EXTERN


{=================================================================}
FUNCTION ln (x : real) : real;
CONST
index = 16;
ln4 = 0.13862943611196e+01;
r3 = 0.33333333333333e+00;
r5 = 0.20000000000000e+00;
r7 = 0.14285714285714e+00;
r9 = 0.11111111111111e+00;
r11 = 0.90909090909091e-01;
r13 = 0.76923076923077e-01;
r15 = 0.66666666666667e-01;
r17 = 0.58823529411765e-01;
r19 = 0.52631578947368e-01;
r21 = 0.47619047619048e-01;
r23 = 0.43478260869565e-01;
r25 = 0.40000000000000e-01;
r27 = 0.37037037037037e-01;
r29 = 0.34482758620690e-01;
r31 = 0.32258064516129e-01;
VAR
div_count, i : integer;
result, term, term2 : real;
p :  ARRAY [1..index] OF real;

BEGIN  (* ln - natural logarithm *)

IF x <= 0.0 THEN
       ln :=  - 0.99999999999999e+63
ELSE
       BEGIN
         (* x must be in range 0.7 to 2.85 *)
       
       div_count := 0;
       WHILE x < 0.7 DO
              BEGIN
              x := x * 4;
              div_count := div_count - 1;
              END;
       WHILE x > 2.85 DO
              BEGIN
              x := x / 4;
              div_count := div_count + 1;
              END;
       term := (x - 1.0) / (x + 1.0);
       term2 := sqr(term);
       FOR i := 1 TO index DO
              BEGIN
              p[i] := term;
              IF (abs(term) <= 0.9e-51) THEN
                     term := 0.0
              ELSE
                     term := term * term2;
              END;
       result := 2.0 * (p[1] + (p[2] * r3) + (p[3] * r5) + (p[4] * 
              r7) + (p[5] * r9) + (p[6] * r11) + (p[7] * r13) + (
              p[8] * r15) + (p[9] * r17) + (p[10] * r19) + (p[11] * 
              r21) + (p[12] * r23) + (p[13] * r25) + (p[14] * r27) + (
              p[15] * r29) + (p[16] * r31));
       ln := result + div_count * ln4;
       END;  (* else *)
END;  (* ln *)  .