From 4a67a9aefae30d05cc54bdc79bd836c2b4456ca1 Mon Sep 17 00:00:00 2001 From: Lugovtsov Gleb Date: Tue, 15 Nov 2022 16:39:40 +0300 Subject: [PATCH] work on project --- project/data-processing/gen-data.ipynb | 275 + project/data-processing/main.cpp | 0 .../pocketfft-cpp/pocketfft_demo.cc | 87 + .../pocketfft-cpp/pocketfft_hdronly.h | 3583 +++++++++ project/data-processing/sig1.csv | 7001 +++++++++++++++++ project/data-processing/sig2.csv | 7001 +++++++++++++++++ 6 files changed, 17947 insertions(+) create mode 100644 project/data-processing/gen-data.ipynb create mode 100644 project/data-processing/main.cpp create mode 100644 project/data-processing/pocketfft-cpp/pocketfft_demo.cc create mode 100644 project/data-processing/pocketfft-cpp/pocketfft_hdronly.h create mode 100644 project/data-processing/sig1.csv create mode 100644 project/data-processing/sig2.csv diff --git a/project/data-processing/gen-data.ipynb b/project/data-processing/gen-data.ipynb new file mode 100644 index 0000000..8112286 --- /dev/null +++ b/project/data-processing/gen-data.ipynb @@ -0,0 +1,275 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 220, + "id": "50f27832-a7b1-4fac-b9b8-988606608b84", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 344, + "id": "80a10edc-520c-4b05-af86-29dbb440717e", + "metadata": {}, + "outputs": [], + "source": [ + "l = int(7e3)\n", + "t = np.linspace(0, 1e-6, l)" + ] + }, + { + "cell_type": "code", + "execution_count": 345, + "id": "70c787d1-fa7a-4d43-95ec-73f9929f357b", + "metadata": {}, + "outputs": [], + "source": [ + "nu1 = 2e8\n", + "phi1 = 1\n", + "a1 = 0.6\n", + "nu2 = 2e8\n", + "phi2 = 2\n", + "a2 = 0.4" + ] + }, + { + "cell_type": "code", + "execution_count": 346, + "id": "8730fd74-6b30-4b92-87af-7205d5732ac9", + "metadata": {}, + "outputs": [], + "source": [ + "V1 = a1*np.sin(nu1*t/(2*np.pi) + phi1)\n", + "V2 = a2*np.sin(nu2*t/(2*np.pi) + phi2)" + ] + }, + { + "cell_type": "code", + "execution_count": 347, + "id": "b0aaf4c1-aee0-4ecf-99ad-560f93770840", + "metadata": {}, + "outputs": [], + "source": [ + "f = V1\n", + "g = np.random.normal(loc=V2, scale=0.01)" + ] + }, + { + "cell_type": "code", + "execution_count": 348, + "id": "b66882de-6ed3-4931-8049-33c27da52528", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(t, f)\n", + "plt.plot(t, g)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 349, + "id": "e56a0992-4cdc-4839-9aea-91a2497c2696", + "metadata": {}, + "outputs": [], + "source": [ + "with open(r'sig1.csv', 'w') as file:\n", + " string = 'voltage[V],time[ns]\\n'\n", + " for i in range(l):\n", + " string += f'{f[i]:.10f},{t[i]*1e9:.4f}\\n'\n", + " file.write(string)" + ] + }, + { + "cell_type": "code", + "execution_count": 350, + "id": "29fee1dc-eb0e-4e10-958a-640203b7e4ba", + "metadata": {}, + "outputs": [], + "source": [ + "with open(r'sig2.csv', 'w') as file:\n", + " string = 'voltage[V],time[ns]\\n'\n", + " for i in range(l):\n", + " string += f'{g[i]:.10f},{t[i]*1e9:.4f}\\n'\n", + " file.write(string)" + ] + }, + { + "cell_type": "code", + "execution_count": 351, + "id": "c11ded9c-8375-4740-bcf1-3b07bfc07b19", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "Ff = np.fft.fft(f)\n", + "Fg = np.fft.fft(g)\n", + "lamb = Fg / Ff\n", + "freq = np.fft.fftfreq(l)" + ] + }, + { + "cell_type": "code", + "execution_count": 352, + "id": "8bc8887d-bc88-4e3b-99c9-309f2e9ee0eb", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 352, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(freq, np.absolute(lamb))" + ] + }, + { + "cell_type": "code", + "execution_count": 353, + "id": "22214b98-571f-45e4-9fdd-44551aab288a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 353, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(freq, np.angle(lamb))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "95f5907e-94b0-4102-8e01-f313d3fb3aca", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 120, + "id": "c6c2f53c-98a6-4b27-a8b3-03028c24126c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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A4WjxwOkiCigrVqw44/KUlBSVl5ervLz8tGOGDh2qDRs2RPKxAACFPaeNFg8cj+/iAQAAxiGgAIAN0eKB0xFQAMAmLIsHtSF2EFAAAIBxCCgAYEO0eOB0BBQAsAnu4kEsIaAAAADjEFAAwCY4a4JYQkABABsiq8DpCCgAAMA4BBQAsAmL8yaIIQQUALAjLkiBwxFQAACAcQgoAGAXVrc/Ao5EQAEAAMYhoAAAAOMQUADAJnjUPWIJAQUAABiHgAIAAIxDQAEAm+ja1rHo8cDhCCgAAMA4BBQAAGAcAgoA2ETX7+KhwQOnI6AAAADjEFAAAIBxCCgAYBPhd/FErw6gLxBQAACAcQgoAADAOAQUALAJ6zQ/A05EQAEAAMYhoAAAAOMQUADAJrp+/w7fxQOnI6AAAADjEFAAAIBxCCgAYBN0dRBLCCgAAMA4BBQAAGAcAgoA2BDtHjgdAQUAABiHgAIANsFZE8QSAgoA2JDFt/HA4QgoAADAOAQUALCJrmdNaPfA6QgoAADAOAQUAABgHAIKANhE17YOHR44HQEFAAAYh4ACAACMQ0ABAJvo2tbhLh44HQEFAAAYh4ACAACMQ0ABAJuwuvR1eNQ9nI6AAgAAjENAAQAAxiGgAIBNcBcPYklEAWXRokW67rrrlJqaqszMTE2ePFn79+8PG9PU1KTS0lINHjxYAwcOVFFRkWpra8PGVFdXq7CwUP3791dmZqYefPBBtbW1nf/WAAAAR4gooGzbtk2lpaWqqKjQpk2b1NraqgkTJqixsTE0ZtasWXr55Ze1du1abdu2TTU1NbrjjjtCy9vb21VYWKiWlhbt2LFDzzzzjFatWqW5c+f23FYBAABbS4hk8MaNG8Ner1q1SpmZmaqsrNT3v/991dfXa8WKFVq9erXGjx8vSVq5cqWGDx+uiooKjRs3Tq+//rr27dunzZs3y+PxaNSoUVq4cKEeeughzZ8/X0lJST23dQDgILR1EEvO6xqU+vp6SVJGRoYkqbKyUq2trcrPzw+NGTZsmHJycuT3+yVJfr9fI0aMkMfjCY0pKChQMBjU3r17u/2c5uZmBYPBsAkAADjXOQeUjo4O3X///brhhht0zTXXSJICgYCSkpKUnp4eNtbj8SgQCITGdA0nncs7l3Vn0aJFSktLC03Z2dnnWjYAALCBcw4opaWlev/997VmzZqerKdbs2fPVn19fWg6ePBgr38mAJiny4Pa6PfA4SK6BqXTjBkztH79em3fvl1DhgwJzfd6vWppadHRo0fDzqLU1tbK6/WGxuzatSvs/Trv8ukcc7Lk5GQlJyefS6kAAMCGIjqDYlmWZsyYoXXr1mnr1q269NJLw5aPHj1aiYmJ2rJlS2je/v37VV1dLZ/PJ0ny+XyqqqpSXV1daMymTZvkdruVm5t7PtsCAAAcIqIzKKWlpVq9erVeeuklpaamhq4ZSUtLU79+/ZSWlqaSkhKVlZUpIyNDbrdbM2fOlM/n07hx4yRJEyZMUG5urqZNm6YlS5YoEAhozpw5Ki0t5SwJAJxB164OHR44XUQBZfny5ZKkW265JWz+ypUrdc8990iSHnvsMcXFxamoqEjNzc0qKCjQsmXLQmPj4+O1fv16TZ8+XT6fTwMGDFBxcbEWLFhwflsCAAAcI6KAcjYXZaWkpKi8vFzl5eWnHTN06FBt2LAhko8GgJjHSRPEEr6LBwBsiLACpyOgAAAA4xBQAMAmuDAWsYSAAgA2RFiB0xFQAACAcQgoAGATVtdH3XOZLByOgAIAAIxDQAEAAMYhoACATfCoe8QSAgoAADAOAQUAABiHgAIANhHW4oleGUCfIKAAAADjEFAAAIBxCCgAYBNhD2fjNh44HAEFAAAYh4ACAACMQ0ABAJvgLh7EEgIKAAAwDgEFAAAYh4ACADbETTxwOgIKAAAwDgEFAAAYh4ACADYRfhcPPR44GwEFAAAYh4ACADbBWRPEEgIKANgQd/HA6QgoAADAOAQUALAJzpoglhBQAMCGyCpwOgIKAAAwDgEFAGyCsyaIJQQUALAhrkeB0xFQAACAcQgoAGATVpfTJjy0DU5HQAEAAMYhoAAAAOMQUADAJqzTvgCch4ACAACMQ0ABAADGIaAAgE10ffYJHR44HQEFAAAYh4ACAACMQ0ABANvo8qA2nnUPhyOgAAAA4xBQAACAcQgoAGATYXfx0OGBwxFQAACAcQgoAADAOAQUALAJ6zQ/A05EQAEAAMYhoAAAAOMQUADAJriLB7GEgAIAAIxDQAEAm+Dx9oglEQeU7du36/bbb1dWVpZcLpdefPHFsOWWZWnu3Lm66KKL1K9fP+Xn5+ujjz4KG3PkyBFNnTpVbrdb6enpKikp0bFjx85rQwAglljcxwOHizigNDY26tprr1V5eXm3y5csWaInnnhCTz31lHbu3KkBAwaooKBATU1NoTFTp07V3r17tWnTJq1fv17bt2/Xfffdd+5bAQAAHCUh0hUmTpyoiRMndrvMsiwtXbpUc+bM0aRJkyRJf/vb3+TxePTiiy/qrrvu0gcffKCNGzdq9+7dGjNmjCTpySef1I9+9CM9+uijysrKOo/NAQDn4pwJYkmPXoNy4MABBQIB5efnh+alpaUpLy9Pfr9fkuT3+5Wenh4KJ5KUn5+vuLg47dy5s9v3bW5uVjAYDJsAIJZxOQqcrkcDSiAQkCR5PJ6w+R6PJ7QsEAgoMzMzbHlCQoIyMjJCY062aNEipaWlhabs7OyeLBsAABjGFnfxzJ49W/X19aHp4MGD0S4JAPocZ00QS3o0oHi9XklSbW1t2Pza2trQMq/Xq7q6urDlbW1tOnLkSGjMyZKTk+V2u8MmAADgXD0aUC699FJ5vV5t2bIlNC8YDGrnzp3y+XySJJ/Pp6NHj6qysjI0ZuvWrero6FBeXl5PlgMAAGwq4rt4jh07po8//jj0+sCBA9qzZ48yMjKUk5Oj+++/X7/73e90xRVX6NJLL9Vvf/tbZWVlafLkyZKk4cOH67bbbtPPfvYzPfXUU2ptbdWMGTN01113cQcPAJxB12ef8NA2OF3EAeWdd97RD37wg9DrsrIySVJxcbFWrVql3/zmN2psbNR9992no0eP6sYbb9TGjRuVkpISWufZZ5/VjBkzdOuttyouLk5FRUV64oknemBzAACAE0QcUG655ZYzJneXy6UFCxZowYIFpx2TkZGh1atXR/rRAAAgRtjiLh4AgMKe1EaDB05HQAEAAMYhoAAAAOMQUADAJrq2dbiJB05HQAEAAMYhoAAAAOMQUADAJqywu3jo8cDZCCgAAMA4BBQAAGAcAgoA2ET4d/FEsRCgDxBQAACAcQgoAADAOAQUALAJi+/iQQwhoAAAAOMQUADAJjhrglhCQAEAG+IuHjgdAQUAABiHgAIANmFx2gQxhIACALZEWIGzEVAAAIBxCCgAYBOcM0EsIaAAgA1xOQqcjoACAACMQ0ABALvgrAliCAEFAGyIFg+cjoACAACMQ0ABAJuwuvR4LPo9cDgCCgAAMA4BBQAAGIeAAgA20fXCWC6ShdMRUAAAgHEIKAAAwDgEFACwibAWT/TKAPoEAQUAABiHgAIAAIxDQAEAm+ja1uEuHjgdAQUAABiHgAIAAIxDQAEAm7AsvosHsYOAAgAAjENAAQAAxiGgAH3I4tYLnAfrtC8A5yGgAAAA4xBQAMAmOAGHWEJAAfoQf2DQUziU4HQEFAAAYBwCCgDYBudNEDsIKEAf4s8Legp3hMHpCCgAAMA4BBQAsAlOmiCWEFCAPnS8pS3sdVNre5QqgR39+3hr6OfjLRw7cDYCCtCHaoNNYa+/aGiOUiWwo7qGb46fk48lwGkIKEAfCtSHB5Kuf3CAb1Mb/Ob4CRBQ4HAEFKAPnfxHpS7IGRScvS+6BNq6hma1tndEsRqgd0U1oJSXl+uSSy5RSkqK8vLytGvXrmiWA/S69z+vD3v93ye9Bk7Hsiy9/3mwy2vpw0MNUawI6F1RCyjPPfecysrKNG/ePL377ru69tprVVBQoLq6umiVBPSqfze2aP1/10iSfjzyIknSS+99rqPHW6JZFmxi64d1CgSb1D8pXuOHZUqSVr59gOehwLFcVpSO7ry8PF133XX685//LEnq6OhQdna2Zs6cqYcffviM6waDQaWlpam+vl5ut7svygUi0tTaroamNh0+1qx/ftGovTX1ev6dz3T4WLMuvWCAXvxfN2ji49tVU9+krLQU/eS6bI3KTteQQf3lTUvRgKR4uVyuaG8GoqSptV31X7Xqi4ZmffLFMe34+Ev93/c+U2u7pf9xw6UquNqjO/+zQpI0eugg/WjERRp+UaouSuunC1OT1T8xXnFxHD8wTyR/vxP6qKYwLS0tqqys1OzZs0Pz4uLilJ+fL7/fH42SJJ24BXTWc3v02t7aqNUA5xsyqJ+Wbvl/Gjp4gGrqm1RT36Slmz+Kdlmwia9a27Vxb0ADkuLV2NKuyn/9W5X/+ne0y4LDXJ45UP+7ZKwuSusXtRqiElAOHz6s9vZ2eTyesPkej0cffvjhKeObm5vV3PzNxYTBYPCUMT3B/8mXhBP0uv/66LD+66PD0S4DNvV/dlVHuwTEgI/rjun53Z/pV/lXRK2GqASUSC1atEiPPPJIr3/ODZdfoP8YPURrKz/r9c/qKSd3AU4+qdu1TXDqspPXPfObRbp+1+Vnqqu75d/+2af/rJPHf9tnndpJCZ+RGO9SfJxLCXEuJcTHKSHu69ddf/76dWKcS6kpCXL3S9SA5ASdy1n24y3tamxuU2NLu443t6mxuV0t7R1q77DU1mGpvaPj638ttbVbofkdliXLsmTpxAWUnT/L0tfzuiyT9fW/ncu/ed11nF11/p+6Qq9dXX7uXBY+yNXNsjO9j7pZ1rnOyfMS4lxKjI9TwtfHUmLciZ87j5n4r5cnxrvk7peo9K+Pn0i7fJZ14gzLVy3tOt7SruMtJ46fE8fIiWOoNXTMfHNMtbV/ffyo8/+9++Oh6zHV+U8kx9Vp6z7D9iA6xgwdpJ/m5US1hqhcg9LS0qL+/fvrhRde0OTJk0Pzi4uLdfToUb300kth47s7g5Kdnc01KAAA2Egk16BE5S6epKQkjR49Wlu2bAnN6+jo0JYtW+Tz+U4Zn5ycLLfbHTYBAADnilqLp6ysTMXFxRozZozGjh2rpUuXqrGxUffee2+0SgIAAIaIWkC588479cUXX2ju3LkKBAIaNWqUNm7ceMqFswAAIPZE7Tko54PnoAAAYD/GX4MCAABwJgQUAABgHAIKAAAwDgEFAAAYh4ACAACMQ0ABAADGIaAAAADjEFAAAIBxCCgAAMA4UXvU/fnofPhtMBiMciUAAOBsdf7dPpuH2NsyoDQ0NEiSsrOzo1wJAACIVENDg9LS0s44xpbfxdPR0aGamhqlpqbK5XJFu5yoCwaDys7O1sGDB/luol7Efu4b7Oe+w77uG+znb1iWpYaGBmVlZSku7sxXmdjyDEpcXJyGDBkS7TKM43a7Y/7g7wvs577Bfu477Ou+wX4+4dvOnHTiIlkAAGAcAgoAADAOAcUBkpOTNW/ePCUnJ0e7FEdjP/cN9nPfYV/3DfbzubHlRbIAAMDZOIMCAACMQ0ABAADGIaAAAADjEFAAAIBxCCg2dOTIEU2dOlVut1vp6ekqKSnRsWPHzmpdy7I0ceJEuVwuvfjii71bqANEuq+PHDmimTNn6qqrrlK/fv2Uk5OjX/7yl6qvr+/Dqs1XXl6uSy65RCkpKcrLy9OuXbvOOH7t2rUaNmyYUlJSNGLECG3YsKGPKrW/SPb1008/rZtuukmDBg3SoEGDlJ+f/63/Nzgh0mO605o1a+RyuTR58uTeLdCGCCg2NHXqVO3du1ebNm3S+vXrtX37dt13331nte7SpUv5eoAIRLqva2pqVFNTo0cffVTvv/++Vq1apY0bN6qkpKQPqzbbc889p7KyMs2bN0/vvvuurr32WhUUFKiurq7b8Tt27NCUKVNUUlKi9957T5MnT9bkyZP1/vvv93Hl9hPpvn7zzTc1ZcoUvfHGG/L7/crOztaECRP0+eef93Hl9hLpfu706aef6oEHHtBNN93UR5XajAVb2bdvnyXJ2r17d2jeq6++arlcLuvzzz8/47rvvfeedfHFF1uHDh2yJFnr1q3r5Wrt7Xz2dVfPP/+8lZSUZLW2tvZGmbYzduxYq7S0NPS6vb3dysrKshYtWtTt+J/85CdWYWFh2Ly8vDzr5z//ea/W6QSR7uuTtbW1WampqdYzzzzTWyU6wrns57a2Nuv666+3/vrXv1rFxcXWpEmT+qBSe+EMis34/X6lp6drzJgxoXn5+fmKi4vTzp07T7ve8ePH9dOf/lTl5eXyer19Uartneu+Pll9fb3cbrcSEmz51Vc9qqWlRZWVlcrPzw/Ni4uLU35+vvx+f7fr+P3+sPGSVFBQcNrxOOFc9vXJjh8/rtbWVmVkZPRWmbZ3rvt5wYIFyszM5OzqGfAb02YCgYAyMzPD5iUkJCgjI0OBQOC0682aNUvXX3+9Jk2a1NslOsa57uuuDh8+rIULF551C87pDh8+rPb2dnk8nrD5Ho9HH374YbfrBAKBbsef7f9BrDqXfX2yhx56SFlZWacERHzjXPbzW2+9pRUrVmjPnj19UKF9cQbFEA8//LBcLtcZp7P9pXKyf/zjH9q6dauWLl3as0XbVG/u666CwaAKCwuVm5ur+fPnn3/hQB9avHix1qxZo3Xr1iklJSXa5ThGQ0ODpk2bpqeffloXXHBBtMsxGmdQDPHrX/9a99xzzxnHXHbZZfJ6vadceNXW1qYjR46ctnWzdetWffLJJ0pPTw+bX1RUpJtuuklvvvnmeVRuP725rzs1NDTotttuU2pqqtatW6fExMTzLdsRLrjgAsXHx6u2tjZsfm1t7Wn3qdfrjWg8TjiXfd3p0Ucf1eLFi7V582aNHDmyN8u0vUj38yeffKJPP/1Ut99+e2heR0eHpBNnaPfv36/vfOc7vVu0XUT7IhhEpvPCzXfeeSc077XXXjvjhZuHDh2yqqqqwiZJ1uOPP27985//7KvSbedc9rVlWVZ9fb01btw46+abb7YaGxv7olRbGTt2rDVjxozQ6/b2duviiy8+40WyP/7xj8Pm+Xw+LpI9C5Hua8uyrD/+8Y+W2+22/H5/X5ToCJHs56+++uqU38eTJk2yxo8fb1VVVVnNzc19WbrRCCg2dNttt1nf/e53rZ07d1pvvfWWdcUVV1hTpkwJLf/ss8+sq666ytq5c+dp30PcxXNWIt3X9fX1Vl5enjVixAjr448/tg4dOhSa2traorUZRlmzZo2VnJxsrVq1ytq3b5913333Wenp6VYgELAsy7KmTZtmPfzww6Hxb7/9tpWQkGA9+uij1gcffGDNmzfPSkxMtKqqqqK1CbYR6b5evHixlZSUZL3wwgthx25DQ0O0NsEWIt3PJ+Munu4RUGzoyy+/tKZMmWINHDjQcrvd1r333hv2C+TAgQOWJOuNN9447XsQUM5OpPv6jTfesCR1Ox04cCA6G2GgJ5980srJybGSkpKssWPHWhUVFaFlN998s1VcXBw2/vnnn7euvPJKKykpybr66qutV155pY8rtq9I9vXQoUO7PXbnzZvX94XbTKTHdFcElO65LMuy+rqtBAAAcCbcxQMAAIxDQAEAAMYhoAAAAOMQUAAAgHEIKAAAwDgEFAAAYBwCCgAAMA4BBQAAGIeAAgAAjENAAQAAxiGgAAAA4xBQAACAcf4/cxNPJN8xn1UAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "t = np.arange(1024)\n", + "sp = np.fft.fft(np.sin(t))\n", + "freq = np.fft.fftfreq(t.shape[-1])\n", + "plt.plot(freq, abs(sp))\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 122, + "id": "71804e1a-1895-4bbe-9b3a-c46c7a25948a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.000155473701438" + ] + }, + "execution_count": 122, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "omega = freq[abs(sp).argmax()]\n", + "omega * 2*np.pi" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e723f8f7-bb64-4cd1-9d83-38be08e5baeb", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/project/data-processing/main.cpp b/project/data-processing/main.cpp new file mode 100644 index 0000000..e69de29 diff --git a/project/data-processing/pocketfft-cpp/pocketfft_demo.cc b/project/data-processing/pocketfft-cpp/pocketfft_demo.cc new file mode 100644 index 0000000..aa0e787 --- /dev/null +++ b/project/data-processing/pocketfft-cpp/pocketfft_demo.cc @@ -0,0 +1,87 @@ +#include +#include +#include +#include +#include "pocketfft_hdronly.h" + +using namespace std; +using namespace pocketfft; + +// floating point RNG which is good enough for sinmple demos +// Do not use for anything important! +inline double simple_drand() + { + constexpr double norm = 1./RAND_MAX; + return rand()*norm; + } + +template void crand(vector> &v) + { + for (auto & i:v) + i = complex(simple_drand()-0.5, simple_drand()-0.5); + } + +template long double l2err + (const vector &v1, const vector &v2) + { + long double sum1=0, sum2=0; + for (size_t i=0; i), + tmpd=sizeof(complex), + tmpl=sizeof(complex); + for (int i=shape.size()-1; i>=0; --i) + { + stridef[i]=tmpf; + tmpf*=shape[i]; + strided[i]=tmpd; + tmpd*=shape[i]; + stridel[i]=tmpl; + tmpl*=shape[i]; + } + size_t ndata=1; + for (size_t i=0; i> dataf(ndata); + vector> datad(ndata); + vector> datal(ndata); + crand(dataf); + for (size_t i=0; i= 201103L || _MSVC_LANG+0L >= 201103L) +#error This file requires at least C++11 support. +#endif + +#ifndef POCKETFFT_CACHE_SIZE +#define POCKETFFT_CACHE_SIZE 0 +#endif + +#include +#include +#include +#include +#include +#include +#include +#if POCKETFFT_CACHE_SIZE!=0 +#include +#include +#endif + +#ifndef POCKETFFT_NO_MULTITHREADING +#include +#include +#include +#include +#include +#include +#include + +#ifdef POCKETFFT_PTHREADS +# include +#endif +#endif + +#if defined(__GNUC__) +#define POCKETFFT_NOINLINE __attribute__((noinline)) +#define POCKETFFT_RESTRICT __restrict__ +#elif defined(_MSC_VER) +#define POCKETFFT_NOINLINE __declspec(noinline) +#define POCKETFFT_RESTRICT __restrict +#else +#define POCKETFFT_NOINLINE +#define POCKETFFT_RESTRICT +#endif + +namespace pocketfft { + +namespace detail { +using std::size_t; +using std::ptrdiff_t; + +// Always use std:: for functions +template T cos(T) = delete; +template T sin(T) = delete; +template T sqrt(T) = delete; + +using shape_t = std::vector; +using stride_t = std::vector; + +constexpr bool FORWARD = true, + BACKWARD = false; + +// only enable vector support for gcc>=5.0 and clang>=5.0 +#ifndef POCKETFFT_NO_VECTORS +#define POCKETFFT_NO_VECTORS +#if defined(__INTEL_COMPILER) +// do nothing. This is necessary because this compiler also sets __GNUC__. +#elif defined(__clang__) +// AppleClang has their own version numbering +#ifdef __apple_build_version__ +# if (__clang_major__ > 9) || (__clang_major__ == 9 && __clang_minor__ >= 1) +# undef POCKETFFT_NO_VECTORS +# endif +#elif __clang_major__ >= 5 +# undef POCKETFFT_NO_VECTORS +#endif +#elif defined(__GNUC__) +#if __GNUC__>=5 +#undef POCKETFFT_NO_VECTORS +#endif +#endif +#endif + +template struct VLEN { static constexpr size_t val=1; }; + +#ifndef POCKETFFT_NO_VECTORS +#if (defined(__AVX512F__)) +template<> struct VLEN { static constexpr size_t val=16; }; +template<> struct VLEN { static constexpr size_t val=8; }; +#elif (defined(__AVX__)) +template<> struct VLEN { static constexpr size_t val=8; }; +template<> struct VLEN { static constexpr size_t val=4; }; +#elif (defined(__SSE2__)) +template<> struct VLEN { static constexpr size_t val=4; }; +template<> struct VLEN { static constexpr size_t val=2; }; +#elif (defined(__VSX__)) +template<> struct VLEN { static constexpr size_t val=4; }; +template<> struct VLEN { static constexpr size_t val=2; }; +#elif (defined(__ARM_NEON__) || defined(__ARM_NEON)) +template<> struct VLEN { static constexpr size_t val=4; }; +template<> struct VLEN { static constexpr size_t val=2; }; +#else +#define POCKETFFT_NO_VECTORS +#endif +#endif + +// the __MINGW32__ part in the conditional below works around the problem that +// the standard C++ library on Windows does not provide aligned_alloc() even +// though the MinGW compiler advertises C++17 compliance. +// MSVC does not trigger this problem, since it apparently always sets +// __cplusplus to 199711L ... +#if (__cplusplus >= 201703L) && (!defined(__MINGW32__)) +inline void *aligned_alloc(size_t align, size_t size) + { + // aligned_alloc() requires that the requested size is a multiple of "align" + void *ptr = ::aligned_alloc(align,(size+align-1)&(~(align-1))); + if (!ptr) throw std::bad_alloc(); + return ptr; + } +inline void aligned_dealloc(void *ptr) + { free(ptr); } +#else // portable emulation +inline void *aligned_alloc(size_t align, size_t size) + { + align = std::max(align, alignof(max_align_t)); + void *ptr = malloc(size+align); + if (!ptr) throw std::bad_alloc(); + void *res = reinterpret_cast + ((reinterpret_cast(ptr) & ~(uintptr_t(align-1))) + uintptr_t(align)); + (reinterpret_cast(res))[-1] = ptr; + return res; + } +inline void aligned_dealloc(void *ptr) + { if (ptr) free((reinterpret_cast(ptr))[-1]); } +#endif + +template class arr + { + private: + T *p; + size_t sz; + +#if defined(POCKETFFT_NO_VECTORS) + static T *ralloc(size_t num) + { + if (num==0) return nullptr; + void *res = malloc(num*sizeof(T)); + if (!res) throw std::bad_alloc(); + return reinterpret_cast(res); + } + static void dealloc(T *ptr) + { free(ptr); } +#else + static T *ralloc(size_t num) + { + if (num==0) return nullptr; + void *ptr = aligned_alloc(64, num*sizeof(T)); + return static_cast(ptr); + } + static void dealloc(T *ptr) + { aligned_dealloc(ptr); } +#endif + + public: + arr() : p(0), sz(0) {} + arr(size_t n) : p(ralloc(n)), sz(n) {} + arr(arr &&other) + : p(other.p), sz(other.sz) + { other.p=nullptr; other.sz=0; } + ~arr() { dealloc(p); } + + void resize(size_t n) + { + if (n==sz) return; + dealloc(p); + p = ralloc(n); + sz = n; + } + + T &operator[](size_t idx) { return p[idx]; } + const T &operator[](size_t idx) const { return p[idx]; } + + T *data() { return p; } + const T *data() const { return p; } + + size_t size() const { return sz; } + }; + +template struct cmplx { + T r, i; + cmplx() {} + cmplx(T r_, T i_) : r(r_), i(i_) {} + void Set(T r_, T i_) { r=r_; i=i_; } + void Set(T r_) { r=r_; i=T(0); } + cmplx &operator+= (const cmplx &other) + { r+=other.r; i+=other.i; return *this; } + templatecmplx &operator*= (T2 other) + { r*=other; i*=other; return *this; } + templatecmplx &operator*= (const cmplx &other) + { + T tmp = r*other.r - i*other.i; + i = r*other.i + i*other.r; + r = tmp; + return *this; + } + templatecmplx &operator+= (const cmplx &other) + { r+=other.r; i+=other.i; return *this; } + templatecmplx &operator-= (const cmplx &other) + { r-=other.r; i-=other.i; return *this; } + template auto operator* (const T2 &other) const + -> cmplx + { return {r*other, i*other}; } + template auto operator+ (const cmplx &other) const + -> cmplx + { return {r+other.r, i+other.i}; } + template auto operator- (const cmplx &other) const + -> cmplx + { return {r-other.r, i-other.i}; } + template auto operator* (const cmplx &other) const + -> cmplx + { return {r*other.r-i*other.i, r*other.i + i*other.r}; } + template auto special_mul (const cmplx &other) const + -> cmplx + { + using Tres = cmplx; + return fwd ? Tres(r*other.r+i*other.i, i*other.r-r*other.i) + : Tres(r*other.r-i*other.i, r*other.i+i*other.r); + } +}; +template inline void PM(T &a, T &b, T c, T d) + { a=c+d; b=c-d; } +template inline void PMINPLACE(T &a, T &b) + { T t = a; a+=b; b=t-b; } +template inline void MPINPLACE(T &a, T &b) + { T t = a; a-=b; b=t+b; } +template cmplx conj(const cmplx &a) + { return {a.r, -a.i}; } +template void special_mul (const cmplx &v1, const cmplx &v2, cmplx &res) + { + res = fwd ? cmplx(v1.r*v2.r+v1.i*v2.i, v1.i*v2.r-v1.r*v2.i) + : cmplx(v1.r*v2.r-v1.i*v2.i, v1.r*v2.i+v1.i*v2.r); + } + +template void ROT90(cmplx &a) + { auto tmp_=a.r; a.r=-a.i; a.i=tmp_; } +template void ROTX90(cmplx &a) + { auto tmp_= fwd ? -a.r : a.r; a.r = fwd ? a.i : -a.i; a.i=tmp_; } + +// +// twiddle factor section +// +template class sincos_2pibyn + { + private: + using Thigh = typename std::conditional<(sizeof(T)>sizeof(double)), T, double>::type; + size_t N, mask, shift; + arr> v1, v2; + + static cmplx calc(size_t x, size_t n, Thigh ang) + { + x<<=3; + if (x<4*n) // first half + { + if (x<2*n) // first quadrant + { + if (x(std::cos(Thigh(x)*ang), std::sin(Thigh(x)*ang)); + return cmplx(std::sin(Thigh(2*n-x)*ang), std::cos(Thigh(2*n-x)*ang)); + } + else // second quadrant + { + x-=2*n; + if (x(-std::sin(Thigh(x)*ang), std::cos(Thigh(x)*ang)); + return cmplx(-std::cos(Thigh(2*n-x)*ang), std::sin(Thigh(2*n-x)*ang)); + } + } + else + { + x=8*n-x; + if (x<2*n) // third quadrant + { + if (x(std::cos(Thigh(x)*ang), -std::sin(Thigh(x)*ang)); + return cmplx(std::sin(Thigh(2*n-x)*ang), -std::cos(Thigh(2*n-x)*ang)); + } + else // fourth quadrant + { + x-=2*n; + if (x(-std::sin(Thigh(x)*ang), -std::cos(Thigh(x)*ang)); + return cmplx(-std::cos(Thigh(2*n-x)*ang), -std::sin(Thigh(2*n-x)*ang)); + } + } + } + + public: + POCKETFFT_NOINLINE sincos_2pibyn(size_t n) + : N(n) + { + constexpr auto pi = 3.141592653589793238462643383279502884197L; + Thigh ang = Thigh(0.25L*pi/n); + size_t nval = (n+2)/2; + shift = 1; + while((size_t(1)< operator[](size_t idx) const + { + if (2*idx<=N) + { + auto x1=v1[idx&mask], x2=v2[idx>>shift]; + return cmplx(T(x1.r*x2.r-x1.i*x2.i), T(x1.r*x2.i+x1.i*x2.r)); + } + idx = N-idx; + auto x1=v1[idx&mask], x2=v2[idx>>shift]; + return cmplx(T(x1.r*x2.r-x1.i*x2.i), -T(x1.r*x2.i+x1.i*x2.r)); + } + }; + +struct util // hack to avoid duplicate symbols + { + static POCKETFFT_NOINLINE size_t largest_prime_factor (size_t n) + { + size_t res=1; + while ((n&1)==0) + { res=2; n>>=1; } + for (size_t x=3; x*x<=n; x+=2) + while ((n%x)==0) + { res=x; n/=x; } + if (n>1) res=n; + return res; + } + + static POCKETFFT_NOINLINE double cost_guess (size_t n) + { + constexpr double lfp=1.1; // penalty for non-hardcoded larger factors + size_t ni=n; + double result=0.; + while ((n&1)==0) + { result+=2; n>>=1; } + for (size_t x=3; x*x<=n; x+=2) + while ((n%x)==0) + { + result+= (x<=5) ? double(x) : lfp*double(x); // penalize larger prime factors + n/=x; + } + if (n>1) result+=(n<=5) ? double(n) : lfp*double(n); + return result*double(ni); + } + + /* returns the smallest composite of 2, 3, 5, 7 and 11 which is >= n */ + static POCKETFFT_NOINLINE size_t good_size_cmplx(size_t n) + { + if (n<=12) return n; + + size_t bestfac=2*n; + for (size_t f11=1; f11n) + { + if (x>=1; + } + else + return n; + } + } + return bestfac; + } + + /* returns the smallest composite of 2, 3, 5 which is >= n */ + static POCKETFFT_NOINLINE size_t good_size_real(size_t n) + { + if (n<=6) return n; + + size_t bestfac=2*n; + for (size_t f5=1; f5n) + { + if (x>=1; + } + else + return n; + } + } + return bestfac; + } + + static size_t prod(const shape_t &shape) + { + size_t res=1; + for (auto sz: shape) + res*=sz; + return res; + } + + static POCKETFFT_NOINLINE void sanity_check(const shape_t &shape, + const stride_t &stride_in, const stride_t &stride_out, bool inplace) + { + auto ndim = shape.size(); + if (ndim<1) throw std::runtime_error("ndim must be >= 1"); + if ((stride_in.size()!=ndim) || (stride_out.size()!=ndim)) + throw std::runtime_error("stride dimension mismatch"); + if (inplace && (stride_in!=stride_out)) + throw std::runtime_error("stride mismatch"); + } + + static POCKETFFT_NOINLINE void sanity_check(const shape_t &shape, + const stride_t &stride_in, const stride_t &stride_out, bool inplace, + const shape_t &axes) + { + sanity_check(shape, stride_in, stride_out, inplace); + auto ndim = shape.size(); + shape_t tmp(ndim,0); + for (auto ax : axes) + { + if (ax>=ndim) throw std::invalid_argument("bad axis number"); + if (++tmp[ax]>1) throw std::invalid_argument("axis specified repeatedly"); + } + } + + static POCKETFFT_NOINLINE void sanity_check(const shape_t &shape, + const stride_t &stride_in, const stride_t &stride_out, bool inplace, + size_t axis) + { + sanity_check(shape, stride_in, stride_out, inplace); + if (axis>=shape.size()) throw std::invalid_argument("bad axis number"); + } + +#ifdef POCKETFFT_NO_MULTITHREADING + static size_t thread_count (size_t /*nthreads*/, const shape_t &/*shape*/, + size_t /*axis*/, size_t /*vlen*/) + { return 1; } +#else + static size_t thread_count (size_t nthreads, const shape_t &shape, + size_t axis, size_t vlen) + { + if (nthreads==1) return 1; + size_t size = prod(shape); + size_t parallel = size / (shape[axis] * vlen); + if (shape[axis] < 1000) + parallel /= 4; + size_t max_threads = nthreads == 0 ? + std::thread::hardware_concurrency() : nthreads; + return std::max(size_t(1), std::min(parallel, max_threads)); + } +#endif + }; + +namespace threading { + +#ifdef POCKETFFT_NO_MULTITHREADING + +constexpr inline size_t thread_id() { return 0; } +constexpr inline size_t num_threads() { return 1; } + +template +void thread_map(size_t /* nthreads */, Func f) + { f(); } + +#else + +inline size_t &thread_id() + { + static thread_local size_t thread_id_=0; + return thread_id_; + } +inline size_t &num_threads() + { + static thread_local size_t num_threads_=1; + return num_threads_; + } +static const size_t max_threads = std::max(1u, std::thread::hardware_concurrency()); + +class latch + { + std::atomic num_left_; + std::mutex mut_; + std::condition_variable completed_; + using lock_t = std::unique_lock; + + public: + latch(size_t n): num_left_(n) {} + + void count_down() + { + lock_t lock(mut_); + if (--num_left_) + return; + completed_.notify_all(); + } + + void wait() + { + lock_t lock(mut_); + completed_.wait(lock, [this]{ return is_ready(); }); + } + bool is_ready() { return num_left_ == 0; } + }; + +template class concurrent_queue + { + std::queue q_; + std::mutex mut_; + std::atomic size_; + using lock_t = std::lock_guard; + + public: + + void push(T val) + { + lock_t lock(mut_); + ++size_; + q_.push(std::move(val)); + } + + bool try_pop(T &val) + { + if (size_ == 0) return false; + lock_t lock(mut_); + // Queue might have been emptied while we acquired the lock + if (q_.empty()) return false; + + val = std::move(q_.front()); + --size_; + q_.pop(); + return true; + } + + bool empty() const { return size_==0; } + }; + +// C++ allocator with support for over-aligned types +template struct aligned_allocator + { + using value_type = T; + template + aligned_allocator(const aligned_allocator&) {} + aligned_allocator() = default; + + T *allocate(size_t n) + { + void* mem = aligned_alloc(alignof(T), n*sizeof(T)); + return static_cast(mem); + } + + void deallocate(T *p, size_t /*n*/) + { aligned_dealloc(p); } + }; + +class thread_pool + { + // A reasonable guess, probably close enough for most hardware + static constexpr size_t cache_line_size = 64; + struct alignas(cache_line_size) worker + { + std::thread thread; + std::condition_variable work_ready; + std::mutex mut; + std::atomic_flag busy_flag = ATOMIC_FLAG_INIT; + std::function work; + + void worker_main( + std::atomic &shutdown_flag, + std::atomic &unscheduled_tasks, + concurrent_queue> &overflow_work) + { + using lock_t = std::unique_lock; + bool expect_work = true; + while (!shutdown_flag || expect_work) + { + std::function local_work; + if (expect_work || unscheduled_tasks == 0) + { + lock_t lock(mut); + // Wait until there is work to be executed + work_ready.wait(lock, [&]{ return (work || shutdown_flag); }); + local_work.swap(work); + expect_work = false; + } + + bool marked_busy = false; + if (local_work) + { + marked_busy = true; + local_work(); + } + + if (!overflow_work.empty()) + { + if (!marked_busy && busy_flag.test_and_set()) + { + expect_work = true; + continue; + } + marked_busy = true; + + while (overflow_work.try_pop(local_work)) + { + --unscheduled_tasks; + local_work(); + } + } + + if (marked_busy) busy_flag.clear(); + } + } + }; + + concurrent_queue> overflow_work_; + std::mutex mut_; + std::vector> workers_; + std::atomic shutdown_; + std::atomic unscheduled_tasks_; + using lock_t = std::lock_guard; + + void create_threads() + { + lock_t lock(mut_); + size_t nthreads=workers_.size(); + for (size_t i=0; ibusy_flag.clear(); + worker->work = nullptr; + worker->thread = std::thread([worker, this] + { + worker->worker_main(shutdown_, unscheduled_tasks_, overflow_work_); + }); + } + catch (...) + { + shutdown_locked(); + throw; + } + } + } + + void shutdown_locked() + { + shutdown_ = true; + for (auto &worker : workers_) + worker.work_ready.notify_all(); + + for (auto &worker : workers_) + if (worker.thread.joinable()) + worker.thread.join(); + } + + public: + explicit thread_pool(size_t nthreads): + workers_(nthreads) + { create_threads(); } + + thread_pool(): thread_pool(max_threads) {} + + ~thread_pool() { shutdown(); } + + void submit(std::function work) + { + lock_t lock(mut_); + if (shutdown_) + throw std::runtime_error("Work item submitted after shutdown"); + + ++unscheduled_tasks_; + + // First check for any idle workers and wake those + for (auto &worker : workers_) + if (!worker.busy_flag.test_and_set()) + { + --unscheduled_tasks_; + { + lock_t lock(worker.mut); + worker.work = std::move(work); + } + worker.work_ready.notify_one(); + return; + } + + // If no workers were idle, push onto the overflow queue for later + overflow_work_.push(std::move(work)); + } + + void shutdown() + { + lock_t lock(mut_); + shutdown_locked(); + } + + void restart() + { + shutdown_ = false; + create_threads(); + } + }; + +inline thread_pool & get_pool() + { + static thread_pool pool; +#ifdef POCKETFFT_PTHREADS + static std::once_flag f; + std::call_once(f, + []{ + pthread_atfork( + +[]{ get_pool().shutdown(); }, // prepare + +[]{ get_pool().restart(); }, // parent + +[]{ get_pool().restart(); } // child + ); + }); +#endif + + return pool; + } + +/** Map a function f over nthreads */ +template +void thread_map(size_t nthreads, Func f) + { + if (nthreads == 0) + nthreads = max_threads; + + if (nthreads == 1) + { f(); return; } + + auto & pool = get_pool(); + latch counter(nthreads); + std::exception_ptr ex; + std::mutex ex_mut; + for (size_t i=0; i lock(ex_mut); + ex = std::current_exception(); + } + counter.count_down(); + }); + } + counter.wait(); + if (ex) + std::rethrow_exception(ex); + } + +#endif + +} + +// +// complex FFTPACK transforms +// + +template class cfftp + { + private: + struct fctdata + { + size_t fct; + cmplx *tw, *tws; + }; + + size_t length; + arr> mem; + std::vector fact; + + void add_factor(size_t factor) + { fact.push_back({factor, nullptr, nullptr}); } + +template void pass2 (size_t ido, size_t l1, + const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const cmplx * POCKETFFT_RESTRICT wa) const + { + auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+l1*c)]; }; + auto CC = [cc,ido](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+2*c)]; }; + auto WA = [wa, ido](size_t x, size_t i) + { return wa[i-1+x*(ido-1)]; }; + + if (ido==1) + for (size_t k=0; k(CC(i,0,k)-CC(i,1,k),WA(0,i),CH(i,k,1)); + } + } + } + +#define POCKETFFT_PREP3(idx) \ + T t0 = CC(idx,0,k), t1, t2; \ + PM (t1,t2,CC(idx,1,k),CC(idx,2,k)); \ + CH(idx,k,0)=t0+t1; +#define POCKETFFT_PARTSTEP3a(u1,u2,twr,twi) \ + { \ + T ca=t0+t1*twr; \ + T cb{-t2.i*twi, t2.r*twi}; \ + PM(CH(0,k,u1),CH(0,k,u2),ca,cb) ;\ + } +#define POCKETFFT_PARTSTEP3b(u1,u2,twr,twi) \ + { \ + T ca=t0+t1*twr; \ + T cb{-t2.i*twi, t2.r*twi}; \ + special_mul(ca+cb,WA(u1-1,i),CH(i,k,u1)); \ + special_mul(ca-cb,WA(u2-1,i),CH(i,k,u2)); \ + } +template void pass3 (size_t ido, size_t l1, + const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const cmplx * POCKETFFT_RESTRICT wa) const + { + constexpr T0 tw1r=-0.5, + tw1i= (fwd ? -1: 1) * T0(0.8660254037844386467637231707529362L); + + auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+l1*c)]; }; + auto CC = [cc,ido](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+3*c)]; }; + auto WA = [wa, ido](size_t x, size_t i) + { return wa[i-1+x*(ido-1)]; }; + + if (ido==1) + for (size_t k=0; k void pass4 (size_t ido, size_t l1, + const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const cmplx * POCKETFFT_RESTRICT wa) const + { + auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+l1*c)]; }; + auto CC = [cc,ido](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+4*c)]; }; + auto WA = [wa, ido](size_t x, size_t i) + { return wa[i-1+x*(ido-1)]; }; + + if (ido==1) + for (size_t k=0; k(t4); + PM(CH(0,k,0),CH(0,k,2),t2,t3); + PM(CH(0,k,1),CH(0,k,3),t1,t4); + } + else + for (size_t k=0; k(t4); + PM(CH(0,k,0),CH(0,k,2),t2,t3); + PM(CH(0,k,1),CH(0,k,3),t1,t4); + } + for (size_t i=1; i(t4); + CH(i,k,0) = t2+t3; + special_mul(t1+t4,WA(0,i),CH(i,k,1)); + special_mul(t2-t3,WA(1,i),CH(i,k,2)); + special_mul(t1-t4,WA(2,i),CH(i,k,3)); + } + } + } + +#define POCKETFFT_PREP5(idx) \ + T t0 = CC(idx,0,k), t1, t2, t3, t4; \ + PM (t1,t4,CC(idx,1,k),CC(idx,4,k)); \ + PM (t2,t3,CC(idx,2,k),CC(idx,3,k)); \ + CH(idx,k,0).r=t0.r+t1.r+t2.r; \ + CH(idx,k,0).i=t0.i+t1.i+t2.i; + +#define POCKETFFT_PARTSTEP5a(u1,u2,twar,twbr,twai,twbi) \ + { \ + T ca,cb; \ + ca.r=t0.r+twar*t1.r+twbr*t2.r; \ + ca.i=t0.i+twar*t1.i+twbr*t2.i; \ + cb.i=twai*t4.r twbi*t3.r; \ + cb.r=-(twai*t4.i twbi*t3.i); \ + PM(CH(0,k,u1),CH(0,k,u2),ca,cb); \ + } + +#define POCKETFFT_PARTSTEP5b(u1,u2,twar,twbr,twai,twbi) \ + { \ + T ca,cb,da,db; \ + ca.r=t0.r+twar*t1.r+twbr*t2.r; \ + ca.i=t0.i+twar*t1.i+twbr*t2.i; \ + cb.i=twai*t4.r twbi*t3.r; \ + cb.r=-(twai*t4.i twbi*t3.i); \ + special_mul(ca+cb,WA(u1-1,i),CH(i,k,u1)); \ + special_mul(ca-cb,WA(u2-1,i),CH(i,k,u2)); \ + } +template void pass5 (size_t ido, size_t l1, + const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const cmplx * POCKETFFT_RESTRICT wa) const + { + constexpr T0 tw1r= T0(0.3090169943749474241022934171828191L), + tw1i= (fwd ? -1: 1) * T0(0.9510565162951535721164393333793821L), + tw2r= T0(-0.8090169943749474241022934171828191L), + tw2i= (fwd ? -1: 1) * T0(0.5877852522924731291687059546390728L); + + auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+l1*c)]; }; + auto CC = [cc,ido](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+5*c)]; }; + auto WA = [wa, ido](size_t x, size_t i) + { return wa[i-1+x*(ido-1)]; }; + + if (ido==1) + for (size_t k=0; k(da,WA(u1-1,i),CH(i,k,u1)); \ + special_mul(db,WA(u2-1,i),CH(i,k,u2)); \ + } + +template void pass7(size_t ido, size_t l1, + const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const cmplx * POCKETFFT_RESTRICT wa) const + { + constexpr T0 tw1r= T0(0.6234898018587335305250048840042398L), + tw1i= (fwd ? -1 : 1) * T0(0.7818314824680298087084445266740578L), + tw2r= T0(-0.2225209339563144042889025644967948L), + tw2i= (fwd ? -1 : 1) * T0(0.9749279121818236070181316829939312L), + tw3r= T0(-0.9009688679024191262361023195074451L), + tw3i= (fwd ? -1 : 1) * T0(0.433883739117558120475768332848359L); + + auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+l1*c)]; }; + auto CC = [cc,ido](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+7*c)]; }; + auto WA = [wa, ido](size_t x, size_t i) + { return wa[i-1+x*(ido-1)]; }; + + if (ido==1) + for (size_t k=0; k void ROTX45(T &a) const + { + constexpr T0 hsqt2=T0(0.707106781186547524400844362104849L); + if (fwd) + { auto tmp_=a.r; a.r=hsqt2*(a.r+a.i); a.i=hsqt2*(a.i-tmp_); } + else + { auto tmp_=a.r; a.r=hsqt2*(a.r-a.i); a.i=hsqt2*(a.i+tmp_); } + } +template void ROTX135(T &a) const + { + constexpr T0 hsqt2=T0(0.707106781186547524400844362104849L); + if (fwd) + { auto tmp_=a.r; a.r=hsqt2*(a.i-a.r); a.i=hsqt2*(-tmp_-a.i); } + else + { auto tmp_=a.r; a.r=hsqt2*(-a.r-a.i); a.i=hsqt2*(tmp_-a.i); } + } + +template void pass8 (size_t ido, size_t l1, + const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const cmplx * POCKETFFT_RESTRICT wa) const + { + auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+l1*c)]; }; + auto CC = [cc,ido](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+8*c)]; }; + auto WA = [wa, ido](size_t x, size_t i) + { return wa[i-1+x*(ido-1)]; }; + + if (ido==1) + for (size_t k=0; k(a3); + + ROTX90(a7); + PMINPLACE(a5,a7); + ROTX45(a5); + ROTX135(a7); + + PM(a0,a4,CC(0,0,k),CC(0,4,k)); + PM(a2,a6,CC(0,2,k),CC(0,6,k)); + PM(CH(0,k,0),CH(0,k,4),a0+a2,a1); + PM(CH(0,k,2),CH(0,k,6),a0-a2,a3); + ROTX90(a6); + PM(CH(0,k,1),CH(0,k,5),a4+a6,a5); + PM(CH(0,k,3),CH(0,k,7),a4-a6,a7); + } + else + for (size_t k=0; k(a3); + + ROTX90(a7); + PMINPLACE(a5,a7); + ROTX45(a5); + ROTX135(a7); + + PM(a0,a4,CC(0,0,k),CC(0,4,k)); + PM(a2,a6,CC(0,2,k),CC(0,6,k)); + PM(CH(0,k,0),CH(0,k,4),a0+a2,a1); + PM(CH(0,k,2),CH(0,k,6),a0-a2,a3); + ROTX90(a6); + PM(CH(0,k,1),CH(0,k,5),a4+a6,a5); + PM(CH(0,k,3),CH(0,k,7),a4-a6,a7); + } + for (size_t i=1; i(a7); + PMINPLACE(a1,a3); + ROTX90(a3); + PMINPLACE(a5,a7); + ROTX45(a5); + ROTX135(a7); + PM(a0,a4,CC(i,0,k),CC(i,4,k)); + PM(a2,a6,CC(i,2,k),CC(i,6,k)); + PMINPLACE(a0,a2); + CH(i,k,0) = a0+a1; + special_mul(a0-a1,WA(3,i),CH(i,k,4)); + special_mul(a2+a3,WA(1,i),CH(i,k,2)); + special_mul(a2-a3,WA(5,i),CH(i,k,6)); + ROTX90(a6); + PMINPLACE(a4,a6); + special_mul(a4+a5,WA(0,i),CH(i,k,1)); + special_mul(a4-a5,WA(4,i),CH(i,k,5)); + special_mul(a6+a7,WA(2,i),CH(i,k,3)); + special_mul(a6-a7,WA(6,i),CH(i,k,7)); + } + } + } + + +#define POCKETFFT_PREP11(idx) \ + T t1 = CC(idx,0,k), t2, t3, t4, t5, t6, t7, t8, t9, t10, t11; \ + PM (t2,t11,CC(idx,1,k),CC(idx,10,k)); \ + PM (t3,t10,CC(idx,2,k),CC(idx, 9,k)); \ + PM (t4,t9 ,CC(idx,3,k),CC(idx, 8,k)); \ + PM (t5,t8 ,CC(idx,4,k),CC(idx, 7,k)); \ + PM (t6,t7 ,CC(idx,5,k),CC(idx, 6,k)); \ + CH(idx,k,0).r=t1.r+t2.r+t3.r+t4.r+t5.r+t6.r; \ + CH(idx,k,0).i=t1.i+t2.i+t3.i+t4.i+t5.i+t6.i; + +#define POCKETFFT_PARTSTEP11a0(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5,out1,out2) \ + { \ + T ca = t1 + t2*x1 + t3*x2 + t4*x3 + t5*x4 +t6*x5, \ + cb; \ + cb.i=y1*t11.r y2*t10.r y3*t9.r y4*t8.r y5*t7.r; \ + cb.r=-(y1*t11.i y2*t10.i y3*t9.i y4*t8.i y5*t7.i ); \ + PM(out1,out2,ca,cb); \ + } +#define POCKETFFT_PARTSTEP11a(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5) \ + POCKETFFT_PARTSTEP11a0(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5,CH(0,k,u1),CH(0,k,u2)) +#define POCKETFFT_PARTSTEP11(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5) \ + { \ + T da,db; \ + POCKETFFT_PARTSTEP11a0(u1,u2,x1,x2,x3,x4,x5,y1,y2,y3,y4,y5,da,db) \ + special_mul(da,WA(u1-1,i),CH(i,k,u1)); \ + special_mul(db,WA(u2-1,i),CH(i,k,u2)); \ + } + +template void pass11 (size_t ido, size_t l1, + const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const cmplx * POCKETFFT_RESTRICT wa) const + { + constexpr T0 tw1r= T0(0.8412535328311811688618116489193677L), + tw1i= (fwd ? -1 : 1) * T0(0.5406408174555975821076359543186917L), + tw2r= T0(0.4154150130018864255292741492296232L), + tw2i= (fwd ? -1 : 1) * T0(0.9096319953545183714117153830790285L), + tw3r= T0(-0.1423148382732851404437926686163697L), + tw3i= (fwd ? -1 : 1) * T0(0.9898214418809327323760920377767188L), + tw4r= T0(-0.6548607339452850640569250724662936L), + tw4i= (fwd ? -1 : 1) * T0(0.7557495743542582837740358439723444L), + tw5r= T0(-0.9594929736144973898903680570663277L), + tw5i= (fwd ? -1 : 1) * T0(0.2817325568414296977114179153466169L); + + auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+l1*c)]; }; + auto CC = [cc,ido](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+11*c)]; }; + auto WA = [wa, ido](size_t x, size_t i) + { return wa[i-1+x*(ido-1)]; }; + + if (ido==1) + for (size_t k=0; k void passg (size_t ido, size_t ip, + size_t l1, T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const cmplx * POCKETFFT_RESTRICT wa, + const cmplx * POCKETFFT_RESTRICT csarr) const + { + const size_t cdim=ip; + size_t ipph = (ip+1)/2; + size_t idl1 = ido*l1; + + auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+l1*c)]; }; + auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+cdim*c)]; }; + auto CX = [cc, ido, l1](size_t a, size_t b, size_t c) -> T& + { return cc[a+ido*(b+l1*c)]; }; + auto CX2 = [cc, idl1](size_t a, size_t b) -> T& + { return cc[a+idl1*b]; }; + auto CH2 = [ch, idl1](size_t a, size_t b) -> const T& + { return ch[a+idl1*b]; }; + + arr> wal(ip); + wal[0] = cmplx(1., 0.); + for (size_t i=1; i(csarr[i].r,fwd ? -csarr[i].i : csarr[i].i); + + for (size_t k=0; kip) iwal-=ip; + cmplx xwal=wal[iwal]; + iwal+=l; if (iwal>ip) iwal-=ip; + cmplx xwal2=wal[iwal]; + for (size_t ik=0; ikip) iwal-=ip; + cmplx xwal=wal[iwal]; + for (size_t ik=0; ik(x1,wa[idij],CX(i,k,j)); + idij=(jc-1)*(ido-1)+i-1; + special_mul(x2,wa[idij],CX(i,k,jc)); + } + } + } + } + +template void pass_all(T c[], T0 fct) const + { + if (length==1) { c[0]*=fct; return; } + size_t l1=1; + arr ch(length); + T *p1=c, *p2=ch.data(); + + for(size_t k1=0; k1 (ido, l1, p1, p2, fact[k1].tw); + else if(ip==8) + pass8(ido, l1, p1, p2, fact[k1].tw); + else if(ip==2) + pass2(ido, l1, p1, p2, fact[k1].tw); + else if(ip==3) + pass3 (ido, l1, p1, p2, fact[k1].tw); + else if(ip==5) + pass5 (ido, l1, p1, p2, fact[k1].tw); + else if(ip==7) + pass7 (ido, l1, p1, p2, fact[k1].tw); + else if(ip==11) + pass11 (ido, l1, p1, p2, fact[k1].tw); + else + { + passg(ido, ip, l1, p1, p2, fact[k1].tw, fact[k1].tws); + std::swap(p1,p2); + } + std::swap(p1,p2); + l1=l2; + } + if (p1!=c) + { + if (fct!=1.) + for (size_t i=0; i void exec(T c[], T0 fct, bool fwd) const + { fwd ? pass_all(c, fct) : pass_all(c, fct); } + + private: + POCKETFFT_NOINLINE void factorize() + { + size_t len=length; + while ((len&7)==0) + { add_factor(8); len>>=3; } + while ((len&3)==0) + { add_factor(4); len>>=2; } + if ((len&1)==0) + { + len>>=1; + // factor 2 should be at the front of the factor list + add_factor(2); + std::swap(fact[0].fct, fact.back().fct); + } + for (size_t divisor=3; divisor*divisor<=len; divisor+=2) + while ((len%divisor)==0) + { + add_factor(divisor); + len/=divisor; + } + if (len>1) add_factor(len); + } + + size_t twsize() const + { + size_t twsize=0, l1=1; + for (size_t k=0; k11) + twsize+=ip; + l1*=ip; + } + return twsize; + } + + void comp_twiddle() + { + sincos_2pibyn twiddle(length); + size_t l1=1; + size_t memofs=0; + for (size_t k=0; k11) + { + fact[k].tws=mem.data()+memofs; + memofs+=ip; + for (size_t j=0; j class rfftp + { + private: + struct fctdata + { + size_t fct; + T0 *tw, *tws; + }; + + size_t length; + arr mem; + std::vector fact; + + void add_factor(size_t factor) + { fact.push_back({factor, nullptr, nullptr}); } + +/* (a+ib) = conj(c+id) * (e+if) */ +template inline void MULPM + (T1 &a, T1 &b, T2 c, T2 d, T3 e, T3 f) const + { a=c*e+d*f; b=c*f-d*e; } + +template void radf2 (size_t ido, size_t l1, + const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const T0 * POCKETFFT_RESTRICT wa) const + { + auto WA = [wa,ido](size_t x, size_t i) { return wa[i+x*(ido-1)]; }; + auto CC = [cc,ido,l1](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+l1*c)]; }; + auto CH = [ch,ido](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+2*c)]; }; + + for (size_t k=0; k void radf3(size_t ido, size_t l1, + const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const T0 * POCKETFFT_RESTRICT wa) const + { + constexpr T0 taur=-0.5, taui=T0(0.8660254037844386467637231707529362L); + + auto WA = [wa,ido](size_t x, size_t i) { return wa[i+x*(ido-1)]; }; + auto CC = [cc,ido,l1](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+l1*c)]; }; + auto CH = [ch,ido](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+3*c)]; }; + + for (size_t k=0; k void radf4(size_t ido, size_t l1, + const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const T0 * POCKETFFT_RESTRICT wa) const + { + constexpr T0 hsqt2=T0(0.707106781186547524400844362104849L); + + auto WA = [wa,ido](size_t x, size_t i) { return wa[i+x*(ido-1)]; }; + auto CC = [cc,ido,l1](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+l1*c)]; }; + auto CH = [ch,ido](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+4*c)]; }; + + for (size_t k=0; k void radf5(size_t ido, size_t l1, + const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const T0 * POCKETFFT_RESTRICT wa) const + { + constexpr T0 tr11= T0(0.3090169943749474241022934171828191L), + ti11= T0(0.9510565162951535721164393333793821L), + tr12= T0(-0.8090169943749474241022934171828191L), + ti12= T0(0.5877852522924731291687059546390728L); + + auto WA = [wa,ido](size_t x, size_t i) { return wa[i+x*(ido-1)]; }; + auto CC = [cc,ido,l1](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+l1*c)]; }; + auto CH = [ch,ido](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+5*c)]; }; + + for (size_t k=0; k void radfg(size_t ido, size_t ip, size_t l1, + T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const T0 * POCKETFFT_RESTRICT wa, const T0 * POCKETFFT_RESTRICT csarr) const + { + const size_t cdim=ip; + size_t ipph=(ip+1)/2; + size_t idl1 = ido*l1; + + auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> T& + { return cc[a+ido*(b+cdim*c)]; }; + auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> const T& + { return ch[a+ido*(b+l1*c)]; }; + auto C1 = [cc,ido,l1] (size_t a, size_t b, size_t c) -> T& + { return cc[a+ido*(b+l1*c)]; }; + auto C2 = [cc,idl1] (size_t a, size_t b) -> T& + { return cc[a+idl1*b]; }; + auto CH2 = [ch,idl1] (size_t a, size_t b) -> T& + { return ch[a+idl1*b]; }; + + if (ido>1) + { + for (size_t j=1, jc=ip-1; j=ip) iang-=ip; + T0 ar1=csarr[2*iang], ai1=csarr[2*iang+1]; + iang+=l; if (iang>=ip) iang-=ip; + T0 ar2=csarr[2*iang], ai2=csarr[2*iang+1]; + iang+=l; if (iang>=ip) iang-=ip; + T0 ar3=csarr[2*iang], ai3=csarr[2*iang+1]; + iang+=l; if (iang>=ip) iang-=ip; + T0 ar4=csarr[2*iang], ai4=csarr[2*iang+1]; + for (size_t ik=0; ik=ip) iang-=ip; + T0 ar1=csarr[2*iang], ai1=csarr[2*iang+1]; + iang+=l; if (iang>=ip) iang-=ip; + T0 ar2=csarr[2*iang], ai2=csarr[2*iang+1]; + for (size_t ik=0; ik=ip) iang-=ip; + T0 ar=csarr[2*iang], ai=csarr[2*iang+1]; + for (size_t ik=0; ik void radb2(size_t ido, size_t l1, + const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const T0 * POCKETFFT_RESTRICT wa) const + { + auto WA = [wa,ido](size_t x, size_t i) { return wa[i+x*(ido-1)]; }; + auto CC = [cc,ido](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+2*c)]; }; + auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+l1*c)]; }; + + for (size_t k=0; k void radb3(size_t ido, size_t l1, + const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const T0 * POCKETFFT_RESTRICT wa) const + { + constexpr T0 taur=-0.5, taui=T0(0.8660254037844386467637231707529362L); + + auto WA = [wa,ido](size_t x, size_t i) { return wa[i+x*(ido-1)]; }; + auto CC = [cc,ido](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+3*c)]; }; + auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+l1*c)]; }; + + for (size_t k=0; k void radb4(size_t ido, size_t l1, + const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const T0 * POCKETFFT_RESTRICT wa) const + { + constexpr T0 sqrt2=T0(1.414213562373095048801688724209698L); + + auto WA = [wa,ido](size_t x, size_t i) { return wa[i+x*(ido-1)]; }; + auto CC = [cc,ido](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+4*c)]; }; + auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+l1*c)]; }; + + for (size_t k=0; k void radb5(size_t ido, size_t l1, + const T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const T0 * POCKETFFT_RESTRICT wa) const + { + constexpr T0 tr11= T0(0.3090169943749474241022934171828191L), + ti11= T0(0.9510565162951535721164393333793821L), + tr12= T0(-0.8090169943749474241022934171828191L), + ti12= T0(0.5877852522924731291687059546390728L); + + auto WA = [wa,ido](size_t x, size_t i) { return wa[i+x*(ido-1)]; }; + auto CC = [cc,ido](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+5*c)]; }; + auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+l1*c)]; }; + + for (size_t k=0; k void radbg(size_t ido, size_t ip, size_t l1, + T * POCKETFFT_RESTRICT cc, T * POCKETFFT_RESTRICT ch, + const T0 * POCKETFFT_RESTRICT wa, const T0 * POCKETFFT_RESTRICT csarr) const + { + const size_t cdim=ip; + size_t ipph=(ip+1)/ 2; + size_t idl1 = ido*l1; + + auto CC = [cc,ido,cdim](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+cdim*c)]; }; + auto CH = [ch,ido,l1](size_t a, size_t b, size_t c) -> T& + { return ch[a+ido*(b+l1*c)]; }; + auto C1 = [cc,ido,l1](size_t a, size_t b, size_t c) -> const T& + { return cc[a+ido*(b+l1*c)]; }; + auto C2 = [cc,idl1](size_t a, size_t b) -> T& + { return cc[a+idl1*b]; }; + auto CH2 = [ch,idl1](size_t a, size_t b) -> T& + { return ch[a+idl1*b]; }; + + for (size_t k=0; kip) iang-=ip; + T0 ar1=csarr[2*iang], ai1=csarr[2*iang+1]; + iang+=l; if(iang>ip) iang-=ip; + T0 ar2=csarr[2*iang], ai2=csarr[2*iang+1]; + iang+=l; if(iang>ip) iang-=ip; + T0 ar3=csarr[2*iang], ai3=csarr[2*iang+1]; + iang+=l; if(iang>ip) iang-=ip; + T0 ar4=csarr[2*iang], ai4=csarr[2*iang+1]; + for (size_t ik=0; ikip) iang-=ip; + T0 ar1=csarr[2*iang], ai1=csarr[2*iang+1]; + iang+=l; if(iang>ip) iang-=ip; + T0 ar2=csarr[2*iang], ai2=csarr[2*iang+1]; + for (size_t ik=0; ikip) iang-=ip; + T0 war=csarr[2*iang], wai=csarr[2*iang+1]; + for (size_t ik=0; ik void copy_and_norm(T *c, T *p1, T0 fct) const + { + if (p1!=c) + { + if (fct!=1.) + for (size_t i=0; i void exec(T c[], T0 fct, bool r2hc) const + { + if (length==1) { c[0]*=fct; return; } + size_t nf=fact.size(); + arr ch(length); + T *p1=c, *p2=ch.data(); + + if (r2hc) + for(size_t k1=0, l1=length; k1>=2; } + if ((len%2)==0) + { + len>>=1; + // factor 2 should be at the front of the factor list + add_factor(2); + std::swap(fact[0].fct, fact.back().fct); + } + for (size_t divisor=3; divisor*divisor<=len; divisor+=2) + while ((len%divisor)==0) + { + add_factor(divisor); + len/=divisor; + } + if (len>1) add_factor(len); + } + + size_t twsize() const + { + size_t twsz=0, l1=1; + for (size_t k=0; k5) twsz+=2*ip; + l1*=ip; + } + return twsz; + } + + void comp_twiddle() + { + sincos_2pibyn twid(length); + size_t l1=1; + T0 *ptr=mem.data(); + for (size_t k=0; k5) // special factors required by *g functions + { + fact[k].tws=ptr; ptr+=2*ip; + fact[k].tws[0] = 1.; + fact[k].tws[1] = 0.; + for (size_t i=2, ic=2*ip-2; i<=ic; i+=2, ic-=2) + { + fact[k].tws[i ] = twid[i/2*(length/ip)].r; + fact[k].tws[i+1] = twid[i/2*(length/ip)].i; + fact[k].tws[ic] = twid[i/2*(length/ip)].r; + fact[k].tws[ic+1] = -twid[i/2*(length/ip)].i; + } + } + l1*=ip; + } + } + + public: + POCKETFFT_NOINLINE rfftp(size_t length_) + : length(length_) + { + if (length==0) throw std::runtime_error("zero-length FFT requested"); + if (length==1) return; + factorize(); + mem.resize(twsize()); + comp_twiddle(); + } +}; + +// +// complex Bluestein transforms +// + +template class fftblue + { + private: + size_t n, n2; + cfftp plan; + arr> mem; + cmplx *bk, *bkf; + + template void fft(cmplx c[], T0 fct) const + { + arr> akf(n2); + + /* initialize a_k and FFT it */ + for (size_t m=0; m(c[m],bk[m],akf[m]); + auto zero = akf[0]*T0(0); + for (size_t m=n; m(bkf[0]); + for (size_t m=1; m<(n2+1)/2; ++m) + { + akf[m] = akf[m].template special_mul(bkf[m]); + akf[n2-m] = akf[n2-m].template special_mul(bkf[m]); + } + if ((n2&1)==0) + akf[n2/2] = akf[n2/2].template special_mul(bkf[n2/2]); + + /* inverse FFT */ + plan.exec (akf.data(),1.,false); + + /* multiply by b_k */ + for (size_t m=0; m(bk[m])*fct; + } + + public: + POCKETFFT_NOINLINE fftblue(size_t length) + : n(length), n2(util::good_size_cmplx(n*2-1)), plan(n2), mem(n+n2/2+1), + bk(mem.data()), bkf(mem.data()+n) + { + /* initialize b_k */ + sincos_2pibyn tmp(2*n); + bk[0].Set(1, 0); + + size_t coeff=0; + for (size_t m=1; m=2*n) coeff-=2*n; + bk[m] = tmp[coeff]; + } + + /* initialize the zero-padded, Fourier transformed b_k. Add normalisation. */ + arr> tbkf(n2); + T0 xn2 = T0(1)/T0(n2); + tbkf[0] = bk[0]*xn2; + for (size_t m=1; m void exec(cmplx c[], T0 fct, bool fwd) const + { fwd ? fft(c,fct) : fft(c,fct); } + + template void exec_r(T c[], T0 fct, bool fwd) + { + arr> tmp(n); + if (fwd) + { + auto zero = T0(0)*c[0]; + for (size_t m=0; m(tmp.data(),fct); + c[0] = tmp[0].r; + std::copy_n (&tmp[1].r, n-1, &c[1]); + } + else + { + tmp[0].Set(c[0],c[0]*0); + std::copy_n (c+1, n-1, &tmp[1].r); + if ((n&1)==0) tmp[n/2].i=T0(0)*c[0]; + for (size_t m=1; 2*m(tmp.data(),fct); + for (size_t m=0; m class pocketfft_c + { + private: + std::unique_ptr> packplan; + std::unique_ptr> blueplan; + size_t len; + + public: + POCKETFFT_NOINLINE pocketfft_c(size_t length) + : len(length) + { + if (length==0) throw std::runtime_error("zero-length FFT requested"); + size_t tmp = (length<50) ? 0 : util::largest_prime_factor(length); + if (tmp*tmp <= length) + { + packplan=std::unique_ptr>(new cfftp(length)); + return; + } + double comp1 = util::cost_guess(length); + double comp2 = 2*util::cost_guess(util::good_size_cmplx(2*length-1)); + comp2*=1.5; /* fudge factor that appears to give good overall performance */ + if (comp2>(new fftblue(length)); + else + packplan=std::unique_ptr>(new cfftp(length)); + } + + template POCKETFFT_NOINLINE void exec(cmplx c[], T0 fct, bool fwd) const + { packplan ? packplan->exec(c,fct,fwd) : blueplan->exec(c,fct,fwd); } + + size_t length() const { return len; } + }; + +// +// flexible (FFTPACK/Bluestein) real-valued 1D transform +// + +template class pocketfft_r + { + private: + std::unique_ptr> packplan; + std::unique_ptr> blueplan; + size_t len; + + public: + POCKETFFT_NOINLINE pocketfft_r(size_t length) + : len(length) + { + if (length==0) throw std::runtime_error("zero-length FFT requested"); + size_t tmp = (length<50) ? 0 : util::largest_prime_factor(length); + if (tmp*tmp <= length) + { + packplan=std::unique_ptr>(new rfftp(length)); + return; + } + double comp1 = 0.5*util::cost_guess(length); + double comp2 = 2*util::cost_guess(util::good_size_cmplx(2*length-1)); + comp2*=1.5; /* fudge factor that appears to give good overall performance */ + if (comp2>(new fftblue(length)); + else + packplan=std::unique_ptr>(new rfftp(length)); + } + + template POCKETFFT_NOINLINE void exec(T c[], T0 fct, bool fwd) const + { packplan ? packplan->exec(c,fct,fwd) : blueplan->exec_r(c,fct,fwd); } + + size_t length() const { return len; } + }; + + +// +// sine/cosine transforms +// + +template class T_dct1 + { + private: + pocketfft_r fftplan; + + public: + POCKETFFT_NOINLINE T_dct1(size_t length) + : fftplan(2*(length-1)) {} + + template POCKETFFT_NOINLINE void exec(T c[], T0 fct, bool ortho, + int /*type*/, bool /*cosine*/) const + { + constexpr T0 sqrt2=T0(1.414213562373095048801688724209698L); + size_t N=fftplan.length(), n=N/2+1; + if (ortho) + { c[0]*=sqrt2; c[n-1]*=sqrt2; } + arr tmp(N); + tmp[0] = c[0]; + for (size_t i=1; i class T_dst1 + { + private: + pocketfft_r fftplan; + + public: + POCKETFFT_NOINLINE T_dst1(size_t length) + : fftplan(2*(length+1)) {} + + template POCKETFFT_NOINLINE void exec(T c[], T0 fct, + bool /*ortho*/, int /*type*/, bool /*cosine*/) const + { + size_t N=fftplan.length(), n=N/2-1; + arr tmp(N); + tmp[0] = tmp[n+1] = c[0]*0; + for (size_t i=0; i class T_dcst23 + { + private: + pocketfft_r fftplan; + std::vector twiddle; + + public: + POCKETFFT_NOINLINE T_dcst23(size_t length) + : fftplan(length), twiddle(length) + { + sincos_2pibyn tw(4*length); + for (size_t i=0; i POCKETFFT_NOINLINE void exec(T c[], T0 fct, bool ortho, + int type, bool cosine) const + { + constexpr T0 sqrt2=T0(1.414213562373095048801688724209698L); + size_t N=length(); + size_t NS2 = (N+1)/2; + if (type==2) + { + if (!cosine) + for (size_t k=1; k class T_dcst4 + { + private: + size_t N; + std::unique_ptr> fft; + std::unique_ptr> rfft; + arr> C2; + + public: + POCKETFFT_NOINLINE T_dcst4(size_t length) + : N(length), + fft((N&1) ? nullptr : new pocketfft_c(N/2)), + rfft((N&1)? new pocketfft_r(N) : nullptr), + C2((N&1) ? 0 : N/2) + { + if ((N&1)==0) + { + sincos_2pibyn tw(16*N); + for (size_t i=0; i POCKETFFT_NOINLINE void exec(T c[], T0 fct, + bool /*ortho*/, int /*type*/, bool cosine) const + { + size_t n2 = N/2; + if (!cosine) + for (size_t k=0, kc=N-1; k y(N); + { + size_t i=0, m=n2; + for (; mexec(y.data(), fct, true); + { + auto SGN = [](size_t i) + { + constexpr T0 sqrt2=T0(1.414213562373095048801688724209698L); + return (i&2) ? -sqrt2 : sqrt2; + }; + c[n2] = y[0]*SGN(n2+1); + size_t i=0, i1=1, k=1; + for (; k> y(n2); + for(size_t i=0; iexec(y.data(), fct, true); + for(size_t i=0, ic=n2-1; i std::shared_ptr get_plan(size_t length) + { +#if POCKETFFT_CACHE_SIZE==0 + return std::make_shared(length); +#else + constexpr size_t nmax=POCKETFFT_CACHE_SIZE; + static std::array, nmax> cache; + static std::array last_access{{0}}; + static size_t access_counter = 0; + static std::mutex mut; + + auto find_in_cache = [&]() -> std::shared_ptr + { + for (size_t i=0; ilength()==length)) + { + // no need to update if this is already the most recent entry + if (last_access[i]!=access_counter) + { + last_access[i] = ++access_counter; + // Guard against overflow + if (access_counter == 0) + last_access.fill(0); + } + return cache[i]; + } + + return nullptr; + }; + + { + std::lock_guard lock(mut); + auto p = find_in_cache(); + if (p) return p; + } + auto plan = std::make_shared(length); + { + std::lock_guard lock(mut); + auto p = find_in_cache(); + if (p) return p; + + size_t lru = 0; + for (size_t i=1; i class cndarr: public arr_info + { + protected: + const char *d; + + public: + cndarr(const void *data_, const shape_t &shape_, const stride_t &stride_) + : arr_info(shape_, stride_), + d(reinterpret_cast(data_)) {} + const T &operator[](ptrdiff_t ofs) const + { return *reinterpret_cast(d+ofs); } + }; + +template class ndarr: public cndarr + { + public: + ndarr(void *data_, const shape_t &shape_, const stride_t &stride_) + : cndarr::cndarr(const_cast(data_), shape_, stride_) + {} + T &operator[](ptrdiff_t ofs) + { return *reinterpret_cast(const_cast(cndarr::d+ofs)); } + }; + +template class multi_iter + { + private: + shape_t pos; + const arr_info &iarr, &oarr; + ptrdiff_t p_ii, p_i[N], str_i, p_oi, p_o[N], str_o; + size_t idim, rem; + + void advance_i() + { + for (int i_=int(pos.size())-1; i_>=0; --i_) + { + auto i = size_t(i_); + if (i==idim) continue; + p_ii += iarr.stride(i); + p_oi += oarr.stride(i); + if (++pos[i] < iarr.shape(i)) + return; + pos[i] = 0; + p_ii -= ptrdiff_t(iarr.shape(i))*iarr.stride(i); + p_oi -= ptrdiff_t(oarr.shape(i))*oarr.stride(i); + } + } + + public: + multi_iter(const arr_info &iarr_, const arr_info &oarr_, size_t idim_) + : pos(iarr_.ndim(), 0), iarr(iarr_), oarr(oarr_), p_ii(0), + str_i(iarr.stride(idim_)), p_oi(0), str_o(oarr.stride(idim_)), + idim(idim_), rem(iarr.size()/iarr.shape(idim)) + { + auto nshares = threading::num_threads(); + if (nshares==1) return; + if (nshares==0) throw std::runtime_error("can't run with zero threads"); + auto myshare = threading::thread_id(); + if (myshare>=nshares) throw std::runtime_error("impossible share requested"); + size_t nbase = rem/nshares; + size_t additional = rem%nshares; + size_t lo = myshare*nbase + ((myshare=0; --i_) + { + auto i = size_t(i_); + p += arr.stride(i); + if (++pos[i] < arr.shape(i)) + return; + pos[i] = 0; + p -= ptrdiff_t(arr.shape(i))*arr.stride(i); + } + } + ptrdiff_t ofs() const { return p; } + size_t remaining() const { return rem; } + }; + +class rev_iter + { + private: + shape_t pos; + const arr_info &arr; + std::vector rev_axis; + std::vector rev_jump; + size_t last_axis, last_size; + shape_t shp; + ptrdiff_t p, rp; + size_t rem; + + public: + rev_iter(const arr_info &arr_, const shape_t &axes) + : pos(arr_.ndim(), 0), arr(arr_), rev_axis(arr_.ndim(), 0), + rev_jump(arr_.ndim(), 1), p(0), rp(0) + { + for (auto ax: axes) + rev_axis[ax]=1; + last_axis = axes.back(); + last_size = arr.shape(last_axis)/2 + 1; + shp = arr.shape(); + shp[last_axis] = last_size; + rem=1; + for (auto i: shp) + rem *= i; + } + void advance() + { + --rem; + for (int i_=int(pos.size())-1; i_>=0; --i_) + { + auto i = size_t(i_); + p += arr.stride(i); + if (!rev_axis[i]) + rp += arr.stride(i); + else + { + rp -= arr.stride(i); + if (rev_jump[i]) + { + rp += ptrdiff_t(arr.shape(i))*arr.stride(i); + rev_jump[i] = 0; + } + } + if (++pos[i] < shp[i]) + return; + pos[i] = 0; + p -= ptrdiff_t(shp[i])*arr.stride(i); + if (rev_axis[i]) + { + rp -= ptrdiff_t(arr.shape(i)-shp[i])*arr.stride(i); + rev_jump[i] = 1; + } + else + rp -= ptrdiff_t(shp[i])*arr.stride(i); + } + } + ptrdiff_t ofs() const { return p; } + ptrdiff_t rev_ofs() const { return rp; } + size_t remaining() const { return rem; } + }; + +template struct VTYPE {}; +template using vtype_t = typename VTYPE::type; + +#ifndef POCKETFFT_NO_VECTORS +template<> struct VTYPE + { + using type = float __attribute__ ((vector_size (VLEN::val*sizeof(float)))); + }; +template<> struct VTYPE + { + using type = double __attribute__ ((vector_size (VLEN::val*sizeof(double)))); + }; +template<> struct VTYPE + { + using type = long double __attribute__ ((vector_size (VLEN::val*sizeof(long double)))); + }; +#endif + +template arr alloc_tmp(const shape_t &shape, + size_t axsize, size_t elemsize) + { + auto othersize = util::prod(shape)/axsize; + auto tmpsize = axsize*((othersize>=VLEN::val) ? VLEN::val : 1); + return arr(tmpsize*elemsize); + } +template arr alloc_tmp(const shape_t &shape, + const shape_t &axes, size_t elemsize) + { + size_t fullsize=util::prod(shape); + size_t tmpsize=0; + for (size_t i=0; i=VLEN::val) ? VLEN::val : 1); + if (sz>tmpsize) tmpsize=sz; + } + return arr(tmpsize*elemsize); + } + +template void copy_input(const multi_iter &it, + const cndarr> &src, cmplx> *POCKETFFT_RESTRICT dst) + { + for (size_t i=0; i void copy_input(const multi_iter &it, + const cndarr &src, vtype_t *POCKETFFT_RESTRICT dst) + { + for (size_t i=0; i void copy_input(const multi_iter &it, + const cndarr &src, T *POCKETFFT_RESTRICT dst) + { + if (dst == &src[it.iofs(0)]) return; // in-place + for (size_t i=0; i void copy_output(const multi_iter &it, + const cmplx> *POCKETFFT_RESTRICT src, ndarr> &dst) + { + for (size_t i=0; i void copy_output(const multi_iter &it, + const vtype_t *POCKETFFT_RESTRICT src, ndarr &dst) + { + for (size_t i=0; i void copy_output(const multi_iter &it, + const T *POCKETFFT_RESTRICT src, ndarr &dst) + { + if (src == &dst[it.oofs(0)]) return; // in-place + for (size_t i=0; i struct add_vec { using type = vtype_t; }; +template struct add_vec> + { using type = cmplx>; }; +template using add_vec_t = typename add_vec::type; + +template +POCKETFFT_NOINLINE void general_nd(const cndarr &in, ndarr &out, + const shape_t &axes, T0 fct, size_t nthreads, const Exec & exec, + const bool allow_inplace=true) + { + std::shared_ptr plan; + + for (size_t iax=0; iaxlength())) + plan = get_plan(len); + + threading::thread_map( + util::thread_count(nthreads, in.shape(), axes[iax], VLEN::val), + [&] { + constexpr auto vlen = VLEN::val; + auto storage = alloc_tmp(in.shape(), len, sizeof(T)); + const auto &tin(iax==0? in : out); + multi_iter it(tin, out, axes[iax]); +#ifndef POCKETFFT_NO_VECTORS + if (vlen>1) + while (it.remaining()>=vlen) + { + it.advance(vlen); + auto tdatav = reinterpret_cast *>(storage.data()); + exec(it, tin, out, tdatav, *plan, fct); + } +#endif + while (it.remaining()>0) + { + it.advance(1); + auto buf = allow_inplace && it.stride_out() == sizeof(T) ? + &out[it.oofs(0)] : reinterpret_cast(storage.data()); + exec(it, tin, out, buf, *plan, fct); + } + }); // end of parallel region + fct = T0(1); // factor has been applied, use 1 for remaining axes + } + } + +struct ExecC2C + { + bool forward; + + template void operator () ( + const multi_iter &it, const cndarr> &in, + ndarr> &out, T * buf, const pocketfft_c &plan, T0 fct) const + { + copy_input(it, in, buf); + plan.exec(buf, fct, forward); + copy_output(it, buf, out); + } + }; + +template void copy_hartley(const multi_iter &it, + const vtype_t *POCKETFFT_RESTRICT src, ndarr &dst) + { + for (size_t j=0; j void copy_hartley(const multi_iter &it, + const T *POCKETFFT_RESTRICT src, ndarr &dst) + { + dst[it.oofs(0)] = src[0]; + size_t i=1, i1=1, i2=it.length_out()-1; + for (i=1; i void operator () ( + const multi_iter &it, const cndarr &in, ndarr &out, + T * buf, const pocketfft_r &plan, T0 fct) const + { + copy_input(it, in, buf); + plan.exec(buf, fct, true); + copy_hartley(it, buf, out); + } + }; + +struct ExecDcst + { + bool ortho; + int type; + bool cosine; + + template + void operator () (const multi_iter &it, const cndarr &in, + ndarr &out, T * buf, const Tplan &plan, T0 fct) const + { + copy_input(it, in, buf); + plan.exec(buf, fct, ortho, type, cosine); + copy_output(it, buf, out); + } + }; + +template POCKETFFT_NOINLINE void general_r2c( + const cndarr &in, ndarr> &out, size_t axis, bool forward, T fct, + size_t nthreads) + { + auto plan = get_plan>(in.shape(axis)); + size_t len=in.shape(axis); + threading::thread_map( + util::thread_count(nthreads, in.shape(), axis, VLEN::val), + [&] { + constexpr auto vlen = VLEN::val; + auto storage = alloc_tmp(in.shape(), len, sizeof(T)); + multi_iter it(in, out, axis); +#ifndef POCKETFFT_NO_VECTORS + if (vlen>1) + while (it.remaining()>=vlen) + { + it.advance(vlen); + auto tdatav = reinterpret_cast *>(storage.data()); + copy_input(it, in, tdatav); + plan->exec(tdatav, fct, true); + for (size_t j=0; j0) + { + it.advance(1); + auto tdata = reinterpret_cast(storage.data()); + copy_input(it, in, tdata); + plan->exec(tdata, fct, true); + out[it.oofs(0)].Set(tdata[0]); + size_t i=1, ii=1; + if (forward) + for (; i POCKETFFT_NOINLINE void general_c2r( + const cndarr> &in, ndarr &out, size_t axis, bool forward, T fct, + size_t nthreads) + { + auto plan = get_plan>(out.shape(axis)); + size_t len=out.shape(axis); + threading::thread_map( + util::thread_count(nthreads, in.shape(), axis, VLEN::val), + [&] { + constexpr auto vlen = VLEN::val; + auto storage = alloc_tmp(out.shape(), len, sizeof(T)); + multi_iter it(in, out, axis); +#ifndef POCKETFFT_NO_VECTORS + if (vlen>1) + while (it.remaining()>=vlen) + { + it.advance(vlen); + auto tdatav = reinterpret_cast *>(storage.data()); + for (size_t j=0; jexec(tdatav, fct, false); + copy_output(it, tdatav, out); + } +#endif + while (it.remaining()>0) + { + it.advance(1); + auto tdata = reinterpret_cast(storage.data()); + tdata[0]=in[it.iofs(0)].r; + { + size_t i=1, ii=1; + if (forward) + for (; iexec(tdata, fct, false); + copy_output(it, tdata, out); + } + }); // end of parallel region + } + +struct ExecR2R + { + bool r2h, forward; + + template void operator () ( + const multi_iter &it, const cndarr &in, ndarr &out, T * buf, + const pocketfft_r &plan, T0 fct) const + { + copy_input(it, in, buf); + if ((!r2h) && forward) + for (size_t i=2; i void c2c(const shape_t &shape, const stride_t &stride_in, + const stride_t &stride_out, const shape_t &axes, bool forward, + const std::complex *data_in, std::complex *data_out, T fct, + size_t nthreads=1) + { + if (util::prod(shape)==0) return; + util::sanity_check(shape, stride_in, stride_out, data_in==data_out, axes); + cndarr> ain(data_in, shape, stride_in); + ndarr> aout(data_out, shape, stride_out); + general_nd>(ain, aout, axes, fct, nthreads, ExecC2C{forward}); + } + +template void dct(const shape_t &shape, + const stride_t &stride_in, const stride_t &stride_out, const shape_t &axes, + int type, const T *data_in, T *data_out, T fct, bool ortho, size_t nthreads=1) + { + if ((type<1) || (type>4)) throw std::invalid_argument("invalid DCT type"); + if (util::prod(shape)==0) return; + util::sanity_check(shape, stride_in, stride_out, data_in==data_out, axes); + cndarr ain(data_in, shape, stride_in); + ndarr aout(data_out, shape, stride_out); + const ExecDcst exec{ortho, type, true}; + if (type==1) + general_nd>(ain, aout, axes, fct, nthreads, exec); + else if (type==4) + general_nd>(ain, aout, axes, fct, nthreads, exec); + else + general_nd>(ain, aout, axes, fct, nthreads, exec); + } + +template void dst(const shape_t &shape, + const stride_t &stride_in, const stride_t &stride_out, const shape_t &axes, + int type, const T *data_in, T *data_out, T fct, bool ortho, size_t nthreads=1) + { + if ((type<1) || (type>4)) throw std::invalid_argument("invalid DST type"); + if (util::prod(shape)==0) return; + util::sanity_check(shape, stride_in, stride_out, data_in==data_out, axes); + cndarr ain(data_in, shape, stride_in); + ndarr aout(data_out, shape, stride_out); + const ExecDcst exec{ortho, type, false}; + if (type==1) + general_nd>(ain, aout, axes, fct, nthreads, exec); + else if (type==4) + general_nd>(ain, aout, axes, fct, nthreads, exec); + else + general_nd>(ain, aout, axes, fct, nthreads, exec); + } + +template void r2c(const shape_t &shape_in, + const stride_t &stride_in, const stride_t &stride_out, size_t axis, + bool forward, const T *data_in, std::complex *data_out, T fct, + size_t nthreads=1) + { + if (util::prod(shape_in)==0) return; + util::sanity_check(shape_in, stride_in, stride_out, false, axis); + cndarr ain(data_in, shape_in, stride_in); + shape_t shape_out(shape_in); + shape_out[axis] = shape_in[axis]/2 + 1; + ndarr> aout(data_out, shape_out, stride_out); + general_r2c(ain, aout, axis, forward, fct, nthreads); + } + +template void r2c(const shape_t &shape_in, + const stride_t &stride_in, const stride_t &stride_out, const shape_t &axes, + bool forward, const T *data_in, std::complex *data_out, T fct, + size_t nthreads=1) + { + if (util::prod(shape_in)==0) return; + util::sanity_check(shape_in, stride_in, stride_out, false, axes); + r2c(shape_in, stride_in, stride_out, axes.back(), forward, data_in, data_out, + fct, nthreads); + if (axes.size()==1) return; + + shape_t shape_out(shape_in); + shape_out[axes.back()] = shape_in[axes.back()]/2 + 1; + auto newaxes = shape_t{axes.begin(), --axes.end()}; + c2c(shape_out, stride_out, stride_out, newaxes, forward, data_out, data_out, + T(1), nthreads); + } + +template void c2r(const shape_t &shape_out, + const stride_t &stride_in, const stride_t &stride_out, size_t axis, + bool forward, const std::complex *data_in, T *data_out, T fct, + size_t nthreads=1) + { + if (util::prod(shape_out)==0) return; + util::sanity_check(shape_out, stride_in, stride_out, false, axis); + shape_t shape_in(shape_out); + shape_in[axis] = shape_out[axis]/2 + 1; + cndarr> ain(data_in, shape_in, stride_in); + ndarr aout(data_out, shape_out, stride_out); + general_c2r(ain, aout, axis, forward, fct, nthreads); + } + +template void c2r(const shape_t &shape_out, + const stride_t &stride_in, const stride_t &stride_out, const shape_t &axes, + bool forward, const std::complex *data_in, T *data_out, T fct, + size_t nthreads=1) + { + if (util::prod(shape_out)==0) return; + if (axes.size()==1) + return c2r(shape_out, stride_in, stride_out, axes[0], forward, + data_in, data_out, fct, nthreads); + util::sanity_check(shape_out, stride_in, stride_out, false, axes); + auto shape_in = shape_out; + shape_in[axes.back()] = shape_out[axes.back()]/2 + 1; + auto nval = util::prod(shape_in); + stride_t stride_inter(shape_in.size()); + stride_inter.back() = sizeof(cmplx); + for (int i=int(shape_in.size())-2; i>=0; --i) + stride_inter[size_t(i)] = + stride_inter[size_t(i+1)]*ptrdiff_t(shape_in[size_t(i+1)]); + arr> tmp(nval); + auto newaxes = shape_t{axes.begin(), --axes.end()}; + c2c(shape_in, stride_in, stride_inter, newaxes, forward, data_in, tmp.data(), + T(1), nthreads); + c2r(shape_out, stride_inter, stride_out, axes.back(), forward, + tmp.data(), data_out, fct, nthreads); + } + +template void r2r_fftpack(const shape_t &shape, + const stride_t &stride_in, const stride_t &stride_out, const shape_t &axes, + bool real2hermitian, bool forward, const T *data_in, T *data_out, T fct, + size_t nthreads=1) + { + if (util::prod(shape)==0) return; + util::sanity_check(shape, stride_in, stride_out, data_in==data_out, axes); + cndarr ain(data_in, shape, stride_in); + ndarr aout(data_out, shape, stride_out); + general_nd>(ain, aout, axes, fct, nthreads, + ExecR2R{real2hermitian, forward}); + } + +template void r2r_separable_hartley(const shape_t &shape, + const stride_t &stride_in, const stride_t &stride_out, const shape_t &axes, + const T *data_in, T *data_out, T fct, size_t nthreads=1) + { + if (util::prod(shape)==0) return; + util::sanity_check(shape, stride_in, stride_out, data_in==data_out, axes); + cndarr ain(data_in, shape, stride_in); + ndarr aout(data_out, shape, stride_out); + general_nd>(ain, aout, axes, fct, nthreads, ExecHartley{}, + false); + } + +template void r2r_genuine_hartley(const shape_t &shape, + const stride_t &stride_in, const stride_t &stride_out, const shape_t &axes, + const T *data_in, T *data_out, T fct, size_t nthreads=1) + { + if (util::prod(shape)==0) return; + if (axes.size()==1) + return r2r_separable_hartley(shape, stride_in, stride_out, axes, data_in, + data_out, fct, nthreads); + util::sanity_check(shape, stride_in, stride_out, data_in==data_out, axes); + shape_t tshp(shape); + tshp[axes.back()] = tshp[axes.back()]/2+1; + arr> tdata(util::prod(tshp)); + stride_t tstride(shape.size()); + tstride.back()=sizeof(std::complex); + for (size_t i=tstride.size()-1; i>0; --i) + tstride[i-1]=tstride[i]*ptrdiff_t(tshp[i]); + r2c(shape, stride_in, tstride, axes, true, data_in, tdata.data(), fct, nthreads); + cndarr> atmp(tdata.data(), tshp, tstride); + ndarr aout(data_out, shape, stride_out); + simple_iter iin(atmp); + rev_iter iout(aout, axes); + while(iin.remaining()>0) + { + auto v = atmp[iin.ofs()]; + aout[iout.ofs()] = v.r+v.i; + aout[iout.rev_ofs()] = v.r-v.i; + iin.advance(); iout.advance(); + } + } + +} // namespace detail + +using detail::FORWARD; +using detail::BACKWARD; +using detail::shape_t; +using detail::stride_t; +using detail::c2c; +using detail::c2r; +using detail::r2c; +using detail::r2r_fftpack; +using detail::r2r_separable_hartley; +using detail::r2r_genuine_hartley; +using detail::dct; +using detail::dst; + +} // namespace pocketfft + +#undef POCKETFFT_NOINLINE +#undef POCKETFFT_RESTRICT + +#endif // POCKETFFT_HDRONLY_H diff --git a/project/data-processing/sig1.csv b/project/data-processing/sig1.csv new file mode 100644 index 0000000..86f2f21 --- /dev/null +++ b/project/data-processing/sig1.csv @@ -0,0 +1,7001 @@ +voltage[V],time[ns] +0.5048825909,0.0000 +0.5063517199,0.1429 +0.5078103756,0.2858 +0.5092585280,0.4286 +0.5106961471,0.5715 +0.5121232030,0.7144 +0.5135396664,0.8573 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