(* Copyright (C) 1989, Digital Equipment Corporation           *)
(* All rights reserved.                                        *)
(* See the file COPYRIGHT for a full description.              *)

(* Last modified on Fri Nov  3 14:14:31 1989 by muller         *)
(*      modified on Fri Oct 20 11:16:20 1989 by kalsow         *)
(*      modified on Fri Jan 20 12:42:01 1989 by glassman       *)
(*      modified on Thu May 21 17:29:38 1987 by rovner         *)
(*      modified on Sun Jun 22 11:05:15 1986 by violetta       *)

INTERFACE Math;

(* An interface to the C math library

   Programs that call any of these routines must be linked
   with the math library "-lm".

   The detailed semantics of these procedures are defined by
   your local C math library.  To learn the full story about
   any of these functions (e.g. their domains, ranges and
   accuracies), see the appropriate man page.

   Index: floating point, C math interface; 
          C programming, interface to C math library 
*)

(*---- miscellaneous useful constants ----*)

CONST
  Pi     = 3.1415926535897932384626433833;
  LogPi  = 1.1447298858494001741434273514;
  SqrtPi = 1.7724538509055160272981674833;
  E      = 2.7182818284590452353602874714;
  Degree = 0.017453292519943295769236907684;  (* One degree in radians *)


(*---- Exponential and Logarithm functions ----*)

<*EXTERNAL*> PROCEDURE exp (x: LONGREAL): LONGREAL;
(* returns E^x. *)

<*EXTERNAL*> PROCEDURE expm1 (x: LONGREAL): LONGREAL;
(* returns (E^x)-1, even for small x. *)

<*EXTERNAL*> PROCEDURE log (x: LONGREAL): LONGREAL;
(* returns the natural logarithm of x (base E). *)

<*EXTERNAL*> PROCEDURE log10 (x: LONGREAL): LONGREAL;
(* returns the base 10 logarithm of x. *)

<*EXTERNAL*> PROCEDURE log1p (x: LONGREAL): LONGREAL;
(* returns log(1+x), even for small x. *)

<*EXTERNAL*> PROCEDURE pow (x, y: LONGREAL): LONGREAL;
(* returns x^y. *)

<*EXTERNAL*> PROCEDURE sqrt (x: LONGREAL): LONGREAL;
(* returns the square root of x. *)


(*---- Trigonometric functions ----*)

<*EXTERNAL*> PROCEDURE cos (x: LONGREAL): LONGREAL;
(* returns the cosine of x radians. *)

<*EXTERNAL*> PROCEDURE sin (x: LONGREAL): LONGREAL;
(* returns the sine of x radians. *)

<*EXTERNAL*> PROCEDURE tan (x: LONGREAL): LONGREAL;
(* returns the tangent of x radians. *)

<*EXTERNAL*> PROCEDURE acos (x: LONGREAL): LONGREAL;
(* returns the arc cosine of x in radians. *)

<*EXTERNAL*> PROCEDURE asin (x: LONGREAL): LONGREAL;
(* returns the arc sine of x in radians. *)

<*EXTERNAL*> PROCEDURE atan (x: LONGREAL): LONGREAL;
(* returns the arc tangent of x in radians. *)

<*EXTERNAL*> PROCEDURE atan2 (x, y: LONGREAL): LONGREAL;
(* returns the arc tangent of x/y in radians. *)


(*---- Hyperbolic trigonometric functions ----*)

<*EXTERNAL*> PROCEDURE sinh (x: LONGREAL): LONGREAL;
(* returns the hyperbolic sine of x. *)

<*EXTERNAL*> PROCEDURE cosh (x: LONGREAL): LONGREAL;
(* returns the hyperbolic cosine of x. *)

<*EXTERNAL*> PROCEDURE tanh (x: LONGREAL): LONGREAL;
(* returns the hyperbolic tangent of x. *)

<*EXTERNAL*> PROCEDURE asinh (x: LONGREAL): LONGREAL;
(* returns the inverse hyperbolic sine of x *)

<*EXTERNAL*> PROCEDURE acosh (x: LONGREAL): LONGREAL;
(* returns the inverse hyperbolic cosine of x *)

<*EXTERNAL*> PROCEDURE atanh (x: LONGREAL): LONGREAL;
(* returns the inverse hyperbolic tangent of x *)


(*---- Rounding functions ----*)

<*EXTERNAL*> PROCEDURE ceil (x: LONGREAL): LONGREAL;
(* returns the least integer not less than x.
   Note: use the builtin Modula-3 function CEILING. *)

<*EXTERNAL*> PROCEDURE floor (x: LONGREAL): LONGREAL;
(* returns the greatest integer not greater than x.
   Note: use the builtin Modula-3 function FLOOR. *)

<*EXTERNAL*> PROCEDURE rint (x: LONGREAL): LONGREAL;
(* returns the nearest integer value to x.
   Note: the Modula-3 function ROUND may  be appropriate. *)

<*EXTERNAL*> PROCEDURE fabs (x: LONGREAL): LONGREAL;
(* returns the absolute value of x.
   Note: use the builtin Modula-3 function ABS. *)


(*---- Euclidean distance functions ----*)

<*EXTERNAL*> PROCEDURE hypot (x, y: LONGREAL): LONGREAL;
(* returns sqrt (x*x + y*y). *)

<*EXTERNAL*> PROCEDURE cabs (z: Complex): LONGREAL;
TYPE Complex = RECORD x, y: LONGREAL END;
(* returns sqrt (z.x*z.x + z.y*z.y) *)


(*---- Floating point representations ----*)

<*EXTERNAL*> PROCEDURE frexp (x: LONGREAL;  VAR exp: INTEGER): LONGREAL;
(* returns a value y and sets exp such that x = y * 2^exp,
    where ABS(X) is in the interval [0.5, 1). *)

<*EXTERNAL*> PROCEDURE ldexp (x: LONGREAL; exp: INTEGER): LONGREAL;
(* returns x * 2^exp. *)

<*EXTERNAL*> PROCEDURE modf (x: LONGREAL; VAR exp: INTEGER): LONGREAL;
(* returns the positive fractional part of x and sets exp to
   the remaining integer part. *)


(*---- Error functions ----*)

<*EXTERNAL*> PROCEDURE erf (x: LONGREAL): LONGREAL;
(* returns the "error" function of x. *)

<*EXTERNAL*> PROCEDURE erfc (x: LONGREAL): LONGREAL;
(* returns 1.0 - erf(x), even for large x. *) 


(*---- Gamma function ----*)

<*EXTERNAL*> PROCEDURE gamma (x: LONGREAL): LONGREAL;
<*EXTERNAL*> VAR signgam: INTEGER;
(* returns log(ABS(Gamma(ABS(x)))).  The sign of Gamma(ABS(X))
   is returned in signgam. *)


(*---- Bessel functions ----*)

<*EXTERNAL*> PROCEDURE j0 (x: LONGREAL): LONGREAL;
(* returns the zero-order Bessel function of first kind on x. *)

<*EXTERNAL*> PROCEDURE j1 (x: LONGREAL): LONGREAL;
(* returns the first-order Bessel function of first kind on x. *)

<*EXTERNAL*> PROCEDURE jn (n: INTEGER;  x: LONGREAL): LONGREAL;
(* returns the n th-order Bessel function of first kind on x. *)

<*EXTERNAL*> PROCEDURE y0 (x: LONGREAL): LONGREAL;
(* returns the zero-order Bessel function of second kind on x. *)

<*EXTERNAL*> PROCEDURE y1 (x: LONGREAL): LONGREAL;
(* returns the first-order Bessel function of second kind on x. *)

<*EXTERNAL*> PROCEDURE yn (n, x: LONGREAL): LONGREAL;
(* returns the n th-order Bessel function of second kind on x. *)


END Math.