C++ for Scientists - Technische Universität Dresden

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184 CHAPTER 5. META-PROGRAMMING Compute time mult(A, B, C) is 5250 µs. This are 795.794 MFlops. Compute time mult(A, B, C) is 2770 µs. This are 1508.27 MFlops. Compute time mult(A, B, C) is 1990 µs. This are 2099.46 MFlops. Compute time mult(A, B, C) is 2230 µs. This are 1873.51 MFlops. Compute time mult(A, B, C) is 2130 µs. This are 1961.46 MFlops. Compute time mult(A, B, C) is 2930 µs. This are 1425.91 MFlops. Compute time mult(A, B, C) is 2350 µs. This are 1777.84 MFlops. Compute time mult(A, B, C) is 3420 µs. This are 1221.61 MFlops. Compute time mult(A, B, C) is 4010 µs. This are 1041.88 MFlops. Compute time mult(A, B, C) is 2870 µs. This are 1455.72 MFlops. Compute time mult(A, B, C) is 3230 µs. This are 1293.47 MFlops. Compute time mult(A, B, C) is 3060 µs. This are 1365.33 MFlops. Compute time mult(A, B, C) is 2780 µs. This are 1502.85 MFlops. One can see that mult has the same performance as the original implementation which in fact is performing the operations in exactly the same order (so far the compiler optimization does not change the order internally). We see also that the unrolled versions are all faster, up to a speed-up of 2.6. With double matrices the performance is lower in total: Compute time mult(A, B, C) is 10080 µs. This are 414.476 MFlops. Compute time mult(A, B, C) is 8700 µs. This are 480.221 MFlops. Compute time mult(A, B, C) is 7470 µs. This are 559.293 MFlops. Compute time mult(A, B, C) is 5910 µs. This are 706.924 MFlops. Compute time mult(A, B, C) is 3750 µs. This are 1114.11 MFlops. Compute time mult(A, B, C) is 5140 µs. This are 812.825 MFlops. Compute time mult(A, B, C) is 3420 µs. This are 1221.61 MFlops. Compute time mult(A, B, C) is 4590 µs. This are 910.222 MFlops. Compute time mult(A, B, C) is 4310 µs. This are 969.355 MFlops. Compute time mult(A, B, C) is 6280 µs. This are 665.274 MFlops. Compute time mult(A, B, C) is 5310 µs. This are 786.802 MFlops. Compute time mult(A, B, C) is 4290 µs. This are 973.874 MFlops. Compute time mult(A, B, C) is 3490 µs. This are 1197.11 MFlops. It shows that other parametrizations yield more acceleration and that the performance could almost be tripled. Which configuration is best and why is — as mentioned before — not topic of this script; we only show programming techniques. The reader is invited to try this program on his/her own computer. The technique in this section is intended for L1 cache usage. If matrices are larger, one should use more levels of blocking. A general-purpose methodology for locality on L2, L3, main memory, local disk, . . . is recursion. This avoids reimplementation for each cache size and performs even reasonably well in virtually memory, see for instance [?].
5.5. EXERCISES 185 5.5 Exercises 5.5.1 Vector class Revisit the vector example from §??. Make an expression for a scalar times a vector: class scalar times vector expressions { } ; that inherits from base vector. Use the inheritance mechanism to assign scalar times vector expressions into vector. 5.5.2 Vector expression template Make a vector concept, which you call Vector. Make a vector class (you can use std::vector) that satisfies this concept. This vector class should have at least the following members: class my vector { public: typedef double value type ; public: my vector( int n ) ; // Copy Constructor from type itself my vector( my vector& ) ; // Constructor from generic vector template my vector( Vector& ) ; // Assignment operator my vector& operator=( my vector const& v ) ; // Assignment for generic Vector template my vector& operator=( Vector const& v ) ; value type& operator() ( int i ) ; public: // Vector concept int size() const ; value type operator() ( int i ) const ; } ; Make an expression for a scalar times a vector: template class scalar times vector expression{ } ;
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Technische Universität Dresden Fak
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Contents I Understanding C++ 7 Intr
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CONTENTS 5 10.5 Unix and Linux . .
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Part I Understanding C ++ 7
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10 C ++ was not a reliable computer
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12 CHAPTER 1. GOOD AND BAD SCIENTIF
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20 CHAPTER 2. C++ BASICS • std::c
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22 CHAPTER 2. C++ BASICS In the fir
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24 CHAPTER 2. C++ BASICS int main (
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26 CHAPTER 2. C++ BASICS Operator A
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28 CHAPTER 2. C++ BASICS The bitwis
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30 CHAPTER 2. C++ BASICS cast (type
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32 CHAPTER 2. C++ BASICS complicate
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34 CHAPTER 2. C++ BASICS } else if
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36 CHAPTER 2. C++ BASICS eps/= 2.0;
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38 CHAPTER 2. C++ BASICS for (...;
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40 CHAPTER 2. C++ BASICS 2.6.1 Inli
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42 CHAPTER 2. C++ BASICS To make su
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44 CHAPTER 2. C++ BASICS float divi
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46 CHAPTER 2. C++ BASICS The first
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48 CHAPTER 2. C++ BASICS #ifndef at
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50 CHAPTER 2. C++ BASICS float A[7]
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52 CHAPTER 2. C++ BASICS Encapsulat
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54 CHAPTER 2. C++ BASICS As a pract
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56 CHAPTER 2. C++ BASICS A function
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58 CHAPTER 2. C++ BASICS Now that t
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60 CHAPTER 2. C++ BASICS we need sm
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62 CHAPTER 2. C++ BASICS 2.12 Exerc
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64 CHAPTER 2. C++ BASICS 2.13 Opera
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66 CHAPTER 3. CLASSES apply symm bl
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68 CHAPTER 3. CLASSES int main() {
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70 CHAPTER 3. CLASSES class solver
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72 CHAPTER 3. CLASSES • Compilers
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74 CHAPTER 3. CLASSES a real number
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76 CHAPTER 3. CLASSES } return ∗t
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78 CHAPTER 3. CLASSES This mechanis
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80 CHAPTER 3. CLASSES One could not
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82 CHAPTER 3. CLASSES class matrix
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84 CHAPTER 3. CLASSES Approach 3: R
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86 CHAPTER 3. CLASSES of the decrem
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88 CHAPTER 3. CLASSES There are two
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90 CHAPTER 4. GENERIC PROGRAMMING }
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92 CHAPTER 4. GENERIC PROGRAMMING c
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94 CHAPTER 4. GENERIC PROGRAMMING A
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Programming tools Chapter 10 In thi
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10.2. DEBUGGING 237 T& glas::contin
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10.5. UNIX AND LINUX 241 • top: l
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C ++ Libraries for Scientific Compu
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11.3. BOOST.BINDINGS 247 #include
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11.7. GEOMETRIC LIBRARIES 251 11.7.
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Real-World Programming Chapter 12 1
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12.1. TRANSCENDING LEGACY APPLICATI
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Parallelism Chapter 13 13.1 Multi-T
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13.2. MESSAGE PASSING 261 int main
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14.1. COMPUTING AN EIGENFUNCTION OF
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Programmierprojekte Kapitel 15 Die
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15.6. MATRIX-SKALIERUNG 287 Siehe h
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15.10. ANWENDUNG MTL4 AUF TYPEN MIT
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Acknowledgement Chapter 16 Special
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Bibliography [AG04] David Abrahams
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