Jip J. Dekker
fad1b07018
git-subtree-dir: software/minizinc git-subtree-split: 4f10c82056ffcb1041d7ffef29d77a7eef92cf76
311 lines
15 KiB
MiniZinc
311 lines
15 KiB
MiniZinc
/***
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@groupdef stdlib.compare Comparison Builtins
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These builtins implement comparison operations.
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*/
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/** @group stdlib.compare Return if \a x is less than \a y */
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function bool: '<'( $T: x, $T: y);
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/** @group stdlib.compare Return if \a x is less than \a y */
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function var bool: '<'(var $T: x,var $T: y);
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/** @group stdlib.compare Weak comparison: true iff either \a x or \a y is absent, or both
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occur and the value of \a x is less than the value of \a y. */
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function var bool: '<'(var opt int: x, var opt int: y) = absent(x) \/ absent(y) \/ deopt(x) < deopt(y);
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/** @group stdlib.compare Weak comparison: true iff either \a x or \a y is absent, or both
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occur and the value of \a x is less than the value of \a y. */
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function bool: '<'(opt int: x, opt int: y) = absent(x) \/ absent(y) \/ deopt(x) < deopt(y);
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/** @group stdlib.arithmetic Weak comparison: true iff either \a x or \a y is absent, or both
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occur and the value of \a x is less than the value of \a y. */
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function var bool: '<'(var opt float: x, var opt float: y) = absent(x) \/ absent(y) \/ deopt(x) < deopt(y);
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/** @group stdlib.arithmetic Weak comparison: true iff either \a x or \a y is absent, or both
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occur and the value of \a x is less than the value of \a y. */
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function bool: '<'(opt float: x, opt float: y) = absent(x) \/ absent(y) \/ deopt(x) < deopt(y);
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/** @group stdlib.compare Return if \a x is greater than \a y */
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function bool: '>'( $T: x, $T: y);
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/** @group stdlib.compare Return if \a x is greater than \a y */
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function var bool: '>'(var $T: x,var $T: y);
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/** @group stdlib.compare Weak comparison: true iff either \a x or \a y is absent, or both
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occur and the value of \a x is greater than the value of \a y. */
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function var bool: '>'(var opt int: x, var opt int: y) = absent(x) \/ absent(y) \/ deopt(x) > deopt(y);
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/** @group stdlib.compare Weak comparison: true iff either \a x or \a y is absent, or both
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occur and the value of \a x is greater than the value of \a y. */
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function bool: '>'(opt int: x, opt int: y) = absent(x) \/ absent(y) \/ deopt(x) > deopt(y);
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/** @group stdlib.arithmetic Weak comparison: true iff either \a x or \a y is absent, or both
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occur and the value of \a x is greater than the value of \a y. */
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function var bool: '>'(var opt float: x, var opt float: y) = absent(x) \/ absent(y) \/ deopt(x) > deopt(y);
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/** @group stdlib.arithmetic Weak comparison: true iff either \a x or \a y is absent, or both
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occur and the value of \a x is greater than the value of \a y. */
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function bool: '>'(opt float: x, opt float: y) = absent(x) \/ absent(y) \/ deopt(x) > deopt(y);
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/** @group stdlib.compare Return if \a x is less than or equal to \a y */
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function bool: '<='( $T: x, $T: y);
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/** @group stdlib.compare Return if \a x is less than or equal to \a y */
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function var bool: '<='(var $T: x, var $T: y);
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/** @group stdlib.compare Weak comparison: true iff either \a x or \a y is absent, or both
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occur and the value of \a x is less than or equal to the value of \a y. */
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function var bool: '<='(var opt int: x, var opt int: y) = absent(x) \/ absent(y) \/ deopt(x) <= deopt(y);
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/** @group stdlib.compare Weak comparison: true iff either \a x or \a y is absent, or both
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occur and the value of \a x is less than or equal to the value of \a y. */
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function bool: '<='(opt int: x, opt int: y) = absent(x) \/ absent(y) \/ deopt(x) <= deopt(y);
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/** @group stdlib.arithmetic Weak comparison: true iff either \a x or \a y is absent, or both
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occur and the value of \a x is less than or equal to the value of \a y. */
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function var bool: '<='(var opt float: x, var opt float: y) = absent(x) \/ absent(y) \/ deopt(x) <= deopt(y);
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/** @group stdlib.arithmetic Weak comparison: true iff either \a x or \a y is absent, or both
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occur and the value of \a x is less than or equal to the value of \a y. */
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function bool: '<='(opt float: x, opt float: y) = absent(x) \/ absent(y) \/ deopt(x) <= deopt(y);
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/** @group stdlib.compare Return if \a x is greater than or equal to \a y */
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function bool: '>='( $T: x, $T: y);
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/** @group stdlib.compare Return if \a x is greater than or equal to \a y */
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function var bool: '>='(var $T: x,var $T: y);
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/** @group stdlib.compare Weak comparison: true iff either \a x or \a y is absent, or both
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occur and the value of \a x is greater than or equal to the value of \a y. */
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function var bool: '>='(var opt int: x, var opt int: y) = absent(x) \/ absent(y) \/ deopt(x) >= deopt(y);
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/** @group stdlib.compare Weak comparison: true iff either \a x or \a y is absent, or both
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occur and the value of \a x is greater than or equal to the value of \a y. */
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function bool: '>='(opt int: x, opt int: y) = absent(x) \/ absent(y) \/ deopt(x) >= deopt(y);
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/** @group stdlib.arithmetic Weak comparison: true iff either \a x or \a y is absent, or both
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occur and the value of \a x is greater than or equal to the value of \a y. */
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function var bool: '>='(var opt float: x, var opt float: y) = absent(x) \/ absent(y) \/ deopt(x) >= deopt(y);
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/** @group stdlib.arithmetic Weak comparison: true iff either \a x or \a y is absent, or both
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occur and the value of \a x is greater than or equal to the value of \a y. */
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function bool: '>='(opt float: x, opt float: y) = absent(x) \/ absent(y) \/ deopt(x) >= deopt(y);
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/** @group stdlib.compare Return if \a x is equal to \a y */
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function bool: '='( $T: x, $T: y);
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/** @group stdlib.compare Return if \a x is equal to \a y */
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function bool: '='(opt $T: x, opt $T: y) =
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absent(x) /\ absent(y) \/ occurs(x) /\ occurs(y) /\ deopt(x) = deopt(y);
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/** @group stdlib.compare Return if \a x is equal to \a y */
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function var bool: '='(var $T: x,var $T: y);
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/** @group stdlib.compare Return if \a x is equal to \a y */
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function var bool: '='(var opt $T: x,var opt $T: y);
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/** @group stdlib.compare Return if \a x is not equal to \a y */
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function bool: '!='( $T: x, $T: y);
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/** @group stdlib.compare Return if \a x is not equal to \a y */
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function bool: '!='(opt $T: x, opt $T: y) = not (x = y);
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/** @group stdlib.compare Return if \a x is not equal to \a y */
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function var bool: '!='(var $T: x, var $T: y);
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/** @group stdlib.compare Return if \a x is not equal to \a y */
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function var bool: '!='(var opt $T: x, var opt $T: y);
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% Special case comparison operators for integer variable and float constant
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function var bool: '<='(var int: x, float: y) = (x <= floor(y));
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function var bool: '>='(var int: x, float: y) = (x >= ceil(y));
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function var bool: '<='(float: x, var int: y) = (y >= ceil(x));
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function var bool: '>='(float: x, var int: y) = (y <= floor(x));
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function var bool: '<'(var int: x, float: y) = (x <= ceil(y)-1);
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function var bool: '>'(float: x, var int: y) = (y <= ceil(x)-1);
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function var bool: '>'(var int: x, float: y) = (x >= floor(y)+1);
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function var bool: '<'(float: x, var int: y) = (y >= floor(x)+1);
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function var bool: '='(var int: x, float: y) =
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if ceil(y)=floor(y) then x=ceil(y) else false endif;
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function var bool: '='(float: x, var int: y) =
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if ceil(x)=floor(x) then y=ceil(x) else false endif;
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function var bool: '!='(var int: x, float: y) =
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if ceil(y)=floor(y) then x != ceil(y) else true endif;
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function var bool: '!='(float: x, var int: y) =
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if ceil(x)=floor(x) then y != ceil(x) else true endif;
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function bool: '<='(int: x, float: y) = (x <= floor(y));
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function bool: '>='(int: x, float: y) = (x >= ceil(y));
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function bool: '<='(float: x, int: y) = (y >= ceil(x));
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function bool: '>='(float: x, int: y) = (y <= floor(x));
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function bool: '<'(int: x, float: y) = (x <= ceil(y)-1);
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function bool: '>'(float: x, int: y) = (y <= ceil(x)-1);
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function bool: '>'(int: x, float: y) = (x >= floor(y)+1);
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function bool: '<'(float: x, int: y) = (y >= floor(x)+1);
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function bool: '='(int: x, float: y) =
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if ceil(y)=floor(y) then x=ceil(y) else false endif;
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function bool: '='(float: x, int: y) =
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if ceil(x)=floor(x) then y=ceil(x) else false endif;
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function bool: '!='(int: x, float: y) =
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if ceil(y)=floor(y) then x != ceil(y) else true endif;
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function bool: '!='(float: x, int: y) =
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if ceil(x)=floor(x) then y != ceil(x) else true endif;
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/** @group stdlib.compare Return if array \a x is lexicographically smaller than array \a y */
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function bool: '<'(array[$U] of $T: x,array[$U] of $T: y);
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/** @group stdlib.compare Return if array \a x is lexicographically smaller than array \a y */
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function var bool: '<'(array[$U] of var $T: x,array[$U] of var $T: y);
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/** @group stdlib.compare Return if array \a x is lexicographically greater than array \a y */
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function bool: '>'(array[$U] of $T: x,array[$U] of $T: y);
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/** @group stdlib.compare Return if array \a x is lexicographically greater than array \a y */
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function var bool: '>'(array[$U] of var $T: x,array[$U] of var $T: y);
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/** @group stdlib.compare Return if array \a x is lexicographically smaller than or equal to array \a y */
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function bool: '<='(array[$U] of $T: x,array[$U] of $T: y);
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/** @group stdlib.compare Return if array \a x is lexicographically smaller than or equal to array \a y */
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function var bool: '<='(array[$U] of var $T: x,array[$U] of var $T: y);
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/** @group stdlib.compare Return if array \a x is lexicographically greater than or equal to array \a y */
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function bool: '>='(array[$U] of $T: x,array[$U] of $T: y);
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function var bool: '>='(array[$U] of var $T: x,array[$U] of var $T: y);
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/** @group stdlib.compare Return if array \a x is equal to array \a y */
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function bool: '='(array[$T] of int: x,array[$T] of int: y) =
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let {
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array[int] of int: xx = array1d(x);
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array[int] of int: yy = array1d(y);
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} in
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assert(index_sets_agree(x,y), "array index sets do not match",
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forall (i in index_set(xx)) (xx[i]=yy[i])
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);
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/** @group stdlib.compare Return if array \a x is equal to array \a y */
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function var bool: '='(array[$T] of var int: x,array[$T] of var int: y) =
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let {
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array[int] of var int: xx = array1d(x);
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array[int] of var int: yy = array1d(y);
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} in
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assert(index_sets_agree(x,y), "array index sets do not match",
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forall (i in index_set(xx)) (xx[i]=yy[i])
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);
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/** @group stdlib.compare Return if array \a x is equal to array \a y */
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function bool: '='(array[$T] of bool: x,array[$T] of bool: y) =
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let {
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array[int] of bool: xx = array1d(x);
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array[int] of bool: yy = array1d(y);
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} in
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assert(index_sets_agree(x,y), "array index sets do not match",
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forall (i in index_set(xx)) (xx[i]=yy[i])
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);
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/** @group stdlib.compare Return if array \a x is equal to array \a y */
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function var bool: '='(array[$T] of var bool: x,array[$T] of var bool: y) =
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let {
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array[int] of var bool: xx = array1d(x);
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array[int] of var bool: yy = array1d(y);
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} in
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assert(index_sets_agree(x,y), "array index sets do not match",
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forall (i in index_set(xx)) (xx[i]=yy[i])
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);
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/** @group stdlib.compare Return if array \a x is equal to array \a y */
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function bool: '='(array[$T] of set of int: x,array[$T] of set of int: y) =
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let {
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array[int] of set of int: xx = array1d(x);
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array[int] of set of int: yy = array1d(y);
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} in
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assert(index_sets_agree(x,y), "array index sets do not match",
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forall (i in index_set(xx)) (xx[i]=yy[i])
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);
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/** @group stdlib.compare Return if array \a x is equal to array \a y */
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function var bool: '='(array[$T] of var set of int: x,array[$T] of var set of int: y) =
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let {
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array[int] of var set of int: xx = array1d(x);
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array[int] of var set of int: yy = array1d(y);
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} in
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assert(index_sets_agree(x,y), "array index sets do not match",
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forall (i in index_set(xx)) (xx[i]=yy[i])
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);
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/** @group stdlib.compare Return if array \a x is equal to array \a y */
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function bool: '='(array[$T] of float: x,array[$T] of float: y) =
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let {
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array[int] of float: xx = array1d(x);
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array[int] of float: yy = array1d(y);
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} in
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assert(index_sets_agree(x,y), "array index sets do not match",
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forall (i in index_set(xx)) (xx[i]=yy[i])
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);
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/** @group stdlib.compare Return if array \a x is equal to array \a y */
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function var bool: '='(array[$T] of var float: x,array[$T] of var float: y) =
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let {
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array[int] of var float: xx = array1d(x);
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array[int] of var float: yy = array1d(y);
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} in
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assert(index_sets_agree(x,y), "array index sets do not match",
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forall (i in index_set(xx)) (xx[i]=yy[i])
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);
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/** @group stdlib.compare Return if array \a x is not equal to array \a y */
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function bool: '!='(array[$T] of int: x,array[$T] of int: y) =
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let {
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array[int] of int: xx = array1d(x);
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array[int] of int: yy = array1d(y);
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} in
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assert(index_sets_agree(x,y), "array index sets do not match",
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exists (i in index_set(xx)) (xx[i]!=yy[i])
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);
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/** @group stdlib.compare Return if array \a x is not equal to array \a y */
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function var bool: '!='(array[$T] of var int: x,array[$T] of var int: y) =
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let {
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array[int] of var int: xx = array1d(x);
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array[int] of var int: yy = array1d(y);
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} in
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assert(index_sets_agree(x,y), "array index sets do not match",
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exists (i in index_set(xx)) (xx[i]!=yy[i])
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);
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/** @group stdlib.compare Return if array \a x is not equal to array \a y */
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function bool: '!='(array[$T] of bool: x,array[$T] of bool: y) =
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let {
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array[int] of bool: xx = array1d(x);
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array[int] of bool: yy = array1d(y);
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} in
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assert(index_sets_agree(x,y), "array index sets do not match",
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exists (i in index_set(xx)) (xx[i]!=yy[i])
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);
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/** @group stdlib.compare Return if array \a x is not equal to array \a y */
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function var bool: '!='(array[$T] of var bool: x,array[$T] of var bool: y) =
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let {
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array[int] of var bool: xx = array1d(x);
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array[int] of var bool: yy = array1d(y);
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} in
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assert(index_sets_agree(x,y), "array index sets do not match",
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exists (i in index_set(xx)) (xx[i]!=yy[i])
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);
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/** @group stdlib.compare Return if array \a x is not equal to array \a y */
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function bool: '!='(array[$T] of set of int: x,array[$T] of set of int: y) =
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let {
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array[int] of set of int: xx = array1d(x);
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array[int] of set of int: yy = array1d(y);
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} in
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assert(index_sets_agree(x,y), "array index sets do not match",
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exists (i in index_set(xx)) (xx[i]!=yy[i])
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);
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/** @group stdlib.compare Return if array \a x is not equal to array \a y */
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function var bool: '!='(array[$T] of var set of int: x,array[$T] of var set of int: y) =
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let {
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array[int] of var set of int: xx = array1d(x);
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array[int] of var set of int: yy = array1d(y);
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} in
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assert(index_sets_agree(x,y), "array index sets do not match",
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exists (i in index_set(xx)) (xx[i]!=yy[i])
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);
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/** @group stdlib.compare Return if array \a x is not equal to array \a y */
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function bool: '!='(array[$T] of float: x,array[$T] of float: y) =
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let {
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array[int] of float: xx = array1d(x);
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array[int] of float: yy = array1d(y);
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} in
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assert(index_sets_agree(x,y), "array index sets do not match",
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exists (i in index_set(xx)) (xx[i]!=yy[i])
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);
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/** @group stdlib.compare Return if array \a x is not equal to array \a y */
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function var bool: '!='(array[$T] of var float: x,array[$T] of var float: y) =
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let {
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array[int] of var float: xx = array1d(x);
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array[int] of var float: yy = array1d(y);
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} in
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assert(index_sets_agree(x,y), "array index sets do not match",
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exists (i in index_set(xx)) (xx[i]!=yy[i])
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);
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