[Tutor] greater precision?
John Collins
john at netcore.com.au
Mon Oct 29 16:42:15 CET 2012
Hello,
Just checked my py, and 15 was the report! Wish I had known
that factoid - thank you, for a very complete coverage of
the broader intrinsic 'machine' + system precision - it actually
makes sense to me now - it's a calculation!
On 30/10/2012 2:02 AM, eryksun wrote:
<SNIP>
> A double has 53 bits of precisions, which is 53*log10(2) =~ 15.955
> decimal digits. However, one often sees the numbers 15 and 17 quoted
> for the precision. It depends. A double is guaranteed to accurately
> store a string with 15 decimal digits (round trip). But each 15-digit
> decimal string maps to many doubles:
>
> >>> from struct import unpack
>
> >>> format(unpack('d', '\x76\x99\x99\x99\x99\x99\xb9?')[0], '.15f')
> '0.100000000000000'
> >>> format(unpack('d', '\xbd\x99\x99\x99\x99\x99\xb9?')[0], '.15f')
> '0.100000000000000'
>
> >>> 0xbd - 0x76 + 1 # doubles that round to 0.100000000000000
> 72
>
> (Note: my Intel processor is little endian, so the least significant
> byte is index 0 in the packed double, such as '\x76....'.)
>
> However, to exactly represent each double requires 17 decimal digits:
>
> >>> format(unpack('d', '\x76\x99\x99\x99\x99\x99\xb9?')[0], '.17f')
> '0.09999999999999951'
> >>> format(unpack('d', '\x77\x99\x99\x99\x99\x99\xb9?')[0], '.17f')
> '0.09999999999999952'
>
> Python says the precision is 15 decimal digits:
>
> >>> import sys
> >>> sys.float_info.mant_dig # bits of precision
> 53
> >>> sys.float_info.dig # decimal digits
> 15
>
Regs, John.
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