;;;-*- Mode:Text; Base:10 -*-
;Model of single float for IEEE standard 
;This description is by no means an exhaustive explaination

;    s    sign bit
;    exp  exponent
;    frac fraction
;    MSB  most significant bit
;    LSB  least significant bit

       MSB					 LSB
	3 3		2 2
	1 0             3 2			  0
       +-+---------------+-------------------------+
       |s|     exp       |        frac             |
       +-+---------------+-------------------------+

	  [----- 8 -----] [---------- 23 ---------]

;if (exp = 0 = frac) then number is understood to be zero.

;exponent bias is +127,
; thus logical exponent is an integer in the range  [-126, +126].

;fraction has implicit hidden bit at position 23 (if not zero or denormalized).

;    least-positive-single-float = 2**(-126)



;Model of double from for IEEE standard
;(not exaustive)

	6 6         5 5
	3 2         2 1                                                  0
       +-+-----------+----------------------------------------------------+
       |s|   exp     |                    frac                            |
       +-+-----------+----------------------------------------------------+

	 [--- 11 ---] [---------------------- 52 -------------------------]

;if (exp = 0 = frac) then number is understood to be zero.

;exponent bias is +1023,
; thus logical exponent is an integer in the range  [-1022, +1022].

;fraction has implicit hidden bit at position 52 (if not zero or denormalized).

;    least-positive-double-float = 2**(-1022)

; DDB 8/4/88 GSInc@Cambridge

; In reference to Brad's customer's double-precision application...

; B == base == 2
; T == number of base B digits allowed == 53 (including the hidden bit)

; Here are the values which should correspond to the values requested.
; Some values were better represented in hexidecimal, and others in
; standard floating point notation.  Numbers preceeded by
; the characters  " #x "  are in hexidecimal.


	B**(EMIN-1)		==	#x 800000
	;least positive magnitude


	B**EMAX*(1 - B**(-T))   ==      #x 7FEFFFFFFFFFFFFF
	;greatest positive magnatude

		==  (logior (ash (+ 1023. 1023.) 52.) (1- (^ 2 52.)))
						

	B**(-T)			==	1.110223025E-16
	;smallest relative spacing


	B**(1-T)		==	2.220446049E-16
	;largest relative spacing


	LOG10(B)		==	0.3010299957
	;log base 10 of 2


; These numbers should work iff IEEE format is being correctly 
; emulated.