13.10 Math Interface

ORIGIN 'betaenv';
LIB_DEF 'math' '../lib';
(*
 * COPYRIGHT
 *       Copyright (C) Mjolner Informatics, 1984-96
 *       All rights reserved.
 *
 * Math.bet: mathematical functions
 * 
 * This library provides mathematical patterns: trigonometric,
 * hyperbolic, exponential and logarithmic, floating point
 * manipulation and miscellaneous constants.
 *)
--- LIB: Attributes ---

(* miscellaneous constants *)

e:       (# Exit 2.7182818284590452354 #);
log2e:   (# Exit 1.4426950408889634074 #);
log10e:  (# Exit 0.43429448190325182765 #);
ln2:     (# Exit 0.69314718055994530942 #);
ln10:    (# Exit 2.30258509299404568402 #);
pi:      (# Exit 3.14159265358979323846 #);
pihalf:  (# Exit 1.57079632679489661923 #);
piforth: (# Exit 0.78539816339744830962 #);

(* trigonometric functions *)

acos: external
  (* returns the arccosine of x in radians, in the range 0 to pi.  If
   * x is a NaN (Not-a-Number) or if the absolute value of x exceeds
   * 1.0, acos(x) returns a NaN.  Invalid operation/DOMAIN error is
   * signaled if x is a NaN or if |x| > 1.0.
   *)
  (# x,res: @Real;
  enter x
  exit res
  #);
asin: external
  (* returns the arcsine of x in radians, in the range -pi/2 to pi/2.
   * If x is a NaN or if the absolute value of x exceeds 1.0, asin
   * returns a NaN.  Invalid operation/DOMAIN error is signaled if x
   * is a NaN or if |x| > 1.0.
   *)
  (# x,res: @Real;
  enter x
  exit res
  #);
atan: external
  (* returns the arctangent of x, in the range of -pi/2 to pi/2
   * radians.  If x = +-infinity, then atan(x) returns +-pi/2.  If x
   * is +- 0, then atan returns x. If x is a NaN, then atan returns a
   * NaN.  An invalid operation/DOMAIN error is signaled by atan only
   * if x is a NaN.
   *)
  (# x,res: @Real;
  enter x
  exit res
  #);
atan2: external
  (* returns the arctangent of y/x in radians, in the range -pi to
   * pi, using the signs of both arguments to determine the quadrant
   * of the return value.
   * 
   * If x is a NaN or if y is a NaN or if both x and y are infinities,
   * atan2 returns a NaN.  If both x and y are zero, atan2 returns
   * zero.  Invalid operation/DOMAIN error is signaled by atan2 if
   * both x and y are infinite or if either x or y is a NaN.
   *)
  (# y,x,res: @Real;
  enter (y,x)
  exit res
  #);
cos: external
  (* computes the cosine of x, where x is expressed in radians.
   * 
   * The cos function uses an argument reduction based on the
   * remainder function and pi.  The cos function is periodic with
   * respect to pi, so its period differs slightly from its
   * mathematical counterpart and diverges from its counterpart when
   * the argument becomes very large.
   * 
   * If x is infinite or a NaN, then cos returns a NaN and signals
   * invalid/DOMAIN error.
   *)
  (# x,res: @Real;
  enter x
  exit res
  #);
sin: external
  (* computes the sine of x, where x is expressed in radians.
   * 
   * The sin function uses an argument reduction based on the
   * remainder function and pi.  The sin function is periodic with
   * respect to pi, so its period differs slightly from its
   * mathematical counterpart and diverges from its counterpart when
   * the argument becomes very large.
   * 
   * If x is infinite or a NaN, then sin returns a NaN and signals
   *    invalid/DOMAIN error.
   *)
  (# x,res: @Real;
  enter x
  exit res
  #);
tan: external
  (* computes the tangent of x, where x is expressed in radians.
   * 
   * The tan function uses an argument reduction based on the
   * remainder function and pi The tan function is periodic with
   * respect to pi, so its period differs slightly from its
   * mathematical counterpart and diverges from its counterpart when
   * the argument becomes very large.
   *)
  (# x,res: @Real;
  enter x
  exit res
  #);

(* hyperbolic functions *)

cosh: external
  (* returns the hyberbolic cosine of x.
   * 
   * If x is a NaN, cosh returns a NaN.
   *)
  (# x,res: @Real;
  enter x
  exit res
  #);
sinh: external
  (* returns the hyberbolic sine of x.
   * 
   * If x is a NaN, sinh returns a NaN.
   *)
  (# x,res: @Real;
  enter x
  exit res
  #);
tanh: external
  (* returns the hyberbolic tangent of x.
   * 
   * If x is a NaN, tanh returns a NaN.
   *)
  (# x,res: @Real;
  enter x
  exit res
  #);

(* exponential and logarithmic functions *)

exp: external
  (* returns the base-e or natural exponential e^x.
   * 
   * Special cases for exp:
   * 
   * If x = +infinity, then exp returns +infinity and does not signal
   * an exception.  If x = ­infinity, then exp returns 0 and does not
   * signal an exception.  If x is a NaN, then exp returns a NaN.
   *)
  (# x,res: @Real;
  enter x
  exit res
  #);
ldexp: external
  (* returns the quantity x * 2^exp. *)
  (# x,res: @Real;
     exp: @Integer;
  enter (x,exp)
  exit res
  #);
log: external
  (* returns the base e or natural logarithm of its argument x.
   * 
   * Special cases for log:
   * 
   * If x is +infinity, then log returns +infinity and signals no
   * exceptions.  If x is 0, then log returns -infinity and signals
   * divide-by-zero.  If x < 0, then log returns a NaN and signals
   * invalid/DOMAIN error.
   *)
  (# x,res: @Real;
  enter x
  exit res
  #);
log10: external
  (* returns the base 10 logarithm of x.
   * 
   * If x is a NaN or is negative, log10 returns a NaN. If x is
   * +infinity, log10(x) returns +infinity.  If x is zero, log10
   * returns -infinity and signals divide by zero/SING error.
   *)
  (# x,res: @Real;
  enter x
  exit res
  #);

(* floating point manipulation *)

modf: external
  (* returns the fractional part of x and stores the integral part
   * indirectly in the location pointed to by ipPtr.  Both the return
   * value and the value stored in ipPtr share the same sign as x.
   * 
   * If x is infinite, modf returns a zero with the sign of x and sets
   * ipPtr to x.  If x is a NaN, mod returns a NaN and sets ipPtr to
   * the same NaN.
   *)
  (# x,res: @Real;
     ipPtr: @Integer;
  enter (x,ipPtr)
  exit res
  #);
pow: external
  (* returns x^y *)
  (# x,y,res: @Real;
  enter (x,y)
  exit res
  #);
sqrt: external
  (* computes the square root of x.
   * 
   * Special cases for sqrt:
   * 
   * If x is a NaN, sqrt returns a NaN and signals no exceptions.  If
   * x is a NaN or if x < 0, sqrt returns a NaN and signals invalid
   * operation/DOMAIN error.
   *)
  (# x,res: @Real;
  enter x
  exit res
  #);
ceil: external
  (* returns the smallest integer value (in real format) not less
   * than x.
   * 
   * If x is a NaN, ceil returns a NaN.  If x is infinite, ceil
   * returns x.  Invalid operation is signaled by ceil if x is a NaN.
   * If x is a non-integral finite value, ceil signals inexact
   *)
  (# x,res: @Real;
  enter x
  exit res
  #);
fmin: (* Returns the minimum of 2 reals *)
  (# a,b: @real
  enter (a,b)
  do (if (a < b) then a->b if)
  exit b
  #);
fmax: (* Returns the maximum of 2 reals *)
  (# a,b: @real
  enter (a,b)
  do (if (a < b) then b->a if)
  exit a
  #);
fabs: external
  (* returns |x|, the absolute value of x *)
  (# x,res: @Real;
  enter x
  exit res
  #);
floor: external
  (* largest integer value (in real format) not greater than x.
   * 
   * If x is a NaN, floor returns a NaN.  If x is infinite, floor
   * returns x. Invalid operation is signaled by floor if x is a NaN.
   * If x is a non-integral finite value, floor signals inexact.
   *)
  (# x,res: @Real;
  enter x
  exit res
  #);
fmod: external
  (* Whenever possible, the fmod pattern returns the number f with
   * the same sign as x, such that x = i*y + f for some integer i, and
   * |f| < |y|. If y is 0, fmod returns a NaN.
   *)
  (# x,y,f: @Real;
  enter (x,y)
  exit f
  #)