Multiply/Divide a float with a power of two

[per.nordlow]

Hey there!

I want to multiply/divide (shift) a float with variable containing a
power-of-two value: 2, 4, 8, 16, ....

Is there such a function in the C standard library or the glibc library
that does this?

If not has anybody written some clever high-performance "hack" like:
1. Cast float pointer to a 32-bit integer pointer.
2. Perform the a bitwise shift on the mantissa part.
3. Cast it back.


Many thanks in advance,

Per Nordlöw

 

[Giannis Papadopoulos]

Hey there!

I want to multiply/divide (shift) a float with variable containing a
power-of-two value: 2, 4, 8, 16, ....

Is there such a function in the C standard library or the glibc library
that does this?

I don't think there's something like this in the standard library. I
don't know about glibc.

Why don't you just use * and / ?

If not has anybody written some clever high-performance "hack" like:
1. Cast float pointer to a 32-bit integer pointer.
2. Perform the a bitwise shift on the mantissa part.
3. Cast it back.

Maybe because this is the work of the compiler and the processor to
choose that kind of optimizations.

In all modern generic purpose processors there are FP multiplication and
division units, so there is no need for FPU emulation - which is what
you propose. If you have a processor (maybe a DSP) it would make sense,
but in all modern machines it would be useless...

You may speed things up using (1/a) * b, instead of a/b, but there is a
precision penalty.


--
one's freedom stops where others' begin

Giannis Papadopoulos
http://dop.users.uth.gr/
University of Thessaly
Computer & Communications Engineering dept.

 

[P.J. Plauger]

I want to multiply/divide (shift) a float with variable containing a
power-of-two value: 2, 4, 8, 16, ....

Is there such a function in the C standard library or the glibc library
that does this?

If not has anybody written some clever high-performance "hack" like:
1. Cast float pointer to a 32-bit integer pointer.
2. Perform the a bitwise shift on the mantissa part.
3. Cast it back.

[pjp] ldexp(x, 3) returns x * 2^3. Close enough?

P.J. Plauger
Dinkumware, Ltd.
http://www.dinkumware.com

 

[Antonio Contreras]

Hey there!

I want to multiply/divide (shift) a float with variable containing a
power-of-two value: 2, 4, 8, 16, ....

Is there such a function in the C standard library or the glibc library
that does this?

If not has anybody written some clever high-performance "hack" like:
1. Cast float pointer to a 32-bit integer pointer.
2. Perform the a bitwise shift on the mantissa part.
3. Cast it back.

For one thing, this would be implementation dependent, and is more than
certainly OT.

For other thing, the algorithm you describe wouldn't work. IEEE
standarized format (which is the most widespread format AFAIK) uses an
implicit 1 in the mantisa, so shifting the bits in the mantisa will
only multiply/divide the decimal part of the number (when expressed in
binary scientific notation).

If you really want to hack your way through this, the easiest way to do
it is add/substract to the exponent part. Anyway, there are special
cases you should consider:

- An exponent of 0 and a mantisa all 0's means 0. You should leave the
number unaffected.
- An exponent of 0 and a mantisa different of 0 is a special format for
extremely small numbers. In this case there is no implicit one. You
should shift the mantisa in this case. However keep in mind that you
may overflow this special format when multiplying, if this is the case
you should convert to the regular format (shift the mantisa till the
first one goes out, and add to the exponent part).
- An exponent all 1's and a mantisa all 1's means infinit. This value
should not be altered by your operations.
- An exponent all 1's and a mantisa with at least one 0 in it means NaN
(Not a Number, the result you get when you try to divide by 0). This
value should also be left untouched.

(I'm not a 100% sure about the last two cases, I would have to read the
IEEE standard to check. Anyway I am a 100% an exponent of all ones is a
special case.)

As you can see it's much better to simply use * and / and let the FPU
do its job (or whatever FPU emulation software your C implementation
uses if there's no FPU available).

HTH

 

[per.nordlow]

Great!

I had the feeling, such a function existed in the standard.


Thank you very much,

Per Nordlöw

 

[Christian Bau]

Hey there!

I want to multiply/divide (shift) a float with variable containing a
power-of-two value: 2, 4, 8, 16, ....

Is there such a function in the C standard library or the glibc library
that does this?

If not has anybody written some clever high-performance "hack" like:
1. Cast float pointer to a 32-bit integer pointer.
2. Perform the a bitwise shift on the mantissa part.
3. Cast it back.

I suggest to use the "*" or "/" operator.