Source File
pow.go
Belonging Package
math
// Copyright 2009 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 math
func isOddInt( float64) bool {
if Abs() >= (1 << 53) {
// 1 << 53 is the largest exact integer in the float64 format.
// Any number outside this range will be truncated before the decimal point and therefore will always be
// an even integer.
// Without this check and if x overflows int64 the int64(xi) conversion below may produce incorrect results
// on some architectures (and does so on arm64). See issue #57465.
return false
}
, := Modf()
return == 0 && int64()&1 == 1
}
// Special cases taken from FreeBSD's /usr/src/lib/msun/src/e_pow.c
// updated by IEEE Std. 754-2008 "Section 9.2.1 Special values".
// Pow returns x**y, the base-x exponential of y.
//
// Special cases are (in order):
//
// Pow(x, ±0) = 1 for any x
// Pow(1, y) = 1 for any y
// Pow(x, 1) = x for any x
// Pow(NaN, y) = NaN
// Pow(x, NaN) = NaN
// Pow(±0, y) = ±Inf for y an odd integer < 0
// Pow(±0, -Inf) = +Inf
// Pow(±0, +Inf) = +0
// Pow(±0, y) = +Inf for finite y < 0 and not an odd integer
// Pow(±0, y) = ±0 for y an odd integer > 0
// Pow(±0, y) = +0 for finite y > 0 and not an odd integer
// Pow(-1, ±Inf) = 1
// Pow(x, +Inf) = +Inf for |x| > 1
// Pow(x, -Inf) = +0 for |x| > 1
// Pow(x, +Inf) = +0 for |x| < 1
// Pow(x, -Inf) = +Inf for |x| < 1
// Pow(+Inf, y) = +Inf for y > 0
// Pow(+Inf, y) = +0 for y < 0
// Pow(-Inf, y) = Pow(-0, -y)
// Pow(x, y) = NaN for finite x < 0 and finite non-integer y
func (, float64) float64 {
if haveArchPow {
return archPow(, )
}
return pow(, )
}
func pow(, float64) float64 {
switch {
case == 0 || == 1:
return 1
case == 1:
return
case IsNaN() || IsNaN():
return NaN()
case == 0:
switch {
case < 0:
if Signbit() && isOddInt() {
return Inf(-1)
}
return Inf(1)
case > 0:
if Signbit() && isOddInt() {
return
}
return 0
}
case IsInf(, 0):
switch {
case == -1:
return 1
case (Abs() < 1) == IsInf(, 1):
return 0
default:
return Inf(1)
}
case IsInf(, 0):
if IsInf(, -1) {
return Pow(1/, -) // Pow(-0, -y)
}
switch {
case < 0:
return 0
case > 0:
return Inf(1)
}
case == 0.5:
return Sqrt()
case == -0.5:
return 1 / Sqrt()
}
, := Modf(Abs())
if != 0 && < 0 {
return NaN()
}
if >= 1<<63 {
// yi is a large even int that will lead to overflow (or underflow to 0)
// for all x except -1 (x == 1 was handled earlier)
switch {
case == -1:
return 1
case (Abs() < 1) == ( > 0):
return 0
default:
return Inf(1)
}
}
// ans = a1 * 2**ae (= 1 for now).
:= 1.0
:= 0
// ans *= x**yf
if != 0 {
if > 0.5 {
--
++
}
= Exp( * Log())
}
// ans *= x**yi
// by multiplying in successive squarings
// of x according to bits of yi.
// accumulate powers of two into exp.
, := Frexp()
for := int64(); != 0; >>= 1 {
if < -1<<12 || 1<<12 < {
// catch xe before it overflows the left shift below
// Since i !=0 it has at least one bit still set, so ae will accumulate xe
// on at least one more iteration, ae += xe is a lower bound on ae
// the lower bound on ae exceeds the size of a float64 exp
// so the final call to Ldexp will produce under/overflow (0/Inf)
+=
break
}
if &1 == 1 {
*=
+=
}
*=
<<= 1
if < .5 {
+=
--
}
}
// ans = a1*2**ae
// if y < 0 { ans = 1 / ans }
// but in the opposite order
if < 0 {
= 1 /
= -
}
return Ldexp(, )
}
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