[Coco] Re: GCC: DFLOAT / DIRECT_PAGE

[jdaggett at gate.net]

What is used in Color Basic is an adoption of IEEE Standard with an added 
"sub" byte to get 9 decimal digit precision. What it ends up with is 31 bits in the 
mantissa. 9 decimal digit precision is standard calculator display! The RS Basic 
had to do this to use a 6th term in the Taylor Series to calculate the trancendetal 
functions with 9 digit precision. The sixth coefficient of the Taylor Series for the 
Sine function is one over eleven factorial. That is to small a number to be 
represented in standard IEEE single precision floating point.  

There have been as many schemes to do floating point. The IEEE Standard did 
not become a standard until the mid to late 80's. All still have basically the same 
format. A sign, and exponent and a mantissa. How many bytes used to 
represent them and to what precision you want is ultimately the end users 
decision and the computing power available. 

james


On 15 Nov 2003 at 11:36, Theodore A. Evans wrote:

> I did some research on the ANSI C standard as regards floating point.
> You can use any integer radix for the exponent (typically either 2 or
> 10).  You can support rounding by any method that you see fit to.  A
> float needs at least 6 decimal digits of precision (i.e. 20 bits), and
> both a double and a long double require at least 10 decimal digits of
> precision (i.e. 34 bits).  Your radix needs to cover at a minimum the
> range 10^-37 to 10^37, so for a decimal radix you need 7 bits and for
> a binary radix 8 bits.  Concievably a float can be stored in 28 bits
> and both a double and a long double in 42 bits.
> 
> The numbers used in Color BASIC are sufficient for floats, but
> (barely) fall short for double and long double.
> 
> -- 
> Why did I ever start this, anyway?
> Theodore (Alex) Evans            | alxevans at concentric.net
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