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
Copyright © 1990-1991 by R. Sutcliffe
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
Copyright © 1990-1991 by R. Sutcliffe
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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