# Programming:Sin/Cos calculation

## Calculation using lookup table

The calculation is based on a table from 0-90° and on values which are multiplicated by 32767. If you want to get the correct sinus value, you have to divide them by 32767 (you can use 32768 - not a big precision lost, but you can use bit shifting).

Input: HL = angle in degree (0-360°)

Output: HL = SIN(HL) * 32767, A = sign flag (0 if positive, &FF if negative)

```INTSIN:	LD BC, 360
LOOP1:	BIT 7, H	;angle positive?
JR Z, LOOP2	;-> yes, ok
JR LOOP1	;repeat until H>0

LOOP2:	OR A		;reset carry
SBC HL, BC	;angle - 360
JR NC, LOOP2	;->ok if >=0
ADD HL, BC	;else correct value

LD E, L		;angle to DE
LD D, H
LD BC, 90
XOR A		;sign flag = 0
SBC HL, BC	;angle < 90?
JR NC, TEST2	;-> no
EX DE, HL	;else HL = angle
JR GETTAB	;get table value

TEST2:	SBC HL, BC	;angle < 180?
JR NC, TEST3	;-> no
LD HL, 180	;else HL =
OR A		;180 - angle
SBC HL, DE
JR GETTAB	;get table value

TEST3:	DEC A		;sign flag &FF
SBC HL, BC	;angle < 270?
JR NC, TEST4	;-> no
EX DE, HL	;else HL =
OR A		;clear carry
SBC HL, BC	;angle - 180
SBC HL, BC
JR GETTAB	;get table value

TEST4:	LD HL, 360	;if angle >=270
SBC HL, DE	;HL = 360 - angle

GETTAB:	ADD HL, HL	;angle * 2
LD DE, SINTAB	;+ start table
LD E, (HL)	;lowbyte to E
INC HL
LD D, (HL)	;highbyte to D
EX DE, HL	;result to HL
RET

;*****
;Sinustable for angles between 0..90 degrees
;*****
;Values*32767

SINTAB:
DW 0,572,1144,1715,2286
DW 2856,3425,3993,4560,5126
DW 5690,6252,6813,7371,7927
DW 8481,9032,9580,10126,10668
DW 11207,11743,12275,12803,13328
DW 13848,14364,14876,15383,15886
DW 16384,16876,17364,17846,18323
DW 18794,19260,19720,20173,20621
DW 21062,21497,21925,22347,22762
DW 23170,23571,23964,24351,24730
DW 25101,25465,25821,26169,26509
DW 26841,27165,27481,27788,28087
DW 28377,28659,28932,29196,29451
DW 29697,29934,30162,30381,30591
DW 30791,30982,31163,31335,31498
DW 31650,31794,31927,32051,32165
DW 32269,32364,32448,32523,32587
DW 32642,32687,32722,32747,32762
DW 32767
```

## Calculation using the CORDIC algorithm

Andre Adrian wrote a paper about how to implement the calculation of sin/cos on Z80 CPUs. You can read the paper and find the implementation on his homepage http://www.andreadrian.de/oldcpu/Z80_number_cruncher.html .