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