perm filename SAITG3.FAI[S,AIL] blob
sn#191930 filedate 1975-12-15 generic text, type T, neo UTF8
SEARCH HDRFIL
COMPIL(TG3,<TANH$,COSH$,SINH$>,<EXP$,X22,TRIGINI>,<HYPERBOLIC FUNCTIONS>)
BEGIN TANH$
AA← 1
BB←13
TM1←14
TM2←15
HERE(TANH$) ;ENTRY TO TANH ROUTINE
MOVE AA,-1(P) ;PICK UP THE ARGUMENT
MOVM BB, AA ;GET ABSF(ARGUMENT)
CAMGE BB, TA ;RETURN TANH(X)=X IF
JRST EXIT ;ABSF(X) .LE. .00034
CAMLE BB, T2 ;RETURN TANH(X) = 1.0*SIGN(X) IF
JRST TH5 ;ARGUMENT GREATER THAN 12.0
CAMGE BB, T3 ;USE RATIONAL APPROXIMATION IF
JRST TH3 ;ARGUMENT IS LESS THAN 0.17
FMPRI BB,202400 ;GET 2*ARG.
PUSH P,BB ;CALCULATE EXP(2X)
PUSHJ P,EXP$
MOVSI BB, (1.0) ;FORM 1.0
FAD AA, BB ;1 + EXP(2X)
FDVM BB, AA ;(1 + EXP(2X))**-1
FMPRI AA,202400 ;2*(1 + EXP(2X))**-1
FSBRM BB, AA ;1 - 2*(1 + EXP(2X))**-1
SKIPGE -1(P) ;SKIP AHEAD IF ARG WAS GREATER THAN= 0.
MOVNS AA ;OTHERWISE,NEGATE THE ANSWER.
EXIT: SUB P,X22
JRST @2(P)
TH3: FMP AA, T7 ;FORM 4*X*LOG(E) BASE 2
MOVEM AA, TM1 ;SAVE IT IN TM1
FMP AA, AA ;SQUARE IT
MOVEM AA, TM2 ;SAVE IT
FAD AA, T4 ;FORM F↑2 + T4
MOVE BB, T5 ;GET T5 IN ACCUMULATOR BB
FDV BB, AA ;T5/(F↑2 + T4)
FAD BB, T6 ;T6 + T5/(F↑2 + T4)
FMP BB, TM2 ;MULTIPLY BY F↑2
FAD BB, T7 ;ADD T7 (4*LOG(E) BASE 2)
MOVE AA, TM1 ;GET F IN ACCUMULATOR AA
TH5: FDV AA, BB ;DIVIDE F BY PARTIAL SUM
JRST EXIT ;EXIT
TA: 165544410070 ;0.00034
T2: 204600000000 ;12.0
T3: 176534121727 ;0.17
T4: 211535527022 ;349.6699888
T5: 204704333567 ;14.1384514018
T6: 173433723376 ;0.01732867951
T7: 203561250731 ;5.7707801636
BEND TANH$
BEGIN COSH$
AA←13
HERE(COSH$) ;ENTRY TO HYPERBOLIC COSINE ROUTINE.
MOVE 1,-1(P) ;PICK UP THE ARGUMENT.
MOVM AA,1 ;PUT ABS(X) IN AA
CAMLE 2,EIGHT8 ;IF ABS(X) GREATER THAN 88.029,
JRST OV88 ;GO TO OV88.
PUSH P,AA ;O'E, CALC. EXP(ABS(X))
PUSHJ P,EXP$
MOVSI AA,(1.0) ;PUT 1.0 IN AA
FDVR AA,1 ;CALC. 1.0/EXP(ABS(X)).
FADR 1,AA ;CALC. EXP(ABS(X)) + EXP(-ABS(X)).
FDVRI 1,202400 ;DIVIDE THIS BY 2.0.
EXIT: SUB P,X22 ;RETURN.
JRST @2(P)
OV88: FSBR AA,LN2BE ;FORM ABS(X)-LN(2).
CAMG AA,EIGHT8 ;OVERFLOW?
JRST EXPP ;NO,GO AHEAD.
ERR <COSH: Result too large - largest positive number returned>,1
HRLOI 1,377777 ;ANSWER = +INFINITY.
JRST EXIT ;RETURN
EXPP: PUSH P,AA ;CALC. EXP(ABS(X)-LN(2)).
PUSHJ P,EXP$
JRST EXIT ;RETURN.
EIGHT8: 207540074636 ;88.029
LN2BE: 200542710300 ;LOG(2) BASE E.
BEND COSH$
BEGIN SINH$
AA←13
BB←14
SX2←15
HERE(SINH$) ;ENTRY TO HYPERBOLIC SINE ROUTINE.
MOVE 1,-1(P) ;PICK UP THE ARG.
MOVM AA,1 ;GET MAGNITUDE OF ARG IN AA
CAMLE AA,EIGHT8 ;IF ABS(X) GREATER THAN 88.029,
JRST OV88 ;THEN GO TO OV88.
CAMG AA,ONE10T ;IF ABS(X) LESS THAN= 0.10,
JRST SERIES ;THEN GO TO SERIES.
PUSH P,AA ;CALCULATE EXP(ABS(X)).
PUSHJ P,EXP$ ;ABS(X) IS IN AA
HRLZI BB,576400 ;PUT -1.0 IN BB
FDVR BB,1 ;CALC. -EXP(-ABS(X)).
FADR 1,BB ;CALC. EXP(ABS(X))-EXP(-ABS(X)).
FDVRI 1,202400 ;CALC. THIS/2.0
SKIPGE -1(P) ;ANSWER IS POSITIVE.
MOVNS 1,1 ;ANSWER IS NEGATIVE.
EXIT: SUB P,X22
JRST @2(P)
SERIES: FMPR AA,AA ;CALC. X↑2.
JFOV .+1 ;SUPPRESS ERROR MESSAGE FROM OVTRAP.
MOVEM AA,SX2 ;SAVE X↑2 IN SX2.
FDVR AA,ONE120 ;CALC.X↑2/120
JFOV .+1 ;SUPPRESS ERROR MESSAGE FROM OVTRAP.
FADR AA,ONESIX ;CALC. (X↑2/120)+1/6
FMPR AA,SX2 ;MULTIPLY IT BY X↑2.
JFOV .+1 ;SUPPRESS ERROR MESSAGE FROM OVTRAP.
FADRI AA,(1.0) ;ADD 1.0.
FMPR 1,AA ;MULTIPLY BY X.
JRST EXIT ;RETURN.
OV88: FSBR AA,LN2BE ;CALC.ABS(X)-LN(2)
CAMG AA,EIGHT8 ;OVERFLOW?
JRST EXPP ;NO,GO TO CALC.
ERR <SINH: Result too large - largest positive number returned>,1
HRLOI 1,377777 ;SET ANS.=INFINITY.
JRST EXPP+2 ;GO TO SET SIGN OF ANS.
EXPP: PUSH P,AA ;CALC. EXP
PUSHJ P,EXP$
SKIPGE -1(P) ;RETURN ANS. GREATER THAN 0 IF X GREATER THAN 0.
MOVNS 1,1 ;O'E, ANS. LESS THAN 0.
JRST EXIT ;RETURN.
LN2BE: 200542710300 ;LN(2)
EIGHT8: 207540074636 ;88.029
ONE10T: 0.10
ONE120: 207740000000 ;120.0
ONESIX: 0.16666667
BEND SINH$
ENDCOM(TG3)
END