factor/basis/math/vectors/vectors.factor

! Copyright (C) 2005, 2009 Slava Pestov.
! See http://factorcode.org/license.txt for BSD license.
USING: arrays alien.c-types kernel sequences math math.functions
hints math.order math.libm fry combinators byte-arrays accessors ;
QUALIFIED-WITH: alien.c-types c
IN: math.vectors

GENERIC: element-type ( obj -- c-type )

: vneg ( u -- v ) [ neg ] map ;

: v+n ( u n -- v ) [ + ] curry map ;
: n+v ( n u -- v ) [ + ] with map ;
: v-n ( u n -- v ) [ - ] curry map ;
: n-v ( n u -- v ) [ - ] with map ;

: v*n ( u n -- v ) [ * ] curry map ;
: n*v ( n u -- v ) [ * ] with map ;
: v/n ( u n -- v ) [ / ] curry map ;
: n/v ( n u -- v ) [ / ] with map ;

: v+   ( u v -- w ) [ + ] 2map ;
: v-   ( u v -- w ) [ - ] 2map ;
: [v-] ( u v -- w ) [ [-] ] 2map ;
: v*   ( u v -- w ) [ * ] 2map ;
: v/   ( u v -- w ) [ / ] 2map ;
: vmax ( u v -- w ) [ max ] 2map ;
: vmin ( u v -- w ) [ min ] 2map ;

: v+- ( u v -- w )
    [ t ] 2dip
    [ [ not ] 2dip pick [ + ] [ - ] if ] 2map
    nip ;

<PRIVATE

: 2saturate-map ( u v quot -- w )
    pick element-type '[ @ _ c-type-clamp ] 2map ; inline

PRIVATE>

: vs+ ( u v -- w ) [ + ] 2saturate-map ;
: vs- ( u v -- w ) [ - ] 2saturate-map ;
: vs* ( u v -- w ) [ * ] 2saturate-map ;

: vabs ( u -- v ) [ abs ] map ;
: vsqrt ( u -- v ) [ >float fsqrt ] map ;

<PRIVATE

: fp-bitwise-op ( x y seq quot -- z )
    swap element-type {
        { c:double [ [ [ double>bits ] bi@ ] dip call bits>double ] }
        { c:float [ [ [ float>bits ] bi@ ] dip call bits>float ] }
        [ drop call ]
    } case ; inline

: fp-bitwise-unary ( x seq quot -- z )
    swap element-type {
        { c:double [ [ double>bits ] dip call bits>double ] }
        { c:float  [ [ float>bits  ] dip call bits>float  ] }
        [ drop call ]
    } case ; inline

: bitandn ( x y -- z ) [ bitnot ] dip bitand ; inline

GENERIC: new-underlying ( underlying seq -- seq' )

: change-underlying ( seq quot -- seq' )
    '[ underlying>> @ ] keep new-underlying ; inline

PRIVATE>

: vbitand ( u v -- w ) over '[ _ [ bitand ] fp-bitwise-op ] 2map ;
: vbitandn ( u v -- w ) over '[ _ [ bitandn ] fp-bitwise-op ] 2map ;
: vbitor ( u v -- w ) over '[ _ [ bitor ] fp-bitwise-op ] 2map ;
: vbitxor ( u v -- w ) over '[ _ [ bitxor ] fp-bitwise-op ] 2map ;
: vbitnot ( u -- w ) dup '[ _ [ bitnot ] fp-bitwise-unary ] map ;

: vshuffle ( u perm -- v ) swap [ nths ] keep like ;

: vlshift ( u n -- w ) '[ _ shift ] map ;
: vrshift ( u n -- w ) neg '[ _ shift ] map ;

: hlshift ( u n -- w ) '[ _ <byte-array> prepend 16 head ] change-underlying ;
: hrshift ( u n -- w ) '[ _ <byte-array> append 16 tail* ] change-underlying ;

: vand ( u v -- w ) [ and ] 2map ;
: vor  ( u v -- w ) [ or  ] 2map ;
: vxor ( u v -- w ) [ xor ] 2map ;
: vnot ( u -- w )   [ not ] map ;

: v<  ( u v -- w ) [ <   ] { } 2map-as ;
: v<= ( u v -- w ) [ <=  ] { } 2map-as ;
: v>= ( u v -- w ) [ >=  ] { } 2map-as ;
: v>  ( u v -- w ) [ >   ] { } 2map-as ;
: vunordered? ( u v -- w ) [ unordered? ] { } 2map-as ;
: v=  ( u v -- w ) [ =   ] { } 2map-as ;

: v?   ( ? true false -- w ) [ ? ] pick 3map-as ;

: vmask ( u ? -- u' ) swap dup dup vbitxor v? ;

: vfloor    ( u -- v ) [ floor ] map ;
: vceiling  ( u -- v ) [ ceiling ] map ;
: vtruncate ( u -- v ) [ truncate ] map ;

: vsupremum ( seq -- vmax ) [ ] [ vmax ] map-reduce ; 
: vinfimum ( seq -- vmin ) [ ] [ vmin ] map-reduce ; 

: v. ( u v -- x ) [ conjugate * ] [ + ] 2map-reduce ;
: norm-sq ( v -- x ) [ absq ] [ + ] map-reduce ;
: norm ( v -- x ) norm-sq sqrt ;
: normalize ( u -- v ) dup norm v/n ;

: distance ( u v -- x ) [ - absq ] [ + ] 2map-reduce sqrt ;

: set-axis ( u v axis -- w )
    [ [ zero? 2over ? ] dip swap nth ] map-index 2nip ;

<PRIVATE

: 2tetra@ ( p q r s t u v w quot -- )
    dup [ [ 2bi@ ] curry 4dip ] dip 2bi@ ; inline

PRIVATE>

: trilerp ( aaa baa aba bba aab bab abb bbb {t,u,v} -- a_tuv )
    [ first lerp ] [ second lerp ] [ third lerp ] tri-curry
    [ 2tetra@ ] [ 2bi@ ] [ call ] tri* ;

: bilerp ( aa ba ab bb {t,u} -- a_tu )
    [ first lerp ] [ second lerp ] bi-curry
    [ 2bi@ ] [ call ] bi* ;

: vlerp ( a b t -- a_t )
    [ lerp ] 3map ;

: vnlerp ( a b t -- a_t )
    [ lerp ] curry 2map ;

: vbilerp ( aa ba ab bb {t,u} -- a_tu )
    [ first vnlerp ] [ second vnlerp ] bi-curry
    [ 2bi@ ] [ call ] bi* ;

: v~ ( a b epsilon -- ? )
    [ ~ ] curry 2all? ;

HINTS: vneg { array } ;
HINTS: norm-sq { array } ;
HINTS: norm { array } ;
HINTS: normalize { array } ;
HINTS: distance { array array } ;

HINTS: n*v { object array } ;
HINTS: v*n { array object } ;
HINTS: n/v { array } ;
HINTS: v/n { array object } ;

HINTS: v+ { array array } ;
HINTS: v- { array array } ;
HINTS: v* { array array } ;
HINTS: v/ { array array } ;
HINTS: vmax { array array } ;
HINTS: vmin { array array } ;
HINTS: v. { array array } ;

HINTS: vlerp { array array array } ;
HINTS: vnlerp { array array object } ;

HINTS: bilerp { object object object object array } ;
HINTS: trilerp { object object object object object object object object array } ;