Programming:Precalculated square

This article describes an algorithm which precalculates the square from 0*0 to 255*255 and the routine to get the correct square value from the table.

Initialisation

Precalculate the square table.

INITSQ		LD DE, 1	;1st odd number
		LD HL, 0	;HL = 1st square number
		LD B, H		;counter = 256
		LD IX, SQTAB	;startaddress of the square table
SQLOOP		LD (IX), L	;Lowbyte to table
		INC IX
		LD (IX), H	;Highbyte to table
		INC IX
		ADD HL, DE	;add odd number
		INC DE		;next odd number
		INC DE
		DJNZ SQLOOP	;256 times
		RET

Get square from the table

Input: A = Factor

Output: DE = A*A

GETSQ		LD L, A
		LD H, 0		;HL = factor
		ADD HL, HL	;* 2
		LD DE, SQTAB	;+ startaddress of the table
		ADD HL, DE	;= tableaddress
		LD E, (HL)	;E = Lowbyte of the result
		INC HL
		LD D, (HL)	;D = Highbyte of the result
		RET

Table definition

SQTAB		DS 512		;space for the table

Performance Improvements

This routine can be improved somewhat by using a page-aligned table with separate pages for LSB and MSB of the result. In order to do this, the initialisation routine needs to be:

INITSQ		LD DE, 1	;1st odd number
		LD HL, 0	;HL = 1st square number
		LD B, H		;counter = 256
		LD IX, SQTAB	;startaddress of the square table
SQLOOP		LD (IX + 0), L	;Lowbyte to table
		INC HX
		LD (IX + 0), H	;Highbyte to table
		DEC HX
		INC LX
		ADD HL, DE	;add odd number
		INC DE		;next odd number
		INC DE
		DJNZ SQLOOP	;256 times
		RET

And the routine to get the square can now be:

GETSQ		LD L, A
		LD H, SQTAB / 256	;HL = pointer to LSB
		LD E, (HL)		;E = Lowbyte of the result
		INC H
		LD D, (HL)		;D = Highbyte of the result
		RET

This is now a very small routine which could easily be defined as a macro for optimal performance (without the RET).