github.com/s1s1ty/go@v0.0.0-20180207192209-104445e3140f/src/math/big/sqrt_test.go (about)

     1  // Copyright 2017 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package big
     6  
     7  import (
     8  	"fmt"
     9  	"math"
    10  	"math/rand"
    11  	"testing"
    12  )
    13  
    14  // TestFloatSqrt64 tests that Float.Sqrt of numbers with 53bit mantissa
    15  // behaves like float math.Sqrt.
    16  func TestFloatSqrt64(t *testing.T) {
    17  	for i := 0; i < 1e5; i++ {
    18  		r := rand.Float64()
    19  
    20  		got := new(Float).SetPrec(53)
    21  		got.Sqrt(NewFloat(r))
    22  		want := NewFloat(math.Sqrt(r))
    23  		if got.Cmp(want) != 0 {
    24  			t.Fatalf("Sqrt(%g) =\n got %g;\nwant %g", r, got, want)
    25  		}
    26  	}
    27  }
    28  
    29  func TestFloatSqrt(t *testing.T) {
    30  	for _, test := range []struct {
    31  		x    string
    32  		want string
    33  	}{
    34  		// Test values were generated on Wolfram Alpha using query
    35  		//   'sqrt(N) to 350 digits'
    36  		// 350 decimal digits give up to 1000 binary digits.
    37  		{"0.03125", "0.17677669529663688110021109052621225982120898442211850914708496724884155980776337985629844179095519659187673077886403712811560450698134215158051518713749197892665283324093819909447499381264409775757143376369499645074628431682460775184106467733011114982619404115381053858929018135497032545349940642599871090667456829147610370507757690729404938184321879"},
    38  		{"0.125", "0.35355339059327376220042218105242451964241796884423701829416993449768311961552675971259688358191039318375346155772807425623120901396268430316103037427498395785330566648187639818894998762528819551514286752738999290149256863364921550368212935466022229965238808230762107717858036270994065090699881285199742181334913658295220741015515381458809876368643757"},
    39  		{"0.5", "0.70710678118654752440084436210484903928483593768847403658833986899536623923105351942519376716382078636750692311545614851246241802792536860632206074854996791570661133296375279637789997525057639103028573505477998580298513726729843100736425870932044459930477616461524215435716072541988130181399762570399484362669827316590441482031030762917619752737287514"},
    40  		{"2.0", "1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457503"},
    41  		{"3.0", "1.7320508075688772935274463415058723669428052538103806280558069794519330169088000370811461867572485756756261414154067030299699450949989524788116555120943736485280932319023055820679748201010846749232650153123432669033228866506722546689218379712270471316603678615880190499865373798593894676503475065760507566183481296061009476021871903250831458295239598"},
    42  		{"4.0", "2.0"},
    43  
    44  		{"1p512", "1p256"},
    45  		{"4p1024", "2p512"},
    46  		{"9p2048", "3p1024"},
    47  
    48  		{"1p-1024", "1p-512"},
    49  		{"4p-2048", "2p-1024"},
    50  		{"9p-4096", "3p-2048"},
    51  	} {
    52  		for _, prec := range []uint{24, 53, 64, 65, 100, 128, 129, 200, 256, 400, 600, 800, 1000} {
    53  			x := new(Float).SetPrec(prec)
    54  			x.Parse(test.x, 10)
    55  
    56  			got := new(Float).SetPrec(prec).Sqrt(x)
    57  			want := new(Float).SetPrec(prec)
    58  			want.Parse(test.want, 10)
    59  			if got.Cmp(want) != 0 {
    60  				t.Errorf("prec = %d, Sqrt(%v) =\ngot  %g;\nwant %g",
    61  					prec, test.x, got, want)
    62  			}
    63  
    64  			// Square test.
    65  			// If got holds the square root of x to precision p, then
    66  			//   got = √x + k
    67  			// for some k such that |k| < 2**(-p). Thus,
    68  			//   got² = (√x + k)² = x + 2k√n + k²
    69  			// and the error must satisfy
    70  			//   err = |got² - x| ≈ | 2k√n | < 2**(-p+1)*√n
    71  			// Ignoring the k² term for simplicity.
    72  
    73  			// err = |got² - x|
    74  			// (but do intermediate steps with 32 guard digits to
    75  			// avoid introducing spurious rounding-related errors)
    76  			sq := new(Float).SetPrec(prec+32).Mul(got, got)
    77  			diff := new(Float).Sub(sq, x)
    78  			err := diff.Abs(diff).SetPrec(prec)
    79  
    80  			// maxErr = 2**(-p+1)*√x
    81  			one := new(Float).SetPrec(prec).SetInt64(1)
    82  			maxErr := new(Float).Mul(new(Float).SetMantExp(one, -int(prec)+1), got)
    83  
    84  			if err.Cmp(maxErr) >= 0 {
    85  				t.Errorf("prec = %d, Sqrt(%v) =\ngot err  %g;\nwant maxErr %g",
    86  					prec, test.x, err, maxErr)
    87  			}
    88  		}
    89  	}
    90  }
    91  
    92  func TestFloatSqrtSpecial(t *testing.T) {
    93  	for _, test := range []struct {
    94  		x    *Float
    95  		want *Float
    96  	}{
    97  		{NewFloat(+0), NewFloat(+0)},
    98  		{NewFloat(-0), NewFloat(-0)},
    99  		{NewFloat(math.Inf(+1)), NewFloat(math.Inf(+1))},
   100  	} {
   101  		got := new(Float).Sqrt(test.x)
   102  		if got.neg != test.want.neg || got.form != test.want.form {
   103  			t.Errorf("Sqrt(%v) = %v (neg: %v); want %v (neg: %v)",
   104  				test.x, got, got.neg, test.want, test.want.neg)
   105  		}
   106  	}
   107  
   108  }
   109  
   110  // Benchmarks
   111  
   112  func BenchmarkFloatSqrt(b *testing.B) {
   113  	for _, prec := range []uint{64, 128, 256, 1e3, 1e4, 1e5, 1e6} {
   114  		x := NewFloat(2)
   115  		z := new(Float).SetPrec(prec)
   116  		b.Run(fmt.Sprintf("%v", prec), func(b *testing.B) {
   117  			b.ReportAllocs()
   118  			for n := 0; n < b.N; n++ {
   119  				z.Sqrt(x)
   120  			}
   121  		})
   122  	}
   123  }