math
import "math"
math包提供了基本的数学常数和数学函数。
const ( E = 2.71828182845904523536028747135266249775724709369995957496696763 // A001113 Pi = 3.14159265358979323846264338327950288419716939937510582097494459 // A000796 Phi = 1.61803398874989484820458683436563811772030917980576286213544862 // A001622 Sqrt2 = 1.41421356237309504880168872420969807856967187537694807317667974 // A002193 SqrtE = 1.64872127070012814684865078781416357165377610071014801157507931 // A019774 SqrtPi = 1.77245385090551602729816748334114518279754945612238712821380779 // A002161 SqrtPhi = 1.27201964951406896425242246173749149171560804184009624861664038 // A139339 Ln2 = 0.693147180559945309417232121458176568075500134360255254120680009 // A002162 Log2E = 1 / Ln2 Ln10 = 2.30258509299404568401799145468436420760110148862877297603332790 // A002392 Log10E = 1 / Ln10 )
数学常数,参见:http://oeis.org/Axxxxxx
const ( MaxFloat32 = 3.40282346638528859811704183484516925440e+38 // 2**127 * (2**24 - 1) / 2**23 SmallestNonzeroFloat32 = 1.401298464324817070923729583289916131280e-45 // 1 / 2**(127 - 1 + 23) MaxFloat64 = 1.797693134862315708145274237317043567981e+308 // 2**1023 * (2**53 - 1) / 2**52 SmallestNonzeroFloat64 = 4.940656458412465441765687928682213723651e-324 // 1 / 2**(1023 - 1 + 52) )
浮点数的取值极限。Max是该类型所能表示的最大有限值;SmallestNonzero是该类型所能表示的最小非零正数值。
const ( MaxInt8 = 1<<7 - 1 MinInt8 = -1 << 7 MaxInt16 = 1<<15 - 1 MinInt16 = -1 << 15 MaxInt32 = 1<<31 - 1 MinInt32 = -1 << 31 MaxInt64 = 1<<63 - 1 MinInt64 = -1 << 63 MaxUint8 = 1<<8 - 1 MaxUint16 = 1<<16 - 1 MaxUint32 = 1<<32 - 1 MaxUint64 = 1<<64 - 1 )
整数的取值极限。
func NaN
func NaN() float64
函数返回一个IEEE 754“这不是一个数字”值。
func IsNaN
func IsNaN(f float64) (is bool)
报告f是否表示一个NaN(Not A Number)值。
func Inf
func Inf(sign int) float64
如果sign>=0函数返回正无穷大,否则返回负无穷大。
func IsInf
func IsInf(f float64, sign int) bool
如果sign > 0,f是正无穷大时返回真;如果sign<0,f是负无穷大时返回真;sign==0则f是两种无穷大时都返回真。
func Float32bits
func Float32bits(f float32) uint32
函数返回浮点数f的IEEE 754格式二进制表示对应的4字节无符号整数。
func Float32frombits
func Float32frombits(b uint32) float32
函数返回无符号整数b对应的IEEE 754格式二进制表示的4字节浮点数。
func Float64bits
func Float64bits(f float64) uint64
函数返回浮点数f的IEEE 754格式二进制表示对应的8字节无符号整数。
func Float64frombits
func Float64frombits(b uint64) float64
函数返回无符号整数b对应的IEEE 754格式二进制表示的8字节浮点数。
func Signbit
func Signbit(x float64) bool
如果x是一个负数或者负零,返回真。
func Copysign
func Copysign(x, y float64) float64
返回拥有x的量值(绝对值)和y的标志位(正负号)的浮点数。
func Ceil
func Ceil(x float64) float64
返回不小于x的最小整数(的浮点值),特例如下:
Ceil(±0) = ±0 Ceil(±Inf) = ±Inf Ceil(NaN) = NaN
func Floor
func Floor(x float64) float64
返回不大于x的最大整数(的浮点值),特例如下:
Floor(±0) = ±0 Floor(±Inf) = ±Inf Floor(NaN) = NaN
func Trunc
func Trunc(x float64) float64
返回x的整数部分(的浮点值)。特例如下:
Trunc(±0) = ±0 Trunc(±Inf) = ±Inf Trunc(NaN) = NaN
func Modf
func Modf(f float64) (int float64, frac float64)
返回f的整数部分和小数部分,结果的正负号和都x相同;特例如下:
Modf(±Inf) = ±Inf, NaN Modf(NaN) = NaN, NaN
func Nextafter
func Nextafter(x, y float64) (r float64)
参数x到参数y的方向上,下一个可表示的数值;如果x==y将返回x。特例如下:
Nextafter(NaN, y) = NaN Nextafter(x, NaN) = NaN
func Abs
func Abs(x float64) float64
返回x的绝对值;特例如下:
Abs(±Inf) = +Inf Abs(NaN) = NaN
func Max
func Max(x, y float64) float64
返回x和y中最大值,特例如下:
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 Min
func Min(x, y float64) float64
返回x和y中最小值,特例如下:
Min(x, -Inf) = Min(-Inf, x) = -Inf Min(x, NaN) = Min(NaN, x) = NaN Min(-0, ±0) = Min(±0, -0) = -0
func Dim
func Dim(x, y float64) float64
函数返回x-y和0中的最大值,特殊情况:
Dim(+Inf, +Inf) = NaN Dim(-Inf, -Inf) = NaN Dim(x, NaN) = Dim(NaN, x) = NaN
func Mod
func Mod(x, y float64) float64
取余运算,可以理解为 x-Trunc(x/y)*y,结果的正负号和x相同;特例如下:
Mod(±Inf, y) = NaN Mod(NaN, y) = NaN Mod(x, 0) = NaN Mod(x, ±Inf) = x Mod(x, NaN) = NaN
func Remainder
func Remainder(x, y float64) float64
IEEE 754差数求值,即x减去最接近x/y的整数值(如果有两个整数与x/y距离相同,则取其中的偶数)与y的乘积。特例如下:
Remainder(±Inf, y) = NaN Remainder(NaN, y) = NaN Remainder(x, 0) = NaN Remainder(x, ±Inf) = x Remainder(x, NaN) = NaN
func Sqrt
func Sqrt(x float64) float64
返回x的二次方根,特例如下:
Sqrt(+Inf) = +Inf Sqrt(±0) = ±0 Sqrt(x < 0) = NaN Sqrt(NaN) = NaN
func Cbrt
func Cbrt(x float64) float64
返回x的三次方根,特例如下:
Cbrt(±0) = ±0 Cbrt(±Inf) = ±Inf Cbrt(NaN) = NaN
func Hypot
func Hypot(p, q float64) float64
返回Sqrt(p*p + q*q),注意要避免不必要的溢出或下溢。特例如下:
Hypot(±Inf, q) = +Inf Hypot(p, ±Inf) = +Inf Hypot(NaN, q) = NaN Hypot(p, NaN) = NaN
func Sin
func Sin(x float64) float64
求正弦。特例如下:
Sin(±0) = ±0 Sin(±Inf) = NaN Sin(NaN) = NaN
func Cos
func Cos(x float64) float64
求余弦。特例如下:
Cos(±Inf) = NaN Cos(NaN) = NaN
func Tan
func Tan(x float64) float64
求正切。特例如下:
Tan(±0) = ±0 Tan(±Inf) = NaN Tan(NaN) = NaN
func Sincos
func Sincos(x float64) (sin, cos float64)
函数返回Sin(x), Cos(x)。特例如下:
Sincos(±0) = ±0, 1 Sincos(±Inf) = NaN, NaN Sincos(NaN) = NaN, NaN
func Asin
func Asin(x float64) float64
求反正弦(x是弧度)。特例如下:
Asin(±0) = ±0 Asin(x) = NaN if x < -1 or x > 1
func Acos
func Acos(x float64) float64
求反余弦(x是弧度)。特例如下:
Acos(x) = NaN if x < -1 or x > 1
func Atan
func Atan(x float64) float64
求反正切(x是弧度)。特例如下:
Atan(±0) = ±0 Atan(±Inf) = ±Pi/2
func Atan2
func Atan2(y, x float64) float64
类似Atan(y/x),但会根据x,y的正负号确定象限。特例如下(前面的优先):
Atan2(y, NaN) = NaN Atan2(NaN, x) = NaN Atan2(+0, x>=0) = +0 Atan2(-0, x>=0) = -0 Atan2(+0, x<=-0) = +Pi Atan2(-0, x<=-0) = -Pi Atan2(y>0, 0) = +Pi/2 Atan2(y<0, 0) = -Pi/2 Atan2(+Inf, +Inf) = +Pi/4 Atan2(-Inf, +Inf) = -Pi/4 Atan2(+Inf, -Inf) = 3Pi/4 Atan2(-Inf, -Inf) = -3Pi/4 Atan2(y, +Inf) = 0 Atan2(y>0, -Inf) = +Pi Atan2(y<0, -Inf) = -Pi Atan2(+Inf, x) = +Pi/2 Atan2(-Inf, x) = -Pi/2
func Sinh
func Sinh(x float64) float64
求双曲正弦,特例如下:
Sinh(±0) = ±0 Sinh(±Inf) = ±Inf Sinh(NaN) = NaN
func Cosh
func Cosh(x float64) float64
求双曲余弦,特例如下:
Cosh(±0) = 1 Cosh(±Inf) = +Inf Cosh(NaN) = NaN
func Tanh
func Tanh(x float64) float64
求双曲正切,特例如下:
Tanh(±0) = ±0 Tanh(±Inf) = ±1 Tanh(NaN) = NaN
func Asinh
func Asinh(x float64) float64
求反双曲正弦,特例如下:
Asinh(±0) = ±0 Asinh(±Inf) = ±Inf Asinh(NaN) = NaN
func Acosh
func Acosh(x float64) float64
求反双曲余弦,特例如下:
Acosh(+Inf) = +Inf Acosh(x) = NaN if x < 1 Acosh(NaN) = NaN
func Atanh
func Atanh(x float64) float64
求反双曲正切,特例如下:
Atanh(1) = +Inf Atanh(±0) = ±0 Atanh(-1) = -Inf Atanh(x) = NaN if x < -1 or x > 1 Atanh(NaN) = NaN
func Log
func Log(x float64) float64
求自然对数,特例如下:
Log(+Inf) = +Inf Log(0) = -Inf Log(x < 0) = NaN Log(NaN) = NaN
func Log1p
func Log1p(x float64) float64
等价于Log(1+x)。但是在x接近0时,本函数更加精确;特例如下:
Log1p(+Inf) = +Inf Log1p(±0) = ±0 Log1p(-1) = -Inf Log1p(x < -1) = NaN Log1p(NaN) = NaN
func Log2
func Log2(x float64) float64
求2为底的对数;特例和Log相同。
func Log10
func Log10(x float64) float64
求10为底的对数;特例和Log相同。
func Logb
func Logb(x float64) float64
返回x的二进制指数值,可以理解为Trunc(Log2(x));特例如下:
Logb(±Inf) = +Inf Logb(0) = -Inf Logb(NaN) = NaN
func Ilogb
func Ilogb(x float64) int
类似Logb,但返回值是整型;特例如下:
Ilogb(±Inf) = MaxInt32 Ilogb(0) = MinInt32 Ilogb(NaN) = MaxInt32
func Frexp
func Frexp(f float64) (frac float64, exp int)
返回一个标准化小数frac和2的整型指数exp,满足f == frac * 2**exp,且0.5 <= Abs(frac) < 1;特例如下:
Frexp(±0) = ±0, 0 Frexp(±Inf) = ±Inf, 0 Frexp(NaN) = NaN, 0
func Ldexp
func Ldexp(frac float64, exp int) float64
Frexp的反函数,返回 frac * 2**exp。特例如下:
Ldexp(±0, exp) = ±0 Ldexp(±Inf, exp) = ±Inf Ldexp(NaN, exp) = NaN
func Exp
func Exp(x float64) float64
返回E**x;x绝对值很大时可能会溢出为0或者+Inf,x绝对值很小时可能会下溢为1。特例如下:
Exp(+Inf) = +Inf Exp(NaN) = NaN
func Expm1
func Expm1(x float64) float64
等价于Exp(x)-1,但是在x接近零时更精确;x绝对值很大时可能会溢出为-1或+Inf。特例如下:
Expm1(+Inf) = +Inf Expm1(-Inf) = -1 Expm1(NaN) = NaN
func Exp2
func Exp2(x float64) float64
返回2**x;特例和Exp相同。
func Pow
func Pow(x, y float64) float64
返回x**y;特例如下(前面的优先):
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 Pow10
func Pow10(e int) float64
返回10**e;特例如下:
Pow10(e) = +Inf for e > 309 Pow10(e) = 0 for e < -324
func Gamma
func Gamma(x float64) float64
伽玛函数(当x为正整数时,值为(x-1)!)。特例如下:
Gamma(+Inf) = +Inf Gamma(+0) = +Inf Gamma(-0) = -Inf Gamma(x) = NaN for integer x < 0 Gamma(-Inf) = NaN Gamma(NaN) = NaN
func Lgamma
func Lgamma(x float64) (lgamma float64, sign int)
返回Gamma(x)的自然对数和正负号。特例如下:
Lgamma(+Inf) = +Inf Lgamma(0) = +Inf Lgamma(-integer) = +Inf Lgamma(-Inf) = -Inf Lgamma(NaN) = NaN
func Erf
func Erf(x float64) float64
误差函数,特例如下:
Erf(+Inf) = 1 Erf(-Inf) = -1 Erf(NaN) = NaN
func Erfc
func Erfc(x float64) float64
余补误差函数,特例如下:
Erfc(+Inf) = 0 Erfc(-Inf) = 2 Erfc(NaN) = NaN
func J0
func J0(x float64) float64
第一类贝塞尔函数,0阶。特例如下:
J0(±Inf) = 0 J0(0) = 1 J0(NaN) = NaN
func J1
func J1(x float64) float64
第一类贝塞尔函数,1阶。特例如下:
J1(±Inf) = 0 J1(NaN) = NaN
func Jn
func Jn(n int, x float64) float64
第一类贝塞尔函数,n阶。特例如下:
Jn(n, ±Inf) = 0 Jn(n, NaN) = NaN
func Y0
func Y0(x float64) float64
第二类贝塞尔函数,0阶。特例如下:
Y0(+Inf) = 0 Y0(0) = -Inf Y0(x < 0) = NaN Y0(NaN) = NaN
func Y1
func Y1(x float64) float64
第二类贝塞尔函数,1阶。特例如下:
Y1(+Inf) = 0 Y1(0) = -Inf Y1(x < 0) = NaN Y1(NaN) = NaN
func Yn
func Yn(n int, x float64) float64
第二类贝塞尔函数,n阶。特例如下:
Yn(n, +Inf) = 0 Yn(n > 0, 0) = -Inf Yn(n < 0, 0) = +Inf if n is odd, -Inf if n is even Y1(n, x < 0) = NaN Y1(n, NaN) = NaN