)

// 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)
		}

    assertThat(INTEGER_MANY_VALUES_STATS_ITERABLE.populationStandardDeviation())
        .isWithin(ALLOWED_ERROR * sqrt(INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS))
        .of(sqrt(INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / INTEGER_MANY_VALUES_COUNT));
    assertThat(LONG_MANY_VALUES_STATS_ITERATOR.populationStandardDeviation())

        .isWithin(ALLOWED_ERROR * sqrt(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS))
        .of(sqrt(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / LONG_MANY_VALUES_COUNT));
    assertThat(longManyValuesAccumulatorByAddAllVarargs.populationStandardDeviation())
        .isWithin(ALLOWED_ERROR * sqrt(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS))
        .of(sqrt(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / LONG_MANY_VALUES_COUNT));

//
//
// __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.
//

			} else {
				ss = z / cc
			}
		}

		// j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
		// y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)

		var z float64
		if x > Two129 { // |x| > ~6.8056e+38
			z = (1 / SqrtPi) * cc / Sqrt(x)
		} else {
			u := pzero(x)
			v := qzero(x)
			z = (1 / SqrtPi) * (u*cc - v*ss) / Sqrt(x)
		}
		return z // |x| >= 2.0
	}

	}

	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:
//

			} else {
				ss = z / cc
			}
		}

		// j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
		// y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)

		var z float64
		if x > Two129 {
			z = (1 / SqrtPi) * cc / Sqrt(x)
		} else {
			u := pone(x)
			v := qone(x)
			z = (1 / SqrtPi) * (u*cc - v*ss) / Sqrt(x)
		}
		if sign {
			return -z
		}
		return z
	}

// 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