Package math
Overview ▾ Package math provides basic constants and mathematical functions. math包 提供 基本常量和数学函数。
Constants
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
) Mathematical constants. Reference: http://oeis.org/Axxxxxx 数学常数
const ( MaxFloat32 = 3.40282346638528859811704183484516925440e+38 // 2127 * (224 - 1) / 223 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)
) Floating-point limit values. Max is the largest finite value representable by the type. SmallestNonzero is the smallest positive, non-zero value representable by the type. 浮点型限制值. Max是 该类型的 最大有限值 SmallestNonzero表示该类型的一个最小的正,非零值
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 ) Integer limit values. 整数限制值。
func Abs
func Abs(x float64) float64 Abs returns the absolute value of x. Abs返回x的绝对值
Special cases are: 特殊情况:
Abs(±Inf) = +Inf Abs(NaN) = NaN
func Acos
func Acos(x float64) float64 Acos returns the arccosine, in radians, of x. Acos返回反余弦值x
Special case is: 特殊情况: Acos(x) = NaN if x < -1 or x > 1
func Acosh
func Acosh(x float64) float64 Acosh returns the inverse hyperbolic cosine of x. Acosh 返回反双曲余弦值x。
Special cases are: 特殊情况:
Acosh(+Inf) = +Inf Acosh(x) = NaN if x < 1 Acosh(NaN) = NaN
func Asin
func Asin(x float64) float64 Asin returns the arcsine, in radians, of x. Asin返回x的反正弦
Special cases are: 特殊情况:
Asin(±0) = ±0 Asin(x) = NaN if x < -1 or x > 1
func Asinh
func Asinh(x float64) float64 Asinh returns the inverse hyperbolic sine of x. Asinh 返回x的反双曲正弦值。
Special cases are: 特殊情况:
Asinh(±0) = ±0 Asinh(±Inf) = ±Inf Asinh(NaN) = NaN
func Atan
func Atan(x float64) float64 Atan returns the arctangent, in radians, of x. Atan返回反正切值的x
Special cases are: 特殊情况:
Atan(±0) = ±0 Atan(±Inf) = ±Pi/2 func Atan2
func Atan2(y, x float64) float64 Atan2 returns the arc tangent of y/x, using the signs of the two to determine the quadrant of the return value. Atan2返回y/ x的反正切值，使用两个标志来确定返回值的象限。
Special cases are (in order): 特殊情况:
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 Atanh
func Atanh(x float64) float64 Atanh returns the inverse hyperbolic tangent of x. Atanh返回x的反双曲正切值。
Special cases are: 特殊情况:
Atanh(1) = +Inf Atanh(±0) = ±0 Atanh(-1) = -Inf Atanh(x) = NaN if x < -1 or x > 1 Atanh(NaN) = NaN
func Cbrt
func Cbrt(x float64) float64 Cbrt returns the cube root of x. Cbrt返回x的立方根。
Special cases are: 特殊情况:
Cbrt(±0) = ±0 Cbrt(±Inf) = ±Inf Cbrt(NaN) = NaN
func Ceil
func Ceil(x float64) float64 Ceil returns the least integer value greater than or equal to x. 返回大于所述至少一个整数值或等于x。
Special cases are: 特殊情况:
Ceil(±0) = ±0 Ceil(±Inf) = ±Inf Ceil(NaN) = NaN
func Copysign
func Copysign(x, y float64) float64 Copysign returns a value with the magnitude of x and the sign of y. Copysign返回一个值与x的绝对值和y的符号。
func Cos
func Cos(x float64) float64 Cos returns the cosine of the radian argument x. COS返回弧度参数x的余弦值。
Special cases are: 特殊情况:
Cos(±Inf) = NaN Cos(NaN) = NaN
func Cosh
func Cosh(x float64) float64 Cosh returns the hyperbolic cosine of x. Cosh返回x的双曲余弦值。
Special cases are: 特殊情况:
Cosh(±0) = 1 Cosh(±Inf) = +Inf Cosh(NaN) = NaN
func Dim
func Dim(x, y float64) float64 Dim returns the maximum of x-y or 0. Dim返回的最大x-y或0。
Special cases are: 特殊情况:
Dim(+Inf, +Inf) = NaN Dim(-Inf, -Inf) = NaN Dim(x, NaN) = Dim(NaN, x) = NaN
func Erf
func Erf(x float64) float64 Erf returns the error function of x. Erf返回x的误差函数。
Special cases are: 特殊情况:
Erf(+Inf) = 1 Erf(-Inf) = -1 Erf(NaN) = NaN
func Erfc
func Erfc(x float64) float64 Erfc returns the complementary error function of x. Erfc返回x的互补误差函数。
Special cases are: 特殊情况:
Erfc(+Inf) = 0 Erfc(-Inf) = 2 Erfc(NaN) = NaN
func Exp
func Exp(x float64) float64 Exp returns ex, the base-e exponential of x. Exp返回e X，基E X的指数。
Special cases are: 特殊情况:
Exp(+Inf) = +Inf Exp(NaN) = NaN Very large values overflow to 0 or +Inf. Very small values underflow to 1.
func Exp2
func Exp2(x float64) float64 Exp2 returns 2x, the base-2 exponential of x. Exp2 返回2的x，基部2的指数的x。
Special cases are the same as Exp. 特殊情况与ExpExp一样
func Expm1
func Expm1(x float64) float64 Expm1 returns ex - 1, the base-e exponential of x minus 1. It is more accurate than Exp(x) - 1 when x is near zero. 返回e× - 1，x的基e指数减1。 它比Exp(x）的更准确 - 1，当x接近零。
Special cases are: 特殊情况:
Expm1(+Inf) = +Inf Expm1(-Inf) = -1 Expm1(NaN) = NaN Very large values overflow to -1 or +Inf. 非常大的值溢出到-1或+Inf
func Float32bits
func Float32bits(f float32) uint32 Float32bits returns the IEEE 754 binary representation of f. Float32bits返回f的IEEE 754二进制表示。
func Float32frombits
func Float32frombits(b uint32) float32 Float32frombits returns the floating point number corresponding to the IEEE 754 binary representation b. Float32frombits返回对应于IEEE 754的二进制表示B中的浮点数。
func Float64bits
func Float64bits(f float64) uint64 Float64bits returns the IEEE 754 binary representation of f. Float64bits返回f的IEEE 754二进制表示。
func Float64frombits
func Float64frombits(b uint64) float64 Float64frombits returns the floating point number corresponding the IEEE 754 binary representation b. Float64frombits返回相应的IEEE 754二进制表示B中的浮点数。
func Floor
func Floor(x float64) float64 Floor returns the greatest integer value less than or equal to x. Floor返回的最大整数的值小于或等于x。
Special cases are: 特殊情况:
Floor(±0) = ±0 Floor(±Inf) = ±Inf Floor(NaN) = NaN
func Frexp
func Frexp(f float64) (frac float64, exp int) Frexp breaks f into a normalized fraction and an integral power of two. It returns frac and exp satisfying f == frac × 2exp, with the absolute value of frac in the interval [½, 1). Frexp 分解f成 正常化的分数和为2的整数幂 它返回 frac 和 exp 满足 f == frac × 2exp, 在区间 [½, 1) 中的 frac的绝对值.
Special cases are: 特殊情况:
Frexp(±0) = ±0, 0 Frexp(±Inf) = ±Inf, 0 Frexp(NaN) = NaN, 0
func Gamma
func Gamma(x float64) float64 Gamma returns the Gamma function of x. Gamma返回x的Gamma函数
Special cases are: 特殊情况:
Gamma(+Inf) = +Inf Gamma(+0) = +Inf Gamma(-0) = -Inf Gamma(x) = NaN for integer x < 0 Gamma(-Inf) = NaN Gamma(NaN) = NaN
func Hypot
func Hypot(p, q float64) float64 Hypot returns Sqrt(pp + qq), taking care to avoid unnecessary overflow and underflow. Hypot返回 Sqrt(pp + qq),同时注意避免不必要的溢出和下溢。
Special cases are: 特殊情况:
Hypot(±Inf, q) = +Inf Hypot(p, ±Inf) = +Inf Hypot(NaN, q) = NaN Hypot(p, NaN) = NaN
func Ilogb
func Ilogb(x float64) int Ilogb returns the binary exponent of x as an integer. Ilogb返回x的二进制指数为整数。
Special cases are: 特殊情况:
Ilogb(±Inf) = MaxInt32 Ilogb(0) = MinInt32 Ilogb(NaN) = MaxInt32
func Inf
func Inf(sign int) float64 Inf returns positive infinity if sign >= 0, negative infinity if sign < 0. Inf 返回 如果 sign >= 0 是 无穷大, 如果 sign < 0 无穷小.
func IsInf
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. IsInf 根据sign 报告f是否是无穷大.
func IsNaN
func IsNaN(f float64) (is bool) IsNaN reports whether f is an IEEE 754 “not-a-number” value. IsNaN 报告f是否是IEEE754“不是一个数”值。
func J0
func J0(x float64) float64 J0 returns the order-zero Bessel function of the first kind. 返回第一种 0阶的 Bessel 函数
Special cases are: 特殊情况:
J0(±Inf) = 0 J0(0) = 1 J0(NaN) = NaN
func J1
func J1(x float64) float64 J1 returns the order-one Bessel function of the first kind. 返回第一种 1阶的 Bessel 函数
Special cases are: 特殊情况:
J1(±Inf) = 0 J1(NaN) = NaN
func Jn
func Jn(n int, x float64) float64 Jn returns the order-n Bessel function of the first kind. 返回第一种 N阶的 Bessel 函数
Special cases are: 特殊情况:
Jn(n, ±Inf) = 0 Jn(n, NaN) = NaN
func Ldexp
func Ldexp(frac float64, exp int) float64 Ldexp is the inverse of Frexp. It returns frac × 2exp. Ldexp是Frexp的倒数。它返回 frac × 2exp.
Special cases are: 特殊情况:
Ldexp(±0, exp) = ±0 Ldexp(±Inf, exp) = ±Inf Ldexp(NaN, exp) = NaN
func Lgamma
func Lgamma(x float64) (lgamma float64, sign int) Lgamma returns the natural logarithm and sign (-1 or +1) of Gamma(x). Lgamma返回自然对数 Gamma(x)的sign (-1 or +1)
Special cases are: 特殊情况:
Lgamma(+Inf) = +Inf Lgamma(0) = +Inf Lgamma(-integer) = +Inf Lgamma(-Inf) = -Inf Lgamma(NaN) = NaN
func Log
func Log(x float64) float64 Log returns the natural logarithm of x. Log返回x的自然对数。
Special cases are: 特殊情况:
Log(+Inf) = +Inf Log(0) = -Inf Log(x < 0) = NaN Log(NaN) = NaN
func Log10
func Log10(x float64) float64 Log10 returns the decimal logarithm of x. The special cases are the same as for Log. Log10返回x的十进制数.特殊情况 和Log一样
func Log1p
func Log1p(x float64) float64 Log1p returns the natural logarithm of 1 plus its argument x. It is more accurate than Log(1 + x) when x is near zero. 返回1的自然对数加上它的参数x 当x接近零的时候 它比 Log(1 + x) 更准确
Special cases are: 特殊情况:
Log1p(+Inf) = +Inf Log1p(±0) = ±0 Log1p(-1) = -Inf Log1p(x < -1) = NaN Log1p(NaN) = NaN
func Log2
func Log2(x float64) float64 Log2 returns the binary logarithm of x. The special cases are the same as for Log. Log2返回x的二进制数。特殊情况 和Log一样
func Logb
func Logb(x float64) float64 Logb returns the binary exponent of x. Logb返回x的二进制指数。
Special cases are: 特殊情况:
Logb(±Inf) = +Inf Logb(0) = -Inf Logb(NaN) = NaN
func Max
func Max(x, y float64) float64 Max returns the larger of x or y. 返回x和y中的最大值
Special cases are: 特殊情况:
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 Min returns the smaller of x or y. 返回x和y中的最小值
Special cases are: 特殊情况:
Min(x, -Inf) = Min(-Inf, x) = -Inf Min(x, NaN) = Min(NaN, x) = NaN Min(-0, ±0) = Min(±0, -0) = -0
func Mod
func Mod(x, y float64) float64 Mod returns the floating-point remainder of x/y. The magnitude of the result is less than y and its sign agrees with that of x. Mod 返回 x/y剩余的浮点值(就是数学中的模) 结果的幅值小于y ,符号取决于x
Special cases are: 特殊情况:
Mod(±Inf, y) = NaN Mod(NaN, y) = NaN Mod(x, 0) = NaN Mod(x, ±Inf) = x Mod(x, NaN) = NaN
func Modf
func Modf(f float64) (int float64, frac float64) Modf returns integer and fractional floating-point numbers that sum to f. Both values have the same sign as f. 返回整数和小数的浮点数字，总和为f。 这两个值都是和f 相同的符号。
Special cases are: 特殊情况:
Modf(±Inf) = ±Inf, NaN Modf(NaN) = NaN, NaN
func NaN
func NaN() float64 NaN returns an IEEE 754 “not-a-number” value. NaN返回一个IEEE 754“不是一个数”值。
func Nextafter
func Nextafter(x, y float64) (r float64) Nextafter returns the next representable value after x towards y. If x == y, then x is returned. 返回下一个 在x指向y 后 表示的值. 如果 x == y, 返回x
Special cases are: 特殊情况:
Nextafter(NaN, y) = NaN Nextafter(x, NaN) = NaN
func Pow
func Pow(x, y float64) float64 Pow returns xy, the base-x exponential of y. Pow 返回xy,y的基X的指数。
Special cases are (in order): 特殊情况:
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 Pow10 returns 10e, the base-10 exponential of e. 返回 10e,e的基10指数。
Special cases are: 特殊情况:
Pow10(e) = +Inf for e > 309 Pow10(e) = 0 for e < -324
func Remainder
func Remainder(x, y float64) float64 Remainder returns the IEEE 754 floating-point remainder of x/y. 返回 x/y 剩余的 IEEE 754浮点型
Special cases are: 特殊情况:
Remainder(±Inf, y) = NaN Remainder(NaN, y) = NaN Remainder(x, 0) = NaN Remainder(x, ±Inf) = x Remainder(x, NaN) = NaN
func Signbit
func Signbit(x float64) bool Signbit returns true if x is negative or negative zero. 如果x是负或者负0 返回true
func Sin
func Sin(x float64) float64 Sin returns the sine of the radian argument x. 返回弧度参数x的正弦值。
Special cases are: 特殊情况:
Sin(±0) = ±0 Sin(±Inf) = NaN Sin(NaN) = NaN
func Sincos
func Sincos(x float64) (sin, cos float64) Sincos returns Sin(x), Cos(x). 返回 Sin(x), Cos(x).
Special cases are: 特殊情况:
Sincos(±0) = ±0, 1 Sincos(±Inf) = NaN, NaN Sincos(NaN) = NaN, NaN
func Sinh
func Sinh(x float64) float64 Sinh returns the hyperbolic sine of x. 返回x的双曲正弦值。
Special cases are: 特殊情况:
Sinh(±0) = ±0 Sinh(±Inf) = ±Inf Sinh(NaN) = NaN
func Sqrt
func Sqrt(x float64) float64 Sqrt returns the square root of x. 返回x的平方根。
Special cases are: 特殊情况:
Sqrt(+Inf) = +Inf Sqrt(±0) = ±0 Sqrt(x < 0) = NaN Sqrt(NaN) = NaN
func Tan
func Tan(x float64) float64 Tan returns the tangent of the radian argument x. 返回弧度参数x的正切值。
Special cases are: 特殊情况:
Tan(±0) = ±0 Tan(±Inf) = NaN Tan(NaN) = NaN
func Tanh
func Tanh(x float64) float64 Tanh returns the hyperbolic tangent of x. 返回x的双曲正切值。
Special cases are: 特殊情况:
Tanh(±0) = ±0 Tanh(±Inf) = ±1 Tanh(NaN) = NaN
func Trunc
func Trunc(x float64) float64 Trunc returns the integer value of x. 返回x的整数值。
Special cases are: 特殊情况:
Trunc(±0) = ±0 Trunc(±Inf) = ±Inf Trunc(NaN) = NaN
func Y0
func Y0(x float64) float64 Y0 returns the order-zero Bessel function of the second kind. Y0返回 返回第二种 0阶的 Bessel 函数
Special cases are: 特殊情况:
Y0(+Inf) = 0 Y0(0) = -Inf Y0(x < 0) = NaN Y0(NaN) = NaN
func Y1
func Y1(x float64) float64 Y1 returns the order-one Bessel function of the second kind. Y1返回 返回第二种 1阶的 Bessel 函数
Special cases are: 特殊情况:
Y1(+Inf) = 0 Y1(0) = -Inf Y1(x < 0) = NaN Y1(NaN) = NaN
func Yn
func Yn(n int, x float64) float64 Yn returns the order-n Bessel function of the second kind. Yn返回 返回第二种n阶的 Bessel 函数
Special cases are: 特殊情况:
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