/usr/share/gocode/src/github.com/remyoudompheng/bigfft/fft_test.go is in golang-github-remyoudompheng-bigfft-dev 0.0~git20130913.0.a8e77dd-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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import (
"fmt"
. "math/big"
"math/rand"
"testing"
)
func cmpnat(t *testing.T, x, y nat) int {
var a, b Int
a.SetBits(x)
b.SetBits(y)
c := a.Cmp(&b)
if c != 0 {
t.Logf("a.len=%d, b.len=%d", a.BitLen(), b.BitLen())
for i := 0; i < len(x) || i < len(y); i++ {
var u, v Word
if i < len(x) {
u = x[i]
}
if i < len(y) {
v = y[i]
}
if diff := u ^ v; diff != 0 {
t.Logf("diff at word %d: %x", i, diff)
}
}
}
return c
}
func TestRoundTripIntPoly(t *testing.T) {
N := 4
step := 500
if testing.Short() {
N = 2
}
// Sizes 12800 and 34300 may cause problems.
for size := 300; size < 50000; size += step {
n := make(nat, size)
for i := 0; i < N; i++ {
for p := range n {
n[p] = Word(rand.Int63())
}
k, m := fftSize(n, nil)
pol := polyFromNat(n, k, m)
n2 := pol.Int()
if cmpnat(t, n, n2) != 0 {
t.Errorf("different n and n2, size=%d, iter=%d", size, i)
}
}
}
}
func TestFourierSizes(t *testing.T) {
sizes := []int{
2e3, 3e3, 5e3, 7e3, 10e3, 14e3,
2e4, 3e4, 5e4, 7e4, 10e4, 14e4,
2e5, 3e5, 5e5, 7e5, 10e5, 14e5,
2e6, 3e6, 5e6, 7e6, 10e6, 14e6,
2e7, 3e7, 5e7, 7e7, 10e7, 14e7,
2e8, 3e8, 5e8, 7e8, 10e8, 14e8,
}
for _, s := range sizes {
k, m := fftSize(make(nat, s/_W), make(nat, s/_W))
v := valueSize(k, m, 2)
t.Logf("bits=%d => FFT size %d, chunk size = %d, value size = %d",
s, 1<<k, m, v)
needed := 2*m*_W + int(k)
got := v * _W
t.Logf("inefficiency: value/chunk_product=%.2f, fftsize/inputsize=%.2f",
float64(got)/float64(needed), float64(v<<k)/float64(2*s/_W))
if v > 3*m {
t.Errorf("FFT word size %d >> input word size %d", v, m)
}
}
}
func testFourier(t *testing.T, N int, k uint) {
t.Logf("testFourier(t, %d, %d)", N, k)
ωshift := (2 * N * _W) >> k
src := make([]fermat, 1<<k)
dst1 := make([]fermat, 1<<k)
dst2 := make([]fermat, 1<<k)
// random inputs.
for i := range src {
src[i] = make(fermat, N+1)
dst1[i] = make(fermat, N+1)
dst2[i] = make(fermat, N+1)
for p := 0; p < N; p++ {
src[i][p] = Word(rand.Int63())
}
}
// naive transform
tmp := make(fermat, N+1)
for i := range src {
for j := range dst1 {
tmp.Shift(src[i], i*j*ωshift)
dst1[j].Add(dst1[j], tmp)
}
}
// fast transform
fourier(dst2, src, false, N, k)
for i := range src {
if cmpnat(t, nat(dst1[i]), nat(dst2[i])) != 0 {
var x, y Int
x.SetBits(dst1[i])
y.SetBits(dst2[i])
t.Errorf("difference in dst[%d]: %x %x", i, &x, &y)
}
}
}
func TestFourier(t *testing.T) {
// 1-word transforms.
testFourier(t, 1, 2)
testFourier(t, 1, 3)
testFourier(t, 1, 4)
// 2-word transforms
testFourier(t, 2, 2)
testFourier(t, 2, 3)
testFourier(t, 2, 4)
testFourier(t, 4, 4)
testFourier(t, 4, 5)
testFourier(t, 4, 6)
}
// Tests Fourier transform and its reciprocal.
func TestRoundTripPolyValues(t *testing.T) {
Size := 100000
if testing.Short() {
Size = 50
}
// Build a polynomial from an integer.
n := make(nat, Size)
for p := range n {
n[p] = Word(rand.Int63())
}
k, m := fftSize(n, nil)
pol := polyFromNat(n, k, m)
// Transform it.
f := valueSize(k, m, 1)
values := pol.Transform(f)
// Inverse transform.
pol2 := values.InvTransform()
pol2.m = m
t.Logf("k=%d, m=%d", k, m)
// Evaluate and compare.
n2 := pol2.Int()
if cmpnat(t, n, n2) != 0 {
t.Errorf("different n and n2")
}
}
var rnd = rand.New(rand.NewSource(0x43de683f473542af))
func rndNat(n int) nat {
x := make(nat, n)
for i := 0; i < n; i++ {
x[i] = Word(rnd.Int63()<<1 + rnd.Int63n(2))
}
return x
}
func TestMul(t *testing.T) {
sizes := []int{1e3, 5e3, 15e3, 25e3, 70e3, 200e3, 500e3}
iters := 10
if testing.Short() {
iters = 1
}
var x, y Int
for i := 0; i < iters; i++ {
for _, size1 := range sizes {
for _, size2 := range sizes {
x.SetBits(rndNat(size1 / _W))
y.SetBits(rndNat(size2 / _W))
z := new(Int).Mul(&x, &y)
z2 := Mul(&x, &y)
if z.Cmp(z2) != 0 {
t.Errorf("z (%d bits) != z2 (%d bits)", z.BitLen(), z2.BitLen())
logbig(t, new(Int).Xor(z, z2))
}
}
}
}
}
func logbig(t *testing.T, n *Int) {
s := fmt.Sprintf("%x", n)
for len(s) > 64 {
t.Log(s[:64])
s = s[64:]
}
t.Log(s)
}
func benchmarkMulBig(b *testing.B, sizex, sizey int) {
mulx := rndNat(sizex / _W)
muly := rndNat(sizey / _W)
b.ResetTimer()
var x, y, z Int
x.SetBits(mulx)
y.SetBits(muly)
for i := 0; i < b.N; i++ {
z.Mul(&x, &y)
}
}
func benchmarkMulFFT(b *testing.B, sizex, sizey int) {
mulx := rndNat(sizex / _W)
muly := rndNat(sizey / _W)
b.ResetTimer()
var x, y Int
x.SetBits(mulx)
y.SetBits(muly)
for i := 0; i < b.N; i++ {
_ = mulFFT(&x, &y)
}
}
func BenchmarkMulBig_1kb(b *testing.B) { benchmarkMulBig(b, 1e3, 1e3) }
func BenchmarkMulBig_10kb(b *testing.B) { benchmarkMulBig(b, 1e4, 1e4) }
func BenchmarkMulBig_50kb(b *testing.B) { benchmarkMulBig(b, 5e4, 5e4) }
func BenchmarkMulBig_100kb(b *testing.B) { benchmarkMulBig(b, 1e5, 1e5) }
func BenchmarkMulBig_1Mb(b *testing.B) { benchmarkMulBig(b, 1e6, 1e6) }
func BenchmarkMulBig_5Mb(b *testing.B) { benchmarkMulBig(b, 5e6, 5e6) }
func BenchmarkMulBig_10Mb(b *testing.B) { benchmarkMulBig(b, 10e6, 10e6) }
func BenchmarkMulBig_20Mb(b *testing.B) { benchmarkMulBig(b, 20e6, 20e6) }
// 50Mb multiplication takes about 1 minute.
//func BenchmarkMulBig_50Mb(b *testing.B) { benchmarkMulBig(b, 50e6, 50e6) }
func BenchmarkMulFFT_1kb(b *testing.B) { benchmarkMulFFT(b, 1e3, 1e3) }
func BenchmarkMulFFT_10kb(b *testing.B) { benchmarkMulFFT(b, 1e4, 1e4) }
func BenchmarkMulFFT_50kb(b *testing.B) { benchmarkMulFFT(b, 5e4, 5e4) }
func BenchmarkMulFFT_100kb(b *testing.B) { benchmarkMulFFT(b, 1e5, 1e5) }
func BenchmarkMulFFT_1Mb(b *testing.B) { benchmarkMulFFT(b, 1e6, 1e6) }
func BenchmarkMulFFT_5Mb(b *testing.B) { benchmarkMulFFT(b, 5e6, 5e6) }
func BenchmarkMulFFT_10Mb(b *testing.B) { benchmarkMulFFT(b, 10e6, 10e6) }
func BenchmarkMulFFT_20Mb(b *testing.B) { benchmarkMulFFT(b, 20e6, 20e6) }
func BenchmarkMulFFT_50Mb(b *testing.B) { benchmarkMulFFT(b, 50e6, 50e6) }
func BenchmarkMulFFT_100Mb(b *testing.B) { benchmarkMulFFT(b, 100e6, 100e6) }
func benchmarkMul(b *testing.B, sizex, sizey int) {
mulx := rndNat(sizex / _W)
muly := rndNat(sizey / _W)
b.ResetTimer()
for i := 0; i < b.N; i++ {
var x, y Int
x.SetBits(mulx)
y.SetBits(muly)
_ = Mul(&x, &y)
}
}
func BenchmarkMul_1kb(b *testing.B) { benchmarkMul(b, 1e3, 1e3) }
func BenchmarkMul_10kb(b *testing.B) { benchmarkMul(b, 1e4, 1e4) }
func BenchmarkMul_50kb(b *testing.B) { benchmarkMul(b, 5e4, 5e4) }
func BenchmarkMul_100kb(b *testing.B) { benchmarkMul(b, 1e5, 1e5) }
func BenchmarkMul_1Mb(b *testing.B) { benchmarkMul(b, 1e6, 1e6) }
func BenchmarkMul_5Mb(b *testing.B) { benchmarkMul(b, 5e6, 5e6) }
func BenchmarkMul_10Mb(b *testing.B) { benchmarkMul(b, 10e6, 10e6) }
func BenchmarkMul_20Mb(b *testing.B) { benchmarkMul(b, 20e6, 20e6) }
func BenchmarkMul_50Mb(b *testing.B) { benchmarkMul(b, 50e6, 50e6) }
func BenchmarkMul_100Mb(b *testing.B) { benchmarkMul(b, 100e6, 100e6) }
// Unbalanced multiplication benchmarks
func BenchmarkMul_1x5Mb(b *testing.B) { benchmarkMul(b, 1e6, 5e6) }
func BenchmarkMul_1x10Mb(b *testing.B) { benchmarkMul(b, 1e6, 10e6) }
func BenchmarkMul_1x20Mb(b *testing.B) { benchmarkMul(b, 1e6, 20e6) }
func BenchmarkMul_1x50Mb(b *testing.B) { benchmarkMul(b, 1e6, 50e6) }
func BenchmarkMul_5x20Mb(b *testing.B) { benchmarkMul(b, 5e6, 20e6) }
func BenchmarkMul_5x50Mb(b *testing.B) { benchmarkMul(b, 5e6, 50e6) }
func BenchmarkMulBig_1x5Mb(b *testing.B) { benchmarkMulBig(b, 1e6, 5e6) }
func BenchmarkMulBig_1x10Mb(b *testing.B) { benchmarkMulBig(b, 1e6, 10e6) }
func BenchmarkMulBig_1x20Mb(b *testing.B) { benchmarkMulBig(b, 1e6, 20e6) }
func BenchmarkMulBig_1x50Mb(b *testing.B) { benchmarkMulBig(b, 1e6, 50e6) }
func BenchmarkMulBig_5x20Mb(b *testing.B) { benchmarkMulBig(b, 5e6, 20e6) }
func BenchmarkMulBig_5x50Mb(b *testing.B) { benchmarkMulBig(b, 5e6, 50e6) }
func BenchmarkMulFFT_1x5Mb(b *testing.B) { benchmarkMulFFT(b, 1e6, 5e6) }
func BenchmarkMulFFT_1x10Mb(b *testing.B) { benchmarkMulFFT(b, 1e6, 10e6) }
func BenchmarkMulFFT_1x20Mb(b *testing.B) { benchmarkMulFFT(b, 1e6, 20e6) }
func BenchmarkMulFFT_1x50Mb(b *testing.B) { benchmarkMulFFT(b, 1e6, 50e6) }
func BenchmarkMulFFT_5x20Mb(b *testing.B) { benchmarkMulFFT(b, 5e6, 20e6) }
func BenchmarkMulFFT_5x50Mb(b *testing.B) { benchmarkMulFFT(b, 5e6, 50e6) }
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