Apple II manual Mantissa, Exponent

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		*
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