On 07/30/2010 11:28 AM, Eliot Miranda wrote:
[...]
Excellent!! Just by curious, your idea, or what you did in VW, was
to be able to put SmallFloats directly inside the address ? just
like we do nowadays with SmallInteger ?
Yes. The scheme provides IEEE double precision but with a smaller
exponent so the range is the same as the 32-bit single-precision range.
i.e. 3 bits are used as tag bits to distinguish SmallInteger
SmallFloat Character and objects. That leaves 1 bit for sign, 52 bits
for the mantissa and 8 bits for the exponent. The use of 3 tag bits
comes from 64-bit pointers being 8-byte aligned and so having the least
significant 3 bits 0. I don't want to defend that choice now just to
give you a flavour of the representation:
| 8-bit exponent | 52 bit mantissa | sign | tags |
A few more words on the VW SmallDouble implementation: We also use this
representation in GemStone; it works very well.
This representation exactly represents a subset of the possible IEEE
doubles. It's the "common" 1/8th of the total range, with the addition
of +-0.0. Non-zero numbers very close to zero or very far from zero
overflow to normal Float objects in a manner very similar to the way
SmallInteger/LargeInteger work. The infinities and NaNs also must be
represented as normal Floats.
Because between SmallDouble and Float all IEEE doubles can be
represented, all floating-point computations give the correct (per IEEE)
result, but you save memory and computation is generally faster because
you don't access as many bytes in main memory.
Regards,
-Martin
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