Apple II User Manual

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|  TOPIC -- Apple II -- DDJ Floating point article

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Dr. Dobb's Journal, August 1976, pages 17-19.

Floating Point Routines for the 6502

by Roy Rankin, Department of Mechanical Engineering,

   Stanford University, Stanford, CA 94305

   (415) 497-1822

and

   Steve Wozniak, Apple Computer Company

   770 Welch Road, Suite 154

   Palo Alto, CA  94304

   (415) 326-4248

Editor's Note:  Although these routines are for the 6502, it

would appear that one could generate equivalent routines for

most of the "traditional" microprocessors, relatively easily,

by following the flow of the algorithms given in the excellent

comments included in the program listing.  This is particularly

true of the transcendental functions, which were directly modeled

after well-known and proven algorithms, and for which, the

comments are relatively machine independent.

These floating point routines allow 6502 users to perform

most of the more popular and desired floating point and

transcendental functions, namely:

Natural Log - LOG

Common Log - LOG10

Exponential - EXP

Floating Add - FADD

Floating Subtract - FSUB

Floating Multiply - FMUL

Floating Divide - FDIV

Convert Floating to Fixed - FIX

Convert Fixed to Floating - FLOAT

They presume a four-byte floating point operand consisting of

a one-byte exponent ranging from -128 to +127 and a

24-bit two's complement mantissa between 1.0 and 2.0.

The floating point routines were done by Steve Wozniak,

one of the principals in Apple Computer Company.  The

transcendental functions were patterned after those offered by

Hewlett-Packard for their HP2100 minicomputer (with some

modifications), and were done by Roy Rankin, a Ph.D. student

at Stanford University.

There are three error traps; two for overflow, and one for

prohibited logarithm argument.  ERROR (1D06) is the error