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Re: Loss of precision

• To: mathgroup at smc.vnet.net
• Subject: [mg126660] Re: Loss of precision
• From: Richard Fateman <fateman at cs.berkeley.edu>
• Date: Tue, 29 May 2012 05:48:13 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jpnhi8$qa4$1@smc.vnet.net> <jpq6t7$6vs$1@smc.vnet.net>

On 5/26/2012 2:14 AM, danl at wolfram.com wrote:
> On Friday, May 25, 2012 3:57:44 AM UTC-5, sam.... at yahoo.com wrote:
>> Hi,
>>
>> I understand intuitively why Sin[Large Number] cannot be computed too accurately. For example
>>
>> Precision[Sin[SetPrecision[10^10, 100]]] = 89.75
>>
>> We can I find an explanation of precisely why and how 100 becomes 89.75.

Sin[Large Number]  can be computed accurately to any desired number of 
digits.  Just as one can compute pi to any specified number of digits,
one can compute 10^10  or 10^100 modulo pi/2  to any specified number of
digits.

Daniel does describe what Mathematica does, which is hardly
mathematically or computationally inevitable.
RJF