| Routines

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=2*W-1 is formed. v. The series generator is used to return 2**W. 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
| 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
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.