| Introduction | p. 1 |
| Copyright, credits, feedback and updates, licensing, and disclaimer | p. 2 |
| Program language and systems considerations | p. 4 |
| Acknowledgements | p. 5 |
| Using PAMIR | p. 7 |
| Base regions for the PAMIR programs, and normalization conventions | p. 7 |
| Base region definitions | p. 7 |
| Normalization conventions | p. 11 |
| Base region applications | p. 11 |
| Remarks on strategy | p. 13 |
| Sketch of the algorithms | p. 14 |
| Folders in pamir_archive | p. 14 |
| Entering the function and the spatial dimension | p. 15 |
| Basic algorithm module | p. 16 |
| Three versions of the algorithm | p. 17 |
| Default double precision and real(16) option | p. 17 |
| Linking main programs to subroutines | p. 18 |
| Error estimates and thinning | p. 18 |
| User options | p. 20 |
| Contents of programs in the folders | p. 21 |
| Folder simplex123 | p. 21 |
| Folder simplex4 | p. 22 |
| Folder simplex579 | p. 22 |
| Folder simplex579_16 | p. 22 |
| Folder cubel3 | p. 23 |
| Folder cube357 | p. 23 |
| Folder cube357_16 | p. 23 |
| Folder cube579 | p. 24 |
| Folder cube579_l6 | p. 24 |
| Folder constant_jacobian_map | p. 24 |
| Folder loop_exaraples | p. 25 |
| Folder readme | p. 26 |
| Program inputs and outputs | p. 26 |
| Inputs | p. 26 |
| Outputs | p. 30 |
| Function calls, timing estimates, and memory estimates | p. 33 |
| Function call counting | p. 33 |
| Timing estimates | p. 35 |
| Memory estimates | p. 38 |
| Projection of future performance | p. 39 |
| False positives and their avoidance | p. 40 |
| Programming remarks | p. 43 |
| Benchmark examples and comparisons | p. 51 |
| Introduction | p. 51 |
| Lattice Green's Function near the branch cut: comparison of PAMIR with CUBPACK | p. 52 |
| Double Gaussian in seven dimensions: comparison of PAMIR with VEGAS and MISER | p. 58 |
| Two loop self-energy master function | p. 60 |
| Comparison of PAMIR with CUBPACK for polynomial integrals over standard simplex in five dimensions | p. 68 |
| Comparison of PAMIR with CUBPACK for the Feynman-Schwinger integral over standard simplex in five dimensions | p. 72 |
| Comparisons of PAMIR with CUBPACK for hypercube test integrals in five dimensions | p. 75 |
| Double Gaussian | p. 77 |
| Tsuda functions | p. 79 |
| Eighth order polynomial | p. 83 |
| Single Gaussian with generic center in five dimensions | p. 83 |
| Lorentzians in five dimensions: corner peak, edge peak, generic internal peak | p. 86 |
| Oscillatory cosine integrals in five dimensions | p. 89 |
| C0 function in five dimensions | p. 90 |
| Attenuation function of radiation from a disk source | p. 95 |
| High accuracy calculations of double Gaussian integral in seven and nine dimensions on a 64 process cluster | p. 95 |
| Computational integration theory and PAMIR | p. 101 |
| Overview: The philosophy of PAMIR | p. 101 |
| Choice of integration method | p. 102 |
| Choice of integration rule | p. 103 |
| Choice of error estimator | p. 112 |
| Choice of subdivision method and decision method | p. 114 |
| Details of construction of the PAMIR algorithms and programs | p. 117 |
| Simplex properties | p. 117 |
| Simplex subdivision | p. 120 |
| Simplex subdivision algorithms | p. 120 |
| Simplex subdivision properties | p. 125 |
| Hypercube and hyper-rectangle subdivision | p. 130 |
| Hypercube subdivision algorithm | p. 130 |
| Hypercube and subdivision properties | p. 132 |
| Hyper-rectangle subdivision algorithm | p. 134 |
| Vandermonde solvers | p. 135 |
| Parameterized higher order integration formulas for a general simplex | p. 136 |
| Simplex integrals in terms of moments | p. 136 |
| First through third order simplex formulas | p. 142 |
| Fourth order simplex formula | p. 145 |
| Fifth order simplex formula | p. 145 |
| Seventh order simplex formula | p. 146 |
| Ninth order simplex formula | p. 148 |
| Leading term in higher order for simplexes | p. 149 |
| Parameterized higher order integration formulas for axis-parallel hypercubes from moments | p. 149 |
| First and third order formulas | p. 152 |
| Fifth order formula | p. 153 |
| Seventh order formula | p. 154 |
| Ninth order formula | p. 155 |
| Leading term in higher order for hypercubes | p. 155 |
| Redundant function calls in low dimensions p | p. 156 |
| Some details of the cube357 programs | p. 157 |
| Integration over hyper-rectangles | p. 157 |
| Measure var(i) of variation along axis i | p. 158 |
| Some samples of code | p. 158 |
| Basic module | p. 159 |
| Simplex and hypercube rescaling for the "r" and "m" programs | p. 162 |
| Distributing residual subregions to processes in the "m" programs | p. 164 |
| Programming extensions and open questions | p. 165 |
| Test integrals | p. 167 |
| Derivation of the simplex generating function | p. 173 |
| Derivation of the hypercube generating function | p. 175 |
| Mappings between base regions | p. 177 |
| Rule for determining where a point lies with respect to a simplex | p. 181 |
| Expansion for ∑4 | p. 185 |
| Fourth order simplex formula | p. 189 |
| Ninth order simplex formula | p. 193 |
| Ninth order hypercube formula | p. 195 |
| Bibliography | p. 197 |
| Index | p. 201 |
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