ILE Math Bindable API Descriptions

The following information is provided for each math bindable API.

Definition

This column states the nature of the computation performed by the API.

API Name

This column gives the API names of the procedure.

Parameter Type

This column describes the acceptable parameter types that are input to and output by the specified API, and is indicated by the following characters:

32-bit binary integer.

64-bit binary integer.

32-bit single floating-point number.

A 64-bit double floating-point number.

A 32-bit single floating-complex number (both real and imaginary parts are 32 bits long).

A 64-bit double floating-complex number (both real and imaginary parts are 64 bits long).

Note: The characters correspond to the fifth character of the called API.

Equation

This column gives a math equation that represents the computation.

The following notation is used in the equations of the APIs:

|x|

denotes the absolute value of x.

sign(x)

is +1 if x >= 0 or -1 if x < 0.

denotes a function result.

denotes a complex argument, where

z = x + iy.

z1 and z2

denote two complex arguments, where

z1 = x1 + iy1 and z2 = x2 +iy2.

No. Inputs

This column states how many input parameters must be passed to the routine. See Calling Math Bindable APIs for a description of the format of APIs with 1 or 2 input parameters.

Input Range

This column gives the valid range for input parameters. If a parameter is not within the range, an error message is issued. (See the table below for a description of the messages that can be generated by the math bindable APIs.)

For output ranges, see Data Types and Limits for information concerning integer data types, real data types, and complex data types.

Math API Descriptions

  Service Program Name: QLEMF

  Default Public Authority: *USE

  Threadsafe: Yes

Definition

API Name

Para- meter Type

Equation

No. Inputs

Input Range¹

Absolute Function

CEESxABS

I
J
S
D
T
E

f = |x|
or
f = |z|

Any integer number (for parameter type I and J).

Any real number (for parameter types S and D).

Any complex number (for parameter types T and E).

Arccosine

CEESxACS

S
D

f = cos^-1(x)

|x| <= 1

Arcsine

CEESxASN

S
D

f = sin^-1(x)

|x| <= 1

Arctangent

CEESxATN

S
D
T
E

f = tan^-1(x)
or
f = tan^-1(z) = tan^-1(x + iy)

Any real argument (for parameter types S and D).

Any complex argument (for parameter types T and E).

Arctangent2

CEESxAT2

S
D

f = atan2(y/x)

For x > 0,
atan2(y, x) = tan^-1(y/x).

For x < 0 and y > 0,
atan2(y, x) = pi + tan^-1(y/x).

For x < 0 and y < 0,
atan2(y, x) = -pi + tan^-1(x/y).

y is not equal to 0.0 and
x is not equal to 0.0;

y is not equal to +INF or -INF and
x is not equal to +INF or -INF

Conjugate of Complex

CEESxCJG

T
E

f = x - iy for argument z = x + iy.

Any complex number.

Cosine

CEESxCOS

S
D
T
E

f = cos(x)
or
f = cos(z) = cos (x + iy)

Any real argument, in radians, such that
|x| <= 0x432921FB54442D18 ~= pi * 2⁵⁰
~= 3537118876014220.0.
Any complex number such that
|y| <= 88.7228 for FLOAT4 and
|y| <= 709.7827 for FLOAT8,
and x is any real argument.

Cotangent

CEESxCTN

S
D

f = cot(x)

Any real argument, in radians, such that
|x| <= 0x432921FB54442D18 ~= pi * 2⁵⁰
~= 3537118876014220.0.

Error Function and its Complement

CEESxERF CEESxERC

S
D

f equals error function of x equals 2 divided by the square root of pi multiplied by the integral from 0 to x of e raised to minus t squared times d t

Any real argument

Exponential Base e

CEESxEXP

S
D
T
E

f = e^x
or
f = e^z = e^x+iy

-87.3365 <= x <= 88.7228
(for parameter type S).
-708.3964 <= x <= 709.7827
(for parameter type D).
-87.3365 <= x <= 88.7228 and y is any
real number (for parameter type T).
-708.3964 <= x <= 709.7827 and y is
any real number where
|y| <= 0x432921FB54442D18 ~= pi * 2⁵⁰
~= 3537118876014220.0.
(for parameter type E).

Exponentiation

CEESxXPy

I
J
S
D
T
E

f = x^y (See note 2)

Any integer arguments (for CEESIXPI, CEESSXPI, CEESDXPI, CEESTXPI, CEESEXPI, CEESJXPJ, CEESSXPJ, CEESDXPJ, CEESTXPJ, CEESEXPJ).

Any real argument subject to the condition that if x is negative, y must be an integer (for CEESSXPS, CEESDXPD).

For complex data types, see the argument for real data types above (for CEESTXPT, CEESEXPE).

Factorial

CEE4SxFAC

I
J

n! = 1*2*3 ... (n-1)*n.

For parameter type I, any integer <=12. For parameter type J, any integer <=20.

Floating Complex Divide

CEESxDVD

T
E

f = z₁ / z₂ = (x₁ + iy₁) / (x₂ + iy₂)

Any complex number.

Floating Complex Multiply

CEESxMLT

T
E

f = z₁ * z₂ = (x₁ + iy₁) * (x₂ + iy₂)

Any complex number.

Gamma Function

CEESxGMA

S
D

f equals gamma function of x equals integral from 0 to plus infinity of t raised to x minus 1 multiplied by e raised to minus t multiplied by d t

0 < x <= 35.04
(for parameter type S).
0 < x <= 171.6243
(for parameter type D).

Hyperbolic Arctangent

CEESxATH

S
D
T
E

f = tanh^-1(x)
or
f = tanh^-1(z) = tanh^-1(x + iy)

Any real argument such that

|x| <= 1
(for parameter types S and D).
Any complex number such that
x is not equal to 1.0 and y is not equal to 0
(for parameter types T and E).

Hyperbolic Cosine

CEESxCSH

S
D
T
E

f = cosh(x)
or
f = cosh(z) = cosh(x + iy)

Any real argument such that
|x| <= 89.4159 (for FLOAT4)
and |x| <= 709.7827 (for FLOAT8).
Any complex number such that
|x| <= 89.4159 (for FLOAT4)
|x| <= 709.7827 (for FLOAT8).

Hyperbolic Sine

CEESxSNH

S
D
T
E

f = sinh(x)
or
f = sinh(z) = sinh(x + iy)

Any real argument such that
|x| <= 89.4159 (for FLOAT4)
and |x| <= 709.7827 (for FLOAT8).
Any complex number such that
|x| <= 89.4159 (for FLOAT4)
and |x| <= 709.7827 (for FLOAT8).

Hyperbolic Tangent

CEESxTNH

S
D
T
E

f = tanh(x)
or
f = tanh(z) = tanh(x + iy)

Any real argument
(for parameter types S and D).
Any complex number such that
|x| < 43.66825 (for parameter type T),
and |x| < 354.1982
(for parameter type E).

Imaginary Part of Complex

CEESxIMG

T
E

f = y, where z = x + iy.

Any complex number.

Log Gamma Function

CEESxLGM

S
D

f = ln(Gamma (x))

0 < x <= 4.0850*10³⁶
(for parameter type S),
and 0.0 < x <= 2¹⁰¹⁴
(for parameter type D).

Logarithm Base 10

CEESxLG1

S
D

f = log₁₀(x)

x > 0.0

Logarithm Base 2

CEESxLG2

S
D

f = log₂(x)

x > 0.0

Logarithm Base e

CEESxLOG

S
D
T
E

f = log_e(x)
or
f = ln(z) = log_e(|z|) + iatan2(y, x)

x > 0.0 (for parameter types S
and D).
z is not equal to 0+i0 (for parameter types T
and E).

Modular Arithmetic

CEESxMOD

I
J
S
D

f = remainder of x/y (See note 3)

Any two integer numbers such that
y is not equal to 0 (for parameter types I and J).
Any two real numbers such that
y is not equal to 0.0 (for parameter types S
and D).

Nearest 64-Bit Integer

CEESxNJN

S
D

If x >= 0.0
f = sign(x)*n
where n is the largest 64-bit integer
<= |x + 0.5|
or
If x < 0.0
f = sign(x)*n
where n is the largest 64-bit integer
<= |x - 0.5|

Any real number.

Nearest Integer

CEESxNIN

S
D

If x >= 0.0
f = sign(x)*n
where n is the largest integer
<= |x + 0.5|
or
If x < 0.0
f = sign(x)*n
where n is the largest integer
<= |x - 0.5|

Any real number.

Nearest Whole Number

CEESxNWN

S
D

If x >= 0.0
f = sign(x)*n
where n is the largest integer
<= |x + 0.5|
or
If x < 0.0
f = sign(x)*n
where n is the largest integer
<= |x - 0.5|

Any real number.

Positive Difference

CEESxDIM

I
J
S
D

If x > y, f = x - y
or
If x <= y, f = 0

Any integer argument
(for parameter types I and J).
Any real number
(for parameter types S and D).

Sine

CEESxSIN

S
D
T
E

f = sin(x)
or
f = sin(z) = sin(x + iy)

Any real argument, in radians, such that
|x| <= 0x432921FB54442D18 ~= pi*2⁵⁰
~= 3537118876014220.0
(for parameter types S and D).
Any complex number such that
|y| <= 88.7228 (for parameter type T),
and |y| <= 709.7827, and
|x| <= 0x432921FB54442D18 ~= pi*2⁵⁰
~= 3537118876014220.0
(for parameter type E).

Square Root

CEESxSQT

S
D
S
D

f equals the square root of x or f equals the square root of z where z is a complex number

Any real argument such that x >= 0.0
(for parameter types S and D).
Any complex number such that
|z| + |x| <= 1.797693*10³⁰⁸
(for parameter types T and E).

Tangent

CEESxTAN

S
D
T
E

f = tan(x)
or
f = tan(z) = tan(x + iy)

Any real argument, in radians, such that
|x| <= 0x432921FB54442D18 ~= pi*2⁵⁰
~= 3537118876014220.0
(for parameter types S and D).
Any complex number such that
|y| < 43.66825 (for parameter
type T), and |y| < 354.1982
(for parameter type E).

Transfer of Sign

CEESxSGN

I
J
S
D

f = sign(y)|x|

Any integer argument
(for parameter types I and J).
Any real number
(for parameter types S and D).

Truncation

CEESxINT

S
D

f = sign(x)*n,
where n is the largest integer
<= |x|

Any real number.

Notes:

1

For output ranges, see Data Types and Limits, including information about Integer Data Types, Real Data Types, and Complex Data Types.

2

Where x and y have the following combinations, respectively:

integer, integer
real FLOAT4, integer
real FLOAT8, integer
single complex, integer
double complex, integer
real FLOAT4, integer
real FLOAT8, integer
single complex, integer
double complex, integer
64-bit integer, 64-bit integer
real FLOAT4, 64-bit integer
real FLOAT8, 64-bit integer
single complex, 64-bit integer
double complex, 64-bit integer
real FLOAT4, real FLOAT4
real FLOAT8, real FLOAT8
single complex, single complex
double complex, double complex

3

The absolute value of the result is always less than the absolute value of y.

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