//
// __ieee754_log(x)
// Return the logarithm of x
//
// Method :
//   1. Argument Reduction: find k and f such that
//			x = 2**k * (1+f),
//	   where  sqrt(2)/2 < 1+f < sqrt(2) .
//
//   2. Approximation of log(1+f).
//	Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
//		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
//	     	 = 2s + s*R

	DIVF.NE	F0, F2        // 002a821e
	DIVD	F3, F5        // 035b85ee
	NEGF	F0, F1        // 401ab1ee
	NEGD	F4, F5        // 445bb1ee
	ABSF	F0, F1        // c01ab0ee
	ABSD	F4, F5        // c45bb0ee
	SQRTF	F0, F1        // c01ab1ee
	SQRTD	F4, F5        // c45bb1ee
	MOVFD	F0, F1        // c01ab7ee
	MOVDF	F4, F5        // c45bb7ee

	LDREX	(R8), R9      // 9f9f98e1
	LDREXD	(R11), R12    // 9fcfbbe1

	ORPD    X0, X2 // X2= f1
	SHRQ    $52, BX
	ANDL    $0x7FF, BX
	SUBL    $0x3FE, BX
	XORPS   X1, X1 // break dependency for CVTSL2SD
	CVTSL2SD BX, X1 // x1= k, x2= f1
	// if f1 < math.Sqrt2/2 { k -= 1; f1 *= 2 }
	MOVSD   $HSqrt2, X0 // x0= 0.7071, x1= k, x2= f1
	CMPSD   X2, X0, 5 // cmpnlt; x0= 0 or ^0, x1= k, x2 = f1
	MOVSD   $1.0, X3 // x0= 0 or ^0, x1= k, x2 = f1, x3= 1

func zero[T Complex]() T {
	return T(0)
}
func pi[T Complex]() T {
	return T(3.14)
}
func sqrtN1[T Complex]() T {
	return T(-1i)
}

func main() {
	fmt.Println(zero[complex128]())
	fmt.Println(pi[complex128]())
	fmt.Println(sqrtN1[complex128]())
	fmt.Println(zero[complex64]())
	fmt.Println(pi[complex64]())
	fmt.Println(sqrtN1[complex64]())

)

// 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