Re: Fix exp2l inaccuracy (bug 13824)

[Andreas Jaeger <aj at suse dot com>]

On Wednesday, March 21, 2012 23:25:39 Joseph S. Myers wrote:
> I propose this patch to fix bug 13824, inaccuracy of the default exp2l
> implementation (used for ldbl-128 and ldbl-128ibm).  This patch
> handles overflow and underflow (and infinity and NaN arguments) much
> as they are handled in the dbl-64 exp2, then for in-range arguments
> splits the integer and fractional parts, computes expl of M_LN2L times
> the fractional part and scales that exactly with scalbnl.  This (a)
> avoids inaccurate results for integer arguments, as long as expl (0)
> is exactly 1, and (b) avoids the large errors (hundreds of ulps) for
> large arguments that arise from bits lost in the multiplication M_LN2l
> * x being significant for the mantissa after exponentiation (this
> problem arises for exponentials of large inexact numbers, not for
> numbers with small absolute value).
> 
> Tested powerpc, x86 and x86_64 (the latter two in case of any ulps
> updates needed for the new tests).  No ulps updates were needed for
> any of those architectures.

Thanks, this is ok,

Andreas
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