The BBC and Master Computer Public Domain Library

A8A1 ASN

Submitted by Steve Fewell

Description:

Call routine &96DA to get the numeric value (at the current position of the BASIC text pointer) and convert it to a
Floating-Point value (if it was an Integer).

If the FWA sign is positive then jump to &A8AF to calculate the ASN result and exit.

If the FWA sign is negative then:: * Clear the FWA Sign byte (to make the FWA value positive); * Call routine &A8AF to calculate the ASN result for the FWA value; * Jump to &A8D2 to store A (#&FF) in the FWA sign byte (to make the FWA value negative) and exit

[A8AF] Calculate ASN result:
Call routine &A50D to store the FWA value in temporary Floating-point location &0476-&047A.

Call routine &A929 to:: * FWA = FWA * FWA (calculate the square of FWA); * FWA = 1.0 [&BF92] - FWA; * FWA = SQR(FWA) (calculate the square root of FWA)

If the FWA Mantissa byte 1 is zero then jump to &A896 to exit with the FWA set to the floating-point constant at
location &BF2E [which is 1.57079633].

Call &A5B3 to set the FWA = (as the result is a Floating-Point value).
Jump to &A8C6 to set the FWA to the Arc-Tangent of the FWA value [FWA = ATN(FWA)].

The ASN calculation for a non-zero positive value is therefore:
ASN(x) = ATN(x / SQR(1 - (x * x)))

Example 1: ASN(0): [A8AF] Store FWA in &0476; Store FWA in &046C; FWA = FWA * &046C = 0.0; FWA = 1.0 - FWA = 1.0; FWA = SQR(FWA) = 1.0; FWA = &0476 (0) / FWA = 0.0; FWA = ATN(FWA) = 0.0

Example 2: ASN(0.25): [A8AF] Store FWA in &0476; Store FWA in &046C; FWA = FWA * &046C = 0.0625; FWA = 1.0 - FWA = 0.9375; FWA = SQR(FWA) = 0.9682458; FWA = &0476 (0.25) / FWA = 0.2581988; FWA = ATN(FWA) = 0.2526802

Example 3: ASN(-0.75): [A8A4] Sign byte of FWA is negative, so clear the sign of the FWA = 0.75; [A8AF] Store FWA in &0476; Store FWA in &046C; FWA = FWA * &046C = 0.5625; FWA = 1.0 - FWA = 0.4375; FWA = SQR(FWA) = 0.6614378; FWA = &0476 (0.75) / FWA = 1.1338934; FWA = ATN(FWA) = 0.848062; [A8AD] Store A (#&FF) in the FWA sign byte. FWA = -0.848062

This diagram shows the relationship between the trig functions.

Disassembly for the ASN routine

A8A1		032 218 150	20 DA 96	JSR &96DA Get and Check Float (convert if Int)
A8A4	.	165 046	A5 2E	LDA &2E
A8A6		016 007	10 07	BPL 7 --> &A8AF
A8A8	d.	100 046	64 2E	STZ &2E
A8AA		032 175 168	20 AF A8	JSR &A8AF
A8AD	#	128 035	80 23	BRA 35 --> &A8D2 Store A in location &2E (i.e. make result negative) and exit
A8AF		032 013 165	20 0D A5	JSR &A50D Store FWA to &0476 and set argp to &0476
A8B2	)	032 041 169	20 29 A9	JSR &A929
A8B5	1	165 049	A5 31	LDA &31
A8B7		240 005	F0 05	BEQ 5 --> &A8BE
A8B9		032 179 165	20 B3 A5	JSR &A5B3 FWA=&0476/FWA & exit with A=#&FF
A8BC		128 008	80 08	BRA 8 --> &A8C6 Calculate ATN result [FWA=ATN(FWA)]
A8BE	.	169 046	A9 2E	LDA#&2E
A8C0	L	076 150 168	4C 96 A8	JMP &A896 Load FWA with FP constant at &BF00 + A