matrixmultiply 0.3.10

General matrix multiplication for f32 and f64 matrices. Operates on matrices with general layout (they can use arbitrary row and column stride). Detects and uses AVX or SSE2 on x86 platforms transparently for higher performance. Uses a microkernel strategy, so that the implementation is easy to parallelize and optimize. Supports multithreading.
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use matrixmultiply::{sgemm, dgemm};
#[cfg(feature="cgemm")]
use matrixmultiply::{cgemm, zgemm, CGemmOption};

// Common code for tests - generic treatment of f32, f64, c32, c64 and Gemm

pub trait Float : Copy + std::fmt::Debug + PartialEq {
    fn zero() -> Self;
    fn one() -> Self;
    // construct as number x
    fn from(x: i64) -> Self;
    // construct as number x + yi, but ignore y if not complex
    fn from2(x: i64, _y: i64) -> Self { Self::from(x) }
    fn nan() -> Self;
    fn real(self) -> Self { self }
    fn imag(self) -> Self;
    fn is_nan(self) -> bool;
    fn is_complex() -> bool { false }
    fn diff(self, rhs: Self) -> Self;
    // absolute value as f64
    fn abs_f64(self) -> f64;
    fn relative_error_scale() -> f64;
    fn mul_add_assign(&mut self, x: Self, y: Self);
}

impl Float for f32 {
    fn zero() -> Self { 0. }
    fn one() -> Self { 1. }
    fn from(x: i64) -> Self { x as Self }
    fn nan() -> Self { 0./0. }
    fn imag(self) -> Self { 0. }
    fn is_nan(self) -> bool { self.is_nan() }
    fn diff(self, rhs: Self) -> Self { self - rhs }
    fn abs_f64(self) -> f64 { self.abs() as f64 }
    fn relative_error_scale() -> f64 { 1e-6 }
    fn mul_add_assign(&mut self, x: Self, y: Self) {
        *self += x * y;
    }
}

impl Float for f64 {
    fn zero() -> Self { 0. }
    fn one() -> Self { 1. }
    fn from(x: i64) -> Self { x as Self }
    fn nan() -> Self { 0./0. }
    fn imag(self) -> Self { 0. }
    fn is_nan(self) -> bool { self.is_nan() }
    fn diff(self, rhs: Self) -> Self { self - rhs }
    fn abs_f64(self) -> f64 { self.abs() }
    fn relative_error_scale() -> f64 { 1e-12 }
    fn mul_add_assign(&mut self, x: Self, y: Self) {
        *self += x * y;
    }
}

#[allow(non_camel_case_types)]
#[cfg(feature="cgemm")]
pub type c32 = [f32; 2];
#[allow(non_camel_case_types)]
#[cfg(feature="cgemm")]
pub type c64 = [f64; 2];

#[cfg(feature="cgemm")]
impl Float for c32 {
    fn zero() -> Self { [0., 0.] }
    fn one() -> Self { [1., 0.] }
    fn from(x: i64) -> Self { [x as _, 0.] }
    fn from2(x: i64, y: i64) -> Self { [x as _, y as _] }
    fn nan() -> Self { [0./0., 0./0.] }
    fn real(self) -> Self { [self[0], 0.] }
    fn imag(self) -> Self { [self[1], 0.] }
    fn is_nan(self) -> bool { self[0].is_nan() || self[1].is_nan() }
    fn is_complex() -> bool { true }
    fn diff(self, rhs: Self) -> Self {
        [self[0] - rhs[0], self[1] - rhs[1]]
    }
    fn abs_f64(self) -> f64 {
        (self[0].powi(2) + self[1].powi(2)).sqrt() as f64
    }
    fn relative_error_scale() -> f64 { 1e-6 }
    fn mul_add_assign(&mut self, x: Self, y: Self) {
        let [re, im] = c32_mul(x, y);
        self[0] += re;
        self[1] += im;
    }
}

#[cfg(feature="cgemm")]
impl Float for c64 {
    fn zero() -> Self { [0., 0.] }
    fn one() -> Self { [1., 0.] }
    fn from(x: i64) -> Self { [x as _, 0.] }
    fn from2(x: i64, y: i64) -> Self { [x as _, y as _] }
    fn nan() -> Self { [0./0., 0./0.] }
    fn real(self) -> Self { [self[0], 0.] }
    fn imag(self) -> Self { [self[1], 0.] }
    fn is_nan(self) -> bool { self[0].is_nan() || self[1].is_nan() }
    fn is_complex() -> bool { true }
    fn diff(self, rhs: Self) -> Self {
        [self[0] - rhs[0], self[1] - rhs[1]]
    }
    fn abs_f64(self) -> f64 {
        (self[0].powi(2) + self[1].powi(2)).sqrt()
    }
    fn relative_error_scale() -> f64 { 1e-12 }
    fn mul_add_assign(&mut self, x: Self, y: Self) {
        let [re, im] = c64_mul(x, y);
        self[0] += re;
        self[1] += im;
    }
}


#[cfg(feature = "cgemm")]
#[inline(always)]
pub(crate) fn c32_mul(x: c32, y: c32) -> c32 {
    let [a, b] = x;
    let [c, d] = y;
    [a * c - b * d, b * c + a * d]
}

#[cfg(feature = "cgemm")]
#[inline(always)]
pub(crate) fn c64_mul(x: c64, y: c64) -> c64 {
    let [a, b] = x;
    let [c, d] = y;
    [a * c - b * d, b * c + a * d]
}


pub trait Gemm : Sized {
    unsafe fn gemm(
        m: usize, k: usize, n: usize,
        alpha: Self,
        a: *const Self, rsa: isize, csa: isize,
        b: *const Self, rsb: isize, csb: isize,
        beta: Self,
        c: *mut Self, rsc: isize, csc: isize);
}

impl Gemm for f32 {
    unsafe fn gemm(
        m: usize, k: usize, n: usize,
        alpha: Self,
        a: *const Self, rsa: isize, csa: isize,
        b: *const Self, rsb: isize, csb: isize,
        beta: Self,
        c: *mut Self, rsc: isize, csc: isize) {
        sgemm(
            m, k, n,
            alpha,
            a, rsa, csa,
            b, rsb, csb,
            beta,
            c, rsc, csc)
    }
}

impl Gemm for f64 {
    unsafe fn gemm(
        m: usize, k: usize, n: usize,
        alpha: Self,
        a: *const Self, rsa: isize, csa: isize,
        b: *const Self, rsb: isize, csb: isize,
        beta: Self,
        c: *mut Self, rsc: isize, csc: isize) {
        dgemm(
            m, k, n,
            alpha,
            a, rsa, csa,
            b, rsb, csb,
            beta,
            c, rsc, csc)
    }
}

#[cfg(feature="cgemm")]
impl Gemm for c32 {
    unsafe fn gemm(
        m: usize, k: usize, n: usize,
        alpha: Self,
        a: *const Self, rsa: isize, csa: isize,
        b: *const Self, rsb: isize, csb: isize,
        beta: Self,
        c: *mut Self, rsc: isize, csc: isize) {
        cgemm(
            CGemmOption::Standard,
            CGemmOption::Standard,
            m, k, n,
            alpha,
            a, rsa, csa,
            b, rsb, csb,
            beta,
            c, rsc, csc)
    }
}

#[cfg(feature="cgemm")]
impl Gemm for c64 {
    unsafe fn gemm(
        m: usize, k: usize, n: usize,
        alpha: Self,
        a: *const Self, rsa: isize, csa: isize,
        b: *const Self, rsb: isize, csb: isize,
        beta: Self,
        c: *mut Self, rsc: isize, csc: isize) {
        zgemm(
            CGemmOption::Standard,
            CGemmOption::Standard,
            m, k, n,
            alpha,
            a, rsa, csa,
            b, rsb, csb,
            beta,
            c, rsc, csc)
    }
}