Re: 1364 issue 140 and negative exponents

From: Kurt Baty (kurt@wsfdb.wsfdb.com)
Date: Mon May 05 2003 - 14:01:56 PDT

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    > >
    > > > I had figured the results
    > > >
    > > > 2 ** -1 = 1
    > > > -2 ** -1 = -1
    > > >
    > > > were a result of rounding to nearest.
    > > >
    > >
    > > Actually, this rounding is not "round nearest"
    > > this is "round up" (I say "round away-from-zero"
    > > so as to not be confused in negative numbers).
    > > 0.5 would round to 0 in "round nearest".
    >
    > Then I'm confused. If the rounding was "away from zero",
    > then wouldn't all of the combinations whose real result
    > is in the range (0.0,1.0) round to an integer result of 1,
    > and likewise results in the range (-1.0,0.0) would round to
    > a integer result of -1? Your test program results don't
    > indicate this.

    some functions:

            truncate -> real result in the range (0.0 <= fract < 1.0)
                            goes to 0
            ceiling -> real result in the range (0.0 < fract <= 1.0)
                            goes to 1
            round -> real result in the range (0.0 < fract < 0.50)
                            goes to 0
                        real result in the range (0.5 < fract <= 1.0)
                            goes to 1
                        real result is exactly (fract = 0.5)
                            case(rounding mode)
                            up: goes to 1 (round "away from zero")
                            down: goes to 0 (round "towards zero")
                            nearest: if(low bit of abs(integer) part is:
                                    zero: goes to 0
                                    one: goes to 1

    does this help?

    >
    > In case it isn't already obvious, I am not a floating point
    > expert.

    I must be.

    >
    > > > But, my specific question is, are these the results you are
    > > > advocating for these particular operands?
    > >
    > > yes, to took x ** y where x,y are integers and converted
    > > x (integer -> real -> bits(ieee 64 floating point))
    > >
    > > did a x_bits ** y using the pow function
    > >
    > > function [63:0] pow; // l**r, where l is fp64 and r is integer
    > >
    > > converted answer_bits (bits(ieee 64 floating point) -> real -> integer)
    > >
    > > and I make the claim that this is the most "math correct answer".
    >
    > If you applied this methodology to integer division, what result would
    > you get for 1 / 2?
    >

    if the real typed, answer = 0.5
    and verilog converts real to integer by rounding then, 1

    if integer division is truncated by definition then
    integer = truncate(real typed, answer) then 0

            kurt

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