Cost of multiplication relative to addition

steve wrote:
> Jerry Avins wrote:
> 
>> Floating-point addition is more complex than multiplication if a
>> fixed-point multiplier is available. If the addend exponents differ,
>> they must be made the same before addition or subtraction can take
>> place, then the result may need to be renormalized.
>>
> ok, but on the DSP's I have used the emulated foating point multiply
> was only about 10% faster then the emulated floating point ADD  (and
> 100 times slower (full IEEE 754) then fixed point for the typical
> algorithms I run)

You report that with floating-point operations done in software, 
addition is slower than multiplication. What I wrote. Do we disagree?

Jerry
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Ray Andraka wrote:

(snip)

> On the other hand, if you are designing into hardware, say an FPGA 
> (ignoring the embedded multipliers for the moment), you need to 
> construct the multipliers out of gates.  Assuming fixed point, you need 
> n-1 adds for an nxn bit multiplier (those may be arranged in different 
> ways and there are shortcuts to reduce the size of the adder tree, but 
> the point is in terms of gates or circuit area, or delay, the multiplier 
> costs several times the cost of a fixed point add.

> The balance changes if you throw floating point into the mix too.

Yes.

For modern FPGA's with multiplier logic, floating point add is bigger
than floating point multiply.  It is the pre/post normalization logic
that is big, the actual add isn't so big.  Multiply uses a much
simpler normalization system, assuming normalized inputs.

-- glen

Tim Wescott wrote:

(snip)

>> The OP specified "real".  I knew DSP's handled integer multiplies 
>> fast, but do they handle floats as quickly?

> My head kind of floated over that, interpreting as 'actual'.

> There are no real numbers in digital math -- just integers without 
> mantissas, and integers with mantissas.  If he'd said 'floating point' 
> then I would have caught that.

You haven't been programming in Fortran long enough.

-- glen

Jerry Avins wrote:
> steve wrote:
> > Jerry Avins wrote:
> >
> >> Floating-point addition is more complex than multiplication if a
> >> fixed-point multiplier is available. If the addend exponents differ,
> >> they must be made the same before addition or subtraction can take
> >> place, then the result may need to be renormalized.
> >>
> > ok, but on the DSP's I have used the emulated foating point multiply
> > was only about 10% faster then the emulated floating point ADD  (and
> > 100 times slower (full IEEE 754) then fixed point for the typical
> > algorithms I run)
>
> You report that with floating-point operations done in software,
> addition is slower than multiplication. What I wrote. Do we disagree?
> 
on significance only