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MathLib.md

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MathLib

Standard mathematical functions operating on REAL (single-precision float) values. Provides trigonometric, exponential, and random number functions.

MathLib and MathLib0 are identical -- they export the same procedures with the same signatures. Both names exist because different PIM4 compilers historically used one or the other. You can import from either; FROM MathLib IMPORT sqrt and FROM MathLib0 IMPORT sqrt are interchangeable.

Available in PIM4 mode (the default). No special flags needed.

Procedures

Trigonometric

PROCEDURE sin(x: REAL): REAL;

Sine of x (radians).

PROCEDURE cos(x: REAL): REAL;

Cosine of x (radians).

PROCEDURE arctan(x: REAL): REAL;

Arctangent of x, returning a value in radians. To compute atan2(y,x), use arctan(y/x) with appropriate quadrant handling.

Exponential and Logarithmic

PROCEDURE exp(x: REAL): REAL;

Natural exponential: e raised to the power x.

PROCEDURE ln(x: REAL): REAL;

Natural logarithm of x. x must be positive.

Root

PROCEDURE sqrt(x: REAL): REAL;

Square root of x. x must be non-negative.

Rounding

PROCEDURE entier(x: REAL): INTEGER;

Floor function: returns the largest integer not greater than x. This is useful for converting REAL to INTEGER since Modula-2 has no implicit conversions. Note that TRUNC (a builtin) truncates toward zero, while entier rounds toward negative infinity.

entier(3.7)    (* = 3 *)
entier(-3.7)   (* = -4, not -3 *)
TRUNC(-3.7)    (* = -3, truncates toward zero *)

Random Numbers

PROCEDURE Random(): REAL;

Return a pseudo-random REAL in the range [0.0, 1.0). Uses the C rand() function internally.

PROCEDURE Randomize(seed: CARDINAL);

Seed the random number generator. Call this once at program start if you want different sequences on each run. Pass a value like the current time or process ID.

Example

MODULE MathDemo;
FROM InOut IMPORT WriteString, WriteInt, WriteLn;
FROM MathLib IMPORT sqrt, sin, cos, entier, Random, Randomize;

BEGIN
  WriteString("sqrt(144) = ");
  WriteInt(entier(sqrt(144.0)), 1); WriteLn;

  WriteString("sin(0) = ");
  WriteInt(entier(sin(0.0) * 1000.0), 1);
  WriteString(" (x1000)"); WriteLn;

  WriteString("cos(0) = ");
  WriteInt(entier(cos(0.0) * 1000.0), 1);
  WriteString(" (x1000)"); WriteLn;

  Randomize(42);
  WriteString("Random: ");
  WriteInt(entier(Random() * 100.0), 1);
  WriteString("%"); WriteLn
END MathDemo.