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451 lines
8.3 KiB
Markdown
451 lines
8.3 KiB
Markdown
chapter 2a, basic unsigned math
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===============================
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<h3 id="++add"><code>++add</code></h3>
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Add
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++ add :: add
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~/ %add
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|= [a=@ b=@]
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^- @
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?: =(0 a) b
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$(a (dec a), b +(b))
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::
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Produces the sum of `a` and `b` as an atom.
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`a` is an [atom]().
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`b` is an [atom]().
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~zod/try=> (add 2 2)
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4
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~zod/try=> (add 1 1.000.000)
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1.000.001
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~zod/try=> (add 1.333 (mul 2 2))
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1.337
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------------------------------------------------------------------------
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<h3 id="++cap"><code>++cap</code></h3>
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Tree head
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++ cap :: tree head
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~/ %cap
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|= a=@
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^- ?(%2 %3)
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?- a
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%2 %2
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%3 %3
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?(%0 %1) !!
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* $(a (div a 2))
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==
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::
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Tests whether an `a` is in the head or tail of a noun. Produces the
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[cube]() `%2` if it is within the head, or the [cube]() `%3` if is is
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within the tail.
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`a` is an [atom]().
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~zod/try=> (cap 4)
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%2
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~zod/try=> (cap 6)
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%3
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~zod/try=> (cap (add 10 9))
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%2
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------------------------------------------------------------------------
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<h3 id="++dec"><code>++dec</code></h3>
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Decrement
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++ dec :: decrement
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~/ %dec
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|= a=@
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~| %decrement-underflow
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?< =(0 a)
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=+ b=0
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|- ^- @
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?: =(a +(b)) b
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$(b +(b))
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::
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Produces `a-1` as an atom.
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`a` is an [atom]().
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~zod/try=> (dec 7)
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6
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~zod/try=> (dec 0)
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! decrement-underflow
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! exit
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------------------------------------------------------------------------
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<h3 id="++div"><code>++div</code></h3>
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Divide
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++ div :: divide
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~/ %div
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|= [a=@ b=@]
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^- @
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~| 'div'
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?< =(0 b)
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=+ c=0
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|-
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?: (lth a b) c
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$(a (sub a b), c +(c))
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::
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Computes `a` divided by `b`, producing an atom.
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`a` is an [atom]().
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`b` is an [atom]().
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~zod/try=> (div 4 2)
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2
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~zod/try=> (div 17 8)
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2
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~zod/try=> (div 20 30)
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0
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------------------------------------------------------------------------
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<h3 id="++fac"><code>++fac</code></h3>
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Factorial
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++ fac :: factorial
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~/ %fac
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|= a=@
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^- @
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?: =(0 a) 1
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(mul a $(a (dec a)))
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::
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Computes the factorial of `a`, producing an atom.
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`a` is an [atom]().
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~zod/try=> (fac 3)
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6
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~zod/try=> (fac 0)
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1
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~zod/try=> (fac 11)
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39.916.800
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------------------------------------------------------------------------
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<h3 id="++gte"><code>++gte</code></h3>
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Greater-than/equal
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++ gte :: greater-equal
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~/ %gte
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|= [a=@ b=@]
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^- ?
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!(lth a b)
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::
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Tests whether `a` is greater than a number `b`, producing a loobean.
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`a` is an [atom]().
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`b` is an [atom]().
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~zod/try=> (gte 100 10)
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%.y
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~zod/try=> (gte 4 4)
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%.y
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~zod/try=> (gte 3 4)
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%.n
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------------------------------------------------------------------------
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<h3 id="++gth"><code>++gth</code></h3>
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Greater-than
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++ gth :: greater-than
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~/ %gth
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|= [a=@ b=@]
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^- ?
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!(lte a b)
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::
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Tests whether `a` is greater than `b`, producing a loobean.
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`a` is an [atom]().
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`b` is an [atom]().
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~zod/try=> (gth 'd' 'c')
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%.y
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~zod/try=> (gth ~h1 ~m61)
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%.n
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------------------------------------------------------------------------
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<h3 id="++lte"><code>++lte</code></h3>
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Less-than/equal
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++ lte :: less-equal
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~/ %lte
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|= [a=@ b=@]
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|(=(a b) (lth a b))
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::
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Tests whether `a` is less than or equal to `b`, producing a loobean.
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`a` is an [atom]().
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`b` is an [atom]().
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~zod/try=> (lte 4 5)
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%.y
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~zod/try=> (lte 5 4)
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%.n
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~zod/try=> (lte 5 5)
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%.y
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~zod/try=> (lte 0 0)
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%.y
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------------------------------------------------------------------------
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<h3 id="++lth"><code>++lth</code></h3>
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Less-than
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++ lth :: less-than
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~/ %lth
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|= [a=@ b=@]
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^- ?
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?& !=(a b)
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|-
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?| =(0 a)
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?& !=(0 b)
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$(a (dec a), b (dec b))
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== == ==
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::
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Tests whether `a` is less than `b`, producing a loobean.
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`a` is an [atom]().
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`b` is an [atom]().
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~zod/try=> (lth 4 5)
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%.y
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~zod/try=> (lth 5 4)
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%.n
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~zod/try=> (lth 5 5)
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%.n
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~zod/try=> (lth 5 0)
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%.n
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------------------------------------------------------------------------
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<h3 id="++mas"><code>++mas</code></h3>
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Axis within head/tail
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++ mas :: tree body
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~/ %mas
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|= a=@
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^- @
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?- a
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1 !!
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2 1
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3 1
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* (add (mod a 2) (mul $(a (div a 2)) 2))
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==
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::
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------------------------------------------------------------------------
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Computes the axis of `a` within the head or the tail, producing an atom.
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`a` is an [atom]().
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~zod/try=> (mas 3)
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1
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~zod/try=> (mas 4)
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2
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~zod/try=> (mas 5)
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3
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~zod/try=> (mas 6)
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2
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~zod/try=> (mas 0)
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! exit
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~zod/try=> (mas 1)
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! exit
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<h3 id="++max"><code>++max</code></h3>
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Maximum
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++ max :: maximum
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~/ %max
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|= [a=@ b=@]
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^- @
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?: (gth a b) a
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b
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::
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Computes the maximum of `a` and `b`, producing an atom.
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`a` is an [atom]().
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`b` is an [atom]().
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~zod/try=> (max 10 100)
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100
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~zod/try=> (max 10.443 9)
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10.443
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~zod/try=> (max 0 1)
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1
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------------------------------------------------------------------------
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<h3 id="++min"><code>++min</code></h3>
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Minimum
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++ min :: minimum
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~/ %min
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|= [a=@ b=@]
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^- @
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?: (lth a b) a
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b
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::
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Computes the minimum of `a` and `b`, producing an atom.
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`a` is an [atom]().
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`b` is an [atom]().
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~zod/try=> (min 10 100)
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10
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~zod/try=> (min 10.443 9)
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9
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~zod/try=> (min 0 1)
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0
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------------------------------------------------------------------------
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<h3 id="++mod"><code>++mod</code></h3>
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Modulus
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++ mod :: remainder
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~/ %mod
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|= [a=@ b=@]
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^- @
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?< =(0 b)
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(sub a (mul b (div a b)))
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::
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Computes the remainder of dividing `a` by `b`, producing an atom.
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`a` is an [atom]().
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`b` is an [atom]().
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------------------------------------------------------------------------
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<h3 id="++mul"><code>++mul</code></h3>
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Multiply
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++ mul :: multiply
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~/ %mul
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|= [a=@ b=@]
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^- @
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=+ c=0
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|-
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?: =(0 a) c
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$(a (dec a), c (add b c))
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::
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Multiplies `a` by `b`, producing an atom.
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`a` is an [atom]().
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`b` is an [atom]().
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~zod/try=> (mul 3 4)
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12
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~zod/try=> (mul 0 1)
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0
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------------------------------------------------------------------------
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<h3 id="++peg"><code>++peg</code></h3>
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Axis within axis
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++ peg :: tree connect
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~/ %peg
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|= [a=@ b=@]
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^- @
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?- b
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1 a
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2 (mul a 2)
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3 +((mul a 2))
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* (add (mod b 2) (mul $(b (div b 2)) 2))
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==
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::
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Computes the axis of `b` within axis `a`, producing an atom.
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`a` is an [atom]().
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`b` is an [atom]().
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~zod/try=> (peg 4 1)
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4
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~zod/try=> (peg 4 2)
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8
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~zod/try=> (peg 8 45)
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269
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------------------------------------------------------------------------
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<h3 id="++sub"><code>++sub</code></h3>
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Subtract
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++ sub :: subtract
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~/ %sub
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|= [a=@ b=@]
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~| %subtract-underflow
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^- @
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?: =(0 b) a
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$(a (dec a), b (dec b))
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Subtracts `b` from `a`, producing an atom.
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`a` is an [atom]().
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`b` is an [atom]().
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~zod/try=> (sub 10 5)
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5
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~zod/try=> (sub 243 44)
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199
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~zod/try=> (sub 5 0)
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5
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~zod/try=> (sub 0 5)
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! subtract-underflow
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! exit
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------------------------------------------------------------------------
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