Math¶

Usage

use Math;

This module provides mathematical constants and functions.

It includes wrappers for many of the constants in 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.

Rounding -- The rounding mode for floating-point addition (subtraction) is implementation-defined.

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.

param e = 2.71828¶

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

param log2_e = 1.4427¶

log2(e)

param log10_e = 0.434294¶

log10(e)

param ln_2 = 0.693147¶

log(2) (natural logarithm)

param ln_10 = 2.30259¶

log(10) (natural logarithm)

param pi = 3.14159¶

pi - the circumference/the diameter of a circle

param half_pi = 1.5708¶

pi/2

param quarter_pi = 0.785398¶

pi/4

param recipr_pi = 0.31831¶

1/pi

param twice_recipr_pi = 0.63662¶

2/pi

param twice_recipr_sqrt_pi = 1.12838¶

2/sqrt(pi)

param sqrt_2 = 1.41421¶

sqrt(2)

param recipr_sqrt_2 = 0.707107¶

1/sqrt(2)

proc abs(i: int(?w))¶

Returns the absolute value of the integer argument.

Return type:	The type of i.

proc abs(i: uint(?w))

Returns the absolute value of the unsigned integer argument.

Return type:	The type of i.

proc abs(param i: integral) param

Returns the absolute value of the integer param argument i.

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

Returns the magnitude of the real argument r.

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

Returns the magnitude of the real argument x.

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

Returns the real magnitude of the imaginary argument im.

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

Returns the real magnitude of the imaginary argument im.

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

Returns the real magnitude of the complex argument z.

Return type:	The type of the real component of the argument (== w/2).

proc carg(z: complex(?w)): real(w/2)¶

Returns the real phase angle of complex argument z.

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(z: complex(64)): complex(64)

Returns the arc cosine of the argument z.

proc acos(z: complex(128)): complex(128)

Returns the arc cosine of the argument z.

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(z: complex(64)): complex(64)

Returns the inverse hyperbolic cosine of the argument z.

proc acosh(z: complex(128)): complex(128)

Returns the inverse hyperbolic cosine of the argument z.

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(z: complex(64)): complex(64)

Returns the arc sine of the argument z.

proc asin(z: complex(128)): complex(128)

Returns the arc sine of the argument z.

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(z: complex(64)): complex(64)

Returns the inverse hyperbolic sine of the argument z.

proc asinh(z: complex(128)): complex(128)

Returns the inverse hyperbolic sine of the argument z.

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(z: complex(64)): complex(64)

Returns the arc tangent of the argument z.

proc atan(z: complex(128)): complex(128)

Returns the arc tangent of the argument z.

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 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(z: complex(64)): complex(64)

Returns the inverse hyperbolic tangent of the argument z.

proc atanh(z: complex(128)): complex(128)

Returns the inverse hyperbolic tangent of the argument z.

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 conjg(z: complex(?w))¶

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))

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))

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))

proc conjg(z: real(?w))

proc cproj(z: complex(?w)): real(w/2)¶

Returns the projection of z on a Riemann sphere.

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(z: complex(64)): complex(64)

Returns the cosine of the argument z.

proc cos(z: complex(128)): complex(128)

Returns the cosine of the argument z.

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(z: complex(64)): complex(64)

Returns the hyperbolic cosine of the argument z.

proc cosh(z: complex(128)): complex(128)

Returns the hyperbolic cosine of the argument z.

proc divceil(param m: integral, param n: integral) param¶

Returns ceil(m/n), i.e., the fraction m/n rounded up to the nearest integer.

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

proc divceil(m: integral, n: integral)

Returns ceil(m/n), i.e., the fraction m/n rounded up to the nearest integer.

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

proc divceilpos(m: integral, n: integral)¶

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 m: integral, param n: integral) param¶

Returns floor(m/n), i.e., the fraction m/n rounded down to the nearest integer.

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

proc divfloor(m: integral, n: integral)

Returns floor(m/n), i.e., the fraction m/n rounded down to the nearest integer.

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

proc divfloorpos(m: integral, n: integral)¶

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)¶

Returns the error function of the argument x.

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

Returns the error function of the argument x.

proc erfc(x: real(64)): real(64)¶

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

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

Returns the complementary error function of the argument. 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.

proc exp(z: complex(64)): complex(64)

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

proc exp(z: complex(128)): complex(128)

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

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 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 INFINITY: real(64)¶

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

Multiply by an integer power of 2. Returns x * 2**n.

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

proc lgamma(x: real(64)): real(64)¶

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

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

Returns the natural logarithm of the absolute value of the gamma function 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(z: complex(64)): complex(64)

Returns the natural logarithm of the argument z.

proc log(z: complex(128)): complex(128)

Returns the natural logarithm of the argument z.

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(in val: int(?w), baseLog2)¶

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(in val: uint(?w), baseLog2)

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(in val: int(?w))

Returns the base 2 logarithm of the argument x.

Return type:	int(64)

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

proc log2(in val: uint(?w))

Returns the base 2 logarithm of the argument x.

Return type:	int(64)

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

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

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)

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(x: real(?w), y: real(w)): real(w)

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

The return value has the same type as x.

proc NAN: real(64)¶

Returns a value for which isnan will return true.

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

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)

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)¶

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)

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

proc round(x: real(64)): real(64)¶

Returns the rounded integral value of the argument x.

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

Returns the rounded integral value of the argument x.

proc sgn(i: int(?w)): int(8)¶

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)

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

Returns the signum function of the integer param argument i: 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 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(z: complex(64)): complex(64)

Returns the sine of the argument z.

proc sin(z: complex(128)): complex(128)

Returns the sine of the argument z.

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(z: complex(64)): complex(64)

Returns the hyperbolic sine of the argument z.

proc sinh(z: complex(128)): complex(128)

Returns the hyperbolic sine of the argument z.

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(z: complex(64)): complex(64)

Returns the square root of the argument z.

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

Returns the square root of the argument z.

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(z: complex(64)): complex(64)

Returns the tangent of the argument z.

proc tan(z: complex(128)): complex(128)

Returns the tangent of the argument z.

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(z: complex(64)): complex(64)

Returns the hyperbolic tangent of the argument z.

proc tanh(z: complex(128)): complex(128)

Returns the hyperbolic tangent of the argument z.

proc tgamma(x: real(64)): real(64)¶

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

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

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

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 gcd(in a: int, in b: int): int¶

Returns the greatest common divisor of the integer argument a and b.

proc j0(x: real(32)): real(32)¶

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

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

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

proc j1(x: real(32)): real(32)¶

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

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

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

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

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

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

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

proc y0(x: real(32)): real(32)¶

Returns the Bessel function of the second kind of order 0 of x, if and only if the value of x is greater than 0

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

Returns the Bessel function of the second kind of order 0 of x, if and only if the value of x is greater than 0

proc y1(x: real(32)): real(32)¶

Returns the Bessel function of the second kind of order 1 of x, if and only if the value of x is greater than 0

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

Returns the Bessel function of the second kind of order 1 of x, if and only if the value of x is greater than 0

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

Returns the Bessel function of the second kind of order n of x, if and only if the value of x is greater than 0

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

Returns the Bessel function of the second kind of order n of x, if and only if the value of x is greater than 0