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cuelang.org/go / pkg / math

# Package math

v0.2.2
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Published: Jul 18, 2020 | License: | Module:

## Index ¶

### Constants ¶

```const (
MaxExp  = 2147483647  // largest supported exponent
MinExp  = -2147483648 // smallest supported exponent
MaxPrec = 4294967295  // largest (theoretically) supported precision; likely memory-limited
)```

Exponent and precision limits.

```const (
ToNearestEven = 0 // == IEEE 754-2008 roundTiesToEven
ToNearestAway = 1 // == IEEE 754-2008 roundTiesToAway
ToZero        = 2 // == IEEE 754-2008 roundTowardZero
AwayFromZero  = 3 // no IEEE 754-2008 equivalent
ToNegativeInf = 4 // == IEEE 754-2008 roundTowardNegative
ToPositiveInf = 5 // == IEEE 754-2008 roundTowardPositive
)```

These constants define supported rounding modes.

```const (
Below = -1
Exact = 0
Above = 1
)```

Constants describing the Accuracy of a Float.

```const (
E   = 2.71828182845904523536028747135266249775724709369995957496696763 // https://oeis.org/A001113
Pi  = 3.14159265358979323846264338327950288419716939937510582097494459 // https://oeis.org/A000796
Phi = 1.61803398874989484820458683436563811772030917980576286213544862 // https://oeis.org/A001622

Sqrt2   = 1.41421356237309504880168872420969807856967187537694807317667974 // https://oeis.org/A002193
SqrtE   = 1.64872127070012814684865078781416357165377610071014801157507931 // https://oeis.org/A019774
SqrtPi  = 1.77245385090551602729816748334114518279754945612238712821380779 // https://oeis.org/A002161
SqrtPhi = 1.27201964951406896425242246173749149171560804184009624861664038 // https://oeis.org/A139339

Ln2    = 0.693147180559945309417232121458176568075500134360255254120680009 // https://oeis.org/A002162
Log2E  = 1000000000000000000000000000000000000000000000000000000000000000 / 693147180559945309417232121458176568075500134360255254120680009
Ln10   = 2.30258509299404568401799145468436420760110148862877297603332790 // https://oeis.org/A002392
Log10E = 10000000000000000000000000000000000000000000000000000000000000 / 23025850929940456840179914546843642076011014886287729760333279
)```

Mathematical constants.

`const MaxBase = 62`

MaxBase is the largest number base accepted for string conversions.

### func Abs¶

`func Abs(x *internal.Decimal) (*internal.Decimal, error)`

Abs returns the absolute value of x.

Special case: Abs(±Inf) = +Inf

### 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 *internal.Decimal) (*internal.Decimal, error)`

Cbrt returns the cube root of x.

Special cases are:

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

### func Ceil¶

`func Ceil(x *internal.Decimal) (*internal.Decimal, error)`

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 *internal.Decimal) *internal.Decimal`

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 *internal.Decimal) (*internal.Decimal, error)`

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 Erfcinv¶

`func Erfcinv(x float64) float64`

Erfcinv returns the inverse of Erfc(x).

Special cases are:

```Erfcinv(0) = +Inf
Erfcinv(2) = -Inf
Erfcinv(x) = NaN if x < 0 or x > 2
Erfcinv(NaN) = NaN
```

### func Erfinv¶

`func Erfinv(x float64) float64`

Erfinv returns the inverse error function of x.

Special cases are:

```Erfinv(1) = +Inf
Erfinv(-1) = -Inf
Erfinv(x) = NaN if x < -1 or x > 1
Erfinv(NaN) = NaN
```

### func Exp¶

`func Exp(x *internal.Decimal) (*internal.Decimal, error)`

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 *internal.Decimal) (*internal.Decimal, error)`

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 Floor¶

`func Floor(x *internal.Decimal) (*internal.Decimal, error)`

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 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 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 Jacobi¶

`func Jacobi(x, y *big.Int) int`

Jacobi returns the Jacobi symbol (x/y), either +1, -1, or 0. The y argument must be an odd integer.

### 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 Log¶

`func Log(x *internal.Decimal) (*internal.Decimal, error)`

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 *internal.Decimal) (*internal.Decimal, error)`

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 *internal.Decimal) (*internal.Decimal, error)`

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 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 MultipleOf¶

`func MultipleOf(x, y *internal.Decimal) (bool, error)`

MultipleOf reports whether x is a multiple of y.

### func Pow¶

`func Pow(x, y *internal.Decimal) (*internal.Decimal, error)`

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(n int32) *internal.Decimal`

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

### 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 Round¶

`func Round(x *internal.Decimal) (*internal.Decimal, error)`

Round returns the nearest integer, rounding half away from zero.

Special cases are:

```Round(±0) = ±0
Round(±Inf) = ±Inf
Round(NaN) = NaN
```

### func RoundToEven¶

`func RoundToEven(x *internal.Decimal) (*internal.Decimal, error)`

RoundToEven returns the nearest integer, rounding ties to even.

Special cases are:

```RoundToEven(±0) = ±0
RoundToEven(±Inf) = ±Inf
RoundToEven(NaN) = NaN
```

### func Signbit¶

`func Signbit(x *internal.Decimal) bool`

Signbit reports whether 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 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 *internal.Decimal) (*internal.Decimal, error)`

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
Yn(n, x < 0) = NaN
Yn(n, NaN) = NaN
```
Documentation was rendered with GOOS=linux and GOARCH=amd64.