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Mathematical constants.

const ( E = 2.71828182845904523536028747135266249775724709369995957496696763 // http://oeis.org/A001113 Pi = 3.14159265358979323846264338327950288419716939937510582097494459 // http://oeis.org/A000796 Phi = 1.61803398874989484820458683436563811772030917980576286213544862 // http://oeis.org/A001622 Sqrt2 = 1.41421356237309504880168872420969807856967187537694807317667974 // http://oeis.org/A002193 SqrtE = 1.64872127070012814684865078781416357165377610071014801157507931 // http://oeis.org/A019774 SqrtPi = 1.77245385090551602729816748334114518279754945612238712821380779 // http://oeis.org/A002161 SqrtPhi = 1.27201964951406896425242246173749149171560804184009624861664038 // http://oeis.org/A139339 Ln2 = 0.693147180559945309417232121458176568075500134360255254120680009 // http://oeis.org/A002162 Log2E = 1 / Ln2 Ln10 = 2.30258509299404568401799145468436420760110148862877297603332790 // http://oeis.org/A002392 Log10E = 1 / Ln10 )

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.

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) )

Integer limit values.

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 )

func Abs(x float64) float64

Abs returns the absolute value of x.

Special cases are:

Abs(±Inf) = +Inf Abs(NaN) = NaN

func Acos(x float64) float64

Acos returns the arccosine, in radians, of x.

Special case is:

Acos(x) = NaN if x < -1 or x > 1

func Acosh(x float64) float64

Acosh returns the inverse hyperbolic cosine of x.

Special cases are:

Acosh(+Inf) = +Inf Acosh(x) = NaN if x < 1 Acosh(NaN) = NaN

func Asin(x float64) float64

Asin returns the arcsine, in radians, of x.

Special cases are:

Asin(±0) = ±0 Asin(x) = NaN if x < -1 or x > 1

func Asinh(x float64) float64

Asinh returns the inverse hyperbolic sine of x.

Special cases are:

Asinh(±0) = ±0 Asinh(±Inf) = ±Inf Asinh(NaN) = NaN

func Atan(x float64) float64

Atan returns the arctangent, in radians, of x.

Special cases are:

Atan(±0) = ±0 Atan(±Inf) = ±Pi/2

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.

Special cases are (in order):

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(x float64) float64

Atanh returns the inverse hyperbolic tangent of x.

Special cases are:

Atanh(1) = +Inf Atanh(±0) = ±0 Atanh(-1) = -Inf Atanh(x) = NaN if x < -1 or x > 1 Atanh(NaN) = NaN

func Cbrt(x float64) float64

Cbrt returns the cube root of x.

Special cases are:

Cbrt(±0) = ±0 Cbrt(±Inf) = ±Inf Cbrt(NaN) = NaN

func Ceil(x float64) float64

Ceil returns the least integer value greater than or equal to x.

Special cases are:

Ceil(±0) = ±0 Ceil(±Inf) = ±Inf Ceil(NaN) = NaN

func Copysign(x, y float64) float64

Copysign returns a value with the magnitude of x and the sign of y.

func Cos(x float64) float64

Cos returns the cosine of the radian argument x.

Special cases are:

Cos(±Inf) = NaN Cos(NaN) = NaN

func Cosh(x float64) float64

Cosh returns the hyperbolic cosine of x.

Special cases are:

Cosh(±0) = 1 Cosh(±Inf) = +Inf Cosh(NaN) = NaN

func Dim(x, y float64) float64

Dim returns the maximum of x-y or 0.

Special cases are:

Dim(+Inf, +Inf) = NaN Dim(-Inf, -Inf) = NaN Dim(x, NaN) = Dim(NaN, x) = NaN

func Erf(x float64) float64

Erf returns the error function of x.

Special cases are:

Erf(+Inf) = 1 Erf(-Inf) = -1 Erf(NaN) = NaN

func Erfc(x float64) float64

Erfc returns the complementary error function of x.

Special cases are:

Erfc(+Inf) = 0 Erfc(-Inf) = 2 Erfc(NaN) = NaN

func Exp(x float64) float64

Exp returns e**x, the base-e exponential of x.

Special cases are:

Exp(+Inf) = +Inf Exp(NaN) = NaN

Very large values overflow to 0 or +Inf. Very small values underflow to 1.

func Exp2(x float64) float64

Exp2 returns 2**x, the base-2 exponential of x.

Special cases are the same as Exp.

func Expm1(x float64) float64

Expm1 returns e**x - 1, the base-e exponential of x minus 1. It is more accurate than Exp(x) - 1 when x is near zero.

Special cases are:

Expm1(+Inf) = +Inf Expm1(-Inf) = -1 Expm1(NaN) = NaN

Very large values overflow to -1 or +Inf.

func Float32bits(f float32) uint32

Float32bits returns the IEEE 754 binary representation of f.

func Float32frombits(b uint32) float32

Float32frombits returns the floating point number corresponding to the IEEE 754 binary representation b.

func Float64bits(f float64) uint64

Float64bits returns the IEEE 754 binary representation of f.

func Float64frombits(b uint64) float64

Float64frombits returns the floating point number corresponding the IEEE 754 binary representation b.

func Floor(x float64) float64

Floor returns the greatest integer value less than or equal to x.

Special cases are:

Floor(±0) = ±0 Floor(±Inf) = ±Inf Floor(NaN) = NaN

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 × 2**exp, with the absolute value of frac in the interval [½, 1).

Special cases are:

Frexp(±0) = ±0, 0 Frexp(±Inf) = ±Inf, 0 Frexp(NaN) = NaN, 0

func Gamma(x float64) float64

Gamma returns the Gamma function of x.

Special cases are:

Gamma(+Inf) = +Inf Gamma(+0) = +Inf Gamma(-0) = -Inf Gamma(x) = NaN for integer x < 0 Gamma(-Inf) = NaN Gamma(NaN) = NaN

func Hypot(p, q float64) float64

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 Ilogb(x float64) int

Ilogb returns the binary exponent of x as an integer.

Special cases are:

Ilogb(±Inf) = MaxInt32 Ilogb(0) = MinInt32 Ilogb(NaN) = MaxInt32

func Inf(sign int) float64

Inf returns positive infinity if sign >= 0, negative infinity if sign < 0.

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 IsNaN(f float64) (is bool)

IsNaN reports whether f is an IEEE 754 “not-a-number” value.

func J0(x float64) float64

J0 returns the order-zero Bessel function of the first kind.

Special cases are:

J0(±Inf) = 0 J0(0) = 1 J0(NaN) = NaN

func J1(x float64) float64

J1 returns the order-one Bessel function of the first kind.

Special cases are:

J1(±Inf) = 0 J1(NaN) = NaN

func Jn(n int, x float64) float64

Jn returns the order-n Bessel function of the first kind.

Special cases are:

Jn(n, ±Inf) = 0 Jn(n, NaN) = NaN

func Ldexp(frac float64, exp int) float64

Ldexp is the inverse of Frexp. It returns frac × 2**exp.

Special cases are:

Ldexp(±0, exp) = ±0 Ldexp(±Inf, exp) = ±Inf Ldexp(NaN, exp) = NaN

func Lgamma(x float64) (lgamma float64, sign int)

Lgamma returns the natural logarithm and sign (-1 or +1) of Gamma(x).

Special cases are:

Lgamma(+Inf) = +Inf Lgamma(0) = +Inf Lgamma(-integer) = +Inf Lgamma(-Inf) = -Inf Lgamma(NaN) = NaN

func Log(x float64) float64

Log returns the natural logarithm of x.

Special cases are:

Log(+Inf) = +Inf Log(0) = -Inf Log(x < 0) = NaN Log(NaN) = NaN

func Log10(x float64) float64

Log10 returns the decimal logarithm of x. The special cases are the same as for Log.

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.

Special cases are:

Log1p(+Inf) = +Inf Log1p(±0) = ±0 Log1p(-1) = -Inf Log1p(x < -1) = NaN Log1p(NaN) = NaN

func Log2(x float64) float64

Log2 returns the binary logarithm of x. The special cases are the same as for Log.

func Logb(x float64) float64

Logb returns the binary exponent of x.

Special cases are:

Logb(±Inf) = +Inf Logb(0) = -Inf Logb(NaN) = NaN

func Max(x, y float64) float64

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 Min(x, y float64) float64

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 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.

Special cases are:

Mod(±Inf, y) = NaN Mod(NaN, y) = NaN Mod(x, 0) = NaN Mod(x, ±Inf) = x Mod(x, NaN) = NaN

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.

Special cases are:

Modf(±Inf) = ±Inf, NaN Modf(NaN) = NaN, NaN

func NaN() float64

NaN returns an IEEE 754 “not-a-number” value.

func Nextafter(x, y float64) (r float64)

Nextafter returns the next representable float64 value after x towards y.

Special cases are:

Nextafter(x, x) = x Nextafter(NaN, y) = NaN Nextafter(x, NaN) = NaN

func Nextafter32(x, y float32) (r float32)

Nextafter32 returns the next representable float32 value after x towards y.

Special cases are:

Nextafter32(x, x) = x Nextafter32(NaN, y) = NaN Nextafter32(x, NaN) = NaN

func Pow(x, y float64) float64

Pow returns x**y, the base-x exponential of y.

Special cases are (in order):

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(e int) float64

Pow10 returns 10**e, the base-10 exponential of e.

Special cases are:

Pow10(e) = +Inf for e > 309 Pow10(e) = 0 for e < -324

func Remainder(x, y float64) float64

Remainder returns the IEEE 754 floating-point remainder of x/y.

Special cases are:

Remainder(±Inf, y) = NaN Remainder(NaN, y) = NaN Remainder(x, 0) = NaN Remainder(x, ±Inf) = x Remainder(x, NaN) = NaN

func Signbit(x float64) bool

Signbit returns true if x is negative or negative zero.

func Sin(x float64) float64

Sin returns the sine of the radian argument x.

Special cases are:

Sin(±0) = ±0 Sin(±Inf) = NaN Sin(NaN) = NaN

func Sincos(x float64) (sin, cos float64)

Sincos returns Sin(x), Cos(x).

Special cases are:

Sincos(±0) = ±0, 1 Sincos(±Inf) = NaN, NaN Sincos(NaN) = NaN, NaN

func Sinh(x float64) float64

Sinh returns the hyperbolic sine of x.

Special cases are:

Sinh(±0) = ±0 Sinh(±Inf) = ±Inf Sinh(NaN) = NaN

func Sqrt(x float64) float64

Sqrt returns the square root of x.

Special cases are:

Sqrt(+Inf) = +Inf Sqrt(±0) = ±0 Sqrt(x < 0) = NaN Sqrt(NaN) = NaN

func Tan(x float64) float64

Tan returns the tangent of the radian argument x.

Special cases are:

Tan(±0) = ±0 Tan(±Inf) = NaN Tan(NaN) = NaN

func Tanh(x float64) float64

Tanh returns the hyperbolic tangent of x.

Special cases are:

Tanh(±0) = ±0 Tanh(±Inf) = ±1 Tanh(NaN) = NaN

func Trunc(x float64) float64

Trunc returns the integer value of x.

Special cases are:

Trunc(±0) = ±0 Trunc(±Inf) = ±Inf Trunc(NaN) = NaN

func Y0(x float64) float64

Y0 returns the order-zero Bessel function of the second kind.

Special cases are:

Y0(+Inf) = 0 Y0(0) = -Inf Y0(x < 0) = NaN Y0(NaN) = NaN

func Y1(x float64) float64

Y1 returns the order-one Bessel function of the second kind.

Special cases are:

Y1(+Inf) = 0 Y1(0) = -Inf Y1(x < 0) = NaN Y1(NaN) = NaN

func Yn(n int, x float64) float64

Yn returns the order-n Bessel function of the second kind.

Special cases are:

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