var searchIndex = {};
searchIndex["scad_generator"] = {"doc":"This crate is used to generate openscad models using rust.","items":[[3,"LinExtrudeParams","scad_generator","Parameters for the linear extrude function.",null,null],[12,"height","","",0,null],[12,"center","","",0,null],[12,"convexity","","",0,null],[12,"twist","","",0,null],[12,"slices","","",0,null],[3,"ScadObject","","An scad object which is a single scad element and can have zero or more child objects",null,null],[3,"ScadFile","","Object that stores scad objects along with global parameters for\nthe objects. Also has methods for writing the  data to files.",null,null],[4,"CircleType","","Since scad allows creation of circle like objects using either radius or diameter,\nthis enum specifies which format to use",null,null],[13,"Radius","","",1,null],[13,"Diameter","","",1,null],[4,"ScadElement","","Different kinds of scad modules and function. These are parameters\nfor `ScadObjects`.",null,null],[13,"Translate","","",2,null],[13,"Scale","","",2,null],[13,"Rotate","","",2,null],[13,"Mirror","","",2,null],[13,"LinearExtrude","","",2,null],[13,"Difference","","",2,null],[13,"Union","","",2,null],[13,"Hull","","",2,null],[13,"Intersection","","",2,null],[13,"Cube","","",2,null],[13,"Cylinder","","",2,null],[13,"Sphere","","",2,null],[13,"Cone","","",2,null],[13,"Polyhedron","","",2,null],[13,"Polygon","","",2,null],[13,"Import","","",2,null],[13,"Square","","",2,null],[11,"clone","","",1,null],[11,"clone","","",0,null],[11,"default","","",0,{"inputs":[],"output":{"name":"linextrudeparams"}}],[11,"get_code","","",0,null],[11,"clone","","",2,null],[11,"get_code","","Returns scad code for each of the elements",2,null],[11,"clone","","",3,null],[11,"new","","",3,{"inputs":[{"name":"scadelement"}],"output":{"name":"scadobject"}}],[11,"add_child","","",3,null],[11,"get_code","","Returns the scad code for the object.",3,null],[11,"is_important","","Marks the object as important. This will prepend the object code\nwith an ! which tells scad to only render that object and its children.",3,null],[11,"new","","",4,{"inputs":[],"output":{"name":"scadfile"}}],[11,"get_code","","Returns the code for the global parameters as well as all the\nchildren in the file",4,null],[11,"add_object","","",4,null],[11,"set_detail","","Sets the $fn variable for the whole file. This varibale defines  the detail\namount for cylindrical objects",4,null],[11,"write_to_file","","Writes the resulting code to a file",4,null],[0,"scad_macros","","",null,null],[5,"vec3","scad_generator::scad_macros","Utility function for creating nalgebra vectors without having\nto write `na::Vector3::new(x,y,z)`",null,{"inputs":[{"name":"f32"},{"name":"f32"},{"name":"f32"}],"output":{"name":"vector3"}}],[5,"vec2","","Utility function for creating nalgebra vectors without having\nto write `na::Vector2::new(x,y)`",null,{"inputs":[{"name":"f32"},{"name":"f32"}],"output":{"name":"vector2"}}],[8,"ScadType","scad_generator","Trait for converting from rust types to strings compatible with openscad",null,null],[10,"get_code","","",5,null],[14,"scad","","Creates an scad object with optional children",null,null],[14,"qstruct","","Used to create structs with ::new functions that set default values\nwithout having to write an impl for new. ",null,null]],"paths":[[3,"LinExtrudeParams"],[4,"CircleType"],[4,"ScadElement"],[3,"ScadObject"],[3,"ScadFile"],[8,"ScadType"]]};
searchIndex["nalgebra"] = {"doc":"# nalgebra","items":[[3,"Identity","nalgebra","Special identity matrix. All its operation are no-ops.",null,null],[3,"DMatrix","","Matrix with dimensions unknown at compile-time.",null,null],[3,"DMatrix1","","A stack-allocated dynamically sized matrix with at most one row and column.",null,null],[3,"DMatrix2","","A stack-allocated dynamically sized square or rectangular matrix with at most 2 rows and columns.",null,null],[3,"DMatrix3","","A stack-allocated dynamically sized square or rectangular matrix with at most 3 rows and columns.",null,null],[3,"DMatrix4","","A stack-allocated dynamically sized square or rectangular matrix with at most 4 rows and columns.",null,null],[3,"DMatrix5","","A stack-allocated dynamically sized square or rectangular matrix with at most 5 rows and columns.",null,null],[3,"DMatrix6","","A stack-allocated dynamically sized square or rectangular matrix with at most 6 rows and columns.",null,null],[3,"DVector","","Heap allocated, dynamically sized vector.",null,null],[12,"at","","Components of the vector. Contains as much elements as the vector dimension.",0,null],[3,"DVector1","","Stack-allocated, dynamically sized vector with a maximum size of 1.",null,null],[3,"DVector2","","Stack-allocated, dynamically sized vector with a maximum size of 2.",null,null],[3,"DVector3","","Stack-allocated, dynamically sized vector with a maximum size of 3.",null,null],[3,"DVector4","","Stack-allocated, dynamically sized vector with a maximum size of 4.",null,null],[3,"DVector5","","Stack-allocated, dynamically sized vector with a maximum size of 5.",null,null],[3,"DVector6","","Stack-allocated, dynamically sized vector with a maximum size of 6.",null,null],[3,"Isometry2","","Two dimensional **direct** isometry.",null,null],[12,"rotation","","The rotation applicable by this isometry.",1,null],[12,"translation","","The translation applicable by this isometry.",1,null],[3,"Isometry3","","Three dimensional **direct** isometry.",null,null],[12,"rotation","","The rotation applicable by this isometry.",2,null],[12,"translation","","The translation applicable by this isometry.",2,null],[3,"Similarity2","","A two-dimensional similarity transformation.",null,null],[12,"isometry","","The isometry applicable by this similarity transformation.",3,null],[3,"Similarity3","","A three-dimensional similarity transformation.",null,null],[12,"isometry","","The isometry applicable by this similarity transformation.",4,null],[3,"Matrix1","","Square matrix of dimension 1.",null,null],[12,"m11","","",5,null],[3,"Matrix2","","Square matrix of dimension 2.",null,null],[12,"m11","","",6,null],[12,"m21","","",6,null],[12,"m12","","",6,null],[12,"m22","","",6,null],[3,"Matrix3","","Square matrix of dimension 3.",null,null],[12,"m11","","",7,null],[12,"m21","","",7,null],[12,"m31","","",7,null],[12,"m12","","",7,null],[12,"m22","","",7,null],[12,"m32","","",7,null],[12,"m13","","",7,null],[12,"m23","","",7,null],[12,"m33","","",7,null],[3,"Matrix4","","Square matrix of dimension 4.",null,null],[12,"m11","","",8,null],[12,"m21","","",8,null],[12,"m31","","",8,null],[12,"m41","","",8,null],[12,"m12","","",8,null],[12,"m22","","",8,null],[12,"m32","","",8,null],[12,"m42","","",8,null],[12,"m13","","",8,null],[12,"m23","","",8,null],[12,"m33","","",8,null],[12,"m43","","",8,null],[12,"m14","","",8,null],[12,"m24","","",8,null],[12,"m34","","",8,null],[12,"m44","","",8,null],[3,"Matrix5","","Square matrix of dimension 5.",null,null],[12,"m11","","",9,null],[12,"m21","","",9,null],[12,"m31","","",9,null],[12,"m41","","",9,null],[12,"m51","","",9,null],[12,"m12","","",9,null],[12,"m22","","",9,null],[12,"m32","","",9,null],[12,"m42","","",9,null],[12,"m52","","",9,null],[12,"m13","","",9,null],[12,"m23","","",9,null],[12,"m33","","",9,null],[12,"m43","","",9,null],[12,"m53","","",9,null],[12,"m14","","",9,null],[12,"m24","","",9,null],[12,"m34","","",9,null],[12,"m44","","",9,null],[12,"m54","","",9,null],[12,"m15","","",9,null],[12,"m25","","",9,null],[12,"m35","","",9,null],[12,"m45","","",9,null],[12,"m55","","",9,null],[3,"Matrix6","","Square matrix of dimension 6.",null,null],[12,"m11","","",10,null],[12,"m21","","",10,null],[12,"m31","","",10,null],[12,"m41","","",10,null],[12,"m51","","",10,null],[12,"m61","","",10,null],[12,"m12","","",10,null],[12,"m22","","",10,null],[12,"m32","","",10,null],[12,"m42","","",10,null],[12,"m52","","",10,null],[12,"m62","","",10,null],[12,"m13","","",10,null],[12,"m23","","",10,null],[12,"m33","","",10,null],[12,"m43","","",10,null],[12,"m53","","",10,null],[12,"m63","","",10,null],[12,"m14","","",10,null],[12,"m24","","",10,null],[12,"m34","","",10,null],[12,"m44","","",10,null],[12,"m54","","",10,null],[12,"m64","","",10,null],[12,"m15","","",10,null],[12,"m25","","",10,null],[12,"m35","","",10,null],[12,"m45","","",10,null],[12,"m55","","",10,null],[12,"m65","","",10,null],[12,"m16","","",10,null],[12,"m26","","",10,null],[12,"m36","","",10,null],[12,"m46","","",10,null],[12,"m56","","",10,null],[12,"m66","","",10,null],[3,"Rotation2","","Two dimensional rotation matrix.",null,null],[3,"Rotation3","","Three dimensional rotation matrix.",null,null],[3,"Vector1","","Vector of dimension 1.",null,null],[12,"x","","First component of the vector.",11,null],[3,"Vector2","","Vector of dimension 2.",null,null],[12,"x","","First component of the vector.",12,null],[12,"y","","Second component of the vector.",12,null],[3,"Vector3","","Vector of dimension 3.",null,null],[12,"x","","First component of the vector.",13,null],[12,"y","","Second component of the vector.",13,null],[12,"z","","Third component of the vector.",13,null],[3,"Vector4","","Vector of dimension 4.",null,null],[12,"x","","First component of the vector.",14,null],[12,"y","","Second component of the vector.",14,null],[12,"z","","Third component of the vector.",14,null],[12,"w","","Fourth component of the vector.",14,null],[3,"Vector5","","Vector of dimension 5.",null,null],[12,"x","","First component of the vector.",15,null],[12,"y","","Second component of the vector.",15,null],[12,"z","","Third component of the vector.",15,null],[12,"w","","Fourth component of the vector.",15,null],[12,"a","","Fifth of the vector.",15,null],[3,"Vector6","","Vector of dimension 6.",null,null],[12,"x","","First component of the vector.",16,null],[12,"y","","Second component of the vector.",16,null],[12,"z","","Third component of the vector.",16,null],[12,"w","","Fourth component of the vector.",16,null],[12,"a","","Fifth of the vector.",16,null],[12,"b","","Sixth component of the vector.",16,null],[3,"Point1","","Point of dimension 1.",null,null],[12,"x","","First component of the point.",17,null],[3,"Point2","","Point of dimension 2.",null,null],[12,"x","","First component of the point.",18,null],[12,"y","","Second component of the point.",18,null],[3,"Point3","","Point of dimension 3.",null,null],[12,"x","","First component of the point.",19,null],[12,"y","","Second component of the point.",19,null],[12,"z","","Third component of the point.",19,null],[3,"Point4","","Point of dimension 4.",null,null],[12,"x","","First component of the point.",20,null],[12,"y","","Second component of the point.",20,null],[12,"z","","Third component of the point.",20,null],[12,"w","","Fourth component of the point.",20,null],[3,"Point5","","Point of dimension 5.",null,null],[12,"x","","First component of the point.",21,null],[12,"y","","Second component of the point.",21,null],[12,"z","","Third component of the point.",21,null],[12,"w","","Fourth component of the point.",21,null],[12,"a","","Fifth of the point.",21,null],[3,"Point6","","Point of dimension 6.",null,null],[12,"x","","First component of the point.",22,null],[12,"y","","Second component of the point.",22,null],[12,"z","","Third component of the point.",22,null],[12,"w","","Fourth component of the point.",22,null],[12,"a","","Fifth of the point.",22,null],[12,"b","","Sixth component of the point.",22,null],[3,"Perspective3","","A 3D perspective projection stored without any matrix.",null,null],[3,"PerspectiveMatrix3","","A 3D perspective projection stored as a 4D matrix.",null,null],[3,"Orthographic3","","A 3D orthographic projection stored without any matrix.",null,null],[3,"OrthographicMatrix3","","A 3D orthographic projection stored as a 4D matrix.",null,null],[3,"Quaternion","","A quaternion. See `UnitQuaternion` for a quaternion that can be used as a rotation.",null,null],[12,"w","","The scalar component of the quaternion.",23,null],[12,"i","","The first vector component of the quaternion.",23,null],[12,"j","","The second vector component of the quaternion.",23,null],[12,"k","","The third vector component of the quaternion.",23,null],[3,"UnitQuaternion","","A unit quaternion that can represent a 3D rotation.",null,null],[4,"PartialOrdering","","Result of a partial ordering.",null,null],[13,"PartialLess","","Result of a strict comparison.",24,null],[13,"PartialEqual","","Equality relationship.",24,null],[13,"PartialGreater","","Result of a strict comparison.",24,null],[13,"NotComparable","","Result of a comparison between two objects that are not comparable.",24,null],[5,"qr","","QR decomposition using Householder reflections.",null,null],[5,"householder_matrix","","Get the householder matrix corresponding to a reflexion to the hyperplane\ndefined by `vector`. It can be a reflexion contained in a subspace.",null,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"v"}],"output":{"name":"m"}}],[5,"cholesky","","Cholesky decomposition G of a square symmetric positive definite matrix A, such that A = G * G^T",null,{"inputs":[{"name":"m"}],"output":{"name":"result"}}],[5,"hessenberg","","Hessenberg\nReturns the matrix m in Hessenberg form and the corresponding similarity transformation",null,null],[5,"clamp","","Change the input value to ensure it is on the range `[min, max]`.",null,{"inputs":[{"name":"t"},{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[5,"max","","Same as `cmp::max`.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[5,"min","","Same as `cmp::min`.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[5,"inf","","Returns the infimum of `a` and `b`.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[5,"sup","","Returns the supremum of `a` and `b`.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[5,"partial_cmp","","Compare `a` and `b` using a partial ordering relation.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"partialordering"}}],[5,"partial_lt","","Returns `true` iff `a` and `b` are comparable and `a < b`.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"bool"}}],[5,"partial_le","","Returns `true` iff `a` and `b` are comparable and `a <= b`.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"bool"}}],[5,"partial_gt","","Returns `true` iff `a` and `b` are comparable and `a > b`.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"bool"}}],[5,"partial_ge","","Returns `true` iff `a` and `b` are comparable and `a >= b`.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"bool"}}],[5,"partial_min","","Return the minimum of `a` and `b` if they are comparable.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"option"}}],[5,"partial_max","","Return the maximum of `a` and `b` if they are comparable.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"option"}}],[5,"partial_clamp","","Clamp `value` between `min` and `max`. Returns `None` if `value` is not comparable to\n`min` or `max`.",null,{"inputs":[{"name":"t"},{"name":"t"},{"name":"t"}],"output":{"name":"option"}}],[5,"identity","","Create a special identity object.",null,{"inputs":[],"output":{"name":"identity"}}],[5,"zero","","Create a zero-valued value.",null,{"inputs":[],"output":{"name":"t"}}],[5,"is_zero","","Tests is a value is iqual to zero.",null,{"inputs":[{"name":"t"}],"output":{"name":"bool"}}],[5,"one","","Create a one-valued value.",null,{"inputs":[],"output":{"name":"t"}}],[5,"origin","","Returns the trivial origin of an affine space.",null,{"inputs":[],"output":{"name":"p"}}],[5,"center","","Returns the center of two points.",null,{"inputs":[{"name":"p"},{"name":"p"}],"output":{"name":"p"}}],[5,"distance","","Returns the distance between two points.",null,{"inputs":[{"name":"p"},{"name":"p"}],"output":{"name":"n"}}],[5,"distance_squared","","Returns the squared distance between two points.",null,{"inputs":[{"name":"p"},{"name":"p"}],"output":{"name":"n"}}],[5,"translation","","Gets the translation applicable by `m`.",null,{"inputs":[{"name":"m"}],"output":{"name":"v"}}],[5,"inverse_translation","","Gets the inverse translation applicable by `m`.",null,{"inputs":[{"name":"m"}],"output":{"name":"v"}}],[5,"append_translation","","Applies the translation `v` to a copy of `m`.",null,{"inputs":[{"name":"m"},{"name":"v"}],"output":{"name":"m"}}],[5,"translate","","Applies a translation to a point.",null,{"inputs":[{"name":"m"},{"name":"p"}],"output":{"name":"p"}}],[5,"inverse_translate","","Applies an inverse translation to a point.",null,{"inputs":[{"name":"m"},{"name":"p"}],"output":{"name":"p"}}],[5,"rotation","","Gets the rotation applicable by `m`.",null,{"inputs":[{"name":"m"}],"output":{"name":"v"}}],[5,"inverse_rotation","","Gets the inverse rotation applicable by `m`.",null,{"inputs":[{"name":"m"}],"output":{"name":"v"}}],[5,"append_rotation","","Applies the rotation `v` to a copy of `m`.",null,{"inputs":[{"name":"m"},{"name":"v"}],"output":{"name":"m"}}],[5,"prepend_rotation","","Pre-applies the rotation `v` to a copy of `m`.",null,{"inputs":[{"name":"m"},{"name":"v"}],"output":{"name":"m"}}],[5,"rotate","","Applies a rotation to a vector.",null,{"inputs":[{"name":"m"},{"name":"v"}],"output":{"name":"v"}}],[5,"inverse_rotate","","Applies an inverse rotation to a vector.",null,{"inputs":[{"name":"m"},{"name":"v"}],"output":{"name":"v"}}],[5,"append_rotation_wrt_point","","Rotates a copy of `m` by `amount` using `center` as the pivot point.",null,{"inputs":[{"name":"m"},{"name":"av"},{"name":"lv"}],"output":{"name":"m"}}],[5,"append_rotation_wrt_center","","Rotates a copy of `m` by `amount` using `m.translation()` as the pivot point.",null,{"inputs":[{"name":"m"},{"name":"av"}],"output":{"name":"m"}}],[5,"angle_between","","Computes the angle of the rotation needed to transfom `a` to `b`.",null,{"inputs":[{"name":"v"},{"name":"v"}],"output":{"name":"angletype"}}],[5,"rotation_between","","Computes the rotation needed to transform `a` to `b`.",null,{"inputs":[{"name":"v"},{"name":"v"}],"output":{"name":"deltarotationtype"}}],[5,"to_rotation_matrix","","Builds a rotation matrix from `r`.",null,{"inputs":[{"name":"r"}],"output":{"name":"m"}}],[5,"absolute_rotate","","Applies a rotation using the absolute values of its components.",null,{"inputs":[{"name":"m"},{"name":"v"}],"output":{"name":"v"}}],[5,"transformation","","Gets the transformation applicable by `m`.",null,{"inputs":[{"name":"m"}],"output":{"name":"t"}}],[5,"inverse_transformation","","Gets the inverse transformation applicable by `m`.",null,{"inputs":[{"name":"m"}],"output":{"name":"t"}}],[5,"append_transformation","","Gets a transformed copy of `m`.",null,{"inputs":[{"name":"m"},{"name":"t"}],"output":{"name":"m"}}],[5,"transform","","Applies a transformation to a vector.",null,{"inputs":[{"name":"m"},{"name":"v"}],"output":{"name":"v"}}],[5,"inverse_transform","","Applies an inverse transformation to a vector.",null,{"inputs":[{"name":"m"},{"name":"v"}],"output":{"name":"v"}}],[5,"dot","","Computes the dot product of two vectors.",null,{"inputs":[{"name":"v"},{"name":"v"}],"output":{"name":"n"}}],[5,"norm","","Computes the L2 norm of a vector.",null,{"inputs":[{"name":"v"}],"output":{"name":"n"}}],[5,"norm_squared","","Computes the squared L2 norm of a vector.",null,{"inputs":[{"name":"v"}],"output":{"name":"n"}}],[5,"normalize","","Gets the normalized version of a vector.",null,{"inputs":[{"name":"v"}],"output":{"name":"v"}}],[5,"determinant","","Computes the determinant of a square matrix.",null,{"inputs":[{"name":"m"}],"output":{"name":"n"}}],[5,"cross","","Computes the cross product of two vectors.",null,{"inputs":[{"name":"lv"},{"name":"lv"}],"output":{"name":"crossproducttype"}}],[5,"cross_matrix","","Given a vector, computes the matrix which, when multiplied by another vector, computes a cross\nproduct.",null,{"inputs":[{"name":"v"}],"output":{"name":"m"}}],[5,"to_homogeneous","","Converts a matrix or vector to homogeneous coordinates.",null,{"inputs":[{"name":"m"}],"output":{"name":"res"}}],[5,"from_homogeneous","","Converts a matrix or vector from homogeneous coordinates.",null,{"inputs":[{"name":"m"}],"output":{"name":"res"}}],[5,"sample_sphere","","Samples the unit sphere living on the dimension as the samples types.",null,{"inputs":[{"name":"f"}],"output":null}],[5,"approx_eq","","Tests approximate equality.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"bool"}}],[5,"approx_eq_eps","","Tests approximate equality using a custom epsilon.",null,{"inputs":[{"name":"t"},{"name":"t"},{"name":"n"}],"output":{"name":"bool"}}],[5,"abs","","Computes a component-wise absolute value.",null,{"inputs":[{"name":"m"}],"output":{"name":"res"}}],[5,"inverse","","Gets an inverted copy of a matrix.",null,{"inputs":[{"name":"m"}],"output":{"name":"option"}}],[5,"transpose","","Gets a transposed copy of a matrix.",null,{"inputs":[{"name":"m"}],"output":{"name":"m"}}],[5,"outer","","Computes the outer product of two vectors.",null,{"inputs":[{"name":"v"},{"name":"v"}],"output":{"name":"outerproducttype"}}],[5,"covariance","","Computes the covariance of a set of observations.",null,{"inputs":[{"name":"m"}],"output":{"name":"res"}}],[5,"mean","","Computes the mean of a set of observations.",null,{"inputs":[{"name":"m"}],"output":{"name":"n"}}],[5,"eigen_qr","","Computes the eigenvalues and eigenvectors of a square matrix usin the QR algorithm.",null,null],[5,"new_identity","","Construct the identity matrix for a given dimension",null,{"inputs":[{"name":"usize"}],"output":{"name":"m"}}],[5,"repeat","","Create an object by repeating a value.",null,{"inputs":[{"name":"n"}],"output":{"name":"t"}}],[5,"canonical_basis","","Computes the canonical basis for a given dimension.",null,{"inputs":[{"name":"f"}],"output":null}],[5,"orthonormal_subspace_basis","","Computes the basis of the orthonormal subspace of a given vector.",null,{"inputs":[{"name":"v"},{"name":"f"}],"output":null}],[5,"canonical_basis_element","","Gets the (0-based) i-th element of the canonical basis of V.",null,{"inputs":[{"name":"usize"}],"output":{"name":"option"}}],[5,"diagonal","","Gets the diagonal of a square matrix.",null,{"inputs":[{"name":"m"}],"output":{"name":"v"}}],[5,"dimension","","Gets the dimension an object lives in.",null,{"inputs":[],"output":{"name":"usize"}}],[5,"shape","","Gets the indexable range of an object.",null,{"inputs":[{"name":"v"}],"output":{"name":"i"}}],[5,"cast","","Converts an object from one type to another.",null,{"inputs":[{"name":"t"}],"output":{"name":"u"}}],[11,"eq","","",25,null],[11,"ne","","",25,null],[11,"clone","","",25,null],[11,"new_uninitialized","","Creates an uninitialized matrix.",25,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix"}}],[11,"from_element","","Builds a matrix filled with a given constant.",25,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"n"}],"output":{"name":"dmatrix"}}],[11,"from_row_vector","","Builds a matrix filled with the components provided by a vector.\nThe vector contains the matrix data in row-major order.\nNote that `from_column_vector` is much faster than `from_row_vector` since a `DMatrix` stores its data\nin column-major order.",25,null],[11,"from_column_vector","","Builds a matrix filled with the components provided by a vector.\nThe vector contains the matrix data in column-major order.\nNote that `from_column_vector` is much faster than `from_row_vector` since a `DMatrix` stores its data\nin column-major order.",25,null],[11,"from_row_iter","","Builds a matrix filled with the components provided by a source that may be moved into an iterator.\nThe source contains the matrix data in row-major order.\nNote that `from_column_iter` is much faster than `from_row_iter` since a `DMatrix` stores its data\nin column-major order.",25,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"i"}],"output":{"name":"dmatrix"}}],[11,"from_column_iter","","Builds a matrix filled with the components provided by a source that may be moved into an iterator.\nThe source contains the matrix data in column-major order.\nNote that `from_column_iter` is much faster than `from_row_iter` since a `DMatrix` stores its data\nin column-major order.",25,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"i"}],"output":{"name":"dmatrix"}}],[11,"from_fn","","Builds a matrix filled with the results of a function applied to each of its component coordinates.",25,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"f"}],"output":{"name":"dmatrix"}}],[11,"into_vector","","Transforms this matrix into an array. This consumes the matrix and is O(1).\nThe returned vector contains the matrix data in column-major order.",25,null],[11,"new_zeros","","Builds a matrix filled with zeros.",25,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix"}}],[11,"is_zero","","Tests if all components of the matrix are zeroes.",25,null],[11,"reset","","Set this matrix components to zero.",25,null],[11,"new_random","","Builds a matrix filled with random values.",25,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix"}}],[11,"new_ones","","Builds a matrix filled with a given constant.",25,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix"}}],[11,"nrows","","The number of row on the matrix.",25,null],[11,"ncols","","The number of columns on the matrix.",25,null],[11,"as_vector","","Gets a reference to this matrix data.\nThe returned vector contains the matrix data in column-major order.",25,null],[11,"as_mut_vector","","Gets a mutable reference to this matrix data.\nThe returned vector contains the matrix data in column-major order.",25,null],[11,"new_identity","","Builds an identity matrix.",25,{"inputs":[{"name":"usize"}],"output":{"name":"dmatrix"}}],[11,"unsafe_set","","Just like `set` without bounds checking.",25,null],[11,"unsafe_at","","Just like `at` without bounds checking.",25,null],[11,"swap","","",25,null],[11,"shape","","",25,null],[11,"index","","",25,null],[11,"index_mut","","",25,null],[11,"mul","","",25,null],[11,"mul","","",25,null],[11,"mul_assign","","",25,null],[11,"mul_assign","","",25,null],[11,"mul","","",25,null],[11,"mul","","",25,null],[11,"mul","","",0,null],[11,"mul","","",0,null],[11,"mul_assign","","",0,null],[11,"mul_assign","","",0,null],[11,"add","","",25,null],[11,"add","","",25,null],[11,"add_assign","","",25,null],[11,"add_assign","","",25,null],[11,"sub","","",25,null],[11,"sub_assign","","",25,null],[11,"sub","","",25,null],[11,"sub","","",25,null],[11,"sub_assign","","",25,null],[11,"sub_assign","","",25,null],[11,"inverse","","",25,null],[11,"inverse_mut","","",25,null],[11,"transpose","","",25,null],[11,"transpose_mut","","",25,null],[11,"mean","","",25,null],[11,"covariance","","",25,null],[11,"ncols","","",25,null],[11,"set_column","","",25,null],[11,"column","","",25,null],[11,"column_slice","","",25,null],[11,"nrows","","",25,null],[11,"set_row","","",25,null],[11,"row","","",25,null],[11,"row_slice","","",25,null],[11,"from_diagonal","","",25,{"inputs":[{"name":"dvector"}],"output":{"name":"dmatrix"}}],[11,"diagonal","","",25,null],[11,"approx_epsilon","","",25,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",25,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",25,null],[11,"approx_eq_ulps","","",25,null],[11,"fmt","","",25,null],[11,"mul","","",25,null],[11,"div","","",25,null],[11,"add","","",25,null],[11,"eq","","",26,null],[11,"clone","","",26,null],[11,"new_zeros","","Builds a matrix filled with zeros.",26,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix1"}}],[11,"is_zero","","Tests if all components of the matrix are zeroes.",26,null],[11,"reset","","Set this matrix components to zero.",26,null],[11,"new_random","","Builds a matrix filled with random values.",26,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix1"}}],[11,"new_ones","","Builds a matrix filled with a given constant.",26,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix1"}}],[11,"nrows","","The number of row on the matrix.",26,null],[11,"ncols","","The number of columns on the matrix.",26,null],[11,"as_vector","","Gets a reference to this matrix data.\nThe returned vector contains the matrix data in column-major order.",26,null],[11,"as_mut_vector","","Gets a mutable reference to this matrix data.\nThe returned vector contains the matrix data in column-major order.",26,null],[11,"new_identity","","Builds an identity matrix.",26,{"inputs":[{"name":"usize"}],"output":{"name":"dmatrix1"}}],[11,"unsafe_set","","Just like `set` without bounds checking.",26,null],[11,"unsafe_at","","Just like `at` without bounds checking.",26,null],[11,"swap","","",26,null],[11,"shape","","",26,null],[11,"index","","",26,null],[11,"index_mut","","",26,null],[11,"mul","","",26,null],[11,"mul","","",26,null],[11,"mul_assign","","",26,null],[11,"mul_assign","","",26,null],[11,"mul","","",26,null],[11,"mul","","",26,null],[11,"mul","","",27,null],[11,"mul","","",27,null],[11,"mul_assign","","",27,null],[11,"mul_assign","","",27,null],[11,"add","","",26,null],[11,"add","","",26,null],[11,"add_assign","","",26,null],[11,"add_assign","","",26,null],[11,"sub","","",26,null],[11,"sub_assign","","",26,null],[11,"sub","","",26,null],[11,"sub","","",26,null],[11,"sub_assign","","",26,null],[11,"sub_assign","","",26,null],[11,"inverse","","",26,null],[11,"inverse_mut","","",26,null],[11,"transpose","","",26,null],[11,"transpose_mut","","",26,null],[11,"mean","","",26,null],[11,"covariance","","",26,null],[11,"ncols","","",26,null],[11,"set_column","","",26,null],[11,"column","","",26,null],[11,"column_slice","","",26,null],[11,"nrows","","",26,null],[11,"set_row","","",26,null],[11,"row","","",26,null],[11,"row_slice","","",26,null],[11,"from_diagonal","","",26,{"inputs":[{"name":"dvector1"}],"output":{"name":"dmatrix1"}}],[11,"diagonal","","",26,null],[11,"approx_epsilon","","",26,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",26,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",26,null],[11,"approx_eq_ulps","","",26,null],[11,"fmt","","",26,null],[11,"mul","","",26,null],[11,"div","","",26,null],[11,"add","","",26,null],[11,"from_element","","Builds a matrix filled with a given constant.",26,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"n"}],"output":{"name":"dmatrix1"}}],[11,"from_row_vector","","Builds a matrix filled with the components provided by a vector.\nThe vector contains the matrix data in row-major order.\nNote that `from_column_vector` is a lot faster than `from_row_vector` since a `$dmatrix` stores its data\nin column-major order.",26,null],[11,"from_column_vector","","Builds a matrix filled with the components provided by a vector.\nThe vector contains the matrix data in column-major order.\nNote that `from_column_vector` is a lot faster than `from_row_vector` since a `$dmatrix` stores its data\nin column-major order.",26,null],[11,"from_fn","","Builds a matrix using an initialization function.",26,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"f"}],"output":{"name":"dmatrix1"}}],[11,"new_uninitialized","","Creates a new matrix with uninitialized components (with `mem::uninitialized()`).",26,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix1"}}],[11,"eq","","",28,null],[11,"clone","","",28,null],[11,"new_zeros","","Builds a matrix filled with zeros.",28,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix2"}}],[11,"is_zero","","Tests if all components of the matrix are zeroes.",28,null],[11,"reset","","Set this matrix components to zero.",28,null],[11,"new_random","","Builds a matrix filled with random values.",28,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix2"}}],[11,"new_ones","","Builds a matrix filled with a given constant.",28,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix2"}}],[11,"nrows","","The number of row on the matrix.",28,null],[11,"ncols","","The number of columns on the matrix.",28,null],[11,"as_vector","","Gets a reference to this matrix data.\nThe returned vector contains the matrix data in column-major order.",28,null],[11,"as_mut_vector","","Gets a mutable reference to this matrix data.\nThe returned vector contains the matrix data in column-major order.",28,null],[11,"new_identity","","Builds an identity matrix.",28,{"inputs":[{"name":"usize"}],"output":{"name":"dmatrix2"}}],[11,"unsafe_set","","Just like `set` without bounds checking.",28,null],[11,"unsafe_at","","Just like `at` without bounds checking.",28,null],[11,"swap","","",28,null],[11,"shape","","",28,null],[11,"index","","",28,null],[11,"index_mut","","",28,null],[11,"mul","","",28,null],[11,"mul","","",28,null],[11,"mul_assign","","",28,null],[11,"mul_assign","","",28,null],[11,"mul","","",28,null],[11,"mul","","",28,null],[11,"mul","","",29,null],[11,"mul","","",29,null],[11,"mul_assign","","",29,null],[11,"mul_assign","","",29,null],[11,"add","","",28,null],[11,"add","","",28,null],[11,"add_assign","","",28,null],[11,"add_assign","","",28,null],[11,"sub","","",28,null],[11,"sub_assign","","",28,null],[11,"sub","","",28,null],[11,"sub","","",28,null],[11,"sub_assign","","",28,null],[11,"sub_assign","","",28,null],[11,"inverse","","",28,null],[11,"inverse_mut","","",28,null],[11,"transpose","","",28,null],[11,"transpose_mut","","",28,null],[11,"mean","","",28,null],[11,"covariance","","",28,null],[11,"ncols","","",28,null],[11,"set_column","","",28,null],[11,"column","","",28,null],[11,"column_slice","","",28,null],[11,"nrows","","",28,null],[11,"set_row","","",28,null],[11,"row","","",28,null],[11,"row_slice","","",28,null],[11,"from_diagonal","","",28,{"inputs":[{"name":"dvector2"}],"output":{"name":"dmatrix2"}}],[11,"diagonal","","",28,null],[11,"approx_epsilon","","",28,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",28,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",28,null],[11,"approx_eq_ulps","","",28,null],[11,"fmt","","",28,null],[11,"mul","","",28,null],[11,"div","","",28,null],[11,"add","","",28,null],[11,"from_element","","Builds a matrix filled with a given constant.",28,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"n"}],"output":{"name":"dmatrix2"}}],[11,"from_row_vector","","Builds a matrix filled with the components provided by a vector.\nThe vector contains the matrix data in row-major order.\nNote that `from_column_vector` is a lot faster than `from_row_vector` since a `$dmatrix` stores its data\nin column-major order.",28,null],[11,"from_column_vector","","Builds a matrix filled with the components provided by a vector.\nThe vector contains the matrix data in column-major order.\nNote that `from_column_vector` is a lot faster than `from_row_vector` since a `$dmatrix` stores its data\nin column-major order.",28,null],[11,"from_fn","","Builds a matrix using an initialization function.",28,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"f"}],"output":{"name":"dmatrix2"}}],[11,"new_uninitialized","","Creates a new matrix with uninitialized components (with `mem::uninitialized()`).",28,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix2"}}],[11,"eq","","",30,null],[11,"clone","","",30,null],[11,"new_zeros","","Builds a matrix filled with zeros.",30,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix3"}}],[11,"is_zero","","Tests if all components of the matrix are zeroes.",30,null],[11,"reset","","Set this matrix components to zero.",30,null],[11,"new_random","","Builds a matrix filled with random values.",30,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix3"}}],[11,"new_ones","","Builds a matrix filled with a given constant.",30,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix3"}}],[11,"nrows","","The number of row on the matrix.",30,null],[11,"ncols","","The number of columns on the matrix.",30,null],[11,"as_vector","","Gets a reference to this matrix data.\nThe returned vector contains the matrix data in column-major order.",30,null],[11,"as_mut_vector","","Gets a mutable reference to this matrix data.\nThe returned vector contains the matrix data in column-major order.",30,null],[11,"new_identity","","Builds an identity matrix.",30,{"inputs":[{"name":"usize"}],"output":{"name":"dmatrix3"}}],[11,"unsafe_set","","Just like `set` without bounds checking.",30,null],[11,"unsafe_at","","Just like `at` without bounds checking.",30,null],[11,"swap","","",30,null],[11,"shape","","",30,null],[11,"index","","",30,null],[11,"index_mut","","",30,null],[11,"mul","","",30,null],[11,"mul","","",30,null],[11,"mul_assign","","",30,null],[11,"mul_assign","","",30,null],[11,"mul","","",30,null],[11,"mul","","",30,null],[11,"mul","","",31,null],[11,"mul","","",31,null],[11,"mul_assign","","",31,null],[11,"mul_assign","","",31,null],[11,"add","","",30,null],[11,"add","","",30,null],[11,"add_assign","","",30,null],[11,"add_assign","","",30,null],[11,"sub","","",30,null],[11,"sub_assign","","",30,null],[11,"sub","","",30,null],[11,"sub","","",30,null],[11,"sub_assign","","",30,null],[11,"sub_assign","","",30,null],[11,"inverse","","",30,null],[11,"inverse_mut","","",30,null],[11,"transpose","","",30,null],[11,"transpose_mut","","",30,null],[11,"mean","","",30,null],[11,"covariance","","",30,null],[11,"ncols","","",30,null],[11,"set_column","","",30,null],[11,"column","","",30,null],[11,"column_slice","","",30,null],[11,"nrows","","",30,null],[11,"set_row","","",30,null],[11,"row","","",30,null],[11,"row_slice","","",30,null],[11,"from_diagonal","","",30,{"inputs":[{"name":"dvector3"}],"output":{"name":"dmatrix3"}}],[11,"diagonal","","",30,null],[11,"approx_epsilon","","",30,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",30,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",30,null],[11,"approx_eq_ulps","","",30,null],[11,"fmt","","",30,null],[11,"mul","","",30,null],[11,"div","","",30,null],[11,"add","","",30,null],[11,"from_element","","Builds a matrix filled with a given constant.",30,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"n"}],"output":{"name":"dmatrix3"}}],[11,"from_row_vector","","Builds a matrix filled with the components provided by a vector.\nThe vector contains the matrix data in row-major order.\nNote that `from_column_vector` is a lot faster than `from_row_vector` since a `$dmatrix` stores its data\nin column-major order.",30,null],[11,"from_column_vector","","Builds a matrix filled with the components provided by a vector.\nThe vector contains the matrix data in column-major order.\nNote that `from_column_vector` is a lot faster than `from_row_vector` since a `$dmatrix` stores its data\nin column-major order.",30,null],[11,"from_fn","","Builds a matrix using an initialization function.",30,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"f"}],"output":{"name":"dmatrix3"}}],[11,"new_uninitialized","","Creates a new matrix with uninitialized components (with `mem::uninitialized()`).",30,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix3"}}],[11,"eq","","",32,null],[11,"clone","","",32,null],[11,"new_zeros","","Builds a matrix filled with zeros.",32,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix4"}}],[11,"is_zero","","Tests if all components of the matrix are zeroes.",32,null],[11,"reset","","Set this matrix components to zero.",32,null],[11,"new_random","","Builds a matrix filled with random values.",32,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix4"}}],[11,"new_ones","","Builds a matrix filled with a given constant.",32,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix4"}}],[11,"nrows","","The number of row on the matrix.",32,null],[11,"ncols","","The number of columns on the matrix.",32,null],[11,"as_vector","","Gets a reference to this matrix data.\nThe returned vector contains the matrix data in column-major order.",32,null],[11,"as_mut_vector","","Gets a mutable reference to this matrix data.\nThe returned vector contains the matrix data in column-major order.",32,null],[11,"new_identity","","Builds an identity matrix.",32,{"inputs":[{"name":"usize"}],"output":{"name":"dmatrix4"}}],[11,"unsafe_set","","Just like `set` without bounds checking.",32,null],[11,"unsafe_at","","Just like `at` without bounds checking.",32,null],[11,"swap","","",32,null],[11,"shape","","",32,null],[11,"index","","",32,null],[11,"index_mut","","",32,null],[11,"mul","","",32,null],[11,"mul","","",32,null],[11,"mul_assign","","",32,null],[11,"mul_assign","","",32,null],[11,"mul","","",32,null],[11,"mul","","",32,null],[11,"mul","","",33,null],[11,"mul","","",33,null],[11,"mul_assign","","",33,null],[11,"mul_assign","","",33,null],[11,"add","","",32,null],[11,"add","","",32,null],[11,"add_assign","","",32,null],[11,"add_assign","","",32,null],[11,"sub","","",32,null],[11,"sub_assign","","",32,null],[11,"sub","","",32,null],[11,"sub","","",32,null],[11,"sub_assign","","",32,null],[11,"sub_assign","","",32,null],[11,"inverse","","",32,null],[11,"inverse_mut","","",32,null],[11,"transpose","","",32,null],[11,"transpose_mut","","",32,null],[11,"mean","","",32,null],[11,"covariance","","",32,null],[11,"ncols","","",32,null],[11,"set_column","","",32,null],[11,"column","","",32,null],[11,"column_slice","","",32,null],[11,"nrows","","",32,null],[11,"set_row","","",32,null],[11,"row","","",32,null],[11,"row_slice","","",32,null],[11,"from_diagonal","","",32,{"inputs":[{"name":"dvector4"}],"output":{"name":"dmatrix4"}}],[11,"diagonal","","",32,null],[11,"approx_epsilon","","",32,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",32,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",32,null],[11,"approx_eq_ulps","","",32,null],[11,"fmt","","",32,null],[11,"mul","","",32,null],[11,"div","","",32,null],[11,"add","","",32,null],[11,"from_element","","Builds a matrix filled with a given constant.",32,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"n"}],"output":{"name":"dmatrix4"}}],[11,"from_row_vector","","Builds a matrix filled with the components provided by a vector.\nThe vector contains the matrix data in row-major order.\nNote that `from_column_vector` is a lot faster than `from_row_vector` since a `$dmatrix` stores its data\nin column-major order.",32,null],[11,"from_column_vector","","Builds a matrix filled with the components provided by a vector.\nThe vector contains the matrix data in column-major order.\nNote that `from_column_vector` is a lot faster than `from_row_vector` since a `$dmatrix` stores its data\nin column-major order.",32,null],[11,"from_fn","","Builds a matrix using an initialization function.",32,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"f"}],"output":{"name":"dmatrix4"}}],[11,"new_uninitialized","","Creates a new matrix with uninitialized components (with `mem::uninitialized()`).",32,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix4"}}],[11,"eq","","",34,null],[11,"clone","","",34,null],[11,"new_zeros","","Builds a matrix filled with zeros.",34,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix5"}}],[11,"is_zero","","Tests if all components of the matrix are zeroes.",34,null],[11,"reset","","Set this matrix components to zero.",34,null],[11,"new_random","","Builds a matrix filled with random values.",34,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix5"}}],[11,"new_ones","","Builds a matrix filled with a given constant.",34,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix5"}}],[11,"nrows","","The number of row on the matrix.",34,null],[11,"ncols","","The number of columns on the matrix.",34,null],[11,"as_vector","","Gets a reference to this matrix data.\nThe returned vector contains the matrix data in column-major order.",34,null],[11,"as_mut_vector","","Gets a mutable reference to this matrix data.\nThe returned vector contains the matrix data in column-major order.",34,null],[11,"new_identity","","Builds an identity matrix.",34,{"inputs":[{"name":"usize"}],"output":{"name":"dmatrix5"}}],[11,"unsafe_set","","Just like `set` without bounds checking.",34,null],[11,"unsafe_at","","Just like `at` without bounds checking.",34,null],[11,"swap","","",34,null],[11,"shape","","",34,null],[11,"index","","",34,null],[11,"index_mut","","",34,null],[11,"mul","","",34,null],[11,"mul","","",34,null],[11,"mul_assign","","",34,null],[11,"mul_assign","","",34,null],[11,"mul","","",34,null],[11,"mul","","",34,null],[11,"mul","","",35,null],[11,"mul","","",35,null],[11,"mul_assign","","",35,null],[11,"mul_assign","","",35,null],[11,"add","","",34,null],[11,"add","","",34,null],[11,"add_assign","","",34,null],[11,"add_assign","","",34,null],[11,"sub","","",34,null],[11,"sub_assign","","",34,null],[11,"sub","","",34,null],[11,"sub","","",34,null],[11,"sub_assign","","",34,null],[11,"sub_assign","","",34,null],[11,"inverse","","",34,null],[11,"inverse_mut","","",34,null],[11,"transpose","","",34,null],[11,"transpose_mut","","",34,null],[11,"mean","","",34,null],[11,"covariance","","",34,null],[11,"ncols","","",34,null],[11,"set_column","","",34,null],[11,"column","","",34,null],[11,"column_slice","","",34,null],[11,"nrows","","",34,null],[11,"set_row","","",34,null],[11,"row","","",34,null],[11,"row_slice","","",34,null],[11,"from_diagonal","","",34,{"inputs":[{"name":"dvector5"}],"output":{"name":"dmatrix5"}}],[11,"diagonal","","",34,null],[11,"approx_epsilon","","",34,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",34,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",34,null],[11,"approx_eq_ulps","","",34,null],[11,"fmt","","",34,null],[11,"mul","","",34,null],[11,"div","","",34,null],[11,"add","","",34,null],[11,"from_element","","Builds a matrix filled with a given constant.",34,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"n"}],"output":{"name":"dmatrix5"}}],[11,"from_row_vector","","Builds a matrix filled with the components provided by a vector.\nThe vector contains the matrix data in row-major order.\nNote that `from_column_vector` is a lot faster than `from_row_vector` since a `$dmatrix` stores its data\nin column-major order.",34,null],[11,"from_column_vector","","Builds a matrix filled with the components provided by a vector.\nThe vector contains the matrix data in column-major order.\nNote that `from_column_vector` is a lot faster than `from_row_vector` since a `$dmatrix` stores its data\nin column-major order.",34,null],[11,"from_fn","","Builds a matrix using an initialization function.",34,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"f"}],"output":{"name":"dmatrix5"}}],[11,"new_uninitialized","","Creates a new matrix with uninitialized components (with `mem::uninitialized()`).",34,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix5"}}],[11,"eq","","",36,null],[11,"clone","","",36,null],[11,"new_zeros","","Builds a matrix filled with zeros.",36,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix6"}}],[11,"is_zero","","Tests if all components of the matrix are zeroes.",36,null],[11,"reset","","Set this matrix components to zero.",36,null],[11,"new_random","","Builds a matrix filled with random values.",36,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix6"}}],[11,"new_ones","","Builds a matrix filled with a given constant.",36,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix6"}}],[11,"nrows","","The number of row on the matrix.",36,null],[11,"ncols","","The number of columns on the matrix.",36,null],[11,"as_vector","","Gets a reference to this matrix data.\nThe returned vector contains the matrix data in column-major order.",36,null],[11,"as_mut_vector","","Gets a mutable reference to this matrix data.\nThe returned vector contains the matrix data in column-major order.",36,null],[11,"new_identity","","Builds an identity matrix.",36,{"inputs":[{"name":"usize"}],"output":{"name":"dmatrix6"}}],[11,"unsafe_set","","Just like `set` without bounds checking.",36,null],[11,"unsafe_at","","Just like `at` without bounds checking.",36,null],[11,"swap","","",36,null],[11,"shape","","",36,null],[11,"index","","",36,null],[11,"index_mut","","",36,null],[11,"mul","","",36,null],[11,"mul","","",36,null],[11,"mul_assign","","",36,null],[11,"mul_assign","","",36,null],[11,"mul","","",36,null],[11,"mul","","",36,null],[11,"mul","","",37,null],[11,"mul","","",37,null],[11,"mul_assign","","",37,null],[11,"mul_assign","","",37,null],[11,"add","","",36,null],[11,"add","","",36,null],[11,"add_assign","","",36,null],[11,"add_assign","","",36,null],[11,"sub","","",36,null],[11,"sub_assign","","",36,null],[11,"sub","","",36,null],[11,"sub","","",36,null],[11,"sub_assign","","",36,null],[11,"sub_assign","","",36,null],[11,"inverse","","",36,null],[11,"inverse_mut","","",36,null],[11,"transpose","","",36,null],[11,"transpose_mut","","",36,null],[11,"mean","","",36,null],[11,"covariance","","",36,null],[11,"ncols","","",36,null],[11,"set_column","","",36,null],[11,"column","","",36,null],[11,"column_slice","","",36,null],[11,"nrows","","",36,null],[11,"set_row","","",36,null],[11,"row","","",36,null],[11,"row_slice","","",36,null],[11,"from_diagonal","","",36,{"inputs":[{"name":"dvector6"}],"output":{"name":"dmatrix6"}}],[11,"diagonal","","",36,null],[11,"approx_epsilon","","",36,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",36,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",36,null],[11,"approx_eq_ulps","","",36,null],[11,"fmt","","",36,null],[11,"mul","","",36,null],[11,"div","","",36,null],[11,"add","","",36,null],[11,"from_element","","Builds a matrix filled with a given constant.",36,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"n"}],"output":{"name":"dmatrix6"}}],[11,"from_row_vector","","Builds a matrix filled with the components provided by a vector.\nThe vector contains the matrix data in row-major order.\nNote that `from_column_vector` is a lot faster than `from_row_vector` since a `$dmatrix` stores its data\nin column-major order.",36,null],[11,"from_column_vector","","Builds a matrix filled with the components provided by a vector.\nThe vector contains the matrix data in column-major order.\nNote that `from_column_vector` is a lot faster than `from_row_vector` since a `$dmatrix` stores its data\nin column-major order.",36,null],[11,"from_fn","","Builds a matrix using an initialization function.",36,{"inputs":[{"name":"usize"},{"name":"usize"},{"name":"f"}],"output":{"name":"dmatrix6"}}],[11,"new_uninitialized","","Creates a new matrix with uninitialized components (with `mem::uninitialized()`).",36,{"inputs":[{"name":"usize"},{"name":"usize"}],"output":{"name":"dmatrix6"}}],[11,"eq","","",0,null],[11,"ne","","",0,null],[11,"fmt","","",0,null],[11,"clone","","",0,null],[11,"new_uninitialized","","Creates an uninitialized vector.",0,{"inputs":[{"name":"usize"}],"output":{"name":"dvector"}}],[11,"from_element","","Builds a vector filled with a constant.",0,{"inputs":[{"name":"usize"},{"name":"n"}],"output":{"name":"dvector"}}],[11,"from_slice","","Builds a vector filled with the components provided by a vector.",0,null],[11,"from_fn","","Builds a vector filled with the results of a function applied to each of its component coordinates.",0,{"inputs":[{"name":"usize"},{"name":"f"}],"output":{"name":"dvector"}}],[11,"len","","The vector length.",0,null],[11,"from_iter","","",0,{"inputs":[{"name":"i"}],"output":{"name":"dvector"}}],[11,"outer","","",0,null],[11,"is_zero","","Tests if all components of the vector are zeroes.",0,null],[11,"as_ref","","",0,null],[11,"as_mut","","",0,null],[11,"shape","","",0,null],[11,"swap","","",0,null],[11,"unsafe_at","","",0,null],[11,"unsafe_set","","",0,null],[11,"index","","",0,null],[11,"index_mut","","",0,null],[11,"iter","","",0,null],[11,"iter_mut","","",0,null],[11,"axpy","","",0,null],[11,"mul","","",0,null],[11,"mul","","",0,null],[11,"mul_assign","","",0,null],[11,"mul_assign","","",0,null],[11,"div","","",0,null],[11,"div","","",0,null],[11,"div_assign","","",0,null],[11,"div_assign","","",0,null],[11,"add","","",0,null],[11,"add","","",0,null],[11,"add_assign","","",0,null],[11,"add_assign","","",0,null],[11,"sub","","",0,null],[11,"sub","","",0,null],[11,"sub_assign","","",0,null],[11,"sub_assign","","",0,null],[11,"neg","","",0,null],[11,"dot","","",0,null],[11,"norm_squared","","",0,null],[11,"normalize","","",0,null],[11,"normalize_mut","","",0,null],[11,"mean","","",0,null],[11,"approx_epsilon","","",0,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",0,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",0,null],[11,"approx_eq_ulps","","",0,null],[11,"new_zeros","","Builds a vector filled with zeros.",0,{"inputs":[{"name":"usize"}],"output":{"name":"dvector"}}],[11,"new_ones","","Builds a vector filled with ones.",0,{"inputs":[{"name":"usize"}],"output":{"name":"dvector"}}],[11,"new_random","","Builds a vector filled with random values.",0,{"inputs":[{"name":"usize"}],"output":{"name":"dvector"}}],[11,"canonical_basis_with_dimension","","Computes the canonical basis for the given dimension. A canonical basis is a set of\nvectors, mutually orthogonal, with all its component equal to 0.0 except one which is equal\nto 1.0.",0,{"inputs":[{"name":"usize"}],"output":{"name":"vec"}}],[11,"orthogonal_subspace_basis","","Computes a basis of the space orthogonal to the vector. If the input vector is of dimension\n`n`, this will return `n - 1` vectors.",0,null],[11,"is_zero","","Tests if all components of the vector are zeroes.",27,null],[11,"as_ref","","",27,null],[11,"as_mut","","",27,null],[11,"shape","","",27,null],[11,"swap","","",27,null],[11,"unsafe_at","","",27,null],[11,"unsafe_set","","",27,null],[11,"index","","",27,null],[11,"index_mut","","",27,null],[11,"iter","","",27,null],[11,"iter_mut","","",27,null],[11,"axpy","","",27,null],[11,"mul","","",27,null],[11,"mul","","",27,null],[11,"mul_assign","","",27,null],[11,"mul_assign","","",27,null],[11,"div","","",27,null],[11,"div","","",27,null],[11,"div_assign","","",27,null],[11,"div_assign","","",27,null],[11,"add","","",27,null],[11,"add","","",27,null],[11,"add_assign","","",27,null],[11,"add_assign","","",27,null],[11,"sub","","",27,null],[11,"sub","","",27,null],[11,"sub_assign","","",27,null],[11,"sub_assign","","",27,null],[11,"neg","","",27,null],[11,"dot","","",27,null],[11,"norm_squared","","",27,null],[11,"normalize","","",27,null],[11,"normalize_mut","","",27,null],[11,"mean","","",27,null],[11,"approx_epsilon","","",27,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",27,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",27,null],[11,"approx_eq_ulps","","",27,null],[11,"new_zeros","","Builds a vector filled with zeros.",27,{"inputs":[{"name":"usize"}],"output":{"name":"dvector1"}}],[11,"new_ones","","Builds a vector filled with ones.",27,{"inputs":[{"name":"usize"}],"output":{"name":"dvector1"}}],[11,"new_random","","Builds a vector filled with random values.",27,{"inputs":[{"name":"usize"}],"output":{"name":"dvector1"}}],[11,"canonical_basis_with_dimension","","Computes the canonical basis for the given dimension. A canonical basis is a set of\nvectors, mutually orthogonal, with all its component equal to 0.0 except one which is equal\nto 1.0.",27,{"inputs":[{"name":"usize"}],"output":{"name":"vec"}}],[11,"orthogonal_subspace_basis","","Computes a basis of the space orthogonal to the vector. If the input vector is of dimension\n`n`, this will return `n - 1` vectors.",27,null],[11,"len","","The number of elements of this vector.",27,null],[11,"new_uninitialized","","Creates an uninitialized vector of dimension `dimension`.",27,{"inputs":[{"name":"usize"}],"output":{"name":"dvector1"}}],[11,"eq","","",27,null],[11,"clone","","",27,null],[11,"from_element","","Builds a vector filled with a constant.",27,{"inputs":[{"name":"usize"},{"name":"n"}],"output":{"name":"dvector1"}}],[11,"from_slice","","Builds a vector filled with the components provided by a vector.",27,null],[11,"from_fn","","Builds a vector filled with the result of a function.",27,{"inputs":[{"name":"usize"},{"name":"f"}],"output":{"name":"dvector1"}}],[11,"from_iter","","",27,{"inputs":[{"name":"i"}],"output":{"name":"dvector1"}}],[11,"is_zero","","Tests if all components of the vector are zeroes.",29,null],[11,"as_ref","","",29,null],[11,"as_mut","","",29,null],[11,"shape","","",29,null],[11,"swap","","",29,null],[11,"unsafe_at","","",29,null],[11,"unsafe_set","","",29,null],[11,"index","","",29,null],[11,"index_mut","","",29,null],[11,"iter","","",29,null],[11,"iter_mut","","",29,null],[11,"axpy","","",29,null],[11,"mul","","",29,null],[11,"mul","","",29,null],[11,"mul_assign","","",29,null],[11,"mul_assign","","",29,null],[11,"div","","",29,null],[11,"div","","",29,null],[11,"div_assign","","",29,null],[11,"div_assign","","",29,null],[11,"add","","",29,null],[11,"add","","",29,null],[11,"add_assign","","",29,null],[11,"add_assign","","",29,null],[11,"sub","","",29,null],[11,"sub","","",29,null],[11,"sub_assign","","",29,null],[11,"sub_assign","","",29,null],[11,"neg","","",29,null],[11,"dot","","",29,null],[11,"norm_squared","","",29,null],[11,"normalize","","",29,null],[11,"normalize_mut","","",29,null],[11,"mean","","",29,null],[11,"approx_epsilon","","",29,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",29,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",29,null],[11,"approx_eq_ulps","","",29,null],[11,"new_zeros","","Builds a vector filled with zeros.",29,{"inputs":[{"name":"usize"}],"output":{"name":"dvector2"}}],[11,"new_ones","","Builds a vector filled with ones.",29,{"inputs":[{"name":"usize"}],"output":{"name":"dvector2"}}],[11,"new_random","","Builds a vector filled with random values.",29,{"inputs":[{"name":"usize"}],"output":{"name":"dvector2"}}],[11,"canonical_basis_with_dimension","","Computes the canonical basis for the given dimension. A canonical basis is a set of\nvectors, mutually orthogonal, with all its component equal to 0.0 except one which is equal\nto 1.0.",29,{"inputs":[{"name":"usize"}],"output":{"name":"vec"}}],[11,"orthogonal_subspace_basis","","Computes a basis of the space orthogonal to the vector. If the input vector is of dimension\n`n`, this will return `n - 1` vectors.",29,null],[11,"len","","The number of elements of this vector.",29,null],[11,"new_uninitialized","","Creates an uninitialized vector of dimension `dimension`.",29,{"inputs":[{"name":"usize"}],"output":{"name":"dvector2"}}],[11,"eq","","",29,null],[11,"clone","","",29,null],[11,"from_element","","Builds a vector filled with a constant.",29,{"inputs":[{"name":"usize"},{"name":"n"}],"output":{"name":"dvector2"}}],[11,"from_slice","","Builds a vector filled with the components provided by a vector.",29,null],[11,"from_fn","","Builds a vector filled with the result of a function.",29,{"inputs":[{"name":"usize"},{"name":"f"}],"output":{"name":"dvector2"}}],[11,"from_iter","","",29,{"inputs":[{"name":"i"}],"output":{"name":"dvector2"}}],[11,"is_zero","","Tests if all components of the vector are zeroes.",31,null],[11,"as_ref","","",31,null],[11,"as_mut","","",31,null],[11,"shape","","",31,null],[11,"swap","","",31,null],[11,"unsafe_at","","",31,null],[11,"unsafe_set","","",31,null],[11,"index","","",31,null],[11,"index_mut","","",31,null],[11,"iter","","",31,null],[11,"iter_mut","","",31,null],[11,"axpy","","",31,null],[11,"mul","","",31,null],[11,"mul","","",31,null],[11,"mul_assign","","",31,null],[11,"mul_assign","","",31,null],[11,"div","","",31,null],[11,"div","","",31,null],[11,"div_assign","","",31,null],[11,"div_assign","","",31,null],[11,"add","","",31,null],[11,"add","","",31,null],[11,"add_assign","","",31,null],[11,"add_assign","","",31,null],[11,"sub","","",31,null],[11,"sub","","",31,null],[11,"sub_assign","","",31,null],[11,"sub_assign","","",31,null],[11,"neg","","",31,null],[11,"dot","","",31,null],[11,"norm_squared","","",31,null],[11,"normalize","","",31,null],[11,"normalize_mut","","",31,null],[11,"mean","","",31,null],[11,"approx_epsilon","","",31,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",31,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",31,null],[11,"approx_eq_ulps","","",31,null],[11,"new_zeros","","Builds a vector filled with zeros.",31,{"inputs":[{"name":"usize"}],"output":{"name":"dvector3"}}],[11,"new_ones","","Builds a vector filled with ones.",31,{"inputs":[{"name":"usize"}],"output":{"name":"dvector3"}}],[11,"new_random","","Builds a vector filled with random values.",31,{"inputs":[{"name":"usize"}],"output":{"name":"dvector3"}}],[11,"canonical_basis_with_dimension","","Computes the canonical basis for the given dimension. A canonical basis is a set of\nvectors, mutually orthogonal, with all its component equal to 0.0 except one which is equal\nto 1.0.",31,{"inputs":[{"name":"usize"}],"output":{"name":"vec"}}],[11,"orthogonal_subspace_basis","","Computes a basis of the space orthogonal to the vector. If the input vector is of dimension\n`n`, this will return `n - 1` vectors.",31,null],[11,"len","","The number of elements of this vector.",31,null],[11,"new_uninitialized","","Creates an uninitialized vector of dimension `dimension`.",31,{"inputs":[{"name":"usize"}],"output":{"name":"dvector3"}}],[11,"eq","","",31,null],[11,"clone","","",31,null],[11,"from_element","","Builds a vector filled with a constant.",31,{"inputs":[{"name":"usize"},{"name":"n"}],"output":{"name":"dvector3"}}],[11,"from_slice","","Builds a vector filled with the components provided by a vector.",31,null],[11,"from_fn","","Builds a vector filled with the result of a function.",31,{"inputs":[{"name":"usize"},{"name":"f"}],"output":{"name":"dvector3"}}],[11,"from_iter","","",31,{"inputs":[{"name":"i"}],"output":{"name":"dvector3"}}],[11,"is_zero","","Tests if all components of the vector are zeroes.",33,null],[11,"as_ref","","",33,null],[11,"as_mut","","",33,null],[11,"shape","","",33,null],[11,"swap","","",33,null],[11,"unsafe_at","","",33,null],[11,"unsafe_set","","",33,null],[11,"index","","",33,null],[11,"index_mut","","",33,null],[11,"iter","","",33,null],[11,"iter_mut","","",33,null],[11,"axpy","","",33,null],[11,"mul","","",33,null],[11,"mul","","",33,null],[11,"mul_assign","","",33,null],[11,"mul_assign","","",33,null],[11,"div","","",33,null],[11,"div","","",33,null],[11,"div_assign","","",33,null],[11,"div_assign","","",33,null],[11,"add","","",33,null],[11,"add","","",33,null],[11,"add_assign","","",33,null],[11,"add_assign","","",33,null],[11,"sub","","",33,null],[11,"sub","","",33,null],[11,"sub_assign","","",33,null],[11,"sub_assign","","",33,null],[11,"neg","","",33,null],[11,"dot","","",33,null],[11,"norm_squared","","",33,null],[11,"normalize","","",33,null],[11,"normalize_mut","","",33,null],[11,"mean","","",33,null],[11,"approx_epsilon","","",33,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",33,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",33,null],[11,"approx_eq_ulps","","",33,null],[11,"new_zeros","","Builds a vector filled with zeros.",33,{"inputs":[{"name":"usize"}],"output":{"name":"dvector4"}}],[11,"new_ones","","Builds a vector filled with ones.",33,{"inputs":[{"name":"usize"}],"output":{"name":"dvector4"}}],[11,"new_random","","Builds a vector filled with random values.",33,{"inputs":[{"name":"usize"}],"output":{"name":"dvector4"}}],[11,"canonical_basis_with_dimension","","Computes the canonical basis for the given dimension. A canonical basis is a set of\nvectors, mutually orthogonal, with all its component equal to 0.0 except one which is equal\nto 1.0.",33,{"inputs":[{"name":"usize"}],"output":{"name":"vec"}}],[11,"orthogonal_subspace_basis","","Computes a basis of the space orthogonal to the vector. If the input vector is of dimension\n`n`, this will return `n - 1` vectors.",33,null],[11,"len","","The number of elements of this vector.",33,null],[11,"new_uninitialized","","Creates an uninitialized vector of dimension `dimension`.",33,{"inputs":[{"name":"usize"}],"output":{"name":"dvector4"}}],[11,"eq","","",33,null],[11,"clone","","",33,null],[11,"from_element","","Builds a vector filled with a constant.",33,{"inputs":[{"name":"usize"},{"name":"n"}],"output":{"name":"dvector4"}}],[11,"from_slice","","Builds a vector filled with the components provided by a vector.",33,null],[11,"from_fn","","Builds a vector filled with the result of a function.",33,{"inputs":[{"name":"usize"},{"name":"f"}],"output":{"name":"dvector4"}}],[11,"from_iter","","",33,{"inputs":[{"name":"i"}],"output":{"name":"dvector4"}}],[11,"is_zero","","Tests if all components of the vector are zeroes.",35,null],[11,"as_ref","","",35,null],[11,"as_mut","","",35,null],[11,"shape","","",35,null],[11,"swap","","",35,null],[11,"unsafe_at","","",35,null],[11,"unsafe_set","","",35,null],[11,"index","","",35,null],[11,"index_mut","","",35,null],[11,"iter","","",35,null],[11,"iter_mut","","",35,null],[11,"axpy","","",35,null],[11,"mul","","",35,null],[11,"mul","","",35,null],[11,"mul_assign","","",35,null],[11,"mul_assign","","",35,null],[11,"div","","",35,null],[11,"div","","",35,null],[11,"div_assign","","",35,null],[11,"div_assign","","",35,null],[11,"add","","",35,null],[11,"add","","",35,null],[11,"add_assign","","",35,null],[11,"add_assign","","",35,null],[11,"sub","","",35,null],[11,"sub","","",35,null],[11,"sub_assign","","",35,null],[11,"sub_assign","","",35,null],[11,"neg","","",35,null],[11,"dot","","",35,null],[11,"norm_squared","","",35,null],[11,"normalize","","",35,null],[11,"normalize_mut","","",35,null],[11,"mean","","",35,null],[11,"approx_epsilon","","",35,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",35,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",35,null],[11,"approx_eq_ulps","","",35,null],[11,"new_zeros","","Builds a vector filled with zeros.",35,{"inputs":[{"name":"usize"}],"output":{"name":"dvector5"}}],[11,"new_ones","","Builds a vector filled with ones.",35,{"inputs":[{"name":"usize"}],"output":{"name":"dvector5"}}],[11,"new_random","","Builds a vector filled with random values.",35,{"inputs":[{"name":"usize"}],"output":{"name":"dvector5"}}],[11,"canonical_basis_with_dimension","","Computes the canonical basis for the given dimension. A canonical basis is a set of\nvectors, mutually orthogonal, with all its component equal to 0.0 except one which is equal\nto 1.0.",35,{"inputs":[{"name":"usize"}],"output":{"name":"vec"}}],[11,"orthogonal_subspace_basis","","Computes a basis of the space orthogonal to the vector. If the input vector is of dimension\n`n`, this will return `n - 1` vectors.",35,null],[11,"len","","The number of elements of this vector.",35,null],[11,"new_uninitialized","","Creates an uninitialized vector of dimension `dimension`.",35,{"inputs":[{"name":"usize"}],"output":{"name":"dvector5"}}],[11,"eq","","",35,null],[11,"clone","","",35,null],[11,"from_element","","Builds a vector filled with a constant.",35,{"inputs":[{"name":"usize"},{"name":"n"}],"output":{"name":"dvector5"}}],[11,"from_slice","","Builds a vector filled with the components provided by a vector.",35,null],[11,"from_fn","","Builds a vector filled with the result of a function.",35,{"inputs":[{"name":"usize"},{"name":"f"}],"output":{"name":"dvector5"}}],[11,"from_iter","","",35,{"inputs":[{"name":"i"}],"output":{"name":"dvector5"}}],[11,"is_zero","","Tests if all components of the vector are zeroes.",37,null],[11,"as_ref","","",37,null],[11,"as_mut","","",37,null],[11,"shape","","",37,null],[11,"swap","","",37,null],[11,"unsafe_at","","",37,null],[11,"unsafe_set","","",37,null],[11,"index","","",37,null],[11,"index_mut","","",37,null],[11,"iter","","",37,null],[11,"iter_mut","","",37,null],[11,"axpy","","",37,null],[11,"mul","","",37,null],[11,"mul","","",37,null],[11,"mul_assign","","",37,null],[11,"mul_assign","","",37,null],[11,"div","","",37,null],[11,"div","","",37,null],[11,"div_assign","","",37,null],[11,"div_assign","","",37,null],[11,"add","","",37,null],[11,"add","","",37,null],[11,"add_assign","","",37,null],[11,"add_assign","","",37,null],[11,"sub","","",37,null],[11,"sub","","",37,null],[11,"sub_assign","","",37,null],[11,"sub_assign","","",37,null],[11,"neg","","",37,null],[11,"dot","","",37,null],[11,"norm_squared","","",37,null],[11,"normalize","","",37,null],[11,"normalize_mut","","",37,null],[11,"mean","","",37,null],[11,"approx_epsilon","","",37,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",37,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",37,null],[11,"approx_eq_ulps","","",37,null],[11,"new_zeros","","Builds a vector filled with zeros.",37,{"inputs":[{"name":"usize"}],"output":{"name":"dvector6"}}],[11,"new_ones","","Builds a vector filled with ones.",37,{"inputs":[{"name":"usize"}],"output":{"name":"dvector6"}}],[11,"new_random","","Builds a vector filled with random values.",37,{"inputs":[{"name":"usize"}],"output":{"name":"dvector6"}}],[11,"canonical_basis_with_dimension","","Computes the canonical basis for the given dimension. 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matrix.",41,null],[11,"rotate","","",41,null],[11,"inverse_rotate","","",41,null],[11,"rotate","","",41,null],[11,"inverse_rotate","","",41,null],[11,"transform","","",41,null],[11,"inverse_transform","","",41,null],[11,"transform","","",41,null],[11,"inverse_transform","","",41,null],[11,"dimension","","",41,{"inputs":[{"name":"option"}],"output":{"name":"usize"}}],[11,"mul","","",41,null],[11,"mul_assign","","",41,null],[11,"mul","","",41,null],[11,"mul","","",13,null],[11,"mul_assign","","",13,null],[11,"mul","","",41,null],[11,"mul","","",19,null],[11,"mul_assign","","",19,null],[11,"one","","",41,{"inputs":[],"output":{"name":"rotation3"}}],[11,"new_identity","","",41,{"inputs":[{"name":"usize"}],"output":{"name":"rotation3"}}],[11,"to_rotation_matrix","","",41,null],[11,"ncols","","",41,null],[11,"column","","",41,null],[11,"set_column","","",41,null],[11,"nrows","","",41,null],[11,"row","","",41,null],[11,"set_row","","",41,null],[11,"index","","",41,null],[11,"abs","","",41,{"inputs":[{"name":"rotation3"}],"output":{"name":"matrix3"}}],[11,"to_homogeneous","","",41,null],[11,"inverse_mut","","",41,null],[11,"inverse","","",41,null],[11,"transpose","","",41,null],[11,"transpose_mut","","",41,null],[11,"approx_epsilon","","",41,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",41,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq","","",41,null],[11,"approx_eq_eps","","",41,null],[11,"approx_eq_ulps","","",41,null],[11,"from_diagonal","","",41,{"inputs":[{"name":"vector3"}],"output":{"name":"rotation3"}}],[11,"diagonal","","",41,null],[11,"fmt","","",41,null],[11,"eq","","",1,null],[11,"ne","","",1,null],[11,"encode","","",1,null],[11,"decode","","",1,{"inputs":[{"name":"__dn"}],"output":{"name":"result"}}],[11,"clone","","",1,null],[11,"fmt","","",1,null],[11,"eq","","",2,null],[11,"ne","","",2,null],[11,"encode","","",2,null],[11,"decode","","",2,{"inputs":[{"name":"__dn"}],"output":{"name":"result"}}],[11,"clone","","",2,null],[11,"fmt","","",2,null],[11,"new_observer_frame","","Creates an isometry that corresponds to the local frame of an observer standing at the\npoint `eye` and looking toward `target`.",2,{"inputs":[{"name":"point3"},{"name":"point3"},{"name":"vector3"}],"output":{"name":"isometry3"}}],[11,"look_at_rh","","Builds a right-handed look-at view matrix.",2,{"inputs":[{"name":"point3"},{"name":"point3"},{"name":"vector3"}],"output":{"name":"isometry3"}}],[11,"look_at_lh","","Builds a left-handed look-at view matrix.",2,{"inputs":[{"name":"point3"},{"name":"point3"},{"name":"vector3"}],"output":{"name":"isometry3"}}],[11,"new","","Creates a new isometry from an axis-angle rotation, and a vector.",1,{"inputs":[{"name":"vector2"},{"name":"vector1"}],"output":{"name":"isometry2"}}],[11,"new_with_rotation_matrix","","Creates a new isometry from a rotation matrix and a vector.",1,{"inputs":[{"name":"vector2"},{"name":"rotation2"}],"output":{"name":"isometry2"}}],[11,"to_rotation_matrix","","",1,null],[11,"rotation","","",1,null],[11,"inverse_rotation","","",1,null],[11,"append_rotation_mut","","",1,null],[11,"append_rotation","","",1,null],[11,"prepend_rotation_mut","","",1,null],[11,"prepend_rotation","","",1,null],[11,"set_rotation","","",1,null],[11,"dimension","","",1,{"inputs":[{"name":"option"}],"output":{"name":"usize"}}],[11,"one","","",1,{"inputs":[],"output":{"name":"isometry2"}}],[11,"absolute_rotate","","",1,null],[11,"rand","","",1,{"inputs":[{"name":"r"}],"output":{"name":"isometry2"}}],[11,"approx_epsilon","","",1,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",1,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",1,null],[11,"approx_eq_ulps","","",1,null],[11,"to_homogeneous","","",1,null],[11,"inverse_mut","","",1,null],[11,"inverse","","",1,null],[11,"transform","","",1,null],[11,"inverse_transform","","",1,null],[11,"transformation","","",1,null],[11,"inverse_transformation","","",1,null],[11,"append_transformation_mut","","",1,null],[11,"append_transformation","","",1,null],[11,"prepend_transformation_mut","","",1,null],[11,"prepend_transformation","","",1,null],[11,"set_transformation","","",1,null],[11,"rotate","","",1,null],[11,"inverse_rotate","","",1,null],[11,"translation","","",1,null],[11,"inverse_translation","","",1,null],[11,"append_translation_mut","","",1,null],[11,"append_translation","","",1,null],[11,"prepend_translation_mut","","",1,null],[11,"prepend_translation","","",1,null],[11,"set_translation","","",1,null],[11,"translate","","",1,null],[11,"inverse_translate","","",1,null],[11,"mul","","",1,null],[11,"mul_assign","","",1,null],[11,"mul","","",1,null],[11,"mul","","",40,null],[11,"mul_assign","","",1,null],[11,"mul","","",1,null],[11,"mul","","",1,null],[11,"fmt","","",1,null],[11,"new","","Creates a new isometry from an axis-angle rotation, and a vector.",2,{"inputs":[{"name":"vector3"},{"name":"vector3"}],"output":{"name":"isometry3"}}],[11,"new_with_rotation_matrix","","Creates a new isometry from a rotation matrix and a vector.",2,{"inputs":[{"name":"vector3"},{"name":"rotation3"}],"output":{"name":"isometry3"}}],[11,"to_rotation_matrix","","",2,null],[11,"rotation","","",2,null],[11,"inverse_rotation","","",2,null],[11,"append_rotation_mut","","",2,null],[11,"append_rotation","","",2,null],[11,"prepend_rotation_mut","","",2,null],[11,"prepend_rotation","","",2,null],[11,"set_rotation","","",2,null],[11,"dimension","","",2,{"inputs":[{"name":"option"}],"output":{"name":"usize"}}],[11,"one","","",2,{"inputs":[],"output":{"name":"isometry3"}}],[11,"absolute_rotate","","",2,null],[11,"rand","","",2,{"inputs":[{"name":"r"}],"output":{"name":"isometry3"}}],[11,"approx_epsilon","","",2,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",2,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",2,null],[11,"approx_eq_ulps","","",2,null],[11,"to_homogeneous","","",2,null],[11,"inverse_mut","","",2,null],[11,"inverse","","",2,null],[11,"transform","","",2,null],[11,"inverse_transform","","",2,null],[11,"transformation","","",2,null],[11,"inverse_transformation","","",2,null],[11,"append_transformation_mut","","",2,null],[11,"append_transformation","","",2,null],[11,"prepend_transformation_mut","","",2,null],[11,"prepend_transformation","","",2,null],[11,"set_transformation","","",2,null],[11,"rotate","","",2,null],[11,"inverse_rotate","","",2,null],[11,"translation","","",2,null],[11,"inverse_translation","","",2,null],[11,"append_translation_mut","","",2,null],[11,"append_translation","","",2,null],[11,"prepend_translation_mut","","",2,null],[11,"prepend_translation","","",2,null],[11,"set_translation","","",2,null],[11,"translate","","",2,null],[11,"inverse_translate","","",2,null],[11,"mul","","",2,null],[11,"mul_assign","","",2,null],[11,"mul","","",2,null],[11,"mul","","",41,null],[11,"mul_assign","","",2,null],[11,"mul","","",2,null],[11,"mul","","",2,null],[11,"fmt","","",2,null],[11,"eq","","",3,null],[11,"ne","","",3,null],[11,"encode","","",3,null],[11,"decode","","",3,{"inputs":[{"name":"__dn"}],"output":{"name":"result"}}],[11,"clone","","",3,null],[11,"fmt","","",3,null],[11,"eq","","",4,null],[11,"ne","","",4,null],[11,"encode","","",4,null],[11,"decode","","",4,{"inputs":[{"name":"__dn"}],"output":{"name":"result"}}],[11,"clone","","",4,null],[11,"fmt","","",4,null],[11,"new","","Creates a new similarity transformation from a vector, an axis-angle rotation, and a scale factor.",3,{"inputs":[{"name":"vector2"},{"name":"vector1"},{"name":"n"}],"output":{"name":"similarity2"}}],[11,"new_with_rotation_matrix","","Creates a new similarity transformation from a rotation matrix, a vector, and a scale factor.",3,{"inputs":[{"name":"vector2"},{"name":"rotation2"},{"name":"n"}],"output":{"name":"similarity2"}}],[11,"new_with_isometry","","Creates a new similarity transformation from an isometry and a scale factor.",3,{"inputs":[{"name":"isometry2"},{"name":"n"}],"output":{"name":"similarity2"}}],[11,"dimension","","",3,{"inputs":[{"name":"option"}],"output":{"name":"usize"}}],[11,"scale","","The scale factor of this similarity transformation.",3,null],[11,"inverse_scale","","The inverse scale factor of this similarity transformation.",3,null],[11,"append_scale_mut","","Appends in-place a scale to this similarity transformation.",3,null],[11,"append_scale","","Appends a scale to this similarity transformation.",3,null],[11,"prepend_scale_mut","","Prepends in-place a scale to this similarity transformation.",3,null],[11,"prepend_scale","","Prepends a scale to this similarity transformation.",3,null],[11,"set_scale","","Sets the scale of this similarity transformation.",3,null],[11,"one","","",3,{"inputs":[],"output":{"name":"similarity2"}}],[11,"mul","","",3,null],[11,"mul_assign","","",3,null],[11,"mul","","",3,null],[11,"mul_assign","","",3,null],[11,"mul","","",1,null],[11,"mul","","",3,null],[11,"mul_assign","","",3,null],[11,"mul","","",40,null],[11,"mul","","",3,null],[11,"mul","","",3,null],[11,"transformation","","",3,null],[11,"inverse_transformation","","",3,null],[11,"append_transformation_mut","","",3,null],[11,"append_transformation","","",3,null],[11,"prepend_transformation_mut","","",3,null],[11,"prepend_transformation","","",3,null],[11,"set_transformation","","",3,null],[11,"transform","","",3,null],[11,"inverse_transform","","",3,null],[11,"inverse_mut","","",3,null],[11,"inverse","","",3,null],[11,"to_homogeneous","","",3,null],[11,"approx_epsilon","","",3,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",3,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",3,null],[11,"approx_eq_ulps","","",3,null],[11,"rand","","",3,{"inputs":[{"name":"r"}],"output":{"name":"similarity2"}}],[11,"fmt","","",3,null],[11,"new","","Creates a new similarity transformation from a vector, an axis-angle rotation, and a scale factor.",4,{"inputs":[{"name":"vector3"},{"name":"vector3"},{"name":"n"}],"output":{"name":"similarity3"}}],[11,"new_with_rotation_matrix","","Creates a new similarity transformation from a rotation matrix, a vector, and a scale factor.",4,{"inputs":[{"name":"vector3"},{"name":"rotation3"},{"name":"n"}],"output":{"name":"similarity3"}}],[11,"new_with_isometry","","Creates a new similarity transformation from an isometry and a scale factor.",4,{"inputs":[{"name":"isometry3"},{"name":"n"}],"output":{"name":"similarity3"}}],[11,"dimension","","",4,{"inputs":[{"name":"option"}],"output":{"name":"usize"}}],[11,"scale","","The scale factor of this similarity transformation.",4,null],[11,"inverse_scale","","The inverse scale factor of this similarity transformation.",4,null],[11,"append_scale_mut","","Appends in-place a scale to this similarity transformation.",4,null],[11,"append_scale","","Appends a scale to this similarity transformation.",4,null],[11,"prepend_scale_mut","","Prepends in-place a scale to this similarity transformation.",4,null],[11,"prepend_scale","","Prepends a scale to this similarity transformation.",4,null],[11,"set_scale","","Sets the scale of this similarity transformation.",4,null],[11,"one","","",4,{"inputs":[],"output":{"name":"similarity3"}}],[11,"mul","","",4,null],[11,"mul_assign","","",4,null],[11,"mul","","",4,null],[11,"mul_assign","","",4,null],[11,"mul","","",2,null],[11,"mul","","",4,null],[11,"mul_assign","","",4,null],[11,"mul","","",41,null],[11,"mul","","",4,null],[11,"mul","","",4,null],[11,"transformation","","",4,null],[11,"inverse_transformation","","",4,null],[11,"append_transformation_mut","","",4,null],[11,"append_transformation","","",4,null],[11,"prepend_transformation_mut","","",4,null],[11,"prepend_transformation","","",4,null],[11,"set_transformation","","",4,null],[11,"transform","","",4,null],[11,"inverse_transform","","",4,null],[11,"inverse_mut","","",4,null],[11,"inverse","","",4,null],[11,"to_homogeneous","","",4,null],[11,"approx_epsilon","","",4,{"inputs":[{"name":"option"}],"output":{"name":"n"}}],[11,"approx_ulps","","",4,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[11,"approx_eq_eps","","",4,null],[11,"approx_eq_ulps","","",4,null],[11,"rand","","",4,{"inputs":[{"name":"r"}],"output":{"name":"similarity3"}}],[11,"fmt","","",4,null],[11,"eq","","",42,null],[11,"ne","","",42,null],[11,"encode","","",42,null],[11,"decode","","",42,{"inputs":[{"name":"__dn"}],"output":{"name":"result"}}],[11,"clone","","",42,null],[11,"fmt","","",42,null],[11,"eq","","",43,null],[11,"ne","","",43,null],[11,"encode","","",43,null],[11,"decode","","",43,{"inputs":[{"name":"__dn"}],"output":{"name":"result"}}],[11,"clone","","",43,null],[11,"fmt","","",43,null],[11,"new","","Creates a new 3D perspective projection.",42,{"inputs":[{"name":"n"},{"name":"n"},{"name":"n"},{"name":"n"}],"output":{"name":"perspective3"}}],[11,"to_matrix","","Builds a 4D projection matrix (using homogeneous coordinates) for this projection.",42,null],[11,"to_perspective_matrix","","Build a `PerspectiveMatrix3` representing this projection.",42,null],[11,"aspect","","Gets the `width / height` aspect ratio.",42,null],[11,"fovy","","Gets the y field of view of the view frustrum.",42,null],[11,"znear","","Gets the near plane offset of the view frustrum.",42,null],[11,"zfar","","Gets the far plane offset of the view frustrum.",42,null],[11,"set_aspect","","Sets the `width / height` aspect ratio of the view frustrum.",42,null],[11,"set_fovy","","Sets the y field of view of the view frustrum.",42,null],[11,"set_znear","","Sets the near plane offset of the view frustrum.",42,null],[11,"set_zfar","","Sets the far plane offset of the view frustrum.",42,null],[11,"project_point","","Projects a point.",42,null],[11,"project_vector","","Projects a vector.",42,null],[11,"new","","Creates a new perspective matrix from the aspect ratio, y field of view, and near/far planes.",43,{"inputs":[{"name":"n"},{"name":"n"},{"name":"n"},{"name":"n"}],"output":{"name":"perspectivematrix3"}}],[11,"new_with_matrix","","Creates a new perspective projection matrix from a 4D matrix.",43,{"inputs":[{"name":"matrix4"}],"output":{"name":"perspectivematrix3"}}],[11,"as_matrix","","Returns a reference to the 4D matrix (using homogeneous coordinates) of this projection.",43,null],[11,"aspect","","Gets the `width / height` aspect ratio of the view frustrum.",43,null],[11,"fovy","","Gets the y field of view of the view frustrum.",43,null],[11,"znear","","Gets the near plane offset of the view frustrum.",43,null],[11,"zfar","","Gets the far plane offset of the view frustrum.",43,null],[11,"set_aspect","","Updates this projection matrix with a new `width / height` aspect ratio of the view\nfrustrum.",43,null],[11,"set_fovy","","Updates this projection with a new y field of view of the view frustrum.",43,null],[11,"set_znear","","Updates this projection matrix with a new near plane offset of the view frustrum.",43,null],[11,"set_zfar","","Updates this projection matrix with a new far plane offset of the view frustrum.",43,null],[11,"set_znear_and_zfar","","Updates this projection matrix with new near and far plane offsets of the view frustrum.",43,null],[11,"project_point","","Projects a point.",43,null],[11,"project_vector","","Projects a vector.",43,null],[11,"to_matrix","","Returns the 4D matrix (using homogeneous coordinates) of this projection.",43,null],[11,"eq","","",44,null],[11,"ne","","",44,null],[11,"encode","","",44,null],[11,"decode","","",44,{"inputs":[{"name":"__dn"}],"output":{"name":"result"}}],[11,"clone","","",44,null],[11,"fmt","","",44,null],[11,"eq","","",45,null],[11,"ne","","",45,null],[11,"encode","","",45,null],[11,"decode","","",45,{"inputs":[{"name":"__dn"}],"output":{"name":"result"}}],[11,"clone","","",45,null],[11,"fmt","","",45,null],[11,"new","","Creates a new 3D orthographic projection.",44,{"inputs":[{"name":"n"},{"name":"n"},{"name":"n"},{"name":"n"},{"name":"n"},{"name":"n"}],"output":{"name":"orthographic3"}}],[11,"to_matrix","","Builds a 4D projection matrix (using homogeneous coordinates) for this projection.",44,null],[11,"to_orthographic_matrix","","Build a `OrthographicMatrix3` representing this projection.",44,null],[11,"left","","The smallest x-coordinate of the view cuboid.",44,null],[11,"right","","The largest x-coordinate of the view cuboid.",44,null],[11,"bottom","","The smallest y-coordinate of the view cuboid.",44,null],[11,"top","","The largest y-coordinate of the view cuboid.",44,null],[11,"znear","","The near plane offset of the view cuboid.",44,null],[11,"zfar","","The far plane offset of the view cuboid.",44,null],[11,"set_left","","Sets the smallest x-coordinate of the view cuboid.",44,null],[11,"set_right","","Sets the largest x-coordinate of the view cuboid.",44,null],[11,"set_bottom","","Sets the smallest y-coordinate of the view cuboid.",44,null],[11,"set_top","","Sets the largest y-coordinate of the view cuboid.",44,null],[11,"set_znear","","Sets the near plane offset of the view cuboid.",44,null],[11,"set_zfar","","Sets the far plane offset of the view cuboid.",44,null],[11,"project_point","","Projects a point.",44,null],[11,"project_vector","","Projects a vector.",44,null],[11,"new","","Creates a new orthographic projection matrix.",45,{"inputs":[{"name":"n"},{"name":"n"},{"name":"n"},{"name":"n"},{"name":"n"},{"name":"n"}],"output":{"name":"orthographicmatrix3"}}],[11,"new_with_fov","","Creates a new orthographic projection matrix from an aspect ratio and the vertical field of view.",45,{"inputs":[{"name":"n"},{"name":"n"},{"name":"n"},{"name":"n"}],"output":{"name":"orthographicmatrix3"}}],[11,"new_with_matrix","","Creates a new orthographic matrix from a 4D matrix.",45,{"inputs":[{"name":"matrix4"}],"output":{"name":"orthographicmatrix3"}}],[11,"as_matrix","","Returns a reference to the 4D matrix (using homogeneous coordinates) of this projection.",45,null],[11,"left","","The smallest x-coordinate of the view cuboid.",45,null],[11,"right","","The largest x-coordinate of the view cuboid.",45,null],[11,"bottom","","The smallest y-coordinate of the view cuboid.",45,null],[11,"top","","The largest y-coordinate of the view cuboid.",45,null],[11,"znear","","The near plane offset of the view cuboid.",45,null],[11,"zfar","","The far plane offset of the view cuboid.",45,null],[11,"set_left","","Sets the smallest x-coordinate of the view cuboid.",45,null],[11,"set_right","","Sets the largest x-coordinate of the view cuboid.",45,null],[11,"set_bottom","","Sets the smallest y-coordinate of the view cuboid.",45,null],[11,"set_top","","Sets the largest y-coordinate of the view cuboid.",45,null],[11,"set_znear","","Sets the near plane offset of the view cuboid.",45,null],[11,"set_zfar","","Sets the far plane offset of the view cuboid.",45,null],[11,"set_left_and_right","","Sets the view cuboid coordinates along the `x` axis.",45,null],[11,"set_bottom_and_top","","Sets the view cuboid coordinates along the `y` axis.",45,null],[11,"set_znear_and_zfar","","Sets the near and far plane offsets of the view cuboid.",45,null],[11,"project_point","","Projects a point.",45,null],[11,"project_vector","","Projects a vector.",45,null],[11,"to_matrix","","Returns the 4D matrix (using homogeneous coordinates) of this projection.",45,null],[11,"one","","",39,{"inputs":[],"output":{"name":"identity"}}],[11,"inverse","","",39,null],[11,"inverse_mut","","",39,null],[11,"mul","","",39,null],[11,"transpose","","",39,null],[11,"transpose_mut","","",39,null],[11,"translate","","",39,null],[11,"inverse_translate","","",39,null],[11,"rotate","","",39,null],[11,"inverse_rotate","","",39,null],[11,"absolute_rotate","","",39,null],[11,"transform","","",39,null],[11,"inverse_transform","","",39,null],[11,"inverse","","",5,null],[11,"inverse_mut","","",5,null],[11,"inverse","","",6,null],[11,"inverse_mut","","",6,null],[11,"inverse","","",7,null],[11,"inverse_mut","","",7,null],[11,"determinant","","",5,null],[11,"determinant","","",6,null],[11,"determinant","","",7,null],[11,"nrows","","",7,null],[11,"row","","",7,null],[11,"set_row","","",7,null],[11,"ncols","","",7,null],[11,"column","","",7,null],[11,"set_column","","",7,null],[11,"mul","","",7,null],[11,"mul","","",6,null],[11,"mul","","",7,null],[11,"mul","","",13,null],[11,"mul","","",12,null],[11,"mul","","",6,null],[11,"mul","","",7,null],[11,"mul","","",19,null],[11,"mul","","",18,null],[11,"mul","","",6,null],[11,"mul_assign","","",7,null],[11,"mul_assign","","",6,null],[11,"mul_assign","","",13,null],[11,"mul_assign","","",12,null],[11,"mul_assign","","",19,null],[11,"mul_assign","","",18,null],[11,"angle_to","","",12,null],[11,"rotation_to","","",12,null],[11,"angle_to","","",13,null],[11,"rotation_to","","",13,null],[11,"cross","","",12,null],[11,"cross_matrix","","",12,null],[11,"cross","","",13,null],[11,"cross_matrix","","",13,null],[11,"nrows","","",12,null],[11,"row","","",12,null],[11,"set_row","","",12,null],[11,"canonical_basis","","",11,{"inputs":[{"name":"f"}],"output":null}],[11,"orthonormal_subspace_basis","","",11,{"inputs":[{"name":"vector1"},{"name":"f"}],"output":null}],[11,"canonical_basis_element","","",11,{"inputs":[{"name":"usize"}],"output":{"name":"option"}}],[11,"canonical_basis","","",12,{"inputs":[{"name":"f"}],"output":null}],[11,"orthonormal_subspace_basis","","",12,{"inputs":[{"name":"vector2"},{"name":"f"}],"output":null}],[11,"canonical_basis_element","","",12,{"inputs":[{"name":"usize"}],"output":{"name":"option"}}],[11,"canonical_basis","","",13,{"inputs":[{"name":"f"}],"output":null}],[11,"orthonormal_subspace_basis","","",13,{"inputs":[{"name":"vector3"},{"name":"f"}],"output":null}],[11,"canonical_basis_element","","",13,{"inputs":[{"name":"usize"}],"output":{"name":"option"}}],[11,"sample","","",11,{"inputs":[{"name":"f"}],"output":null}],[11,"sample","","",12,{"inputs":[{"name":"f"}],"output":null}],[11,"sample","","",13,{"inputs":[{"name":"f"}],"output":null}],[11,"sample","","",14,{"inputs":[{"name":"f"}],"output":null}],[11,"eq","","",24,null],[11,"encode","","",24,null],[11,"decode","","",24,{"inputs":[{"name":"__d"}],"output":{"name":"result"}}],[11,"clone","","",24,null],[11,"fmt","","",24,null],[11,"is_eq","","Returns `true` if `self` is equal to `Equal`.",24,null],[11,"is_lt","","Returns `true` if `self` is equal to `Less`.",24,null],[11,"is_le","","Returns `true` if `self` is equal to `Less` or `Equal`.",24,null],[11,"is_gt","","Returns `true` if `self` is equal to `Greater`.",24,null],[11,"is_ge","","Returns `true` if `self` is equal to `Greater` or `Equal`.",24,null],[11,"is_not_comparable","","Returns `true` if `self` is equal to `NotComparable`.",24,null],[11,"from_ordering","","Creates a `PartialOrdering` from an `Ordering`.",24,{"inputs":[{"name":"ordering"}],"output":{"name":"partialordering"}}],[11,"to_ordering","","Converts this `PartialOrdering` to an `Ordering`.",24,null],[8,"Absolute","","Trait of objects having an absolute value.\nThis is useful if the object does not have the same type as its absolute value.",null,null],[10,"abs","","Computes some absolute value of this object.\nTypically, this will make all component of a matrix or vector positive.",46,{"inputs":[{"name":"self"}],"output":{"name":"a"}}],[8,"AbsoluteRotate","","Composition of a rotation and an absolute value.",null,null],[10,"absolute_rotate","","This is the same as:",47,null],[8,"ApproxEq","","Trait for testing approximate equality",null,null],[10,"approx_epsilon","","Default epsilon for approximation.",48,{"inputs":[{"name":"option"}],"output":{"name":"eps"}}],[10,"approx_eq_eps","","Tests approximate equality using a custom epsilon.",48,null],[10,"approx_ulps","","Default ULPs for approximation.",48,{"inputs":[{"name":"option"}],"output":{"name":"u32"}}],[10,"approx_eq_ulps","","Tests approximate equality using units in the last place (ULPs)",48,null],[11,"approx_eq","","Tests approximate equality.",48,null],[8,"Axpy","","Trait of objects implementing the `y = ax + y` operation.",null,null],[10,"axpy","","Adds $$a * x$$ to `self`.",49,null],[8,"Basis","","Traits of objects which can form a basis (typically vectors).",null,null],[10,"canonical_basis","","Iterates through the canonical basis of the space in which this object lives.",50,{"inputs":[{"name":"f"}],"output":null}],[10,"orthonormal_subspace_basis","","Iterates through a basis of the subspace orthogonal to `self`.",50,{"inputs":[{"name":"self"},{"name":"f"}],"output":null}],[10,"canonical_basis_element","","Gets the ith element of the canonical basis.",50,{"inputs":[{"name":"usize"}],"output":{"name":"option"}}],[8,"BaseFloat","","Basic floating-point number numeric trait.",null,null],[10,"pi","","Archimedes' constant.",51,{"inputs":[],"output":{"name":"self"}}],[10,"two_pi","","2.0 * pi.",51,{"inputs":[],"output":{"name":"self"}}],[10,"frac_pi_2","","pi / 2.0.",51,{"inputs":[],"output":{"name":"self"}}],[10,"frac_pi_3","","pi / 3.0.",51,{"inputs":[],"output":{"name":"self"}}],[10,"frac_pi_4","","pi / 4.0.",51,{"inputs":[],"output":{"name":"self"}}],[10,"frac_pi_6","","pi / 6.0.",51,{"inputs":[],"output":{"name":"self"}}],[10,"frac_pi_8","","pi / 8.0.",51,{"inputs":[],"output":{"name":"self"}}],[10,"frac_1_pi","","1.0 / pi.",51,{"inputs":[],"output":{"name":"self"}}],[10,"frac_2_pi","","2.0 / pi.",51,{"inputs":[],"output":{"name":"self"}}],[10,"frac_2_sqrt_pi","","2.0 / sqrt(pi).",51,{"inputs":[],"output":{"name":"self"}}],[10,"e","","Euler's number.",51,{"inputs":[],"output":{"name":"self"}}],[10,"log2_e","","log2(e).",51,{"inputs":[],"output":{"name":"self"}}],[10,"log10_e","","log10(e).",51,{"inputs":[],"output":{"name":"self"}}],[10,"ln_2","","ln(2.0).",51,{"inputs":[],"output":{"name":"self"}}],[10,"ln_10","","ln(10.0).",51,{"inputs":[],"output":{"name":"self"}}],[8,"BaseNum","","Basic integral numeric trait.",null,null],[8,"Bounded","","Types that have maximum and minimum value.",null,null],[10,"min_value","","The minimum value.",52,{"inputs":[],"output":{"name":"self"}}],[10,"max_value","","The maximum value.",52,{"inputs":[],"output":{"name":"self"}}],[8,"Cast","","Traits of objects which can be created from an object of type `T`.",null,null],[10,"from","","Converts an element of type `T` to an element of type `Self`.",53,{"inputs":[{"name":"t"}],"output":{"name":"self"}}],[8,"Column","","Trait to access columns of a matrix or vector.",null,null],[10,"ncols","","The number of column of this matrix or vector.",54,null],[10,"column","","Reads the `i`-th column of `self`.",54,null],[10,"set_column","","Writes the `i`-th column of `self`.",54,null],[8,"ColumnSlice","","Trait to access part of a column of a matrix",null,null],[10,"column_slice","","Returns a view to a slice of a column of a matrix.",55,null],[8,"RowSlice","","Trait to access part of a row of a matrix",null,null],[10,"row_slice","","Returns a view to a slice of a row of a matrix.",56,null],[8,"Covariance","","Trait for computing the covariance of a set of data.",null,null],[10,"covariance","","Computes the covariance of the obsevations stored by `m`:",57,null],[11,"covariance_to","","Computes the covariance of the obsevations stored by `m`:",57,null],[8,"Cross","","Trait of elements having a cross product.",null,null],[16,"CrossProductType","","The cross product output.",58,null],[10,"cross","","Computes the cross product between two elements (usually vectors).",58,null],[8,"CrossMatrix","","Trait of elements having a cross product operation which can be expressed as a matrix.",null,null],[10,"cross_matrix","","The matrix associated to any cross product with this vector. I.e. `v.cross(anything)` =\n`v.cross_matrix().rmul(anything)`.",59,null],[8,"Determinant","","Trait of objects having a determinant. Typically used by square matrices.",null,null],[10,"determinant","","Returns the determinant of `m`.",60,null],[8,"Diagonal","","Trait to get the diagonal of square matrices.",null,null],[10,"from_diagonal","","Creates a new matrix with the given diagonal.",61,{"inputs":[{"name":"v"}],"output":{"name":"self"}}],[10,"diagonal","","The diagonal of this matrix.",61,null],[8,"Dimension","","Trait of objects having a spacial dimension known at compile time.",null,null],[10,"dimension","","The dimension of the object.",62,{"inputs":[{"name":"option"}],"output":{"name":"usize"}}],[8,"Dot","","Traits of objects having a dot product.",null,null],[10,"dot","","Computes the dot (inner) product of two vectors.",63,null],[8,"EigenQR","","Trait for computing the eigenvector and eigenvalues of a square matrix usin the QR algorithm.",null,null],[10,"eigen_qr","","Computes the eigenvectors and eigenvalues of this matrix.",64,null],[8,"Eye","","Trait for constructing the identity matrix",null,null],[10,"new_identity","","Return the identity matrix of specified dimension",65,{"inputs":[{"name":"usize"}],"output":{"name":"self"}}],[8,"FloatPoint","","Trait of points with components implementing the `BaseFloat` trait.",null,null],[11,"distance_squared","","Computes the square distance between two points.",66,null],[11,"distance","","Computes the distance between two points.",66,null],[8,"FloatVector","","Trait of vector with components implementing the `BaseFloat` trait.",null,null],[8,"FromHomogeneous","","Traits of objects which can be build from an homogeneous coordinate form.",null,null],[10,"from","","Builds an object from its homogeneous coordinate form.",67,{"inputs":[{"name":"u"}],"output":{"name":"self"}}],[8,"Indexable","","This is a workaround of current Rust limitations.",null,null],[10,"swap","","Swaps the `i`-th element of `self` with its `j`-th element.",68,null],[10,"unsafe_at","","Reads the `i`-th element of `self`.",68,null],[10,"unsafe_set","","Writes to the `i`-th element of `self`.",68,null],[8,"Inverse","","Trait of objects having an inverse. Typically used to implement matrix inverse.",null,null],[10,"inverse","","Returns the inverse of `m`.",69,null],[10,"inverse_mut","","In-place version of `inverse`.",69,null],[8,"Iterable","","This is a workaround of current Rust limitations.",null,null],[10,"iter","","Gets a vector-like read-only iterator.",70,null],[8,"IterableMut","","This is a workaround of current Rust limitations.",null,null],[10,"iter_mut","","Gets a vector-like read-write iterator.",71,null],[8,"Matrix","","Trait of matrices.",null,null],[8,"Mean","","Trait for computing the mean of a set of data.",null,null],[10,"mean","","Computes the mean of the observations stored by `v`.",72,null],[8,"Norm","","Traits of objects having an euclidian norm.",null,null],[11,"norm","","Computes the norm of `self`.",73,null],[10,"norm_squared","","Computes the squared norm of `self`.",73,null],[10,"normalize","","Gets the normalized version of a copy of `v`.",73,null],[10,"normalize_mut","","Normalizes `self`.",73,null],[8,"NumPoint","","Trait grouping most common operations on points.",null,null],[8,"NumVector","","Trait grouping most common operations on vectors.",null,null],[8,"Origin","","The zero element of a vector space, seen as an element of its embeding affine space.",null,null],[10,"origin","","The trivial origin.",74,{"inputs":[],"output":{"name":"self"}}],[10,"is_origin","","Returns true if this points is exactly the trivial origin.",74,null],[8,"Outer","","Traits of objects having an outer product.",null,null],[16,"OuterProductType","","Result type of the outer product.",75,null],[10,"outer","","Computes the outer product: `a * b`",75,null],[8,"PartialOrder","","Pointwise ordering operations.",null,null],[10,"inf","","Returns the infimum of this value and another",76,null],[10,"sup","","Returns the supremum of this value and another",76,null],[10,"partial_cmp","","Compare `self` and `other` using a partial ordering relation.",76,null],[11,"partial_le","","Returns `true` iff `self` and `other` are comparable and `self <= other`.",76,null],[11,"partial_lt","","Returns `true` iff `self` and `other` are comparable and `self < other`.",76,null],[11,"partial_ge","","Returns `true` iff `self` and `other` are comparable and `self >= other`.",76,null],[11,"partial_gt","","Returns `true` iff `self` and `other` are comparable and `self > other`.",76,null],[11,"partial_min","","Return the minimum of `self` and `other` if they are comparable.",76,null],[11,"partial_max","","Return the maximum of `self` and `other` if they are comparable.",76,null],[11,"partial_clamp","","Clamp `value` between `min` and `max`. Returns `None` if `value` is not comparable to\n`min` or `max`.",76,null],[8,"PointAsVector","","Trait that relates a point of an affine space to a vector of the associated vector space.",null,null],[16,"Vector","","The vector type of the vector space associated to this point's affine space.",77,null],[10,"to_vector","","Converts this point to its associated vector.",77,null],[10,"as_vector","","Converts a reference to this point to a reference to its associated vector.",77,null],[10,"set_coords","","Sets the coordinates of this point to match those of a given vector.",77,null],[8,"Repeat","","Trait for constructiong an object repeating a value.",null,null],[10,"repeat","","Returns a value with filled by `val`.",78,{"inputs":[{"name":"n"}],"output":{"name":"self"}}],[8,"Rotate","","Trait of objects able to rotate other objects.",null,null],[10,"rotate","","Applies a rotation to `v`.",79,null],[10,"inverse_rotate","","Applies an inverse rotation to `v`.",79,null],[8,"Rotation","","Trait of object which can represent a rotation, and to which new rotations can be appended. A\nrotation is assumed to be an isometry without translation and without reflexion.",null,null],[10,"rotation","","Gets the rotation associated with `self`.",80,null],[10,"inverse_rotation","","Gets the inverse rotation associated with `self`.",80,null],[10,"append_rotation_mut","","Appends a rotation to this object.",80,null],[10,"append_rotation","","Appends the rotation `amount` to a copy of `t`.",80,null],[10,"prepend_rotation_mut","","Prepends a rotation to this object.",80,null],[10,"prepend_rotation","","Prepends the rotation `amount` to a copy of `t`.",80,null],[10,"set_rotation","","Sets the rotation of `self`.",80,null],[8,"RotationMatrix","","Trait of transformation having a rotation extractable as a rotation matrix. This can typically\nbe implemented by quaternions to convert them to a rotation matrix.",null,null],[16,"Output","","The output rotation matrix type.",81,null],[10,"to_rotation_matrix","","Gets the rotation matrix represented by `self`.",81,null],[8,"RotationWithTranslation","","Various composition of rotation and translation.",null,null],[11,"append_rotation_wrt_point","","Applies a rotation centered on a specific point.",82,null],[11,"append_rotation_wrt_point_mut","","Rotates `self` using a specific center of rotation.",82,null],[11,"append_rotation_wrt_center","","Applies a rotation centered on the translation of `m`.",82,null],[11,"append_rotation_wrt_center_mut","","Applies a rotation centered on the translation of `m`.",82,null],[8,"RotationTo","","Trait of object that can be rotated to be superimposed with another one of the same nature.",null,null],[16,"AngleType","","Type of the angle between two elements.",83,null],[16,"DeltaRotationType","","Type of the rotation between two elements.",83,null],[10,"angle_to","","Computes an angle nedded to transform the first element to the second one using a\nrotation.",83,null],[10,"rotation_to","","Computes the smallest rotation needed to transform the first element to the second one.",83,null],[8,"Row","","Trait to access rows of a matrix or a vector.",null,null],[10,"nrows","","The number of column of `self`.",84,null],[10,"row","","Reads the `i`-th row of `self`.",84,null],[10,"set_row","","Writes the `i`-th row of `self`.",84,null],[8,"Shape","","The shape of an indexable object.",null,null],[10,"shape","","Returns the shape of an indexable object.",85,null],[8,"SquareMatrix","","Trait implemented by square matrices.",null,null],[8,"ToHomogeneous","","Traits of objects which can be put in homogeneous coordinates form.",null,null],[10,"to_homogeneous","","Gets the homogeneous coordinates form of this object.",86,null],[8,"Transform","","Trait of objects able to transform other objects.",null,null],[10,"transform","","Applies a transformation to `v`.",87,null],[10,"inverse_transform","","Applies an inverse transformation to `v`.",87,null],[8,"Transformation","","Trait of object which represent a transformation, and to which new transformations can\nbe appended.",null,null],[10,"transformation","","Gets the transformation of `self`.",88,null],[10,"inverse_transformation","","Gets the inverse transformation of `self`.",88,null],[10,"append_transformation_mut","","Appends a transformation to this object.",88,null],[10,"append_transformation","","Appends the transformation `amount` to a copy of `t`.",88,null],[10,"prepend_transformation_mut","","Prepends a transformation to this object.",88,null],[10,"prepend_transformation","","Prepends the transformation `amount` to a copy of `t`.",88,null],[10,"set_transformation","","Sets the transformation of `self`.",88,null],[8,"Translate","","Trait of objects able to translate other objects. This is typically\nimplemented by vectors to translate points.",null,null],[10,"translate","","Apply a translation to an object.",89,null],[10,"inverse_translate","","Apply an inverse translation to an object.",89,null],[8,"Translation","","Trait of object which represent a translation, and to wich new translation\ncan be appended.",null,null],[10,"translation","","Gets the translation associated with this object.",90,null],[10,"inverse_translation","","Gets the inverse translation associated with this object.",90,null],[10,"append_translation_mut","","Appends a translation to this object.",90,null],[10,"append_translation","","Appends the translation `amount` to a copy of `t`.",90,null],[10,"prepend_translation_mut","","Prepends a translation to this object.",90,null],[10,"prepend_translation","","Prepends the translation `amount` to a copy of `t`.",90,null],[10,"set_translation","","Sets the translation.",90,null],[8,"Transpose","","Trait of objects which can be transposed.",null,null],[10,"transpose","","Computes the transpose of a matrix.",91,null],[10,"transpose_mut","","In-place version of `transposed`.",91,null],[8,"UniformSphereSample","","Trait of vectors able to sample a unit sphere.",null,null],[10,"sample","","Iterate through the samples.",92,{"inputs":[{"name":"f"}],"output":null}],[14,"assert_approx_eq_eps","","Asserts approximate equality within a given tolerance of two values with the\n`ApproxEq` trait.",null,null],[14,"assert_approx_eq_ulps","","Asserts approximate equality within a given tolerance of two values with the\n`ApproxEq` trait, with tolerance specified in ULPs.",null,null],[14,"assert_approx_eq","","Asserts approximate equality of two values with the `ApproxEq` trait.",null,null],[11,"append_rotation_wrt_point","","Applies a rotation centered on a specific point.",82,null],[11,"append_rotation_wrt_point_mut","","Rotates `self` using a specific center of rotation.",82,null],[11,"append_rotation_wrt_center","","Applies a rotation centered on the translation of `m`.",82,null],[11,"append_rotation_wrt_center_mut","","Applies a rotation centered on the translation of `m`.",82,null],[11,"norm","","Computes the norm of `self`.",73,null],[11,"distance_squared","","Computes the square distance between two points.",66,null],[11,"distance","","Computes the distance between two points.",66,null],[11,"partial_le","","Returns `true` iff `self` and `other` are comparable and `self <= other`.",76,null],[11,"partial_lt","","Returns `true` iff `self` and `other` are comparable and `self < other`.",76,null],[11,"partial_ge","","Returns `true` iff `self` and `other` are comparable and `self >= other`.",76,null],[11,"partial_gt","","Returns `true` iff `self` and `other` are comparable and `self > other`.",76,null],[11,"partial_min","","Return the minimum of `self` and `other` if they are comparable.",76,null],[11,"partial_max","","Return the maximum of `self` and `other` if they are comparable.",76,null],[11,"partial_clamp","","Clamp `value` between `min` and `max`. Returns `None` if `value` is not comparable to\n`min` or `max`.",76,null],[11,"approx_eq","","Tests approximate equality.",48,null],[11,"covariance_to","","Computes the covariance of the obsevations stored by `m`:",57,null],[11,"norm","","Computes the norm of `self`.",73,null],[11,"append_rotation_wrt_point","","Applies a rotation centered on a specific point.",82,null],[11,"append_rotation_wrt_point_mut","","Rotates `self` using a specific center of rotation.",82,null],[11,"append_rotation_wrt_center","","Applies a rotation centered on the translation of `m`.",82,null],[11,"append_rotation_wrt_center_mut","","Applies a rotation centered on the translation of `m`.",82,null],[11,"distance_squared","","Computes the square distance between two points.",66,null],[11,"distance","","Computes the distance between two points.",66,null],[11,"approx_eq","","Tests approximate equality.",48,null],[11,"covariance_to","","Computes the covariance of the obsevations stored by `m`:",57,null],[11,"partial_le","","Returns `true` iff `self` and `other` are comparable and `self <= other`.",76,null],[11,"partial_lt","","Returns `true` iff `self` and `other` are comparable and `self < other`.",76,null],[11,"partial_ge","","Returns `true` iff `self` and `other` are comparable and `self >= other`.",76,null],[11,"partial_gt","","Returns `true` iff `self` and `other` are comparable and `self > other`.",76,null],[11,"partial_min","","Return the minimum of `self` and `other` if they are comparable.",76,null],[11,"partial_max","","Return the maximum of `self` and `other` if they are comparable.",76,null],[11,"partial_clamp","","Clamp `value` between `min` and `max`. Returns `None` if `value` is not comparable to\n`min` or `max`.",76,null]],"paths":[[3,"DVector"],[3,"Isometry2"],[3,"Isometry3"],[3,"Similarity2"],[3,"Similarity3"],[3,"Matrix1"],[3,"Matrix2"],[3,"Matrix3"],[3,"Matrix4"],[3,"Matrix5"],[3,"Matrix6"],[3,"Vector1"],[3,"Vector2"],[3,"Vector3"],[3,"Vector4"],[3,"Vector5"],[3,"Vector6"],[3,"Point1"],[3,"Point2"],[3,"Point3"],[3,"Point4"],[3,"Point5"],[3,"Point6"],[3,"Quaternion"],[4,"PartialOrdering"],[3,"DMatrix"],[3,"DMatrix1"],[3,"DVector1"],[3,"DMatrix2"],[3,"DVector2"],[3,"DMatrix3"],[3,"DVector3"],[3,"DMatrix4"],[3,"DVector4"],[3,"DMatrix5"],[3,"DVector5"],[3,"DMatrix6"],[3,"DVector6"],[3,"UnitQuaternion"],[3,"Identity"],[3,"Rotation2"],[3,"Rotation3"],[3,"Perspective3"],[3,"PerspectiveMatrix3"],[3,"Orthographic3"],[3,"OrthographicMatrix3"],[8,"Absolute"],[8,"AbsoluteRotate"],[8,"ApproxEq"],[8,"Axpy"],[8,"Basis"],[8,"BaseFloat"],[8,"Bounded"],[8,"Cast"],[8,"Column"],[8,"ColumnSlice"],[8,"RowSlice"],[8,"Covariance"],[8,"Cross"],[8,"CrossMatrix"],[8,"Determinant"],[8,"Diagonal"],[8,"Dimension"],[8,"Dot"],[8,"EigenQR"],[8,"Eye"],[8,"FloatPoint"],[8,"FromHomogeneous"],[8,"Indexable"],[8,"Inverse"],[8,"Iterable"],[8,"IterableMut"],[8,"Mean"],[8,"Norm"],[8,"Origin"],[8,"Outer"],[8,"PartialOrder"],[8,"PointAsVector"],[8,"Repeat"],[8,"Rotate"],[8,"Rotation"],[8,"RotationMatrix"],[8,"RotationWithTranslation"],[8,"RotationTo"],[8,"Row"],[8,"Shape"],[8,"ToHomogeneous"],[8,"Transform"],[8,"Transformation"],[8,"Translate"],[8,"Translation"],[8,"Transpose"],[8,"UniformSphereSample"]]};
searchIndex["num"] = {"doc":"A collection of numeric types and traits for Rust.","items":[[3,"BigInt","num","A big signed integer type.",null,null],[3,"BigUint","","A big unsigned integer type.",null,null],[6,"Rational","","Alias for a `Ratio` of machine-sized integers.",null,null],[6,"BigRational","","Alias for arbitrary precision rationals.",null,null],[3,"Complex","","A complex number in Cartesian form.",null,null],[12,"re","","Real portion of the complex number",0,null],[12,"im","","Imaginary portion of the complex number",0,null],[8,"Integer","","",null,null],[10,"div_floor","","Floored integer division.",1,null],[10,"mod_floor","","Floored integer modulo, satisfying:",1,null],[10,"gcd","","Greatest Common Divisor (GCD).",1,null],[10,"lcm","","Lowest Common Multiple (LCM).",1,null],[10,"divides","","Deprecated, use `is_multiple_of` instead.",1,null],[10,"is_multiple_of","","Returns `true` if `other` is a multiple of `self`.",1,null],[10,"is_even","","Returns `true` if the number is even.",1,null],[10,"is_odd","","Returns `true` if the number is odd.",1,null],[10,"div_rem","","Simultaneous truncated integer division and modulus.\nReturns `(quotient, remainder)`.",1,null],[11,"div_mod_floor","","Simultaneous floored integer division and modulus.\nReturns `(quotient, remainder)`.",1,null],[5,"range","","Returns an iterator over the given range [start, stop) (that is, starting\nat start (inclusive), and ending at stop (exclusive)).",null,{"inputs":[{"name":"a"},{"name":"a"}],"output":{"name":"range"}}],[5,"range_inclusive","","Return an iterator over the range [start, stop]",null,{"inputs":[{"name":"a"},{"name":"a"}],"output":{"name":"rangeinclusive"}}],[5,"range_step","","Return an iterator over the range [start, stop) by `step`. It handles overflow by stopping.",null,{"inputs":[{"name":"a"},{"name":"a"},{"name":"a"}],"output":{"name":"rangestep"}}],[5,"range_step_inclusive","","Return an iterator over the range [start, stop] by `step`. It handles overflow by stopping.",null,{"inputs":[{"name":"a"},{"name":"a"},{"name":"a"}],"output":{"name":"rangestepinclusive"}}],[8,"Num","","The base trait for numeric types",null,null],[16,"FromStrRadixErr","","",2,null],[10,"from_str_radix","","Convert from a string and radix <= 36.",2,{"inputs":[{"name":"str"},{"name":"u32"}],"output":{"name":"result"}}],[8,"Zero","","Defines an additive identity element for `Self`.",null,null],[10,"zero","","Returns the additive identity element of `Self`, `0`.",3,{"inputs":[],"output":{"name":"self"}}],[10,"is_zero","","Returns `true` if `self` is equal to the additive identity.",3,null],[8,"One","","Defines a multiplicative identity element for `Self`.",null,null],[10,"one","","Returns the multiplicative identity element of `Self`, `1`.",4,{"inputs":[],"output":{"name":"self"}}],[8,"Signed","","Useful functions for signed numbers (i.e. numbers that can be negative).",null,null],[10,"abs","","Computes the absolute value.",5,null],[10,"abs_sub","","The positive difference of two numbers.",5,null],[10,"signum","","Returns the sign of the number.",5,null],[10,"is_positive","","Returns true if the number is positive and false if the number is zero or negative.",5,null],[10,"is_negative","","Returns true if the number is negative and false if the number is zero or positive.",5,null],[8,"Unsigned","","A trait for values which cannot be negative",null,null],[8,"Bounded","","Numbers which have upper and lower bounds",null,null],[10,"min_value","","returns the smallest finite number this type can represent",6,{"inputs":[],"output":{"name":"self"}}],[10,"max_value","","returns the largest finite number this type can represent",6,{"inputs":[],"output":{"name":"self"}}],[8,"Saturating","","Saturating math operations",null,null],[10,"saturating_add","","Saturating addition operator.\nReturns a+b, saturating at the numeric bounds instead of overflowing.",7,null],[10,"saturating_sub","","Saturating subtraction operator.\nReturns a-b, saturating at the numeric bounds instead of overflowing.",7,null],[8,"CheckedAdd","","Performs addition that returns `None` instead of wrapping around on\noverflow.",null,null],[10,"checked_add","","Adds two numbers, checking for overflow. If overflow happens, `None` is\nreturned.",8,null],[8,"CheckedSub","","Performs subtraction that returns `None` instead of wrapping around on underflow.",null,null],[10,"checked_sub","","Subtracts two numbers, checking for underflow. If underflow happens,\n`None` is returned.",9,null],[8,"CheckedMul","","Performs multiplication that returns `None` instead of wrapping around on underflow or\noverflow.",null,null],[10,"checked_mul","","Multiplies two numbers, checking for underflow or overflow. If underflow\nor overflow happens, `None` is returned.",10,null],[8,"CheckedDiv","","Performs division that returns `None` instead of panicking on division by zero and instead of\nwrapping around on underflow and overflow.",null,null],[10,"checked_div","","Divides two numbers, checking for underflow, overflow and division by\nzero. If any of that happens, `None` is returned.",11,null],[8,"PrimInt","","",null,null],[10,"count_ones","","Returns the number of ones in the binary representation of `self`.",12,null],[10,"count_zeros","","Returns the number of zeros in the binary representation of `self`.",12,null],[10,"leading_zeros","","Returns the number of leading zeros in the binary representation\nof `self`.",12,null],[10,"trailing_zeros","","Returns the number of trailing zeros in the binary representation\nof `self`.",12,null],[10,"rotate_left","","Shifts the bits to the left by a specified amount amount, `n`, wrapping\nthe truncated bits to the end of the resulting integer.",12,null],[10,"rotate_right","","Shifts the bits to the right by a specified amount amount, `n`, wrapping\nthe truncated bits to the beginning of the resulting integer.",12,null],[10,"signed_shl","","Shifts the bits to the left by a specified amount amount, `n`, filling\nzeros in the least significant bits.",12,null],[10,"signed_shr","","Shifts the bits to the right by a specified amount amount, `n`, copying\nthe "sign bit" in the most significant bits even for unsigned types.",12,null],[10,"unsigned_shl","","Shifts the bits to the left by a specified amount amount, `n`, filling\nzeros in the least significant bits.",12,null],[10,"unsigned_shr","","Shifts the bits to the right by a specified amount amount, `n`, filling\nzeros in the most significant bits.",12,null],[10,"swap_bytes","","Reverses the byte order of the integer.",12,null],[10,"from_be","","Convert an integer from big endian to the target's endianness.",12,{"inputs":[{"name":"self"}],"output":{"name":"self"}}],[10,"from_le","","Convert an integer from little endian to the target's endianness.",12,{"inputs":[{"name":"self"}],"output":{"name":"self"}}],[10,"to_be","","Convert `self` to big endian from the target's endianness.",12,null],[10,"to_le","","Convert `self` to little endian from the target's endianness.",12,null],[10,"pow","","Raises self to the power of `exp`, using exponentiation by squaring.",12,null],[8,"Float","","",null,null],[10,"nan","","Returns the `NaN` value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"infinity","","Returns the infinite value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"neg_infinity","","Returns the negative infinite value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"neg_zero","","Returns `-0.0`.",13,{"inputs":[],"output":{"name":"self"}}],[10,"min_value","","Returns the smallest finite value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"min_positive_value","","Returns the smallest positive, normalized value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"max_value","","Returns the largest finite value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"is_nan","","Returns `true` if this value is `NaN` and false otherwise.",13,null],[10,"is_infinite","","Returns `true` if this value is positive infinity or negative infinity and\nfalse otherwise.",13,null],[10,"is_finite","","Returns `true` if this number is neither infinite nor `NaN`.",13,null],[10,"is_normal","","Returns `true` if the number is neither zero, infinite,\n[subnormal][subnormal], or `NaN`.",13,null],[10,"classify","","Returns the floating point category of the number. If only one property\nis going to be tested, it is generally faster to use the specific\npredicate instead.",13,null],[10,"floor","","Returns the largest integer less than or equal to a number.",13,null],[10,"ceil","","Returns the smallest integer greater than or equal to a number.",13,null],[10,"round","","Returns the nearest integer to a number. Round half-way cases away from\n`0.0`.",13,null],[10,"trunc","","Return the integer part of a number.",13,null],[10,"fract","","Returns the fractional part of a number.",13,null],[10,"abs","","Computes the absolute value of `self`. Returns `Float::nan()` if the\nnumber is `Float::nan()`.",13,null],[10,"signum","","Returns a number that represents the sign of `self`.",13,null],[10,"is_sign_positive","","Returns `true` if `self` is positive, including `+0.0` and\n`Float::infinity()`.",13,null],[10,"is_sign_negative","","Returns `true` if `self` is negative, including `-0.0` and\n`Float::neg_infinity()`.",13,null],[10,"mul_add","","Fused multiply-add. Computes `(self * a) + b` with only one rounding\nerror. This produces a more accurate result with better performance than\na separate multiplication operation followed by an add.",13,null],[10,"recip","","Take the reciprocal (inverse) of a number, `1/x`.",13,null],[10,"powi","","Raise a number to an integer power.",13,null],[10,"powf","","Raise a number to a floating point power.",13,null],[10,"sqrt","","Take the square root of a number.",13,null],[10,"exp","","Returns `e^(self)`, (the exponential function).",13,null],[10,"exp2","","Returns `2^(self)`.",13,null],[10,"ln","","Returns the natural logarithm of the number.",13,null],[10,"log","","Returns the logarithm of the number with respect to an arbitrary base.",13,null],[10,"log2","","Returns the base 2 logarithm of the number.",13,null],[10,"log10","","Returns the base 10 logarithm of the number.",13,null],[10,"max","","Returns the maximum of the two numbers.",13,null],[10,"min","","Returns the minimum of the two numbers.",13,null],[10,"abs_sub","","The positive difference of two numbers.",13,null],[10,"cbrt","","Take the cubic root of a number.",13,null],[10,"hypot","","Calculate the length of the hypotenuse of a right-angle triangle given\nlegs of length `x` and `y`.",13,null],[10,"sin","","Computes the sine of a number (in radians).",13,null],[10,"cos","","Computes the cosine of a number (in radians).",13,null],[10,"tan","","Computes the tangent of a number (in radians).",13,null],[10,"asin","","Computes the arcsine of a number. Return value is in radians in\nthe range [-pi/2, pi/2] or NaN if the number is outside the range\n[-1, 1].",13,null],[10,"acos","","Computes the arccosine of a number. Return value is in radians in\nthe range [0, pi] or NaN if the number is outside the range\n[-1, 1].",13,null],[10,"atan","","Computes the arctangent of a number. Return value is in radians in the\nrange [-pi/2, pi/2];",13,null],[10,"atan2","","Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).",13,null],[10,"sin_cos","","Simultaneously computes the sine and cosine of the number, `x`. Returns\n`(sin(x), cos(x))`.",13,null],[10,"exp_m1","","Returns `e^(self) - 1` in a way that is accurate even if the\nnumber is close to zero.",13,null],[10,"ln_1p","","Returns `ln(1+n)` (natural logarithm) more accurately than if\nthe operations were performed separately.",13,null],[10,"sinh","","Hyperbolic sine function.",13,null],[10,"cosh","","Hyperbolic cosine function.",13,null],[10,"tanh","","Hyperbolic tangent function.",13,null],[10,"asinh","","Inverse hyperbolic sine function.",13,null],[10,"acosh","","Inverse hyperbolic cosine function.",13,null],[10,"atanh","","Inverse hyperbolic tangent function.",13,null],[10,"integer_decode","","Returns the mantissa, base 2 exponent, and sign as integers, respectively.\nThe original number can be recovered by `sign * mantissa * 2 ^ exponent`.\nThe floating point encoding is documented in the [Reference][floating-point].",13,null],[8,"ToPrimitive","","A generic trait for converting a value to a number.",null,null],[11,"to_isize","","Converts the value of `self` to an `isize`.",14,null],[11,"to_i8","","Converts the value of `self` to an `i8`.",14,null],[11,"to_i16","","Converts the value of `self` to an `i16`.",14,null],[11,"to_i32","","Converts the value of `self` to an `i32`.",14,null],[10,"to_i64","","Converts the value of `self` to an `i64`.",14,null],[11,"to_usize","","Converts the value of `self` to a `usize`.",14,null],[11,"to_u8","","Converts the value of `self` to an `u8`.",14,null],[11,"to_u16","","Converts the value of `self` to an `u16`.",14,null],[11,"to_u32","","Converts the value of `self` to an `u32`.",14,null],[10,"to_u64","","Converts the value of `self` to an `u64`.",14,null],[11,"to_f32","","Converts the value of `self` to an `f32`.",14,null],[11,"to_f64","","Converts the value of `self` to an `f64`.",14,null],[8,"FromPrimitive","","A generic trait for converting a number to a value.",null,null],[11,"from_isize","","Convert an `isize` to return an optional value of this type. If the\nvalue cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"isize"}],"output":{"name":"option"}}],[11,"from_i8","","Convert an `i8` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i8"}],"output":{"name":"option"}}],[11,"from_i16","","Convert an `i16` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i16"}],"output":{"name":"option"}}],[11,"from_i32","","Convert an `i32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i32"}],"output":{"name":"option"}}],[10,"from_i64","","Convert an `i64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i64"}],"output":{"name":"option"}}],[11,"from_usize","","Convert a `usize` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"usize"}],"output":{"name":"option"}}],[11,"from_u8","","Convert an `u8` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u8"}],"output":{"name":"option"}}],[11,"from_u16","","Convert an `u16` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u16"}],"output":{"name":"option"}}],[11,"from_u32","","Convert an `u32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u32"}],"output":{"name":"option"}}],[10,"from_u64","","Convert an `u64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u64"}],"output":{"name":"option"}}],[11,"from_f32","","Convert a `f32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"f32"}],"output":{"name":"option"}}],[11,"from_f64","","Convert a `f64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"f64"}],"output":{"name":"option"}}],[8,"NumCast","","An interface for casting between machine scalars.",null,null],[10,"from","","Creates a number from another value that can be converted into\na primitive via the `ToPrimitive` trait.",16,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[0,"cast","","",null,null],[8,"ToPrimitive","num::cast","A generic trait for converting a value to a number.",null,null],[11,"to_isize","","Converts the value of `self` to an `isize`.",14,null],[11,"to_i8","","Converts the value of `self` to an `i8`.",14,null],[11,"to_i16","","Converts the value of `self` to an `i16`.",14,null],[11,"to_i32","","Converts the value of `self` to an `i32`.",14,null],[10,"to_i64","","Converts the value of `self` to an `i64`.",14,null],[11,"to_usize","","Converts the value of `self` to a `usize`.",14,null],[11,"to_u8","","Converts the value of `self` to an `u8`.",14,null],[11,"to_u16","","Converts the value of `self` to an `u16`.",14,null],[11,"to_u32","","Converts the value of `self` to an `u32`.",14,null],[10,"to_u64","","Converts the value of `self` to an `u64`.",14,null],[11,"to_f32","","Converts the value of `self` to an `f32`.",14,null],[11,"to_f64","","Converts the value of `self` to an `f64`.",14,null],[8,"FromPrimitive","","A generic trait for converting a number to a value.",null,null],[11,"from_isize","","Convert an `isize` to return an optional value of this type. If the\nvalue cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"isize"}],"output":{"name":"option"}}],[11,"from_i8","","Convert an `i8` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i8"}],"output":{"name":"option"}}],[11,"from_i16","","Convert an `i16` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i16"}],"output":{"name":"option"}}],[11,"from_i32","","Convert an `i32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i32"}],"output":{"name":"option"}}],[10,"from_i64","","Convert an `i64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i64"}],"output":{"name":"option"}}],[11,"from_usize","","Convert a `usize` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"usize"}],"output":{"name":"option"}}],[11,"from_u8","","Convert an `u8` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u8"}],"output":{"name":"option"}}],[11,"from_u16","","Convert an `u16` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u16"}],"output":{"name":"option"}}],[11,"from_u32","","Convert an `u32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u32"}],"output":{"name":"option"}}],[10,"from_u64","","Convert an `u64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u64"}],"output":{"name":"option"}}],[11,"from_f32","","Convert a `f32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"f32"}],"output":{"name":"option"}}],[11,"from_f64","","Convert a `f64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"f64"}],"output":{"name":"option"}}],[5,"cast","","Cast from one machine scalar to another.",null,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[8,"NumCast","","An interface for casting between machine scalars.",null,null],[10,"from","","Creates a number from another value that can be converted into\na primitive via the `ToPrimitive` trait.",16,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[6,"BigDigit","num::bigint","A `BigDigit` is a `BigUint`'s composing element.",null,null],[6,"DoubleBigDigit","","A `DoubleBigDigit` is the internal type used to do the computations.  Its\nsize is the double of the size of `BigDigit`.",null,null],[17,"ZERO_BIG_DIGIT","","",null,null],[0,"big_digit","","",null,null],[17,"BITS","num::bigint::big_digit","",null,null],[17,"BASE","","",null,null],[5,"from_doublebigdigit","","Split one `DoubleBigDigit` into two `BigDigit`s.",null,null],[5,"to_doublebigdigit","","Join two `BigDigit`s into one `DoubleBigDigit`",null,{"inputs":[{"name":"u32"},{"name":"u32"}],"output":{"name":"u64"}}],[3,"BigUint","num::bigint","A big unsigned integer type.",null,null],[8,"ToBigUint","","A generic trait for converting a value to a `BigUint`.",null,null],[10,"to_biguint","","Converts the value of `self` to a `BigUint`.",17,null],[4,"Sign","","A Sign is a `BigInt`'s composing element.",null,null],[13,"Minus","","",18,null],[13,"NoSign","","",18,null],[13,"Plus","","",18,null],[3,"BigInt","","A big signed integer type.",null,null],[8,"ToBigInt","","A generic trait for converting a value to a `BigInt`.",null,null],[10,"to_bigint","","Converts the value of `self` to a `BigInt`.",19,null],[8,"RandBigInt","","",null,null],[10,"gen_biguint","","Generate a random `BigUint` of the given bit size.",20,null],[10,"gen_bigint","","Generate a random BigInt of the given bit size.",20,null],[10,"gen_biguint_below","","Generate a random `BigUint` less than the given bound. Fails\nwhen the bound is zero.",20,null],[10,"gen_biguint_range","","Generate a random `BigUint` within the given range. The lower\nbound is inclusive; the upper bound is exclusive. Fails when\nthe upper bound is not greater than the lower bound.",20,null],[10,"gen_bigint_range","","Generate a random `BigInt` within the given range. The lower\nbound is inclusive; the upper bound is exclusive. Fails when\nthe upper bound is not greater than the lower bound.",20,null],[4,"ParseBigIntError","","",null,null],[13,"ParseInt","","",21,null],[13,"Other","","",21,null],[3,"Complex","num::complex","A complex number in Cartesian form.",null,null],[12,"re","","Real portion of the complex number",0,null],[12,"im","","Imaginary portion of the complex number",0,null],[6,"Complex32","","",null,null],[6,"Complex64","","",null,null],[8,"Integer","num::integer","",null,null],[10,"div_floor","","Floored integer division.",1,null],[10,"mod_floor","","Floored integer modulo, satisfying:",1,null],[10,"gcd","","Greatest Common Divisor (GCD).",1,null],[10,"lcm","","Lowest Common Multiple (LCM).",1,null],[10,"divides","","Deprecated, use `is_multiple_of` instead.",1,null],[10,"is_multiple_of","","Returns `true` if `other` is a multiple of `self`.",1,null],[10,"is_even","","Returns `true` if the number is even.",1,null],[10,"is_odd","","Returns `true` if the number is odd.",1,null],[10,"div_rem","","Simultaneous truncated integer division and modulus.\nReturns `(quotient, remainder)`.",1,null],[11,"div_mod_floor","","Simultaneous floored integer division and modulus.\nReturns `(quotient, remainder)`.",1,null],[5,"div_rem","","Simultaneous integer division and modulus",null,null],[5,"div_floor","","Floored integer division",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[5,"mod_floor","","Floored integer modulus",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[5,"div_mod_floor","","Simultaneous floored integer division and modulus",null,null],[5,"gcd","","Calculates the Greatest Common Divisor (GCD) of the number and `other`. The\nresult is always positive.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[5,"lcm","","Calculates the Lowest Common Multiple (LCM) of the number and `other`.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[3,"Range","num::iter","An iterator over the range [start, stop)",null,null],[5,"range","","Returns an iterator over the given range [start, stop) (that is, starting\nat start (inclusive), and ending at stop (exclusive)).",null,{"inputs":[{"name":"a"},{"name":"a"}],"output":{"name":"range"}}],[3,"RangeInclusive","","An iterator over the range [start, stop]",null,null],[5,"range_inclusive","","Return an iterator over the range [start, stop]",null,{"inputs":[{"name":"a"},{"name":"a"}],"output":{"name":"rangeinclusive"}}],[3,"RangeStep","","An iterator over the range [start, stop) by `step`. It handles overflow by stopping.",null,null],[5,"range_step","","Return an iterator over the range [start, stop) by `step`. It handles overflow by stopping.",null,{"inputs":[{"name":"a"},{"name":"a"},{"name":"a"}],"output":{"name":"rangestep"}}],[3,"RangeStepInclusive","","An iterator over the range [start, stop] by `step`. It handles overflow by stopping.",null,null],[5,"range_step_inclusive","","Return an iterator over the range [start, stop] by `step`. It handles overflow by stopping.",null,{"inputs":[{"name":"a"},{"name":"a"},{"name":"a"}],"output":{"name":"rangestepinclusive"}}],[0,"identities","num::traits","",null,null],[8,"Zero","num::traits::identities","Defines an additive identity element for `Self`.",null,null],[10,"zero","","Returns the additive identity element of `Self`, `0`.",3,{"inputs":[],"output":{"name":"self"}}],[10,"is_zero","","Returns `true` if `self` is equal to the additive identity.",3,null],[8,"One","","Defines a multiplicative identity element for `Self`.",null,null],[10,"one","","Returns the multiplicative identity element of `Self`, `1`.",4,{"inputs":[],"output":{"name":"self"}}],[0,"sign","num::traits","",null,null],[8,"Signed","num::traits::sign","Useful functions for signed numbers (i.e. numbers that can be negative).",null,null],[10,"abs","","Computes the absolute value.",5,null],[10,"abs_sub","","The positive difference of two numbers.",5,null],[10,"signum","","Returns the sign of the number.",5,null],[10,"is_positive","","Returns true if the number is positive and false if the number is zero or negative.",5,null],[10,"is_negative","","Returns true if the number is negative and false if the number is zero or positive.",5,null],[8,"Unsigned","","A trait for values which cannot be negative",null,null],[0,"ops","num::traits","",null,null],[0,"saturating","num::traits::ops","",null,null],[8,"Saturating","num::traits::ops::saturating","Saturating math operations",null,null],[10,"saturating_add","","Saturating addition operator.\nReturns a+b, saturating at the numeric bounds instead of overflowing.",7,null],[10,"saturating_sub","","Saturating subtraction operator.\nReturns a-b, saturating at the numeric bounds instead of overflowing.",7,null],[0,"checked","num::traits::ops","",null,null],[8,"CheckedAdd","num::traits::ops::checked","Performs addition that returns `None` instead of wrapping around on\noverflow.",null,null],[10,"checked_add","","Adds two numbers, checking for overflow. If overflow happens, `None` is\nreturned.",8,null],[8,"CheckedSub","","Performs subtraction that returns `None` instead of wrapping around on underflow.",null,null],[10,"checked_sub","","Subtracts two numbers, checking for underflow. If underflow happens,\n`None` is returned.",9,null],[8,"CheckedMul","","Performs multiplication that returns `None` instead of wrapping around on underflow or\noverflow.",null,null],[10,"checked_mul","","Multiplies two numbers, checking for underflow or overflow. If underflow\nor overflow happens, `None` is returned.",10,null],[8,"CheckedDiv","","Performs division that returns `None` instead of panicking on division by zero and instead of\nwrapping around on underflow and overflow.",null,null],[10,"checked_div","","Divides two numbers, checking for underflow, overflow and division by\nzero. If any of that happens, `None` is returned.",11,null],[0,"bounds","num::traits","",null,null],[8,"Bounded","num::traits::bounds","Numbers which have upper and lower bounds",null,null],[10,"min_value","","returns the smallest finite number this type can represent",6,{"inputs":[],"output":{"name":"self"}}],[10,"max_value","","returns the largest finite number this type can represent",6,{"inputs":[],"output":{"name":"self"}}],[0,"float","num::traits","",null,null],[8,"Float","num::traits::float","",null,null],[10,"nan","","Returns the `NaN` value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"infinity","","Returns the infinite value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"neg_infinity","","Returns the negative infinite value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"neg_zero","","Returns `-0.0`.",13,{"inputs":[],"output":{"name":"self"}}],[10,"min_value","","Returns the smallest finite value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"min_positive_value","","Returns the smallest positive, normalized value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"max_value","","Returns the largest finite value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"is_nan","","Returns `true` if this value is `NaN` and false otherwise.",13,null],[10,"is_infinite","","Returns `true` if this value is positive infinity or negative infinity and\nfalse otherwise.",13,null],[10,"is_finite","","Returns `true` if this number is neither infinite nor `NaN`.",13,null],[10,"is_normal","","Returns `true` if the number is neither zero, infinite,\n[subnormal][subnormal], or `NaN`.",13,null],[10,"classify","","Returns the floating point category of the number. If only one property\nis going to be tested, it is generally faster to use the specific\npredicate instead.",13,null],[10,"floor","","Returns the largest integer less than or equal to a number.",13,null],[10,"ceil","","Returns the smallest integer greater than or equal to a number.",13,null],[10,"round","","Returns the nearest integer to a number. Round half-way cases away from\n`0.0`.",13,null],[10,"trunc","","Return the integer part of a number.",13,null],[10,"fract","","Returns the fractional part of a number.",13,null],[10,"abs","","Computes the absolute value of `self`. Returns `Float::nan()` if the\nnumber is `Float::nan()`.",13,null],[10,"signum","","Returns a number that represents the sign of `self`.",13,null],[10,"is_sign_positive","","Returns `true` if `self` is positive, including `+0.0` and\n`Float::infinity()`.",13,null],[10,"is_sign_negative","","Returns `true` if `self` is negative, including `-0.0` and\n`Float::neg_infinity()`.",13,null],[10,"mul_add","","Fused multiply-add. Computes `(self * a) + b` with only one rounding\nerror. This produces a more accurate result with better performance than\na separate multiplication operation followed by an add.",13,null],[10,"recip","","Take the reciprocal (inverse) of a number, `1/x`.",13,null],[10,"powi","","Raise a number to an integer power.",13,null],[10,"powf","","Raise a number to a floating point power.",13,null],[10,"sqrt","","Take the square root of a number.",13,null],[10,"exp","","Returns `e^(self)`, (the exponential function).",13,null],[10,"exp2","","Returns `2^(self)`.",13,null],[10,"ln","","Returns the natural logarithm of the number.",13,null],[10,"log","","Returns the logarithm of the number with respect to an arbitrary base.",13,null],[10,"log2","","Returns the base 2 logarithm of the number.",13,null],[10,"log10","","Returns the base 10 logarithm of the number.",13,null],[10,"max","","Returns the maximum of the two numbers.",13,null],[10,"min","","Returns the minimum of the two numbers.",13,null],[10,"abs_sub","","The positive difference of two numbers.",13,null],[10,"cbrt","","Take the cubic root of a number.",13,null],[10,"hypot","","Calculate the length of the hypotenuse of a right-angle triangle given\nlegs of length `x` and `y`.",13,null],[10,"sin","","Computes the sine of a number (in radians).",13,null],[10,"cos","","Computes the cosine of a number (in radians).",13,null],[10,"tan","","Computes the tangent of a number (in radians).",13,null],[10,"asin","","Computes the arcsine of a number. Return value is in radians in\nthe range [-pi/2, pi/2] or NaN if the number is outside the range\n[-1, 1].",13,null],[10,"acos","","Computes the arccosine of a number. Return value is in radians in\nthe range [0, pi] or NaN if the number is outside the range\n[-1, 1].",13,null],[10,"atan","","Computes the arctangent of a number. Return value is in radians in the\nrange [-pi/2, pi/2];",13,null],[10,"atan2","","Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).",13,null],[10,"sin_cos","","Simultaneously computes the sine and cosine of the number, `x`. Returns\n`(sin(x), cos(x))`.",13,null],[10,"exp_m1","","Returns `e^(self) - 1` in a way that is accurate even if the\nnumber is close to zero.",13,null],[10,"ln_1p","","Returns `ln(1+n)` (natural logarithm) more accurately than if\nthe operations were performed separately.",13,null],[10,"sinh","","Hyperbolic sine function.",13,null],[10,"cosh","","Hyperbolic cosine function.",13,null],[10,"tanh","","Hyperbolic tangent function.",13,null],[10,"asinh","","Inverse hyperbolic sine function.",13,null],[10,"acosh","","Inverse hyperbolic cosine function.",13,null],[10,"atanh","","Inverse hyperbolic tangent function.",13,null],[10,"integer_decode","","Returns the mantissa, base 2 exponent, and sign as integers, respectively.\nThe original number can be recovered by `sign * mantissa * 2 ^ exponent`.\nThe floating point encoding is documented in the [Reference][floating-point].",13,null],[0,"cast","num::traits","",null,null],[8,"ToPrimitive","num::traits::cast","A generic trait for converting a value to a number.",null,null],[11,"to_isize","","Converts the value of `self` to an `isize`.",14,null],[11,"to_i8","","Converts the value of `self` to an `i8`.",14,null],[11,"to_i16","","Converts the value of `self` to an `i16`.",14,null],[11,"to_i32","","Converts the value of `self` to an `i32`.",14,null],[10,"to_i64","","Converts the value of `self` to an `i64`.",14,null],[11,"to_usize","","Converts the value of `self` to a `usize`.",14,null],[11,"to_u8","","Converts the value of `self` to an `u8`.",14,null],[11,"to_u16","","Converts the value of `self` to an `u16`.",14,null],[11,"to_u32","","Converts the value of `self` to an `u32`.",14,null],[10,"to_u64","","Converts the value of `self` to an `u64`.",14,null],[11,"to_f32","","Converts the value of `self` to an `f32`.",14,null],[11,"to_f64","","Converts the value of `self` to an `f64`.",14,null],[8,"FromPrimitive","","A generic trait for converting a number to a value.",null,null],[11,"from_isize","","Convert an `isize` to return an optional value of this type. If the\nvalue cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"isize"}],"output":{"name":"option"}}],[11,"from_i8","","Convert an `i8` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i8"}],"output":{"name":"option"}}],[11,"from_i16","","Convert an `i16` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i16"}],"output":{"name":"option"}}],[11,"from_i32","","Convert an `i32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i32"}],"output":{"name":"option"}}],[10,"from_i64","","Convert an `i64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i64"}],"output":{"name":"option"}}],[11,"from_usize","","Convert a `usize` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"usize"}],"output":{"name":"option"}}],[11,"from_u8","","Convert an `u8` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u8"}],"output":{"name":"option"}}],[11,"from_u16","","Convert an `u16` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u16"}],"output":{"name":"option"}}],[11,"from_u32","","Convert an `u32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u32"}],"output":{"name":"option"}}],[10,"from_u64","","Convert an `u64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u64"}],"output":{"name":"option"}}],[11,"from_f32","","Convert a `f32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"f32"}],"output":{"name":"option"}}],[11,"from_f64","","Convert a `f64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"f64"}],"output":{"name":"option"}}],[5,"cast","","Cast from one machine scalar to another.",null,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[8,"NumCast","","An interface for casting between machine scalars.",null,null],[10,"from","","Creates a number from another value that can be converted into\na primitive via the `ToPrimitive` trait.",16,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[0,"int","num::traits","",null,null],[8,"PrimInt","num::traits::int","",null,null],[10,"count_ones","","Returns the number of ones in the binary representation of `self`.",12,null],[10,"count_zeros","","Returns the number of zeros in the binary representation of `self`.",12,null],[10,"leading_zeros","","Returns the number of leading zeros in the binary representation\nof `self`.",12,null],[10,"trailing_zeros","","Returns the number of trailing zeros in the binary representation\nof `self`.",12,null],[10,"rotate_left","","Shifts the bits to the left by a specified amount amount, `n`, wrapping\nthe truncated bits to the end of the resulting integer.",12,null],[10,"rotate_right","","Shifts the bits to the right by a specified amount amount, `n`, wrapping\nthe truncated bits to the beginning of the resulting integer.",12,null],[10,"signed_shl","","Shifts the bits to the left by a specified amount amount, `n`, filling\nzeros in the least significant bits.",12,null],[10,"signed_shr","","Shifts the bits to the right by a specified amount amount, `n`, copying\nthe "sign bit" in the most significant bits even for unsigned types.",12,null],[10,"unsigned_shl","","Shifts the bits to the left by a specified amount amount, `n`, filling\nzeros in the least significant bits.",12,null],[10,"unsigned_shr","","Shifts the bits to the right by a specified amount amount, `n`, filling\nzeros in the most significant bits.",12,null],[10,"swap_bytes","","Reverses the byte order of the integer.",12,null],[10,"from_be","","Convert an integer from big endian to the target's endianness.",12,{"inputs":[{"name":"self"}],"output":{"name":"self"}}],[10,"from_le","","Convert an integer from little endian to the target's endianness.",12,{"inputs":[{"name":"self"}],"output":{"name":"self"}}],[10,"to_be","","Convert `self` to big endian from the target's endianness.",12,null],[10,"to_le","","Convert `self` to little endian from the target's endianness.",12,null],[10,"pow","","Raises self to the power of `exp`, using exponentiation by squaring.",12,null],[8,"Num","num::traits","The base trait for numeric types",null,null],[16,"FromStrRadixErr","","",2,null],[10,"from_str_radix","","Convert from a string and radix <= 36.",2,{"inputs":[{"name":"str"},{"name":"u32"}],"output":{"name":"result"}}],[4,"FloatErrorKind","","",null,null],[13,"Empty","","",22,null],[13,"Invalid","","",22,null],[3,"ParseFloatError","","",null,null],[12,"kind","","",23,null],[8,"CheckedDiv","","Performs division that returns `None` instead of panicking on division by zero and instead of\nwrapping around on underflow and overflow.",null,null],[10,"checked_div","","Divides two numbers, checking for underflow, overflow and division by\nzero. If any of that happens, `None` is returned.",11,null],[8,"One","","Defines a multiplicative identity element for `Self`.",null,null],[10,"one","","Returns the multiplicative identity element of `Self`, `1`.",4,{"inputs":[],"output":{"name":"self"}}],[8,"Float","","",null,null],[10,"nan","","Returns the `NaN` value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"infinity","","Returns the infinite value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"neg_infinity","","Returns the negative infinite value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"neg_zero","","Returns `-0.0`.",13,{"inputs":[],"output":{"name":"self"}}],[10,"min_value","","Returns the smallest finite value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"min_positive_value","","Returns the smallest positive, normalized value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"max_value","","Returns the largest finite value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"is_nan","","Returns `true` if this value is `NaN` and false otherwise.",13,null],[10,"is_infinite","","Returns `true` if this value is positive infinity or negative infinity and\nfalse otherwise.",13,null],[10,"is_finite","","Returns `true` if this number is neither infinite nor `NaN`.",13,null],[10,"is_normal","","Returns `true` if the number is neither zero, infinite,\n[subnormal][subnormal], or `NaN`.",13,null],[10,"classify","","Returns the floating point category of the number. If only one property\nis going to be tested, it is generally faster to use the specific\npredicate instead.",13,null],[10,"floor","","Returns the largest integer less than or equal to a number.",13,null],[10,"ceil","","Returns the smallest integer greater than or equal to a number.",13,null],[10,"round","","Returns the nearest integer to a number. Round half-way cases away from\n`0.0`.",13,null],[10,"trunc","","Return the integer part of a number.",13,null],[10,"fract","","Returns the fractional part of a number.",13,null],[10,"abs","","Computes the absolute value of `self`. Returns `Float::nan()` if the\nnumber is `Float::nan()`.",13,null],[10,"signum","","Returns a number that represents the sign of `self`.",13,null],[10,"is_sign_positive","","Returns `true` if `self` is positive, including `+0.0` and\n`Float::infinity()`.",13,null],[10,"is_sign_negative","","Returns `true` if `self` is negative, including `-0.0` and\n`Float::neg_infinity()`.",13,null],[10,"mul_add","","Fused multiply-add. Computes `(self * a) + b` with only one rounding\nerror. This produces a more accurate result with better performance than\na separate multiplication operation followed by an add.",13,null],[10,"recip","","Take the reciprocal (inverse) of a number, `1/x`.",13,null],[10,"powi","","Raise a number to an integer power.",13,null],[10,"powf","","Raise a number to a floating point power.",13,null],[10,"sqrt","","Take the square root of a number.",13,null],[10,"exp","","Returns `e^(self)`, (the exponential function).",13,null],[10,"exp2","","Returns `2^(self)`.",13,null],[10,"ln","","Returns the natural logarithm of the number.",13,null],[10,"log","","Returns the logarithm of the number with respect to an arbitrary base.",13,null],[10,"log2","","Returns the base 2 logarithm of the number.",13,null],[10,"log10","","Returns the base 10 logarithm of the number.",13,null],[10,"max","","Returns the maximum of the two numbers.",13,null],[10,"min","","Returns the minimum of the two numbers.",13,null],[10,"abs_sub","","The positive difference of two numbers.",13,null],[10,"cbrt","","Take the cubic root of a number.",13,null],[10,"hypot","","Calculate the length of the hypotenuse of a right-angle triangle given\nlegs of length `x` and `y`.",13,null],[10,"sin","","Computes the sine of a number (in radians).",13,null],[10,"cos","","Computes the cosine of a number (in radians).",13,null],[10,"tan","","Computes the tangent of a number (in radians).",13,null],[10,"asin","","Computes the arcsine of a number. Return value is in radians in\nthe range [-pi/2, pi/2] or NaN if the number is outside the range\n[-1, 1].",13,null],[10,"acos","","Computes the arccosine of a number. Return value is in radians in\nthe range [0, pi] or NaN if the number is outside the range\n[-1, 1].",13,null],[10,"atan","","Computes the arctangent of a number. Return value is in radians in the\nrange [-pi/2, pi/2];",13,null],[10,"atan2","","Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).",13,null],[10,"sin_cos","","Simultaneously computes the sine and cosine of the number, `x`. Returns\n`(sin(x), cos(x))`.",13,null],[10,"exp_m1","","Returns `e^(self) - 1` in a way that is accurate even if the\nnumber is close to zero.",13,null],[10,"ln_1p","","Returns `ln(1+n)` (natural logarithm) more accurately than if\nthe operations were performed separately.",13,null],[10,"sinh","","Hyperbolic sine function.",13,null],[10,"cosh","","Hyperbolic cosine function.",13,null],[10,"tanh","","Hyperbolic tangent function.",13,null],[10,"asinh","","Inverse hyperbolic sine function.",13,null],[10,"acosh","","Inverse hyperbolic cosine function.",13,null],[10,"atanh","","Inverse hyperbolic tangent function.",13,null],[10,"integer_decode","","Returns the mantissa, base 2 exponent, and sign as integers, respectively.\nThe original number can be recovered by `sign * mantissa * 2 ^ exponent`.\nThe floating point encoding is documented in the [Reference][floating-point].",13,null],[8,"CheckedAdd","","Performs addition that returns `None` instead of wrapping around on\noverflow.",null,null],[10,"checked_add","","Adds two numbers, checking for overflow. If overflow happens, `None` is\nreturned.",8,null],[8,"Signed","","Useful functions for signed numbers (i.e. numbers that can be negative).",null,null],[10,"abs","","Computes the absolute value.",5,null],[10,"abs_sub","","The positive difference of two numbers.",5,null],[10,"signum","","Returns the sign of the number.",5,null],[10,"is_positive","","Returns true if the number is positive and false if the number is zero or negative.",5,null],[10,"is_negative","","Returns true if the number is negative and false if the number is zero or positive.",5,null],[8,"ToPrimitive","","A generic trait for converting a value to a number.",null,null],[11,"to_isize","","Converts the value of `self` to an `isize`.",14,null],[11,"to_i8","","Converts the value of `self` to an `i8`.",14,null],[11,"to_i16","","Converts the value of `self` to an `i16`.",14,null],[11,"to_i32","","Converts the value of `self` to an `i32`.",14,null],[10,"to_i64","","Converts the value of `self` to an `i64`.",14,null],[11,"to_usize","","Converts the value of `self` to a `usize`.",14,null],[11,"to_u8","","Converts the value of `self` to an `u8`.",14,null],[11,"to_u16","","Converts the value of `self` to an `u16`.",14,null],[11,"to_u32","","Converts the value of `self` to an `u32`.",14,null],[10,"to_u64","","Converts the value of `self` to an `u64`.",14,null],[11,"to_f32","","Converts the value of `self` to an `f32`.",14,null],[11,"to_f64","","Converts the value of `self` to an `f64`.",14,null],[8,"FromPrimitive","","A generic trait for converting a number to a value.",null,null],[11,"from_isize","","Convert an `isize` to return an optional value of this type. If the\nvalue cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"isize"}],"output":{"name":"option"}}],[11,"from_i8","","Convert an `i8` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i8"}],"output":{"name":"option"}}],[11,"from_i16","","Convert an `i16` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i16"}],"output":{"name":"option"}}],[11,"from_i32","","Convert an `i32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i32"}],"output":{"name":"option"}}],[10,"from_i64","","Convert an `i64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i64"}],"output":{"name":"option"}}],[11,"from_usize","","Convert a `usize` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"usize"}],"output":{"name":"option"}}],[11,"from_u8","","Convert an `u8` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u8"}],"output":{"name":"option"}}],[11,"from_u16","","Convert an `u16` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u16"}],"output":{"name":"option"}}],[11,"from_u32","","Convert an `u32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u32"}],"output":{"name":"option"}}],[10,"from_u64","","Convert an `u64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u64"}],"output":{"name":"option"}}],[11,"from_f32","","Convert a `f32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"f32"}],"output":{"name":"option"}}],[11,"from_f64","","Convert a `f64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"f64"}],"output":{"name":"option"}}],[5,"cast","","Cast from one machine scalar to another.",null,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[8,"PrimInt","","",null,null],[10,"count_ones","","Returns the number of ones in the binary representation of `self`.",12,null],[10,"count_zeros","","Returns the number of zeros in the binary representation of `self`.",12,null],[10,"leading_zeros","","Returns the number of leading zeros in the binary representation\nof `self`.",12,null],[10,"trailing_zeros","","Returns the number of trailing zeros in the binary representation\nof `self`.",12,null],[10,"rotate_left","","Shifts the bits to the left by a specified amount amount, `n`, wrapping\nthe truncated bits to the end of the resulting integer.",12,null],[10,"rotate_right","","Shifts the bits to the right by a specified amount amount, `n`, wrapping\nthe truncated bits to the beginning of the resulting integer.",12,null],[10,"signed_shl","","Shifts the bits to the left by a specified amount amount, `n`, filling\nzeros in the least significant bits.",12,null],[10,"signed_shr","","Shifts the bits to the right by a specified amount amount, `n`, copying\nthe "sign bit" in the most significant bits even for unsigned types.",12,null],[10,"unsigned_shl","","Shifts the bits to the left by a specified amount amount, `n`, filling\nzeros in the least significant bits.",12,null],[10,"unsigned_shr","","Shifts the bits to the right by a specified amount amount, `n`, filling\nzeros in the most significant bits.",12,null],[10,"swap_bytes","","Reverses the byte order of the integer.",12,null],[10,"from_be","","Convert an integer from big endian to the target's endianness.",12,{"inputs":[{"name":"self"}],"output":{"name":"self"}}],[10,"from_le","","Convert an integer from little endian to the target's endianness.",12,{"inputs":[{"name":"self"}],"output":{"name":"self"}}],[10,"to_be","","Convert `self` to big endian from the target's endianness.",12,null],[10,"to_le","","Convert `self` to little endian from the target's endianness.",12,null],[10,"pow","","Raises self to the power of `exp`, using exponentiation by squaring.",12,null],[8,"CheckedSub","","Performs subtraction that returns `None` instead of wrapping around on underflow.",null,null],[10,"checked_sub","","Subtracts two numbers, checking for underflow. If underflow happens,\n`None` is returned.",9,null],[8,"CheckedMul","","Performs multiplication that returns `None` instead of wrapping around on underflow or\noverflow.",null,null],[10,"checked_mul","","Multiplies two numbers, checking for underflow or overflow. If underflow\nor overflow happens, `None` is returned.",10,null],[8,"Bounded","","Numbers which have upper and lower bounds",null,null],[10,"min_value","","returns the smallest finite number this type can represent",6,{"inputs":[],"output":{"name":"self"}}],[10,"max_value","","returns the largest finite number this type can represent",6,{"inputs":[],"output":{"name":"self"}}],[8,"NumCast","","An interface for casting between machine scalars.",null,null],[10,"from","","Creates a number from another value that can be converted into\na primitive via the `ToPrimitive` trait.",16,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[8,"Unsigned","","A trait for values which cannot be negative",null,null],[8,"Saturating","","Saturating math operations",null,null],[10,"saturating_add","","Saturating addition operator.\nReturns a+b, saturating at the numeric bounds instead of overflowing.",7,null],[10,"saturating_sub","","Saturating subtraction operator.\nReturns a-b, saturating at the numeric bounds instead of overflowing.",7,null],[8,"Zero","","Defines an additive identity element for `Self`.",null,null],[10,"zero","","Returns the additive identity element of `Self`, `0`.",3,{"inputs":[],"output":{"name":"self"}}],[10,"is_zero","","Returns `true` if `self` is equal to the additive identity.",3,null],[3,"Ratio","num::rational","Represents the ratio between 2 numbers.",null,null],[6,"Rational","","Alias for a `Ratio` of machine-sized integers.",null,null],[6,"Rational32","","",null,null],[6,"Rational64","","",null,null],[6,"BigRational","","Alias for arbitrary precision rationals.",null,null],[3,"ParseRatioError","","",null,null],[5,"zero","num","Returns the additive identity, `0`.",null,{"inputs":[],"output":{"name":"t"}}],[5,"one","","Returns the multiplicative identity, `1`.",null,{"inputs":[],"output":{"name":"t"}}],[5,"abs","","Computes the absolute value.",null,{"inputs":[{"name":"t"}],"output":{"name":"t"}}],[5,"abs_sub","","The positive difference of two numbers.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[5,"signum","","Returns the sign of the number.",null,{"inputs":[{"name":"t"}],"output":{"name":"t"}}],[5,"pow","","Raises a value to the power of exp, using exponentiation by squaring.",null,{"inputs":[{"name":"t"},{"name":"usize"}],"output":{"name":"t"}}],[5,"checked_pow","","Raises a value to the power of exp, returning `None` if an overflow occurred.",null,{"inputs":[{"name":"t"},{"name":"usize"}],"output":{"name":"option"}}],[11,"new","num::bigint","Creates and initializes a BigInt.",24,{"inputs":[{"name":"sign"},{"name":"vec"}],"output":{"name":"bigint"}}],[11,"from_biguint","","Creates and initializes a `BigInt`.",24,{"inputs":[{"name":"sign"},{"name":"biguint"}],"output":{"name":"bigint"}}],[11,"from_slice","","Creates and initializes a `BigInt`.",24,null],[11,"from_bytes_be","","Creates and initializes a `BigInt`.",24,null],[11,"from_bytes_le","","Creates and initializes a `BigInt`.",24,null],[11,"to_bytes_le","","Returns the sign and the byte representation of the `BigInt` in little-endian byte order.",24,null],[11,"to_bytes_be","","Returns the sign and the byte representation of the `BigInt` in big-endian byte order.",24,null],[11,"to_str_radix","","Returns the integer formatted as a string in the given radix.\n`radix` must be in the range `[2, 36]`.",24,null],[11,"sign","","Returns the sign of the `BigInt` as a `Sign`.",24,null],[11,"parse_bytes","","Creates and initializes a `BigInt`.",24,null],[11,"bits","","Determines the fewest bits necessary to express the `BigInt`,\nnot including the sign.",24,null],[11,"to_biguint","","Converts this `BigInt` into a `BigUint`, if it's not negative.",24,null],[11,"checked_add","","",24,null],[11,"checked_sub","","",24,null],[11,"checked_mul","","",24,null],[11,"checked_div","","",24,null],[11,"description","num::rational","",25,null],[11,"mul","","",26,null],[11,"mul","","",26,null],[11,"sub","","",26,null],[11,"sub","","",26,null],[11,"abs","","",26,null],[11,"abs_sub","","",26,null],[11,"signum","","",26,null],[11,"is_positive","","",26,null],[11,"is_negative","","",26,null],[11,"cmp","","",26,null],[11,"one","","",26,{"inputs":[],"output":{"name":"ratio"}}],[11,"div","","",26,null],[11,"div","","",26,null],[11,"zero","","",26,{"inputs":[],"output":{"name":"ratio"}}],[11,"is_zero","","",26,null],[11,"fmt","","Renders as `numer/denom`. If denom=1, renders as numer.",26,null],[11,"fmt","","",25,null],[11,"decode","","",26,{"inputs":[{"name":"__dt"}],"output":{"name":"result"}}],[11,"hash","","",26,null],[11,"neg","","",26,null],[11,"add","","",26,null],[11,"add","","",26,null],[11,"eq","","",26,null],[11,"eq","","",25,null],[11,"ne","","",25,null],[11,"encode","","",26,null],[11,"partial_cmp","","",26,null],[11,"rem","","",26,null],[11,"rem","","",26,null],[11,"from_str","","Parses `numer/denom` or just `numer`.",26,{"inputs":[{"name":"str"}],"output":{"name":"result"}}],[11,"fmt","","",26,null],[11,"fmt","","",25,null],[11,"from_str_radix","","Parses `numer/denom` where the numbers are in base `radix`.",26,{"inputs":[{"name":"str"},{"name":"u32"}],"output":{"name":"result"}}],[11,"clone","","",26,null],[11,"clone","","",25,null],[11,"mul","num::complex","",0,null],[11,"mul","","",0,null],[11,"mul","","",0,null],[11,"mul","","",0,null],[11,"sub","","",0,null],[11,"sub","","",0,null],[11,"sub","","",0,null],[11,"sub","","",0,null],[11,"encode","","",0,null],[11,"div","","",0,null],[11,"div","","",0,null],[11,"div","","",0,null],[11,"div","","",0,null],[11,"fmt","","",0,null],[11,"hash","","",0,null],[11,"neg","","",0,null],[11,"add","","",0,null],[11,"add","","",0,null],[11,"add","","",0,null],[11,"add","","",0,null],[11,"eq","","",0,null],[11,"ne","","",0,null],[11,"zero","","",0,{"inputs":[],"output":{"name":"complex"}}],[11,"is_zero","","",0,null],[11,"decode","","",0,{"inputs":[{"name":"__dt"}],"output":{"name":"result"}}],[11,"fmt","","",0,null],[11,"from","","",0,{"inputs":[{"name":"t"}],"output":{"name":"complex"}}],[11,"from","","",0,{"inputs":[{"name":"t"}],"output":{"name":"complex"}}],[11,"one","","",0,{"inputs":[],"output":{"name":"complex"}}],[11,"clone","","",0,null],[11,"to_bigint","num::bigint","",24,null],[11,"to_bigint","","",27,null],[11,"checked_add","","",27,null],[11,"checked_add","","",24,null],[11,"sub","","",27,null],[11,"sub","","",24,null],[11,"sub","","",24,null],[11,"sub","","",27,null],[11,"from_str_radix","","Creates and initializes a `BigUint`.",27,{"inputs":[{"name":"str"},{"name":"u32"}],"output":{"name":"result"}}],[11,"from_str_radix","","Creates and initializes a BigInt.",24,{"inputs":[{"name":"str"},{"name":"u32"}],"output":{"name":"result"}}],[11,"fmt","","",27,null],[11,"fmt","","",24,null],[11,"to_i64","","",27,null],[11,"to_u64","","",27,null],[11,"to_f32","","",27,null],[11,"to_f64","","",27,null],[11,"to_i64","","",24,null],[11,"to_u64","","",24,null],[11,"to_f32","","",24,null],[11,"to_f64","","",24,null],[11,"div","","",27,null],[11,"div","","",27,null],[11,"div","","",24,null],[11,"div","","",24,null],[11,"div_rem","","",27,null],[11,"div_floor","","",27,null],[11,"mod_floor","","",27,null],[11,"div_mod_floor","","",27,null],[11,"gcd","","Calculates the Greatest Common Divisor (GCD) of the number and `other`.",27,null],[11,"lcm","","Calculates the Lowest Common Multiple (LCM) of the number and `other`.",27,null],[11,"divides","","Deprecated, use `is_multiple_of` instead.",27,null],[11,"is_multiple_of","","Returns `true` if the number is a multiple of `other`.",27,null],[11,"is_even","","Returns `true` if the number is divisible by `2`.",27,null],[11,"is_odd","","Returns `true` if the number is not divisible by `2`.",27,null],[11,"div_rem","","",24,null],[11,"div_floor","","",24,null],[11,"mod_floor","","",24,null],[11,"div_mod_floor","","",24,null],[11,"gcd","","Calculates the Greatest Common Divisor (GCD) of the number and `other`.",24,null],[11,"lcm","","Calculates the Lowest Common Multiple (LCM) of the number and `other`.",24,null],[11,"divides","","Deprecated, use `is_multiple_of` instead.",24,null],[11,"is_multiple_of","","Returns `true` if the number is a multiple of `other`.",24,null],[11,"is_even","","Returns `true` if the number is divisible by `2`.",24,null],[11,"is_odd","","Returns `true` if the number is not divisible by `2`.",24,null],[11,"shl","","",27,null],[11,"shl","","",24,null],[11,"checked_div","","",27,null],[11,"checked_div","","",24,null],[11,"neg","","",27,null],[11,"neg","","Negate Sign value.",18,null],[11,"neg","","",24,null],[11,"eq","","",27,null],[11,"eq","","",24,null],[11,"eq","","",18,null],[11,"eq","","",21,null],[11,"ne","","",21,null],[11,"bitand","","",27,null],[11,"bitand","","",27,null],[11,"to_biguint","","",24,null],[11,"to_biguint","","",27,null],[11,"fmt","","",27,null],[11,"fmt","","",18,null],[11,"fmt","","",24,null],[11,"fmt","","",21,null],[11,"from","","",27,{"inputs":[{"name":"u64"}],"output":{"name":"biguint"}}],[11,"from","","",24,{"inputs":[{"name":"i64"}],"output":{"name":"bigint"}}],[11,"from","","",24,{"inputs":[{"name":"u64"}],"output":{"name":"bigint"}}],[11,"from","","",24,{"inputs":[{"name":"biguint"}],"output":{"name":"bigint"}}],[11,"from","","",21,{"inputs":[{"name":"parseinterror"}],"output":{"name":"parsebiginterror"}}],[11,"from","","",27,{"inputs":[{"name":"u8"}],"output":{"name":"biguint"}}],[11,"from","","",27,{"inputs":[{"name":"u16"}],"output":{"name":"biguint"}}],[11,"from","","",27,{"inputs":[{"name":"u32"}],"output":{"name":"biguint"}}],[11,"from","","",27,{"inputs":[{"name":"usize"}],"output":{"name":"biguint"}}],[11,"from","","",24,{"inputs":[{"name":"i8"}],"output":{"name":"bigint"}}],[11,"from","","",24,{"inputs":[{"name":"i16"}],"output":{"name":"bigint"}}],[11,"from","","",24,{"inputs":[{"name":"i32"}],"output":{"name":"bigint"}}],[11,"from","","",24,{"inputs":[{"name":"isize"}],"output":{"name":"bigint"}}],[11,"from","","",24,{"inputs":[{"name":"u8"}],"output":{"name":"bigint"}}],[11,"from","","",24,{"inputs":[{"name":"u16"}],"output":{"name":"bigint"}}],[11,"from","","",24,{"inputs":[{"name":"u32"}],"output":{"name":"bigint"}}],[11,"from","","",24,{"inputs":[{"name":"usize"}],"output":{"name":"bigint"}}],[11,"shr","","",27,null],[11,"shr","","",24,null],[11,"checked_mul","","",27,null],[11,"checked_mul","","",24,null],[11,"fmt","","",27,null],[11,"fmt","","",24,null],[11,"clone","","",27,null],[11,"clone","","",18,null],[11,"clone","","",24,null],[11,"bitor","","",27,null],[11,"bitor","","",27,null],[11,"description","","",21,null],[11,"mul","","",18,null],[11,"mul","","",27,null],[11,"mul","","",27,null],[11,"mul","","",24,null],[11,"mul","","",24,null],[11,"abs","","",24,null],[11,"abs_sub","","",24,null],[11,"signum","","",24,null],[11,"is_positive","","",24,null],[11,"is_negative","","",24,null],[11,"one","","",27,{"inputs":[],"output":{"name":"biguint"}}],[11,"one","","",24,{"inputs":[],"output":{"name":"bigint"}}],[11,"cmp","","",27,null],[11,"cmp","","",24,null],[11,"cmp","","",18,null],[11,"zero","","",27,{"inputs":[],"output":{"name":"biguint"}}],[11,"is_zero","","",27,null],[11,"zero","","",24,{"inputs":[],"output":{"name":"bigint"}}],[11,"is_zero","","",24,null],[11,"fmt","","",27,null],[11,"fmt","","",24,null],[11,"fmt","","",21,null],[11,"default","","",27,{"inputs":[],"output":{"name":"biguint"}}],[11,"default","","",24,{"inputs":[],"output":{"name":"bigint"}}],[11,"decode","","",27,{"inputs":[{"name":"__d"}],"output":{"name":"result"}}],[11,"decode","","",18,{"inputs":[{"name":"__d"}],"output":{"name":"result"}}],[11,"decode","","",24,{"inputs":[{"name":"__d"}],"output":{"name":"result"}}],[11,"hash","","",27,null],[11,"hash","","",18,null],[11,"hash","","",24,null],[11,"from_i64","","",27,{"inputs":[{"name":"i64"}],"output":{"name":"option"}}],[11,"from_u64","","",27,{"inputs":[{"name":"u64"}],"output":{"name":"option"}}],[11,"from_f64","","",27,{"inputs":[{"name":"f64"}],"output":{"name":"option"}}],[11,"from_i64","","",24,{"inputs":[{"name":"i64"}],"output":{"name":"option"}}],[11,"from_u64","","",24,{"inputs":[{"name":"u64"}],"output":{"name":"option"}}],[11,"from_f64","","",24,{"inputs":[{"name":"f64"}],"output":{"name":"option"}}],[11,"add","","",27,null],[11,"add","","",24,null],[11,"add","","",24,null],[11,"add","","",27,null],[11,"fmt","","",27,null],[11,"fmt","","",24,null],[11,"partial_cmp","","",27,null],[11,"partial_cmp","","",24,null],[11,"partial_cmp","","",18,null],[11,"encode","","",27,null],[11,"encode","","",18,null],[11,"encode","","",24,null],[11,"rem","","",27,null],[11,"rem","","",27,null],[11,"rem","","",24,null],[11,"rem","","",24,null],[11,"from_str","","",27,{"inputs":[{"name":"str"}],"output":{"name":"result"}}],[11,"from_str","","",24,{"inputs":[{"name":"str"}],"output":{"name":"result"}}],[11,"checked_sub","","",27,null],[11,"checked_sub","","",24,null],[11,"bitxor","","",27,null],[11,"bitxor","","",27,null],[11,"fmt","","",27,null],[11,"fmt","","",24,null],[11,"fmt","num::traits","",22,null],[11,"fmt","","",23,null],[11,"next_back","num::iter","",28,null],[11,"next_back","","",29,null],[11,"next","","",28,null],[11,"size_hint","","",28,null],[11,"next","","",29,null],[11,"size_hint","","",29,null],[11,"next","","",30,null],[11,"next","","",31,null],[11,"clone","","",28,null],[11,"clone","","",29,null],[11,"clone","","",30,null],[11,"clone","","",31,null],[11,"new","num::bigint","Creates and initializes a `BigUint`.",27,{"inputs":[{"name":"vec"}],"output":{"name":"biguint"}}],[11,"from_slice","","Creates and initializes a `BigUint`.",27,null],[11,"from_bytes_be","","Creates and initializes a `BigUint`.",27,null],[11,"from_bytes_le","","Creates and initializes a `BigUint`.",27,null],[11,"to_bytes_le","","Returns the byte representation of the `BigUint` in little-endian byte order.",27,null],[11,"to_bytes_be","","Returns the byte representation of the `BigUint` in big-endian byte order.",27,null],[11,"to_str_radix","","Returns the integer formatted as a string in the given radix.\n`radix` must be in the range `[2, 36]`.",27,null],[11,"parse_bytes","","Creates and initializes a `BigUint`.",27,null],[11,"bits","","Determines the fewest bits necessary to express the `BigUint`.",27,null],[11,"new","num::complex","Create a new Complex",0,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"complex"}}],[11,"i","","Returns imaginary unit",0,{"inputs":[],"output":{"name":"complex"}}],[11,"norm_sqr","","Returns the square of the norm (since `T` doesn't necessarily\nhave a sqrt function), i.e. `re^2 + im^2`.",0,null],[11,"scale","","Multiplies `self` by the scalar `t`.",0,null],[11,"unscale","","Divides `self` by the scalar `t`.",0,null],[11,"conj","","Returns the complex conjugate. i.e. `re - i im`",0,null],[11,"inv","","Returns `1/self`",0,null],[11,"norm","","Calculate |self|",0,null],[11,"arg","","Calculate the principal Arg of self.",0,null],[11,"to_polar","","Convert to polar form (r, theta), such that `self = r * exp(i\n* theta)`",0,null],[11,"from_polar","","Convert a polar representation into a complex number.",0,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"complex"}}],[11,"exp","","Computes `e^(self)`, where `e` is the base of the natural logarithm.",0,null],[11,"ln","","Computes the principal value of natural logarithm of `self`.",0,null],[11,"sqrt","","Computes the principal value of the square root of `self`.",0,null],[11,"sin","","Computes the sine of `self`.",0,null],[11,"cos","","Computes the cosine of `self`.",0,null],[11,"tan","","Computes the tangent of `self`.",0,null],[11,"asin","","Computes the principal value of the inverse sine of `self`.",0,null],[11,"acos","","Computes the principal value of the inverse cosine of `self`.",0,null],[11,"atan","","Computes the principal value of the inverse tangent of `self`.",0,null],[11,"sinh","","Computes the hyperbolic sine of `self`.",0,null],[11,"cosh","","Computes the hyperbolic cosine of `self`.",0,null],[11,"tanh","","Computes the hyperbolic tangent of `self`.",0,null],[11,"asinh","","Computes the principal value of inverse hyperbolic sine of `self`.",0,null],[11,"acosh","","Computes the principal value of inverse hyperbolic cosine of `self`.",0,null],[11,"atanh","","Computes the principal value of inverse hyperbolic tangent of `self`.",0,null],[11,"is_nan","","Checks if the given complex number is NaN",0,null],[11,"is_infinite","","Checks if the given complex number is infinite",0,null],[11,"is_finite","","Checks if the given complex number is finite",0,null],[11,"is_normal","","Checks if the given complex number is normal",0,null],[11,"from_integer","num::rational","Creates a ratio representing the integer `t`.",26,{"inputs":[{"name":"t"}],"output":{"name":"ratio"}}],[11,"new_raw","","Creates a ratio without checking for `denom == 0` or reducing.",26,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"ratio"}}],[11,"new","","Create a new Ratio. Fails if `denom == 0`.",26,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"ratio"}}],[11,"to_integer","","Converts to an integer.",26,null],[11,"numer","","Gets an immutable reference to the numerator.",26,null],[11,"denom","","Gets an immutable reference to the denominator.",26,null],[11,"is_integer","","Returns true if the rational number is an integer (denominator is 1).",26,null],[11,"reduced","","Returns a `reduce`d copy of self.",26,null],[11,"recip","","Returns the reciprocal.",26,null],[11,"floor","","Rounds towards minus infinity.",26,null],[11,"ceil","","Rounds towards plus infinity.",26,null],[11,"round","","Rounds to the nearest integer. Rounds half-way cases away from zero.",26,null],[11,"trunc","","Rounds towards zero.",26,null],[11,"fract","","Returns the fractional part of a number.",26,null],[11,"pow","","Raises the ratio to the power of an exponent",26,null],[11,"from_float","","Converts a float into a rational number.",26,{"inputs":[{"name":"t"}],"output":{"name":"option"}}]],"paths":[[3,"Complex"],[8,"Integer"],[8,"Num"],[8,"Zero"],[8,"One"],[8,"Signed"],[8,"Bounded"],[8,"Saturating"],[8,"CheckedAdd"],[8,"CheckedSub"],[8,"CheckedMul"],[8,"CheckedDiv"],[8,"PrimInt"],[8,"Float"],[8,"ToPrimitive"],[8,"FromPrimitive"],[8,"NumCast"],[8,"ToBigUint"],[4,"Sign"],[8,"ToBigInt"],[8,"RandBigInt"],[4,"ParseBigIntError"],[4,"FloatErrorKind"],[3,"ParseFloatError"],[3,"BigInt"],[3,"ParseRatioError"],[3,"Ratio"],[3,"BigUint"],[3,"Range"],[3,"RangeInclusive"],[3,"RangeStep"],[3,"RangeStepInclusive"]]};
searchIndex["num_rational"] = {"doc":"Rational numbers","items":[[3,"Ratio","num_rational","Represents the ratio between 2 numbers.",null,null],[3,"ParseRatioError","","",null,null],[6,"Rational","","Alias for a `Ratio` of machine-sized integers.",null,null],[6,"Rational32","","",null,null],[6,"Rational64","","",null,null],[6,"BigRational","","Alias for arbitrary precision rationals.",null,null],[11,"encode","","",0,null],[11,"decode","","",0,{"inputs":[{"name":"__dt"}],"output":{"name":"result"}}],[11,"clone","","",0,null],[11,"hash","","",0,null],[11,"fmt","","",0,null],[11,"from_integer","","Creates a ratio representing the integer `t`.",0,{"inputs":[{"name":"t"}],"output":{"name":"ratio"}}],[11,"new_raw","","Creates a ratio without checking for `denom == 0` or reducing.",0,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"ratio"}}],[11,"new","","Create a new Ratio. Fails if `denom == 0`.",0,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"ratio"}}],[11,"to_integer","","Converts to an integer.",0,null],[11,"numer","","Gets an immutable reference to the numerator.",0,null],[11,"denom","","Gets an immutable reference to the denominator.",0,null],[11,"is_integer","","Returns true if the rational number is an integer (denominator is 1).",0,null],[11,"reduced","","Returns a `reduce`d copy of self.",0,null],[11,"recip","","Returns the reciprocal.",0,null],[11,"floor","","Rounds towards minus infinity.",0,null],[11,"ceil","","Rounds towards plus infinity.",0,null],[11,"round","","Rounds to the nearest integer. Rounds half-way cases away from zero.",0,null],[11,"trunc","","Rounds towards zero.",0,null],[11,"fract","","Returns the fractional part of a number.",0,null],[11,"pow","","Raises the ratio to the power of an exponent",0,null],[11,"from_float","","Converts a float into a rational number.",0,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[11,"cmp","","",0,null],[11,"partial_cmp","","",0,null],[11,"eq","","",0,null],[11,"mul","","",0,null],[11,"mul","","",0,null],[11,"div","","",0,null],[11,"div","","",0,null],[11,"add","","",0,null],[11,"add","","",0,null],[11,"sub","","",0,null],[11,"sub","","",0,null],[11,"rem","","",0,null],[11,"rem","","",0,null],[11,"neg","","",0,null],[11,"zero","","",0,{"inputs":[],"output":{"name":"ratio"}}],[11,"is_zero","","",0,null],[11,"one","","",0,{"inputs":[],"output":{"name":"ratio"}}],[11,"from_str_radix","","Parses `numer/denom` where the numbers are in base `radix`.",0,{"inputs":[{"name":"str"},{"name":"u32"}],"output":{"name":"result"}}],[11,"abs","","",0,null],[11,"abs_sub","","",0,null],[11,"signum","","",0,null],[11,"is_positive","","",0,null],[11,"is_negative","","",0,null],[11,"fmt","","Renders as `numer/denom`. If denom=1, renders as numer.",0,null],[11,"from_str","","Parses `numer/denom` or just `numer`.",0,{"inputs":[{"name":"str"}],"output":{"name":"result"}}],[11,"clone","","",1,null],[11,"fmt","","",1,null],[11,"eq","","",1,null],[11,"ne","","",1,null],[11,"fmt","","",1,null],[11,"description","","",1,null]],"paths":[[3,"Ratio"],[3,"ParseRatioError"]]};
searchIndex["num_bigint"] = {"doc":"A Big integer (signed version: `BigInt`, unsigned version: `BigUint`).","items":[[3,"BigUint","num_bigint","A big unsigned integer type.",null,null],[3,"BigInt","","A big signed integer type.",null,null],[4,"Sign","","A Sign is a `BigInt`'s composing element.",null,null],[13,"Minus","","",0,null],[13,"NoSign","","",0,null],[13,"Plus","","",0,null],[4,"ParseBigIntError","","",null,null],[13,"ParseInt","","",1,null],[13,"Other","","",1,null],[0,"big_digit","","",null,null],[5,"from_doublebigdigit","num_bigint::big_digit","Split one `DoubleBigDigit` into two `BigDigit`s.",null,null],[5,"to_doublebigdigit","","Join two `BigDigit`s into one `DoubleBigDigit`",null,{"inputs":[{"name":"bigdigit"},{"name":"bigdigit"}],"output":{"name":"doublebigdigit"}}],[17,"BITS","","",null,null],[17,"BASE","","",null,null],[6,"BigDigit","num_bigint","A `BigDigit` is a `BigUint`'s composing element.",null,null],[6,"DoubleBigDigit","","A `DoubleBigDigit` is the internal type used to do the computations.  Its\nsize is the double of the size of `BigDigit`.",null,null],[17,"ZERO_BIG_DIGIT","","",null,null],[8,"ToBigUint","","A generic trait for converting a value to a `BigUint`.",null,null],[10,"to_biguint","","Converts the value of `self` to a `BigUint`.",2,null],[8,"ToBigInt","","A generic trait for converting a value to a `BigInt`.",null,null],[10,"to_bigint","","Converts the value of `self` to a `BigInt`.",3,null],[8,"RandBigInt","","",null,null],[10,"gen_biguint","","Generate a random `BigUint` of the given bit size.",4,null],[10,"gen_bigint","","Generate a random BigInt of the given bit size.",4,null],[10,"gen_biguint_below","","Generate a random `BigUint` less than the given bound. Fails\nwhen the bound is zero.",4,null],[10,"gen_biguint_range","","Generate a random `BigUint` within the given range. The lower\nbound is inclusive; the upper bound is exclusive. Fails when\nthe upper bound is not greater than the lower bound.",4,null],[10,"gen_bigint_range","","Generate a random `BigInt` within the given range. The lower\nbound is inclusive; the upper bound is exclusive. Fails when\nthe upper bound is not greater than the lower bound.",4,null],[11,"encode","","",5,null],[11,"decode","","",5,{"inputs":[{"name":"__d"}],"output":{"name":"result"}}],[11,"clone","","",5,null],[11,"fmt","","",5,null],[11,"hash","","",5,null],[11,"eq","","",5,null],[11,"partial_cmp","","",5,null],[11,"cmp","","",5,null],[11,"default","","",5,{"inputs":[],"output":{"name":"biguint"}}],[11,"fmt","","",5,null],[11,"fmt","","",5,null],[11,"fmt","","",5,null],[11,"fmt","","",5,null],[11,"fmt","","",5,null],[11,"from_str","","",5,{"inputs":[{"name":"str"}],"output":{"name":"result"}}],[11,"from_str_radix","","Creates and initializes a `BigUint`.",5,{"inputs":[{"name":"str"},{"name":"u32"}],"output":{"name":"result"}}],[11,"bitand","","",5,null],[11,"bitand","","",5,null],[11,"bitor","","",5,null],[11,"bitor","","",5,null],[11,"bitxor","","",5,null],[11,"bitxor","","",5,null],[11,"shl","","",5,null],[11,"shr","","",5,null],[11,"zero","","",5,{"inputs":[],"output":{"name":"biguint"}}],[11,"is_zero","","",5,null],[11,"one","","",5,{"inputs":[],"output":{"name":"biguint"}}],[11,"add","","",5,null],[11,"add","","",5,null],[11,"sub","","",5,null],[11,"sub","","",5,null],[11,"mul","","",5,null],[11,"mul","","",5,null],[11,"div","","",5,null],[11,"div","","",5,null],[11,"rem","","",5,null],[11,"rem","","",5,null],[11,"neg","","",5,null],[11,"checked_add","","",5,null],[11,"checked_sub","","",5,null],[11,"checked_mul","","",5,null],[11,"checked_div","","",5,null],[11,"div_rem","","",5,null],[11,"div_floor","","",5,null],[11,"mod_floor","","",5,null],[11,"div_mod_floor","","",5,null],[11,"gcd","","Calculates the Greatest Common Divisor (GCD) of the number and `other`.",5,null],[11,"lcm","","Calculates the Lowest Common Multiple (LCM) of the number and `other`.",5,null],[11,"divides","","Deprecated, use `is_multiple_of` instead.",5,null],[11,"is_multiple_of","","Returns `true` if the number is a multiple of `other`.",5,null],[11,"is_even","","Returns `true` if the number is divisible by `2`.",5,null],[11,"is_odd","","Returns `true` if the number is not divisible by `2`.",5,null],[11,"to_i64","","",5,null],[11,"to_u64","","",5,null],[11,"to_f32","","",5,null],[11,"to_f64","","",5,null],[11,"from_i64","","",5,{"inputs":[{"name":"i64"}],"output":{"name":"option"}}],[11,"from_u64","","",5,{"inputs":[{"name":"u64"}],"output":{"name":"option"}}],[11,"from_f64","","",5,{"inputs":[{"name":"f64"}],"output":{"name":"option"}}],[11,"from","","",5,{"inputs":[{"name":"u64"}],"output":{"name":"self"}}],[11,"from","","",5,{"inputs":[{"name":"u8"}],"output":{"name":"self"}}],[11,"from","","",5,{"inputs":[{"name":"u16"}],"output":{"name":"self"}}],[11,"from","","",5,{"inputs":[{"name":"u32"}],"output":{"name":"self"}}],[11,"from","","",5,{"inputs":[{"name":"usize"}],"output":{"name":"self"}}],[11,"to_biguint","","",6,null],[11,"to_biguint","","",5,null],[11,"new","","Creates and initializes a `BigUint`.",5,{"inputs":[{"name":"vec"}],"output":{"name":"biguint"}}],[11,"from_slice","","Creates and initializes a `BigUint`.",5,null],[11,"from_bytes_be","","Creates and initializes a `BigUint`.",5,null],[11,"from_bytes_le","","Creates and initializes a `BigUint`.",5,null],[11,"to_bytes_le","","Returns the byte representation of the `BigUint` in little-endian byte order.",5,null],[11,"to_bytes_be","","Returns the byte representation of the `BigUint` in big-endian byte order.",5,null],[11,"to_str_radix","","Returns the integer formatted as a string in the given radix.\n`radix` must be in the range `[2, 36]`.",5,null],[11,"parse_bytes","","Creates and initializes a `BigUint`.",5,null],[11,"bits","","Determines the fewest bits necessary to express the `BigUint`.",5,null],[11,"encode","","",0,null],[11,"decode","","",0,{"inputs":[{"name":"__d"}],"output":{"name":"result"}}],[11,"eq","","",0,null],[11,"partial_cmp","","",0,null],[11,"cmp","","",0,null],[11,"clone","","",0,null],[11,"fmt","","",0,null],[11,"hash","","",0,null],[11,"neg","","Negate Sign value.",0,null],[11,"mul","","",0,null],[11,"encode","","",6,null],[11,"decode","","",6,{"inputs":[{"name":"__d"}],"output":{"name":"result"}}],[11,"clone","","",6,null],[11,"fmt","","",6,null],[11,"hash","","",6,null],[11,"eq","","",6,null],[11,"partial_cmp","","",6,null],[11,"cmp","","",6,null],[11,"default","","",6,{"inputs":[],"output":{"name":"bigint"}}],[11,"fmt","","",6,null],[11,"fmt","","",6,null],[11,"fmt","","",6,null],[11,"fmt","","",6,null],[11,"fmt","","",6,null],[11,"from_str","","",6,{"inputs":[{"name":"str"}],"output":{"name":"result"}}],[11,"from_str_radix","","Creates and initializes a BigInt.",6,{"inputs":[{"name":"str"},{"name":"u32"}],"output":{"name":"result"}}],[11,"shl","","",6,null],[11,"shr","","",6,null],[11,"zero","","",6,{"inputs":[],"output":{"name":"bigint"}}],[11,"is_zero","","",6,null],[11,"one","","",6,{"inputs":[],"output":{"name":"bigint"}}],[11,"abs","","",6,null],[11,"abs_sub","","",6,null],[11,"signum","","",6,null],[11,"is_positive","","",6,null],[11,"is_negative","","",6,null],[11,"add","","",6,null],[11,"add","","",6,null],[11,"sub","","",6,null],[11,"sub","","",6,null],[11,"mul","","",6,null],[11,"mul","","",6,null],[11,"div","","",6,null],[11,"div","","",6,null],[11,"rem","","",6,null],[11,"rem","","",6,null],[11,"neg","","",6,null],[11,"checked_add","","",6,null],[11,"checked_sub","","",6,null],[11,"checked_mul","","",6,null],[11,"checked_div","","",6,null],[11,"div_rem","","",6,null],[11,"div_floor","","",6,null],[11,"mod_floor","","",6,null],[11,"div_mod_floor","","",6,null],[11,"gcd","","Calculates the Greatest Common Divisor (GCD) of the number and `other`.",6,null],[11,"lcm","","Calculates the Lowest Common Multiple (LCM) of the number and `other`.",6,null],[11,"divides","","Deprecated, use `is_multiple_of` instead.",6,null],[11,"is_multiple_of","","Returns `true` if the number is a multiple of `other`.",6,null],[11,"is_even","","Returns `true` if the number is divisible by `2`.",6,null],[11,"is_odd","","Returns `true` if the number is not divisible by `2`.",6,null],[11,"to_i64","","",6,null],[11,"to_u64","","",6,null],[11,"to_f32","","",6,null],[11,"to_f64","","",6,null],[11,"from_i64","","",6,{"inputs":[{"name":"i64"}],"output":{"name":"option"}}],[11,"from_u64","","",6,{"inputs":[{"name":"u64"}],"output":{"name":"option"}}],[11,"from_f64","","",6,{"inputs":[{"name":"f64"}],"output":{"name":"option"}}],[11,"from","","",6,{"inputs":[{"name":"i64"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"i8"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"i16"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"i32"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"isize"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"u64"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"u8"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"u16"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"u32"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"usize"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"biguint"}],"output":{"name":"self"}}],[11,"to_bigint","","",6,null],[11,"to_bigint","","",5,null],[11,"new","","Creates and initializes a BigInt.",6,{"inputs":[{"name":"sign"},{"name":"vec"}],"output":{"name":"bigint"}}],[11,"from_biguint","","Creates and initializes a `BigInt`.",6,{"inputs":[{"name":"sign"},{"name":"biguint"}],"output":{"name":"bigint"}}],[11,"from_slice","","Creates and initializes a `BigInt`.",6,null],[11,"from_bytes_be","","Creates and initializes a `BigInt`.",6,null],[11,"from_bytes_le","","Creates and initializes a `BigInt`.",6,null],[11,"to_bytes_le","","Returns the sign and the byte representation of the `BigInt` in little-endian byte order.",6,null],[11,"to_bytes_be","","Returns the sign and the byte representation of the `BigInt` in big-endian byte order.",6,null],[11,"to_str_radix","","Returns the integer formatted as a string in the given radix.\n`radix` must be in the range `[2, 36]`.",6,null],[11,"sign","","Returns the sign of the `BigInt` as a `Sign`.",6,null],[11,"parse_bytes","","Creates and initializes a `BigInt`.",6,null],[11,"bits","","Determines the fewest bits necessary to express the `BigInt`,\nnot including the sign.",6,null],[11,"to_biguint","","Converts this `BigInt` into a `BigUint`, if it's not negative.",6,null],[11,"checked_add","","",6,null],[11,"checked_sub","","",6,null],[11,"checked_mul","","",6,null],[11,"checked_div","","",6,null],[11,"fmt","","",1,null],[11,"eq","","",1,null],[11,"ne","","",1,null],[11,"fmt","","",1,null],[11,"description","","",1,null],[11,"from","","",1,{"inputs":[{"name":"parseinterror"}],"output":{"name":"parsebiginterror"}}]],"paths":[[4,"Sign"],[4,"ParseBigIntError"],[8,"ToBigUint"],[8,"ToBigInt"],[8,"RandBigInt"],[3,"BigUint"],[3,"BigInt"]]};
searchIndex["num_complex"] = {"doc":"Complex numbers.","items":[[3,"Complex","num_complex","A complex number in Cartesian form.",null,null],[12,"re","","Real portion of the complex number",0,null],[12,"im","","Imaginary portion of the complex number",0,null],[6,"Complex32","","",null,null],[6,"Complex64","","",null,null],[11,"encode","","",0,null],[11,"decode","","",0,{"inputs":[{"name":"__dt"}],"output":{"name":"result"}}],[11,"eq","","",0,null],[11,"ne","","",0,null],[11,"clone","","",0,null],[11,"hash","","",0,null],[11,"fmt","","",0,null],[11,"new","","Create a new Complex",0,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"complex"}}],[11,"i","","Returns imaginary unit",0,{"inputs":[],"output":{"name":"complex"}}],[11,"norm_sqr","","Returns the square of the norm (since `T` doesn't necessarily\nhave a sqrt function), i.e. `re^2 + im^2`.",0,null],[11,"scale","","Multiplies `self` by the scalar `t`.",0,null],[11,"unscale","","Divides `self` by the scalar `t`.",0,null],[11,"conj","","Returns the complex conjugate. i.e. `re - i im`",0,null],[11,"inv","","Returns `1/self`",0,null],[11,"norm","","Calculate |self|",0,null],[11,"arg","","Calculate the principal Arg of self.",0,null],[11,"to_polar","","Convert to polar form (r, theta), such that `self = r * exp(i\n* theta)`",0,null],[11,"from_polar","","Convert a polar representation into a complex number.",0,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"complex"}}],[11,"exp","","Computes `e^(self)`, where `e` is the base of the natural logarithm.",0,null],[11,"ln","","Computes the principal value of natural logarithm of `self`.",0,null],[11,"sqrt","","Computes the principal value of the square root of `self`.",0,null],[11,"sin","","Computes the sine of `self`.",0,null],[11,"cos","","Computes the cosine of `self`.",0,null],[11,"tan","","Computes the tangent of `self`.",0,null],[11,"asin","","Computes the principal value of the inverse sine of `self`.",0,null],[11,"acos","","Computes the principal value of the inverse cosine of `self`.",0,null],[11,"atan","","Computes the principal value of the inverse tangent of `self`.",0,null],[11,"sinh","","Computes the hyperbolic sine of `self`.",0,null],[11,"cosh","","Computes the hyperbolic cosine of `self`.",0,null],[11,"tanh","","Computes the hyperbolic tangent of `self`.",0,null],[11,"asinh","","Computes the principal value of inverse hyperbolic sine of `self`.",0,null],[11,"acosh","","Computes the principal value of inverse hyperbolic cosine of `self`.",0,null],[11,"atanh","","Computes the principal value of inverse hyperbolic tangent of `self`.",0,null],[11,"is_nan","","Checks if the given complex number is NaN",0,null],[11,"is_infinite","","Checks if the given complex number is infinite",0,null],[11,"is_finite","","Checks if the given complex number is finite",0,null],[11,"is_normal","","Checks if the given complex number is normal",0,null],[11,"from","","",0,{"inputs":[{"name":"t"}],"output":{"name":"complex"}}],[11,"from","","",0,{"inputs":[{"name":"t"}],"output":{"name":"complex"}}],[11,"add","","",0,null],[11,"add","","",0,null],[11,"sub","","",0,null],[11,"sub","","",0,null],[11,"mul","","",0,null],[11,"mul","","",0,null],[11,"div","","",0,null],[11,"div","","",0,null],[11,"neg","","",0,null],[11,"add","","",0,null],[11,"sub","","",0,null],[11,"mul","","",0,null],[11,"div","","",0,null],[11,"add","","",0,null],[11,"sub","","",0,null],[11,"mul","","",0,null],[11,"div","","",0,null],[11,"zero","","",0,{"inputs":[],"output":{"name":"complex"}}],[11,"is_zero","","",0,null],[11,"one","","",0,{"inputs":[],"output":{"name":"complex"}}],[11,"fmt","","",0,null]],"paths":[[3,"Complex"]]};
searchIndex["rand"] = {"doc":"Utilities for random number generation","items":[[3,"Generator","rand","Iterator which will generate a stream of random items.",null,null],[3,"AsciiGenerator","","Iterator which will continuously generate random ascii characters.",null,null],[3,"XorShiftRng","","An Xorshift[1] random number\ngenerator.",null,null],[3,"Open01","","A wrapper for generating floating point numbers uniformly in the\nopen interval `(0,1)` (not including either endpoint).",null,null],[12,"0","","",0,null],[3,"Closed01","","A wrapper for generating floating point numbers uniformly in the\nclosed interval `[0,1]` (including both endpoints).",null,null],[12,"0","","",1,null],[3,"StdRng","","The standard RNG. This is designed to be efficient on the current\nplatform.",null,null],[3,"ThreadRng","","The thread-local RNG.",null,null],[5,"weak_rng","","Create a weak random number generator with a default algorithm and seed.",null,{"inputs":[],"output":{"name":"xorshiftrng"}}],[5,"thread_rng","","Retrieve the lazily-initialized thread-local random number\ngenerator, seeded by the system. Intended to be used in method\nchaining style, e.g. `thread_rng().gen::<i32>()`.",null,{"inputs":[],"output":{"name":"threadrng"}}],[5,"random","","Generates a random value using the thread-local random number generator.",null,{"inputs":[],"output":{"name":"t"}}],[5,"sample","","Randomly sample up to `amount` elements from an iterator.",null,{"inputs":[{"name":"r"},{"name":"i"},{"name":"usize"}],"output":{"name":"vec"}}],[0,"distributions","","Sampling from random distributions.",null,null],[3,"RandSample","rand::distributions","A wrapper for generating types that implement `Rand` via the\n`Sample` & `IndependentSample` traits.",null,null],[3,"Weighted","","A value with a particular weight for use with `WeightedChoice`.",null,null],[12,"weight","","The numerical weight of this item",2,null],[12,"item","","The actual item which is being weighted",2,null],[3,"WeightedChoice","","A distribution that selects from a finite collection of weighted items.",null,null],[0,"range","","Generating numbers between two others.",null,null],[3,"Range","rand::distributions::range","Sample values uniformly between two bounds.",null,null],[8,"SampleRange","","The helper trait for types that have a sensible way to sample\nuniformly between two values. This should not be used directly,\nand is only to facilitate `Range`.",null,null],[10,"construct_range","","Construct the `Range` object that `sample_range`\nrequires. This should not ever be called directly, only via\n`Range::new`, which will check that `low < high`, so this\nfunction doesn't have to repeat the check.",3,{"inputs":[{"name":"self"},{"name":"self"}],"output":{"name":"range"}}],[10,"sample_range","","Sample a value from the given `Range` with the given `Rng` as\na source of randomness.",3,{"inputs":[{"name":"range"},{"name":"r"}],"output":{"name":"self"}}],[11,"clone","","",4,null],[11,"new","","Create a new `Range` instance that samples uniformly from\n`[low, high)`. Panics if `low >= high`.",4,{"inputs":[{"name":"x"},{"name":"x"}],"output":{"name":"range"}}],[11,"sample","","",4,null],[11,"ind_sample","","",4,null],[0,"gamma","rand::distributions","The Gamma and derived distributions.",null,null],[3,"Gamma","rand::distributions::gamma","The Gamma distribution `Gamma(shape, scale)` distribution.",null,null],[3,"ChiSquared","","The chi-squared distribution `χ²(k)`, where `k` is the degrees of\nfreedom.",null,null],[3,"FisherF","","The Fisher F distribution `F(m, n)`.",null,null],[3,"StudentT","","The Student t distribution, `t(nu)`, where `nu` is the degrees of\nfreedom.",null,null],[11,"clone","","",5,null],[11,"new","","Construct an object representing the `Gamma(shape, scale)`\ndistribution.",5,{"inputs":[{"name":"f64"},{"name":"f64"}],"output":{"name":"gamma"}}],[11,"sample","","",5,null],[11,"ind_sample","","",5,null],[11,"clone","","",6,null],[11,"new","","Create a new chi-squared distribution with degrees-of-freedom\n`k`. Panics if `k < 0`.",6,{"inputs":[{"name":"f64"}],"output":{"name":"chisquared"}}],[11,"sample","","",6,null],[11,"ind_sample","","",6,null],[11,"clone","","",7,null],[11,"new","","Create a new `FisherF` distribution, with the given\nparameter. Panics if either `m` or `n` are not positive.",7,{"inputs":[{"name":"f64"},{"name":"f64"}],"output":{"name":"fisherf"}}],[11,"sample","","",7,null],[11,"ind_sample","","",7,null],[11,"clone","","",8,null],[11,"new","","Create a new Student t distribution with `n` degrees of\nfreedom. Panics if `n <= 0`.",8,{"inputs":[{"name":"f64"}],"output":{"name":"studentt"}}],[11,"sample","","",8,null],[11,"ind_sample","","",8,null],[0,"normal","rand::distributions","The normal and derived distributions.",null,null],[3,"StandardNormal","rand::distributions::normal","A wrapper around an `f64` to generate N(0, 1) random numbers\n(a.k.a.  a standard normal, or Gaussian).",null,null],[12,"0","","",9,null],[3,"Normal","","The normal distribution `N(mean, std_dev**2)`.",null,null],[3,"LogNormal","","The log-normal distribution `ln N(mean, std_dev**2)`.",null,null],[11,"clone","","",9,null],[11,"rand","","",9,{"inputs":[{"name":"r"}],"output":{"name":"standardnormal"}}],[11,"clone","","",10,null],[11,"new","","Construct a new `Normal` distribution with the given mean and\nstandard deviation.",10,{"inputs":[{"name":"f64"},{"name":"f64"}],"output":{"name":"normal"}}],[11,"sample","","",10,null],[11,"ind_sample","","",10,null],[11,"clone","","",11,null],[11,"new","","Construct a new `LogNormal` distribution with the given mean\nand standard deviation.",11,{"inputs":[{"name":"f64"},{"name":"f64"}],"output":{"name":"lognormal"}}],[11,"sample","","",11,null],[11,"ind_sample","","",11,null],[0,"exponential","rand::distributions","The exponential distribution.",null,null],[3,"Exp1","rand::distributions::exponential","A wrapper around an `f64` to generate Exp(1) random numbers.",null,null],[12,"0","","",12,null],[3,"Exp","","The exponential distribution `Exp(lambda)`.",null,null],[11,"clone","","",12,null],[11,"rand","","",12,{"inputs":[{"name":"r"}],"output":{"name":"exp1"}}],[11,"clone","","",13,null],[11,"new","","Construct a new `Exp` with the given shape parameter\n`lambda`. Panics if `lambda <= 0`.",13,{"inputs":[{"name":"f64"}],"output":{"name":"exp"}}],[11,"sample","","",13,null],[11,"ind_sample","","",13,null],[8,"Sample","rand::distributions","Types that can be used to create a random instance of `Support`.",null,null],[10,"sample","","Generate a random value of `Support`, using `rng` as the\nsource of randomness.",14,null],[8,"IndependentSample","","`Sample`s that do not require keeping track of state.",null,null],[10,"ind_sample","","Generate a random value.",15,null],[11,"clone","","",16,null],[11,"sample","","",16,null],[11,"ind_sample","","",16,null],[11,"new","","",16,{"inputs":[],"output":{"name":"randsample"}}],[11,"clone","","",2,null],[11,"new","","Create a new `WeightedChoice`.",17,null],[11,"sample","","",17,null],[11,"ind_sample","","",17,null],[0,"isaac","rand","The ISAAC random number generator.",null,null],[3,"IsaacRng","rand::isaac","A random number generator that uses the ISAAC algorithm[1].",null,null],[3,"Isaac64Rng","","A random number generator that uses ISAAC-64[1], the 64-bit\nvariant of the ISAAC algorithm.",null,null],[11,"new_unseeded","","Create an ISAAC random number generator using the default\nfixed seed.",18,{"inputs":[],"output":{"name":"isaacrng"}}],[11,"clone","","",18,null],[11,"next_u32","","",18,null],[11,"reseed","","",18,null],[11,"from_seed","","Create an ISAAC random number generator with a seed. This can\nbe any length, although the maximum number of elements used is\n256 and any more will be silently ignored. A generator\nconstructed with a given seed will generate the same sequence\nof values as all other generators constructed with that seed.",18,null],[11,"rand","","",18,{"inputs":[{"name":"r"}],"output":{"name":"isaacrng"}}],[11,"new_unseeded","","Create a 64-bit ISAAC random number generator using the\ndefault fixed seed.",19,{"inputs":[],"output":{"name":"isaac64rng"}}],[11,"clone","","",19,null],[11,"next_u32","","",19,null],[11,"next_u64","","",19,null],[11,"reseed","","",19,null],[11,"from_seed","","Create an ISAAC random number generator with a seed. This can\nbe any length, although the maximum number of elements used is\n256 and any more will be silently ignored. A generator\nconstructed with a given seed will generate the same sequence\nof values as all other generators constructed with that seed.",19,null],[11,"rand","","",19,{"inputs":[{"name":"r"}],"output":{"name":"isaac64rng"}}],[0,"chacha","rand","The ChaCha random number generator.",null,null],[3,"ChaChaRng","rand::chacha","A random number generator that uses the ChaCha20 algorithm [1].",null,null],[11,"clone","","",20,null],[11,"new_unseeded","","Create an ChaCha random number generator using the default\nfixed key of 8 zero words.",20,{"inputs":[],"output":{"name":"chacharng"}}],[11,"set_counter","","Sets the internal 128-bit ChaCha counter to\na user-provided value. This permits jumping\narbitrarily ahead (or backwards) in the pseudorandom stream.",20,null],[11,"next_u32","","",20,null],[11,"reseed","","",20,null],[11,"from_seed","","Create a ChaCha generator from a seed,\nobtained from a variable-length u32 array.\nOnly up to 8 words are used; if less than 8\nwords are used, the remaining are set to zero.",20,null],[11,"rand","","",20,{"inputs":[{"name":"r"}],"output":{"name":"chacharng"}}],[0,"reseeding","rand","A wrapper around another RNG that reseeds it after it\ngenerates a certain number of random bytes.",null,null],[3,"ReseedingRng","rand::reseeding","A wrapper around any RNG which reseeds the underlying RNG after it\nhas generated a certain number of random bytes.",null,null],[12,"reseeder","","Controls the behaviour when reseeding the RNG.",21,null],[3,"ReseedWithDefault","","Reseed an RNG using a `Default` instance. This reseeds by\nreplacing the RNG with the result of a `Default::default` call.",null,null],[8,"Reseeder","","Something that can be used to reseed an RNG via `ReseedingRng`.",null,null],[10,"reseed","","Reseed the given RNG.",22,null],[11,"new","","Create a new `ReseedingRng` with the given parameters.",21,{"inputs":[{"name":"r"},{"name":"u64"},{"name":"rsdr"}],"output":{"name":"reseedingrng"}}],[11,"reseed_if_necessary","","Reseed the internal RNG if the number of bytes that have been\ngenerated exceed the threshold.",21,null],[11,"next_u32","","",21,null],[11,"next_u64","","",21,null],[11,"fill_bytes","","",21,null],[11,"reseed","","",21,null],[11,"from_seed","","Create a new `ReseedingRng` from the given reseeder and\nseed. This uses a default value for `generation_threshold`.",21,null],[11,"clone","","",23,null],[11,"reseed","","",23,null],[11,"default","","",23,{"inputs":[],"output":{"name":"reseedwithdefault"}}],[11,"rand","rand","",0,{"inputs":[{"name":"r"}],"output":{"name":"open01"}}],[11,"rand","","",1,{"inputs":[{"name":"r"}],"output":{"name":"closed01"}}],[11,"rand","","",0,{"inputs":[{"name":"r"}],"output":{"name":"open01"}}],[11,"rand","","",1,{"inputs":[{"name":"r"}],"output":{"name":"closed01"}}],[0,"os","","Interfaces to the operating system provided random number\ngenerators.",null,null],[3,"OsRng","rand::os","A random number generator that retrieves randomness straight from\nthe operating system. Platform sources:",null,null],[11,"new","","Create a new `OsRng`.",24,{"inputs":[],"output":{"name":"result"}}],[11,"next_u32","","",24,null],[11,"next_u64","","",24,null],[11,"fill_bytes","","",24,null],[0,"read","rand","A wrapper around any Read to treat it as an RNG.",null,null],[3,"ReadRng","rand::read","An RNG that reads random bytes straight from a `Read`. This will\nwork best with an infinite reader, but this is not required.",null,null],[11,"new","","Create a new `ReadRng` from a `Read`.",25,{"inputs":[{"name":"r"}],"output":{"name":"readrng"}}],[11,"next_u32","","",25,null],[11,"next_u64","","",25,null],[11,"fill_bytes","","",25,null],[8,"Rand","rand","A type that can be randomly generated using an `Rng`.",null,null],[10,"rand","","Generates a random instance of this type using the specified source of\nrandomness.",26,{"inputs":[{"name":"r"}],"output":{"name":"self"}}],[8,"Rng","","A random number generator.",null,null],[10,"next_u32","","Return the next random u32.",27,null],[11,"next_u64","","Return the next random u64.",27,null],[11,"next_f32","","Return the next random f32 selected from the half-open\ninterval `[0, 1)`.",27,null],[11,"next_f64","","Return the next random f64 selected from the half-open\ninterval `[0, 1)`.",27,null],[11,"fill_bytes","","Fill `dest` with random data.",27,null],[11,"gen","","Return a random value of a `Rand` type.",27,null],[11,"gen_iter","","Return an iterator that will yield an infinite number of randomly\ngenerated items.",27,null],[11,"gen_range","","Generate a random value in the range [`low`, `high`).",27,null],[11,"gen_weighted_bool","","Return a bool with a 1 in n chance of true",27,null],[11,"gen_ascii_chars","","Return an iterator of random characters from the set A-Z,a-z,0-9.",27,null],[11,"choose","","Return a random element from `values`.",27,null],[11,"shuffle","","Shuffle a mutable slice in place.",27,null],[8,"SeedableRng","","A random number generator that can be explicitly seeded to produce\nthe same stream of randomness multiple times.",null,null],[10,"reseed","","Reseed an RNG with the given seed.",28,null],[10,"from_seed","","Create a new RNG with the given seed.",28,{"inputs":[{"name":"seed"}],"output":{"name":"self"}}],[11,"next","","",29,null],[11,"next","","",30,null],[11,"clone","","",31,null],[11,"new_unseeded","","Creates a new XorShiftRng instance which is not seeded.",31,{"inputs":[],"output":{"name":"xorshiftrng"}}],[11,"next_u32","","",31,null],[11,"reseed","","Reseed an XorShiftRng. This will panic if `seed` is entirely 0.",31,null],[11,"from_seed","","Create a new XorShiftRng. This will panic if `seed` is entirely 0.",31,null],[11,"rand","","",31,{"inputs":[{"name":"r"}],"output":{"name":"xorshiftrng"}}],[11,"clone","","",32,null],[11,"new","","Create a randomly seeded instance of `StdRng`.",32,{"inputs":[],"output":{"name":"result"}}],[11,"next_u32","","",32,null],[11,"next_u64","","",32,null],[11,"reseed","","",32,null],[11,"from_seed","","",32,null],[11,"clone","","",33,null],[11,"next_u32","","",33,null],[11,"next_u64","","",33,null],[11,"fill_bytes","","",33,null]],"paths":[[3,"Open01"],[3,"Closed01"],[3,"Weighted"],[8,"SampleRange"],[3,"Range"],[3,"Gamma"],[3,"ChiSquared"],[3,"FisherF"],[3,"StudentT"],[3,"StandardNormal"],[3,"Normal"],[3,"LogNormal"],[3,"Exp1"],[3,"Exp"],[8,"Sample"],[8,"IndependentSample"],[3,"RandSample"],[3,"WeightedChoice"],[3,"IsaacRng"],[3,"Isaac64Rng"],[3,"ChaChaRng"],[3,"ReseedingRng"],[8,"Reseeder"],[3,"ReseedWithDefault"],[3,"OsRng"],[3,"ReadRng"],[8,"Rand"],[8,"Rng"],[8,"SeedableRng"],[3,"Generator"],[3,"AsciiGenerator"],[3,"XorShiftRng"],[3,"StdRng"],[3,"ThreadRng"]]};
searchIndex["rustc_serialize"] = {"doc":"Support code for encoding and decoding types.","items":[[0,"base64","rustc_serialize","Base64 binary-to-text encoding",null,null],[3,"Config","rustc_serialize::base64","Contains configuration parameters for `to_base64`.",null,null],[12,"char_set","","Character set to use",0,null],[12,"newline","","Newline to use",0,null],[12,"pad","","True to pad output with `=` characters",0,null],[12,"line_length","","`Some(len)` to wrap lines at `len`, `None` to disable line wrapping",0,null],[4,"CharacterSet","","Available encoding character sets",null,null],[13,"Standard","","The standard character set (uses `+` and `/`)",1,null],[13,"UrlSafe","","The URL safe character set (uses `-` and `_`)",1,null],[4,"Newline","","Available newline types",null,null],[13,"LF","","A linefeed (i.e. Unix-style newline)",2,null],[13,"CRLF","","A carriage return and a linefeed (i.e. Windows-style newline)",2,null],[4,"FromBase64Error","","Errors that can occur when decoding a base64 encoded string",null,null],[13,"InvalidBase64Byte","","The input contained a character not part of the base64 format",3,null],[13,"InvalidBase64Length","","The input had an invalid length",3,null],[7,"STANDARD","","Configuration for RFC 4648 standard base64 encoding",null,null],[7,"URL_SAFE","","Configuration for RFC 4648 base64url encoding",null,null],[7,"MIME","","Configuration for RFC 2045 MIME base64 encoding",null,null],[8,"ToBase64","","A trait for converting a value to base64 encoding.",null,null],[10,"to_base64","","Converts the value of `self` to a base64 value following the specified\nformat configuration, returning the owned string.",4,null],[8,"FromBase64","","A trait for converting from base64 encoded values.",null,null],[10,"from_base64","","Converts the value of `self`, interpreted as base64 encoded data, into\nan owned vector of bytes, returning the vector.",5,null],[11,"clone","","",1,null],[11,"fmt","","",1,null],[11,"clone","","",2,null],[11,"fmt","","",2,null],[11,"clone","","",0,null],[11,"fmt","","",0,null],[11,"clone","","",3,null],[11,"fmt","","",3,null],[11,"description","","",3,null],[11,"fmt","","",3,null],[0,"hex","rustc_serialize","Hex binary-to-text encoding",null,null],[4,"FromHexError","rustc_serialize::hex","Errors that can occur when decoding a hex encoded string",null,null],[13,"InvalidHexCharacter","","The input contained a character not part of the hex format",6,null],[13,"InvalidHexLength","","The input had an invalid length",6,null],[8,"ToHex","","A trait for converting a value to hexadecimal encoding",null,null],[10,"to_hex","","Converts the value of `self` to a hex value, returning the owned\nstring.",7,null],[8,"FromHex","","A trait for converting hexadecimal encoded values",null,null],[10,"from_hex","","Converts the value of `self`, interpreted as hexadecimal encoded data,\ninto an owned vector of bytes, 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`write!`",null,{"inputs":[{"name":"t"}],"output":{"name":"asprettyjson"}}],[6,"Array","","",null,null],[6,"Object","","",null,null],[6,"BuilderError","","",null,null],[6,"EncodeResult","","",null,null],[6,"DecodeResult","","",null,null],[8,"ToJson","","A trait for converting values to JSON",null,null],[10,"to_json","","Converts the value of `self` to an instance of 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will be written in human-readable\nJSON to the specified writer",17,{"inputs":[{"name":"write"}],"output":{"name":"encoder"}}],[11,"new","","Creates a new encoder whose output will be written in compact\nJSON to the specified writer",17,{"inputs":[{"name":"write"}],"output":{"name":"encoder"}}],[11,"set_indent","","Set the number of spaces to indent for each level.\nThis is safe to set during 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a json value from an `&mut io::Read`",9,{"inputs":[{"name":"read"}],"output":{"name":"result"}}],[11,"from_str","","Decodes a json value from a string",9,{"inputs":[{"name":"str"}],"output":{"name":"result"}}],[11,"pretty","","Borrow this json object as a pretty object to generate a pretty\nrepresentation for it via `Display`.",9,null],[11,"find","","If the Json value is an Object, returns the value associated with the provided key.\nOtherwise, returns None.",9,null],[11,"find_path","","Attempts to get a nested Json Object for each key in `keys`.\nIf any key is found not to exist, find_path will return None.\nOtherwise, it will return the Json value associated with the final key.",9,null],[11,"search","","If the Json value is an Object, performs a depth-first search until\na value associated with the provided key is found. If no value is found\nor the Json value is not an Object, returns None.",9,null],[11,"is_object","","Returns true if the Json value is an Object. Returns false otherwise.",9,null],[11,"as_object","","If the Json value is an Object, returns the associated BTreeMap.\nReturns None otherwise.",9,null],[11,"as_object_mut","","If the Json value is an Object, returns the associated mutable BTreeMap.\nReturns None otherwise.",9,null],[11,"is_array","","Returns true if the Json value is an Array. Returns false otherwise.",9,null],[11,"as_array","","If the Json value is an Array, returns the associated vector.\nReturns None otherwise.",9,null],[11,"as_array_mut","","If the Json value is an Array, returns the associated mutable vector.\nReturns None otherwise.",9,null],[11,"is_string","","Returns true if the Json value is a String. Returns false otherwise.",9,null],[11,"as_string","","If the Json value is a String, returns the associated str.\nReturns None otherwise.",9,null],[11,"is_number","","Returns true if the Json value is a Number. Returns false otherwise.",9,null],[11,"is_i64","","Returns true if the Json value is a i64. Returns false otherwise.",9,null],[11,"is_u64","","Returns true if the Json value is a u64. Returns false otherwise.",9,null],[11,"is_f64","","Returns true if the Json value is a f64. Returns false otherwise.",9,null],[11,"as_i64","","If the Json value is a number, return or cast it to a i64.\nReturns None otherwise.",9,null],[11,"as_u64","","If the Json value is a number, return or cast it to a u64.\nReturns None otherwise.",9,null],[11,"as_f64","","If the Json value is a number, return or cast it to a f64.\nReturns None otherwise.",9,null],[11,"is_boolean","","Returns true if the Json value is a Boolean. 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