combinations of k bits wp34s

[Andrew Nikitin]

The bitwise operations on a calculator is surprisingly fun.

// If input word contains k bits, then the result is next word 

// containing k bits

// Must be in integer (binary?) mode

// Start with MASKR k

  LBL'NXC'

    RCL X

    +/-

    RCL Y

    AND

    RCL+ Y

    RCL L

    RCL Z

    RCL Z

    NOT

    AND

    x[<->] Y

    /

    SR 01

    +

    RTN

I would love to hear stories about using them (bitwise operations) in realistic problems.

[Paul Dale]

Nice program, one of the few I've seen so far that use integer mode. You might need to specify the integer sign mode though.

Also, the shuffle [<->] command would save a couple of steps I think.

- Pauli

[Thomas Klemm]

Is there a reason why the use of L is not supported as in:

[<->] XYLX

Cheers

Thomas

[Paul Dale]

Blame Walter :-) The shuffle command originally accepted five registers and L was permitted in any position, then it was removed and later reinstated in its current form after much discussion and finally the keyboard and display code was added.

Allowing the fifth register was an unnecessary complication and the current form fits the opcode layout a lot better.

- Pauli

[Walter B]

I don't remember the L-part of that discussion ;-) One could ask, however, why that command doesn't allow for shuffling A, B, C, and D as well to generate maximum confusion. Luckily, we don't have sufficient op-codes left. Anyway, enough potential to create a big mess on the stack.

d:-)

[Thomas Klemm]

It was confusing that the letter L was accepted but instead Y is used. The same happens for A, B, C, D and J, K. This might be a remainder of this discussion?

Cheers

Thomas

[Paul Dale]

This is a bug. Soon to be fixed.

- Pauli

[Paul Dale]

The L part was very very early on before the command was dropped.

- Pauli

[Didier Lachieze]

Very nice program! Here is a slightly more compact version (3 steps less):

  LBL'NXC'

    FILL

    +/-

    AND

    STO T

    +

    STO Z

    NOT

    AND

    RCL/ Z

    SR 01

    +

    RTN

Btw I would be interested by a detailed explanation of how you found this formula.

Edited: 25 Aug 2013, 6:22 p.m.

[Paul Dale]

I found this pretty quickly, although it doesn't appear to be exactly the same algorithm, it is pretty well explained.

- Pauli

[Andrew Nikitin]

I once read a book about combinatorial algorithms. From there I learned a trick: x&(-x) leaves the lowest set bit in x. I do not remember the exact details, but it dawned on me that I can use that to implement standard "next combination" generation algorithm (locate rightmost group of consecutive ones, in that group move leftmost bit one step left, move others all the way to the right) entirely in mix of bitwise/arithmetic operations. Turned out, you do not even need too many.

Edited: 25 Aug 2013, 10:24 p.m.

[mjcohen]

The book you want is

Hacker's Delight (2nd Edition) by Henry S. Warren.

It's even available in a Kindle edition for $26.