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Diffstat (limited to 'src/math/big/sqrt_test.go')
-rw-r--r-- | src/math/big/sqrt_test.go | 126 |
1 files changed, 126 insertions, 0 deletions
diff --git a/src/math/big/sqrt_test.go b/src/math/big/sqrt_test.go new file mode 100644 index 0000000..d314711 --- /dev/null +++ b/src/math/big/sqrt_test.go @@ -0,0 +1,126 @@ +// Copyright 2017 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 big + +import ( + "fmt" + "math" + "math/rand" + "testing" +) + +// TestFloatSqrt64 tests that Float.Sqrt of numbers with 53bit mantissa +// behaves like float math.Sqrt. +func TestFloatSqrt64(t *testing.T) { + for i := 0; i < 1e5; i++ { + if i == 1e2 && testing.Short() { + break + } + r := rand.Float64() + + got := new(Float).SetPrec(53) + got.Sqrt(NewFloat(r)) + want := NewFloat(math.Sqrt(r)) + if got.Cmp(want) != 0 { + t.Fatalf("Sqrt(%g) =\n got %g;\nwant %g", r, got, want) + } + } +} + +func TestFloatSqrt(t *testing.T) { + for _, test := range []struct { + x string + want string + }{ + // Test values were generated on Wolfram Alpha using query + // 'sqrt(N) to 350 digits' + // 350 decimal digits give up to 1000 binary digits. + {"0.03125", "0.17677669529663688110021109052621225982120898442211850914708496724884155980776337985629844179095519659187673077886403712811560450698134215158051518713749197892665283324093819909447499381264409775757143376369499645074628431682460775184106467733011114982619404115381053858929018135497032545349940642599871090667456829147610370507757690729404938184321879"}, + {"0.125", "0.35355339059327376220042218105242451964241796884423701829416993449768311961552675971259688358191039318375346155772807425623120901396268430316103037427498395785330566648187639818894998762528819551514286752738999290149256863364921550368212935466022229965238808230762107717858036270994065090699881285199742181334913658295220741015515381458809876368643757"}, + {"0.5", "0.70710678118654752440084436210484903928483593768847403658833986899536623923105351942519376716382078636750692311545614851246241802792536860632206074854996791570661133296375279637789997525057639103028573505477998580298513726729843100736425870932044459930477616461524215435716072541988130181399762570399484362669827316590441482031030762917619752737287514"}, + {"2.0", "1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457503"}, + {"3.0", "1.7320508075688772935274463415058723669428052538103806280558069794519330169088000370811461867572485756756261414154067030299699450949989524788116555120943736485280932319023055820679748201010846749232650153123432669033228866506722546689218379712270471316603678615880190499865373798593894676503475065760507566183481296061009476021871903250831458295239598"}, + {"4.0", "2.0"}, + + {"1p512", "1p256"}, + {"4p1024", "2p512"}, + {"9p2048", "3p1024"}, + + {"1p-1024", "1p-512"}, + {"4p-2048", "2p-1024"}, + {"9p-4096", "3p-2048"}, + } { + for _, prec := range []uint{24, 53, 64, 65, 100, 128, 129, 200, 256, 400, 600, 800, 1000} { + x := new(Float).SetPrec(prec) + x.Parse(test.x, 10) + + got := new(Float).SetPrec(prec).Sqrt(x) + want := new(Float).SetPrec(prec) + want.Parse(test.want, 10) + if got.Cmp(want) != 0 { + t.Errorf("prec = %d, Sqrt(%v) =\ngot %g;\nwant %g", + prec, test.x, got, want) + } + + // Square test. + // If got holds the square root of x to precision p, then + // got = √x + k + // for some k such that |k| < 2**(-p). Thus, + // got² = (√x + k)² = x + 2k√n + k² + // and the error must satisfy + // err = |got² - x| ≈ | 2k√n | < 2**(-p+1)*√n + // Ignoring the k² term for simplicity. + + // err = |got² - x| + // (but do intermediate steps with 32 guard digits to + // avoid introducing spurious rounding-related errors) + sq := new(Float).SetPrec(prec+32).Mul(got, got) + diff := new(Float).Sub(sq, x) + err := diff.Abs(diff).SetPrec(prec) + + // maxErr = 2**(-p+1)*√x + one := new(Float).SetPrec(prec).SetInt64(1) + maxErr := new(Float).Mul(new(Float).SetMantExp(one, -int(prec)+1), got) + + if err.Cmp(maxErr) >= 0 { + t.Errorf("prec = %d, Sqrt(%v) =\ngot err %g;\nwant maxErr %g", + prec, test.x, err, maxErr) + } + } + } +} + +func TestFloatSqrtSpecial(t *testing.T) { + for _, test := range []struct { + x *Float + want *Float + }{ + {NewFloat(+0), NewFloat(+0)}, + {NewFloat(-0), NewFloat(-0)}, + {NewFloat(math.Inf(+1)), NewFloat(math.Inf(+1))}, + } { + got := new(Float).Sqrt(test.x) + if got.neg != test.want.neg || got.form != test.want.form { + t.Errorf("Sqrt(%v) = %v (neg: %v); want %v (neg: %v)", + test.x, got, got.neg, test.want, test.want.neg) + } + } + +} + +// Benchmarks + +func BenchmarkFloatSqrt(b *testing.B) { + for _, prec := range []uint{64, 128, 256, 1e3, 1e4, 1e5, 1e6} { + x := NewFloat(2) + z := new(Float).SetPrec(prec) + b.Run(fmt.Sprintf("%v", prec), func(b *testing.B) { + b.ReportAllocs() + for n := 0; n < b.N; n++ { + z.Sqrt(x) + } + }) + } +} |