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//! Non-SIMD, pure Rust simulation of matrix multiplication algorithm //! //! There are two simulators included here. Both are based on the idea //! of treating the transform and input matrices as infinite streams //! that wrap around. These streams are read sequentially and //! multiplied together to get a product stream. The product stream is //! then apportioned into dot products. //! //! Using this method, the generated dot products fill the output //! matrix by progressing along the diagonal, with wrap-around. So //! long as the number of columns in the input and output matrices //! does not have the number of rows in the transform matrix as a //! factor, all elements in the output matrix will be populated. //! //! Example: 4x3 transform x 3x5 input/output matrices //! //! ```ascii //! | a b c | | i0 i3 i6 i9 ic | | 0 16 12 8 4 | //! | d e f | x | i1 i4 i7 ia id | = | 5 1 17 13 9 | //! | g h i | | i2 i5 i8 ib ie | |10 6 2 18 14 | //! | j k l | |15 11 7 3 19 | //! ``` //! //! This shows the order that elements are written to the output //! matrix. As can be seen, the entire matrix is filled. //! //! Example: 4x3 transform x 3x3 input/output matrices //! //! ```ascii //! | a b c | | i0 i3 i6 | | 0 4 8 | //! | d e f | x | i1 i4 i7 | = | 9 1 5 | //! | g h i | | i2 i5 i8 | | 6 10 2 | //! | j k l | | 3 7 11 | //! ``` //! //! This also works since the number of output columns (3) does not //! have the number of rows in the transform matrix (4) as a factor. //! //! However: 4x3 transform x 3x4 input/output matrices //! //! ```ascii //! | a b c | | i0 i3 i6 i9 | | 0 - - - | //! | d e f | x | i1 i4 i7 ia | = | - 1 - - | //! | g h i | | i2 i5 i8 ib | | - - 2 - | //! | j k l | | - - - 3 | //! ``` //! //! Here, the next output starts back at the original output location, //! so the output matrix will not be filled. Extending the matrix to //! be a larger multiple of 4 will not help, either. //! //! If the number of rows in the transform matrix is n, and the number //! of columns in the input and output matrices is c, then: //! //! * if n = 1, then c can be any positive value; //! * if n > 1, then c is conditional on gcd(n,c) != n != c //! //! Note the additional condition which I didn't mention //! above. Basically if n is a multiple of c or c is a multiple of n, //! the wrap-around will not work properly. //! //! # Bytewise Simulation //! //! The first simulation uses //! [TransformMatrix](struct.TransformMatrix.html), //! [InputMatrix](struct.InputMatrix.html) and //! [OutputMatrix](struct.OutputMatrix.html) structs to store the //! matrices. The first two implement [Iterator] to simulate reading //! them as infinite streams. The //! [MultipyStream](struct.MultipyStream.html) struct simulates the //! cross product of these streams, and it also implements [Iterator]. //! //! The [warm_multiply](fn.warm_multiply.html) function simulates the matrix multiplication //! algorithm by doing byte-by-byte reads from the //! [MultipyStream](struct.MultipyStream.html). //! //! # SIMD Simulation //! //! The second simulation changes from byte-wise reading from matrices //! with simd-wise reading. //! //! * reimplement versions of the transform and input matrices //! * reuse original output matrix //! * new generic Simd trait //! * concrete SimSimd implementation using `\[u8; 8\]` as its vector type //! * matrices being read from implement Iterator<Item=SimSimd> //! * separate function `simsimd_warm_multiply()` using the above //! //! The main reason for reimplementing the two matrix types is that //! the existing ones already implement [Iterator], and it's not //! possible to reimplement it using a different [Iterator::Item] //! type. //! //! The implementation of Simd and matrix multiply in the crate's main //! module and SIMD code in the architecture-dependent modules follow //! the same general design as above. // Wrap-around reads/multiplies on matrices // // Basics of how to do this with SIMD reads: // // * all reads will be aligned (assuming start of matrix is) // * use read buffers comprising two SIMD registers // * extract a full SIMD register from buffer // * as data is extracted, set reg0 = reg1, reg1 = 0 // * (this is passed on to the multiply engine) // // If the matrix is a multiple of the SIMD register, there's no // challenge at all: // // * reads cannot go past end of matrix // * looping just consists of resetting the read pointer // // At end of matrix buffer: // // r0 r1 // +----------------+----------------+ // | : | : | // +----------------+----------------+ // `................' // // // The dotted area represents the last part of the matrix. After it, // r1 should start reading from the start of the matrix again. If we // use an aligned read, we will have to combine the part of r1 that we // already have with a shifted version // // r0 r1 r2 // +----------------+----------------+----------------+ // | : | : | : | // +----------------+----------------+----------------+ // `................'................' // end matrix restart matrix // // (r2 won't be explicitly stored, but it helps to show the problem) // // At the 'restart matrix' step, we are reading from aligned memory, // but we have to spread it over two registers, so we will have a mask // (to select the part of r1 that we got in the last loop) combined // with a shift. // // In terms of masks: // // r1 <- (r1 & old_bytes) | (new_bytes >> overlap) // r2 <- (new_bytes << (16 - overlap) // // If we can ensure that the empty bytes are zero, it just becomes a // problem involving 'or' and a couple of shifts. The amount of the // shift can be stored in a normal (non-vector) register, and regular // logical left and right shifts ensure that the newly added bits are // always zero. // // The only downside is that all memory reads involve a couple of // extra shifts, which may not be necessary in all cases (ie, where // the matrix is a multiple of the simd width). // // The only subtlety involved here is handling the overlapping // reads. For example, if we have r0 already, we have to detect that // reading r1 involves an overlap, and that requires reading overlap // bytes from the end of the matrix and then doing a second read from // the start of the matrix and correctly or'ing them together, plus // correctly calculating the new overlap value (which will be applied // to all subsequent reads). Again, this can be done by basic // arithmetic (if read_would_overlap {...}), and it doesn't influence // our choice of SIMD intrinsics. // // Note that if we zero out (simd - 1) elements directly after the // matrix as it is stored in memory, we can later OR it with the // correct data taken from the (shifted) restart. Also, it prevents us // from reading from uninitialised memory. // // This is nice and simple and easily portable without needing to // delve too deeply into the docs. // Apportionment of subproducts to output dot products // // Every kw bytes that we process from the input generates enough // multiplications // // kw might be > simd size, in which case we have three subcases: // // a) the product vector lies entirely within this kw range // b) the start of the vector belongs to the previous range // c) the end of the vector belongs to the next range // // In the case of kw <= simd size, the range can appear at the start, // the end, the middle, or it can straddle either end. // // It might be possible to use masks, but we would have to use // register pairs since we can't just rotate the mask without them. // // r0 r1 r2 // +----------------+----------------+----------------+ // | : : | : | : | // +----------------+----------------+----------------+ // `..........'...........'...........' // this kw next kw ... // // // For kw <= simd, the mask is the same width all the time and we // rotate it to the right by kw each time. (and shift left by simd // every time we consume r0) // // For kw > simd, we have two masks, one for the start of the range // and one for the end. We rotate both of them every time we consume // kw products: // // r0 r1 r2 // +----------------+----------------+----------------+ // | : | | : | // +----------------+----------------+----------------+ // `..................................' // start mask + full vector + end mask // // Masks need not be explictly stored. We can copy the vector and use // a pair of shifts to mask out only the portion we're interested in. // // Note that there is no need to keep the full kw range in a set of // registers. Instead, we can calculate the sum for each simd (or // sub-simd) region and accumulate it in a single u8. // // Sum across dot product // // When summing across a full 16-bit vector, we can do this with 4 // rotates and 4 xors: // // v ^= rot(v, 8) // v ^= rot(v, 4) // v ^= rot(v, 2) // v ^= rot(v, 1) // // All elements of the vector will then contain the sum. // // The order of the operations does not matter, so if we wanted to // only do as many shifts as needed, we could loop, starting with the // smallest rotation and working up to the largest. Something like: // // next_power_of_2 = 1 // while remaining < next_power_of_2 // v ^= rot(v, next_power_of_2) // next_power_of_2 <<= 1 // // (the sum will not be spread across all elements of the vector, // though. I think it comes out in element next_power_of_2 - 1) // // // Output tape // // After calculating a dot product, we store it at the current output // pointer, then we advance along the diagonal. When we go past the // bottom or right side of the matrix, we reset the row or column, // respectively, to zero. // // If c has a factor that is coprime to k and n, then each time we // wrap around the output matrix, we will be starting from a new point // in the first column so that after n wrap-arounds we will be // starting again at 0,0 and the whole output matrix will have been // filled. // // Open Question // // My original implementation used only a single register for storing // products. It also kept 'total' and 'next_total' as complete // vectors. It used masks to: // // * extract parts at the start of the current vector as belonging to // the current dot product // // * the inverse mask to apportion the remaining // // Some questions: // // * whether explicit masks are needed or appropriate (would shifts be // better?) // // * whether to implement the product tape as two registers or stick // with the one (considering that we end up with two registers // anyway, for // // * whether my original code was correct for both the kw <= simd and // kw >simd cases // // One important feature of the mask is that it zeroes out products // from the previous dot product. // // // Simulation // // // just set w=1 and type = u8 for convenience use crate::*; use core::mem::size_of; /// Transform matrix for first simulation. Uses row-wise data storage. #[derive(Debug, Clone)] pub struct TransformMatrix { n : usize, // rows k : usize, // cols array : Vec<u8>, // row-wise storage read_pointer : usize, } impl TransformMatrix { fn new(n : usize, k : usize) -> Self { let array = vec![0; n * k]; let read_pointer = 0; Self { n, k, array, read_pointer } } fn fill(&mut self, slice : &[u8]) -> &Self { self.array.copy_from_slice(slice); self } } /// Bytewise wrap-around iteration of `TransformMatrix` impl Iterator for TransformMatrix { type Item = u8; fn next(&mut self) -> Option<Self::Item> { let val = self.array[self.read_pointer]; self.read_pointer += 1; if self.read_pointer >= self.n * self.k { self.read_pointer -= self.n * self.k; } Some(val) } } /// Input matrix for first simulation. Uses column-wise /// data storage. #[derive(Debug, Clone)] pub struct InputMatrix { k : usize, // rows c : usize, // cols array : Vec<u8>, // colwise storage read_pointer : usize, } impl InputMatrix { fn new(k : usize, c : usize) -> Self { let array = vec![0; k * c]; let read_pointer = 0; Self { k, c, array, read_pointer } } fn fill(&mut self, slice : &[u8]) -> &mut Self { self.array.copy_from_slice(slice); self } } /// Bytewise wrap-around iteration of `InputMatrix` impl Iterator for InputMatrix { type Item = u8; fn next(&mut self) -> Option<Self::Item> { let val = self.array[self.read_pointer]; self.read_pointer += 1; if self.read_pointer >= self.c * self.k { self.read_pointer -= self.c * self.k; } Some(val) } } use guff::*; // MultiplyStream will "zip" the two iters above // #[derive(Debug)] /// Structure for holding iterators over `TransformMatrix` and /// `InputMatrix` pub struct MultiplyStream<'a> { // We don't care what type is producing the u8s xform : &'a mut Iterator<Item=u8>, input : &'a mut Iterator<Item=u8>, // can't I store a ref to something implementing GaloisField? // field : &'a dyn GaloisField<E=u8, EE=u16, SEE=i16>, field : &'a F8, // use concrete implementation instead } /// Simulate multiplication (cross product) of two matrix streams impl<'a> Iterator for MultiplyStream<'a> { type Item = u8; fn next(&mut self) -> Option<Self::Item> { let a = self.xform.next().unwrap(); let b = self.input.next().unwrap(); Some(self.field.mul(a,b)) } } /// Output matrix for first simulation. Supports row-wise and /// column-wise storage. #[derive(Debug)] pub struct OutputMatrix { n : usize, // rows c : usize, // cols array : Vec<u8>, // row : usize, col : usize, rowwise : bool } impl OutputMatrix { fn new(n : usize, c : usize, rowwise : bool) -> Self { let array = vec![0; n * c]; let row = 0; let col = 0; Self { n, c, array, row, col, rowwise } } fn new_rowwise(n : usize, c : usize) -> Self { Self::new(n, c, true) } fn new_colwise(n : usize, c : usize) -> Self { Self::new(n, c, false) } fn write_next(&mut self, e : u8) { let size = self.n * self.c; if self.rowwise { self.array[self.row * self.c + self.col] = e; } else { // if col-wise (like input matrix) self.array[self.row + self.col * self.n] = e; } self.row += 1; if self.row == self.n { self.row = 0 } self.col += 1; if self.col == self.c { self.col = 0 } } } /// First (byte-wise) matrix multiply simulation /// /// "warm": "wrap-around read matrix" /// /// This routine treats the transform and input matrices as being /// infinite byte streams, multiplies them, then apportions the /// products to the correct dot product sums. Completed dot products /// are written out sequentially along the diagonal of the output /// matrix. /// /// Provided the number of columns in the input and output matrices /// (both set to the same value) has a factor that is relatively prime /// to both dimensions of the transform matrix, the diagonal traversal /// of the output matrix is guaranteed to write to every cell in the /// matrix. /// pub fn warm_multiply(xform : &mut TransformMatrix, input : &mut InputMatrix, output : &mut OutputMatrix) { // using into_iter() below moves ownership, so pull out any data // we need first let c = input.c; let n = xform.n; let k = xform.k; assert!(k > 0); assert!(n > 0); assert!(c > 0); assert_eq!(input.k, k); assert_eq!(output.c, c); assert_eq!(output.n, n); // searching for prime factors ... needs more work assert_ne!(k, gcd(k,c)); // set up a MultiplyStream let xiter = xform.into_iter(); let iiter = input.into_iter(); let mut mstream = MultiplyStream { xform : xiter, input : iiter, field : &guff::new_gf8(0x11b,0x1b), }; // the algorithm is trivial once we have an infinite stream let mut dp_counter = 0; let mut partial_sum = 0u8; // multiplying an n * k transform by a k * c input matrix: // // n * c dot products per matrix multiplication // // k multiplies per dot product // // Grand total of n * k * c multiplies: let mut m = mstream.take(n * k * c); loop { // actual SIMD code will get 8 or 16 values at a time, but for // testing the algorithm, it's OK to go byte-by-byte let p = m.next(); if p == None { break } let p = p.unwrap(); // eprintln!("Product: {}", p); // add product to sum partial_sum ^= p; dp_counter += 1; // dot-product wrap around if dp_counter == k { output.write_next(partial_sum); partial_sum = 0u8; dp_counter = 0; } } } /// Interleave row-wise data for storage in column-wise matrix /// /// The fast matrix multiply works best when all reads (apart from /// wrap-around reads) are contiguous in memory. That suits the case /// where we're encoding using RS, striping or IDA, since each column /// of the input message corresponds to a contiguous chunk of input. /// /// When decoding, though, the input has row-wise organisation: each /// stripe, share or parity is contiguous. /// /// For this case, we need to interleave k contiguous streams. /// /// Note that there's no need to de-interleave on the output, since we /// can choose between row-wise and col-wise writes. Neither should /// have any impact on the speed of the program, since we never read /// from the output matrix. /// /// Passed in a vector of slices and interleaves them into another /// slice 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 mut iter = s.iter(); slice_iters.push(iter); } for _ in 0 .. cols { for mut slice in &mut slice_iters { *dest.next().unwrap() = *slice.next().unwrap(); } } } /// Simulated SIMD engine type /// /// A trait that can be used to simulate a SIMD engine. Can be /// implemented for native vector type such as `\[u8;8\]` pub trait Simd { /// elemental type, eg u8 type E; /// vector type, eg [u8; 8] type V; /// pairwise multiplication of vector elements fn cross_product(a : Self, b : Self) -> Self; /// consume and sum products from m0, m1 vector buffers fn sum_across_n(m0 : Self, m1 : Self, n : usize, off : usize) -> (Self::E, Self); } /// Newtype for faking Simd architecture /// #[derive(Debug, Clone, Copy)] pub struct SimSimd { vec : [u8; 8], } /// Implement Simd using `\[u8;8\]` for vector storage impl Simd for SimSimd { type V = [u8; 8]; type E = u8; fn cross_product(a : Self, b : Self) -> Self { let mut prod = [0u8; 8]; let f = new_gf8(0x11b,0x1b); for i in 0..8 { prod[i] = f.mul(a.vec[i], b.vec[i]) } Self { vec : prod } } // fn sum_across_n(m0 : Self, m1 : Self, mut n : usize, off : usize) -> (Self::E, Self) { assert!(n <= 8); let mut sum = 0u8; if off + n >= 8 { // straddle, will return m1 // let next_n = n + off - 8; for i in off .. 8 { sum ^= m0.vec[i] } n -= 8 - off; // can become zero for i in 0 .. n { sum ^= m1.vec[i] } // we don't change m1, but some routines might return (sum, m1) } else { // non-straddling, will return m0 for i in off .. off + n { sum ^= m0.vec[i] } return (sum, m0) } } } /// Input matrix type for second simulation #[derive(Debug)] pub struct SimSimdInputMatrix { k : usize, // rows c : usize, // cols array : Vec<u8>, // colwise storage read_pointer : usize, // other simd engines may differ here } impl SimSimdInputMatrix { // rather than copying this code, could just use // SimSimdInputMatrix { k: ... }-style construction (cuts down on // boilerplate here, but more of it in test cases/demo code. fn new(k : usize, c : usize) -> Self { let array = vec![0; k * c]; let read_pointer = 0; Self { k, c, array, read_pointer } } fn fill(&mut self, slice : &[u8]) -> &mut Self { self.array.copy_from_slice(slice); self } } /// Wrap-around Simd reads from input matrix impl Iterator for SimSimdInputMatrix { type Item = SimSimd; #[inline(always)] fn next(&mut self) -> Option<Self::Item> { // let simd_width = size_of::<SimSimd>(); let mut val = [0u8;8]; let mut offset = self.read_pointer; for i in 0..8 { val[i] = self.array[offset]; offset += 1; if offset == self.k * self.c { offset = 0; } } self.read_pointer = offset; Some(SimSimd{vec : val}) } } // same for TransformMatrix, but skip constructor boilerplate. Prefix // all names with SimSimd as before: /// Transform matrix type for second simulation #[derive(Debug, Clone)] pub struct SimSimdTransformMatrix { n : usize, // rows k : usize, // cols array : Vec<u8>, // colwise storage read_pointer : usize, } // put back in "boilerplate" impl SimSimdTransformMatrix { fn new(n : usize, k : usize) -> Self { let array = vec![0; n * k]; let read_pointer = 0; Self { n, k, array, read_pointer } } fn fill(&mut self, slice : &[u8]) -> &Self { self.array.copy_from_slice(slice); self } } // implementation differences: (rowwise) layout and naming of // rows/cols. // // I would have saved some typing if I had just made a "Matrix" and // stored rowwise/colwise parameter) /// Wrap-around Simd reads from transform matrix impl Iterator for SimSimdTransformMatrix { type Item = SimSimd; #[inline(always)] fn next(&mut self) -> Option<Self::Item> { // let simd_width = size_of::<SimSimd>(); let mut val = [0u8;8]; let mut offset = self.read_pointer; for i in 0..8 { val[i] = self.array[offset]; offset += 1; if offset == self.n * self.k { offset = 0; } } self.read_pointer = offset; Some(SimSimd{vec : val}) } } // No need to reimplement OutputMatrix // Won't implement the pseudo "multiply" stream // This routine should be a good basis for a generic routine: // // warm_multiply<S : Simd>(...) // // (at least if I've figured things out correctly) /// Second (simd-wise) matrix multiply simulation pub fn simsimd_warm_multiply(xform : &mut SimSimdTransformMatrix, input : &mut SimSimdInputMatrix, output : &mut OutputMatrix) { // using into_iter() below moves ownership, so pull out any data // we need first let c = input.c; let n = xform.n; let k = xform.k; assert!(k > 0); assert!(n > 0); assert!(c > 0); assert_eq!(input.k, k); assert_eq!(output.c, c); assert_eq!(output.n, n); // searching for prime factors ... needs more work? if k != 1 { assert_ne!(k, gcd(k,c)) } // set up iterators let xiter = xform.into_iter(); let iiter = input.into_iter(); let field = guff::new_gf8(0x11b,0x1b); // algorithm not so trivial any more, but still quite simple let mut dp_counter = 0; let mut sum = 0u8; // we don't have mstream any more since we handle it ourselves // read ahead two products let mut i0 : SimSimd; let mut x0 : SimSimd; // Question: can rustc determine that None is never returned? x0 = xiter.next().unwrap(); i0 = iiter.next().unwrap(); let mut m0 = SimSimd::cross_product(x0,i0); x0 = xiter.next().unwrap(); i0 = iiter.next().unwrap(); let mut m1 = SimSimd::cross_product(x0,i0); let mut offset_mod_simd = 0; let mut total_dps = 0; let target = n * k * c; while total_dps < target { // actual SIMD code: will get 8 values at a time // at top of loop we should always have m0, m1 full // apportion parts of m0,m1 to sum // handle case where k >= simd_width while dp_counter + 8 <= k { let (part, new_m) = SimSimd::sum_across_n(m0,m1,8,offset_mod_simd); sum ^= part; m0 = new_m; x0 = xiter.next().unwrap(); i0 = iiter.next().unwrap(); m1 = SimSimd::cross_product(x0,i0); // new m1 dp_counter += 8; // offset_mod_simd unchanged } // above may have set dp_counter to k already. if dp_counter < k { // If not, ... let want = k - dp_counter; // always strictly positive // eprintln!("Calling sum_across_n with m0 {:?}, m1 {:?}, n {}, offset {}", // m0.vec, m1.vec, want, offset_mod_simd); let (part, new_m) = SimSimd::sum_across_n(m0,m1,want,offset_mod_simd); // eprintln!("got sum {}, new m {:?}", part, new_m.vec); sum ^= part; if offset_mod_simd + want >= 8 { // consumed m0 and maybe some of m1 too m0 = new_m; // nothing left in old m0, so m0 <- m1 x0 = xiter.next().unwrap(); i0 = iiter.next().unwrap(); m1 = SimSimd::cross_product(x0,i0); // new m1 } else { // got what we needed from m0 but it still has some // unused data left in it m0 = new_m; // no new m1 } // offset calculation the same for both arms above offset_mod_simd += want; if offset_mod_simd >= 8 { offset_mod_simd -= 8 } } // sum now has a full dot product eprintln!("Sum: {}", sum); output.write_next(sum); sum = 0u8; dp_counter = 0; total_dps += 1; } } // Epilogue // // Writing the above two simulations has been very useful to me as a // way of: // // * proving the logic correct (gcd property and simd product // apportionment) // * implementing abstract concept of infinite tapes // * figuring out a good division of labour and how to organise that // in terms of rust types // // From here, I should be able to quite easily implement real SIMD // matrix multiplication based on the second simulation/prototype // above. // // Observations // // Traits are very useful, but I think that I tend to overuse them // when thinking about how to design something. In a couple of places, // a more functional style would have been appropriate. // // Newtypes are very useful, and without them, it would be pretty // difficult to make Simd types generic across platforms. // // Iterators are also a very useful feature, but I notice that in my // code above, the compiler can't eliminate the check for a panic when // calling unwrap(). This is despite my iterator code never returning // None. Since I don't need any of the other features of the Iterator // trait, I won't be using it in my "real" code. // // I think that I've learned a lot more about Rust thanks to this // exercise. It's also helped me clarify some points about my original // PS3 implementation and improve the overall design. The new Rust // code looks a lot nicer, I think, and it shouldn't be much less // efficient. // // "Real" SIMD // // I'll continue to use an Elem associated type for the wrapped SIMD // vector types. I'll want to make the multiplication routine generic // across all support SIMD architectures, including the simulated/fake // one above. // // There will be a bit of extra boilerplate to let the compiler know // that Elem is something that has xor defined for it, and that it can // be zeroed. // // I'd like to have non-destructive type conversion, eg between // Poly8x8_t (a wrapped type) and [u8;8]. // // I'm sticking with u8 fields for the moment, but I should be able to // implement larger fields without too much difficulty. An extra bit // of work will be needed to deal with endian conversion there if // input data is coming from an external source. // // Don't use Iterator trait. // // Do implement interleaver for each arch, but have default software // (non-SIMD) implementation. Do this as a separate step when loading // data into matrix. // // #[cfg(test)] mod tests { use super::*; // use std::iter::Iterator; #[test] fn make_transform() { let mut input = TransformMatrix::new(4,3); let vec : Vec<u8> = (1u8..=12).collect(); input.fill(&vec[..]); let elem = input.next(); assert_eq!(elem, Some(1)); // we can't use take() because it moves ownership of input, so // we have to call next() repeatedly. let mut part : Vec<u8> = Vec::with_capacity(24); for _ in 1..=5 { part.push(input.next().unwrap()) } assert_eq!(part, [2,3,4,5,6]); // wrapping around part.truncate(0); for _ in 1..=12 { part.push(input.next().unwrap()) } assert_eq!(part, [7,8,9,10,11,12,1,2,3,4,5,6]); } #[test] fn make_input() { let mut input = InputMatrix::new(4,3); let vec : Vec<u8> = (1u8..=12).collect(); input.fill(&vec[..]); let elem = input.next(); assert_eq!(elem, Some(1)); // we can't use take() because it moves ownership of input, so // we have to call next() repeatedly. let mut part : Vec<u8> = Vec::with_capacity(24); for _ in 1..=5 { part.push(input.next().unwrap()) } assert_eq!(part, [2,3,4,5,6]); // wrapping around part.truncate(0); for _ in 1..=12 { part.push(input.next().unwrap()) } assert_eq!(part, [7,8,9,10,11,12,1,2,3,4,5,6]); } #[test] fn identity_multiply_colwise() { let identity = [1,0,0, 0,1,0, 0,0,1]; let mut transform = TransformMatrix::new(3,3); transform.fill(&identity[..]); // 4 is coprime to 3 let mut input = InputMatrix::new(3,4); let vec : Vec<u8> = (1u8..=12).collect(); input.fill(&vec[..]); let mut output = OutputMatrix::new_colwise(3,4); // works if output is stored in colwise format warm_multiply(&mut transform, &mut input, &mut output); assert_eq!(output.array, vec); } #[test] fn identity_multiply_rowwise() { let identity = [1,0,0, 0,1,0, 0,0,1]; let mut transform = TransformMatrix::new(3,3); transform.fill(&identity[..]); // 4 is coprime to 3 let mut input = InputMatrix::new(3,4); let vec : Vec<u8> = (1u8..=12).collect(); input.fill(&vec[..]); let mut output = OutputMatrix::new_rowwise(3,4); warm_multiply(&mut transform, &mut input, &mut output); // works only if output is stored in colwise format: // assert_eq!(output.array, vec); // need to transpose matrix (actually original list)... do it // by hand (actually, to be correct: interleave original) let mut transposed = vec![0u8; 12]; let transposed = [ vec[0], vec[3], vec [6], vec[9], vec[1], vec[4], vec [7], vec[10], vec[2], vec[5], vec [8], vec[11], ]; assert_eq!(output.array, transposed); } #[test] fn test_interleave() { let a0 = [0, 3, 6, 9]; let a1 = [1, 4, 7, 10]; let a2 = [2, 5, 8, 11]; let vec = vec![&a0[..], &a1[..], &a2[..] ]; let mut dest = vec![0 ; 12]; interleave_streams(&mut dest, &vec); assert_eq!(dest, [0,1,2,3,4,5,6,7,8,9,10,11]); } // Rework above tests for simd version // ----------------------------------- #[test] fn make_simd_transform() { let mut input = SimSimdTransformMatrix::new(4,3); let vec : Vec<u8> = (0u8..12).collect(); input.fill(&vec[..]); let mut elem = input.next(); // returns a full simd vector assert_eq!(elem.unwrap().vec, [0u8,1,2,3,4,5,6,7]); // wrapping around elem = input.next(); // returns a full simd vector assert_eq!(elem.unwrap().vec, [8u8,9,10,11,0,1,2,3]); } #[test] fn make_simd_input() { let mut input = SimSimdInputMatrix::new(4,3); let vec : Vec<u8> = (0u8..12).collect(); input.fill(&vec[..]); let mut elem = input.next(); // returns a full simd vector assert_eq!(elem.unwrap().vec, [0u8,1,2,3,4,5,6,7]); // wrapping around elem = input.next(); // returns a full simd vector assert_eq!(elem.unwrap().vec, [8u8,9,10,11,0,1,2,3]); } #[test] fn simd_identity_multiply_colwise() { let identity = [1,0,0, 0,1,0, 0,0,1]; let mut transform = SimSimdTransformMatrix::new(3,3); transform.fill(&identity[..]); // 4 is coprime to 3 let mut input = SimSimdInputMatrix::new(3,4); let vec : Vec<u8> = (1u8..=12).collect(); input.fill(&vec[..]); let mut output = OutputMatrix::new_colwise(3,4); // works if output is stored in colwise format simsimd_warm_multiply(&mut transform, &mut input, &mut output); assert_eq!(output.array, vec); } #[test] fn simd_identity_multiply_rowwise() { let identity = [1,0,0, 0,1,0, 0,0,1]; let mut transform = SimSimdTransformMatrix::new(3,3); transform.fill(&identity[..]); // 4 is coprime to 3 let mut input = SimSimdInputMatrix::new(3,4); let vec : Vec<u8> = (1u8..=12).collect(); input.fill(&vec[..]); let mut output = OutputMatrix::new_rowwise(3,4); simsimd_warm_multiply(&mut transform, &mut input, &mut output); // works only if output is stored in colwise format: // assert_eq!(output.array, vec); // need to transpose matrix (actually original list)... do it // by hand (actually, to be correct: interleave original) let mut transposed = vec![0u8; 12]; let transposed = [ vec[0], vec[3], vec [6], vec[9], vec[1], vec[4], vec [7], vec[10], vec[2], vec[5], vec [8], vec[11], ]; assert_eq!(output.array, transposed); } // Either of the above routines should have visited each code // pathway apart from those paths relating to k >= 8. This is due // to the coprime property (all possible straddling scenarios are // tested). // To test the paths relating to k >= 8, just use bigger identity // matrices. #[test] fn simd_identity_k8_multiply_colwise() { let identity = [ 1,0,0,0 ,0,0,0,0, 0,1,0,0 ,0,0,0,0, 0,0,1,0 ,0,0,0,0, 0,0,0,1 ,0,0,0,0, 0,0,0,0 ,1,0,0,0, 0,0,0,0 ,0,1,0,0, 0,0,0,0 ,0,0,1,0, 0,0,0,0 ,0,0,0,1, ]; let mut transform = SimSimdTransformMatrix::new(8,8); transform.fill(&identity[..]); // 7 is coprime to 8 let mut input = SimSimdInputMatrix::new(8,7); let vec : Vec<u8> = (1u8..=56).collect(); input.fill(&vec[..]); let mut output = OutputMatrix::new_colwise(8,7); // works if output is stored in colwise format simsimd_warm_multiply(&mut transform, &mut input, &mut output); assert_eq!(output.array, vec); } #[test] fn simd_identity_k9_multiply_colwise() { let identity = [ 1,0,0, 0,0,0, 0,0,0, 0,1,0, 0,0,0, 0,0,0, 0,0,1, 0,0,0, 0,0,0, 0,0,0, 1,0,0, 0,0,0, 0,0,0, 0,1,0, 0,0,0, 0,0,0, 0,0,1, 0,0,0, 0,0,0, 0,0,0, 1,0,0, 0,0,0, 0,0,0, 0,1,0, 0,0,0, 0,0,0, 0,0,1, ]; let mut transform = SimSimdTransformMatrix::new(9,9); transform.fill(&identity[..]); // 17 is coprime to 9 let mut input = SimSimdInputMatrix::new(9,17); let vec : Vec<u8> = (1u8..=9 * 17).collect(); input.fill(&vec[..]); let mut output = OutputMatrix::new_colwise(9,17); // works if output is stored in colwise format simsimd_warm_multiply(&mut transform, &mut input, &mut output); assert_eq!(output.array, vec); } // Also test "degenerate" cases where matrices are less than simd // size. The real SIMD code might not be able to handle this // properly. At least not without specially-written wrap-around // matrix implementations. #[test] fn simd_identity_k1_multiply_colwise() { let identity = [ 1, ]; let mut transform = SimSimdTransformMatrix::new(1,1); transform.fill(&identity[..]); // 2 is coprime to 1 let mut input = SimSimdInputMatrix::new(1,2); let vec : Vec<u8> = (1u8..=2).collect(); input.fill(&vec[..]); let mut output = OutputMatrix::new_colwise(1,2); // works if output is stored in colwise format simsimd_warm_multiply(&mut transform, &mut input, &mut output); assert_eq!(output.array, vec); } #[test] fn simd_identity_k2_multiply_colwise() { let identity = [ 1,0, 0,1, ]; let mut transform = SimSimdTransformMatrix::new(2,2); transform.fill(&identity[..]); // 7 is coprime to 2 let mut input = SimSimdInputMatrix::new(2,7); let vec : Vec<u8> = (1u8..=14).collect(); input.fill(&vec[..]); let mut output = OutputMatrix::new_colwise(2,7); // works if output is stored in colwise format simsimd_warm_multiply(&mut transform, &mut input, &mut output); assert_eq!(output.array, vec); } }