github.com/guyezi/gofrontend@v0.0.0-20200228202240-7a62a49e62c0/libgo/go/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  	"runtime"
    12  	"testing"
    13  )
    14  
    15  // TestFloatSqrt64 tests that Float.Sqrt of numbers with 53bit mantissa
    16  // behaves like float math.Sqrt.
    17  func TestFloatSqrt64(t *testing.T) {
    18  	// This test fails for gccgo on 386 with a one ULP difference,
    19  	// presumably due to the use of extended precision floating
    20  	// point.
    21  	if runtime.Compiler == "gccgo" && runtime.GOARCH == "386" {
    22  		t.Skip("skipping on gccgo for 386; gets a one ULP difference")
    23  	}
    24  
    25  	for i := 0; i < 1e5; i++ {
    26  		if i == 1e2 && testing.Short() {
    27  			break
    28  		}
    29  		r := rand.Float64()
    30  
    31  		got := new(Float).SetPrec(53)
    32  		got.Sqrt(NewFloat(r))
    33  		want := NewFloat(math.Sqrt(r))
    34  		if got.Cmp(want) != 0 {
    35  			t.Fatalf("Sqrt(%g) =\n got %g;\nwant %g", r, got, want)
    36  		}
    37  	}
    38  }
    39  
    40  func TestFloatSqrt(t *testing.T) {
    41  	for _, test := range []struct {
    42  		x    string
    43  		want string
    44  	}{
    45  		// Test values were generated on Wolfram Alpha using query
    46  		//   'sqrt(N) to 350 digits'
    47  		// 350 decimal digits give up to 1000 binary digits.
    48  		{"0.03125", "0.17677669529663688110021109052621225982120898442211850914708496724884155980776337985629844179095519659187673077886403712811560450698134215158051518713749197892665283324093819909447499381264409775757143376369499645074628431682460775184106467733011114982619404115381053858929018135497032545349940642599871090667456829147610370507757690729404938184321879"},
    49  		{"0.125", "0.35355339059327376220042218105242451964241796884423701829416993449768311961552675971259688358191039318375346155772807425623120901396268430316103037427498395785330566648187639818894998762528819551514286752738999290149256863364921550368212935466022229965238808230762107717858036270994065090699881285199742181334913658295220741015515381458809876368643757"},
    50  		{"0.5", "0.70710678118654752440084436210484903928483593768847403658833986899536623923105351942519376716382078636750692311545614851246241802792536860632206074854996791570661133296375279637789997525057639103028573505477998580298513726729843100736425870932044459930477616461524215435716072541988130181399762570399484362669827316590441482031030762917619752737287514"},
    51  		{"2.0", "1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457503"},
    52  		{"3.0", "1.7320508075688772935274463415058723669428052538103806280558069794519330169088000370811461867572485756756261414154067030299699450949989524788116555120943736485280932319023055820679748201010846749232650153123432669033228866506722546689218379712270471316603678615880190499865373798593894676503475065760507566183481296061009476021871903250831458295239598"},
    53  		{"4.0", "2.0"},
    54  
    55  		{"1p512", "1p256"},
    56  		{"4p1024", "2p512"},
    57  		{"9p2048", "3p1024"},
    58  
    59  		{"1p-1024", "1p-512"},
    60  		{"4p-2048", "2p-1024"},
    61  		{"9p-4096", "3p-2048"},
    62  	} {
    63  		for _, prec := range []uint{24, 53, 64, 65, 100, 128, 129, 200, 256, 400, 600, 800, 1000} {
    64  			x := new(Float).SetPrec(prec)
    65  			x.Parse(test.x, 10)
    66  
    67  			got := new(Float).SetPrec(prec).Sqrt(x)
    68  			want := new(Float).SetPrec(prec)
    69  			want.Parse(test.want, 10)
    70  			if got.Cmp(want) != 0 {
    71  				t.Errorf("prec = %d, Sqrt(%v) =\ngot  %g;\nwant %g",
    72  					prec, test.x, got, want)
    73  			}
    74  
    75  			// Square test.
    76  			// If got holds the square root of x to precision p, then
    77  			//   got = √x + k
    78  			// for some k such that |k| < 2**(-p). Thus,
    79  			//   got² = (√x + k)² = x + 2k√n + k²
    80  			// and the error must satisfy
    81  			//   err = |got² - x| ≈ | 2k√n | < 2**(-p+1)*√n
    82  			// Ignoring the k² term for simplicity.
    83  
    84  			// err = |got² - x|
    85  			// (but do intermediate steps with 32 guard digits to
    86  			// avoid introducing spurious rounding-related errors)
    87  			sq := new(Float).SetPrec(prec+32).Mul(got, got)
    88  			diff := new(Float).Sub(sq, x)
    89  			err := diff.Abs(diff).SetPrec(prec)
    90  
    91  			// maxErr = 2**(-p+1)*√x
    92  			one := new(Float).SetPrec(prec).SetInt64(1)
    93  			maxErr := new(Float).Mul(new(Float).SetMantExp(one, -int(prec)+1), got)
    94  
    95  			if err.Cmp(maxErr) >= 0 {
    96  				t.Errorf("prec = %d, Sqrt(%v) =\ngot err  %g;\nwant maxErr %g",
    97  					prec, test.x, err, maxErr)
    98  			}
    99  		}
   100  	}
   101  }
   102  
   103  func TestFloatSqrtSpecial(t *testing.T) {
   104  	for _, test := range []struct {
   105  		x    *Float
   106  		want *Float
   107  	}{
   108  		{NewFloat(+0), NewFloat(+0)},
   109  		{NewFloat(-0), NewFloat(-0)},
   110  		{NewFloat(math.Inf(+1)), NewFloat(math.Inf(+1))},
   111  	} {
   112  		got := new(Float).Sqrt(test.x)
   113  		if got.neg != test.want.neg || got.form != test.want.form {
   114  			t.Errorf("Sqrt(%v) = %v (neg: %v); want %v (neg: %v)",
   115  				test.x, got, got.neg, test.want, test.want.neg)
   116  		}
   117  	}
   118  
   119  }
   120  
   121  // Benchmarks
   122  
   123  func BenchmarkFloatSqrt(b *testing.B) {
   124  	for _, prec := range []uint{64, 128, 256, 1e3, 1e4, 1e5, 1e6} {
   125  		x := NewFloat(2)
   126  		z := new(Float).SetPrec(prec)
   127  		b.Run(fmt.Sprintf("%v", prec), func(b *testing.B) {
   128  			b.ReportAllocs()
   129  			for n := 0; n < b.N; n++ {
   130  				z.Sqrt(x)
   131  			}
   132  		})
   133  	}
   134  }