go源碼閱讀筆記（math.1）

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go源碼閱讀筆記（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) = NaNfunc 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}

求一個數的絕對值Abs()函數
主要地方在於
if x == 0 {
return 0 // return correctly abs(-0)
}

這裡是考慮當x=-0的情境，所以返回0

bits.go

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

數值表示遵循IEEE 754標準

• uvnan,NaN, Not a Number
• uvinf,正無窮大
• uvneginf,負無窮大

函數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是正數，就返回正無窮大，如果是負數就返回負無窮大

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}

該函數判斷一個數是否是NaN
如果不想使用浮點硬體，可以按照注釋所說的這種方式計算

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

uint32(x>>shift)&mask == mask，x的高12位為0x7FF
x != uvinf，x不是正無窮大
x != uvneginf，x不是負無窮大

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}

判斷一個數是不是無窮大數

同樣，如果不想使用浮點硬體，可以按照注釋所說的這種方式計算

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}

這個不懂什麼意思

遺留問題，MaxFloat64和-MaxFloat64是多少呢？

另一個

Float64frombits(v)像是把一個數轉化成float64，是如何?的呢？

一些數學函數……

func Acosh(x float64) float64
返回x的反雙曲餘弦值
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