Spectrum ROM: Routine at 3833

The address of this routine is found in the table of addresses. It is called via the calculator literal +22 by the routine at acs. It is also called indirectly via fp_calc_2.

This subroutine handles the function ASN X and returns a real number from -π/2 to π/2 inclusive which is equal to the value in radians of the angle whose sine is X. Thereby if Y=ASN X then X=SIN Y.

This subroutine uses the trigonometric identity TAN (Y/2)=SIN Y/(1+COS Y) to obtain TAN (Y/2) and hence (using ATN) Y/2 and finally Y.

The address of this routine is found in the table of addresses. It is called via the calculator literal +22 by the routine at acs. It is also called indirectly via fp_calc_2. This subroutine handles the function ASN X and returns a real number from -π/2 to π/2 inclusive which is equal to the value in radians of the angle whose sine is X. Thereby if Y=ASN X then X=SIN Y. This subroutine uses the trigonometric identity TAN (Y/2)=SIN Y/(1+COS Y) to obtain TAN (Y/2) and hence (using ATN) Y/2 and finally Y.
asn	3833	RST $28	X
	3834	DEFB $31	duplicate: X, X
	3835	DEFB $31	duplicate: X, X, X
	3836	DEFB $04	multiply: X, X*X
	3837	DEFB $A1	stk_one: X, X*X, 1
	3838	DEFB $03	subtract: X, X*X-1
	3839	DEFB $1B	negate: X, 1-X*X
	383A	DEFB $28	sqr: X, SQR (1-X*X)
	383B	DEFB $A1	stk_one: X, SQR (1-X*X), 1
	383C	DEFB $0F	addition: X, 1+SQR (1-X*X)
	383D	DEFB $05	division: X/(1+SQR (1-X*X))=TAN (Y/2)
	383E	DEFB $24	atn: Y/2
	383F	DEFB $31	duplicate: Y/2, Y/2
	3840	DEFB $0F	addition: Y=ASN X
	3841	DEFB $38	end_calc
	3842	RET	Finished: 'last value'=ASN X.