16-bit BCD
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The following code for ca65 converts a 16-bit unsigned integer to decimal digits, in roughly 700 cycles, without using the decimal mode that was removed from the 2A03.
To understand how curDigit is used, see Wikipedia:Ring counter.
<source lang="6502tasm">
- bcd16.s
- version 20060201
- Copyright (C) 2006 Damian Yerrick
- Copying and distribution of this file, with or without
- modification, are permitted in any medium without royalty provided
- the copyright notice and this notice are preserved in any source
- code copies. This file is offered as-is, without any warranty.
.p02
.exportzp bcdNum, bcdResult .export bcdConvert
- bcdConvert
- Given a number in bcdNum (16-bit), converts it to 5 decimal digits
- in bcdResult. Unlike most 6502 binary-to-decimal converters, this
- subroutine doesn't use the decimal mode that was removed from the
- 2A03 variant of the 6502 processor.
- For each value of n from 4 to 1, it compares the number to 8*10^n,
- then 4*10^n, then 2*10^n, then 1*10^n, each time subtracting if
- possible. After finishing all the comparisons and subtractions in
- each decimal place value, it writes the digit to the output array
- as a byte value in the range [0, 9]. Finally, it writes the
- remainder to element 0.
- Extension to 24-bit and larger numbers is straightforward
- Add a third bcdTable, increase BCD_BITS, and extend the
- trial subtraction.
- Constants _________________________________________________________
- BCD_BITS
- The highest possible number of bits in the BCD output. Should
- roughly equal 4 * log10(2) * x, where x is the width in bits
- of the largest binary number to be put in bcdNum.
- bcdTableLo[y], bcdTableHi[y]
- Contains (1 << y) converted from BCD to binary.
BCD_BITS = 19
- Variables _________________________________________________________
- bcdNum (input)
- Number to be converted to decimal (16-bit little endian).
- Overwritten.
- bcdResult (output)
- Decimal digits of result (5-digit little endian).
- X
- Offset of current digit being worked on.
- Y
- Offset into bcdTable*.
- curDigit
- The lower holds the digit being constructed.
- The upper nibble contains a sentinel value; when a 1 is shifted
- out, the byte is complete and should be copied to result.
- (This behavior is called a "ring counter".)
- Overwritten.
- b
- Low byte of the result of trial subtraction.
- Overwritten.
bcdNum = 0 bcdResult = 2 curDigit = 7 b = 2
- Completes within 670 cycles.
bcdConvert:
lda #$80 >> ((BCD_BITS - 1) & 3) sta curDigit ldx #(BCD_BITS - 1) >> 2 ldy #BCD_BITS - 5
@loop:
; Trial subtract this bit to A:b sec lda bcdNum sbc bcdTableLo,y sta b lda bcdNum+1 sbc bcdTableHi,y
; If A:b > bcdNum then bcdNum = A:b bcc @trial_lower sta bcdNum+1 lda b sta bcdNum
@trial_lower:
; Copy bit from carry into digit and pick up ; end-of-digit sentinel into carry rol curDigit dey bcc @loop
; Copy digit into result lda curDigit sta bcdResult,x lda #$10 ; Empty digit; sentinel at 4 bits sta curDigit ; If there are digits left, do those dex bne @loop lda bcdNum sta bcdResult rts
bcdTableLo:
.byt <10, <20, <40, <80 .byt <100, <200, <400, <800 .byt <1000, <2000, <4000, <8000 .byt <10000, <20000, <40000
bcdTableHi:
.byt >10, >20, >40, >80 .byt >100, >200, >400, >800 .byt >1000, >2000, >4000, >8000 .byt >10000, >20000, >40000
</source>
