Questions about IEEE754 floating point in D

[Trip Volpe]

I'm currently writing a compiler for my own language in D, and one of the things I'm implementing at the moment is the processing of floating-point literals. My primary reference is William Clinger's "How to read floating point numbers accurately," which is available here: ftp://ftp.ccs.neu.edu/pub/people/will/howtoread.pdf

Clinger describes a method for guaranteeing the selection of the binary floating-point number most closely approximating the number input in decimal (or any other base). So far so good, but along the way I've had occasion to consider what D itself is doing, and I have a couple of questions:

1. Does D guarantee the closest approximation for decimal floating-point literals? I ask mainly because for unit testing it would be convenient to be able to write

    expect( 0.001 == nearestDouble( 1, -3, 10 ) );

as opposed to manually checking the mantissa and exponent. :-)


2. Minimum exponent. In D, double.min_exp is equal to -1021. However, the Wikipedia article on IEEE754-2008 and appendix D in Sun's Numerical Computation Guide ("What Every Computer Scientist Should Know About Floating-Point Arithmetic", http://docs.sun.com/source/806-3568/ncg_goldberg.html) list Emin for the IEEE754 double format as -1022. Is this an error?

As expected under the standard, D has no trouble producing a normalized double with exponent less than -1021:

     DoubleRep dr;
     dr.value = 0x1p-1022;
     writefln("f = %d, e = %d", dr.fraction, dr.exponent);

This prints "f = 0, e = 1", which corresponds to a mantissa of 1.0 and an exponent of -1022, as expected. If you try 0x1p-1023, you get a denormal, also as expected, with an exponent field of 0. Subtract DoubleRep.bias and you get -1023, which according to the standard must be Emin - 1. So why isn't double.min_exp equal to -1022?