(FILECREATED " 5-JAN-83 20:48:00" <BLISP>AARITH.;3 18482
changes to: (FNS ARCCOS)
(VARS AARITHCOMS)
previous date: " 1-DEC-81 17:10:06" <BLISP>AARITH.;1)
(* Copyright (c) 1981, 1983 by Xerox Corporation)
(PRETTYCOMPRINT AARITHCOMS)
(RPAQQ AARITHCOMS [(FNS SIN TAN ARCSIN ARCCOS ARCCOS1 COS LOG ANTILOG FEXPT LINEAR/INTERPOLATE ARCTAN
ARCTAN2 ATAN)
(ARRAY SINE.VALUE.ARRAY ARCSINE.VALUE.ARRAY LOG.VALUE.ARRAY ANTILOG.VALUE.ARRAY)
(VARS DEGREESPERRADIAN)
(FNS CREATEFUNCTIONVALUEARRAY)
(DECLARE: EVAL@COMPILE DONTCOPY (RECORDS FunctionValueTable)
(ADDVARS (DONTCOMPILEFNS CREATEFUNCTIONVALUEARRAY))
(PROP MACRO ArgumentIndex ValueIndex)
(GLOBALVARS SINE.VALUE.ARRAY ARCSINE.VALUE.ARRAY DEGREESPERRADIAN
LOG.VALUE.ARRAY ANTILOG.VALUE.ARRAY)
(LOCALVARS . T)
(CONSTANTS (PI 3.141593])
(DEFINEQ
(SIN
[LAMBDA (X RADIANFLG) (* lmm "23-JUN-80 21:46")
(LINEAR/INTERPOLATE (COND
((MINUSP X)
(* iremainder works differently for negative numbers.)
(FPLUS 360.0 (FREMAINDER (COND
(RADIANFLG (FTIMES X DEGREESPERRADIAN))
(T X))
360.0)))
(T (FREMAINDER (COND
(RADIANFLG (FTIMES X DEGREESPERRADIAN))
(T X))
360.0)))
SINE.VALUE.ARRAY])
(TAN
[LAMBDA (X RADIANSFLG) (* lmm "23-JUN-80 21:46")
(FQUOTIENT (SIN X RADIANSFLG)
(COS X RADIANSFLG])
(ARCSIN
[LAMBDA (X RADIANSFLG) (* rrb " 1-DEC-81 17:09")
(COND
((OR (FLESSP X -1.0)
(FGREATERP X 1.0))
(ERROR "ARCSIN: arg not in range" X))
(RADIANSFLG (FQUOTIENT (LINEAR/INTERPOLATE X ARCSINE.VALUE.ARRAY)
DEGREESPERRADIAN))
(T (LINEAR/INTERPOLATE X ARCSINE.VALUE.ARRAY])
(ARCCOS
[LAMBDA (X RADIANSFLG) (* ejs: " 5-OCT-82 19:34")
(COND
((OR (FLESSP X -1.0)
(FGREATERP X 1.0))
(ERROR "ARCCOS: arg not in range" X))
(T (COND
((FGREATERP (ABS X)
.98) (* For X .gt. .98, the routine below is terribly inaccurate.
ARCCOS1 is 7 times slower (currently), but produces the correct result)
(ARCCOS1 X RADIANSFLG))
(T (FPLUS (COND
(RADIANSFLG (CONSTANT (FQUOTIENT PI 2.0)))
(T 90.0))
(ARCSIN (FMINUS X)
RADIANSFLG])
(ARCCOS1
[LAMBDA (X RADIANSFLG) (* ejs: " 5-OCT-82 19:34")
(* Generate ARCCOS the hard way. Have to do this for X .ge.
.98, else we get bad results from (90-arcsin
(x)))
(FDIFFERENCE (COND
(RADIANSFLG (CONSTANT (FQUOTIENT PI 2.0)))
(T 90.0))
(ARCTAN [FQUOTIENT X (SQRT (FDIFFERENCE 1.0 (FTIMES X X]
RADIANSFLG])
(COS
[LAMBDA (X RADIANFLG) (* lmm "23-JUN-80 21:47")
(SIN (FDIFFERENCE 90.0 (COND
(RADIANFLG (FTIMES X DEGREESPERRADIAN))
(T X])
(LOG
[LAMBDA (X) (* lmm "18-AUG-80 14:29")
(PROG ((FACTOR 0)
(E 2.718282)
(1OVERE .3678794))
(COND
((NOT (FGREATERP X 0.0))
(ERROR "LOG OF NON-POSITIVE NUMBER:" X)))
(while (FGREATERP X E)
do (add FACTOR 1)
(SETQ X (FTIMES X 1OVERE)))
(while (FGREATERP 1.0 X)
do (add FACTOR -1)
(SETQ X (FTIMES X E)))
(RETURN (FPLUS FACTOR (LINEAR/INTERPOLATE X LOG.VALUE.ARRAY])
(ANTILOG
[LAMBDA (X) (* lmm "18-AUG-80 14:29")
(PROG ((FACTOR 1.0)
(E 2.718282)
(1OVERE .3678794))
(while (FGREATERP X 1.0)
do (SETQ FACTOR (FTIMES FACTOR E))
(SETQ X (FDIFFERENCE X 1.0)))
(while (FGREATERP 0.0 X)
do (SETQ FACTOR (FTIMES FACTOR 1OVERE))
(SETQ X (FPLUS X 1.0)))
(RETURN (FTIMES FACTOR (LINEAR/INTERPOLATE X ANTILOG.VALUE.ARRAY])
(FEXPT
[LAMBDA (X Y) (* lmm "18-AUG-80 14:06")
(ANTILOG (FTIMES Y (LOG X])
(LINEAR/INTERPOLATE
[LAMBDA (X VALUEARRAY) (* rrb " 2-MAY-80 17:19")
(* find the value of a function by linear interpolation on the set of value in VALUEARRAY. Entries in value array
are pairs of the argument in X cell and fn{x} in N+1.)
(COND
((FLESSP X (fetch FirstArgument of VALUEARRAY))
(HELP "function argument is less than interpolation range." X)))
(PROG ((NENTRIES (fetch NumberOfEntries of VALUEARRAY))
SMALLER) (* calculate the table index of the table entry just less than the input value)
[COND
((IGREATERP [SETQ SMALLER (ADD1 (FIX (FTIMES (fetch NumberOfEntries of VALUEARRAY)
(FQUOTIENT (FDIFFERENCE X
(fetch FirstArgument
of VALUEARRAY))
(fetch ArgumentRange
of VALUEARRAY]
(fetch NumberOfEntries of VALUEARRAY))
(* should only happen when number passed in is the last value in table.)
(RETURN (ELT VALUEARRAY (ValueIndex (ADD1 (fetch NumberOfEntries of VALUEARRAY]
(RETURN (COND
((IGEQ SMALLER (fetch LastArgumentIndex of VALUEARRAY))
(HELP "X is greaterp than range of interpolation." X))
(T (FPLUS (ELT VALUEARRAY (ValueIndex SMALLER))
(FTIMES (FDIFFERENCE (ELT VALUEARRAY (ValueIndex (ADD1 SMALLER)))
(ELT VALUEARRAY (ValueIndex SMALLER)))
(FQUOTIENT (FDIFFERENCE X (ELT VALUEARRAY (ArgumentIndex
SMALLER)))
(FDIFFERENCE (ELT VALUEARRAY (ArgumentIndex
(ADD1 SMALLER)))
(ELT VALUEARRAY (ArgumentIndex SMALLER])
(ARCTAN
[LAMBDA (X RADIANSFLG) (* rrb "14-SEP-81 17:12")
(COND
[(FGREATERP 0.0 X)
(FDIFFERENCE (ATAN 1.0 X RADIANSFLG)
(COND
(RADIANSFLG PI)
(T 180.0]
(T (ATAN 1.0 X RADIANSFLG])
(ARCTAN2
[LAMBDA (X Y RADIANSFLG) (* rrb "14-SEP-81 17:56")
(* don't understand it but it agrees to several decimal places with interlisp-10
-
rrb)
(PROG ((MAG (ARCTAN (FQUOTIENT X Y)
RADIANSFLG)))
(RETURN (COND
[(FGREATERP 0.0 X)
(FDIFFERENCE MAG (COND
(RADIANSFLG PI)
(T 180.0]
((EQUAL X 0.0)
(* Agree with interlisp-10)
(COND
((FGREATERP 0.0 Y)
(COND
(RADIANSFLG (CONSTANT (FDIFFERENCE 0.0 PI)))
(T -180.0)))
(T MAG)))
(T MAG])
(ATAN
[LAMBDA (X Y RADIANSFLG) (* rrb "14-SEP-81 18:09")
(* version of arctan which returns value in radians between 0 and 2 PI.)
(PROG ((Y (FLOAT Y))
(X (FLOAT X))
ABSX ABSY TEMP TEMP2 (ANS -.004054058))
(SETQ ABSY (ABS Y))
(SETQ ABSX (ABS X))
(SETQ TEMP (FQUOTIENT (FDIFFERENCE ABSY ABSX)
(FPLUS ABSY ABSX)))
(SETQ TEMP2 (FTIMES TEMP TEMP))
(for MAGICVALUE in (QUOTE (.02186123 -.05590989 .09642004 -.1390853 .1994654 -.3332986
.9999994))
do (SETQ ANS (FPLUS (FTIMES ANS TEMP2)
MAGICVALUE)))
(SETQ ANS (FTIMES ANS TEMP))
(SETQ TEMP (ABS ANS))
[COND
((OR (FLESSP .7855 TEMP)
(FLESSP TEMP .7853))
(SETQ ANS (FPLUS ANS .7853982)))
((FLESSP ANS 0.0)
(SETQ ANS (FQUOTIENT ABSY ABSX)))
(T (SETQ ANS (FPLUS (FQUOTIENT ABSX ABSY)
1.570796]
(SETQ TEMP ANS)
(SETQ ANS (FDIFFERENCE 3.141593 ANS))
[COND
((FLESSP 0.0 X)
(SETQ TEMP (PROG1 ANS (SETQ ANS TEMP]
(SETQ TEMP (FTIMES TEMP 2))
[COND
((FLESSP Y 0.0)
(SETQ ANS (FPLUS ANS TEMP]
(RETURN (COND
(RADIANSFLG ANS)
(T (FTIMES ANS (CONSTANT (FQUOTIENT 180 PI])
)
(SETQ SINE.VALUE.ARRAY (READARRAY 204 0))
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NIL
)(SETQ ARCSINE.VALUE.ARRAY (READARRAY 204 0))
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)(SETQ LOG.VALUE.ARRAY (READARRAY 404 0))
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1.349859
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1.363425
.32
1.377128
.33
1.390968
.34
1.404948
.35
1.419068
.36
1.433329
.37
1.447735
.38
1.462285
.39
1.476981
.4
1.491825
.41
1.506818
.42
1.521962
.43
1.537258
.44
1.552707
.45
1.568312
.46
1.584074
.47
1.599994
.48
1.616074
.49
1.632316
.5
1.648721
.51
1.665291
.52
1.682028
.53
1.698932
.54
1.716007
.55
1.733253
.56
1.750673
.57
1.768267
.58
1.786038
.59
1.803988
.6
1.822119
.61
1.840431
.62
1.858928
.63
1.877611
.64
1.896481
.65
1.915541
.66
1.934792
.67
1.954237
.68
1.973878
.69
1.993716
.7
2.013753
.71
2.033991
.72
2.054433
.73
2.075081
.74
2.095935
.75
2.117
.76
2.138276
.77
2.159766
.78
2.181472
.79
2.203396
.8
2.225541
.81
2.247908
.82
2.2705
.83
2.293319
.84
2.316367
.85
2.339647
.86
2.363161
.87
2.386911
.88
2.4109
.89
2.435129
.9
2.459603
.91
2.484322
.9199999
2.50929
.9299999
2.534509
.9399999
2.559981
.9499999
2.585709
.9599999
2.611696
.9699999
2.637944
.9799999
2.664456
.9899999
2.691234
1
2.718282
NIL
)
(RPAQQ DEGREESPERRADIAN 57.29578)
(DEFINEQ
(CREATEFUNCTIONVALUEARRAY
[LAMBDA (FN LOW HIGH NUMBER) (* lmm "23-JUN-80 21:38")
(* create an array of values of a function. This is designed to run on MAXC2 to create a functionvalue array that
will be shipped to the Dorado.)
(* NUMBER is the number of intervals.)
(PROG [(FVARRAY (ARRAY (IPLUS (ITIMES (ADD1 NUMBER)
2)
2]
(replace NumberOfEntries of FVARRAY with NUMBER)
(replace ArgumentRange of FVARRAY with (FDIFFERENCE HIGH LOW))
(for ARG←LOW until (FGREATERP ARG HIGH) bind (INCREMENT ←(FQUOTIENT (fetch ArgumentRange
of FVARRAY)
NUMBER))
as INDEX from 1 to NUMBER
do (SETA FVARRAY (ArgumentIndex INDEX)
ARG)
(SETA FVARRAY (ValueIndex INDEX)
(APPLY* FN ARG))
(SETQ ARG (FPLUS ARG INCREMENT))
finally (SETA FVARRAY (ArgumentIndex (ADD1 NUMBER))
HIGH)
(SETA FVARRAY (ValueIndex (ADD1 NUMBER))
(APPLY* FN HIGH)))
(RETURN FVARRAY])
)
(DECLARE: EVAL@COMPILE DONTCOPY
[DECLARE: EVAL@COMPILE
(ARRAYRECORD FunctionValueTable (NumberOfEntries ArgumentRange FirstArgument)
[ACCESSFNS FunctionValueTable
((LastArgumentIndex (ADD1 (ITIMES (fetch NumberOfEntries
of DATUM)
2])
]
(ADDTOVAR DONTCOMPILEFNS CREATEFUNCTIONVALUEARRAY)
(PUTPROPS ArgumentIndex MACRO ((N)
(ADD1 (ITIMES N 2))))
(PUTPROPS ValueIndex MACRO ((N)
(ITIMES (ADD1 N)
2)))
(DECLARE: DOEVAL@COMPILE DONTCOPY
(ADDTOVAR GLOBALVARS SINE.VALUE.ARRAY ARCSINE.VALUE.ARRAY DEGREESPERRADIAN LOG.VALUE.ARRAY
ANTILOG.VALUE.ARRAY)
)
(DECLARE: DOEVAL@COMPILE DONTCOPY
(LOCALVARS . T)
)
(DECLARE: EVAL@COMPILE
(RPAQQ PI 3.141593)
(CONSTANTS (PI 3.141593))
)
)
(PUTPROPS AARITH COPYRIGHT ("Xerox Corporation" 1981 1983))
(DECLARE: DONTCOPY
(FILEMAP (NIL (885 8006 (SIN 895 . 1370) (TAN 1372 . 1515) (ARCSIN 1517 . 1852) (ARCCOS 1854 . 2414) (
ARCCOS1 2416 . 2834) (COS 2836 . 2999) (LOG 3001 . 3503) (ANTILOG 3505 . 3958) (FEXPT 3960 . 4075) (
LINEAR/INTERPOLATE 4077 . 5782) (ARCTAN 5784 . 6032) (ARCTAN2 6034 . 6681) (ATAN 6683 . 8004)) (16493
17620 (CREATEFUNCTIONVALUEARRAY 16503 . 17618)))))
STOP