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Re: MachinePrecission and FPU

• To: mathgroup at smc.vnet.net
• Subject: [mg81314] Re: MachinePrecission and FPU
• From: "marks at wolfram.com" <marks at wolfram.com>
• Date: Wed, 19 Sep 2007 05:23:11 -0400 (EDT)
• References: <fcnl4n$s65$1@smc.vnet.net><46EF98F4.8060601@gmail.com>

There is currently no way to set the rounding mode at run-time.
However this is not the cause of the issue at hand.

The reason for the difference is that a/b does not parse
to divide but rather multiplication by a reciprocal.

In[1]:= FullForm[a/b]

Out[1]//FullForm= Times[a, Power[b, -1]]

Therefore there are two potential rounding errors here,
one in reciprocation of 0.006 and one in the subsequent
multiplication by 0.03.

In[2]:= InputForm[0.03/0.006]

Out[2]//InputForm= 4.999999999999999

If this difference is important, it id possible to directly
access floating point division by calling Divide:

In[3]:= InputForm[Divide[0.03, 0.006]]

Out[3]//InputForm= 5.

Note that other differences between Mathematica and
a C/C++ program may easily occur. These might
arise from a different order of floating point operations
or architectural subtleties - for example an optimizing
compiler's use of Intel's extended (80 bit) double
arithmetic being used instead of IEEE 64 bit double
precision.

Mark Sofroniou,
Wolfram Research