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math/big: faster "pure Go" addition/subtraction for long vectors
(platforms w/o corresponding assembly kernels) For short vector adds there's some erradic slow-down, but overall these routines have become significantly faster. This only matters for platforms w/o native (assembly) versions of these kernels, so we are not concerned about the minor slow-down for short vectors. This code was already reviewed under Mercurial (golang.org/cl/172810043) but wasn't submitted before the switch to git. Benchmarks run on 2.3GHz Intel Core i7, running OS X 10.9.5, with the respective AddVV and AddVW assembly routines disabled. benchmark old ns/op new ns/op delta BenchmarkAddVV_1 6.59 7.09 +7.59% BenchmarkAddVV_2 10.3 10.1 -1.94% BenchmarkAddVV_3 10.9 12.6 +15.60% BenchmarkAddVV_4 13.9 15.6 +12.23% BenchmarkAddVV_5 16.8 17.3 +2.98% BenchmarkAddVV_1e1 29.5 29.9 +1.36% BenchmarkAddVV_1e2 246 232 -5.69% BenchmarkAddVV_1e3 2374 2185 -7.96% BenchmarkAddVV_1e4 58942 22292 -62.18% BenchmarkAddVV_1e5 668622 225279 -66.31% BenchmarkAddVW_1 6.81 5.58 -18.06% BenchmarkAddVW_2 7.69 6.86 -10.79% BenchmarkAddVW_3 9.56 8.32 -12.97% BenchmarkAddVW_4 12.1 9.53 -21.24% BenchmarkAddVW_5 13.2 10.9 -17.42% BenchmarkAddVW_1e1 23.4 18.0 -23.08% BenchmarkAddVW_1e2 175 141 -19.43% BenchmarkAddVW_1e3 1568 1266 -19.26% BenchmarkAddVW_1e4 15425 12596 -18.34% BenchmarkAddVW_1e5 156737 133539 -14.80% BenchmarkFibo 381678466 132958666 -65.16% benchmark old MB/s new MB/s speedup BenchmarkAddVV_1 9715.25 9028.30 0.93x BenchmarkAddVV_2 12461.72 12622.60 1.01x BenchmarkAddVV_3 17549.64 15243.82 0.87x BenchmarkAddVV_4 18392.54 16398.29 0.89x BenchmarkAddVV_5 18995.23 18496.57 0.97x BenchmarkAddVV_1e1 21708.98 21438.28 0.99x BenchmarkAddVV_1e2 25956.53 27506.88 1.06x BenchmarkAddVV_1e3 26947.93 29286.66 1.09x BenchmarkAddVV_1e4 10857.96 28709.46 2.64x BenchmarkAddVV_1e5 9571.91 28409.21 2.97x BenchmarkAddVW_1 1175.28 1433.98 1.22x BenchmarkAddVW_2 2080.01 2332.54 1.12x BenchmarkAddVW_3 2509.28 2883.97 1.15x BenchmarkAddVW_4 2646.09 3356.83 1.27x BenchmarkAddVW_5 3020.69 3671.07 1.22x BenchmarkAddVW_1e1 3425.76 4441.40 1.30x BenchmarkAddVW_1e2 4553.17 5642.96 1.24x BenchmarkAddVW_1e3 5100.14 6318.72 1.24x BenchmarkAddVW_1e4 5186.15 6350.96 1.22x BenchmarkAddVW_1e5 5104.07 5990.74 1.17x Change-Id: I7a62023b1105248a0e85e5b9819d3fd4266123d4 Reviewed-on: https://go-review.googlesource.com/2480 Reviewed-by: Russ Cox <rsc@golang.org> Reviewed-by: Alan Donovan <adonovan@google.com>
This commit is contained in:
Robert Griesemer
parent
80b3ff9f82
commit
067acd51b0
@ -70,7 +70,7 @@ func mulWW_g(x, y Word) (z1, z0 Word) {
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// z1<<_W + z0 = x*y + c
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func mulAddWWW_g(x, y, c Word) (z1, z0 Word) {
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z1, zz0 := mulWW(x, y)
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z1, zz0 := mulWW_g(x, y)
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if z0 = zz0 + c; z0 < zz0 {
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z1++
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}
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@ -154,32 +154,82 @@ func divWW_g(u1, u0, v Word) (q, r Word) {
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return q1*_B2 + q0, (un21*_B2 + un0 - q0*v) >> s
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}
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// Keep for performance debugging.
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// Using addWW_g is likely slower.
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const use_addWW_g = false
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// The resulting carry c is either 0 or 1.
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func addVV_g(z, x, y []Word) (c Word) {
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for i := range z {
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c, z[i] = addWW_g(x[i], y[i], c)
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if use_addWW_g {
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for i := range z {
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c, z[i] = addWW_g(x[i], y[i], c)
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}
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return
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}
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for i, xi := range x[:len(z)] {
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yi := y[i]
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zi := xi + yi + c
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z[i] = zi
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// see "Hacker's Delight", section 2-12 (overflow detection)
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c = (xi&yi | (xi|yi)&^zi) >> (_W - 1)
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}
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return
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}
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// The resulting carry c is either 0 or 1.
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func subVV_g(z, x, y []Word) (c Word) {
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for i := range z {
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c, z[i] = subWW_g(x[i], y[i], c)
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if use_addWW_g {
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for i := range z {
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c, z[i] = subWW_g(x[i], y[i], c)
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}
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return
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}
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for i, xi := range x[:len(z)] {
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yi := y[i]
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zi := xi - yi - c
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z[i] = zi
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// see "Hacker's Delight", section 2-12 (overflow detection)
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c = (yi&^xi | (yi|^xi)&zi) >> (_W - 1)
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}
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return
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}
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// Argument y must be either 0 or 1.
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// The resulting carry c is either 0 or 1.
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func addVW_g(z, x []Word, y Word) (c Word) {
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if use_addWW_g {
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c = y
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for i := range z {
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c, z[i] = addWW_g(x[i], c, 0)
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}
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return
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}
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c = y
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for i := range z {
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c, z[i] = addWW_g(x[i], c, 0)
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for i, xi := range x[:len(z)] {
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zi := xi + c
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z[i] = zi
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c = xi &^ zi >> (_W - 1)
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}
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return
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}
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func subVW_g(z, x []Word, y Word) (c Word) {
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if use_addWW_g {
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c = y
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for i := range z {
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c, z[i] = subWW_g(x[i], c, 0)
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}
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return
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}
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c = y
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for i := range z {
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c, z[i] = subWW_g(x[i], c, 0)
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for i, xi := range x[:len(z)] {
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zi := xi - c
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z[i] = zi
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c = (zi &^ xi) >> (_W - 1)
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}
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return
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}
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@ -222,6 +272,7 @@ func mulAddVWW_g(z, x []Word, y, r Word) (c Word) {
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return
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}
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// TODO(gri) Remove use of addWW_g here and then we can remove addWW_g and subWW_g.
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func addMulVVW_g(z, x []Word, y Word) (c Word) {
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for i := range z {
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z1, z0 := mulAddWWW_g(x[i], y, z[i])
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@ -254,7 +254,7 @@ func benchmarkFunVW(b *testing.B, f funVW, n int) {
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x := rndV(n)
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y := rndW()
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z := make([]Word, n)
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b.SetBytes(int64(n * _W))
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b.SetBytes(int64(n * _S))
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b.ResetTimer()
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for i := 0; i < b.N; i++ {
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f(z, x, y)
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@ -769,3 +769,55 @@ func BenchmarkExp3Power0x10000(b *testing.B) { ExpHelper(b, 3, 0x10000) }
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func BenchmarkExp3Power0x40000(b *testing.B) { ExpHelper(b, 3, 0x40000) }
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func BenchmarkExp3Power0x100000(b *testing.B) { ExpHelper(b, 3, 0x100000) }
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func BenchmarkExp3Power0x400000(b *testing.B) { ExpHelper(b, 3, 0x400000) }
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func fibo(n int) nat {
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switch n {
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case 0:
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return nil
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case 1:
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return nat{1}
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}
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f0 := fibo(0)
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f1 := fibo(1)
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var f2 nat
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for i := 1; i < n; i++ {
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f2 = f2.add(f0, f1)
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f0, f1, f2 = f1, f2, f0
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}
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return f1
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}
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var fiboNums = []string{
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"0",
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"55",
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"6765",
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"832040",
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"102334155",
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"12586269025",
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"1548008755920",
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"190392490709135",
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"23416728348467685",
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"2880067194370816120",
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"354224848179261915075",
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}
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func TestFibo(t *testing.T) {
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for i, want := range fiboNums {
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n := i * 10
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got := fibo(n).decimalString()
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if got != want {
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t.Errorf("fibo(%d) failed: got %s want %s", n, got, want)
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}
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}
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}
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func BenchmarkFibo(b *testing.B) {
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for i := 0; i < b.N; i++ {
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fibo(1e0)
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fibo(1e1)
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fibo(1e2)
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fibo(1e3)
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fibo(1e4)
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fibo(1e5)
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}
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}
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