USING: kernel math math.functions math.derivatives accessors words generalizations sequences generic fry locals compiler.units continuations quotations combinators combinators.smart macros effects ; IN: math.dual TUPLE: dual ordinary-part epsilon-part ; C: dual ! Ordinary numbers implement the dual protocol by returning ! themselves as the ordinary part, and 0 as the epsilon part. M: number ordinary-part>> ; M: number epsilon-part>> drop 0 ; : unpack-dual ( dual -- ordinary-part epsilon-part ) [ ordinary-part>> ] [ epsilon-part>> ] bi ; > length ; MACRO: ordinary-op ( word -- ) [ input-length ] keep '[ [ ordinary-part>> ] _ napply _ execute ] ; ! Takes n dual numbers o1 e1 o2 e2 ... on en and weaves their ! ordinary and epsilon parts to produce ! e1 o1 o2 ... on e2 o1 o2 ... on ... en o1 o2 ... on ! This allows a set of partial derivatives each to be evaluated ! at the same point. MACRO: duals>weave ( n -- ) dup dup dup '[ [ [ epsilon-part>> ] _ napply ] _ nkeep [ ordinary-part>> ] _ napply _ nweave ] ; MACRO: chain-rule ( word -- x ) [ input-length ] [ "derivative" word-prop ] [ input-length 1+ ] tri '[ [ _ duals>weave _ _ nspread ] sum-outputs ] ; PRIVATE> ! dual-op is similar to execute, but promotes the word to ! operate on duals. Uses the "derivative" word-prop, which ! holds a list of quotations giving the partial derivative of ! the word with respect to each of its argumets. MACRO: dual-op ( word -- ) [ ] [ input-length ] [ ] tri '[ [ _ ordinary-op ] _ nkeep _ chain-rule ] ; : define-dual-method ( word -- ) [ \ dual swap create-method ] keep '[ _ dual-op ] define ; ! Specialize math functions to operate on dual numbers. [ { sqrt exp log sin cos tan sinh cosh tanh atan } [ define-dual-method ] each ] with-compilation-unit ! Inverse methods { asin, acos, asinh, acosh, atanh } are not ! generic, so there is no way to specialize them for dual ! numbers. ! Arithmetic methods are not generic (yet?), so we have to ! define special versions of them to operate on dual numbers. : d+ ( x y -- x+y ) \ + dual-op ; : d- ( x y -- x+y ) \ - dual-op ; : d* ( x y -- x*y ) \ * dual-op ; : d/ ( x y -- x/y ) \ / dual-op ; : d^ ( x y -- x^y ) \ ^ dual-op ;