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//! # A crate for working with Cauchy and Vandermonde matrices //! //! A small collection of routines for creating matrices that can be //! used to implement erasure (error-correction) schemes or threshold //! schemes using Galois fields. //! //! Note that this crate only provides data for insertion into a //! matrix. For the missing functionality, see: //! //! * [guff](https://crates.io/crates/guff) : basic operations over //! finite fields, including vector operations //! * [guff-matrix](https://crates.io/crates/guff-matrix) : full set //! of matrix types and operations //! //! # Using finite field matrix operations for threshold schemes //! //! A "threshold scheme" is a mathematical method for securely //! splitting a secret into a number of "shares" such that: //! //! * if a set number (the "threshold") of shares are combined, the //! original secret can be recovered //! //! * if fewer shares than the threshold are combined, no information //! about the secret is revealed //! //! ## Module Focus //! //! This module focuses in particular on Michael O. Rabin's //! "Information Dispersal Algorithm" (IDA). In it, splitting a secret //! is achieved by: //! //! * creating a transform matrix that has the required threshold property //! //! * placing the secret into an input matrix, padding it if needed //! //! * calculating transform x input to get an output matrix //! //! * reading off each share as a row of the transform matrix and the //! corresponding row of the output matrix //! //! To reconstruct the secret: //! //! * take the supplied transform matrix rows and put them into a //! square matrix //! //! * calculate the inverse of the matrix //! //! * form a new input matrix from the corresponding output data rows //! //! * calculate inverse x input //! //! * read the secret back from the output matrix //! //! More details of the algorithm can be found [later](todo). //! // will need to use external gf_2px //use num; use num_traits::identities::{One,Zero}; use guff::*; //impl From<u32> for NumericOps { // fn from(val: u32) -> Self { val as Self } //} /// ## Vandermonde-form matrix /// ```ascii /// /// | 0 1 2 k-1 | /// | 0 0 0 ... 0 | /// | | /// | 0 1 2 k-1 | /// | 1 1 1 ... 1 | /// | | /// | : : : : : | /// | | /// | 0 1 2 k-1 | /// | n-1 n-1 n-1 ... n-1 | /// ``` /// /// Can be used for Reed-Solomon coding, or a version of it, /// anyway. This is not the most general form of a Vandermonde matrix, /// but it is useful as a particular case since it doesn't require any /// parameters to produce it. /// /// Return is as a single vector of n rows, each of k elements pub fn vandermonde_matrix<G> (field : &G, k: usize, n : usize) -> Vec<G::E> where G : GaloisField, G::E : Into<usize>, G::EE : Into<usize> { let zero = G::E::zero(); let one = G::E::one(); let mut v = Vec::<G::E>::new(); if k < 1 || n < 1 { return v } // If pow() is expensive, can use repeated multiplications below. // range op won't work, so use while loop let mut row = zero; while row.into() < n { let mut col = G::EE::zero(); while col.into() < k { v.push(field.pow(row, col)); col = col + G::EE::one(); } row = row + one } v } /// ## Cauchy-form matrix generated from a key /// /// ```ascii /// k columns /// /// | 1 1 1 | /// | ------- ------- ... ------- | /// | x1 + y1 x1 + y2 x1 + yk | /// | | /// | 1 1 1 | /// | ------- ------- ... ------- | /// | x2 + y1 x2 + y2 x2 + yk | n rows /// | | /// | : : : : | /// | | /// | 1 1 1 | /// | ------- ------- ... ------- | /// | xn + y1 xn + y2 xn + yk | ///``` /// /// All [y1 .. yk, x1 .. xn] field values must be distinct non-zero /// values /// /// **TODO**: Check that all input values are distinct. Can put all /// elements on a heap and then check that no parent node has a child /// node equal to it. Alternatively, check the condition as we're /// building the heap? That should work, too. /// /// **TODO**: use a random number number generator to select k + n distinct /// field elements (eg, Floyd's algorithm for shuffling/selection from /// an array of all field elements if the field size is small, or a /// modification of the heap approach above for when it's impractical /// to list all the field elements) /// /// I've ordered the elements with y values first since these will be /// reused across all rows. I will allow passing in a vector that has /// more x values than are required /// /// We don't operate on k, n to produce field values, so they can be /// passed in as regular types pub fn cauchy_matrix<G> (field : &G, key : &Vec<G::E>, k: usize, n : usize) -> Vec<G::E> where G : GaloisField, { let mut v = Vec::<G::E>::new(); let vlen = key.len(); // I can change signature to return a Result later, but for now // can return a null vector to indicate failure. let min_key_size = k + n; if vlen < min_key_size { println!("Key should have at least {} elements", min_key_size); return v } // slice format? let y : &[G::E] = &key[0..k]; let x : &[G::E] = &key[k..]; // populate vector row by row for i in 0..n { for j in 0..k { v.push(field.inv(x[i] ^ y[j])) } } v } /// # Generate inverse Cauchy matrix using a key /// /// If the "key" used to generate the forward Cauchy matrix is saved, /// it can be used to calculate the inverse more efficiently than /// doing full Gaussian elimination. /// /// See: /// * <https://en.wikipedia.org/wiki/Cauchy_matrix> /// * <https://proofwiki.org/wiki/Inverse_of_Cauchy_Matrix> /// /// Note that the inverse is a k\*k matrix, so 2\*k distinct values /// must be passed in: /// /// * the fixed `y1 .. yk` values /// * a selection of k x values corresponding to the /// k rows being combined pub fn cauchy_inverse_matrix<G> (field : &G, key : &Vec<G::E>, k: usize) -> Vec<G::E> where G : GaloisField { let one = G::E::one(); let mut v = Vec::<G::E>::new(); let vlen = key.len(); if vlen != 2 * k { println!("Must supply k y values and k x values"); return v } // slice as before let y : &[G::E] = &key[0..k]; let x : &[G::E] = &key[k..]; // the reference version works, but the optimised version // doesn't. Only enabling reference version for now. if k != 0 { // was k < 3 // this is the basic reference algorithm let n = k; // alias to use i, j, k for loops for i in 0..n { // row for j in 0..n { // column let mut top = one; for k in 0..n { top = field.mul(top, x[j] ^ y[k]); top = field.mul(top, x[k] ^ y[i]); } let mut bot = x[j] ^ y[i]; for k in 0..n { if k == j { continue } bot = field.mul(bot, x[j] ^ x[k]); } for k in 0..n { if k == i { continue } bot = field.mul(bot, y[i] ^ y[k]); } top = field.mul(top, field.inv(bot)); v.push(top); // row-wise } } } else { // TODO: find bug in this code // // optimised version of the above that notes that we // calculate the following in the inner loop: // // * product of row except for ... (n-1 multiplications) // * product of col except for ... (n-1 multiplications) // // These can be calculated outside the main loop and reused. // // let n = k; let mut imemo = Vec::<G::E>::with_capacity(k); for i in 0..n { let mut bot = one; let yi = y[i]; for k in 0..n { if k == i { continue } bot = field.mul(bot, yi ^ y[k]); } imemo.push(bot) } let mut jmemo = Vec::<G::E>::with_capacity(k); for j in 0..n { let mut bot = one; let xj = x[j]; for k in 0..n { if k == j { continue } bot = field.mul(bot, xj ^ x[k]); } jmemo.push(bot) } for i in 0..n { for j in 0..n { let mut top = field.mul(x[j] ^ y[0], x[0] ^ y[i]); for k in 0..n { top = field.mul(top, x[j] ^ y[k]); top = field.mul(top, x[k] ^ y[i]); } let mut bot = x[j] ^ y[i]; // inner loops eliminated: bot = field.mul(bot, imemo[i]); bot = field.mul(bot, jmemo[j]); top = field.mul(top, field.inv(bot)); v.push(top) } } } v } // I guess that I might have to implement a matrix here for now. The // easiest way to test that the two Cauchy fns are correct is to // calculate the forward and inverse matrices from the same key, // multiply them together and check if we have an identity matrix. // // I'll need a matrix inversion routine if I want to check the // correctness of the Vandermonde matrix code, though. I wonder, // though, are there any short-cuts to calculating the inverse of // that? // Can't derive Copy due to Vec not implementing it. Will need to // implement a copy constructor so. // #[derive(Debug)] // pub struct Matrix<T, P> // where T : NumericOps, P : NumericOps { // rows : usize, // cols : usize, // data : Vec<T>, // _phantom : P, // rowwise : bool, // } // Vector stuff done in guff crate /* // vector product ... multiply each vector element -> new vector fn vector_mul<G>(field : &G, dst : &mut [G::E], a : &[G::E], b : &[G::E]) where G : GaloisField { // let prod = T::one; let (mut a_iter, mut b_iter) = (a.iter(), b.iter()); for d in dst.iter_mut() { *d = field.mul(*a_iter.next().unwrap(), *b_iter.next().unwrap()) } } // dot product ... sum of items in vector product -> value fn dot_product<G>(field : &G, a : &[G::E], b : &[G::E]) -> G::E where G : GaloisField { let mut sum = G::E::zero(); for (a_item, b_item) in a.iter().zip(b) { sum = sum ^ field.mul(*a_item, *b_item); } sum } */ // Matrix stuff done in guff-matrix // I think that I'll make rowwise and colwise matrices different // types. Different type constraints, anyway. This makes sense for // matrices that are passed into a multiplication routine, but I'm not // sure about return values... // // There are two patterns I'm interested in. // // Split pattern: // // k window window // +----+ +----- … -----+ +----- … -----+ // |-> | || | |-> | > contiguous // n | | k |v | n |-> | // | | +----- … -----+ | | // +----+ v contiguous +----- … -----+ // // transform x input = output // // ROWWISE COLWISE ROWWISE // // // Combine pattern: // // k window window // +----+ +----- … -----+ +----- … -----+ // |-> | |-> | || | v contiguous // k | | k |-> | k |v | // +----+ +----- … -----+ +----- … -----+ // > contiguous // // transform x input = output // // ROWWISE ROWWISE COLWISE // // // The arrows show the optimal organisation for I/O: not necessarily // for actual matrix multiplication. // // viz.: // // When splitting, single input stream is read into a contiguous block // of memory, one column at a time, while several output streams are // also contiguous. // // When combining, each of the several (rowwise) input streams are // contiguous, and the single (colwise) output stream is contiguous. // // So basically the split version has an unavoidable scatter pattern // at the output, while the combine has an unavoidable gather pattern // at the input. We could try out some buffering strategy that // internally transposes sub-matrix blocks (storing them in SIMD // registers and working on them there) and translating their // reads/writes so that they're in the "correct" form in // memory. That's for another day, though. // // The most important thing from the above is that (ignoring the // organisation of the transform matrix, which is always ROWWISE) our // multiply will always take input data in one layout and output a // matrix of the opposite layout. That basically answers my question // about whether it's a good idea to have ROWWISE/COLWISE variants of // matrices. It does seem to be. // // sketch of the above idea... /* struct RowWiseAdaptedMatrix<T> { // copy of all fields that a regular Matrix has, except layout } struct ColWiseAdaptedMatrix<T> { // copy of all fields that a regular Matrix has, except layout } trait MatrixOps<T> { // default, non-specialised stuff fn rows(); // all the accessors and regular stuff that a Matrix does above. // Then, gaps for specialised (composable) methods below: fn kernel(); } impl MatrixOps<T,P> { // default implementations } impl<T> MatrixOps<T> for RowWiseAdaptedMatrix<T> { fn kernel () { // specialised kernel goes here } } // Another way to do it is to just use type constraints on // functions. That is probably simpler: fn split<T,P>(field : &impl GenericField<T,P>, transform<T> : R, input<T> : C, output<T> : R) where T : NumericOps, P : NumericOps, R : MatrixOps + RowWise, C : MatrixOps + ColWise { // write split-specific kernel here } // This would be supported by: // * empty traits for RowWise and ColWise // * two specialised structs that have the traits composed in // * different constructors for giving us concrete instances // * coordination between other matrix fns that always make // clear which subtypes of matrix they expect/provide // * helper functions for swapping (transposing) or reinterpreting(?) // matrix subtype */ // comment out matrix code /* // Put Accessors into a separate trait. I'm trying to see if I can get // a default implementation that has the same members. Mmm... probably // not. I suppose that a macro is the only solution to avoiding all // the boilerplate. // Needs to be generic on T due to dealing with Vec<T> pub trait Accessors<T : NumericOps> { fn rows(&self) -> usize; fn cols(&self) -> usize; fn rowcol(&self) -> (usize, usize) { (self.rows(), self.cols()) } // internally, assume all implementations work with Vec<T> fn vec(&self) -> &Vec<T>; fn vec_as_mut(&mut self) -> &mut Vec<T>; fn vec_as_mut_slice(&mut self) -> &[T]; } // Things that we can do with a matrix without knowing its layout pub trait LayoutAgnostic<T : NumericOps> : Accessors<T> { fn zero(&mut self) { let slice : &mut[T] = &mut self.vec_as_mut()[..]; for elem in slice.iter_mut() { *elem = T::zero() } } fn one(&mut self) { // sets matrix as identity let (rows, cols) = self.rowcol(); if rows != cols { panic!("Must have rows==cols to set up as identity matrix") } let slice : &mut[T] = &mut self.vec_as_mut()[..]; let diag = rows + 1; // count mod this let mut index = 0; for elem in slice.iter_mut() { if index == 0 { *elem = T::one() } else { *elem = T::zero() } index = (index + 1) % diag } } // will have external transpose() for non-square matrices which // will create a new matrix with a new layout. This one flips // values along the diagonal without changing the layout fn transpose_square(&mut self) { let rows = self.rows(); if rows != self.cols() { panic!("Matrix is not square") } let v = self.vec_as_mut(); // swap values at i,j with j,i for all i != j // we don't need to know anything about layout for i in 1..rows { for j in 0..i { // safe way of swapping values without temp variable? // should be... // (v[i * rows + j], v[j * rows + i]) // = (v[j * rows + i], v[i * rows + j]) let t = v[i * rows + j]; v[i * rows + j] = v[j * rows + i]; v[j * rows + i] = t; } } } } // Things that require knowing about the matrix's layout pub trait LayoutSpecific<T : NumericOps> : Accessors<T> { // These essentially fix the layout fn is_rowwise(&self) -> bool; fn is_colwise(&self) -> bool { ! &self.is_rowwise() } fn _rowcol_to_index(&self, row : usize, col : usize) -> usize; // cursor/index pointer into vec (derived from above; no overflow // checks since Vec will catch it). The use case for these is to // make one initial call to whichever/both you want to use, // setting the index to 0. Then, in your loops, simply add the // correct offset. Calling move_* inside your loop isn't too bad // either assuming LLVM can notice that self.rows()/.cols() is a // loop invariant. It might even do the same for .is_rowwise(). fn move_right(&self, index : usize) -> usize { if self.is_rowwise() { index + 1 } else { index + self.rows() } } fn move_down(&self, index : usize) -> usize { if self.is_rowwise() { index + self.cols() } else { index + 1 } } // higher-level users of the first three fn getval(&self, row : usize, col : usize) -> T { self.vec()[self._rowcol_to_index(row, col)] } fn setval(&mut self, row : usize, col : usize, val : T) { // need to use two statements below because you can't use // self both mutably (updating the vector) and immutably let index = self._rowcol_to_index(row, col); self.vec_as_mut()[index] = val; } } // What do they call fns in rust that are called with // module::something()? Whatever they're called, it probably makes // more sense to call things like matrix multiply that way /* // All variants will use the same structure format, but we give them // different names to distinguish them struct RowwiseMatrix<T : NumericOps> { rows : usize, cols : usize, v : Vec<T>, } impl<T : NumericOps> Accessors<T> for RowwiseMatrix<T> { fn rows(&self) -> usize { self.rows } fn cols(&self) -> usize { self.cols } fn vec_as_mut_slice(&self) -> &[T] { &self.v[..] } fn vec_as_mut(&mut self) -> &mut Vec<T> { &mut (self.v) } } struct ColwiseMatrix<T : NumericOps> { rows : usize, cols : usize, v : Vec<T>, } impl<T : NumericOps> Accessors<T> for ColwiseMatrix<T> { fn rows(&self) -> usize { self.rows } fn cols(&self) -> usize { self.cols } fn vec_as_mut_slice(&self) -> & [T] { &self.v[..] } fn vec_as_mut(&mut self) -> &mut Vec<T> { &mut (self.v) } } */ pub struct CheckedMatrix<T : NumericOps> { rows : usize, cols : usize, v : Vec<T>, is_rowwise : bool, // checked at run time } impl<T : NumericOps> Accessors<T> for CheckedMatrix<T> { fn rows(&self) -> usize { self.rows } fn cols(&self) -> usize { self.cols } fn vec(&self) -> &Vec<T> { &self.v } fn vec_as_mut(&mut self) -> &mut Vec<T> { &mut (self.v) } fn vec_as_mut_slice(&mut self) -> &[T] { &self.v[..] } } impl<T : NumericOps> LayoutAgnostic<T> for CheckedMatrix<T> { } impl<T : NumericOps> LayoutSpecific<T> for CheckedMatrix<T> { fn is_rowwise(&self) -> bool { self.is_rowwise } fn _rowcol_to_index(&self, row : usize, col : usize) -> usize { // won't check that row/col are within allowed range if self.is_rowwise { row * self.cols + col } else { col * self.rows + row } } } // what should our return type be? // // * just the struct type? // * an impl line? // x combine both? (can't have -> Struct : Foo Bar) fn construct_checked_matrix<T : NumericOps> (rows : usize, cols : usize, rowwise : bool) -> CheckedMatrix<T> // where T: NumericOps, M : Accessors<T> + LayoutAgnostic<T> + LayoutSpecific<T> { let v = vec![T::zero(); rows * cols]; CheckedMatrix::<T> { // gains a concrete type rows : rows, cols : cols, v : v, is_rowwise : rowwise } } */ // Following on from the names above, I think I'll rename the two // traits that each struct should implement according to whether it's // layout-neutral or layout-specific/-sensitive. // Is this a good approach? // // I think it's OK. In "normal" OO, we'd have a base "Matrix" class // from which we'd extend into row-wise and column-wise forms. Then // the constructors would return types that are still classed as // "Matrix" objects, no matter what the subclass name. // // We can't do that in Rust because there's no object inheritance. // // What we can do is return an object that satisfies trait interfaces. // // A problem arises when we want to store different struct variants in // a single vector or variable. Even if all the variants are the same // size, a return type of "implements Foo" does not guarantee that, // and the type system can't go and check. // // Actually, though, that's also a problem in standard OO. The // solution there is that we allocate objects on the heap and store // pointers to them. // // I think that the way I'm handling it is the proper Rust way of // doing things. For example, if the distinction between the different // object variants matters, we can call the appropriate constructor // (or manually construct the object) and store it with the // appropriate struct type. As an example, a "transform" object that // does encoding or decoding using IDA or Reed-Solomon coding will // probably want to use specific row-wise or column-wise variants for // the input, transform and output matrices. // // If the application doesn't care about the internal details, it can // cast the returned object as something that "implements matrix // operations on <some numeric type>". It loses the ability to // ascertain the exact type of the underlying struct from that point // on, though. // // There is a bit of extra boilerplate for all the three matrix types // above. The accessors have to be attached to the structs (because // traits deal with methods, not attributes) #[cfg(test)] mod tests { use super::*; // use num_traits::identities::{One,Zero}; // External crate only used in development/testing use guff_matrix::*; use guff_matrix::x86::*; #[test] fn vandermonde_works() { let f = new_gf8(0x11b, 0x1b); let v = vandermonde_matrix(&f, 5, 5); for i in 5..10 { assert_eq!(1, v[i], "expect row 1 all 1s"); } for i in 0..5 { // check column 0, including 0**0 = 1 assert_eq!(1, v[i * 5], "expect col 0 all 1s"); // check column 1 let index = i * 5 + 1; assert_eq!(i, v[index].into(), "expect col 1 ascending 0..n"); } } // The only sure-fire way to test the functions is to do a matrix // multiplication, then do the inverse and check whether the // result is the same as the original... // // I should have most of what I need in guff-matrix crate const SAMPLE_DATA : [u8; 20] = [ 1u8, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ]; // Direct copy from guff_matrix::simulator pub fn interleave_streams(dest : &mut [u8], slices : &Vec<&[u8]>) { let cols = dest.len() / slices.len(); let mut dest = dest.iter_mut(); let mut slice_iters : Vec::<_> = Vec::with_capacity(slices.len()); for s in slices { let iter = s.iter(); slice_iters.push(iter); } for _ in 0 .. cols { for slice in &mut slice_iters { *dest.next().unwrap() = *slice.next().unwrap(); } } } #[test] fn test_cauchy_transform() { // 4x4 xform matrix is the smallest allowed right now let key = vec![ 1, 2, 3, 4, 5, 6, 7, 8 ]; let field = new_gf8(0x11b, 0x1b); let cauchy_data = cauchy_matrix(&field, &key, 4, 4); // guff-matrix needs either/both/all: // * architecture-neutral matrix type (NoSimd option) // * automatic selection of arch-specific type (with fallback) // * new_matrix() type constructors? // // For now, though, the only concrete matrix types that are // implemented are for supporting x86 simd operation, so use // those (clunky) names... let mut xform = X86SimpleMatrix::<x86::X86u8x16Long0x11b> ::new(4,4,true); xform.fill(&cauchy_data); // must choose cols appropriately (gcd requirement) let mut input = X86SimpleMatrix::<x86::X86u8x16Long0x11b> ::new(4,5,false); input.fill(&SAMPLE_DATA); let mut output = X86SimpleMatrix::<x86::X86u8x16Long0x11b> ::new(4,5,true); // use non-SIMD multiply reference_matrix_multiply(&mut xform, &mut input, &mut output, &field); // We will also need a transposition (interleaving) step to // convert the rowwise output matrix from above into colwise // format for the inverse transform // Right now, only implementation of interleaver is in the // simulation module... copying it in here // we need to do some up-front work to use that: let array = output.as_slice(); let slices : Vec<&[u8]> = array.chunks(5).collect(); let mut dest = [0u8; 20]; interleave_streams(&mut dest, &slices); // Do the inverse transform (same key) let cauchy_data = cauchy_inverse_matrix(&field, &key, 4); let mut xform = X86SimpleMatrix::<x86::X86u8x16Long0x11b> ::new(4,4,true); xform.fill(&cauchy_data); let mut input = X86SimpleMatrix::<x86::X86u8x16Long0x11b> ::new(4,5,false); input.fill(&dest); let mut output = X86SimpleMatrix::<x86::X86u8x16Long0x11b> ::new(4,5,false); // use non-SIMD multiply reference_matrix_multiply(&mut xform, &mut input, &mut output, &field); assert_eq!(output.as_slice(), &SAMPLE_DATA); } // Another test I could do would be to multiply the Cauchy matrix // by its inverse and check that the result is the identity // matrix. However, as it currently stands, guff-matrix doesn't // allow for general-purpose matrix multiply yet, since it's // optimised for xform/input matrix pairs that satisfy the gcd // property. // // Ah, I think I can ... no gcd checks in matrix_multiply #[test] fn test_inv_inv_cauchy() { // 4x4 xform matrix is the smallest allowed right now let key = vec![ 1, 2, 3, 4, 5, 6, 7, 8 ]; let field = new_gf8(0x11b, 0x1b); let forward_data = cauchy_matrix(&field, &key, 4, 4); let mut xform = X86SimpleMatrix::<x86::X86u8x16Long0x11b> ::new(4,4,true); xform.fill(&forward_data); // data returned from cauchy_inverse_matrix needs to be // interleaved if it's in the 'input' position let inverse_data = cauchy_inverse_matrix(&field, &key, 4); let array = inverse_data; let slices : Vec<&[u8]> = array.chunks(4).collect(); let mut dest = [0u8; 16]; interleave_streams(&mut dest, &slices); let mut input = X86SimpleMatrix::<x86::X86u8x16Long0x11b> ::new(4,4,false); input.fill(&dest); let mut output = X86SimpleMatrix::<x86::X86u8x16Long0x11b> ::new(4,4,true); // use non-SIMD multiply reference_matrix_multiply(&mut xform, &mut input, &mut output, &field); assert_eq!(output.as_slice(), [ 1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1 ] ) } // Can't test Vandermonde yet because I haven't implemented matrix // inversion here or in guff-matrix /* // Might as well start writing some test cases #[test] fn test_making_vectors() { // can we convert u8 to T? let a = [0u8,1,2,3,4]; // do I have to clone() to prevent getting refs? let v1 : Vec<u8> = a.iter().cloned().collect(); let v2 : Vec<u8> = a.iter().cloned().collect(); let mut v3 : Vec<u8> = a.iter().cloned().collect(); let f = new_gf8(0x11b,0x1b); // should change v3 assert_eq!(v1, v3); vector_mul(&f, &mut v3, &v1, &v2); assert_ne!(v1, v3); } */ /* #[test] fn test_dot_products() { // I'll only use mul by zero or one so that I can mentally // calculate the result without needing to know results of // more complex field multiplications let a = [0u8, 1, 1, 9, 4, 8, 4]; let b = [0u8, 0, 2, 0, 1, 1, 1]; // do I have to clone() to prevent getting refs? let v1 : Vec<u8> = a.iter().cloned().collect(); let v2 : Vec<u8> = b.iter().cloned().collect(); let f = new_gf8(0x11b,0x1b); // should change v3 assert_ne!(v1, v2); let sum = dot_product(&f, &v1, &v2); assert_eq!(sum, 0 ^ 0 ^ 2 ^ 0 ^ 4 ^ 8 ^ 4); } #[test] fn test_construct_checked_matrix() { let mat = construct_checked_matrix::<u8>(3, 4, false); assert_eq!(3, mat.rows()); assert_eq!(4, mat.cols()); assert_eq!(false, mat.is_rowwise()); assert_eq!(true , mat.is_colwise()); } // fn sig that requires a certain trait be implemented fn looking_for_accessors<T>(mat : &impl Accessors<T>) where T : NumericOps { assert!(mat.rows() > 0) } // we get a struct, so pass it to looking_for_accessors() above #[test] fn test_impl_accessors_satisfied() { let mat = construct_checked_matrix::<u8>(3, 4, false); // no compile error, and assert above passes looking_for_accessors(&mat); } // Various simple things to test ... // // * initial matrix is zeroed // * identity works // * we can compare output of vec accessor with a list #[test] fn basic_vec_comparison() { let mut mat = construct_checked_matrix::<u8>(3, 3, true); // it seems we have to compare as slice ... no big deal assert_eq!([0u8; 9], &mat.vec()[..]); mat.one(); assert_eq!([1u8, 0, 0, 0, 1, 0, 0, 0, 1], &mat.vec()[..]); mat.zero(); assert_eq!([0u8; 9], &mat.vec()[..]); // What if we compare shared ref with mutable slice? // surprisingly, this works with no compiler complaint. assert_eq!([0u8; 9], mat.vec_as_mut_slice()); } #[test] fn mutate_single_vec_elements() { let mut mat = construct_checked_matrix::<u8>(3, 3, true); { // drop v after use: see below let mut v = mat.vec_as_mut(); v[0] = 1; v[4] = 1; v[8] = 1; } let mut identity = construct_checked_matrix::<u8>(3, 3, true); identity.one(); // maybe make this a fluent interface? assert_eq!(mat.vec(), identity.vec()); // without the braces above, the assignment below would cause // the compiler to complain about mixing mutable/immutable // borrows. So we drop the original v and then recreate it // here after the immutable borrow in mat.vec() above. let mut v = mat.vec_as_mut(); v[0] = 1; } // basic test of _rowcol_to_index (suffices for all matrix sizes) #[test] fn test_rowwise_checked() { // 2x2 matrix gives a truth table of sorts let rowwise = construct_checked_matrix::<u8>(2, 2, true); assert_eq!(0, rowwise._rowcol_to_index(0,0)); assert_eq!(1, rowwise._rowcol_to_index(0,1)); assert_eq!(2, rowwise._rowcol_to_index(1,0)); assert_eq!(3, rowwise._rowcol_to_index(1,1)); let colwise = construct_checked_matrix::<u8>(2, 2, false); assert_eq!(0, colwise._rowcol_to_index(0,0)); assert_eq!(1, colwise._rowcol_to_index(1,0)); // these two assert_eq!(2, colwise._rowcol_to_index(0,1)); // swapped assert_eq!(3, colwise._rowcol_to_index(1,1)); } // "cursors" are another way to traverse rows/columns. If these // work, we don't need to check any larger matrix sizes. #[test] fn test_cursor_checked() { // 2x2 matrix gives a truth table of sorts let rowwise = construct_checked_matrix::<u8>(2, 2, true); assert_eq!(1, rowwise.move_right(0)); assert_eq!(2, rowwise.move_down(0)); let colwise = construct_checked_matrix::<u8>(2, 2, false); assert_eq!(2, colwise.move_right(0)); assert_eq!(1, colwise.move_down(0)); } // Other stuff relating to orientation also needs checking. We // can't assume anything about how any other layout-specific // functions will reason about it, and which of the above // functions they use. // // I might refactor the above tests so that it's easier to reuse // them when I implement the other two (non-checked) layouts // // something like "assert_rowwise_cursor(mat)" // I can nearly test cauchy functions ... just need a multiply routine #[test] fn test_cauchy_inverse_identity() { todo!() } */ }