ActiveGo 1.8Package math
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Constants
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 ¶
func Abs(x float64) float64
Abs returns the absolute value of x.
Special cases are:
Abs(±Inf) = +Inf Abs(NaN) = NaN
func Acos ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
func Copysign(x, y float64) float64
Copysign returns a value with the magnitude of x and the sign of y.
func Cos ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
func Exp2(x float64) float64
Exp2 returns 2**x, the base-2 exponential of x.
Special cases are the same as Exp.
func Expm1 ¶
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 ¶
func Float32bits(f float32) uint32
Float32bits returns the IEEE 754 binary representation of f.
func Float32frombits ¶
func Float32frombits(b uint32) float32
Float32frombits returns the floating point number corresponding to the IEEE 754 binary representation b.
func Float64bits ¶
func Float64bits(f float64) uint64
Float64bits returns the IEEE 754 binary representation of f.
func Float64frombits ¶
func Float64frombits(b uint64) float64
Float64frombits returns the floating point number corresponding the IEEE 754 binary representation b.
func Floor ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
func Inf(sign int) float64
Inf returns positive infinity if sign >= 0, negative infinity if sign < 0.
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.
func IsNaN ¶
func IsNaN(f float64) (is bool)
IsNaN reports whether f is an IEEE 754 “not-a-number” value.
func J0 ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
func Log10(x float64) float64
Log10 returns the decimal logarithm of x. The special cases are the same as for Log.
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.
Special cases are:
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.
func Logb ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
func NaN() float64
NaN returns an IEEE 754 “not-a-number” value.
func Nextafter ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
func Signbit(x float64) bool
Signbit returns true if x is negative or negative zero.
func Sin ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
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 ¶
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