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Add apl-reshape (dyadic ⍴, cycling), apl-transpose (monadic ⍉, reverse axes), apl-transpose-dyadic (dyadic ⍉, permutation), plus helpers apl-strides / apl-flat->multi / apl-multi->flat. lib/apl/tests/structural.sx: 27 new tests covering ravel, reshape, monadic/dyadic transpose across scalar/vector/matrix/3-D cases. test.sh now runs structural.sx via its own inline framework (skips stale tests/runtime.sx which targeted a pre-Phase-2 list-based API). Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
439 lines
11 KiB
Plaintext
439 lines
11 KiB
Plaintext
; APL Runtime — array model + scalar primitives
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;
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; Array = SX dict {:shape (d1 d2 ...) :ravel (v1 v2 ...)}
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; Scalar: rank 0, shape (), one element in ravel
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; Vector: rank 1, shape (n), n elements in ravel
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; Matrix: rank 2, shape (r c), r*c elements in ravel
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; ============================================================
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; Array constructors
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; ============================================================
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(define make-array (fn (shape ravel) {:ravel ravel :shape shape}))
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(define apl-scalar (fn (v) {:ravel (list v) :shape (list)}))
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(define apl-vector (fn (elems) {:ravel elems :shape (list (len elems))}))
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; enclose — wrap any value in a rank-0 box
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(define enclose (fn (v) (apl-scalar v)))
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; disclose — unwrap rank-0 box, returning the first element
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(define disclose (fn (arr) (first (get arr :ravel))))
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; ============================================================
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; Array accessors
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; ============================================================
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(define array-rank (fn (arr) (len (get arr :shape))))
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(define scalar? (fn (arr) (= (len (get arr :shape)) 0)))
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(define array-ref (fn (arr i) (nth (get arr :ravel) i)))
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; ============================================================
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; System variables
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; ============================================================
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(define apl-io 1)
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; ============================================================
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; Broadcast engine
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; ============================================================
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(define
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broadcast-monadic
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(fn (f arr) (make-array (get arr :shape) (map f (get arr :ravel)))))
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(define
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broadcast-dyadic
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(fn
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(f a b)
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(cond
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((and (scalar? a) (scalar? b))
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(apl-scalar (f (first (get a :ravel)) (first (get b :ravel)))))
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((scalar? a)
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(let
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((sv (first (get a :ravel))))
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(make-array
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(get b :shape)
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(map (fn (x) (f sv x)) (get b :ravel)))))
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((scalar? b)
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(let
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((sv (first (get b :ravel))))
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(make-array
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(get a :shape)
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(map (fn (x) (f x sv)) (get a :ravel)))))
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(else
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(if
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(equal? (get a :shape) (get b :shape))
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(make-array (get a :shape) (map f (get a :ravel) (get b :ravel)))
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(error "length error: shape mismatch"))))))
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; ============================================================
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; Arithmetic primitives
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; ============================================================
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; Monadic + : identity
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(define apl-plus-m (fn (a) (broadcast-monadic (fn (x) x) a)))
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; Dyadic +
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(define apl-add (fn (a b) (broadcast-dyadic (fn (x y) (+ x y)) a b)))
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; Monadic - : negate
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(define apl-neg-m (fn (a) (broadcast-monadic (fn (x) (- 0 x)) a)))
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; Dyadic -
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(define apl-sub (fn (a b) (broadcast-dyadic (fn (x y) (- x y)) a b)))
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; Monadic × : signum
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(define
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apl-signum
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(fn
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(a)
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(broadcast-monadic
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(fn (x) (cond ((> x 0) 1) ((< x 0) -1) (else 0)))
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a)))
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; Dyadic ×
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(define apl-mul (fn (a b) (broadcast-dyadic (fn (x y) (* x y)) a b)))
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; Monadic ÷ : reciprocal
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(define apl-recip (fn (a) (broadcast-monadic (fn (x) (/ 1 x)) a)))
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; Dyadic ÷
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(define apl-div (fn (a b) (broadcast-dyadic (fn (x y) (/ x y)) a b)))
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; Monadic ⌈ : ceiling
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(define apl-ceil (fn (a) (broadcast-monadic (fn (x) (ceil x)) a)))
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; Dyadic ⌈ : max
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(define
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apl-max
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(fn (a b) (broadcast-dyadic (fn (x y) (if (>= x y) x y)) a b)))
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; Monadic ⌊ : floor
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(define apl-floor (fn (a) (broadcast-monadic (fn (x) (floor x)) a)))
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; Dyadic ⌊ : min
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(define
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apl-min
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(fn (a b) (broadcast-dyadic (fn (x y) (if (<= x y) x y)) a b)))
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; Monadic * : e^x
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(define apl-exp (fn (a) (broadcast-monadic (fn (x) (exp x)) a)))
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; Dyadic * : power
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(define apl-pow (fn (a b) (broadcast-dyadic (fn (x y) (pow x y)) a b)))
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; Monadic ⍟ : natural log
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(define apl-ln (fn (a) (broadcast-monadic (fn (x) (log x)) a)))
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; Dyadic ⍟ : log base (a⍟b = log base a of b)
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(define
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apl-log
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(fn (a b) (broadcast-dyadic (fn (x y) (/ (log y) (log x))) a b)))
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; Monadic | : absolute value
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(define
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apl-abs
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(fn (a) (broadcast-monadic (fn (x) (if (< x 0) (- 0 x) x)) a)))
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; Dyadic | : modulo (a|b = b mod a)
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(define
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apl-mod
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(fn
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(a b)
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(broadcast-dyadic
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(fn (x y) (if (= x 0) y (- y (* x (floor (/ y x))))))
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a
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b)))
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; Monadic ! : factorial
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(define
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apl-fact
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(fn
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(a)
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(broadcast-monadic
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(fn
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(n)
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(let
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((loop nil))
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(begin
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(set!
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loop
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(fn (i acc) (if (> i n) acc (loop (+ i 1) (* acc i)))))
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(loop 1 1))))
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a)))
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; Dyadic ! : binomial coefficient n!k (a=n, b=k => a choose b)
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(define
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apl-binomial
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(fn
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(a b)
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(broadcast-dyadic
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(fn
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(n k)
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(let
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((loop nil))
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(begin
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(set!
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loop
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(fn
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(i num den)
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(if
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(> i k)
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(/ num den)
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(loop (+ i 1) (* num (- (+ n 1) i)) (* den i)))))
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(loop 1 1 1))))
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a
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b)))
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; Monadic ○ : pi times x
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(define
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apl-pi-times
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(fn (a) (broadcast-monadic (fn (x) (* 3.14159 x)) a)))
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; Dyadic ○ : trig functions (a○b, a=code, b=value)
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(define
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apl-trig
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(fn
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(a b)
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(broadcast-dyadic
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(fn
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(n x)
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(cond
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((= n 0) (pow (- 1 (* x x)) 0.5))
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((= n 1) (sin x))
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((= n 2) (cos x))
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((= n 3) (tan x))
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((= n -1) (asin x))
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((= n -2) (acos x))
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((= n -3) (atan x))
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(else (error "circle: unsupported trig code"))))
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a
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b)))
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; ============================================================
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; Comparison primitives (return 0 or 1)
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; ============================================================
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(define
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apl-lt
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(fn (a b) (broadcast-dyadic (fn (x y) (if (< x y) 1 0)) a b)))
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(define
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apl-le
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(fn (a b) (broadcast-dyadic (fn (x y) (if (<= x y) 1 0)) a b)))
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(define
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apl-eq
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(fn (a b) (broadcast-dyadic (fn (x y) (if (= x y) 1 0)) a b)))
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(define
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apl-ge
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(fn (a b) (broadcast-dyadic (fn (x y) (if (>= x y) 1 0)) a b)))
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(define
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apl-gt
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(fn (a b) (broadcast-dyadic (fn (x y) (if (> x y) 1 0)) a b)))
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(define
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apl-ne
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(fn (a b) (broadcast-dyadic (fn (x y) (if (= x y) 0 1)) a b)))
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; ============================================================
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; Logical primitives
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; ============================================================
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; Monadic ~ : logical not
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(define
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apl-not
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(fn (a) (broadcast-monadic (fn (x) (if (= x 0) 1 0)) a)))
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; Dyadic ∧ : logical and
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(define
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apl-and
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(fn
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(a b)
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(broadcast-dyadic
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(fn (x y) (if (and (not (= x 0)) (not (= y 0))) 1 0))
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a
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b)))
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; Dyadic ∨ : logical or
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(define
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apl-or
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(fn
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(a b)
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(broadcast-dyadic
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(fn (x y) (if (or (not (= x 0)) (not (= y 0))) 1 0))
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a
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b)))
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; Dyadic ⍱ : logical nor
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(define
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apl-nor
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(fn
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(a b)
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(broadcast-dyadic
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(fn (x y) (if (or (not (= x 0)) (not (= y 0))) 0 1))
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a
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b)))
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; Dyadic ⍲ : logical nand
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(define
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apl-nand
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(fn
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(a b)
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(broadcast-dyadic
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(fn (x y) (if (and (not (= x 0)) (not (= y 0))) 0 1))
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a
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b)))
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; ============================================================
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; Shape primitives
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; ============================================================
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; Monadic ⍴ : shape — returns shape as a vector array
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(define apl-shape (fn (arr) (apl-vector (get arr :shape))))
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; Monadic , : ravel — returns a rank-1 vector of all elements
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(define apl-ravel (fn (arr) (apl-vector (get arr :ravel))))
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; Monadic ≢ : tally — first dimension (1 for scalar)
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(define
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apl-tally
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(fn
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(arr)
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(if
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(scalar? arr)
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(apl-scalar 1)
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(apl-scalar (first (get arr :shape))))))
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; Monadic ≡ : depth
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; simple number/string value → 0
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; array containing only non-arrays → 0
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; array containing arrays → 1 + max depth of elements
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(define
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apl-depth
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(fn
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(arr)
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(define item-depth nil)
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(set!
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item-depth
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(fn
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(v)
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(if
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(and
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(dict? v)
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(not (= nil (get v :shape nil)))
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(not (= nil (get v :ravel nil))))
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(+ 1 (first (get (apl-depth v) :ravel)))
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0)))
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(let
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((depths (map item-depth (get arr :ravel))))
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(apl-scalar (reduce (fn (a b) (if (> a b) a b)) 0 depths)))))
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; Monadic ⍳ : iota — vector 1..n (with ⎕IO=1)
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(define
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apl-iota
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(fn
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(n-arr)
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(let
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((n (first (get n-arr :ravel))) (build nil))
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(begin
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(set!
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build
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(fn (i acc) (if (< i 1) acc (build (- i 1) (cons i acc)))))
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(apl-vector (build n (list)))))))
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(define
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apl-strides
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(fn
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(shape)
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(map
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(fn (i) (reduce * 1 (drop shape (+ i 1))))
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(range 0 (len shape)))))
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(define
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apl-flat->multi
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(fn
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(flat shape strides)
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(map
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(fn (i) (mod (floor (/ flat (nth strides i))) (nth shape i)))
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(range 0 (len shape)))))
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(define
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apl-multi->flat
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(fn (coords strides) (reduce + 0 (map * coords strides))))
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(define
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apl-reshape
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(fn
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(shape-arr data-arr)
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(let
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((new-shape (if (scalar? shape-arr) (list (disclose shape-arr)) (get shape-arr :ravel)))
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(src-ravel
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(if
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(scalar? data-arr)
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(list (disclose data-arr))
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(get data-arr :ravel))))
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(let
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((new-size (reduce * 1 new-shape)) (src-len (len src-ravel)))
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(let
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((new-ravel (if (= new-size 0) (list) (if (= src-len 0) (map (fn (i) 0) (range 0 new-size)) (map (fn (i) (nth src-ravel (mod i src-len))) (range 0 new-size))))))
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(make-array new-shape new-ravel))))))
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(define
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apl-transpose
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(fn
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(arr)
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(let
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((shape (get arr :shape)) (ravel (get arr :ravel)))
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(if
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(< (len shape) 2)
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arr
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(let
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((new-shape (reverse shape)) (strides (apl-strides shape)))
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(let
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((new-strides (apl-strides new-shape)) (new-size (len ravel)))
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(make-array
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new-shape
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(map
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(fn
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(new-flat)
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(let
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((new-coords (apl-flat->multi new-flat new-shape new-strides)))
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(nth
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ravel
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(apl-multi->flat (reverse new-coords) strides))))
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(range 0 new-size)))))))))
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(define
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apl-transpose-dyadic
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(fn
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(perm-arr data-arr)
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(let
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((perm (map (fn (p) (- p apl-io)) (get perm-arr :ravel)))
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(shape (get data-arr :shape))
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(ravel (get data-arr :ravel)))
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(let
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((new-shape (map (fn (k) (nth shape k)) perm))
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(strides (apl-strides shape)))
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(let
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((inv-perm (map (fn (j) (index-of perm j)) (range 0 (len perm))))
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(new-strides (apl-strides new-shape))
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(new-size (len ravel)))
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(make-array
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new-shape
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(map
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(fn
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(new-flat)
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(let
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((new-coords (apl-flat->multi new-flat new-shape new-strides)))
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(let
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((old-coords (map (fn (i) (nth new-coords (nth inv-perm i))) (range 0 (len shape)))))
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(nth ravel (apl-multi->flat old-coords strides)))))
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(range 0 new-size))))))))
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