Re: floating point number radix

[dik@zuring.UUCP]

In article <8510190414.AA24234@UCB-VAX> BRYAN@SU-SIERRA.ARPA (Doug Bryan) writes:
>[3.5.7(6)]
>The reference manual states that the minimum number of binary digits, B,
>required after the point in the binary mantissa of a floating point
>number is...
>
>	ceiling (D * ln(10)/ln(2) + 1.0)
>
>where D is the minimal number of decimal digits in the decimal mantissa.
>
>Consider D = 3...
>
>	ceiling (3 * ln(10)/ln(2) + 1.0) = ceiling (10.9657) = 11
>
>But... is not 10 binary digits sufficient to represent 3 decimal digits?
>		2**(-10) < 10**(-3)
>We think the "+ 1.0" in the above expression can be removed. 
>
>doug bryan and geoff mendal
>
No.  The relative precision of the binary representation should not be
less than that of the decimal representation.  For difits 3 the relative
precision of the decimal representation ranges from 1 in 500 to 1 in 999,
and with 10 bits for the binary representation from 1 in 512 to 1 in 1023.
And indeed we find the following:
	819/8192 = .099975
	818/8192 = .099853
	817/8192 = .099731
So there is no representation for .0998, a valid digits 3 number.
-- 
dik t. winter, cwi, amsterdam, nederland
UUCP: {seismo|decvax|philabs}!mcvax!dik