Accuracy and the power function

[walter b]

(02-19-2014 09:54 AM)Werner Wrote:  In your example, %%LN(6.28318530718) is off by one ULP.
Secondly, the 15-digit routines (%%*, %%+, %%-, %%/) do not round, they truncate. They are, after all, meant as intermediates to produce a correctly rounded 12-digit result (for the elementary operations).

Code:


          %%LN                    %% 372 %%*              %%EXP
exact   1.8378770664094112978.. 683.69026870430100..    8.37357721132000..e296
HP48    1.83787706640940        683.690268704296        8.37357721127809e296
trunc15 1.83787706640941        683.690268704300        8.37357721131159e296
round15                         683.690268704301        8.37357721131998e296

Not only is the %%LN one ULP off, but the subsequent multiplication by 372 actually ends in ..968, but is truncated to ..96. The last line demonstrates what a 15-digit %%LN, 15-digit %%EXP and 15-digit rounding arithmetic would produce.

Anything special you want to tell us using %% ??

d#-?