Help needed with Picaxe maths please

[stevesmythe]

In post #2 of this thread, Boriz uses what looks like some very compact code but I can't get my head round the Picaxe maths. Please could someone translate these two lines into conventional maths and explain it for me? I have tried reading the manual but I still can't understand it.

b1=b1+2 max 3//3 and

b0=b0+b1-1//4

I'd be much obliged. Thanks.

 

[PieM]

Picaxe Manual2 :
The division (/) command returns the quotient (whole number) word of a word*word division.
The modulus (// or %) command returns the remainder of the calculation.

 

[stevesmythe]

Yes, I have read the manual, but the left-right order of calculation plus the modulus combined with the MAX leaves me confused. Perhaps you could rewrite those two expressions in conventional maths for me?

 

[eggdweather]

The maths is processed left to right with no precedence.
The line is processed like this:
B1 is added to 2, then that result is limited to 3 then divided by 3 returning the modulus
If b1+2 was 3 then max has no effect and 3//3 would be 0 there was no remainder
If b1+2 was 10 then max 3 would yield 3 as above 3//3 would be 0
If b1+2 was 2 then max 3 would be 2 and 2//3 would be 2

 

[stevesmythe]

OK. Thanks eggdweather. Got it now.

I was also puzzled by b0=b0+b1-1//4 in the case where b0=0 and b1=0.

That would mean that b0=(0+0-1)//4 or -1 mod 4 but I thought that Picaxe can't handle negative numbers?

 

[westaust55]

Correct, the PICAXE math does not "handle" negative numbers.

What happens if the result of a subtraction gives a value less than zero is that the result has under flow.

If you are using a byte variable for the result,
0 - 1 ==> 255
Think of a byte (0 - 255 range) and 0 equates to 256 i.e. The lower 8 bits (= byte) are all zero's.

For a word variable result and during internal math (always performed to 16-bits)
0 - 1 ==> 65535

 

[hippy]

It seems that "b1=b1+2 max 3//3" is intended to toggle b1 between 0 and 2 every time it is executed. Not sure why it's done that way but would guess "because it works".

An alternative would be -

b1 = b1 ^ 2

 

[stevesmythe]

So, -1 mod 4 (=3) is evaluated as 65535 mod 4 which is also 3.

 

[hippy]

So, -1 mod 4 (=3) is evaluated as 65535 mod 4 which is also 3.

That is correct. It's basically creating running a repeating sequence 0 to 3 then switching to a reversed repeating sequence, 3 to 0.

The way I would have done it is ...

b1 = 1
Do
  For w2 = 0 To 20
    LookUp b0,("A","B","C","D"),b2
    SerTxd( b2 )
    b0 = b0 + b1 // 4
  Next
  b1 = -b1
Loop

Run that through PE6 simulator and you will see "ABCDABCDA..." then it switches to "DCBADCBAD...", then back to "ABCDA..." again.

 

[stevesmythe]

That's much easier to understand Hippy. Thanks