## Appendix 9--ISO Mathematics Library Modules

### A9.1 RealMath

```DEFINITION MODULE RealMath;

(* Mathematical functions for the type REAL *)

CONST
pi   = 3.1415926535897932384626433832795028841972;
exp1 = 2.7182818284590452353602874713526624977572;

PROCEDURE sqrt (x: REAL): REAL;
(* Returns the positive square root of x *)

PROCEDURE exp (x: REAL): REAL;
(* Returns the exponential of x *)

PROCEDURE ln (x: REAL): REAL;
(* Returns the natural logarithm of x *)

(* The angle in all trigonometric functions is measured in radians *)

PROCEDURE sin (x: REAL): REAL;
(* Returns the sine of x *)

PROCEDURE cos (x: REAL): REAL;
(* Returns the cosine of x *)

PROCEDURE tan (x: REAL): REAL;
(* Returns the tangent of x *)

PROCEDURE arcsin (x: REAL): REAL;
(* Returns the arcsine of x *)

PROCEDURE arccos (x: REAL): REAL;
(* Returns the arccosine of x *)

PROCEDURE arctan (x: REAL): REAL;
(* Returns the arctangent of x *)

PROCEDURE power (base, exponent: REAL): REAL;
(* Returns the value of the number base raised to the power exponent *)

PROCEDURE round (x: REAL): INTEGER;
(* Returns the value of x rounded to the nearest integer *)

PROCEDURE IsRMathException (): BOOLEAN;
(* Returns TRUE if the current coroutine is in the exceptional execution state because of the raising of an exception in a routine from this module; otherwise returns FALSE.  *)

END RealMath.```

### A9.2 LongMath

```DEFINITION MODULE LongMath;

(* Mathematical functions for the type LONGREAL *)

CONST
pi   = 3.1415926535897932384626433832795028841972;
exp1 = 2.7182818284590452353602874713526624977572;

PROCEDURE sqrt (x: LONGREAL): LONGREAL;
(* Returns the positive square root of x *)

PROCEDURE exp (x: LONGREAL): LONGREAL;
(* Returns the exponential of x *)

PROCEDURE ln (x: LONGREAL): LONGREAL;
(* Returns the natural logarithm of x *)

(* The angle in all trigonometric functions is measured in radians *)

PROCEDURE sin (x: LONGREAL): LONGREAL;
(* Returns the sine of x *)

PROCEDURE cos (x: LONGREAL): LONGREAL;
(* Returns the cosine of x *)

PROCEDURE tan (x: LONGREAL): LONGREAL;
(* Returns the tangent of x *)

PROCEDURE arcsin (x: LONGREAL): LONGREAL;
(* Returns the arcsine of x *)

PROCEDURE arccos (x: LONGREAL): LONGREAL;
(* Returns the arccosine of x *)

PROCEDURE arctan (x: LONGREAL): LONGREAL;
(* Returns the arctangent of x *)

PROCEDURE power (base, exponent: LONGREAL): LONGREAL;
(* Returns the value of the number base raised to the power exponent *)

PROCEDURE round (x: LONGREAL): INTEGER;
(* Returns the value of x rounded to the nearest integer *)

PROCEDURE IsRMathException (): BOOLEAN;
(* Returns TRUE if the current coroutine is in the exceptional execution state because of the raising of an exception in a routine from this module; otherwise returns FALSE.  *)

END LongMath.```

### A9.3 ComplexMath

```DEFINITION MODULE ComplexMath;

(* =========================================
Original COMPLEX specification and
design of ComplexMath
Assigned to the BSI for standards work

===========================================*)

(* Mathematical functions for the type COMPLEX *)

CONST
i =    CMPLX (0.0, 1.0);
one =  CMPLX (1.0, 0.0);
zero = CMPLX (0.0, 0.0);

PROCEDURE abs (z: COMPLEX): REAL;
(* Returns the length of z *)

PROCEDURE arg (z: COMPLEX): REAL;
(* Returns the angle that z subtends to the positive real axis *)

PROCEDURE conj (z: COMPLEX): COMPLEX;
(* Returns the complex conjugate of z *)

PROCEDURE power (base: COMPLEX; exponent: REAL): COMPLEX;
(* Returns the value of the number base raised to the power exponent *)

PROCEDURE sqrt (z: COMPLEX): COMPLEX;
(* Returns the principal square root of z *)

PROCEDURE exp (z: COMPLEX): COMPLEX;
(* Returns the complex exponential of z *)

PROCEDURE ln (z: COMPLEX): COMPLEX;
(* Returns the principal value of the natural logarithm of z *)

PROCEDURE sin (z: COMPLEX): COMPLEX;
(* Returns the sine of z *)

PROCEDURE cos (z: COMPLEX): COMPLEX;
(* Returns the cosine of z *)

PROCEDURE tan (z: COMPLEX): COMPLEX;
(* Returns the tangent of z *)

PROCEDURE arcsin (z: COMPLEX): COMPLEX;
(* Returns the arcsine of z *)

PROCEDURE arccos (z: COMPLEX): COMPLEX;
(* Returns the arccosine of z *)

PROCEDURE arctan (z: COMPLEX): COMPLEX;
(* Returns the arctangent of z *)

PROCEDURE polarToComplex (abs, arg: REAL): COMPLEX;
(* Returns the complex number with the specified polar coordinates *)

PROCEDURE scalarMult (scalar: REAL; z: COMPLEX): COMPLEX;
(* Returns the scalar product of scalar with z *)

PROCEDURE IsCMathException (): BOOLEAN;
(* Returns TRUE if the current coroutine is in the exceptional execution state  because of the raising of an exception in a routine from this module; otherwise returns FALSE. *)

END ComplexMath.```

### A9.4 LongComplexMath

```DEFINITION MODULE LongComplexMath;

(* =========================================
Original COMPLEX specification and
design of ComplexMath
Assigned to the BSI for standards work
===========================================*)

(* Mathematical functions for the type LONGCOMPLEX *)

CONST
i =    CMPLX (0.0, 1.0);
one =  CMPLX (1.0, 0.0);
zero = CMPLX (0.0, 0.0);

PROCEDURE abs (z: LONGCOMPLEX): LONGREAL;
(* Returns the length of z *)

PROCEDURE arg (z: LONGCOMPLEX): LONGREAL;
(* Returns the angle that z subtends to the positive real axis *)

PROCEDURE conj (z: LONGCOMPLEX): LONGCOMPLEX;
(* Returns the complex conjugate of z *)

PROCEDURE power (base: LONGCOMPLEX; exponent: LONGREAL): LONGCOMPLEX;
(* Returns the value of the number base raised to the power exponent *)

PROCEDURE sqrt (z: LONGCOMPLEX): LONGCOMPLEX;
(* Returns the principal square root of z *)

PROCEDURE exp (z: LONGCOMPLEX): LONGCOMPLEX;
(* Returns the complex exponential of z *)

PROCEDURE ln (z: LONGCOMPLEX): LONGCOMPLEX;
(* Returns the principal value of the natural logarithm of z *)

PROCEDURE sin (z: LONGCOMPLEX): LONGCOMPLEX;
(* Returns the sine of z *)

PROCEDURE cos (z: LONGCOMPLEX): LONGCOMPLEX;
(* Returns the cosine of z *)

PROCEDURE tan (z: LONGCOMPLEX): LONGCOMPLEX;
(* Returns the tangent of z *)

PROCEDURE arcsin (z: LONGCOMPLEX): LONGCOMPLEX;
(* Returns the arcsine of z *)

PROCEDURE arccos (z: LONGCOMPLEX): LONGCOMPLEX;
(* Returns the arccosine of z *)

PROCEDURE arctan (z: LONGCOMPLEX): LONGCOMPLEX;
(* Returns the arctangent of z *)

PROCEDURE polarToComplex (abs, arg: LONGREAL): LONGCOMPLEX;
(* Returns the complex number with the specified polar coordinates *)

PROCEDURE scalarMult (scalar: LONGREAL; z: LONGCOMPLEX): LONGCOMPLEX;
(* Returns the scalar product of scalar with z *)

PROCEDURE IsCMathException (): BOOLEAN;
(* Returns TRUE if the current coroutine is in the exceptional execution state  because of the raising of an exception in a routine from this module; otherwise returns FALSE. *)

END LongComplexMath.```

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