# Math¶

Usage

```use Math;
```

or

```import Math;
```

This module provides frequently used mathematical constants and functions.

It includes wrappers for many of the constants and functions in the C Math library, which is part of the C Language Standard (ISO/IEC 9899) as described in Section 7.12. Please consult that standard for an authoritative description of the expected properties of those constants and routines.

In general, where the C math library provides a double and a float version of a function, the float version has a suffix ‘f’. In the Chapel interface, the suffix is dropped, and the type of the operand determines which version is called – according to the usual function overloading and resolution rules. Normally, the result has the same precision as the argument(s). Please consult the C standard for specifics.

Error Handling – At present, Chapel does not provide control over error handling in the Math module. The default behavior is as if the macro `math_errhandling` is set to 0: Given erroneous input at run-time, all math functions will return an implementation-defined value; no exception will be generated.

## Automatically Available Symbols¶

Note

These symbols can also be accessed using `Math.` as their qualified access prefix.

`gcd`

`fma`

## Automatically Included Constant and Function Definitions¶

proc abs(x: int(?w))

Returns the absolute value of the integer argument.

Return type

The type of x.

proc abs(x: uint(?w))

Returns the absolute value of the unsigned integer argument.

Return type

The type of x.

proc abs(param x: integral) param

Returns the absolute value of the integer param argument x.

proc abs(x: real(64)): real(64)

Returns the magnitude of the real argument x.

proc abs(x: real(32)): real(32)

Returns the magnitude of the real argument x.

proc abs(x: imag(64)): real(64)

Returns the real magnitude of the imaginary argument x.

proc abs(x: imag(32)): real(32)

Returns the real magnitude of the imaginary argument x.

proc abs(x: complex(?w)): real(w/2)

Returns the magnitude (often called modulus) of complex x.

In concert with the related `phase` (a.k.a. argument) of x, it can be used to recompute x.

Return type

`real(w/2)` when x has a type of `complex(w)`.

proc abs(i: int(?w))

Warning

The argument name ‘i’ is deprecated for ‘abs’, please use ‘x’ instead

Returns the absolute value of the integer argument.

Return type

The type of i.

proc abs(i: uint(?w))

Warning

The argument name ‘i’ is deprecated for ‘abs’, please use ‘x’ instead

Returns the absolute value of the unsigned integer argument.

Return type

The type of i.

proc abs(param i: integral) param

Warning

The argument name ‘i’ is deprecated for param function ‘abs’, please use ‘x’ instead

Returns the absolute value of the integer param argument i.

proc abs(r: real(64)): real(64)

Warning

The argument name ‘r’ is deprecated for ‘abs’, please use ‘x’ instead

Returns the magnitude of the real argument r.

proc abs(im: imag(64)): real(64)

Warning

The argument name ‘im’ is deprecated for ‘abs’, please use ‘x’ instead

Returns the real magnitude of the imaginary argument im.

proc abs(im: imag(32)): real(32)

Warning

The argument name ‘im’ is deprecated for ‘abs’, please use ‘x’ instead

Returns the real magnitude of the imaginary argument im.

proc abs(z: complex(?w)): real(w/2)

Warning

The argument name ‘z’ is deprecated for ‘abs’, please use ‘x’ instead

Returns the magnitude (often called modulus) of complex z.

In concert with the related `phase` (a.k.a. argument) of z, it can be used to recompute z.

Return type

`real(w/2)` when z has a type of `complex(w)`.

proc carg(z: complex(?w)): real(w/2)

Warning

‘carg’ is deprecated, please use `phase` instead

Returns the phase (often called argument) of complex z, an angle (in radians).

In concert with the related `abs`, the magnitude (a.k.a. modulus) of z, it can be used to recompute z.

Return type

`real(w/2)` when z has a type of `complex(w)`.

proc cbrt(x: real(64)): real(64)

Returns the cube root of the argument x.

proc cbrt(x: real(32)): real(32)

Returns the cube root of the argument x.

proc ceil(x: real(64)): real(64)

Returns the value of the argument x rounded up to the nearest integer.

proc ceil(x: real(32)): real(32)

Returns the value of the argument x rounded up to the nearest integer.

proc conj(x: complex(?w))

Returns the complex conjugate of the complex argument x.

Return type

A complex number of the same type as x.

proc conj(x: imag(?w))

Returns the complex conjugate of the imaginary argument x.

Return type

An imaginary number of the same type as x.

proc conj(x: int(?w))

Returns the argument x.

Return type

A number that is not complex or imaginary of the same type as x.

proc conj(x: uint(?w))
proc conj(x: real(?w))
proc conjg(z: complex(?w))

Warning

‘conjg’ with a ‘z’ argument has been deprecated, please use ‘conj’ with an ‘x’ argument instead

Returns the complex conjugate of the complex argument z.

Return type

A complex number of the same type as z.

proc conjg(z: imag(?w))

Warning

‘conjg’ with a ‘z’ argument has been deprecated, please use ‘conj’ with an ‘x’ argument instead

Returns the complex conjugate of the imaginary argument z.

Return type

An imaginary number of the same type as z.

proc conjg(z: int(?w))

Warning

‘conjg’ with a ‘z’ argument has been deprecated, please use ‘conj’ with an ‘x’ argument instead

Returns the argument z.

Return type

A number that is not complex or imaginary of the same type as z.

proc conjg(z: uint(?w))

Warning

‘conjg’ with a ‘z’ argument has been deprecated, please use ‘conj’ with an ‘x’ argument instead

proc conjg(z: real(?w))

Warning

‘conjg’ with a ‘z’ argument has been deprecated, please use ‘conj’ with an ‘x’ argument instead

proc cproj(z: complex(?w)): complex(w)

Warning

‘cproj’ has been deprecated, please use `riemProj` instead

Returns the projection of z on a Riemann sphere.

proc floor(x: real(64)): real(64)

Returns the value of the argument x rounded down to the nearest integer.

proc floor(x: real(32)): real(32)

Returns the value of the argument x rounded down to the nearest integer.

proc inf param: real(64)

Returns a value for which `isInf` will return true.

proc INFINITY param: real(64)

Warning

‘INFINITY’ has been deprecated in favor of `inf`, please use that instead

Returns a value for which `isInf` will return true.

proc isFinite(x: real(64)): bool

Returns true if the argument x is a representation of a finite value; false otherwise.

proc isFinite(x: real(32)): bool

Returns true if the argument x is a representation of a finite value; false otherwise.

proc isfinite(x: real(64)): bool

Warning

‘isfinite’ is deprecated in favor of `isFinite`, please use that instead

Returns true if the argument x is a representation of a finite value; false otherwise.

proc isfinite(x: real(32)): bool

Warning

‘isfinite’ is deprecated in favor of `isFinite`, please use that instead

Returns true if the argument x is a representation of a finite value; false otherwise.

proc isInf(x: real(64)): bool

Returns true if the argument x is a representation of infinity; false otherwise.

proc isInf(x: real(32)): bool

Returns true if the argument x is a representation of infinity; false otherwise.

proc isinf(x: real(64)): bool

Warning

‘isinf’ is deprecated in favor of `isInf`, please use that instead

Returns true if the argument x is a representation of infinity; false otherwise.

proc isinf(x: real(32)): bool

Warning

‘isinf’ is deprecated in favor of `isInf`, please use that instead

Returns true if the argument x is a representation of infinity; false otherwise.

proc isNan(x: real(64)): bool

Returns true if the argument x does not represent a valid number; false otherwise.

proc isNan(x: real(32)): bool

Returns true if the argument x does not represent a valid number; false otherwise.

proc isnan(x: real(64)): bool

Warning

‘isnan’ is deprecated in favor of `isNan`, please use that instead

Returns true if the argument x does not represent a valid number; false otherwise.

proc isnan(x: real(32)): bool

Warning

‘isnan’ is deprecated in favor of `isNan`, please use that instead

Returns true if the argument x does not represent a valid number; false otherwise.

proc max(x, y)  where !isArray(x) && !isArray(y) && !(isNumeric(_desync(x.type)) && isNumeric(_desync(y.type)))

Returns the maximum value of two arguments using the `>` operator for comparison. If one of the arguments is `Math.nan`, the result is also nan.

Return type

The type of x.

proc max(x, y, z ...?k)

Returns the maximum value of 3 or more arguments using the above call.

proc max(param x: numeric, param y: numeric) param  where !(isComplex(x) || isComplex(y))

Returns the maximum of 2 param `int`, `uint`, `real`, or `imag` values as a param.

proc min(x, y)  where !isArray(x) && !isArray(y) && !(isNumeric(_desync(x.type)) && isNumeric(_desync(y.type)))

Returns the minimum value of two arguments using the `<` operator for comparison.

If one of the arguments is `Math.nan`, the result is also nan.

Return type

The type of x.

proc min(x, y, z ...?k)

Returns the minimum value of 3 or more arguments using the above call.

proc min(param x: numeric, param y: numeric) param  where !(isComplex(x) || isComplex(y))

Returns the minimum of 2 param `int`, `uint`, `real`, or `imag` values as a param.

proc mod(param m: integral, param n: integral) param

Warning

The argument names ‘m’ and ‘n’ are deprecated for param ‘mod’, please use ‘x’ and ‘y’ instead

Computes the mod operator on the two arguments, defined as `mod(m,n) = m - n * floor(m / n)`.

The result is always >= 0 if n > 0. It is an error if n == 0.

proc mod(m: integral, n: integral)

Warning

The argument names ‘m’ and ‘n’ are deprecated for ‘mod’, please use ‘x’ and ‘y’ instead

Computes the mod operator on the two arguments, defined as `mod(m,n) = m - n * floor(m / n)`.

If the arguments are of unsigned type, then fewer conditionals will be evaluated at run time.

The result is always >= 0 if n > 0. It is an error if n == 0.

proc mod(param x: integral, param y: integral) param

Computes the mod operator on the two arguments, defined as `mod(x,y) = x - y * floor(x / y)`.

The result is always >= 0 if y > 0. It is an error if y == 0.

Note

This does not have the same behavior as the Modulus Operators (%) when y is negative.

proc mod(x: integral, y: integral)

Computes the mod operator on the two arguments, defined as `mod(x,y) = x - y * floor(x / y)`.

If the arguments are of unsigned type, then fewer conditionals will be evaluated at run time.

The result is always >= 0 if y > 0. It is an error if y == 0.

Note

This does not have the same behavior as the Modulus Operators (%) when y is negative.

proc mod(x: real(32), y: real(32)): real(32)

Computes the mod operator on the two numbers, defined as `mod(x,y) = x - y * floor(x / y)`.

proc mod(x: real(64), y: real(64)): real(64)

Computes the mod operator on the two numbers, defined as `mod(x,y) = x - y * floor(x / y)`.

proc nan param: real(64)

Returns a value for which `isNan` will return true.

proc NAN param: real(64)

Warning

‘NAN’ is deprecated in favor of `nan`, please use that instead

Returns a value for which `isNan` will return true.

proc phase(x: complex(?w)): real(w/2)

Returns the phase (often called argument) of complex x, an angle (in radians).

In concert with the related `abs`, the magnitude (a.k.a. modulus) of x, it can be used to recompute x.

Return type

`real(w/2)` when x has a type of `complex(w)`.

proc riemProj(x: complex(?w)): complex(w)

Returns the projection of x on a Riemann sphere.

proc round(x: real(64)): real(64)

Returns the nearest integral value of the argument x, returning that value which is larger than x in absolute value for the half-way case.

proc round(x: real(32)): real(32)

Returns the nearest integral value of the argument x, returning that value which is larger than x in absolute value for the half-way case.

proc sgn(i: int(?w)): int(8)

Warning

The argument name ‘i’ is deprecated for ‘sgn’, please use ‘x’ instead

Returns the signum function of the integer argument i: 1 if positive, -1 if negative, 0 if zero.

proc sgn(i: uint(?w)): uint(8)

Warning

The argument name ‘i’ is deprecated for ‘sgn’, please use ‘x’ instead

Returns the signum function of the unsigned integer argument i: 1 if positive, -1 if negative, 0 if zero.

proc sgn(param i: integral) param

Warning

The argument name ‘i’ is deprecated for param ‘sgn’, please use ‘x’ instead

Returns the signum function of the integer param argument i: 1 if positive, -1 if negative, 0 if zero.

proc sgn(x: int(?w)): int(8)

Returns the signum function of the integer argument x: 1 if positive, -1 if negative, 0 if zero.

proc sgn(x: uint(?w)): uint(8)

Returns the signum function of the unsigned integer argument x: 1 if positive, -1 if negative, 0 if zero.

proc sgn(param x: integral) param

Returns the signum function of the integer param argument x: 1 if positive, -1 if negative, 0 if zero.

proc sgn(x: real(?w)): int(8)

Returns the signum function of the real argument x: 1 if positive, -1 if negative, 0 if zero.

proc sqrt(x: real(64)): real(64)

Returns the square root of the argument x.

It is an error if the x is less than zero.

proc sqrt(x: real(32)): real(32)

Returns the square root of the argument x.

It is an error if x is less than zero.

proc sqrt(x: complex(64)): complex(64)

Returns the square root of the argument z.

proc sqrt(x: complex(128)): complex(128)

Returns the square root of the argument z.

proc sqrt(z: complex(64)): complex(64)

Warning

The argument name ‘z’ is deprecated for ‘sqrt’, please use ‘x’ instead

Returns the square root of the argument z.

proc sqrt(z: complex(128)): complex(128)

Warning

The argument name ‘z’ is deprecated for ‘sqrt’, please use ‘x’ instead

Returns the square root of the argument z.

proc trunc(x: real(64)): real(64)

Returns the nearest integral value to the argument x that is not larger than x in absolute value.

proc trunc(x: real(32)): real(32)

Returns the nearest integral value to the argument x that is not larger than x in absolute value.

proc isClose(x, y, relTol = 1e-5, absTol = 0.0): bool

Returns true if x and y are approximately equal, else returns false.

relTol specifies the relative tolerance for differences between x and y, while absTol specifies the absolute tolerance. Both must be positive when specified.

x and y must be either real, imag, or complex.

proc isclose(x, y, rtol = 1e-5, atol = 0.0): bool

Warning

isclose with ‘rtol’ and ‘atol’ arguments is now deprecated, please use `isClose` with ‘relTol’ and ‘absTol’ arguments instead

Returns true if x and y are approximately equal, else returns false.

proc signbit(x: real(32)): bool

Warning

signbit is unstable and may change its name in the future

Returns true if the sign of x is negative, else returns false. It detects the sign bit of zeroes, infinities, and nans

proc signbit(x: real(64)): bool

Warning

signbit is unstable and may change its name in the future

Returns true if the sign of x is negative, else returns false. It detects the sign bit of zeroes, infinities, and nans

## Constant and Function Definitions for Math¶

param e = 2.7182818284590452354

e - exp(1) or the base of the natural logarithm

param log2E = 1.4426950408889634074

log2(e)

param log2_e = 1.4426950408889634074

Warning

‘log2_e’ is deprecated, please use `log2E` instead

log2(e)

param log10E = 0.43429448190325182765

log10(e)

param log10_e = 0.43429448190325182765

Warning

‘log10_e’ is deprecated, please use `log10E` instead

log10(e)

param ln2 = 0.69314718055994530942

ln(2) (natural logarithm)

param ln_2 = 0.69314718055994530942

Warning

‘ln_2’ is deprecated, please use `ln2` instead

log(2) (natural logarithm)

param ln10 = 2.30258509299404568402

ln(10) (natural logarithm)

param ln_10 = 2.30258509299404568402

Warning

‘ln_10’ is deprecated, please use `ln10` instead

log(10) (natural logarithm)

param pi = 3.14159265358979323846

pi - the circumference/the diameter of a circle

param halfPi = 1.57079632679489661923

Warning

‘halfPi’ is unstable due to questions about its utility. If you are seeing negative performance impacts from using ‘pi/2’ instead of this ‘param’, please let us know!

pi/2

param half_pi = 1.57079632679489661923

Warning

‘half_pi’ is deprecated, please use `halfPi` or ‘pi/2’ instead

pi/2

param quarterPi = 0.78539816339744830962

Warning

‘quarterPi’ is unstable due to questions about its utility. If you are seeing negative performance impacts from using ‘pi/4’ instead of this ‘param’, please let us know!

pi/4

param quarter_pi = 0.78539816339744830962

Warning

‘quarter_pi’ is deprecated, please use `quarterPi` or ‘pi/4’ instead

pi/4

param reciprPi = 0.31830988618379067154

Warning

‘reciprPi’ is unstable due to questions about its utility. If you are seeing negative performance impacts from using ‘1/pi’ instead of this ‘param’, please let us know!

1/pi

param recipr_pi = 0.31830988618379067154

Warning

‘recipr_pi’ is deprecated, please use `reciprPi` or ‘1/pi’ instead

1/pi

param twiceReciprPi = 0.63661977236758134308

Warning

‘twiceReciprPi’ is unstable due to questions about its utility. If you are seeing negative performance impacts from using ‘2/pi’ instead of this ‘param’, please let us know!

2/pi

param twice_recipr_pi = 0.63661977236758134308

Warning

‘twice_recipr_pi’ is deprecated, please use `twiceReciprPi` or ‘2/pi’ instead

2/pi

param twiceReciprSqrtPi = 1.12837916709551257390

Warning

‘twiceReciprSqrtPi’ is unstable due to questions about its utility. If you are using this symbol, please let us know!

2/sqrt(pi)

param twice_recipr_sqrt_pi = 1.12837916709551257390

Warning

‘twice_recipr_sqrt_pi’ is deprecated, please use `twiceReciprSqrtPi` or ‘2/sqrt(pi)’ instead

2/sqrt(pi)

param sqrt2 = 1.41421356237309504880

Warning

‘sqrt2’ is unstable due to questions about its utility. If you are using this symbol, please let us know!

sqrt(2)

param sqrt_2 = 1.41421356237309504880

Warning

‘sqrt_2’ is deprecated, please use `sqrt2` or ‘sqrt(2)’ instead

sqrt(2)

param reciprSqrt2 = 0.70710678118654752440

Warning

‘reciprSqrt2’ is unstable due to questions about its utility. If you are using this symbol, please let us know!

1/sqrt(2)

param recipr_sqrt_2 = 0.70710678118654752440

Warning

‘recipr_sqrt_2’ is deprecated, please use `reciprSqrt2` or ‘1/sqrt(2)’ instead

1/sqrt(2)

proc acos(x: real(64)): real(64)

Returns the arc cosine of the argument x.

It is an error if x is less than -1 or greater than 1.

proc acos(x: real(32)): real(32)

Returns the arc cosine of the argument x.

It is an error if x is less than -1 or greater than 1.

proc acos(x: complex(64)): complex(64)

Returns the arc cosine of the argument x.

proc acos(x: complex(128)): complex(128)

Returns the arc cosine of the argument x.

proc acosh(x: real(64)): real(64)

Returns the inverse hyperbolic cosine of the argument x.

It is an error if x is less than 1.

proc acosh(x: real(32)): real(32)

Returns the inverse hyperbolic cosine of the argument x.

It is an error if x is less than 1.

proc acosh(x: complex(64)): complex(64)

Returns the inverse hyperbolic cosine of the argument x.

proc acosh(x: complex(128)): complex(128)

Returns the inverse hyperbolic cosine of the argument x.

proc asin(x: real(64)): real(64)

Returns the arc sine of the argument x.

It is an error if x is less than -1 or greater than 1.

proc asin(x: real(32)): real(32)

Returns the arc sine of the argument x.

It is an error if x is less than -1 or greater than 1.

proc asin(x: complex(64)): complex(64)

Returns the arc sine of the argument x.

proc asin(x: complex(128)): complex(128)

Returns the arc sine of the argument x.

proc asinh(x: real(64)): real(64)

Returns the inverse hyperbolic sine of the argument x.

proc asinh(x: real(32)): real(32)

Returns the inverse hyperbolic sine of the argument x.

proc asinh(x: complex(64)): complex(64)

Returns the inverse hyperbolic sine of the argument x.

proc asinh(x: complex(128)): complex(128)

Returns the inverse hyperbolic sine of the argument x.

proc atan(x: real(64)): real(64)

Returns the arc tangent of the argument x.

proc atan(x: real(32)): real(32)

Returns the arc tangent of the argument x.

proc atan(x: complex(64)): complex(64)

Returns the arc tangent of the argument x.

proc atan(x: complex(128)): complex(128)

Returns the arc tangent of the argument x.

proc atan2(y: real(64), x: real(64)): real(64)

Returns the arc tangent of the ratio of the two arguments.

This is equivalent to the arc tangent of y / x except that the signs of y and x are used to determine the quadrant of the result.

proc atan2(y: real(32), x: real(32)): real(32)

Returns the arc tangent of the ratio of the two arguments.

This is equivalent to the arc tangent of y / x except that the signs of y and x are used to determine the quadrant of the result.

proc atanh(x: real(64)): real(64)

Returns the inverse hyperbolic tangent of the argument x.

It is an error if x is less than -1 or greater than 1.

proc atanh(x: real(32)): real(32)

Returns the inverse hyperbolic tangent of the argument x.

It is an error if x is less than -1 or greater than 1.

proc atanh(x: complex(64)): complex(64)

Returns the inverse hyperbolic tangent of the argument x.

proc atanh(x: complex(128)): complex(128)

Returns the inverse hyperbolic tangent of the argument x.

proc cos(x: real(64)): real(64)

Returns the cosine of the argument x.

proc cos(x: real(32)): real(32)

Returns the cosine of the argument x.

proc cos(x: complex(64)): complex(64)

Returns the cosine of the argument x.

proc cos(x: complex(128)): complex(128)

Returns the cosine of the argument x.

proc cosh(x: real(64)): real(64)

Returns the hyperbolic cosine of the argument x.

proc cosh(x: real(32)): real(32)

Returns the hyperbolic cosine of the argument x.

proc cosh(x: complex(64)): complex(64)

Returns the hyperbolic cosine of the argument x.

proc cosh(x: complex(128)): complex(128)

Returns the hyperbolic cosine of the argument x.

proc divCeil(param x: integral, param y: integral) param

Returns `ceil`(x/y), i.e., the fraction x/y rounded up to the nearest integer.

If the arguments are of unsigned type, then fewer conditionals will be evaluated at run time.

proc divCeil(x: integral, y: integral)

Returns `ceil`(x/y), i.e., the fraction x/y rounded up to the nearest integer.

If the arguments are of unsigned type, then fewer conditionals will be evaluated at run time.

proc divCeilPos(x: integral, y: integral)

Warning

divCeilPos is unstable due to questions about its utility. If you find this function valuable, please let us know!

A variant of `divCeil` that performs no runtime checks. The user must ensure that both arguments are strictly positive (not 0) and are of a signed integer type (not uint).

proc divFloor(param x: integral, param y: integral) param

Returns `floor`(x/y), i.e., the fraction x/y rounded down to the nearest integer.

If the arguments are of unsigned type, then fewer conditionals will be evaluated at run time.

proc divFloor(x: integral, y: integral)

Returns `floor`(x/y), i.e., the fraction x/y rounded down to the nearest integer.

If the arguments are of unsigned type, then fewer conditionals will be evaluated at run time.

proc divFloorPos(x: integral, y: integral)

Warning

divFloorPos is unstable due to questions about its utility. If you find this function valuable, please let us know!

A variant of `divFloor` that performs no runtime checks. The user must ensure that both arguments are strictly positive (not 0) and are of a signed integer type (not uint).

proc erf(x: real(64)): real(64)

Warning

‘erf’ is unstable and may be renamed or moved to a different module in the future

Returns the error function of the argument x. This is equivalent to `2/sqrt(pi)` * the integral of `exp(-t**2)dt` from 0 to x.

proc erf(x: real(32)): real(32)

Warning

‘erf’ is unstable and may be renamed or moved to a different module in the future

Returns the error function of the argument x. This is equivalent to `2/sqrt(pi)` * the integral of `exp(-t**2)dt` from 0 to x.

proc erfc(x: real(64)): real(64)

Warning

‘erfc’ is unstable and may be renamed or moved to a different module in the future

Returns the complementary error function of the argument x. This is equivalent to 1.0 - `erf`(x).

proc erfc(x: real(32)): real(32)

Warning

‘erfc’ is unstable and may be renamed or moved to a different module in the future

Returns the complementary error function of the argument x. This is equivalent to 1.0 - `erf`(x).

proc exp(x: real(64)): real(64)

Returns the value of the Napierian `e` raised to the power of the argument x.

proc exp(x: real(32)): real(32)

Returns the value of the Napierian `e` raised to the power of the argument x.

proc exp(x: complex(64)): complex(64)

Returns the value of the Napierian `e` raised to the power of the argument x.

proc exp(x: complex(128)): complex(128)

Returns the value of the Napierian `e` raised to the power of the argument x.

proc exp2(x: real(64)): real(64)

Returns the value of 2 raised to the power of the argument x.

proc exp2(x: real(32)): real(32)

Returns the value of 2 raised to the power of the argument x.

proc expm1(x: real(64)): real(64)

Returns one less than the value of the Napierian `e` raised to the power of the argument x.

proc expm1(x: real(32)): real(32)

Returns one less than the value of the Napierian `e` raised to the power of the argument x.

proc gamma(x: real(64)): real(64)

Returns the gamma function of the argument x.

proc gamma(x: real(32)): real(32)

Returns the gamma function of the argument x.

proc ldExp(x: real(64), exp: int(32)): real(64)

Returns the value of the argument x multiplied by 2 raised to the argument exp power, i.e., `x * 2**exp`.

proc ldExp(x: real(32), exp: int(32)): real(32)

Returns the value of the argument x multiplied by 2 raised to the argument exp power, i.e., `x * 2**exp`.

proc ldexp(x: real(64), n: int(32)): real(64)

Warning

‘ldexp’ with an ‘n’ argument has been deprecated, please use `ldExp` with an ‘exp’ argument instead

Returns the value of the argument x multiplied by 2 raised to the argument n power, i.e., `x * 2**n`.

proc ldexp(x: real(32), n: int(32)): real(32)

Warning

‘ldexp’ with an ‘n’ argument has been deprecated, please use `ldExp` with an ‘exp’ argument instead

Returns the value of the argument x multiplied by 2 raised to the argument n power, i.e., `x * 2**n`.

proc lnGamma(x: real(64)): real(64)

Returns the natural logarithm of the absolute value of the gamma function of the argument x.

proc lnGamma(x: real(32)): real(32)

Returns the natural logarithm of the absolute value of the gamma function of the argument x.

proc lgamma(x: real(64)): real(64)

Warning

‘lgamma’ has been deprecated in favor of `lnGamma`, please use that instead

Returns the natural logarithm of the absolute value of the gamma function of the argument x.

proc lgamma(x: real(32)): real(32)

Warning

‘lgamma’ has been deprecated in favor of `lnGamma`, please use that instead

Returns the natural logarithm of the absolute value of the gamma function of the argument x.

proc ln(x: real(64)): real(64)

Returns the natural logarithm of the argument x.

It is an error if x is less than or equal to zero.

proc ln(x: real(32)): real(32)

Returns the natural logarithm of the argument x.

It is an error if x is less than or equal to zero.

proc ln(x: complex(64)): complex(64)

Returns the natural logarithm of the argument x.

proc ln(x: complex(128)): complex(128)

Returns the natural logarithm of the argument x.

proc log(x: real(64)): real(64)

Returns the natural logarithm of the argument x.

It is an error if x is less than or equal to zero.

proc log(x: real(32)): real(32)

Returns the natural logarithm of the argument x.

It is an error if x is less than or equal to zero.

proc log(x: complex(64)): complex(64)

Returns the natural logarithm of the argument x.

proc log(x: complex(128)): complex(128)

Returns the natural logarithm of the argument x.

proc log10(x: real(64)): real(64)

Returns the base 10 logarithm of the argument x.

It is an error if x is less than or equal to zero.

proc log10(x: real(32)): real(32)

Returns the base 10 logarithm of the argument x.

It is an error if x is less than or equal to zero.

proc log1p(x: real(64)): real(64)

Returns the natural logarithm of x + 1.

It is an error if x is less than or equal to -1.

proc log1p(x: real(32)): real(32)

Returns the natural logarithm of x + 1.

It is an error if x is less than or equal to -1.

proc logBasePow2(x: int(?w), exp)

Warning

‘logBasePow2’ is unstable due to questions about its utility. If you rely on this function, please let us know!

Returns the log to the base 2**exp of the given x value. If exp is 1, then returns the log to the base 2; if exp is 2, then returns the log to the base 4, etc. Any fractional part is discarded.

Return type

int

proc logBasePow2(x: uint(?w), exp)

Warning

‘logBasePow2’ is unstable due to questions about its utility. If you rely on this function, please let us know!

Returns the log to the base 2**exp of the given x value. If exp is 1, then returns the log to the base 2; if exp is 2, then returns the log to the base 4, etc. Any fractional part is discarded.

Return type

int

proc logBasePow2(val: int(?w), baseLog2)

Warning

The ‘val’ and ‘baseLog2’ argument names are now deprecated, please use ‘x’ and ‘exp’ respectively

Returns the log to the base 2**baseLog2 of the given in value. If baseLog2 is 1, then returns the log to the base 2; if baseLog2 is 2, then returns the log to the base 4, etc. Any fractional part is discarded.

Return type

int

proc logBasePow2(val: uint(?w), baseLog2)

Warning

The ‘val’ and ‘baseLog2’ argument names are now deprecated, please use ‘x’ and ‘exp’ respectively

Returns the log to the base 2**baseLog2 of the given in value. If baseLog2 is 1, then returns the log to the base 2; if baseLog2 is 2, then returns the log to the base 4, etc. Any fractional part is discarded.

Return type

int

proc log2(x: real(64)): real(64)

Returns the base 2 logarithm of the argument x.

It is an error if x is less than or equal to zero.

proc log2(x: real(32)): real(32)

Returns the base 2 logarithm of the argument x.

It is an error if x is less than or equal to zero.

proc log2(x: int(?w))

Warning

The version of ‘log2’ that takes an int argument is unstable

Returns the base 2 logarithm of the argument x, rounded down.

Return type

int

It is an error if x is less than or equal to zero.

proc log2(x: uint(?w))

Warning

The version of ‘log2’ that takes an uint argument is unstable

Returns the base 2 logarithm of the argument x, rounded down.

Return type

int

It is an error if x is equal to zero.

proc nearbyint(x: real(64)): real(64)

Warning

nearbyint is unstable while we design more thorough rounding support

Returns the rounded integral value of the argument x determined by the current rounding direction. `nearbyint` will not raise the “inexact” floating-point exception.

proc nearbyint(x: real(32)): real(32)

Warning

nearbyint is unstable while we design more thorough rounding support

Returns the rounded integral value of the argument x determined by the current rounding direction. `nearbyint` will not raise the “inexact” floating-point exception.

proc rint(x: real(64)): real(64)

Warning

rint is unstable while we design more thorough rounding support

Returns the rounded integral value of the argument x determined by the current rounding direction. `rint` may raise the “inexact” floating-point exception.

proc rint(x: real(32)): real(32)

Warning

rint is unstable while we design more thorough rounding support

Returns the rounded integral value of the argument x determined by the current rounding direction. `rint` may raise the “inexact” floating-point exception.

proc sin(x: real(64)): real(64)

Returns the sine of the argument x.

proc sin(x: real(32)): real(32)

Returns the sine of the argument x.

proc sin(x: complex(64)): complex(64)

Returns the sine of the argument x.

proc sin(x: complex(128)): complex(128)

Returns the sine of the argument x.

proc sinh(x: real(64)): real(64)

Returns the hyperbolic sine of the argument x.

proc sinh(x: real(32)): real(32)

Returns the hyperbolic sine of the argument x.

proc sinh(x: complex(64)): complex(64)

Returns the hyperbolic sine of the argument x.

proc sinh(x: complex(128)): complex(128)

Returns the hyperbolic sine of the argument x.

proc tan(x: real(64)): real(64)

Returns the tangent of the argument x.

proc tan(x: real(32)): real(32)

Returns the tangent of the argument x.

proc tan(x: complex(64)): complex(64)

Returns the tangent of the argument x.

proc tan(x: complex(128)): complex(128)

Returns the tangent of the argument x.

proc tanh(x: real(64)): real(64)

Returns the hyperbolic tangent of the argument x.

proc tanh(x: real(32)): real(32)

Returns the hyperbolic tangent of the argument x.

proc tanh(x: complex(64)): complex(64)

Returns the hyperbolic tangent of the argument x.

proc tanh(x: complex(128)): complex(128)

Returns the hyperbolic tangent of the argument x.

proc tgamma(x: real(64)): real(64)

Warning

‘tgamma’ has been deprecated in favor of `gamma`, please use that instead

Returns the gamma function of the argument x.

proc tgamma(x: real(32)): real(32)

Warning

‘tgamma’ has been deprecated in favor of `gamma`, please use that instead

Returns the gamma function of the argument x.

proc gcd(in x: int, in y: int): int

Returns the greatest common divisor of the integer arguments x and y.

proc gcd(in x: int(32), in y: int(32)): int(32)

Returns the greatest common divisor of the integer arguments x and y.

proc gcd(in x: int(16), in y: int(16)): int(16)

Returns the greatest common divisor of the integer arguments x and y.

proc gcd(in x: int(8), in y: int(8)): int(8)

Returns the greatest common divisor of the integer arguments x and y.

proc gcd(in x: uint(64), in y: uint(64)): uint(64)

Returns the greatest common divisor of the unsigned integer arguments x and y.

proc gcd(in x: uint(32), in y: uint(32)): uint(32)

Returns the greatest common divisor of the unsigned integer arguments x and y.

proc gcd(in x: uint(16), in y: uint(16)): uint(16)

Returns the greatest common divisor of the unsigned integer arguments x and y.

proc gcd(in x: uint(8), in y: uint(8)): uint(8)

Returns the greatest common divisor of the unsigned integer arguments x and y.

proc j0(x: real(32)): real(32)

Warning

‘j0’ is unstable and may be renamed or moved to a different module in the future

Returns the Bessel function of the first kind of order 0 of x.

proc j0(x: real(64)): real(64)

Warning

‘j0’ is unstable and may be renamed or moved to a different module in the future

Returns the Bessel function of the first kind of order 0 of x.

proc j1(x: real(32)): real(32)

Warning

‘j1’ is unstable and may be renamed or moved to a different module in the future

Returns the Bessel function of the first kind of order 1 of x.

proc j1(x: real(64)): real(64)

Warning

‘j1’ is unstable and may be renamed or moved to a different module in the future

Returns the Bessel function of the first kind of order 1 of x.

proc jn(n: int, x: real(32)): real(32)

Warning

‘jn’ is unstable and may be renamed or moved to a different module in the future

Returns the Bessel function of the first kind of order n of x.

proc jn(n: int, x: real(64)): real(64)

Warning

‘jn’ is unstable and may be renamed or moved to a different module in the future

Returns the Bessel function of the first kind of order n of x.

proc y0(x: real(32)): real(32)

Warning

‘y0’ is unstable and may be renamed or moved to a different module in the future

Returns the Bessel function of the second kind of order 0 of x, where x must be greater than 0.

proc y0(x: real(64)): real(64)

Warning

‘y0’ is unstable and may be renamed or moved to a different module in the future

Returns the Bessel function of the second kind of order 0 of x, where x must be greater than 0.

proc y1(x: real(32)): real(32)

Warning

‘y1’ is unstable and may be renamed or moved to a different module in the future

Returns the Bessel function of the second kind of order 1 of x, where x must be greater than 0.

proc y1(x: real(64)): real(64)

Warning

‘y1’ is unstable and may be renamed or moved to a different module in the future

Returns the Bessel function of the second kind of order 1 of x, where x must be greater than 0.

proc yn(n: int, x: real(32)): real(32)

Warning

‘yn’ is unstable and may be renamed or moved to a different module in the future

Returns the Bessel function of the second kind of order n of x, where x must be greater than 0.

proc yn(n: int, x: real(64)): real(64)

Warning

‘yn’ is unstable and may be renamed or moved to a different module in the future

Returns the Bessel function of the second kind of order n of x, where x must be greater than 0.

proc fma(x: real(64), y: real(64), z: real(64)): real(64)

Warning

The ‘fma()’ procedure was recently added, and may change based on feedback

Performs a fused multiply-add operation that multiplies `x` and `y` and adds `z` to the result. The advantage of `fma()` over the expression `(x*y)+z` is that it avoids the additional error introduced by performing two separate floating point operations. It can also be faster on machines that implement the operation as a single instruction.

Note

When compiling with `CHPL_TARGET_COMPILER=llvm`, this procedure should reliably generate a single hardware instruction on `x86` if `--specialize` is thrown and `CHPL_TARGET_CPU` is set (provided that the `x86` CPU supports hardware FMA).

When compiling with C, this procedure will call out to the `fma()` routines defined in the C header math.h. Any optimization performed is decided by the C compiler.

proc fma(x: real(32), y: real(32), z: real(32)): real(32)

Warning

The ‘fma()’ procedure was recently added, and may change based on feedback

proc fma(x: imag(64), y: imag(64), z: imag(64)): imag(64)

Warning

The ‘fma()’ procedure was recently added, and may change based on feedback

proc fma(x: imag(32), y: imag(32), z: imag(32)): imag(32)

Warning

The ‘fma()’ procedure was recently added, and may change based on feedback