1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
|
// Usage: go test -run=TestCalibrate -calibrate
package bigfft
import (
"flag"
"fmt"
"testing"
"time"
)
var calibrate = flag.Bool("calibrate", false, "run calibration test")
// measureMul benchmarks math/big versus FFT for a given input size
// (in bits).
func measureMul(th int) (tBig, tFFT time.Duration) {
bigLoad := func(b *testing.B) { benchmarkMulBig(b, th, th) }
fftLoad := func(b *testing.B) { benchmarkMulFFT(b, th, th) }
res1 := testing.Benchmark(bigLoad)
res2 := testing.Benchmark(fftLoad)
tBig = time.Duration(res1.NsPerOp())
tFFT = time.Duration(res2.NsPerOp())
return
}
func roundDur(d time.Duration) time.Duration {
if d > 100*time.Millisecond {
return d / time.Millisecond * time.Millisecond
} else {
return d / time.Microsecond * time.Microsecond
}
}
func TestCalibrateThreshold(t *testing.T) {
if !*calibrate {
t.Log("not calibrating, use -calibrate to do so.")
return
}
lower := int(1e3) // math/big is faster at this size.
upper := int(300e3) // FFT is faster at this size.
var sizes [9]int
var speedups [9]float64
for i := 0; i < 3; i++ {
for idx := 1; idx <= 9; idx++ {
sz := ((10-idx)*lower + idx*upper) / 10
big, fft := measureMul(sz)
spd := float64(big) / float64(fft)
sizes[idx-1] = sz
speedups[idx-1] = spd
fmt.Printf("speedup of FFT over math/big at size %d bits: %.2f (%s vs %s)\n",
sz, spd, roundDur(big), roundDur(fft))
}
narrow := false
for idx, s := range speedups {
if s < .98 {
lower = sizes[idx]
narrow = true
} else {
break
}
}
for idx := range speedups {
if speedups[8-idx] > 1.02 {
upper = sizes[8-idx]
narrow = true
} else {
break
}
}
if lower >= upper {
panic("impossible")
}
if !narrow || (upper-lower) <= 10 {
break
}
}
fmt.Printf("sizes: %d\n", sizes)
fmt.Printf("speedups: %.2f\n", speedups)
}
func measureFFTSize(w int, k uint) time.Duration {
load := func(b *testing.B) {
x := rndNat(w)
y := rndNat(w)
for i := 0; i < b.N; i++ {
m := (w+w)>>k + 1
xp := polyFromNat(x, k, m)
yp := polyFromNat(y, k, m)
rp := xp.Mul(&yp)
_ = rp.Int()
}
}
res := testing.Benchmark(load)
return time.Duration(res.NsPerOp())
}
func TestCalibrateFFT(t *testing.T) {
if !*calibrate {
t.Log("not calibrating, use -calibrate to do so.")
return
}
lows := [...]int{10, 10, 10, 10,
20, 50, 100, 200, 500, // 8
1000, 2000, 5000, 10000, // 12
20000, 50000, 100e3, 200e3, // 16
}
his := [...]int{100, 100, 100, 200,
500, 1000, 2000, 5000, 10000, // 8
50e3, 100e3, 200e3, 800e3, // 12
2e6, 5e6, 10e6, 20e6, // 16
}
for k := uint(3); k <= 16; k++ {
// Measure the speedup between k and k+1
low := lows[k] // FFT of size 1<<k known to be faster
hi := his[k] // FFT of size 2<<k known to be faster
var sizes [9]int
var speedups [9]float64
for i := 0; i < 3; i++ {
for idx := 1; idx <= 9; idx++ {
sz := ((10-idx)*low + idx*hi) / 10
t1, t2 := measureFFTSize(sz, k), measureFFTSize(sz, k+1)
spd := float64(t1) / float64(t2)
sizes[idx-1] = sz
speedups[idx-1] = spd
fmt.Printf("speedup of %d vs %d at size %d words: %.2f (%s vs %s)\n",
k+1, k, sz, spd, roundDur(t1), roundDur(t2))
}
narrow := false
for idx, s := range speedups {
if s < .98 {
low = sizes[idx]
narrow = true
} else {
break
}
}
for idx := range speedups {
if speedups[8-idx] > 1.02 {
hi = sizes[8-idx]
narrow = true
} else {
break
}
}
if low >= hi {
panic("impossible")
}
if !narrow || (hi-low) <= 10 {
break
}
}
fmt.Printf("sizes: %d\n", sizes)
fmt.Printf("speedups: %.2f\n", speedups)
}
}
|
