class Math

Abs returns the absolute value of x.

Special cases are:

Abs(±Inf) = +Inf
Abs(NaN) = NaN

Acos returns the arccosine, in radians, of x.

Special case is:

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

Acosh returns the inverse hyperbolic cosine of x.

Special cases are:

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

Asin returns the arcsine, in radians, of x.

Special cases are:

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

Asinh returns the inverse hyperbolic sine of x.

Special cases are:

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

Atan returns the arctangent, in radians, of x.

Special cases are:

Atan(±0) = ±0
Atan(±Inf) = ±Pi/2

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

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

Cbrt returns the cube root of x.

Special cases are:

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

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

Special cases are:

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

Copysign returns a value with the magnitude of f and the sign of sign.

Cos returns the cosine of the radian argument x.

Special cases are:

Cos(±Inf) = NaN
Cos(NaN) = NaN

Cosh returns the hyperbolic cosine of x.

Special cases are:

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

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

Erf returns the error function of x.

Special cases are:

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

Erfc returns the complementary error function of x.

Special cases are:

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

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

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

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.

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

Special cases are the same as Exp.

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.

FMA returns x * y + z, computed with only one rounding. (That is, FMA returns the fused multiply-add of x, y, and z.)

Float32bits returns the IEEE 754 binary representation of f, with the sign bit of f and the result in the same bit position. Float32bits(Float32frombits(x)) == x.

Float32frombits returns the floating-point number corresponding to the IEEE 754 binary representation b, with the sign bit of b and the result in the same bit position. Float32frombits(Float32bits(x)) == x.

Float64bits returns the IEEE 754 binary representation of f, with the sign bit of f and the result in the same bit position, and Float64bits(Float64frombits(x)) == x.

Float64frombits returns the floating-point number corresponding to the IEEE 754 binary representation b, with the sign bit of b and the result in the same bit position. Float64frombits(Float64bits(x)) == x.

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

Special cases are:

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

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

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

Hypot returns Sqrt(pp + qq), 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

Ilogb returns the binary exponent of x as an integer.

Special cases are:

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

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

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.

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

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

Special cases are:

J0(±Inf) = 0
J0(0) = 1
J0(NaN) = NaN

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

Special cases are:

J1(±Inf) = 0
J1(NaN) = NaN

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

Special cases are:

Jn(n, ±Inf) = 0
Jn(n, NaN) = NaN

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

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

Log returns the natural logarithm of x.

Special cases are:

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

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

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

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

Logb returns the binary exponent of x.

Special cases are:

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

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

Note that this differs from the built-in function max when called with NaN and +Inf.

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

Note that this differs from the built-in function min when called with NaN and -Inf.

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

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

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

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

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

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

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

Special cases are:

Pow10(n) =    0 for n < -323
Pow10(n) = +Inf for n > 308

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

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

Special cases are:

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

RoundToEven returns the nearest integer, rounding ties to even.

Special cases are:

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

Signbit reports whether x is negative or negative zero.

Sin returns the sine of the radian argument x.

Special cases are:

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

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

Special cases are:

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

Sinh returns the hyperbolic sine of x.

Special cases are:

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

Sqrt returns the square root of x.

Special cases are:

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

Tan returns the tangent of the radian argument x.

Special cases are:

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

Tanh returns the hyperbolic tangent of x.

Special cases are:

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

Trunc returns the integer value of x.

Special cases are:

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

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

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

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