Apple II User Manual

mant1 and act as floating point registers.  On entry to

the subroutines these registers contain the numbers to

be operated upon and contain the result on return,  The

function of the registers is given before each entry point

in the source listing.  There are three error traps which

will cause a software interrupts.  ERROT (1D06) is

encountered if the argument in the log routine is less

than or equal to zero.  OVFLW (1E3B) will be executed if

the argument of EXP is too large.  Overflow detected by

the basic floating point routines will cause OVFL (1FE4)

to be executed.  The routines do not give underflow

errors, but set the number to zero if underflow occurs.

Readers of Dr. Dobbs's journal should note that when

these routines were published in that journal the math

function LOG contained an error which prevented the

correct result from being given if the argument was less

than 1.  This error has been correted in the present list-

ing and marked with "MOD 9/76."

   1                   *           SEPTEMBER 11, 1976
   2                   *     BASIC FLOATING POINT ROUTINES

   3                   *       FOR 6502 MICROPROCESSOR
   4                   *       BY R. RANKIN AND S. WOZNIAK

   5                   *
   6                   *     CONSISTING OF:

   7                   *        NATURAL LOG
   8                   *        COMMON LOG

   9                   *        EXPONENTIAL (E**X)
  10                   *        FLOAT      FIX

  11                   *        FADD       FSUB
  12                   *        FMUL       FDIV

  13                   *
  14                   *

  15                   *     FLOATING POINT REPRESENTATION (4-BYTES)
  16                   *                    EXPONENT BYTE 1

  17                   *                    MANTISSA BYTES 2-4
  18                   *

  19                   *     MANTISSA:    TWO'S COMPLIMENT REPRESENTATION WITH SIGN IN
  20                   *       MSB OF HIGH-ORDER BYTE.  MANTISSA IS NORMALIZED WITH AN

  21                   *       ASSUMED DECIMAL POINT BETWEEN BITS 5 AND 6 OF THE HIGH-ORDER
  22                   *       BYTE.  THUS THE MANTISSA IS IN THE RANGE 1. TO 2. EXCEPT

  23                   *       WHEN THE NUMBER IS LESS THAN 2**(-128).
  24                   *

  25                   *     EXPONENT:    THE EXPONENT REPRESENTS POWERS OF TWO.  THE
  26                   *       REPRESENTATION IS 2'S COMPLIMENT EXCEPT THAT THE SIGN

  27                   *       BIT (BIT 7) IS COMPLIMENTED.  THIS ALLOWS DIRECT COMPARISON
  28                   *       OF EXPONENTS FOR SIZE SINCE THEY ARE STORED IN INCREASING

  29                   *       NUMERICAL SEQUENCE RANGING FROM $00 (-128) TO $FF (+127)
  30                   *       ($ MEANS NUMBER IS HEXADECIMAL).

  31                   *
  32                   *     REPRESENTATION OF DECIMAL NUMBERS:    THE PRESENT FLOATING

  33                   *       POINT REPRESENTATION ALLOWS DECIMAL NUMBERS IN THE
APPROXIMATE

  34                   *       RANGE OF 10**(-38) THROUGH 10**(38) WITH 6 TO 7 SIGNIFICANT
  35                   *       DIGITS.

  36                   *
  37                   *

  38  0003                    ORG 3        SET BASE PAGE ADRESSES