Spectrum ROM: Routine at 14261

The address of this routine is found in the table of addresses. It is called via the calculator literal 31 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 31 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	14261	RST 40	X
Perform step i.
	14262	DEFB 57	get_argt: W
Perform step ii. The subroutine from now on is common to both the SINE and COSINE functions.
C_ENT	14263	DEFB 49	duplicate: W, W
	14264	DEFB 49	duplicate: W, W, W
	14265	DEFB 4	multiply: W, W*W
	14266	DEFB 49	duplicate: W, WW, WW
	14267	DEFB 15	addition: W, 2WW
	14268	DEFB 161	stk_one: W, 2WW, 1
	14269	DEFB 3	subtract: W, 2WW-1=Z
Perform step iii, passing to the series generator the parameter '6' and the six constants required.
	14270	DEFB 134	series_06: W, Z
	14271	DEFB 20,230
	14273	DEFB 92,31,11
	14276	DEFB 163,143,56,238
	14280	DEFB 233,21,99,187,35
	14285	DEFB 238,146,13,205,237
	14290	DEFB 241,35,93,27,234
At the end of the last loop the 'last value' is (SIN (π*W/2))/W. Perform step iv.
	14295	DEFB 4	multiply: SIN (π*W/2)=SIN X (or COS X)
	14296	DEFB 56	end_calc
	14297	RET	Finished: 'last value'=SIN X (or COS X).