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// 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.
// Copyright ©2015 The Gonum 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 math32
import (
"math"
)
const (
unan = 0x7fc00000
uinf = 0x7f800000
uneginf = 0xff800000
mask = 0x7f8 >> 3
shift = 32 - 8 - 1
bias = 127
)
// Abs returns the absolute value of x.
//
// Special cases are:
//
// Abs(±Inf) = +Inf
// Abs(NaN) = NaN
func Abs(x float32) float32 {
switch {
case x < 0:
return -x
case x == 0:
return 0 // return correctly abs(-0)
}
return x
}
// Copysign returns a value with the magnitude
// of x and the sign of y.
func Copysign(x, y float32) float32 {
const sign = 1 << 31
return math.Float32frombits(math.Float32bits(x)&^sign | math.Float32bits(y)&sign)
}
// 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
// Hypot(p, NaN) = NaN
func Hypot(p, q float32) float32 {
// special cases
switch {
case IsInf(p, 0) || IsInf(q, 0):
return Inf(1)
case IsNaN(p) || IsNaN(q):
return NaN()
}
if p < 0 {
p = -p
}
if q < 0 {
q = -q
}
if p < q {
p, q = q, p
}
if p == 0 {
return 0
}
q = q / p
return p * Sqrt(1+q*q)
}
// Inf returns positive infinity if sign >= 0, negative infinity if sign < 0.
func Inf(sign int) float32 {
var v uint32
if sign >= 0 {
v = uinf
} else {
v = uneginf
}
return math.Float32frombits(v)
}
// IsInf reports whether f is an infinity, according to sign.
// If sign > 0, IsInf reports whether f is positive infinity.
// If sign < 0, IsInf reports whether f is negative infinity.
// If sign == 0, IsInf reports whether f is either infinity.
func IsInf(f float32, sign int) bool {
// Test for infinity by comparing against maximum float.
// To avoid the floating-point hardware, could use:
// x := math.Float32bits(f);
// return sign >= 0 && x == uinf || sign <= 0 && x == uneginf;
return sign >= 0 && f > math.MaxFloat32 || sign <= 0 && f < -math.MaxFloat32
}
// IsNaN reports whether f is an IEEE 754 “not-a-number” value.
func IsNaN(f float32) (is bool) {
// IEEE 754 says that only NaNs satisfy f != f.
// To avoid the floating-point hardware, could use:
// x := math.Float32bits(f);
// return uint32(x>>shift)&mask == mask && x != uinf && x != uneginf
return f != f
}
// Max returns the larger of x or y.
//
// Special cases are:
//
// Max(x, +Inf) = Max(+Inf, x) = +Inf
// Max(x, NaN) = Max(NaN, x) = NaN
// Max(+0, ±0) = Max(±0, +0) = +0
// Max(-0, -0) = -0
func Max(x, y float32) float32 {
// special cases
switch {
case IsInf(x, 1) || IsInf(y, 1):
return Inf(1)
case IsNaN(x) || IsNaN(y):
return NaN()
case x == 0 && x == y:
if Signbit(x) {
return y
}
return x
}
if x > y {
return x
}
return y
}
// Min returns the smaller of x or y.
//
// Special cases are:
//
// Min(x, -Inf) = Min(-Inf, x) = -Inf
// Min(x, NaN) = Min(NaN, x) = NaN
// Min(-0, ±0) = Min(±0, -0) = -0
func Min(x, y float32) float32 {
// special cases
switch {
case IsInf(x, -1) || IsInf(y, -1):
return Inf(-1)
case IsNaN(x) || IsNaN(y):
return NaN()
case x == 0 && x == y:
if Signbit(x) {
return x
}
return y
}
if x < y {
return x
}
return y
}
// NaN returns an IEEE 754 “not-a-number” value.
func NaN() float32 { return math.Float32frombits(unan) }
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