So you have a need, a need for a particular routine. Well it just may be here.

- Square calculator Calculates a 16-bit unsigned integer square
- Root calculator Calculates the 8-bit root of a 16-bit integer
- Ring buffer Setting up an interrupt serviced buffer
- Pseudo random Generating 8-bit pseudo random numbers

### Square Calculator

This routine calculates the 16-bit unsigned integer square of a signed 16-bit integer in the range +/-255 (decimal).

; by Lee Davison; Calculates the 16 bit unsigned integer square of the signed ; 16 bit integer in Numberl/Numberh. ; The result is always in the range 0 to 65025 and is held in Squarel/Squareh ; ; The maximum input range is only +/-255 and no checking is done to ensure that ; this is so. ; ; This routine is useful if you are trying to draw circles as for any circle ; ; x^2+y^2=r^2 where x and y are the co-ordinates of any point on the circle and ; r is the circle radius ; ; Destroys all registers .ORG 8000 ; these must be in RAM Numberl ; number to square low byte Numberh = Numberl+ ; number to square high byte .word $FFFF Squarel ; square low byte Squareh = Squarel+1 ; square high byte .word $FFFF Tempsq ; temp byte for intermediate result .byte $00 .ORG 8192 ; any address will do Square LDA #$00 ; clear A STA Squarel ; clear square low byte ; (the high byte gets shifted out) LDA Numberl ; get number low byte LDX Numberh ; get number high byte BPL NoNneg ; if +ve don't negate it ; else do a two's complement EOR #$FF ; invert SEC ; +1 ADC #$00 ; and add it NoNneg: STA Tempsq ; save ABS(number) LDX #$08 ; set bit count Nextr2bit: ASL Squarel ; low byte *2 ROL Squareh ; high byte *2+carry from low ASL A ; shift number byte BCC NoSqadd ; don't do add if C = 0 TAY ; save A CLC ; clear carry for add LDA Tempsq ; get number ADC Squarel ; add number^2 low byte STA Squarel ; save number^2 low byte LDA #$00 ; clear A ADC Squareh ; add number^2 high byte STA Squareh ; save number^2 high byte TYA ; get A back NoSqadd: DEX ; decrement bit count BNE Nextr2bit ; go do next bit RTS

### Square Root Calculator

This routine calculates the 8-bit integer square root and 9 bit integer remainder of an unsigned 16-bit integer.

; by Lee Davison ; Calculates the 8 bit root and 9 bit remainder of a 16 bit unsigned integer in ; Numberl/Numberh. The result is always in the range 0 to 255 and is held in ; Root, the remainder is in the range 0 to 511 and is held in Reml/Remh ; ; partial results are held in templ/temph ; ; This routine is the complement to the integer square program. ; ; Destroys A, X registers. ; variables - must be in RAM Numberl = $F0 ; number to find square root of low byte Numberh = Numberl+1 ; number to find square root of high byte Reml = $F2 ; remainder low byte Remh = Reml+1 ; remainder high byte templ = $F4 ; temp partial low byte temph = templ+1 ; temp partial high byte Root = $F6 ; square root *= $8000 ; can be anywhere, ROM or RAM SqRoot LDA #$00 ; clear A STA Reml ; clear remainder low byte STA Remh ; clear remainder high byte STA Root ; clear Root LDX #$08 ; 8 pairs of bits to do Loop ASL Root ; Root = Root * 2 ASL Numberl ; shift highest bit of number .. ROL Numberh ; ROL Reml ; .. into remainder ROL Remh ; ASL Numberl ; shift highest bit of number .. ROL Numberh ; ROL Reml ; .. into remainder ROL Remh ; LDA Root ; copy Root .. STA templ ; .. to templ LDA #$00 ; clear byte STA temph ; clear temp high byte SEC ; +1 ROL templ ; temp = temp * 2 + 1 ROL temph ; LDA Remh ; get remainder high byte CMP temph ; comapre with partial high byte BCC Next ; skip sub if remainder high byte smaller BNE Subtr ; do sub if &lt;&gt; (must be remainder&gt;partial !) LDA Reml ; get remainder low byte CMP templ ; comapre with partial low byte BCC Next ; skip sub if remainder low byte smaller ; else remainder&gt;=partial so subtract then ; and add 1 to root. carry is always set here Subtr LDA Reml ; get remainder low byte SBC templ ; subtract partial low byte STA Reml ; save remainder low byte LDA Remh ; get remainder high byte SBC temph ; subtract partial high byte STA Remh ; save remainder high byte INC Root ; increment Root Next DEX ; decrement bit pair count BNE Loop ; loop if not all done RTS

### 256-Byte Data Buffer

This routine is an interrupt serviced 256 byte data buffer for serial ports and the like.

Very similar code was used to supply the stepper motor driver routine with line co-ordinate pairs.

This is not a finished solution, you will need to add your own code to drive the target of the buffer.

; By Lee Davison ; code for an interrupt serviced data buffer. similar code is used to drive ; the XY stepper motors on a plotter with new position information every 5mS ; and also to allow pen up/down movement time of 70mS ; buffer and variables must be in RAM Buffer ; 256 byte buffer (must start at page edge) .ds $100 BRindx ; buffer read index .byte $00 BWindx ; buffer write index .byte $00 Sendf ; am sending flag .byte $00 WByte ; temp store for the byte to be sent .byte $00 ; write the data to the buffer a byte at a time and increment the pointer. ; the routine is called with the byte to write in A. If the interrupt ; device is idle when this routine is called it will wake it up by doing ; a BRK before it exits ; destroys the Y register ; can be ROM or RAM Incwritb STA WByte ; save byte to write LDA BRindx ; get read index SEC ; set carry for subtract SBC BWindx ; subtract write index BEQ Dowrite ; if equal then buffer empty so do write CMP #$02 ; need at least n+1 bytes to avoid rollover BCC Incwritb ; loop if no space ; construct and write data to buffer Dowrite LDY BWindx ; get write index LDA WByte ; get byte to write STA Buffer,Y ; save it INY ; increment index to next byte STY BWindx ; save new write index byte ; now see if the interrupt service routine is already running or if it's ; idle LDA Sendf ; get the sending flag BNE Doingit ; skip call if running BRK ; software call to interrupt routine NOP ; need this as return from BRK is +1 byte! CLI ; enable the interrupts Doingit RTS ; this is the interrupt service routine. takes a byte a time from the ; buffer and does some thing with it. also sets up the device(s) for ; the next interrupt ; no registers altered BuffIRQ PHA ; save A TXA ; copy X PHA ; save X TYA ; copy Y PHA ; save Y ; insert code here to ensure this is the interrupt you want. if it ; isn't then just exit quietly via ResExit the end of the routine Getnext JSR Increadb ; increment pointer and read byte from buffer BCS ExitIRQ ; branch if no byte to do ; here would be the guts of the routine such as sending the byte to ; the ACIA or a printer port or some other byte device. it will also ; ensure the device is set to generate an interrupt when it's completed ; it's task LDA #$FF ; set byte STA Sendf ; set sending flag JMP ResExit ; restore the registers &amp;amp; exit ; all done, clear the flag restore the ; registers &amp;amp; exit ExitIRQ LDA #$00 ; clear byte STA Sendf ; clear sending flag ResExit PLA ; pull Y TAY ; restore it PLA ; pull X TAX ; restore it PLA ; restore A RTI ; this was an interrupt service request ; so exit properly ; get byte from the buffer and increment the pointer. If the buffer is empty ; then exit with the carry flag set else exit with carry clear and the byte ; in A Increadb LDY BRindx ; get buffer read index CPY BWindx ; compare write index BEQ NOktoread ; branch if empty (= sets carry) LDA Buffer,Y ; get byte from buffer INY ; increment pointer STY BRindx ; save buffer read index CLC ; clear not ok flag NOktoread RTS

### 6502 8 bit PRNG

This is a short piece of code that generates a maximal length, 8 bit, pseudo random

number sequence. This routine is no great shakes in the speed stakes, it’s just a demo of a usefull

technique.

; by Lee Davison ; returns pseudo random 8 bit number in A. Affects A, X and Y. ; (r_seed) is the byte from which the number is generated and MUST be ; initialised to a non zero value or this function will always return ; zero. Also r_seed must be in RAM, you can see why...... rand_8 LDA r_seed ; get seed AND #$B8 ; mask non feedback bits ; for maximal length run with 8 bits we need ; taps at b7, b5, b4 and b3 LDX #$05 ; bit count (shift top 5 bits) LDY #$00 ; clear feedback count F_loop ASL A ; shift bit into carry BCC bit_clr ; branch if bit = 0 INY ; increment feedback count (b0 is XOR all the ; shifted bits from A) bit_clr DEX ; decrement count BNE F_loop ; loop if not all done no_clr TYA ; copy feedback count LSR A ; bit 0 into Cb LDA r_seed ; get seed back ROL A ; rotate carry into byte STA r_seed ; save number as next seed RTS ; done r_seed .byte 1 ; prng seed byte (must not be zero)

**Other number lengths**

A maximal length pseudo random number generator is basically just a shif register with feedback from the later stages to generate the next input bit. The form for a generator of length *n* with feedback from *t* is shown below.

**Pseudo random sequence generator**

You don’t have to limit the length to only 8 bits, any number of bits from two upwards will work if you chose the right feedback tap(s). Here is a table of some values.

Bits [n] |
Tap(s) [t] |
Length |
Bits [n] |
Tap(s) [t] |
Length |

2 | 1 | 3 | 3 | 2 | 7 |

4 | 3 | 15 | 5 | 3 | 31 |

6 | 5 | 63 | 7 | 6 | 127 |

8 |
6,5,4 |
255 |
9 | 5 | 511 |

10 | 7 | 1023 | 11 | 9 | 2047 |

15 | 14 | 32767 | 16 |
15,13,4 |
65535 |

17 | 14 | 131071 | 18 | 11 | 262143 |

20 | 17 | 1048575 | 21 | 19 | 2097151 |

22 | 21 | 4194303 | 23 | 18 | 8388607 |

24 |
23,22,17 |
16777215 |
25 | 22 | 33554431 |

28 | 25 | 268435455 | 29 | 27 | 536870911 |

31 | 28 | 2147483647 |

In the last case, with 31 bits, if you took a new value once a second the sequence

wouldn’t repeat for over sixty eight years. Even clocked at 1MHz it would still take

over thirty five minutes to cycle through every state.

**Faster, shorter method**

The above pseudo random number generator is known as a Fibonacci generator and, while it works, it turns out there is a much better generator to implement with a microprocessor.

**Galois pseudo random sequence generator.**

The Galois generator needs only to test the state of one bit and that can be tested after

the shift has been performed. The state of this bit determines whether the feedback term

is exclusive ORed with the result. This single bit test and multiple bit feedback is

easily done as can be seen from the code below.

; returns pseudo random 8 bit number in A. Affects A. (r_seed) is the ; byte from which the number is generated and MUST be initialised to a ; non zero value or this function will always return zero. Also r_seed ; must be in RAM, you can see why...... rand_8 LDA r_seed ; get seed ASL ; shift byte BCC no_eor ; branch if no carry EOR #$CF ; else EOR with $CF no_eor STA r_seed ; save number as next seed RTS ; done r_seed .byte 1 ; prng seed byte, must not be zero

You don’t have to limit the length to only 8 bits, any number of bits from three upwards will work if you chose the right feedback value. Here is a table of some values that have been chosen to give a feedback value that fits in a byte, this makes implementation on an 8 bit micro as short as possible. For these values bit n is the least significant bit in the value and the tested bit is the bit shifted out from bit 1.

Bits [n] |
Feedback |
Length |
Bits [n] |
Feedback |
Length |

3 | $03 | 7 | 4 | $03 | 15 |

5 | $17 | 31 | 6 | $27 | 63 |

7 | $4B | 127 | 8 |
$CF |
255 |

9 | $B7 | 511 | 10 | $E7 | 1023 |

11 | $EB | 2047 | 12 | $EB | 4095 |

13 | $BB | 8191 | 14 | $BB | 16383 |

15 | $DD | 32767 | 16 |
$D7 |
65535 |

17 | $AF | 131071 | 18 | $E7 | 262143 |

19 | $AF | 524287 | 20 | $F3 | 1048575 |

21 | $B7 | 2097151 | 22 | $BB | 4194303 |

23 | $F3 | 8388607 | 24 |
$DB |
16777215 |

25 | $93 | 33554431 | 26 | $B1 | 67108863 |

27 | $B1 | 134217727 | 28 | $E1 | 268435455 |

29 | $C3 | 536870911 | 30 | $AF | 1073741823 |

31 | $8B | 2147483647 | 32 |
$AF |
4294967295 |

This is now the form of sequence generator used to generate values for the RND() function in EhBASIC.

**“The generation of random numbers is too important to be left to chance.”**

Robert R. Coveyou.