)

// 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)
		}

//
//
// __ieee754_acosh(x)
// Method :
//	Based on
//	        acosh(x) = log [ x + sqrt(x*x-1) ]
//	we have
//	        acosh(x) := log(x)+ln2,	if x is large; else
//	        acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
//	        acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
//
// Special cases:
//	acosh(x) is NaN with signal if x<1.
//	acosh(NaN) is NaN without signal.
//

	}

	absx := Abs(x)

	var f float64
	var iu uint64
	k := 1
	if absx < Sqrt2M1 { //  |x| < Sqrt(2)-1
		if absx < Small { // |x| < 2**-29
			if absx < Tiny { // |x| < 2**-54
				return x
			}
			return x - x*x*0.5
		}
		if x > Sqrt2HalfM1 { // Sqrt(2)/2-1 < x
			// (Sqrt(2)/2-1) < x < (Sqrt(2)-1)
			k = 0
			f = x
			iu = 1
		}
	}
	var c float64
	if k != 0 {
		var u float64

// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

// Issue 16804: internal error for math.Sqrt as statement
//              rather than expression

package main

import "math"

func sqrt() {
	math.Sqrt(2.0)

//
//
// asinh(x)
// Method :
//	Based on
//	        asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
//	we have
//	asinh(x) := x  if  1+x*x=1,
//	         := sign(x)*(log(x)+ln2) for large |x|, else
//	         := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
//	         := sign(x)*log1p(|x| + x**2/(1 + sqrt(1+x**2)))
//

// Asinh returns the inverse hyperbolic sine of x.
//
// Special cases are:
//

// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package math

/*
	Hypot -- sqrt(p*p + q*q), but overflows only if the result does.
*/

// Hypot returns [Sqrt](p*p + q*q), taking care to avoid
// unnecessary overflow and underflow.
//
// Special cases are:
//
//	Hypot(±Inf, q) = +Inf
//	Hypot(p, ±Inf) = +Inf
//	Hypot(NaN, q) = NaN

 */

const blockSize = 64 // A DCT block is 8x8.

type block [blockSize]int32

const (
	w1 = 2841 // 2048*sqrt(2)*cos(1*pi/16)
	w2 = 2676 // 2048*sqrt(2)*cos(2*pi/16)
	w3 = 2408 // 2048*sqrt(2)*cos(3*pi/16)
	w5 = 1609 // 2048*sqrt(2)*cos(5*pi/16)
	w6 = 1108 // 2048*sqrt(2)*cos(6*pi/16)
	w7 = 565  // 2048*sqrt(2)*cos(7*pi/16)

	w1pw7 = w1 + w7
	w1mw7 = w1 - w7
	w2pw6 = w2 + w6
	w2mw6 = w2 - w6
	w3pw5 = w3 + w5

	// standard deviation is sqrt( average( (x - xbar)^2 ) )
	// = sqrt( Integral( x^2 + xbar^2 -2*x*xbar dt ) / Duration )
	// = sqrt( ( Integral( x^2 dt ) + Duration * xbar^2 - 2*xbar*Integral(x dt) ) / Duration)
	// = sqrt( Integral(x^2 dt)/Duration - xbar^2 )
	variance := igr.IntegralXX/igr.ElapsedSeconds - avg*avg
	if variance >= 0 {
		return avg, math.Sqrt(variance)
	}
	return avg, math.NaN()

		// Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x)
		if x >= Two302 { // x > 2**302

			// (x >> n**2)
			//          Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
			//          Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
			//          Let s=sin(x), c=cos(x),
			//              xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
			//
			//                 n    sin(xn)*sqt2    cos(xn)*sqt2
			//              ----------------------------------

with an architecture tag, followed by a colon and a quoted Go-style
regexp to be matched. For example, the following test:

  func Sqrt(x float64) float64 {
  	   // amd64:"SQRTSD"
  	   // arm64:"FSQRTD"
  	   return math.Sqrt(x)
  }

verifies that math.Sqrt calls are intrinsified to a SQRTSD instruction
on amd64, and to a FSQRTD instruction on arm64.