Floating point to string

[Bill Baxter]

Joe wrote:
> Bill Baxter wrote:
>> Joe wrote:
>>> Derek Parnell wrote:
>>>> On Wed, 18 Jul 2007 21:28:47 -0500, Joe wrote:
>>>>
>>>>> How to do get a full string representation of a floating point?
>>>>>
>>>>> I've tried toString() on a floating point and the default precision 
>>>>> for numbers after the decimal point is 6.  I've also tried using 
>>>>> format strings, but I can't seem to get a full textual 
>>>>> representation of a floating point.  Is there some trick I'm missing?
>>>>
>>>> Try this ...
>>>> <dcode>
>>>> import std.stdio;
>>>> import std.string;
>>>>
>>>> string FullTextValue(T)(T x)
>>>> {
>>>>     string s;
>>>>
>>>>     static if(is (T:long))
>>>>         const fmt = "%-52d";
>>>>     else
>>>>     static if(is (T:real))
>>>>         const fmt = "%52.52f";
>>>>     else
>>>>         const fmt = "%-s";
>>>>
>>>>     s = std.string.format( fmt, x);
>>>>     for (int i = s.length-1; i >= 0; i--)
>>>>     {
>>>>         if (s[i] == '.')
>>>>         {
>>>>             s.length = i+2;
>>>>             break;
>>>>         }
>>>>         if ((s[i] != '0' && s[i] != ' ') || (i == 0))
>>>>         {
>>>>             s.length = i+1;
>>>>             break;
>>>>         }
>>>>     }
>>>>     return s;
>>>> }
>>>> void main()
>>>> {
>>>>     real x;
>>>>     double y;
>>>>     float z;
>>>>     long a;
>>>>
>>>>     x = 12345678901234567890.1234567890123456789;
>>>>     y = x;
>>>>     z = x;
>>>>     a = cast(typeof(a))x;
>>>>
>>>>     writefln("real   '%s'", FullTextValue(x));
>>>>     writefln("double '%s'", FullTextValue(y));
>>>>     writefln("float  '%s'", FullTextValue(z));
>>>>     writefln("long   '%s'", FullTextValue(a));
>>>>
>>>>     x = 0.1234567890123456789;
>>>>     y = x;
>>>>     z = x;
>>>>     a = cast(typeof(a))x;
>>>>
>>>>     writefln("real   '%s'", FullTextValue(x));
>>>>     writefln("double '%s'", FullTextValue(y));
>>>>     writefln("float  '%s'", FullTextValue(z));
>>>>     writefln("long   '%s'", FullTextValue(a));
>>>>
>>>> }
>>>> </dcode>
>>>>
>>>
>>> Thanks.
>>>
>>> Out of curiosity (note: I haven't run this example yet), is 52 a 
>>> magic number for the floating point types in D?  Is there a way at 
>>> runtime to get at the number of digits available after the decimal 
>>> point depending on whether it's a float, double or real?
>>
>> I think he's taking that from the number of mantissa bits in IEEE 
>> double  precision floating point.  There certainly can't be more 
>> meaningful decimal digits of accuracy than there are binary digits.  
>> Don could probably tell it much better than me, but it works out to be 
>> about 16 decimal digits of accuracy.  Goes something like this: 
>> Smallest thing you can represent in an IEEE double with the mantissa 
>> only is 2^-52 (or maybe 2^-53?).  Which works out to about 10^-16, so 
>> that means with decimal point, only about 16 digits can have meaning.  
>> So use 20 and you should be safe -- for doubles anyway.  For floats 
>> it's about 8 decimal digits.
>>
>> Oh, about your actual question -- float_var.dig tells you the # of 
>> decimal digits of precision:
>> http://www.digitalmars.com/d/property.html - "Properties for Floating 
>> Point Types"
>>
>>
>> --bb
> 
> I appreciate the explanation.  While I still don't grasp all the 
> details, this helps a lot.

Maybe it helps to think of trying to store the number 1.000..0001 and 
consider how many zeros can go in there before the computer thinks it's 
just 1.  That's roughly the number of sigificant digits you have. 
Another way of saying that is -- for what value of x does 1+2^-x give 
you just 1 using doubles?  It's about x=52 because IEEE doubles have 52 
mantissa bits (and there's an implicit 1 at the beginning that isn't 
stored in the mantissa).

--bb