Spectrum ROM: Routine at 14020

14020: THE 'EXPONENTIAL' FUNCTION (offset 38)

Used by the routine at to_power. The address of this routine is found in the table of addresses. It is called indirectly via fp_calc_2. This subroutine handles the function EXP X and is the first of four routines that use the series generator to produce Chebyshev polynomials. The approximation to EXP X is found as follows: i. X is divided by LN 2 to give Y, so that 2*Y is now the required result. ii. The value N is found, such that N=INT Y. iii. The value W=Y-N is found; 0<=W<=1, as required for the series to converge. iv. The argument Z=2W-1 is formed. v. The series generator is used to return 2W. vi. Finally N is added to the exponent, giving 2(N+W), which is 2**Y and therefore the required answer.
exp	14020	RST 40	X
Perform step i.
	14021	DEFB 61	re_stack: X (in full floating-point form)
	14022	DEFB 52	stk_data: X, 1/LN 2
	14023	DEFB 241,56,170,59,41	stk_data: X, 1/LN 2
	14028	DEFB 4	multiply: X/LN 2=Y
Perform step ii.
	14029	DEFB 49	duplicate: Y, Y
	14030	DEFB 39	int: Y, INT Y=N
	14031	DEFB 195	st_mem_3: Y, N (mem-3 holds N)
Perform step iii.
	14032	DEFB 3	subtract: Y-N=W
Perform step iv.
	14033	DEFB 49	duplicate: W, W
	14034	DEFB 15	addition: 2*W
	14035	DEFB 161	stk_one: 2*W, 1
	14036	DEFB 3	subtract: 2*W-1=Z
Perform step v, passing to the series generator the parameter '8' and the eight constants required.
	14037	DEFB 136	series_08: Z
	14038	DEFB 19,54
	14040	DEFB 88,101,102
	14043	DEFB 157,120,101,64
	14047	DEFB 162,96,50,201
	14051	DEFB 231,33,247,175,36
	14056	DEFB 235,47,176,176,20
	14061	DEFB 238,126,187,148,88
	14066	DEFB 241,58,126,248,207
At the end of the last loop the 'last value' is 2**W. Perform step vi.
	14071	DEFB 227	get_mem_3: 2**W, N
	14072	DEFB 56	end_calc
	14073	CALL FP_TO_A	The absolute value of N mod 256 is put into the A register.
	14076	JR NZ,N_NEGTV	Jump forward if N was negative.
	14078	JR C,REPORT_6_2	Error if ABS N>255.
	14080	ADD A,(HL)	Now add ABS N to the exponent.
	14081	JR NC,RESULT_OK	Jump unless e>255.
Report 6 - Number too big.
REPORT_6_2	14083	RST 8	Call the error handling routine.
	14084	DEFB 5	Call the error handling routine.
N_NEGTV	14085	JR C,RSLT_ZERO	The result is to be zero if N<-255.
	14087	SUB (HL)	Subtract ABS N from the exponent as N was negative.
	14088	JR NC,RSLT_ZERO	Zero result if e less than zero.
	14090	NEG	Minus e is changed to e.
RESULT_OK	14092	LD (HL),A	The exponent, e, is entered.
	14093	RET	Finished: 'last value' is EXP X.
RSLT_ZERO	14094	RST 40	Use the calculator to make the 'last value' zero.
	14095	DEFB 2	delete (the stack is now empty)
	14096	DEFB 160	stk_zero: 0
	14097	DEFB 56	end_calc
	14098	RET	Finished, with EXP X=0.