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Re: MachinePrecission and FPU

• To: mathgroup at smc.vnet.net
• Subject: [mg81535] Re: MachinePrecission and FPU
• From: dh <dh at metrohm.ch>
• Date: Wed, 26 Sep 2007 06:55:22 -0400 (EDT)
• References: <fcnl4n$s65$1@smc.vnet.net><46EF98F4.8060601@gmail.com> <fcqq33$1ap$1@smc.vnet.net>

Hi Mark,

thank's a lot for your reply. It solved the problem, although I would 

never have guessed the reason (Times Inverse[] instead of Divide). This 

code was inside a Floor what amplified the error from tiny to appreciable.

thank's again, Daniel



marks at wolfram.com wrote:

> 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

> 

>