XTFN ;SF-ISC/RWF - MATH FUNCTIONS ;3/14/89 11:05 ;
;;7.1;KERNEL;;May 11, 1993
LN ;%LN=LN(%X) (log base e)
S %T=%X,(%LN,%D)=0 Q:%X'>0
LN2 IF %T'<1 S %T=.5*%T,%D=%D+1 G LN2
LN3 IF %T<.5 S %T=2*%T,%D=%D-1 G LN3
S %T=(%T-.707107)/(%T+.707107),%LN=%T*%T,%LN=+$J((((.598979*%LN+.961471)*%LN+2.88539)*%T+%D-.5)*.693147,1,6)
K %D,%T Q
;
EXP ;%E=EXP(%X) (e to the %X power)
S %E=0,%B=1.4427*%X\1+1 Q:%B>90
S %E=.693147*%B-%X,%A=.00132988-(.000141316*%E),%A=((%A*%E-.00830136)*%E+.0416574)*%E,%E=(((%A-.166665)*%E+.5)*%E-1)*%E+1,%A=2
IF %B'>0 S %A=.5,%B=-%B
F %I=1:1:%B S %E=%A*%E
S %E=+$J(%E,1,6) K %A,%B,%I Q
;
PWR ;%P=%X^%Y (uses LN and EXP)
S %P=$S(%Y=1:%X,1:1) Q:%Y=0!(%Y=1) S %E=0,%G=%X,%H=%Y
IF %X<0,%Y\1=%Y S %P=1-(2*%Y)+(4*(%Y/2)\1),%X=-%X
IF %X D LN S %X=%Y*%LN D EXP
S %P=%P*%E,%X=%G,%Y=%H IF %Y>1,%X#1+(%Y#1)=0 S %P=$J(%P,1,0) ;INTEGERS
K %G,%H,%E,%LN Q
LOG ;%L=LOG(%X) (log base 10) uses LN
N %LN D LN I %LN=0 S %L=0 Q ;error
S %L=+$J(%LN/2.302585,1,6) Q
;
TAN ;%Y=TAN(%X) ;tan X = sin X/cos X
D SIN S %TN=%Y D COS S %Y=$J(%TN/%Y,1,6) K %TN Q
SIN ;%Y=SIN(%X), %X in radians
S %T=%X G C
COS ;%Y=COS(%X), %X in radians
S %T=%X+1.5707963
C IF %T<-1.5707963 S %T=-3.14159265-%T
IF %T>3.14159265 S %T=%T-6.2831853 G C
S %T2=%T,%Y=%T,%T4=1,%T3=-1
F %=3:2:11 S %T4=%T4*(%-1)*%,%T2=%T2*%T*%T,%Y=%T2/%T4*%T3+%Y,%T3=-%T3
S %Y=+$J(%Y,1,6) K %,%T,%T2,%T3,%T4 Q
;
DTR ;DEGREES TO RADIANS
S %X=$J(%X/57.29577951,1,7) Q
RTD ;RADIANS TO DEGREES
S %X=$J(%X*57.29577951,1,5) Q
PI S %X=3.1415927 Q ;%X=PIE
;
SQRT ;%Y=SQRT(%X)
S %Y=0 Q:%X'>0 S %Y=%X+1/2
L S %T=%Y,%Y=%X/%T+%T/2 G L:%Y<%T
Q
SD ;SX=SUM, SSX=SUM OF SQUARES, N=COUNT
S SD=-1,%X=-1 Q:N<2
S %X=N*SSX-(SX*SX)/(N*(N-1)) D SQRT S SD=%Y,%X=SX/N Q
XTFN ;SF-ISC/RWF - MATH FUNCTIONS ;3/14/89 11:05 ;
+1 ;;7.1;KERNEL;;May 11, 1993
LN ;%LN=LN(%X) (log base e)
+1 SET %T=%X
SET (%LN,%D)=0
IF %X'>0
QUIT
LN2 IF %T'<1
SET %T=.5*%T
SET %D=%D+1
GOTO LN2
LN3 IF %T<.5
SET %T=2*%T
SET %D=%D-1
GOTO LN3
+1 SET %T=(%T-.707107)/(%T+.707107)
SET %LN=%T*%T
SET %LN=+$JUSTIFY((((.598979*%LN+.961471)*%LN+2.88539)*%T+%D-.5)*.693147,1,6)
+2 KILL %D,%T
QUIT
+3 ;
EXP ;%E=EXP(%X) (e to the %X power)
+1 SET %E=0
SET %B=1.4427*%X\1+1
IF %B>90
QUIT
+2 SET %E=.693147*%B-%X
SET %A=.00132988-(.000141316*%E)
SET %A=((%A*%E-.00830136)*%E+.0416574)*%E
SET %E=(((%A-.166665)*%E+.5)*%E-1)*%E+1
SET %A=2
+3 IF %B'>0
SET %A=.5
SET %B=-%B
+4 FOR %I=1:1:%B
SET %E=%A*%E
+5 SET %E=+$JUSTIFY(%E,1,6)
KILL %A,%B,%I
QUIT
+6 ;
PWR ;%P=%X^%Y (uses LN and EXP)
+1 SET %P=$SELECT(%Y=1:%X,1:1)
IF %Y=0!(%Y=1)
QUIT
SET %E=0
SET %G=%X
SET %H=%Y
+2 IF %X<0
IF %Y\1=%Y
SET %P=1-(2*%Y)+(4*(%Y/2)\1)
SET %X=-%X
+3 IF %X
DO LN
SET %X=%Y*%LN
DO EXP
+4 ;INTEGERS
SET %P=%P*%E
SET %X=%G
SET %Y=%H
IF %Y>1
IF %X#1+(%Y#1)=0
SET %P=$JUSTIFY(%P,1,0)
+5 KILL %G,%H,%E,%LN
QUIT
LOG ;%L=LOG(%X) (log base 10) uses LN
+1 ;error
NEW %LN
DO LN
IF %LN=0
SET %L=0
QUIT
+2 SET %L=+$JUSTIFY(%LN/2.302585,1,6)
QUIT
+3 ;
TAN ;%Y=TAN(%X) ;tan X = sin X/cos X
+1 DO SIN
SET %TN=%Y
DO COS
SET %Y=$JUSTIFY(%TN/%Y,1,6)
KILL %TN
QUIT
SIN ;%Y=SIN(%X), %X in radians
+1 SET %T=%X
GOTO C
COS ;%Y=COS(%X), %X in radians
+1 SET %T=%X+1.5707963
C IF %T<-1.5707963
SET %T=-3.14159265-%T
+1 IF %T>3.14159265
SET %T=%T-6.2831853
GOTO C
+2 SET %T2=%T
SET %Y=%T
SET %T4=1
SET %T3=-1
+3 FOR %=3:2:11
SET %T4=%T4*(%-1)*%
SET %T2=%T2*%T*%T
SET %Y=%T2/%T4*%T3+%Y
SET %T3=-%T3
+4 SET %Y=+$JUSTIFY(%Y,1,6)
KILL %,%T,%T2,%T3,%T4
QUIT
+5 ;
DTR ;DEGREES TO RADIANS
+1 SET %X=$JUSTIFY(%X/57.29577951,1,7)
QUIT
RTD ;RADIANS TO DEGREES
+1 SET %X=$JUSTIFY(%X*57.29577951,1,5)
QUIT
PI ;%X=PIE
SET %X=3.1415927
QUIT
+1 ;
SQRT ;%Y=SQRT(%X)
+1 SET %Y=0
IF %X'>0
QUIT
SET %Y=%X+1/2
L SET %T=%Y
SET %Y=%X/%T+%T/2
IF %Y<%T
GOTO L
+1 QUIT
SD ;SX=SUM, SSX=SUM OF SQUARES, N=COUNT
+1 SET SD=-1
SET %X=-1
IF N<2
QUIT
+2 SET %X=N*SSX-(SX*SX)/(N*(N-1))
DO SQRT
SET SD=%Y
SET %X=SX/N
QUIT
