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Sunday, January 18, 2004

Adventures in 64 bits

Michael Lucas-Smith expands his adventure with registers to the 64-bit world.

The 64-bit world is interesting for another reason: data representation. Not only does the IA-64 have a large number of registers, and not only can you "rename" them so that they don't always refer to the same physical register, but since they are 64-bits wide you can fit a lot of data into them as "immediates" in a dynamic language like Smalltalk.

How would you represent a 64-bit floating point number in Smalltalk?

In the 32-bit world, you would have a 32-bit object reference where some number of bits would indicate the "tag" or the data type and some number would indicate the memory location where the data actually resides. The tag may be zero bits if all data is stored in memory and never immediately in the reference itself. Another option is to use a 2-bit tag, say the lowest two bits, to indicate the data type and then align the allocated memory to account for the "wasting" of the lowest two bits. (They indicate tags instead of pointing to byte aligned allocations.)

These two bits are then 00 or masked off to get to the allocated memory. Otherwise some other pattern (11, 10, 01) indicates the data is immediately in the reference itself. This may be a 30-bit integer (again, the tag is wasted), or a character (some other byte or 2-byte integer in the upper 16-bit word) or some other design. (Google should turn up some creative designs, this is off the top of my tired head.)

But for 64 bits the world of encoding gets *very* interesting. Back to the 64-bit floating point number...

In the 64-bit world, just represent a 64-bit FP number as... hey, a 64-bit FP number. Use all the bits!

But then how do you represent everything else if all the bits are used for FP? Well, there are a large number of 64-bit arrangements that are not actually FP numbers, rather they are "Not a Numbers" or NaNs. But not all 64 bits are used to indicate some arrangement is a NaN. Actually a small number of bits are used to indicate NaN (something like 10 or 11).

A very large number of integers can be represented as 64-bit FPs. Only the *really* *really* large need to be memory allocated. A lot of other interesting data can be represented immediately in the 64-bits (and so passed around in registers, stored immediately in vectors and matrices, etc.) These data might be characters (easily up to 32-bits of character data, more bits could represent common fonts, styles, etc.) 32-bit color, the same.

Dynamic languages like Smalltalk become significantly more efficient for number crunching (engineering, finance) because they're no longer using memory allocated numbers for floats and large integers.

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Portland, Oregon, United States
I'm usually writing from my favorite location on the planet, the pacific northwest of the u.s. I write for myself only and unless otherwise specified my posts here should not be taken as representing an official position of my employer. Contact me at my gee mail account, username patrickdlogan.