go源码阅读笔记（math.1）

abs.go

func Abs(x float64) float64

package math

// Abs returns the absolute value of x.
//
// Special cases are:
//  Abs(±Inf) = +Inf
//  Abs(NaN) = NaN
func Abs(x float64) float64 {
    // TODO: once golang.org/issue/13095 is fixed, change this to:
    // return Float64frombits(Float64bits(x) &^ (1 << 63))
    // But for now, this generates better code and can also be inlined:
    if x < 0 {
        return -x
    }
    if x == 0 {
        return 0 // return correctly abs(-0)
    }
    return x
}

求一个数的绝对值Abs()函数
主要地方在于
if x == 0 {
return 0 // return correctly abs(-0)
}

这里是考虑当x=-0的场景，所以返回0

bits.go

const (
    uvnan    = 0x7FF8000000000001
    uvinf    = 0x7FF0000000000000
    uvneginf = 0xFFF0000000000000
    mask     = 0x7FF
    shift    = 64 - 11 - 1
    bias     = 1023
)

数值表示遵循IEEE 754标准

• uvnan,NaN, Not a Number
• uvinf,正无穷大
• uvneginf,负无穷大

函数func Inf(sign int) float64

// Inf returns positive infinity if sign >= 0, negative infinity if sign < 0.
func Inf(sign int) float64 {
    var v uint64
    if sign >= 0 {
        v = uvinf
    } else {
        v = uvneginf
    }
    return Float64frombits(v)
}

如果sign是正数，就返回正无穷大，如果是负数就返回负无穷大

func NaN() float64

// NaN returns an IEEE 754 ``not-a-number'' value.
func NaN() float64 { return Float64frombits(uvnan) }

NaN()返回NaN值

func IsNaN(f float64) (is bool)

// IsNaN reports whether f is an IEEE 754 ``not-a-number'' value.
func IsNaN(f float64) (is bool) {
    // IEEE 754 says that only NaNs satisfy f != f.
    // To avoid the floating-point hardware, could use:
    //  x := Float64bits(f);
    //  return uint32(x>>shift)&mask == mask && x != uvinf && x != uvneginf
    return f != f
}

该函数判断一个数是否是NaN
如果不想使用浮点硬件，可以按照注释所说的这种方式计算

x := Float64bits(f);
return uint32(x>>shift)&mask == mask && x != uvinf && x != uvneginf

uint32(x>>shift)&mask == mask，x的高12位为0x7FF
x != uvinf，x不是正无穷大
x != uvneginf，x不是负无穷大

func IsInf(f float64, sign int) bool

// 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 float64, sign int) bool {
    // Test for infinity by comparing against maximum float.
    // To avoid the floating-point hardware, could use:
    //  x := Float64bits(f);
    //  return sign >= 0 && x == uvinf || sign <= 0 && x == uvneginf;
    return sign >= 0 && f > MaxFloat64 || sign <= 0 && f < -MaxFloat64
}

判断一个数是不是无穷大数

同样，如果不想使用浮点硬件，可以按照注释所说的这种方式计算

func normalize(x float64) (y float64, exp int)

// normalize returns a normal number y and exponent exp
// satisfying x == y × 2**exp. It assumes x is finite and non-zero.
func normalize(x float64) (y float64, exp int) {
    const SmallestNormal = 2.2250738585072014e-308 // 2**-1022
    if Abs(x) < SmallestNormal {
        return x * (1 << 52), -52
    }
    return x, 0
}

这个不懂什么意思

遗留问题，MaxFloat64和-MaxFloat64是多少呢？

另一个

Float64frombits(v)像是把一个数转化成float64，是如何实现的呢？

一些数学函数……

func Acosh(x float64) float64
返回x的反双曲余弦值
func Asin(x float64) float64
func Acos(x float64) float64
func Asinh(x float64) float64
func Atan(x float64) float64
func Atan2(y, x float64) float64
func Atanh(x float64) float64