Spectrum ROM: Routine at 37B5

The address of this routine is found in the table of addresses. It is called via the calculator literal +1F by the routines at DRAW, CD_PRMS1 and tan. It is also called indirectly via fp_calc_2.

This subroutine handles the function SIN X and is the third of the four routines that use the series generator to produce Chebyshev polynomials.

The approximation to SIN X is found as follows:

i. The argument X is reduced to W, such that SIN (π*W/2)=SIN X. Note that -1<=W<=1, as required for the series to converge.
ii. The argument Z=2*W*W-1 is formed.
iii. The series generator is used to return (SIN (π*W/2))/W.
iv. Finally a simple multiplication by W gives SIN X.

The address of this routine is found in the table of addresses. It is called via the calculator literal +1F by the routines at DRAW, CD_PRMS1 and tan. It is also called indirectly via fp_calc_2. This subroutine handles the function SIN X and is the third of the four routines that use the series generator to produce Chebyshev polynomials. The approximation to SIN X is found as follows: i. The argument X is reduced to W, such that SIN (πW/2)=SIN X. Note that -1<=W<=1, as required for the series to converge. ii. The argument Z=2WW-1 is formed. iii. The series generator is used to return (SIN (πW/2))/W. iv. Finally a simple multiplication by W gives SIN X.
sin	37B5	RST $28	X
Perform step i.
	37B6	DEFB $39	get_argt: W
Perform step ii. The subroutine from now on is common to both the SINE and COSINE functions.
C_ENT	37B7	DEFB $31	duplicate: W, W
	37B8	DEFB $31	duplicate: W, W, W
	37B9	DEFB $04	multiply: W, W*W
	37BA	DEFB $31	duplicate: W, WW, WW
	37BB	DEFB $0F	addition: W, 2WW
	37BC	DEFB $A1	stk_one: W, 2WW, 1
	37BD	DEFB $03	subtract: W, 2WW-1=Z
Perform step iii, passing to the series generator the parameter '6' and the six constants required.
	37BE	DEFB $86	series_06: W, Z
	37BF	DEFB $14,$E6
	37C1	DEFB $5C,$1F,$0B
	37C4	DEFB $A3,$8F,$38,$EE
	37C8	DEFB $E9,$15,$63,$BB,$23
	37CD	DEFB $EE,$92,$0D,$CD,$ED
	37D2	DEFB $F1,$23,$5D,$1B,$EA
At the end of the last loop the 'last value' is (SIN (π*W/2))/W. Perform step iv.
	37D7	DEFB $04	multiply: SIN (π*W/2)=SIN X (or COS X)
	37D8	DEFB $38	end_calc
	37D9	RET	Finished: 'last value'=SIN X (or COS X).