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Routines |
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The address of this routine is found in the table of addresses. It is called via the calculator literal +24 by the routine at asn. It is also called indirectly via fp_calc_2.
This subroutine handles the function ATN X and is the last of the four routines that use the series generator to produce Chebyshev polynomials. It returns a real number between -π/2 and π/2, which is equal to the value in radians of the angle whose tan is X.
The approximation to ATN X is found as follows:
i. The values W and Y are found for three cases of X, such that:
In each case, -1<=Y<=1, as required for the series to converge.
ii. The argument Z is formed, such that:
iii. The series generator is used to produce the required function.
iv. Finally a simple multiplication and addition give ATN X.
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Perform step i.
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atn | 37E2 | CALL re_stack | Use the full floating-point form of X. | |||||||
37E5 | LD A,(HL) | Fetch the exponent of X. | ||||||||
37E6 | CP $81 | Jump forward for case i: Y=X. | ||||||||
37E8 | JR C,SMALL | |||||||||
37EA | RST $28 | X | ||||||||
37EB | DEFB $A1 | stk_one: X, 1 | ||||||||
37EC | DEFB $1B | negate: X, -1 | ||||||||
37ED | DEFB $01 | exchange: -1, X | ||||||||
37EE | DEFB $05 | division: -1/X | ||||||||
37EF | DEFB $31 | duplicate: -1/X, -1/X | ||||||||
37F0 | DEFB $36 | less_0: -1/X, (1/0) | ||||||||
37F1 | DEFB $A3 | stk_pi_2: -1/X, (1/0), π/2 | ||||||||
37F2 | DEFB $01 | exchange: -1/X, π/2, (1/0) | ||||||||
37F3 | DEFB $00 | jump_true to CASES for case ii: -1/X, π/2 | ||||||||
37F4 | DEFB $06 | |||||||||
37F5 | DEFB $1B | negate: -1/X, -π/2 | ||||||||
37F6 | DEFB $33 | jump to CASES for case iii: -1/X, -π/2 | ||||||||
37F7 | DEFB $03 | |||||||||
SMALL | 37F8 | RST $28 | ||||||||
37F9 | DEFB $A0 | stk_zero: Y, 0; continue for case i: W=0 | ||||||||
Perform step ii.
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CASES | 37FA | DEFB $01 | exchange: W, Y | |||||||
37FB | DEFB $31 | duplicate: W, Y, Y | ||||||||
37FC | DEFB $31 | duplicate: W, Y, Y, Y | ||||||||
37FD | DEFB $04 | multiply: W, Y, Y*Y | ||||||||
37FE | DEFB $31 | duplicate: W, Y, Y*Y, Y*Y | ||||||||
37FF | DEFB $0F | addition: W, Y, 2*Y*Y | ||||||||
3800 | DEFB $A1 | stk_one: W, Y, 2*Y*Y, 1 | ||||||||
3801 | DEFB $03 | subtract: W, Y, 2*Y*Y-1=Z | ||||||||
Perform step iii, passing to the series generator the parameter '12', and the twelve constants required.
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3802 | DEFB $8C | series_0C: W, Y, Z | ||||||||
3803 | DEFB $10,$B2 | |||||||||
3805 | DEFB $13,$0E | |||||||||
3807 | DEFB $55,$E4,$8D | |||||||||
380A | DEFB $58,$39,$BC | |||||||||
380D | DEFB $5B,$98,$FD | |||||||||
3810 | DEFB $9E,$00,$36,$75 | |||||||||
3814 | DEFB $A0,$DB,$E8,$B4 | |||||||||
3818 | DEFB $63,$42,$C4 | |||||||||
381B | DEFB $E6,$B5,$09,$36,$BE | |||||||||
3820 | DEFB $E9,$36,$73,$1B,$5D | |||||||||
3825 | DEFB $EC,$D8,$DE,$63,$BE | |||||||||
382A | DEFB $F0,$61,$A1,$B3,$0C | |||||||||
At the end of the last loop the 'last value' is:
Perform step iv.
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382F | DEFB $04 | multiply: W, ATN X (case i) or W, ATN (-1/X) (cases ii and iii) | ||||||||
3830 | DEFB $0F | addition: ATN X (all cases now) | ||||||||
3831 | DEFB $38 | end_calc | ||||||||
3832 | RET | Finished: 'last value'=ATN X. |
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