(FILECREATED "28-Jul-86 14:17:15" ("compiled on " {ERIS}<ROACH>CML>CMLFLOAT.;21) "23-Jul-86 04:26:56" 
"COMPILE-FILEd" in "Xerox Lisp 23-Jul-86 ..." dated "23-Jul-86 04:52:47")
(FILECREATED "28-Jul-86 14:12:13" {ERIS}<ROACH>CML>CMLFLOAT.;21 80481 changes to: (VARS CMLFLOATCOMS) 
(FNS CL:SQRT %%SQRT-COMPLEX) previous date: "23-Jul-86 18:31:49" {ERIS}<ROACH>CML>CMLFLOAT.;20)
(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. *) (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. *) (FNS %%FLOAT) (CONSTANTS (MOST-POSITIVE-FIXNUM 
65535) (MOST-NEGATIVE-FIXNUM -65536) (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))) *) (CONSTANTS (
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))) *) (CONSTANTS (
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)) (CONSTANTS (PI (%%FLOAT 16457 4059))) (DECLARE: 
EVAL@COMPILE DONTCOPY (CONSTANTS (%%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 (CONSTANTS (%%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 (DECLARE: 
EVAL@COMPILE DONTCOPY (CONSTANTS (%%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. *) (DECLARE: EVAL@COMPILE DONTCOPY (CONSTANTS (%%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. *) (DECLARE: EVAL@COMPILE DONTCOPY (CONSTANTS (%%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. *) (DECLARE: 
EVAL@COMPILE DONTCOPY (CONSTANTS (%%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 *) (DECLARE: EVAL@COMPILE DONTCOPY (CONSTANTS (%%SQRT3 (%%FLOAT 16349 
46039)) (%%2-SQRT3 (%%FLOAT 16009 12451)) (%%INV-2-SQRT3 (%%FLOAT 16494 55788))) (FILES (LOADCOMP) 
LLFLOAT)) (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 %%SQRT-PERFECT CL:SQRT %%LOG-COMPLEX CL:LOG %%EXPT-COMPLEX-POWER %%EXPT-COMPLEX 
%%EXPT-INTEGER CL:EXPT %%EXP-COMPLEX %%EXP-FLOAT EXP)))))
%%FLOAT D1
(I 1 LOWORD I 0 HIWORD) @A��NIL
NIL
()
(RPAQQ MOST-POSITIVE-FIXNUM 65535)
(RPAQQ 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)
(CONSTANTS (MOST-POSITIVE-FIXNUM 65535) (MOST-NEGATIVE-FIXNUM -65536) (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))
(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)
(CONSTANTS (SINGLE-FLOAT-EPSILON (%%FLOAT 13312 0)) (SHORT-FLOAT-EPSILON SINGLE-FLOAT-EPSILON) (
DOUBLE-FLOAT-EPSILON SINGLE-FLOAT-EPSILON) (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)
(CONSTANTS (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))
(RPAQ PI (%%FLOAT 16457 4059))
(CONSTANTS (PI (%%FLOAT 16457 4059)))
%%MAKE-ARRAY D1
(P 0 ARRAY I 0 LIST) 1
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(11Q FLOATP)
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(RPAQ %%LOG-BASE2-E (%%FLOAT 16312 43579))
(CONSTANTS (%%LOG-BASE2-E (%%FLOAT 16312 43579)))
(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)) /

@
Hd`�@	3�@	igHob��(50Q CHECK-TYPE-FAIL 33Q %%EXP-FLOAT 20Q %%EXP-COMPLEX)
(40Q NUMBER 30Q FLOATP 11Q COMPLEXTYPE#)
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%%EXP-FLOAT D1
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%%EXP-COMPLEX D1
(L (0 Z)) 
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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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%%EXPT-FLOAT D1
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%%EXPT-COMPLEX-POWER D1
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NIL
()
(RPAQ %%LOG-PPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 16042 22803) (%%FLOAT 49484 23590) (%%FLOAT 17044 17982
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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
(L (0 -args-)) ce
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( 117Q (OR COMPLEX NUMBER) 72Q 3.141593)
%%LOG-FLOAT D1
(P 4 ANSWER P 3 Z2 P 2 Z P 1 EXP P 0 R I 0 X) {
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%%LOG-COMPLEX D1
(L (0 Z)) 
@		@	
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NIL
( 51Q 2.0)
(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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( 201Q .0002441406 160Q 1.570796 126Q 3.141593 110Q 6.283186)
%%SIN-COMPLEX D1
(L (0 Z)) #
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(RPAQ %%TAN-PPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 13237 21090) (%%FLOAT 47141 15825) (%%FLOAT 15246 8785)
 (%%FLOAT 48655 48761) (%%FLOAT 16256 0))))
(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)) /

@
Hd`�@	3�@	igHob��(50Q CHECK-TYPE-FAIL 33Q %%TAN-FLOAT 20Q %%TAN-COMPLEX)
(40Q RADIANS 30Q FLOATP 11Q COMPLEXTYPE#)
( 45Q (OR COMPLEX NUMBER))
%%TAN-FLOAT D1
(P 4 RECIPFLG P 3 SIGN I 0 X) �
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( 153Q .0002441406 130Q .7853982 106Q -.7853982 63Q 1.570796 45Q 3.141593 35Q 1.0 23Q -1.0)
%%TAN-COMPLEX D1
(L (0 Z)) )
@	
@	Yj�I�HI
	��o@
(46Q CL:ERROR 34Q \FZEROP 30Q %%/ 12Q CL:COS 3 CL:SIN)
NIL
( 42Q "~S undefined tangent.")
(RPAQ %%ASIN-PPOLY (%%MAKE-ARRAY (LIST (%%FLOAT 16007 50045) (%%FLOAT 49549 8020) (%%FLOAT 17236 15848
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(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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HYdl�@	`�@	I3�@	igHob��(64Q CHECK-TYPE-FAIL 47Q %%ASIN-FLOAT 33Q %%ASIN-COMPLEX 20Q %%ASIN-FLOAT)
(54Q NUMBER 44Q FLOATP 25Q COMPLEXTYPE#)
( 61Q (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) �P@ZoJ�do�oJ
�oJ�i�jJ�Z�Jo�i�oJ�o�	�oJ�J�-JdֻJK�
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�\I�oLo�ռH�jLռA�oL�L(166Q %%/ 101Q CL:SQRT 32Q ERROR)
(153Q ARRAYP 150Q %%ASIN-QPOLY 132Q ARRAYP 127Q %%ASIN-PPOLY)
( 222Q 1.570796 203Q 2.0 176Q 1.570796 106Q .0002441406 75Q .5 67Q 1.0 56Q .5 37Q 0.0 26Q "ARCSIN: arg not in range"
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%%ASIN-COMPLEX D1
(L (0 Z)) 
@	k@d��	�			(25Q %%COMPLEX-MINUS 22Q %%COMPLEX-TIMESI 17Q CL:LOG 13Q CL:SQRT 3 %%COMPLEX-TIMESI)
NIL
()
ACOS D1
(L (0 NUMBER)) =
@
HYdl�@i
`�@	I3�@i
igHob��(66Q CHECK-TYPE-FAIL 51Q %%ASIN-FLOAT 34Q %%ACOS-COMPLEX 21Q %%ASIN-FLOAT)
(56Q NUMBER 45Q FLOATP 26Q COMPLEXTYPE#)
( 63Q (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)
NIL
()
CL:ATAN D1
(L (1 Y 0 X)) "A�@A
@d	��@		(37Q %%ATAN-FLOAT 30Q %%ATAN-COMPLEX 22Q COMPLEXP 14Q %%ATAN-FLOAT)
(34Q FLOATP 11Q FLOATP 5 FLOATP)
()
%%ATAN-FLOAT1 D1
(L (0 X)) i
j@�jd@�	�o@�@	k@�@o�k�@o�
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	�(145Q %%ATAN-FLOAT2 142Q %%/ 127Q %%ATAN-FLOAT2 124Q %%/ 61Q %%ATAN-FLOAT2 56Q %%/ 27Q %%ATAN-FLOAT2 12Q %%ATAN-FLOAT1)
NIL
( 135Q 1.570796 116Q 1.732051 107Q 1.732051 103Q 1.047198 73Q 3.732051 65Q .5235988 52Q 1.732051 42Q 1.732051
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%%ATAN-FLOAT2 D1
(L (0 X)) ,
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%%ATAN-DOMAIN-CHECK D1
(L (0 Z)) '

@	
Hj�H�H	�
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%%ATAN-FLOAT D1
(L (1 X 0 Y)) �
A�@j�@d�Zd	�To@
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	o�(227Q %%ATAN-FLOAT1 224Q %%/ 215Q %%ATAN-FLOAT1 212Q %%/ 201Q PLUSP 173Q %%ATAN-FLOAT1 170Q %%/ 154Q PLUSP 147Q %%ATAN-FLOAT1 144Q %%/ 135Q PLUSP 127Q PLUSP 113Q PLUSP 106Q %%= 73Q %%SIGNUM 66Q %%= 60Q CL:ERROR 47Q %%= 40Q %%= 20Q \FZEROP)
NIL
( 233Q 3.141593 161Q 3.141593 122Q 3.141593 77Q 1.570796 55Q "Error in double entry atan both 0." 26Q 0.0)
%%ATAN-COMPLEX D1
(L (0 Z)) /

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(54Q CL:ERROR 43Q %%COMPLEX-MINUS 40Q %%COMPLEX-TIMESI 30Q CL:LOG 25Q %%/ 11Q %%COMPLEX-TIMESI 3 %%ATAN-DOMAIN-CHECK)
NIL
( 50Q "Argument not in domain for atan. ~S" 34Q .5)
CIS D1
(L (0 RADIANS)) 
@d	��o@
	@	
(31Q COMPLEX 26Q CL:SIN 22Q CL:COS 16Q CL:ERROR 4 COMPLEXP)
NIL
( 12Q "Argument to CIS is complex: ~S")
SINH D1
(L (0 NUMBER)) 

@	
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NIL
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COSH D1
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TANH D1
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ASINH D1
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NIL
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ACOSH D1
(L (0 NUMBER)) 
@dd�k�	�	(14Q CL:LOG 10Q CL:SQRT)
NIL
()
ATANH D1
(L (0 NUMBER)) "
@	�@k�k@�
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(37Q CL:ERROR 21Q CL:LOG 16Q %%/ 3 %%ATANH-DOMAIN-CHECK)
NIL
( 33Q "~S argument out of range." 25Q .5)
%%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. *) (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. *) (FNS %%FLOAT) (CONSTANTS (MOST-POSITIVE-FIXNUM 
65535) (MOST-NEGATIVE-FIXNUM -65536) (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))) *) (CONSTANTS (
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))) *) (CONSTANTS (
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)) (CONSTANTS (PI (%%FLOAT 16457 4059))) (DECLARE: 
EVAL@COMPILE DONTCOPY (CONSTANTS (%%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 (CONSTANTS (%%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 (DECLARE: 
EVAL@COMPILE DONTCOPY (CONSTANTS (%%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. *) (DECLARE: EVAL@COMPILE DONTCOPY (CONSTANTS (%%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. *) (DECLARE: EVAL@COMPILE DONTCOPY (CONSTANTS (%%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. *) (DECLARE: 
EVAL@COMPILE DONTCOPY (CONSTANTS (%%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 *) (DECLARE: EVAL@COMPILE DONTCOPY (CONSTANTS (%%SQRT3 (%%FLOAT 16349 
46039)) (%%2-SQRT3 (%%FLOAT 16009 12451)) (%%INV-2-SQRT3 (%%FLOAT 16494 55788))) (FILES (LOADCOMP) 
LLFLOAT)) (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