XLFMTH ;SF-ISC/RWF,HINES/CFB,DW - MATH FUNCTIONS;07/16/93 10:21 ;03/03/95 15:29
;;8.0;KERNEL;;Jul 10, 1995
ABS(X) ;absolute value
Q $S(X<0:-X,1:X)
LN(X,PR) ;log base e
N L,M,N,O,P,Y,LIM S PR=$$PR($G(PR),11) D A G Q
LOG(X,PR) ;log base 10
N L,M,N,O,P,Y,LIM S PR=$$PR($G(PR),11) D A S Y=Y/2.30258509298749 G Q
;
A S M=1 I X>0 F N=0:1 Q:(X/M)<10 S M=M*10
I X<1 F N=0:-1 Q:(X/M)>.1 S M=M*.1
S X=X/M
B S X=(X-1)/(X+1),(Y,L)=X D LIM F O=3:2 S L=L*X*X,M=L/O,Y=M+Y S:M<0 M=-M Q:M<LIM
S Y=Y*2+(N*2.30258509298749) Q
;
EXP(X,PR) ;e to the X power
N L,M,N,O,P,Y,LIM S PR=$$PR($G(PR),11) D EX G Q
;
EX S (Y,L)=X,Y=Y+1 D LIM F O=2:1 S L=L*X/O,Y=Y+L Q:($TR(L,"-")<LIM)
Q
PWR(Y,X,PR) ;X to the Y power
N L,M,N,O,P,LIM S PR=$$PR($G(PR),11) D P G Q
;
P S:X<0 X=X*-1,Y=1/Y S P=X,X=Y D A S X=Y*P D EX
Q
LIM S LIM=$S((PR+3)'>11:PR+3,1:11),@("LIM=1E-"_LIM) Q
;
Q Q +$J(Y,0,$S((PR-$L(Y\1))'<0:PR-$L(Y\1),1:0))
PR(PR,PL) Q $S('$L(PR):PL,PR>PL:PL,1:PR)
E(PR) ;e
N Y S Y=2.71828182845905 S PR=$$PR($G(PR),12) G Q
PI(PR) ;PI
N Y S Y=3.14159265358979 S PR=$$PR($G(PR),12) G Q
;
SQRT(X,PR) ;square root of X
N Y,T S Y=0,PR=$$PR($G(PR),12) Q:X'>0 Y S Y=X+.5
L F S T=Y,Y=X/T+T/2 Q:Y'<T
G Q
SD(%S1,%S2,%N) ;%S1=SUM, %S2=SUM OF SQUARES, %N=COUNT
N %X,%SD S %SD=-1,%X=-1 Q:%N<2 %SD
S %X=%N*%S2-(%S1*%S1)/(%N*(%N-1)),%SD=$$SQRT(%X),%X=%S1/%N Q %SD
MIN(%1,%2) Q $S(%1<%2:%1,1:%2)
MAX(%1,%2) Q $S(%1<%2:%2,1:%1)
;
DMSDEC(X,PR) ;degrees:min:sec to decimal
N Y S PR=$$PR($G(PR),12),Y=$P(X,":")+($P(X,":",2)/60)+($P(X,":",3)/3600) G Q
DECDMS(X,PR) ;decimal to degrees:min:sec
N Y S PR=$$PR($G(PR),5),Y=X\1,X=X-(X\1)*60,Y=Y_":"_(X\1),X=X-(X\1)*60,X=+$J(X,0,$S((PR-$L(X\1))'<0:PR-$L(X\1),1:0)) Q Y_":"_X
DTR(X,PR) ;degrees to radians
N Y S Y=X*3.14159265358979/180 S PR=$$PR($G(PR),12) G Q
RTD(X,PR) ;radians to degrees
N Y S Y=X*180/3.14159265358979 S PR=$$PR($G(PR),12) G Q
SINDEG(X,PR) ;sine in degrees
S:X[":" X=$$DMSDEC(X,12) S PR=$$PR($G(PR),10),X=$$DTR(X) Q $$SIN(X,PR)
SIN(X,PR) ;sine in radians
N L,M,N,O,P,Y,LIM,SIGN S PR=$$PR($G(PR),10) D S G Q
S S X=X#(2*3.14159265358979),(Y,L)=X,SIGN=-1 D LIM F O=3:2 S L=L/(O-1)*X/O*X,Y=Y+(SIGN*L) Q:($TR(L,"-")<LIM) S SIGN=SIGN*-1
Q
CSCDEG(X,PR) ;cosecant in degrees
S:X[":" X=$$DMSDEC(X,12) S PR=$$PR($G(PR),10),X=$$DTR(X) Q $$CSC(X,PR)
CSC(X,PR) ;cosecant in radians
N L,M,N,O,P,Y,LIM,SIGN S PR=$$PR($G(PR),10) D S S Y=1/Y G Q
COSDEG(X,PR) ;cosine in degrees
S:X[":" X=$$DMSDEC(X,12) S PR=$$PR($G(PR),10),X=$$DTR(X) Q $$COS(X,PR)
COS(X,PR) ;cosine in radians
N L,M,N,O,P,Y,LIM,SIGN S PR=$$PR($G(PR),10) D C G Q
C S X=X#(2*3.14159265358979),(Y,L)=1,SIGN=-1 D LIM F O=2:2 S L=L*X*X/(O-1*O),Y=Y+(SIGN*L) Q:($TR(L,"-")<LIM) S SIGN=SIGN*-1
Q
SECDEG(X,PR) ;secant in degrees
S:X[":" X=$$DMSDEC(X,12) S PR=$$PR($G(PR),10),X=$$DTR(X) Q $$SEC(X,PR)
SEC(X,PR) ;secant in radians
N L,M,N,O,P,Y,LIM,SIGN S PR=$$PR($G(PR),10) D C S Y=1/Y G Q
TANDEG(X,PR) ;tangent in degrees
S:X[":" X=$$DMSDEC(X,12) S PR=$$PR($G(PR),10),X=$$DTR(X) Q $$TAN(X,PR)
TAN(X,PR) ;tangent in radians
N L,M,N,O,P,Y,LIM,S,SIGN S PR=$$PR($G(PR),10) D S S S=Y D C S Y=S/Y G Q
COTDEG(X,PR) ;cotangent in degrees
S:X[":" X=$$DMSDEC(X,12) S PR=$$PR($G(PR),10),X=$$DTR(X) Q $$COT(X,PR)
COT(X,PR) ;contangent in radians
N L,M,N,O,P,Y,LIM,C,SIGN S PR=$$PR($G(PR),10) D C S C=Y D S S Y=C/Y G Q
ASINDEG(X,PR) ;arc-sine in degrees
G ASIND^XLFMTH1
ASIN(X,PR) ;arc-sine in radians
G ASIN^XLFMTH1
ACOSDEG(X,PR) ;arc-cosine in degrees
G ACOSD^XLFMTH1
ACOS(X,PR) ;arc-cosine in radians
G ACOS^XLFMTH1
ATANDEG(X,PR) ;arc-tangent in degrees
G ATAND^XLFMTH1
ATAN(X,PR) ;arc-tangent in radians
G ATAN^XLFMTH1
ACOTDEG(X,PR) ;arc-cotangent in degrees
G ACOTD^XLFMTH1
ACOT(X,PR) ;arc-cotangent in radians
G ACOT^XLFMTH1
ASECDEG(X,PR) ;arc-secant in degrees
G ASECD^XLFMTH1
ASEC(X,PR) ;arc-secant in radians
G ASEC^XLFMTH1
ACSCDEG(X,PR) ;arc-cosecant in degrees
G ACSCD^XLFMTH1
ACSC(X,PR) ;arc-cosecant in radians
G ACSC^XLFMTH1
--- Routine Detail --- with STRUCTURED ROUTINE LISTING ---[H[J[2J[HXLFMTH 4041 printed Dec 13, 2024@02:02:50 Page 2
XLFMTH ;SF-ISC/RWF,HINES/CFB,DW - MATH FUNCTIONS;07/16/93 10:21 ;03/03/95 15:29
+1 ;;8.0;KERNEL;;Jul 10, 1995
ABS(X) ;absolute value
+1 QUIT $SELECT(X<0:-X,1:X)
LN(X,PR) ;log base e
+1 NEW L,M,N,O,P,Y,LIM
SET PR=$$PR($GET(PR),11)
DO A
GOTO Q
LOG(X,PR) ;log base 10
+1 NEW L,M,N,O,P,Y,LIM
SET PR=$$PR($GET(PR),11)
DO A
SET Y=Y/2.30258509298749
GOTO Q
+2 ;
A SET M=1
IF X>0
FOR N=0:1
if (X/M)<10
QUIT
SET M=M*10
+1 IF X<1
FOR N=0:-1
if (X/M)>.1
QUIT
SET M=M*.1
+2 SET X=X/M
B SET X=(X-1)/(X+1)
SET (Y,L)=X
DO LIM
FOR O=3:2
SET L=L*X*X
SET M=L/O
SET Y=M+Y
if M<0
SET M=-M
if M<LIM
QUIT
+1 SET Y=Y*2+(N*2.30258509298749)
QUIT
+2 ;
EXP(X,PR) ;e to the X power
+1 NEW L,M,N,O,P,Y,LIM
SET PR=$$PR($GET(PR),11)
DO EX
GOTO Q
+2 ;
EX SET (Y,L)=X
SET Y=Y+1
DO LIM
FOR O=2:1
SET L=L*X/O
SET Y=Y+L
if ($TRANSLATE(L,"-")<LIM)
QUIT
+1 QUIT
PWR(Y,X,PR) ;X to the Y power
+1 NEW L,M,N,O,P,LIM
SET PR=$$PR($GET(PR),11)
DO P
GOTO Q
+2 ;
P if X<0
SET X=X*-1
SET Y=1/Y
SET P=X
SET X=Y
DO A
SET X=Y*P
DO EX
+1 QUIT
LIM SET LIM=$SELECT((PR+3)'>11:PR+3,1:11)
SET @("LIM=1E-"_LIM)
QUIT
+1 ;
Q QUIT +$JUSTIFY(Y,0,$SELECT((PR-$LENGTH(Y\1))'<0:PR-$LENGTH(Y\1),1:0))
PR(PR,PL) QUIT $SELECT('$LENGTH(PR):PL,PR>PL:PL,1:PR)
E(PR) ;e
+1 NEW Y
SET Y=2.71828182845905
SET PR=$$PR($GET(PR),12)
GOTO Q
PI(PR) ;PI
+1 NEW Y
SET Y=3.14159265358979
SET PR=$$PR($GET(PR),12)
GOTO Q
+2 ;
SQRT(X,PR) ;square root of X
+1 NEW Y,T
SET Y=0
SET PR=$$PR($GET(PR),12)
if X'>0
QUIT Y
SET Y=X+.5
L FOR
SET T=Y
SET Y=X/T+T/2
if Y'<T
QUIT
+1 GOTO Q
SD(%S1,%S2,%N) ;%S1=SUM, %S2=SUM OF SQUARES, %N=COUNT
+1 NEW %X,%SD
SET %SD=-1
SET %X=-1
if %N<2
QUIT %SD
+2 SET %X=%N*%S2-(%S1*%S1)/(%N*(%N-1))
SET %SD=$$SQRT(%X)
SET %X=%S1/%N
QUIT %SD
MIN(%1,%2) QUIT $SELECT(%1<%2:%1,1:%2)
MAX(%1,%2) QUIT $SELECT(%1<%2:%2,1:%1)
+1 ;
DMSDEC(X,PR) ;degrees:min:sec to decimal
+1 NEW Y
SET PR=$$PR($GET(PR),12)
SET Y=$PIECE(X,":")+($PIECE(X,":",2)/60)+($PIECE(X,":",3)/3600)
GOTO Q
DECDMS(X,PR) ;decimal to degrees:min:sec
+1 NEW Y
SET PR=$$PR($GET(PR),5)
SET Y=X\1
SET X=X-(X\1)*60
SET Y=Y_":"_(X\1)
SET X=X-(X\1)*60
SET X=+$JUSTIFY(X,0,$SELECT((PR-$LENGTH(X\1))'<0:PR-$LENGTH(X\1),1:0))
QUIT Y_":"_X
DTR(X,PR) ;degrees to radians
+1 NEW Y
SET Y=X*3.14159265358979/180
SET PR=$$PR($GET(PR),12)
GOTO Q
RTD(X,PR) ;radians to degrees
+1 NEW Y
SET Y=X*180/3.14159265358979
SET PR=$$PR($GET(PR),12)
GOTO Q
SINDEG(X,PR) ;sine in degrees
+1 if X["
SET X=$$DMSDEC(X,12)
SET PR=$$PR($GET(PR),10)
SET X=$$DTR(X)
QUIT $$SIN(X,PR)
SIN(X,PR) ;sine in radians
+1 NEW L,M,N,O,P,Y,LIM,SIGN
SET PR=$$PR($GET(PR),10)
DO S
GOTO Q
S SET X=X#(2*3.14159265358979)
SET (Y,L)=X
SET SIGN=-1
DO LIM
FOR O=3:2
SET L=L/(O-1)*X/O*X
SET Y=Y+(SIGN*L)
if ($TRANSLATE(L,"-")<LIM)
QUIT
SET SIGN=SIGN*-1
+1 QUIT
CSCDEG(X,PR) ;cosecant in degrees
+1 if X["
SET X=$$DMSDEC(X,12)
SET PR=$$PR($GET(PR),10)
SET X=$$DTR(X)
QUIT $$CSC(X,PR)
CSC(X,PR) ;cosecant in radians
+1 NEW L,M,N,O,P,Y,LIM,SIGN
SET PR=$$PR($GET(PR),10)
DO S
SET Y=1/Y
GOTO Q
COSDEG(X,PR) ;cosine in degrees
+1 if X["
SET X=$$DMSDEC(X,12)
SET PR=$$PR($GET(PR),10)
SET X=$$DTR(X)
QUIT $$COS(X,PR)
COS(X,PR) ;cosine in radians
+1 NEW L,M,N,O,P,Y,LIM,SIGN
SET PR=$$PR($GET(PR),10)
DO C
GOTO Q
C SET X=X#(2*3.14159265358979)
SET (Y,L)=1
SET SIGN=-1
DO LIM
FOR O=2:2
SET L=L*X*X/(O-1*O)
SET Y=Y+(SIGN*L)
if ($TRANSLATE(L,"-")<LIM)
QUIT
SET SIGN=SIGN*-1
+1 QUIT
SECDEG(X,PR) ;secant in degrees
+1 if X["
SET X=$$DMSDEC(X,12)
SET PR=$$PR($GET(PR),10)
SET X=$$DTR(X)
QUIT $$SEC(X,PR)
SEC(X,PR) ;secant in radians
+1 NEW L,M,N,O,P,Y,LIM,SIGN
SET PR=$$PR($GET(PR),10)
DO C
SET Y=1/Y
GOTO Q
TANDEG(X,PR) ;tangent in degrees
+1 if X["
SET X=$$DMSDEC(X,12)
SET PR=$$PR($GET(PR),10)
SET X=$$DTR(X)
QUIT $$TAN(X,PR)
TAN(X,PR) ;tangent in radians
+1 NEW L,M,N,O,P,Y,LIM,S,SIGN
SET PR=$$PR($GET(PR),10)
DO S
SET S=Y
DO C
SET Y=S/Y
GOTO Q
COTDEG(X,PR) ;cotangent in degrees
+1 if X["
SET X=$$DMSDEC(X,12)
SET PR=$$PR($GET(PR),10)
SET X=$$DTR(X)
QUIT $$COT(X,PR)
COT(X,PR) ;contangent in radians
+1 NEW L,M,N,O,P,Y,LIM,C,SIGN
SET PR=$$PR($GET(PR),10)
DO C
SET C=Y
DO S
SET Y=C/Y
GOTO Q
ASINDEG(X,PR) ;arc-sine in degrees
+1 GOTO ASIND^XLFMTH1
ASIN(X,PR) ;arc-sine in radians
+1 GOTO ASIN^XLFMTH1
ACOSDEG(X,PR) ;arc-cosine in degrees
+1 GOTO ACOSD^XLFMTH1
ACOS(X,PR) ;arc-cosine in radians
+1 GOTO ACOS^XLFMTH1
ATANDEG(X,PR) ;arc-tangent in degrees
+1 GOTO ATAND^XLFMTH1
ATAN(X,PR) ;arc-tangent in radians
+1 GOTO ATAN^XLFMTH1
ACOTDEG(X,PR) ;arc-cotangent in degrees
+1 GOTO ACOTD^XLFMTH1
ACOT(X,PR) ;arc-cotangent in radians
+1 GOTO ACOT^XLFMTH1
ASECDEG(X,PR) ;arc-secant in degrees
+1 GOTO ASECD^XLFMTH1
ASEC(X,PR) ;arc-secant in radians
+1 GOTO ASEC^XLFMTH1
ACSCDEG(X,PR) ;arc-cosecant in degrees
+1 GOTO ACSCD^XLFMTH1
ACSC(X,PR) ;arc-cosecant in radians
+1 GOTO ACSC^XLFMTH1
