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LinearAlgebraTests.scala
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LinearAlgebraTests.scala
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package lms.verify
class LinearAlgebraTests extends TestSuite {
val under = "linp"
trait Matrices extends Dsl with DataOps {
val N = 100
// like for the low-level versions, verifying that the calculated index
// is within the valid range only works when it's extracted out...
val index_fun = toplevel("index",
{ (rows: Rep[Int], cols: Rep[Int], r: Rep[Int], c: Rep[Int]) =>
requires(0 < rows && rows < N && 0 < cols && cols < N && 0 <= r && 0 <= c && r < rows && c < cols)
ensures{result: Rep[Int] => 0 <= result && result < rows*cols}
r*cols+c
})
class Matrix[T:Iso](val a: Pointer[T], val rows: Rep[Int], val cols: Rep[Int]) {
def size = rows*cols
def index(r: Rep[Int], c: Rep[Int]) = index_fun(rows, cols, r, c)
def apply(r: Rep[Int], c: Rep[Int]) = a(index(r,c))
def update(p: (Rep[Int],Rep[Int]), v: T): Rep[Unit] = {
val r = p._1; val c = p._2
a(index(r, c)) = v
}
def valid = size>0 && a.valid(0 until size)
def reflectMutableInput = a.reflectMutableInput(0 until size)
def setEach(f: (Rep[Int], Rep[Int]) => T) = {
this.reflectMutableInput
for (r <- 0 until this.rows) {
for (c <- 0 until this.cols) {
this((r,c)) = f(r,c)
}
}
}
def setFrom[A:Iso](f: List[A] => T, ms: List[Matrix[A]])(implicit eq: Eq[T]) = {
def r(i: Rep[Int]): T = f(ms.map{m => m.a(i)})
def p(n: Rep[Int]): Rep[Boolean] = forall{j: Rep[Int] => (0 <= j && j < n) ==> (
this.a(j) deep_equal r(j)
)}
ms.foreach{m => requires(this.rows == m.rows && this.cols == m.cols)}
// TODO: higher-level separation?
requires(and_list(ms.map{m => forall{i: Rep[Int] => forall{j: Rep[Int] =>
((0 <= i && i < this.size) && (0 <= j && j < m.size)) ==>
separated(this.a, i, m.a, j)
}}}))
// TODO: using 'ensures' limits how setFrom can be used...
ensures{result: Rep[Unit] => p(this.size)}
this.reflectMutableInput
// for the From2 example, it helps to reinforce separation...
ms.foreach{m => _assert(separated(this.a, 0, m.a, 0))}
for (i <- 0 until this.size) {
loop_invariant(p(i))
this.a(i) = r(i)
// ditto for From2...
ms.foreach{m => _assert(separated(this.a, i, m.a, i))}
}
}
def setFrom1[A:Iso](f: A => T, m: Matrix[A])(implicit eq: Eq[T]) = {
setFrom[A]({ms => f(ms(0))}, scala.collection.immutable.List(m))
}
def setFrom2[A:Iso](f: (A,A) => T, m1: Matrix[A], m2: Matrix[A])(implicit eq: Eq[T]) = {
setFrom[A]({ms => f(ms(0), ms(1))}, scala.collection.immutable.List(m1, m2))
}
}
implicit def matrixIso[T:Iso](implicit ev: Inv[Matrix[T]]) = isodata[Matrix[T],(Pointer[T],Rep[Int],Rep[Int])](
"matrix_" + implicitly[Iso[T]].id,
{x: Matrix[T] => (x.a, x.rows, x.cols)},
{x: (Pointer[T],Rep[Int],Rep[Int]) => new Matrix(x._1, x._2, x._3)}
)
implicit def matrixInv[T:Inv] = invariant[Matrix[T]] { x =>
x.rows < N && x.cols < N && // needed for overflow in index calculation
0 < x.rows && 0 < x.cols && x.valid && (
(0 until x.rows).forall{ r => (0 until x.cols).forall{ c => x(r,c).check }})
}
implicit def matrixEq[T:Eq:Iso] = equality[Matrix[T]] { (x, y) =>
x.rows == y.rows && x.cols == y.cols && (
(0 until x.rows).forall{ r => (0 until x.cols).forall{ c =>
x(r,c) deep_equal y(r,c) }})
}
}
trait BoolAlgebra extends Dsl {
type X = Rep[Boolean]
def zero: Rep[Boolean] = unit(false)
def infix_+(x1: X, x2: X): X = x1 || x2
def infix_*(x1: X, x2: X): X = x1 && x2
}
test("1") {
trait Linp1 extends Matrices with BoolAlgebra {
toplevel("mult", { (a: Matrix[X], b: Matrix[X], o: Matrix[X]) =>
requires(a.cols == b.rows && a.rows == o.rows && b.cols == o.cols)
o.reflectMutableInput
for (r <- 0 until a.rows) {
for (c <- 0 until b.cols) {
o((r,c)) = zero
for (i <- 0 until a.cols) {
o((r,c)) = o(r,c) + a(r,i) * b(i,c)
}
}
}
})
}
check("1", (new Linp1 with Impl).code)
}
test("2") {
trait Linp2 extends Matrices with BoolAlgebra {
val add = toplevel("add", { (a: Matrix[X], b: Matrix[X], o: Matrix[X]) =>
requires(a.rows == b.rows && a.rows == o.rows && a.cols == b.cols && a.cols == o.cols)
o.setEach{ (r: Rep[Int], c: Rep[Int]) =>
a(r,c) + b(r,c)
}
})
val scalar_mult = toplevel("scalar_mult", { (a: X, b: Matrix[X], o: Matrix[X]) =>
requires(b.rows == o.rows && b.cols == o.cols)
o.setEach{ (r: Rep[Int], c: Rep[Int]) =>
a*b(r,c)
}
})
}
check("2", (new Linp2 with Impl).code)
}
test("3") {
trait Linp3 extends Matrices with BoolAlgebra {
val add = toplevel("add", { (a: Matrix[X], b: Matrix[X], o: Matrix[X]) =>
o.setFrom2({ (ai: X, bi: X) => ai + bi }, a, b)
})
val scalar_mult = toplevel("scalar_mult", { (a: X, b: Matrix[X], o: Matrix[X]) =>
o.setFrom1({ (bi: X) => a*bi }, b)
// now easy to prove,
// thanks to all the annotations added by setFrom
ensures{result: Rep[Unit] => (a == zero) ==>
(0 until o.rows).forall{r =>
(0 until o.cols).forall{c =>
o(r,c) == zero }}}
})
}
check("3", (new Linp3 with Impl).code)
}
}
class LowLinearAlgebraTests extends TestSuite {
val under = "lina"
test("1") {
trait Lina1 extends Dsl {
val N = 100
val index = toplevel("index",
{ (r: Rep[Int], c: Rep[Int], ra: Rep[Int], ca: Rep[Int]) => r*ca+c },
{ (r: Rep[Int], c: Rep[Int], ra: Rep[Int], ca: Rep[Int]) =>
ra > 0 && ca > 0 && 0 <= r && r < ra && 0 <= c && c < ca &&
ra < N && ca < N },
{ (r: Rep[Int], c: Rep[Int], ra: Rep[Int], ca: Rep[Int]) => result: Rep[Int] =>
0 <= result && result < ra*ca })
val mm_mult = toplevel("mm_mult",
{ (ma: Rep[Array[Int]], ra: Rep[Int], ca: Rep[Int],
mb: Rep[Array[Int]], rb: Rep[Int], cb: Rep[Int],
mc: Rep[Array[Int]], rc: Rep[Int], cc: Rep[Int]) =>
reflectMutableInput(mc)
loop(
{r: Rep[Int] => unit(0) <= r && r <= ra},
{r: Rep[Int] => List(r, mc within (0 until rc*cc))},
{r: Rep[Int] => ra-r}) {
for (r <- 0 until ra) {
loop(
{c: Rep[Int] => unit(0) <= c && c <= cb},
{c: Rep[Int] => List(c, mc within (0 until rc*cc))},
{c: Rep[Int] => cb-c}) {
for (c <- 0 until cb) {
mc(index(r, c, rc, cc)) = 0
loop(
{i: Rep[Int] => unit(0) <= i && i <= ca},
{i: Rep[Int] => List(i, mc within (0 until rc*cc))},
{i: Rep[Int] => ca-i}) {
for (i <- 0 until ca) {
mc(index(r, c, rc, cc)) = mc(index(r, c, rc, cc)) + ma(index(r, i, ra, ca)) * mb(index(i, c, rb, cb))
}
}
}
}
}
}
},
{ (ma: Rep[Array[Int]], ra: Rep[Int], ca: Rep[Int],
mb: Rep[Array[Int]], rb: Rep[Int], cb: Rep[Int],
mc: Rep[Array[Int]], rc: Rep[Int], cc: Rep[Int]) =>
ra > 0 && ca > 0 && rb > 0 && cc > 0 &&
ca == rb && ra == rc && cc == cb &&
ra < N && ca < N && rb < N && cb < N && rc < N && cc < N &&
valid(ma, 0 until ra*ca) &&
valid(mb, 0 until rb*cb) &&
valid(mc, 0 until rc*cc)
},
{ (ma: Rep[Array[Int]], ra: Rep[Int], ca: Rep[Int],
mb: Rep[Array[Int]], rb: Rep[Int], cb: Rep[Int],
mc: Rep[Array[Int]], rc: Rep[Int], cc: Rep[Int]) =>
result: Rep[Unit] =>
unit(true)
})
}
check("1", (new Lina1 with Impl).code)
}
test("1b") {
trait Lina1b extends Dsl {
val N = 100
val index = toplevel("index",
{ (r: Rep[Int], c: Rep[Int], ra: Rep[Int], ca: Rep[Int]) => r*ca+c },
{ (r: Rep[Int], c: Rep[Int], ra: Rep[Int], ca: Rep[Int]) =>
ra > 0 && ca > 0 && 0 <= r && r < ra && 0 <= c && c < ca &&
ra < N && ca < N },
{ (r: Rep[Int], c: Rep[Int], ra: Rep[Int], ca: Rep[Int]) => result: Rep[Int] =>
0 <= result && result < ra*ca })
case class Matrix(m: Rep[Array[Int]], r: Rep[Int], c: Rep[Int]) extends {
def req: Rep[Boolean] = r > 0 && c > 0 && r < N && c < N && valid(m, 0 until r*c)
class Aux(i: Rep[Int]) {
def apply(j: Rep[Int]) = m(index(i, j, r, c))
def update(j: Rep[Int], v: Rep[Int]) = m(index(i, j, r, c)) = v
}
def apply(i: Rep[Int]) = new Aux(i)
}
def toplevel_matrix(name: String, f: (Matrix, Matrix, Matrix) => Rep[Unit], pre: (Matrix, Matrix, Matrix) => Rep[Boolean], post: (Matrix, Matrix, Matrix) => Rep[Unit] => Rep[Boolean]): (Matrix, Matrix, Matrix) => Rep[Unit] = {
val g = toplevel(name,
(m1: Rep[Array[Int]], r1: Rep[Int], c1: Rep[Int], m2: Rep[Array[Int]], r2: Rep[Int], c2: Rep[Int], m3: Rep[Array[Int]], r3: Rep[Int], c3: Rep[Int]) => f(Matrix(m1, r1, c1), Matrix(m2, r2, c2), Matrix(m3, r3, c3)),
{(m1: Rep[Array[Int]], r1: Rep[Int], c1: Rep[Int], m2: Rep[Array[Int]], r2: Rep[Int], c2: Rep[Int], m3: Rep[Array[Int]], r3: Rep[Int], c3: Rep[Int]) =>
val o1 = Matrix(m1, r1, c1)
val o2 = Matrix(m2, r2, c2)
val o3 = Matrix(m3, r3, c3)
o1.req && o2.req && o3.req && pre(o1, o2, o3)},
(m1: Rep[Array[Int]], r1: Rep[Int], c1: Rep[Int], m2: Rep[Array[Int]], r2: Rep[Int], c2: Rep[Int], m3: Rep[Array[Int]], r3: Rep[Int], c3: Rep[Int]) => post(Matrix(m1, r1, c1), Matrix(m2, r2, c2), Matrix(m3, r3, c3)))
(a: Matrix, b: Matrix, o: Matrix) => g(a.m, a.r, a.c, b.m, b.r, b.c, o.m, o.r, o.c)
}
val mm_mult = toplevel_matrix("mm_mult",
{ (a: Matrix, b: Matrix, o: Matrix) =>
reflectMutableInput(o.m, 0 until o.r*o.c)
for (r <- 0 until a.r) {
for (c <- 0 until b.c) {
o(r)(c) = 0
for (i <- 0 until a.c) {
o(r)(c) = o(r)(c) + a(r)(i) * b(i)(c)
}
}
}
},
{ (a: Matrix, b: Matrix, o: Matrix) =>
a.c == b.r && a.r == o.r && o.c == b.c
},
{ (a: Matrix, b: Matrix, o: Matrix) =>
result: Rep[Unit] =>
unit(true)
})
}
check("1b", (new Lina1b with Impl).code)
}
test("2") {
trait Lina2 extends Dsl {
def index_where(suffix: String, predicate: Rep[Int] => Rep[Boolean]) = {
toplevel("index_where_" + suffix,
{ (v: Rep[Array[Int]], n: Rep[Int], o: Rep[Array[Int]]) =>
reflectMutableInput(o)
assigns(o, 0 until n)
var r = 0
loop({i: Rep[Int] => unit(0) <= i && i <= n &&
unit(0) <= r && r <= i &&
forall{j: Rep[Int] => (0 <= j && j < r) ==> (0 <= o(j) && o(j) < i)} &&
forall{j: Rep[Int] => (0 < j && j < r) ==> (o(j-1) < o(j))}},
{i: Rep[Int] => List(i, r, o within (0 until n))},
{i: Rep[Int] => n-i}) {
for (i <- 0 until n) {
if (predicate(v(i))) {
o(r) = i
r += 1
}
}
}
r: Rep[Int]
},
{ (v: Rep[Array[Int]], n: Rep[Int], o: Rep[Array[Int]]) => n > 0 && valid(v, 0 until n) && valid(o, 0 until n)},
{ (v: Rep[Array[Int]], n: Rep[Int], o: Rep[Array[Int]]) => (result: Rep[Int]) =>
0 <= result && result <= n &&
forall{i: Rep[Int] => (0 <= i && i < result) ==> (0 <= o(i) && o(i) < n)} &&
forall{i: Rep[Int] => (0 < i && i < result) ==> (o(i-1) < o(i))}
})
}
def even(n: Rep[Int]) = n % 2 == 0
val index_where_even = index_where("even", even)
}
check("2", (new Lina2 with Impl).code)
}
}