[136] | 1 | #include <typeinfo>
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| 2 | #include <iostream>
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| 3 | #include <Eigen/Core>
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| 4 | #include "BenchTimer.h"
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| 5 | using namespace Eigen;
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| 6 | using namespace std;
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| 7 |
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| 8 | template<typename T>
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| 9 | EIGEN_DONT_INLINE typename T::Scalar sqsumNorm(const T& v)
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| 10 | {
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| 11 | return v.norm();
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| 12 | }
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| 13 |
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| 14 | template<typename T>
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| 15 | EIGEN_DONT_INLINE typename T::Scalar hypotNorm(const T& v)
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| 16 | {
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| 17 | return v.hypotNorm();
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| 18 | }
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| 19 |
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| 20 | template<typename T>
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| 21 | EIGEN_DONT_INLINE typename T::Scalar blueNorm(const T& v)
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| 22 | {
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| 23 | return v.blueNorm();
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| 24 | }
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| 25 |
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| 26 | template<typename T>
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| 27 | EIGEN_DONT_INLINE typename T::Scalar lapackNorm(T& v)
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| 28 | {
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| 29 | typedef typename T::Scalar Scalar;
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| 30 | int n = v.size();
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| 31 | Scalar scale = 0;
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| 32 | Scalar ssq = 1;
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| 33 | for (int i=0;i<n;++i)
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| 34 | {
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| 35 | Scalar ax = internal::abs(v.coeff(i));
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| 36 | if (scale >= ax)
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| 37 | {
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| 38 | ssq += internal::abs2(ax/scale);
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| 39 | }
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| 40 | else
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| 41 | {
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| 42 | ssq = Scalar(1) + ssq * internal::abs2(scale/ax);
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| 43 | scale = ax;
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| 44 | }
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| 45 | }
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| 46 | return scale * internal::sqrt(ssq);
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| 47 | }
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| 48 |
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| 49 | template<typename T>
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| 50 | EIGEN_DONT_INLINE typename T::Scalar twopassNorm(T& v)
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| 51 | {
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| 52 | typedef typename T::Scalar Scalar;
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| 53 | Scalar s = v.cwise().abs().maxCoeff();
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| 54 | return s*(v/s).norm();
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| 55 | }
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| 56 |
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| 57 | template<typename T>
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| 58 | EIGEN_DONT_INLINE typename T::Scalar bl2passNorm(T& v)
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| 59 | {
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| 60 | return v.stableNorm();
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| 61 | }
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| 62 |
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| 63 | template<typename T>
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| 64 | EIGEN_DONT_INLINE typename T::Scalar divacNorm(T& v)
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| 65 | {
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| 66 | int n =v.size() / 2;
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| 67 | for (int i=0;i<n;++i)
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| 68 | v(i) = v(2*i)*v(2*i) + v(2*i+1)*v(2*i+1);
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| 69 | n = n/2;
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| 70 | while (n>0)
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| 71 | {
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| 72 | for (int i=0;i<n;++i)
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| 73 | v(i) = v(2*i) + v(2*i+1);
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| 74 | n = n/2;
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| 75 | }
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| 76 | return internal::sqrt(v(0));
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| 77 | }
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| 78 |
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| 79 | #ifdef EIGEN_VECTORIZE
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| 80 | Packet4f internal::plt(const Packet4f& a, Packet4f& b) { return _mm_cmplt_ps(a,b); }
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| 81 | Packet2d internal::plt(const Packet2d& a, Packet2d& b) { return _mm_cmplt_pd(a,b); }
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| 82 |
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| 83 | Packet4f internal::pandnot(const Packet4f& a, Packet4f& b) { return _mm_andnot_ps(a,b); }
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| 84 | Packet2d internal::pandnot(const Packet2d& a, Packet2d& b) { return _mm_andnot_pd(a,b); }
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| 85 | #endif
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| 86 |
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| 87 | template<typename T>
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| 88 | EIGEN_DONT_INLINE typename T::Scalar pblueNorm(const T& v)
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| 89 | {
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| 90 | #ifndef EIGEN_VECTORIZE
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| 91 | return v.blueNorm();
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| 92 | #else
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| 93 | typedef typename T::Scalar Scalar;
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| 94 |
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| 95 | static int nmax = 0;
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| 96 | static Scalar b1, b2, s1m, s2m, overfl, rbig, relerr;
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| 97 | int n;
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| 98 |
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| 99 | if(nmax <= 0)
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| 100 | {
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| 101 | int nbig, ibeta, it, iemin, iemax, iexp;
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| 102 | Scalar abig, eps;
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| 103 |
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| 104 | nbig = std::numeric_limits<int>::max(); // largest integer
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| 105 | ibeta = std::numeric_limits<Scalar>::radix; //NumTraits<Scalar>::Base; // base for floating-point numbers
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| 106 | it = std::numeric_limits<Scalar>::digits; //NumTraits<Scalar>::Mantissa; // number of base-beta digits in mantissa
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| 107 | iemin = std::numeric_limits<Scalar>::min_exponent; // minimum exponent
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| 108 | iemax = std::numeric_limits<Scalar>::max_exponent; // maximum exponent
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| 109 | rbig = std::numeric_limits<Scalar>::max(); // largest floating-point number
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| 110 |
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| 111 | // Check the basic machine-dependent constants.
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| 112 | if(iemin > 1 - 2*it || 1+it>iemax || (it==2 && ibeta<5)
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| 113 | || (it<=4 && ibeta <= 3 ) || it<2)
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| 114 | {
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| 115 | eigen_assert(false && "the algorithm cannot be guaranteed on this computer");
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| 116 | }
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| 117 | iexp = -((1-iemin)/2);
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| 118 | b1 = std::pow(ibeta, iexp); // lower boundary of midrange
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| 119 | iexp = (iemax + 1 - it)/2;
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| 120 | b2 = std::pow(ibeta,iexp); // upper boundary of midrange
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| 121 |
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| 122 | iexp = (2-iemin)/2;
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| 123 | s1m = std::pow(ibeta,iexp); // scaling factor for lower range
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| 124 | iexp = - ((iemax+it)/2);
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| 125 | s2m = std::pow(ibeta,iexp); // scaling factor for upper range
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| 126 |
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| 127 | overfl = rbig*s2m; // overfow boundary for abig
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| 128 | eps = std::pow(ibeta, 1-it);
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| 129 | relerr = internal::sqrt(eps); // tolerance for neglecting asml
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| 130 | abig = 1.0/eps - 1.0;
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| 131 | if (Scalar(nbig)>abig) nmax = abig; // largest safe n
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| 132 | else nmax = nbig;
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| 133 | }
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| 134 |
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| 135 | typedef typename internal::packet_traits<Scalar>::type Packet;
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| 136 | const int ps = internal::packet_traits<Scalar>::size;
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| 137 | Packet pasml = internal::pset1(Scalar(0));
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| 138 | Packet pamed = internal::pset1(Scalar(0));
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| 139 | Packet pabig = internal::pset1(Scalar(0));
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| 140 | Packet ps2m = internal::pset1(s2m);
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| 141 | Packet ps1m = internal::pset1(s1m);
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| 142 | Packet pb2 = internal::pset1(b2);
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| 143 | Packet pb1 = internal::pset1(b1);
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| 144 | for(int j=0; j<v.size(); j+=ps)
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| 145 | {
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| 146 | Packet ax = internal::pabs(v.template packet<Aligned>(j));
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| 147 | Packet ax_s2m = internal::pmul(ax,ps2m);
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| 148 | Packet ax_s1m = internal::pmul(ax,ps1m);
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| 149 | Packet maskBig = internal::plt(pb2,ax);
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| 150 | Packet maskSml = internal::plt(ax,pb1);
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| 151 |
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| 152 | // Packet maskMed = internal::pand(maskSml,maskBig);
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| 153 | // Packet scale = internal::pset1(Scalar(0));
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| 154 | // scale = internal::por(scale, internal::pand(maskBig,ps2m));
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| 155 | // scale = internal::por(scale, internal::pand(maskSml,ps1m));
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| 156 | // scale = internal::por(scale, internal::pandnot(internal::pset1(Scalar(1)),maskMed));
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| 157 | // ax = internal::pmul(ax,scale);
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| 158 | // ax = internal::pmul(ax,ax);
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| 159 | // pabig = internal::padd(pabig, internal::pand(maskBig, ax));
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| 160 | // pasml = internal::padd(pasml, internal::pand(maskSml, ax));
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| 161 | // pamed = internal::padd(pamed, internal::pandnot(ax,maskMed));
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| 162 |
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| 163 |
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| 164 | pabig = internal::padd(pabig, internal::pand(maskBig, internal::pmul(ax_s2m,ax_s2m)));
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| 165 | pasml = internal::padd(pasml, internal::pand(maskSml, internal::pmul(ax_s1m,ax_s1m)));
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| 166 | pamed = internal::padd(pamed, internal::pandnot(internal::pmul(ax,ax),internal::pand(maskSml,maskBig)));
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| 167 | }
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| 168 | Scalar abig = internal::predux(pabig);
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| 169 | Scalar asml = internal::predux(pasml);
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| 170 | Scalar amed = internal::predux(pamed);
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| 171 | if(abig > Scalar(0))
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| 172 | {
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| 173 | abig = internal::sqrt(abig);
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| 174 | if(abig > overfl)
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| 175 | {
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| 176 | eigen_assert(false && "overflow");
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| 177 | return rbig;
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| 178 | }
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| 179 | if(amed > Scalar(0))
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| 180 | {
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| 181 | abig = abig/s2m;
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| 182 | amed = internal::sqrt(amed);
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| 183 | }
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| 184 | else
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| 185 | {
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| 186 | return abig/s2m;
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| 187 | }
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| 188 |
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| 189 | }
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| 190 | else if(asml > Scalar(0))
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| 191 | {
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| 192 | if (amed > Scalar(0))
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| 193 | {
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| 194 | abig = internal::sqrt(amed);
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| 195 | amed = internal::sqrt(asml) / s1m;
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| 196 | }
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| 197 | else
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| 198 | {
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| 199 | return internal::sqrt(asml)/s1m;
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| 200 | }
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| 201 | }
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| 202 | else
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| 203 | {
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| 204 | return internal::sqrt(amed);
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| 205 | }
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| 206 | asml = std::min(abig, amed);
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| 207 | abig = std::max(abig, amed);
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| 208 | if(asml <= abig*relerr)
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| 209 | return abig;
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| 210 | else
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| 211 | return abig * internal::sqrt(Scalar(1) + internal::abs2(asml/abig));
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| 212 | #endif
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| 213 | }
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| 214 |
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| 215 | #define BENCH_PERF(NRM) { \
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| 216 | Eigen::BenchTimer tf, td, tcf; tf.reset(); td.reset(); tcf.reset();\
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| 217 | for (int k=0; k<tries; ++k) { \
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| 218 | tf.start(); \
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| 219 | for (int i=0; i<iters; ++i) NRM(vf); \
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| 220 | tf.stop(); \
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| 221 | } \
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| 222 | for (int k=0; k<tries; ++k) { \
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| 223 | td.start(); \
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| 224 | for (int i=0; i<iters; ++i) NRM(vd); \
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| 225 | td.stop(); \
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| 226 | } \
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| 227 | for (int k=0; k<std::max(1,tries/3); ++k) { \
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| 228 | tcf.start(); \
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| 229 | for (int i=0; i<iters; ++i) NRM(vcf); \
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| 230 | tcf.stop(); \
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| 231 | } \
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| 232 | std::cout << #NRM << "\t" << tf.value() << " " << td.value() << " " << tcf.value() << "\n"; \
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| 233 | }
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| 234 |
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| 235 | void check_accuracy(double basef, double based, int s)
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| 236 | {
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| 237 | double yf = basef * internal::abs(internal::random<double>());
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| 238 | double yd = based * internal::abs(internal::random<double>());
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| 239 | VectorXf vf = VectorXf::Ones(s) * yf;
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| 240 | VectorXd vd = VectorXd::Ones(s) * yd;
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| 241 |
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| 242 | std::cout << "reference\t" << internal::sqrt(double(s))*yf << "\t" << internal::sqrt(double(s))*yd << "\n";
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| 243 | std::cout << "sqsumNorm\t" << sqsumNorm(vf) << "\t" << sqsumNorm(vd) << "\n";
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| 244 | std::cout << "hypotNorm\t" << hypotNorm(vf) << "\t" << hypotNorm(vd) << "\n";
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| 245 | std::cout << "blueNorm\t" << blueNorm(vf) << "\t" << blueNorm(vd) << "\n";
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| 246 | std::cout << "pblueNorm\t" << pblueNorm(vf) << "\t" << pblueNorm(vd) << "\n";
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| 247 | std::cout << "lapackNorm\t" << lapackNorm(vf) << "\t" << lapackNorm(vd) << "\n";
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| 248 | std::cout << "twopassNorm\t" << twopassNorm(vf) << "\t" << twopassNorm(vd) << "\n";
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| 249 | std::cout << "bl2passNorm\t" << bl2passNorm(vf) << "\t" << bl2passNorm(vd) << "\n";
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| 250 | }
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| 251 |
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| 252 | void check_accuracy_var(int ef0, int ef1, int ed0, int ed1, int s)
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| 253 | {
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| 254 | VectorXf vf(s);
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| 255 | VectorXd vd(s);
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| 256 | for (int i=0; i<s; ++i)
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| 257 | {
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| 258 | vf[i] = internal::abs(internal::random<double>()) * std::pow(double(10), internal::random<int>(ef0,ef1));
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| 259 | vd[i] = internal::abs(internal::random<double>()) * std::pow(double(10), internal::random<int>(ed0,ed1));
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| 260 | }
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| 261 |
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| 262 | //std::cout << "reference\t" << internal::sqrt(double(s))*yf << "\t" << internal::sqrt(double(s))*yd << "\n";
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| 263 | std::cout << "sqsumNorm\t" << sqsumNorm(vf) << "\t" << sqsumNorm(vd) << "\t" << sqsumNorm(vf.cast<long double>()) << "\t" << sqsumNorm(vd.cast<long double>()) << "\n";
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| 264 | std::cout << "hypotNorm\t" << hypotNorm(vf) << "\t" << hypotNorm(vd) << "\t" << hypotNorm(vf.cast<long double>()) << "\t" << hypotNorm(vd.cast<long double>()) << "\n";
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| 265 | std::cout << "blueNorm\t" << blueNorm(vf) << "\t" << blueNorm(vd) << "\t" << blueNorm(vf.cast<long double>()) << "\t" << blueNorm(vd.cast<long double>()) << "\n";
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| 266 | std::cout << "pblueNorm\t" << pblueNorm(vf) << "\t" << pblueNorm(vd) << "\t" << blueNorm(vf.cast<long double>()) << "\t" << blueNorm(vd.cast<long double>()) << "\n";
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| 267 | std::cout << "lapackNorm\t" << lapackNorm(vf) << "\t" << lapackNorm(vd) << "\t" << lapackNorm(vf.cast<long double>()) << "\t" << lapackNorm(vd.cast<long double>()) << "\n";
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| 268 | std::cout << "twopassNorm\t" << twopassNorm(vf) << "\t" << twopassNorm(vd) << "\t" << twopassNorm(vf.cast<long double>()) << "\t" << twopassNorm(vd.cast<long double>()) << "\n";
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| 269 | // std::cout << "bl2passNorm\t" << bl2passNorm(vf) << "\t" << bl2passNorm(vd) << "\t" << bl2passNorm(vf.cast<long double>()) << "\t" << bl2passNorm(vd.cast<long double>()) << "\n";
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| 270 | }
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| 271 |
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| 272 | int main(int argc, char** argv)
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| 273 | {
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| 274 | int tries = 10;
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| 275 | int iters = 100000;
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| 276 | double y = 1.1345743233455785456788e12 * internal::random<double>();
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| 277 | VectorXf v = VectorXf::Ones(1024) * y;
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| 278 |
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| 279 | // return 0;
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| 280 | int s = 10000;
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| 281 | double basef_ok = 1.1345743233455785456788e15;
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| 282 | double based_ok = 1.1345743233455785456788e95;
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| 283 |
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| 284 | double basef_under = 1.1345743233455785456788e-27;
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| 285 | double based_under = 1.1345743233455785456788e-303;
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| 286 |
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| 287 | double basef_over = 1.1345743233455785456788e+27;
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| 288 | double based_over = 1.1345743233455785456788e+302;
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| 289 |
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| 290 | std::cout.precision(20);
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| 291 |
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| 292 | std::cerr << "\nNo under/overflow:\n";
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| 293 | check_accuracy(basef_ok, based_ok, s);
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| 294 |
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| 295 | std::cerr << "\nUnderflow:\n";
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| 296 | check_accuracy(basef_under, based_under, s);
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| 297 |
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| 298 | std::cerr << "\nOverflow:\n";
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| 299 | check_accuracy(basef_over, based_over, s);
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| 300 |
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| 301 | std::cerr << "\nVarying (over):\n";
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| 302 | for (int k=0; k<1; ++k)
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| 303 | {
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| 304 | check_accuracy_var(20,27,190,302,s);
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| 305 | std::cout << "\n";
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| 306 | }
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| 307 |
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| 308 | std::cerr << "\nVarying (under):\n";
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| 309 | for (int k=0; k<1; ++k)
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| 310 | {
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| 311 | check_accuracy_var(-27,20,-302,-190,s);
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| 312 | std::cout << "\n";
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| 313 | }
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| 314 |
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| 315 | std::cout.precision(4);
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| 316 | std::cerr << "Performance (out of cache):\n";
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| 317 | {
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| 318 | int iters = 1;
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| 319 | VectorXf vf = VectorXf::Random(1024*1024*32) * y;
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| 320 | VectorXd vd = VectorXd::Random(1024*1024*32) * y;
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| 321 | VectorXcf vcf = VectorXcf::Random(1024*1024*32) * y;
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| 322 | BENCH_PERF(sqsumNorm);
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| 323 | BENCH_PERF(blueNorm);
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| 324 | // BENCH_PERF(pblueNorm);
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| 325 | // BENCH_PERF(lapackNorm);
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| 326 | // BENCH_PERF(hypotNorm);
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| 327 | // BENCH_PERF(twopassNorm);
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| 328 | BENCH_PERF(bl2passNorm);
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| 329 | }
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| 330 |
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| 331 | std::cerr << "\nPerformance (in cache):\n";
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| 332 | {
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| 333 | int iters = 100000;
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| 334 | VectorXf vf = VectorXf::Random(512) * y;
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| 335 | VectorXd vd = VectorXd::Random(512) * y;
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| 336 | VectorXcf vcf = VectorXcf::Random(512) * y;
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| 337 | BENCH_PERF(sqsumNorm);
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| 338 | BENCH_PERF(blueNorm);
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| 339 | // BENCH_PERF(pblueNorm);
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| 340 | // BENCH_PERF(lapackNorm);
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| 341 | // BENCH_PERF(hypotNorm);
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| 342 | // BENCH_PERF(twopassNorm);
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| 343 | BENCH_PERF(bl2passNorm);
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| 344 | }
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| 345 | }
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