SEARCH HDRFIL
COMPIL(TG1,<SIN$,COS$,SIND$,COSD$,SQRT$,RAN$>,<TRIGINI,X22,.RSEED>,<SIN, SQRT ROUTINES>)
BEGIN SIN$
AA←13
BB←14
CC←15
HERE(COSD$)			;ENTRY TO COSINE DEGREES ROUTINE.
	MOVE	BB,-1(P)	;PICK UP THE ARG.
	FADR	BB,CD1		;ADD 90 DEGREES.
	JRST	CONVER		;CONVERT TO RADIANS
HERE(SIND$)			;ENTRY TO SINE DEGREES ROUTINE.
	MOVE	BB,-1(P)	;PICK UP THE ARG.
CONVER:	FDVR	BB,SCD1		;CONVERT TO RADIANS
	JFOV	.+1		;SUPPRESS ERROR MESSAGE ON UNDERFLOW.
	JRST	S1		;ENTER SINE ROUTINE.
HERE(COS$) 			;ENTRY TO COSINE RADIANS ROUTINE.
	MOVE	BB,-1(P)	;PICK UP THE ARG.
	FADR	BB,PIOT		;ADD PI/2.
	JRST	S1		;ENTER SINE ROUTINE.
HERE(SIN$)			;ENTRY TO SINE RADIANS ROUTINE.
	MOVE	BB,-1(P)	;PICK UP THE ARG.
S1:	MOVEM	BB,-1(P)	;SAVE THE ARG.
	MOVMS	BB		;GET ABS OF ARG.
	CAMG	BB,SP2		;SIN(X)=X IF X LESS THAN 2↑-9.
	JRST	S3A		;EXIT WITH ARG. IN B.
	FDV	BB,PIOT		;DIVIDE X BY PI/2.
	CAMG	BB,ONE		;IS X/(PI/2) LESS THAN 1.0 ?
	JRST	S2		;YES,ARG IN 1ST QUADRANT ALREADY.
	MULI	BB,400		;NO,SEPARATE FRACTION AND EXP.
	ASH	CC,-202(BB)	;GET X MODULO 2PI.
	JFOV	.+1		;SUPRESS ERROR MESSAGE FROM OVTRAP.
	MOVEI	BB,200		;PREPARE FLOATING FRACTION.
	ROT	CC,3		;SAVE THREE BITS TO DETERMINE QUADRANT.
	LSHC	BB,33		;ARGUMENT NOW IN THE RANGE (-1,1).
	FAD	BB,SP3		;NORMALIZE THE ARGUMENT.
	JUMPE	CC,S2		;REDUCED TO 1ST QUAD IF BITS 000.
	TLCE	CC,1000		;SUBTRACT 1.0 FROM ARG IF BITS ARE
	FSB	BB,ONE		;001 OR 011.
	TLCE	CC,3000		;CHECK FOR FIRST QUADRANT, 001.
	TLNN	CC,3000		;CHECK FOR THIRD QUADRANT, 010.
	MOVNS	BB		;001,010.
S2:	SKIPGE	-1(P)		;CHECK SIGN OF ORIGINAL ARG.
	MOVNS	BB		;SIN(-X)=-SIN(X).
	MOVEM	BB,-1(P)	;STORE REDUCED ARG.
	FMPR	BB,BB		;CALCULATE X↑X
	MOVE	AA,SC9		;GET 1ST CONSTANT.
	FMP	AA,BB		;MULTIPLY BY X↑2
	FAD	AA,SC7		;ADD IN NEXT CONSTANT.
	FMP	AA,BB		;MULTIPLY BY X↑2.
	FAD	AA,SC5		;ADD IN NEXT CONSTANT.
	FMP	AA,BB		;MULTIPLY BY X↑2.
	FAD	AA,SC3		;ADD IN NEXT CONSTANT.
	FMP	AA,BB		;MULTIPLY BY X↑2.
	FAD	AA,PIOT		;ADD IN LAST CONSTANT.
S2B:	FMPR	AA,-1(P)	;MULTIPLY BY X.
	SKIPA	1,AA		;ANSWER IN 1
S3A:	MOVE	1,-1(P)		;ANSWER IN 1.
	SUB	P,X22
	JRST	@2(P)
SC3:	577265210372
SC5:	175506321276
SC7:	606315546346
SC9:	164475536722
SP2:	170000000000
SP3:	0
CD1:	90.0
SCD1:	206712273406
PIOT:	201622077325
ONE:	1.0
BEND SIN$
BEGIN SQRT$
	AA←13
	BB←14
	F←15
HERE(SQRT$)			;ENTRY TO SQUARE ROOT ROUTINE
	SKIPG	BB,-1(P)	;PICK UP ARG. CHECK IF GREATER THAN 0
	JRST	SQRT4		;NO, HANDLE NON-POSITIVE ARGUMENT
	MOVEI	AA,0		;GET EXPONENT TO AA
	LSHC	AA,=9
	SUBI	AA,201		;GET TRUE EXPONENT + 1
	ROT	AA,-1		;DIVIDE BY 2
	JUMPL	AA,SQRT3	;JUMP IF FRACTION GREATER THAN .5
	LSH	BB,-=9		;RESTORE POSITION OF FRACTION IN BB
	FSC	BB,177		;AND FIX UP EXPONENT .25 LESS THAN F LESS THAN .5
	MOVEM	BB,F		;SAVE FRACTION
	FMPRI	BB,200640
	FADRI	BB,177465
SQRT1:	MOVE	1,F		;1ST ITERATION OF NEWTON
	FDV	1,BB		; F/APPROX
	FAD	BB,1		; APPROX  +  F/APPROX
	FSC	BB,-1		; .5*( APPROX  +  F/APPROX)
	MOVE 	1,F		;2ND ITERATION OF NEWTON
	FDV	1,BB		; F/APPROX
	FADR	1,BB		; APPROX + F/APPROX
	FSC	1,(AA)		;HALVE AND SCALE EXPONENT
EXIT:	SUB	P,X22
	JRST	@2(P)
SQRT3:	LSH	BB,-=9		;RESTORE POSITION OF FRACTION IN BB
	FSC	BB,200		;AND FIX UP EXPONENT .5 LESS THAN= F LESS THAN 1
	MOVEM	BB,F		;SAVE FRACTION
	FMPRI	BB,200450
	FADRI	BB,177660
	JRST	SQRT1		;NOW GO ITERATE
SQRT4:	JUMPE	BB,ZERO
	ERR <SQRT: Negative argument - 0 returned>,1
ZERO:	MOVEI	1,0		;HERE ON NON-POSITIVE ARG. RETURN ZERO
	JRST	EXIT
BEND SQRT$
BEGIN RAN$
       AA←13
       BB←14
INTERNAL RAN$
RAN$:
	MOVE	AA,-1(P)		;IF ARG = 0 THEN
	JUMPE	AA,R1		;USE PREVIOUS RANDOM NO.
	TLZ	AA,760000	;OTHERWISE MASK 5 BITS
	MOVEM	AA,.RSEED	;AND STORE NEW NO.
R1:	MOVE	AA,K		;GET K [14**29(MOD2**31 -1)]
	MUL	AA,.RSEED	;MULTIPLY WITH LAST RANDOM NUMBER
	ASHC	AA,4		;SEPARATE RESULT IN TWO 31 BIT WORDS
	LSH	BB,-4
	ADD	AA,BB		;ADD THEM TOGETHER
	TLZE	AA,760000	;SKIP IF RESULT LESS THAN 31 BITS
	ADDI	AA,1
	MOVEM	AA,.RSEED	;STORE NEW RN IN INTEGER MODE
	HLRZ	1,AA		;CONVERT TO FP IN TWO STEPS IN
	FSC	1,216		;ORDER TO LOOSE NO LOW ORDER
	HRLI	AA,0		;BITS
	FSC	AA,174
	FAD	1,AA
	SUB	P,X22
	JRST	@2(P)		;EXIT
K:     =630360016        ;14**29(MOD 2**31 -1)
BEND RAN$
ENDCOM(TG1)
END