EXP-FLOAT 
%%EXP-COMPLEX)) (COMS (* EXPT *) (FNS CL:EXPT %%EXPT-INTEGER %%EXPT-FLOAT %%EXPT-COMPLEX 
%%EXPT-COMPLEX-POWER)) (COMS (* LOG *) (COMS (INITVARS (%%LOG2 (%%FLOAT 16177 29208)) (%%SQRT2 (
%%FLOAT 16309 1267))) (* * %%LOG-PPOLY and %%LOG-QPOLY contain P and Q coefficients of Harris et al 
LOGE 2707 rational approximation to (LOG X) in interval ((SQRT .5) (SQRT 2)) . *) (VARS (%%LOG-PPOLY (
%%MAKE-ARRAY (LIST (%%FLOAT 16042 22803) (%%FLOAT 49484 23590) (%%FLOAT 17044 17982) (%%FLOAT 49926 
37153) (%%FLOAT 17046 5367)))) (%%LOG-QPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 16256 0) (%%FLOAT 49512 9103)
 (%%FLOAT 16992 42274) (%%FLOAT 49823 38048) (%%FLOAT 16918 5367)))))) (FNS CL:LOG %%LOG-FLOAT 
%%LOG-COMPLEX)) (COMS (* SQRT *) (FNS CL:SQRT %%SQRT-FLOAT %%SQRT-COMPLEX)) (COMS (* SIN *) (COMS (* *
 %%SIN-EPSILON is sufficiently small that (SIN X) = X for X in interval (0 %%SIN-EPSILON) %. It 
suffices to take %%SIN-EPSILON a little bit smaller than (SQRT (CL:* 6 SINGLE-FLOAT-EPSILON)) which we
 get by the Taylor series expansion (SIN X) = (+ X (/ (EXPT X 3) 6) ...) (The relative error caused by
 ommitting (/ (EXPT X 3) 6) isn't observable.) Comparison against %%SIN-EPSILON is used to avoid 
POLYEVAL microcode underflow when computing SIN. *) (INITVARS (%%SIN-EPSILON (%%FLOAT 14720 0))) (* * 
%%SIN-PPOLY and %%SIN-QPOLY contain adapted P and Q coefficients of Harris et al SIN 3374 rational 
approximation to (SIN X) in interval (0 (/ PI 2)) %. The coefficients for %%SIN-PPOLY and %%SIN-QPOLY 
have been computed from Harris using extended precision routines and the relations %%SIN-PPOLY = (
REVERSE (for I from 0 as ENTRY in PS collect (/ (CL:* (EXPT (/ 2 PI) (1+ (CL:* 2 I))) ENTRY) Q0))) and
 %%SIN-QPOLY = (REVERSE (for I from 0 as ENTRY in QS collect (/ (CL:* (EXPT (/ 2 PI) (CL:* 2 I)) ENTRY
) Q0))) *) (VARS (%%SIN-PPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 45236 25611) (%%FLOAT 13589 26148) (%%FLOAT
 47286 34797) (%%FLOAT 15295 3306) (%%FLOAT 48666 34805) (%%FLOAT 16256 0)))) (%%SIN-QPOLY (
%%MAKE-ARRAY (LIST (%%FLOAT 11384 52865) (%%FLOAT 12553 9550) (%%FLOAT 13604 38385) (%%FLOAT 14593 
18841) (%%FLOAT 15489 5549) (%%FLOAT 16256 0)))))) (FNS CL:SIN %%SIN-FLOAT %%SIN-COMPLEX)) (COMS (* 
COS *) (FNS CL:COS %%COS-COMPLEX)) (COMS (* TAN *) (COMS (* * %%TAN-EPSILON is sufficiently small that
 (TAN X) = X for X in interval (0 %%TAN-EPSILON) %. It suffices to take %%TAN-EPSILON a little bit 
smaller than (SQRT (CL:* 3 SINGLE-FLOAT-EPSILON)) which we get by the Taylor series expansion (TAN X) 
= (+ X (/ (EXPT X 3) 3) ...) (The relative error caused by ommitting (/ (EXPT X 3) 3) isn't 
observable.) Comparison against %%TAN-EPSILON is used to avoid POLYEVAL microcode underflow when 
computing TAN. *) (INITVARS (%%TAN-EPSILON (%%FLOAT 14720 0))) (* * %%TAN-PPOLY and %%TAN-QPOLY 
contain adapted P and Q coefficients of Harris et al TAN 4288 rational approximation to (TAN X) in 
interval (-PI/4 PI/4) %. The coefficients for %%TAN-PPOLY and %%TAN-QPOLY have been computed from 
Harris using extended precision routines and the relations %%TAN-PPOLY = (REVERSE (for I from 0 as 
ENTRY in PS collect (/ (CL:* (EXPT (/ 4 PI) (1+ (CL:* 2 I))) ENTRY) Q0))) and %%TAN-QPOLY = (REVERSE (
for I from 0 as ENTRY in QS collect (/ (CL:* (EXPT (/ 4 PI) (CL:* 2 I)) ENTRY) Q0))) *) (VARS (
%%TAN-PPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 13237 21090) (%%FLOAT 47141 15825) (%%FLOAT 15246 8785) (
%%FLOAT 48655 48761) (%%FLOAT 16256 0)))) (%%TAN-QPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 45267 36947) (
%%FLOAT 13848 46875) (%%FLOAT 47612 53738) (%%FLOAT 15596 52854) (%%FLOAT 48882 35303) (%%FLOAT 16256 
0)))))) (FNS CL:TAN %%TAN-FLOAT %%TAN-COMPLEX)) (COMS (* ASIN *) (COMS (* * %%ASIN-EPSILON is 
sufficiently small that (ASIN X) = X for X in interval (0 %%ASIN-EPSILON) %. It suffices to take 
%%ASIN-EPSILON a little bit smaller than (CL:* 2 SINGLE-FLOAT-EPSILON) which we get by the Taylor 
series expansion (ASIN X) = (+ X (/ (EXPT X 3) 6) ...) (The relative error caused by ommitting (/ (
EXPT X 3) 6) isn't observable.) Comparison against %%ASIN-EPSILON is used to avoid POLYEVAL microcode 
underflow when computing SIN. *) (INITVARS (%%ASIN-EPSILON (%%FLOAT 14720 0))) (* * %%ASIN-PPOLY and 
%%ASIN-QPOLY contain P and Q coefficients of Harris et al ARCSN 4671 rational approximation to (ASIN X
) in interval (0 (SQRT .5)) . *) (VARS (%%ASIN-PPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 16007 50045) (
%%FLOAT 49549 8020) (%%FLOAT 17236 15848) (%%FLOAT 50285 63464) (%%FLOAT 17650 31235) (%%FLOAT 50403 
62852) (%%FLOAT 17440 39471)))) (%%ASIN-QPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 16256 0) (%%FLOAT 49672 
25817) (%%FLOAT 17308 55260) (%%FLOAT 50326 38098) (%%FLOAT 17674 22210) (%%FLOAT 50417 22451) (
%%FLOAT 17440 39471)))))) (FNS ASIN %%ASIN-FLOAT %%ASIN-COMPLEX)) (COMS (* ACOS *) (FNS ACOS 
%%ACOS-COMPLEX)) (COMS (* ATAN *) (INITVARS (%%SQRT3 (%%FLOAT 16349 46039)) (%%2-SQRT3 (%%FLOAT 16009 
12451)) (%%INV-2-SQRT3 (%%FLOAT 16494 55788))) (FNS CL:ATAN %%ATAN-FLOAT1 %%ATAN-FLOAT2 
%%ATAN-DOMAIN-CHECK %%ATAN-FLOAT %%ATAN-COMPLEX)) (COMS (* CIS *) (FNS CIS)) (COMS (* SINH COSH TANH *
) (FNS SINH COSH TANH)) (COMS (* ASINH ACOSH ATANH *) (FNS ASINH ACOSH ATANH %%ATANH-DOMAIN-CHECK)) (
PROP FILETYPE CMLFLOAT) (DECLARE: DONTEVAL@LOAD DOEVAL@COMPILE DONTCOPY COMPILERVARS (ADDVARS (NLAMA) 
(NLAML) (LAMA %%ATANH-DOMAIN-CHECK ATANH ACOSH ASINH TANH COSH SINH CIS %%ATAN-COMPLEX %%ATAN-FLOAT 
%%ATAN-DOMAIN-CHECK %%ATAN-FLOAT2 %%ATAN-FLOAT1 CL:ATAN %%ACOS-COMPLEX ACOS %%ASIN-COMPLEX ASIN 
%%TAN-COMPLEX CL:TAN %%COS-COMPLEX CL:COS %%SIN-COMPLEX CL:SIN CL:SQRT %%LOG-COMPLEX CL:LOG 
%%EXPT-COMPLEX-POWER %%EXPT-COMPLEX %%EXPT-INTEGER CL:EXPT %%EXP-COMPLEX %%EXP-FLOAT EXP)))))
(PUTPROPS CMLFLOAT COPYRIGHT ("Xerox Corporation" 1986))
STOP