github.com/primecitizens/pcz/std@v0.2.1/math/pow.go (about)

     1  // Copyright 2009 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 math
     6  
     7  func isOddInt(x float64) bool {
     8  	xi, xf := Modf(x)
     9  	return xf == 0 && int64(xi)&1 == 1
    10  }
    11  
    12  // Special cases taken from FreeBSD's /usr/src/lib/msun/src/e_pow.c
    13  // updated by IEEE Std. 754-2008 "Section 9.2.1 Special values".
    14  
    15  // Pow returns x**y, the base-x exponential of y.
    16  //
    17  // Special cases are (in order):
    18  //
    19  //	Pow(x, ±0) = 1 for any x
    20  //	Pow(1, y) = 1 for any y
    21  //	Pow(x, 1) = x for any x
    22  //	Pow(NaN, y) = NaN
    23  //	Pow(x, NaN) = NaN
    24  //	Pow(±0, y) = ±Inf for y an odd integer < 0
    25  //	Pow(±0, -Inf) = +Inf
    26  //	Pow(±0, +Inf) = +0
    27  //	Pow(±0, y) = +Inf for finite y < 0 and not an odd integer
    28  //	Pow(±0, y) = ±0 for y an odd integer > 0
    29  //	Pow(±0, y) = +0 for finite y > 0 and not an odd integer
    30  //	Pow(-1, ±Inf) = 1
    31  //	Pow(x, +Inf) = +Inf for |x| > 1
    32  //	Pow(x, -Inf) = +0 for |x| > 1
    33  //	Pow(x, +Inf) = +0 for |x| < 1
    34  //	Pow(x, -Inf) = +Inf for |x| < 1
    35  //	Pow(+Inf, y) = +Inf for y > 0
    36  //	Pow(+Inf, y) = +0 for y < 0
    37  //	Pow(-Inf, y) = Pow(-0, -y)
    38  //	Pow(x, y) = NaN for finite x < 0 and finite non-integer y
    39  func Pow(x, y float64) float64 {
    40  	return pow(x, y)
    41  }
    42  
    43  func pow(x, y float64) float64 {
    44  	switch {
    45  	case y == 0 || x == 1:
    46  		return 1
    47  	case y == 1:
    48  		return x
    49  	case IsNaN(x) || IsNaN(y):
    50  		return NaN()
    51  	case x == 0:
    52  		switch {
    53  		case y < 0:
    54  			if isOddInt(y) {
    55  				return Copysign(Inf(1), x)
    56  			}
    57  			return Inf(1)
    58  		case y > 0:
    59  			if isOddInt(y) {
    60  				return x
    61  			}
    62  			return 0
    63  		}
    64  	case IsInf(y, 0):
    65  		switch {
    66  		case x == -1:
    67  			return 1
    68  		case (Abs(x) < 1) == IsInf(y, 1):
    69  			return 0
    70  		default:
    71  			return Inf(1)
    72  		}
    73  	case IsInf(x, 0):
    74  		if IsInf(x, -1) {
    75  			return Pow(1/x, -y) // Pow(-0, -y)
    76  		}
    77  		switch {
    78  		case y < 0:
    79  			return 0
    80  		case y > 0:
    81  			return Inf(1)
    82  		}
    83  	case y == 0.5:
    84  		return Sqrt(x)
    85  	case y == -0.5:
    86  		return 1 / Sqrt(x)
    87  	}
    88  
    89  	yi, yf := Modf(Abs(y))
    90  	if yf != 0 && x < 0 {
    91  		return NaN()
    92  	}
    93  	if yi >= 1<<63 {
    94  		// yi is a large even int that will lead to overflow (or underflow to 0)
    95  		// for all x except -1 (x == 1 was handled earlier)
    96  		switch {
    97  		case x == -1:
    98  			return 1
    99  		case (Abs(x) < 1) == (y > 0):
   100  			return 0
   101  		default:
   102  			return Inf(1)
   103  		}
   104  	}
   105  
   106  	// ans = a1 * 2**ae (= 1 for now).
   107  	a1 := 1.0
   108  	ae := 0
   109  
   110  	// ans *= x**yf
   111  	if yf != 0 {
   112  		if yf > 0.5 {
   113  			yf--
   114  			yi++
   115  		}
   116  		a1 = Exp(yf * Log(x))
   117  	}
   118  
   119  	// ans *= x**yi
   120  	// by multiplying in successive squarings
   121  	// of x according to bits of yi.
   122  	// accumulate powers of two into exp.
   123  	x1, xe := Frexp(x)
   124  	for i := int64(yi); i != 0; i >>= 1 {
   125  		if xe < -1<<12 || 1<<12 < xe {
   126  			// catch xe before it overflows the left shift below
   127  			// Since i !=0 it has at least one bit still set, so ae will accumulate xe
   128  			// on at least one more iteration, ae += xe is a lower bound on ae
   129  			// the lower bound on ae exceeds the size of a float64 exp
   130  			// so the final call to Ldexp will produce under/overflow (0/Inf)
   131  			ae += xe
   132  			break
   133  		}
   134  		if i&1 == 1 {
   135  			a1 *= x1
   136  			ae += xe
   137  		}
   138  		x1 *= x1
   139  		xe <<= 1
   140  		if x1 < .5 {
   141  			x1 += x1
   142  			xe--
   143  		}
   144  	}
   145  
   146  	// ans = a1*2**ae
   147  	// if y < 0 { ans = 1 / ans }
   148  	// but in the opposite order
   149  	if y < 0 {
   150  		a1 = 1 / a1
   151  		ae = -ae
   152  	}
   153  	return Ldexp(a1, ae)
   154  }