Re: [eigen] Proposal: Include Constants to NumTraits |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Proposal: Include Constants to NumTraits*From*: Gael Guennebaud <gael.guennebaud@xxxxxxxxx>*Date*: Fri, 6 Apr 2012 22:00:17 +0200*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=mime-version:in-reply-to:references:from:date:message-id:subject:to :content-type:content-transfer-encoding; bh=xuMTK8aHgcxncgUcrV1EO1lx2bdJpoCbROqKPt4IhOY=; b=yifFZ6C1J3zZioa2dA0B9OyDpPJcKXnm8mCicuD8bom7CIP66GIJ8SIyKjFhPpanxI LUVgyvK3eLY0vgLvMceVCOeL695EOvYfiCVuLHWMQsQDMA4slspKrIIrUdbVfMnD90eR byfpUEgVqyb7h1S30lgu/IVgQpAyVLRSJt/K5uxeRyUDQz3FizB7yfOex+dX4HWrPPcI s5G/za0iaTB6w3r1ynGkQcjIlRlPtNClDghY3KiuDH1NnkLULuBRKjQ4h3iNOWEWpu4P xP2Ki6EPbkv/rY3WuNVeOzNvMUgqFg7OeHXQOm3tGMYAqmAyhdx9oqDDpdRhIHYO3dq4 N5aQ==

On a similar topic, NumTraits could provide a "Constant" type to be used to cast constant numbers like 0, 1, 2, 0.5, etc. instead of using Scalar which can be significantly more expensive for some scalar types. gael. On Fri, Apr 6, 2012 at 9:57 PM, Gael Guennebaud <gael.guennebaud@xxxxxxxxx> wrote: > Hi, > > I guess the list of such constants can be very large to cover all > application domains, so I'm not sure that's the scope of Eigen. The > idea is to have the constants that are needed for Eigen's algorithm > only, and if that feature is already well covered by boost then I > don't see a huge need for us to do a clone. > > cheers, > gael > > On Fri, Apr 6, 2012 at 6:24 AM, Pavel Holoborodko <pavel@xxxxxxxxxxxxxxx> wrote: >> Eigen is well designed to be invariant of scalar types. >> >> However I think there is one point for improvement - mathematical >> constants. >> They tied to scalar type (to its precision, e.g. double vs. multiple >> precision) and frequently needed in computations. >> >> Now, in true generic code in order to use matching-to-scalar constant we >> have to do something like: pi = acos(Scalar(-1)) (FFT module). >> Obviously this can (and should) be improved. >> >> We already handle machine epsilon by NumTraits. Why don't we include other >> constants to NumTraits? >> So that we can use them as follows >> >> typedef typename MatrixType::Scalar Scalar; >> typedef typename NumTraits<Scalar>::Real RealScalar; >> >> const RealScalar Pi = NumTraits<RealScalar>::Pi(); >> const RealScalar Euler = NumTraits<RealScalar>::Euler(); >> const RealScalar Log2 = NumTraits<RealScalar>::Log2(); >> const RealScalar Catalan = NumTraits<RealScalar>::Catalan(); >> ... >> >> // Use constants in the code below >> // ... >> >> This would make writing generic code much easier (and code will be cleaner). >> >> This is especially important for multiple precision types - where computing >> of const. takes a lot of resources. >> Additional layer of abstraction will allow us to cache const. without >> recomputing them every time. >> >> For built-in scalar types these functions will be one-liners without any >> overhead. >> >> Also it has sense to include Inf(), Nan() as special values (similar >> to std::numeric_limits<Scalar> ). >> >> Would appreciate any comments. >> >> (Boost has similar library - e.g. boost::math::constants::pi<Scalar>();)

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**References**:**[eigen] Proposal: Include Constants to NumTraits***From:*Pavel Holoborodko

**Re: [eigen] Proposal: Include Constants to NumTraits***From:*Gael Guennebaud

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