FLOAT Library Documentation 
 
FLOAT contains the floating point arithmetic routines, and some
functions visible to the user's program.
 
 
GENERAL INFORMATION
 
These routines will execute only on a Z-80. They use the
alternate registers and some of the undocumented instructions
of that processor. They do not conform to the IEEE floating
point standard. The routines were written by Neil Colvin, and
are worth study. They are the best code I have ever seen for
the Z-80.      - Jim Van Zandt 
  
 
FLOATING POINT FORMAT 
 
Each floating point number is 6 bytes long, and consists of a
40 bit fraction (most significant byte in the highest address)
and an 8 bit exponent. For nonzero numbers, the fraction f has
a value in the range 0.5 <= f < 1.0. Since its most significant
bit would always be 1, it would carry no information and is
replaced by the sign bit (set for a negative number). The
exponent is 80H if the number is in the range 0.5 <= x < 1.0,
and is increased by 1 for each place the binary point of f
should be moved to the right. For example:
 
	Representation 			Number	 
	00h,00h,00h,00h,00h,80h		0.5	 
	00h,00h,00h,00h,80h,80h		-0.5 
	00h,00h,00h,00h,00h,81h		1.0 
	00h,00h,00h,00h,00h,7fh		0.25 
	0fah,33h,0f3h,04h,035h,80h	sqrt(.5) = .707106... 
	38h,0a9h,0d8h,5bh,5eh,7fh	1/log(10) = .43429...
	21h,0a2h,0dah,0fh,49h,81h	pi/2 = 1.5707... 
 
 
ARITHMETIC OPERATIONS
 
Each of the primary operations (DADD, DSUB, DMUL, and DDIV)
takes its first operand from the stack (under the return
address) and the second from the fixed location FA (for
Floating point Accumulator). The result of the operation is
left in FA. For example, we have the following C expression and
its translation into calls to floating point operations:
  
	;double a,b,c,d; 
	;main() 
	QMAIN: 
	;{	a=b+c/d; 
		LD HL,QB	;get address of 1st operand 
		CALL DLOAD	;put operand in FA  
		CALL DPUSH	;move from FA to stack 
		LD HL,QC	;put 2nd operand...  
		CALL DLOAD 
		CALL DPUSH	;...on stack 
		LD HL,QD 
		CALL DLOAD	;put D in FA 
		CALL DDIV	;find c/d 
		CALL DADD	;find b+c/d  
		LD HL,QA	;load destination address  
		CALL DSTORE	;save result  
	;} 
		RET 
 
	QA:	DS 6		;declare storage space  
	QB:	DS 6 
	QC:	DS 6 
	QD:	DS 6 
 
 
FUNCTIONS 
 
Each of these functions return a double: 
 
float(x); double x;	integer to floating point conversion 
fmod(x,y); double x,y;	mod(x,y) 
			if 0 < y then 0 <= mod(x,y) < y and  
			x = n*y + mod(x,y) for some integer n 
fabs(x); double x;	absolute value 
floor(x); double x;	largest integer not greater than 
ceil(x); double x;	smallest integer not less than 
rand();			random number in range 0...1 
  
This function returns an int: 
  
int ifix(x); double x;	floating point to integer 
			(takes floor first) 

.