Ethiopian multiplication: Difference between revisions

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=={{header|Ursala}}==

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This solution makes use of the functions odd, double, and half, which respectively

The first implementation below relies on the representation of natural numbers as lists of bits,

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check the parity, double a given natural number, or perform truncating division by two. These

lsb first, so that halving is the same as taking the tail, doubling

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functions are normally imported from the nat library but defined here explicitly for

is inserting a zero, and filtering for oddness is filtering by the head,

the sake of completeness.

all of which are expressible as primitives.

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odd = ~&ihB

#import nat

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double = ~&iNiCB

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half = ~&itB

emul = @lrtK33PDNlCrXK9rhPFlS sum:-0

</lang>

The functions above are defined in terms of bit manipulations exploiting the concrete representations

Here is a more verbose version (in keeping with the spirit of the task) treating natural numbers

as abstract types, and ~~explicitly using~~ the operators for distribution (*-), triangular iteration (|\),

of natural numbers. The remaining code treats natural numbers instead as abstract types by way of the library API, and uses the operators for distribution (*-), triangular iteration (|\),

and filtering (*~) among others.

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emul = sum:-0@rS+ odd@l*~+ ^|(~&,double)|\+ *-^|\~& @iNC ~&h~=0->tx :^/half@h ~&

</lang>

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~~The~~ ~~program above~~ makes use of the functions odd, double, and half, which respectively

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check ~~for~~ ~~whether or not a number is even~~, double a given number, or perform truncating

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~~division by two. These~~ functions are imported from the nat library ~~and~~ ~~would~~ ~~not~~ be

be redefined in practice. To comply with the task specification, they can be defined

as follows.

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odd = ~&ihB

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double = ~&iNiCB

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half = ~&itB

</lang>

test program: