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// Copyright 2013 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package types2_test
import (
"bytes"
"cmd/compile/internal/syntax"
"flag"
"fmt"
"io/ioutil"
"testing"
. "cmd/compile/internal/types2"
)
var (
H = flag.Int("H", 5, "Hilbert matrix size")
out = flag.String("out", "", "write generated program to out")
)
func TestHilbert(t *testing.T) {
// generate source
src := program(*H, *out)
if *out != "" {
ioutil.WriteFile(*out, src, 0666)
return
}
// parse source
f, err := syntax.Parse(syntax.NewFileBase("hilbert.go"), bytes.NewReader(src), nil, nil, 0)
if err != nil {
t.Fatal(err)
}
// type-check file
DefPredeclaredTestFuncs() // define assert built-in
conf := Config{Importer: defaultImporter()}
_, err = conf.Check(f.PkgName.Value, []*syntax.File{f}, nil)
if err != nil {
t.Fatal(err)
}
}
func program(n int, out string) []byte {
var g gen
g.p(`// Code generated by: go test -run=Hilbert -H=%d -out=%q. DO NOT EDIT.
// +`+`build ignore
// This program tests arbitrary precision constant arithmetic
// by generating the constant elements of a Hilbert matrix H,
// its inverse I, and the product P = H*I. The product should
// be the identity matrix.
package main
func main() {
if !ok {
printProduct()
return
}
println("PASS")
}
`, n, out)
g.hilbert(n)
g.inverse(n)
g.product(n)
g.verify(n)
g.printProduct(n)
g.binomials(2*n - 1)
g.factorials(2*n - 1)
return g.Bytes()
}
type gen struct {
bytes.Buffer
}
func (g *gen) p(format string, args ...interface{}) {
fmt.Fprintf(&g.Buffer, format, args...)
}
func (g *gen) hilbert(n int) {
g.p(`// Hilbert matrix, n = %d
const (
`, n)
for i := 0; i < n; i++ {
g.p("\t")
for j := 0; j < n; j++ {
if j > 0 {
g.p(", ")
}
g.p("h%d_%d", i, j)
}
if i == 0 {
g.p(" = ")
for j := 0; j < n; j++ {
if j > 0 {
g.p(", ")
}
g.p("1.0/(iota + %d)", j+1)
}
}
g.p("\n")
}
g.p(")\n\n")
}
func (g *gen) inverse(n int) {
g.p(`// Inverse Hilbert matrix
const (
`)
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
s := "+"
if (i+j)&1 != 0 {
s = "-"
}
g.p("\ti%d_%d = %s%d * b%d_%d * b%d_%d * b%d_%d * b%d_%d\n",
i, j, s, i+j+1, n+i, n-j-1, n+j, n-i-1, i+j, i, i+j, i)
}
g.p("\n")
}
g.p(")\n\n")
}
func (g *gen) product(n int) {
g.p(`// Product matrix
const (
`)
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
g.p("\tp%d_%d = ", i, j)
for k := 0; k < n; k++ {
if k > 0 {
g.p(" + ")
}
g.p("h%d_%d*i%d_%d", i, k, k, j)
}
g.p("\n")
}
g.p("\n")
}
g.p(")\n\n")
}
func (g *gen) verify(n int) {
g.p(`// Verify that product is the identity matrix
const ok =
`)
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
if j == 0 {
g.p("\t")
} else {
g.p(" && ")
}
v := 0
if i == j {
v = 1
}
g.p("p%d_%d == %d", i, j, v)
}
g.p(" &&\n")
}
g.p("\ttrue\n\n")
// verify ok at type-check time
if *out == "" {
g.p("const _ = assert(ok)\n\n")
}
}
func (g *gen) printProduct(n int) {
g.p("func printProduct() {\n")
for i := 0; i < n; i++ {
g.p("\tprintln(")
for j := 0; j < n; j++ {
if j > 0 {
g.p(", ")
}
g.p("p%d_%d", i, j)
}
g.p(")\n")
}
g.p("}\n\n")
}
func (g *gen) binomials(n int) {
g.p(`// Binomials
const (
`)
for j := 0; j <= n; j++ {
if j > 0 {
g.p("\n")
}
for k := 0; k <= j; k++ {
g.p("\tb%d_%d = f%d / (f%d*f%d)\n", j, k, j, k, j-k)
}
}
g.p(")\n\n")
}
func (g *gen) factorials(n int) {
g.p(`// Factorials
const (
f0 = 1
f1 = 1
`)
for i := 2; i <= n; i++ {
g.p("\tf%d = f%d * %d\n", i, i-1, i)
}
g.p(")\n\n")
}
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