Talk:Generalised floating point addition: Difference between revisions
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# Suppose I want to compute a + b. Is it acceptible to first convert them into machine native format, add up, then convert back to whatever base they were in? Could a and b be in different bases to begin with? --[[User:Ledrug|Ledrug]] 16:52, 28 October 2011 (UTC) |
# Suppose I want to compute a + b. Is it acceptible to first convert them into machine native format, add up, then convert back to whatever base they were in? Could a and b be in different bases to begin with? --[[User:Ledrug|Ledrug]] 16:52, 28 October 2011 (UTC) |
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1. Why? |
1. re: Why? |
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This pattern (or subsets of this pattern) happen often enough that it is worth implementing it in general. Hence the emphasis on a "Mixin" or Template" solution. More generally the "DIGITS" are not specifically numerical, they only require a "+" operation, a digit index, MSD, LSD and the concept of ZERO. |
This pattern (or subsets of this pattern) happen often enough that it is worth implementing it in general. Hence the emphasis on a "Mixin" or Template" solution. More generally the "DIGITS" are not specifically numerical, they only require a "+" operation, a digit index, MSD, LSD and the concept of ZERO. |
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2. ... allow them to be in different bases? |
2. re: ... allow them to be in different bases? |
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That would depend on a natural example of the significand, the base and the exponent in different bases. [[wp:IEEE_754-2008#Basic_formats|IEEE_754 Basic_formats]] has [[wp:Decimal128_floating-point_format|Decimal128 floating-point format]] appears to be an example BCD significand and "modified" Binary exponent. /* I'm guessing that this is because the input and output data are decimal */. But your suggestion is reasonably close and if it can be implemented reasonably cleanly then it would probably fit the Rosettacode's spirit of "codifying your suggestion". The one thing I love about Rosettacode is the surprises that emanate from other languages and other interpretations. |
That would depend on a natural example of the significand, the base and the exponent in different bases. [[wp:IEEE_754-2008#Basic_formats|IEEE_754 Basic_formats]] has [[wp:Decimal128_floating-point_format|Decimal128 floating-point format]] appears to be an example BCD significand and "modified" Binary exponent. /* I'm guessing that this is because the input and output data are decimal */. But your suggestion is reasonably close and if it can be implemented reasonably cleanly then it would probably fit the Rosettacode's spirit of "codifying your suggestion". The one thing I love about Rosettacode is the surprises that emanate from other languages and other interpretations. |
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3. ... Is it acceptible to first convert them into machine native format. |
3. re: ... Is it acceptible to first convert them into machine native format. |
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I saw this more as a Templating and significand "list processing" "algorithm" definition task. /* Esp as the "DIGITS" may not even be numerical. */ So my preference is to avoid normalising to a canonical form based on a specific hardware implementation. [ If you know what I mean... I can almost say that last paragraph in one breath... :-) ] |
I saw this more as a Templating and significand "list processing" "algorithm" definition task. /* Esp as the "DIGITS" may not even be numerical. */ So my preference is to avoid normalising to a canonical form based on a specific hardware implementation. [ If you know what I mean... I can almost say that last paragraph in one breath... :-) ] |
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Revision as of 11:11, 29 October 2011
Clarify?
I have a few questions:
- Why?
- A floating point number involves three integers: the significand, the base and the exponent. Wouldn't it be more of a hoot to allow them to be in different bases?
- Suppose I want to compute a + b. Is it acceptible to first convert them into machine native format, add up, then convert back to whatever base they were in? Could a and b be in different bases to begin with? --Ledrug 16:52, 28 October 2011 (UTC)
1. re: Why?
This pattern (or subsets of this pattern) happen often enough that it is worth implementing it in general. Hence the emphasis on a "Mixin" or Template" solution. More generally the "DIGITS" are not specifically numerical, they only require a "+" operation, a digit index, MSD, LSD and the concept of ZERO.
2. re: ... allow them to be in different bases?
That would depend on a natural example of the significand, the base and the exponent in different bases. IEEE_754 Basic_formats has Decimal128 floating-point format appears to be an example BCD significand and "modified" Binary exponent. /* I'm guessing that this is because the input and output data are decimal */. But your suggestion is reasonably close and if it can be implemented reasonably cleanly then it would probably fit the Rosettacode's spirit of "codifying your suggestion". The one thing I love about Rosettacode is the surprises that emanate from other languages and other interpretations.
3. re: ... Is it acceptible to first convert them into machine native format.
I saw this more as a Templating and significand "list processing" "algorithm" definition task. /* Esp as the "DIGITS" may not even be numerical. */ So my preference is to avoid normalising to a canonical form based on a specific hardware implementation. [ If you know what I mean... I can almost say that last paragraph in one breath... :-) ]
NevilleDNZ 11:10, 29 October 2011 (UTC)