perm filename SAITG2.FAI[S,AIL] blob
sn#191929 filedate 1975-12-15 generic text, type T, neo UTF8
SEARCH HDRFIL
COMPIL(TG2,<ATAN$,ASIN$,ACOS$,ATAN2$>,<OVPCWD,TRIGINI,X33,SQRT$,X22,X11>
,<ARC-TRIG ROUTINES>)
BEGIN ATAN$
AA←1
BB←13
CC←14
DD←15
HERE(ATAN$) ;ENTRY TO ARCTANGENT ROUTINE
MOVE AA,-1(P) ;PICK UP THE ARGUMENT IN AA
ATAN1: MOVM BB, AA ;GET ABSF OF ARGUMENT
CAMG BB, A1 ;IF X LESS THAN 2↑-33, THEN RETURN WITH...
JRST EXIT ;ATAN(X) = X
HLLO DD, AA ;SAVE SIGN, SET RH(DD) = -1
CAML BB, A2 ;IF AA GREATER THAN 2↑33, THEN RETURN WITH
JRST AT4 ;ATAN(X) = PI/2
MOVSI CC, (1.0) ;FORM 1.0 IN CC
CAMG BB, CC ;IS ABSF(X) GREATER THAN 1.0?
TRZA DD, -1 ;IF BB .LE. 1.0, THEN RH(DD) = 0
FDVM CC, BB ;BB IS REPLACED BY 1.0/BB
TLC DD, (DD) ;XOR SIGN WITH .G. 1.0 INDICATOR
PUSH P,BB ;SAVE THE ARGUMENT
FMP BB, BB ;GET BB↑2
MOVE CC, KB3 ;PICK UP A CONSTANT
FAD CC, BB ;ADD BB↑2
MOVE AA, KA3 ;ADD IN NEXT CONSTANT
FDVM AA, CC ;FORM -A3/(B↑2 + B3)
FAD CC, BB ;ADD BB↑2 TO PARTIAL SUM
FAD CC, KB2 ;ADD B2 TO PARTIAL SUM
MOVE AA, KA2 ;PICK UP -A2
FDVM AA, CC ;DIVIDE PARTIAL SUM BY -A2
FAD CC, BB ;ADD BB↑2 TO PARTIAL SUM
FAD CC, KB1 ;ADD B1 TO PARTIAL SUM
MOVE AA, KA1 ;PICK UP A1
FDV AA, CC ;DIVIDE PARTIAL SUM BY A1
FAD AA, KB0 ;ADD B0
FMP AA,(P) ;MULTIPLY BY ORIGINAL ARGUMENT
TRNE DD, -1 ;CHECK .G. 1.0 INDICATOR
FSB AA, PIOT ;ATAN(AA) = -(ATAN(1/AA)-PI/2)
SUB P,X11
SKIPA 0,0 ;SKIP
AT4: MOVE AA, PIOT ;GET PI/2 AS ANSWER
SKIPGE DD ;LH(DD) = -SGN(BB) IF BB GREATER THAN 1.0
MOVNS AA ;NEGATE ANSWER
EXIT: SUB P,X22
JRST @2(P)
A1: 145000000000 ;2**-33
A2: 233000000000 ;2**33
KB0: 176545543401 ;0.1746554388
KB1: 203660615617 ;6.762139240
KB2: 202650373270 ;3.316335425
KB3: 201562663021 ;1.448631538
KA1: 202732621643 ;3.709256262
KA2: 574071125540 ;-7.106760045
KA3: 600360700773 ;-0.2647686202
PIOT: 201622077325 ;PI/2
BEND ATAN$
BEGIN ASIN$
AA←13
BB←1
HERE(ASIN$) ;ENTRY TO ASIN ROUTINE
MOVM BB,-1(P) ;GET MAGNITUDE OF ARG. IN BB
CAMLE BB,ONE ;IS THE MAGNITUDE OF THE ARG. LE 1.0?
JRST TOOLRG ;NO, GO TO ERROR RETURN.
MOVN AA,-1(P) ;GET THE NEGATIVE OF ARG
FMP AA,-1(P) ;CALCULATE -(X↑2)
JFOV .+1 ;SUPPRESS ERROR MESSAGE FROM OVTRAP
FAD AA, ONE ;CALCULATE 1-(X↑2)
JUMPE AA, ASIN1 ;WAS X EITHER -1.0 OR 1.0?
PUSH P,AA ;NO,
PUSHJ P,SQRT$ ;CALCULATE SQRT(1-X↑2)
MOVE AA,-1(P) ;GET THE ARGUMENT BACK AGAIN
FDV AA,BB ;CALCULATE X/SQRT(1-X↑2)
PUSH P,AA ;THEN
PUSHJ P,ATAN$ ;CALCULATE ATAN(X/SQRT(1-X↑2)),.
EXIT: SUB P,X22
JRST @2(P)
TOOLRG: ERR <ASIN: Argument mangitude greater than 1.0; 0 returned>,1
TDZA BB,BB
ASIN1: MOVE BB, PIOT ;ANSWER IS EITHER PI/2 OR-PI/2
SKIPG -1(P) ;WAS ORIGINAL ARGUMENT POSITIVE?
MOVNS BB ;NO, GET -PI/2
JRST EXIT
PIOT: 201622077325 ;PI/2
ONE: 1.0
BEND ASIN$
BEGIN ACOS$
HERE(ACOS$) ;ENTRY TO ACOS ROUTINE.
MOVM 1,-1(P) ;GET /ARG./ IN AC 1.
CAMLE 1,ONE ;IS MAGNITUDE OF ARG. GT 1.0?
JRST TOOLRG ;YES, GO TO ERROR RETURN.
JUMPE 1,ZERARG ;IF ARG=0, GO TO ZERARG.
FMPR 1,1 ;X↑2 IN AC 1.
JFOV .+1 ;SUPPRESS ERROR MESSAGE FROM OVTRAP
MOVNS 1 ;-X↑2 IN AC 1.
FAD 1,ONE ;1.0-X↑2 IN AC 1.
PUSH P,1
PUSHJ P,SQRT$ ;CALC. $SQRT(1.0-X↑2).
FDVR 1,-1(P) ;($SQRT(1.0-X↑2))/X IS IN AC 1.
JFOV .+1 ;SUPPRESS ERROR MESSAGE FROM OVTRAP
PUSH P,1
PUSHJ P,ATAN$ ;FIND $ATAN($SQRT(1.0-X↑2)/X).
SKIPL -1(P) ;SKIP IF ORIGINAL ARG LESS THAN 0.
JRST EXIT ;RETURN.
FAD 1,PII ;ANSWER IS PI + ANSWER IN AC 1.
EXIT: SUB P,X22
JRST @2(P)
TOOLRG: ERR <ACOS: Argument magnitude greater than 1.0; 0 returned>,1
TDZA 1,1 ;RETURN ZERO.
ZERARG: MOVE 1,PI2 ;ANSWER IS PI/2
JRST EXIT
ONE: 1.0
PI2: 201622077325
PII: 202622077325
BEND ACOS$
BEGIN ATAN2$
AA←13
BB←1
HERE(ATAN2$) ;ENTRY POINT TO ATAN2 ROUTINE
JFOV .+1 ;CLEAR FLAGS FOR GOOD MEASURE (JAM)
MOVE AA,-2(P) ;PICK UP FIRST ARGUMENT
MOVE BB,-1(P) ;PICK UP SECOND ARGUMENT
FDVR AA, BB ;FORM AA/BB
JFOV OVUNFO ;EXTRA JFCL BECAUSE OF FDV HARDWARE BUG
JFOV OVUNFO ;SUPPRESS ERROR MESSAGE FROM
PUSH P,AA ;CALCULATE ATAN(AA/BB)
PUSHJ P,ATAN$
SKIPL -1(P) ;IF BB GREATER THAN 0, SGN(ATAN2)=SGN(A)
JRST EXIT ;EXIT
JUMPGE BB, ATAN2A ;IS BB POSITIVE?
FADR BB, PII ;NO, SECOND QUADRANT, ADD PI
EXIT: SUB P,X33
JRST @3(P)
ATAN2A: FSBR BB, PII ;YES,3RD QUADRANT, SUBTRACT PI
JRST EXIT ;EXIT
OVUNFO: SKIPN AA,OVPCWD ;PICK UP FLAGS.
JSP AA,.+1
TLNE AA,100 ;SKIP IF OVERFLOW
JRST UNDER
MOVE BB,HALFPI ;ANSWER TO PI OVER 2
SKIPGE -2(P) ;SKIP IF ANS IS TO BE +
MOVNS BB
JRST EXIT
UNDER: JUMPL BB,BNEG
MOVEI BB,0
JRST EXIT ;RETURN 0
BNEG: MOVE BB,PII
SKIPGE -2(P)
MOVNS BB
JRST EXIT
PII: 202622077325 ;PII
HALFPI: 201622077325 ;PII/2
BEND ATAN2$
ENDCOM(TG2)
END