Gecko [ 167.86.127.34 ]

Name	Size	Permission
accuracy_string.go	414 B	-rw-r--r--
arith.go	5.68 KB	-rw-r--r--
arith_386.s	4.67 KB	-rw-r--r--
arith_amd64.go	277 B	-rw-r--r--
arith_amd64.s	9.71 KB	-rw-r--r--
arith_arm.s	4.47 KB	-rw-r--r--
arith_arm64.s	9.94 KB	-rw-r--r--
arith_decl.go	707 B	-rw-r--r--
arith_decl_pure.go	1.24 KB	-rw-r--r--
arith_decl_s390x.go	791 B	-rw-r--r--
arith_mips64x.s	917 B	-rw-r--r--
arith_mipsx.s	913 B	-rw-r--r--
arith_ppc64x.s	12.62 KB	-rw-r--r--
arith_s390x.s	29.12 KB	-rw-r--r--
arith_s390x_test.go	1014 B	-rw-r--r--
arith_test.go	12.29 KB	-rw-r--r--
arith_wasm.s	757 B	-rw-r--r--
bits_test.go	5.07 KB	-rw-r--r--
calibrate_test.go	4.63 KB	-rw-r--r--
decimal.go	6.52 KB	-rw-r--r--
decimal_test.go	3.33 KB	-rw-r--r--
doc.go	3.79 KB	-rw-r--r--
example_rat_test.go	1.68 KB	-rw-r--r--
example_test.go	3.94 KB	-rw-r--r--
float.go	44.14 KB	-rw-r--r--
float_test.go	51.94 KB	-rw-r--r--
floatconv.go	8.36 KB	-rw-r--r--
floatconv_test.go	24.28 KB	-rw-r--r--
floatexample_test.go	3.63 KB	-rw-r--r--
floatmarsh.go	3.34 KB	-rw-r--r--
floatmarsh_test.go	3.64 KB	-rw-r--r--
ftoa.go	13.55 KB	-rw-r--r--
gcd_test.go	2.16 KB	-rw-r--r--
hilbert_test.go	2.88 KB	-rw-r--r--
int.go	29.56 KB	-rw-r--r--
int_test.go	51.93 KB	-rw-r--r--
intconv.go	6.68 KB	-rw-r--r--
intconv_test.go	10.01 KB	-rw-r--r--
intmarsh.go	2.09 KB	-rw-r--r--
intmarsh_test.go	2.8 KB	-rw-r--r--
nat.go	33.76 KB	-rw-r--r--
nat_test.go	18.87 KB	-rw-r--r--
natconv.go	14.57 KB	-rw-r--r--
natconv_test.go	16.85 KB	-rw-r--r--
prime.go	10.34 KB	-rw-r--r--
prime_test.go	7.1 KB	-rw-r--r--
rat.go	13.49 KB	-rw-r--r--
rat_test.go	18.54 KB	-rw-r--r--
ratconv.go	9.49 KB	-rw-r--r--
ratconv_test.go	14.96 KB	-rw-r--r--
ratmarsh.go	1.95 KB	-rw-r--r--
ratmarsh_test.go	3.04 KB	-rw-r--r--
roundingmode_string.go	501 B	-rw-r--r--
sqrt.go	3.59 KB	-rw-r--r--
sqrt_test.go	4.81 KB	-rw-r--r--

Code Editor : sqrt.go

// 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 "math"

var (
	three = NewFloat(3.0)
)

// Sqrt sets z to the rounded square root of x, and returns it.
//
// If z's precision is 0, it is changed to x's precision before the
// operation. Rounding is performed according to z's precision and
// rounding mode.
//
// The function panics if z < 0. The value of z is undefined in that
// case.
func (z *Float) Sqrt(x *Float) *Float {
	if debugFloat {
		x.validate()
	}

if z.prec == 0 {
		z.prec = x.prec
	}

if x.Sign() == -1 {
		// following IEEE754-2008 (section 7.2)
		panic(ErrNaN{"square root of negative operand"})
	}

// handle ±0 and +∞
	if x.form != finite {
		z.acc = Exact
		z.form = x.form
		z.neg = x.neg // IEEE754-2008 requires √±0 = ±0
		return z
	}

// MantExp sets the argument's precision to the receiver's, and
	// when z.prec > x.prec this will lower z.prec. Restore it after
	// the MantExp call.
	prec := z.prec
	b := x.MantExp(z)
	z.prec = prec

// Compute √(z·2**b) as
	//   √( z)·2**(½b)     if b is even
	//   √(2z)·2**(⌊½b⌋)   if b > 0 is odd
	//   √(½z)·2**(⌈½b⌉)   if b < 0 is odd
	switch b % 2 {
	case 0:
		// nothing to do
	case 1:
		z.exp++
	case -1:
		z.exp--
	}
	// 0.25 <= z < 2.0

// Solving x² - z = 0 directly requires a Quo call, but it's
	// faster for small precisions.
	//
	// Solving 1/x² - z = 0 avoids the Quo call and is much faster for
	// high precisions.
	//
	// 128bit precision is an empirically chosen threshold.
	if z.prec <= 128 {
		z.sqrtDirect(z)
	} else {
		z.sqrtInverse(z)
	}

// re-attach halved exponent
	return z.SetMantExp(z, b/2)
}

// Compute √x (up to prec 128) by solving
//   t² - x = 0
// for t, starting with a 53 bits precision guess from math.Sqrt and
// then using at most two iterations of Newton's method.
func (z *Float) sqrtDirect(x *Float) {
	// let
	//   f(t) = t² - x
	// then
	//   g(t) = f(t)/f'(t) = ½(t² - x)/t
	// and the next guess is given by
	//   t2 = t - g(t) = ½(t² + x)/t
	u := new(Float)
	ng := func(t *Float) *Float {
		u.prec = t.prec
		u.Mul(t, t)        // u = t²
		u.Add(u, x)        //   = t² + x
		u.exp--            //   = ½(t² + x)
		return t.Quo(u, t) //   = ½(t² + x)/t
	}

xf, _ := x.Float64()
	sq := NewFloat(math.Sqrt(xf))

switch {
	case z.prec > 128:
		panic("sqrtDirect: only for z.prec <= 128")
	case z.prec > 64:
		sq.prec *= 2
		sq = ng(sq)
		fallthrough
	default:
		sq.prec *= 2
		sq = ng(sq)
	}

z.Set(sq)
}

// Compute √x (to z.prec precision) by solving
//   1/t² - x = 0
// for t (using Newton's method), and then inverting.
func (z *Float) sqrtInverse(x *Float) {
	// let
	//   f(t) = 1/t² - x
	// then
	//   g(t) = f(t)/f'(t) = -½t(1 - xt²)
	// and the next guess is given by
	//   t2 = t - g(t) = ½t(3 - xt²)
	u := newFloat(z.prec)
	v := newFloat(z.prec)
	ng := func(t *Float) *Float {
		u.prec = t.prec
		v.prec = t.prec
		u.Mul(t, t)     // u = t²
		u.Mul(x, u)     //   = xt²
		v.Sub(three, u) // v = 3 - xt²
		u.Mul(t, v)     // u = t(3 - xt²)
		u.exp--         //   = ½t(3 - xt²)
		return t.Set(u)

}

xf, _ := x.Float64()
	sqi := newFloat(z.prec)
	sqi.SetFloat64(1 / math.Sqrt(xf))
	for prec := z.prec + 32; sqi.prec < prec; {
		sqi.prec *= 2
		sqi = ng(sqi)
	}
	// sqi = 1/√x

// x/√x = √x
	z.Mul(x, sqi)
}

// newFloat returns a new *Float with space for twice the given
// precision.
func newFloat(prec2 uint32) *Float {
	z := new(Float)
	// nat.make ensures the slice length is > 0
	z.mant = z.mant.make(int(prec2/_W) * 2)
	return z
}

${this.title}

Code Editor : sqrt.go