common/include/inv_pow2_table.hpp - datasketches-cpp - Git at Google

 /*
  * Licensed to the Apache Software Foundation (ASF) under one
  * or more contributor license agreements.  See the NOTICE file
  * distributed with this work for additional information
  * regarding copyright ownership.  The ASF licenses this file
  * to you under the Apache License, Version 2.0 (the
  * "License"); you may not use this file except in compliance
  * with the License.  You may obtain a copy of the License at
  *
  *   http://www.apache.org/licenses/LICENSE-2.0
  *
  * Unless required by applicable law or agreed to in writing,
  * software distributed under the License is distributed on an
  * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
  * KIND, either express or implied.  See the License for the
  * specific language governing permissions and limitations
  * under the License.
  */

 #ifndef INV_POW_2_TAB_HPP_
 #define INV_POW_2_TAB_HPP_

 #include <cmath>

 namespace datasketches {

 // the table was created by the following procedure:

 //void fill_inverse_power_of_2_table() {
 //  for (int i = 0; i < 256; i++) {
 //    inverse_powers_of_2_table[i] = pow(2.0, (-1.0 * ((double) i)));
 //    printf("%.17g", inverse_powers_of_2_table[i]);
 //    if (i != 255) printf(", ");
 //    if ((i + 1) % 4 == 0) printf("\n");
 //  }
 //}

 static const double INVERSE_POWERS_OF_2[256] = {
     1, 0.5, 0.25, 0.125,
     0.0625, 0.03125, 0.015625, 0.0078125,
     0.00390625, 0.001953125, 0.0009765625, 0.00048828125,
     0.000244140625, 0.0001220703125, 6.103515625e-05, 3.0517578125e-05,
     1.52587890625e-05, 7.62939453125e-06, 3.814697265625e-06, 1.9073486328125e-06,
     9.5367431640625e-07, 4.76837158203125e-07, 2.384185791015625e-07, 1.1920928955078125e-07,
     5.9604644775390625e-08, 2.9802322387695312e-08, 1.4901161193847656e-08, 7.4505805969238281e-09,
     3.7252902984619141e-09, 1.862645149230957e-09, 9.3132257461547852e-10, 4.6566128730773926e-10,
     2.3283064365386963e-10, 1.1641532182693481e-10, 5.8207660913467407e-11, 2.9103830456733704e-11,
     1.4551915228366852e-11, 7.2759576141834259e-12, 3.637978807091713e-12, 1.8189894035458565e-12,
     9.0949470177292824e-13, 4.5474735088646412e-13, 2.2737367544323206e-13, 1.1368683772161603e-13,
     5.6843418860808015e-14, 2.8421709430404007e-14, 1.4210854715202004e-14, 7.1054273576010019e-15,
     3.5527136788005009e-15, 1.7763568394002505e-15, 8.8817841970012523e-16, 4.4408920985006262e-16,
     2.2204460492503131e-16, 1.1102230246251565e-16, 5.5511151231257827e-17, 2.7755575615628914e-17,
     1.3877787807814457e-17, 6.9388939039072284e-18, 3.4694469519536142e-18, 1.7347234759768071e-18,
     8.6736173798840355e-19, 4.3368086899420177e-19, 2.1684043449710089e-19, 1.0842021724855044e-19,
     5.4210108624275222e-20, 2.7105054312137611e-20, 1.3552527156068805e-20, 6.7762635780344027e-21,
     3.3881317890172014e-21, 1.6940658945086007e-21, 8.4703294725430034e-22, 4.2351647362715017e-22,
     2.1175823681357508e-22, 1.0587911840678754e-22, 5.2939559203393771e-23, 2.6469779601696886e-23,
     1.3234889800848443e-23, 6.6174449004242214e-24, 3.3087224502121107e-24, 1.6543612251060553e-24,
     8.2718061255302767e-25, 4.1359030627651384e-25, 2.0679515313825692e-25, 1.0339757656912846e-25,
     5.169878828456423e-26, 2.5849394142282115e-26, 1.2924697071141057e-26, 6.4623485355705287e-27,
     3.2311742677852644e-27, 1.6155871338926322e-27, 8.0779356694631609e-28, 4.0389678347315804e-28,
     2.0194839173657902e-28, 1.0097419586828951e-28, 5.0487097934144756e-29, 2.5243548967072378e-29,
     1.2621774483536189e-29, 6.3108872417680944e-30, 3.1554436208840472e-30, 1.5777218104420236e-30,
     7.8886090522101181e-31, 3.944304526105059e-31, 1.9721522630525295e-31, 9.8607613152626476e-32,
     4.9303806576313238e-32, 2.4651903288156619e-32, 1.2325951644078309e-32, 6.1629758220391547e-33,
     3.0814879110195774e-33, 1.5407439555097887e-33, 7.7037197775489434e-34, 3.8518598887744717e-34,
     1.9259299443872359e-34, 9.6296497219361793e-35, 4.8148248609680896e-35, 2.4074124304840448e-35,
     1.2037062152420224e-35, 6.018531076210112e-36, 3.009265538105056e-36, 1.504632769052528e-36,
     7.5231638452626401e-37, 3.76158192263132e-37, 1.88079096131566e-37, 9.4039548065783001e-38,
     4.70197740328915e-38, 2.350988701644575e-38, 1.1754943508222875e-38, 5.8774717541114375e-39,
     2.9387358770557188e-39, 1.4693679385278594e-39, 7.3468396926392969e-40, 3.6734198463196485e-40,
     1.8367099231598242e-40, 9.1835496157991212e-41, 4.5917748078995606e-41, 2.2958874039497803e-41,
     1.1479437019748901e-41, 5.7397185098744507e-42, 2.8698592549372254e-42, 1.4349296274686127e-42,
     7.1746481373430634e-43, 3.5873240686715317e-43, 1.7936620343357659e-43, 8.9683101716788293e-44,
     4.4841550858394146e-44, 2.2420775429197073e-44, 1.1210387714598537e-44, 5.6051938572992683e-45,
     2.8025969286496341e-45, 1.4012984643248171e-45, 7.0064923216240854e-46, 3.5032461608120427e-46,
     1.7516230804060213e-46, 8.7581154020301067e-47, 4.3790577010150533e-47, 2.1895288505075267e-47,
     1.0947644252537633e-47, 5.4738221262688167e-48, 2.7369110631344083e-48, 1.3684555315672042e-48,
     6.8422776578360209e-49, 3.4211388289180104e-49, 1.7105694144590052e-49, 8.5528470722950261e-50,
     4.276423536147513e-50, 2.1382117680737565e-50, 1.0691058840368783e-50, 5.3455294201843913e-51,
     2.6727647100921956e-51, 1.3363823550460978e-51, 6.6819117752304891e-52, 3.3409558876152446e-52,
     1.6704779438076223e-52, 8.3523897190381114e-53, 4.1761948595190557e-53, 2.0880974297595278e-53,
     1.0440487148797639e-53, 5.2202435743988196e-54, 2.6101217871994098e-54, 1.3050608935997049e-54,
     6.5253044679985245e-55, 3.2626522339992623e-55, 1.6313261169996311e-55, 8.1566305849981557e-56,
     4.0783152924990778e-56, 2.0391576462495389e-56, 1.0195788231247695e-56, 5.0978941156238473e-57,
     2.5489470578119236e-57, 1.2744735289059618e-57, 6.3723676445298091e-58, 3.1861838222649046e-58,
     1.5930919111324523e-58, 7.9654595556622614e-59, 3.9827297778311307e-59, 1.9913648889155653e-59,
     9.9568244445778267e-60, 4.9784122222889134e-60, 2.4892061111444567e-60, 1.2446030555722283e-60,
     6.2230152778611417e-61, 3.1115076389305709e-61, 1.5557538194652854e-61, 7.7787690973264271e-62,
     3.8893845486632136e-62, 1.9446922743316068e-62, 9.7234613716580339e-63, 4.861730685829017e-63,
     2.4308653429145085e-63, 1.2154326714572542e-63, 6.0771633572862712e-64, 3.0385816786431356e-64,
     1.5192908393215678e-64, 7.596454196607839e-65, 3.7982270983039195e-65, 1.8991135491519597e-65,
     9.4955677457597987e-66, 4.7477838728798994e-66, 2.3738919364399497e-66, 1.1869459682199748e-66,
     5.9347298410998742e-67, 2.9673649205499371e-67, 1.4836824602749686e-67, 7.4184123013748428e-68,
     3.7092061506874214e-68, 1.8546030753437107e-68, 9.2730153767185535e-69, 4.6365076883592767e-69,
     2.3182538441796384e-69, 1.1591269220898192e-69, 5.7956346104490959e-70, 2.897817305224548e-70,
     1.448908652612274e-70, 7.2445432630613699e-71, 3.6222716315306849e-71, 1.8111358157653425e-71,
     9.0556790788267124e-72, 4.5278395394133562e-72, 2.2639197697066781e-72, 1.131959884853339e-72,
     5.6597994242666952e-73, 2.8298997121333476e-73, 1.4149498560666738e-73, 7.074749280333369e-74,
     3.5373746401666845e-74, 1.7686873200833423e-74, 8.8434366004167113e-75, 4.4217183002083556e-75,
     2.2108591501041778e-75, 1.1054295750520889e-75, 5.5271478752604446e-76, 2.7635739376302223e-76,
     1.3817869688151111e-76, 6.9089348440755557e-77, 3.4544674220377779e-77, 1.7272337110188889e-77
 };

 } /* namespace datasketches */

 #endif
	/*
	* Licensed to the Apache Software Foundation (ASF) under one
	* or more contributor license agreements. See the NOTICE file
	* distributed with this work for additional information
	* regarding copyright ownership. The ASF licenses this file
	* to you under the Apache License, Version 2.0 (the
	* "License"); you may not use this file except in compliance
	* with the License. You may obtain a copy of the License at
	*
	* http://www.apache.org/licenses/LICENSE-2.0
	*
	* Unless required by applicable law or agreed to in writing,
	* software distributed under the License is distributed on an
	* "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
	* KIND, either express or implied. See the License for the
	* specific language governing permissions and limitations
	* under the License.
	*/

	#ifndef INV_POW_2_TAB_HPP_
	#define INV_POW_2_TAB_HPP_

	#include <cmath>

	namespace datasketches {

	// the table was created by the following procedure:

	//void fill_inverse_power_of_2_table() {
	// for (int i = 0; i < 256; i++) {
	// inverse_powers_of_2_table[i] = pow(2.0, (-1.0 * ((double) i)));
	// printf("%.17g", inverse_powers_of_2_table[i]);
	// if (i != 255) printf(", ");
	// if ((i + 1) % 4 == 0) printf("\n");
	// }
	//}

	static const double INVERSE_POWERS_OF_2[256] = {
	1, 0.5, 0.25, 0.125,
	0.0625, 0.03125, 0.015625, 0.0078125,
	0.00390625, 0.001953125, 0.0009765625, 0.00048828125,
	0.000244140625, 0.0001220703125, 6.103515625e-05, 3.0517578125e-05,
	1.52587890625e-05, 7.62939453125e-06, 3.814697265625e-06, 1.9073486328125e-06,
	9.5367431640625e-07, 4.76837158203125e-07, 2.384185791015625e-07, 1.1920928955078125e-07,
	5.9604644775390625e-08, 2.9802322387695312e-08, 1.4901161193847656e-08, 7.4505805969238281e-09,
	3.7252902984619141e-09, 1.862645149230957e-09, 9.3132257461547852e-10, 4.6566128730773926e-10,
	2.3283064365386963e-10, 1.1641532182693481e-10, 5.8207660913467407e-11, 2.9103830456733704e-11,
	1.4551915228366852e-11, 7.2759576141834259e-12, 3.637978807091713e-12, 1.8189894035458565e-12,
	9.0949470177292824e-13, 4.5474735088646412e-13, 2.2737367544323206e-13, 1.1368683772161603e-13,
	5.6843418860808015e-14, 2.8421709430404007e-14, 1.4210854715202004e-14, 7.1054273576010019e-15,
	3.5527136788005009e-15, 1.7763568394002505e-15, 8.8817841970012523e-16, 4.4408920985006262e-16,
	2.2204460492503131e-16, 1.1102230246251565e-16, 5.5511151231257827e-17, 2.7755575615628914e-17,
	1.3877787807814457e-17, 6.9388939039072284e-18, 3.4694469519536142e-18, 1.7347234759768071e-18,
	8.6736173798840355e-19, 4.3368086899420177e-19, 2.1684043449710089e-19, 1.0842021724855044e-19,
	5.4210108624275222e-20, 2.7105054312137611e-20, 1.3552527156068805e-20, 6.7762635780344027e-21,
	3.3881317890172014e-21, 1.6940658945086007e-21, 8.4703294725430034e-22, 4.2351647362715017e-22,
	2.1175823681357508e-22, 1.0587911840678754e-22, 5.2939559203393771e-23, 2.6469779601696886e-23,
	1.3234889800848443e-23, 6.6174449004242214e-24, 3.3087224502121107e-24, 1.6543612251060553e-24,
	8.2718061255302767e-25, 4.1359030627651384e-25, 2.0679515313825692e-25, 1.0339757656912846e-25,
	5.169878828456423e-26, 2.5849394142282115e-26, 1.2924697071141057e-26, 6.4623485355705287e-27,
	3.2311742677852644e-27, 1.6155871338926322e-27, 8.0779356694631609e-28, 4.0389678347315804e-28,
	2.0194839173657902e-28, 1.0097419586828951e-28, 5.0487097934144756e-29, 2.5243548967072378e-29,
	1.2621774483536189e-29, 6.3108872417680944e-30, 3.1554436208840472e-30, 1.5777218104420236e-30,
	7.8886090522101181e-31, 3.944304526105059e-31, 1.9721522630525295e-31, 9.8607613152626476e-32,
	4.9303806576313238e-32, 2.4651903288156619e-32, 1.2325951644078309e-32, 6.1629758220391547e-33,
	3.0814879110195774e-33, 1.5407439555097887e-33, 7.7037197775489434e-34, 3.8518598887744717e-34,
	1.9259299443872359e-34, 9.6296497219361793e-35, 4.8148248609680896e-35, 2.4074124304840448e-35,
	1.2037062152420224e-35, 6.018531076210112e-36, 3.009265538105056e-36, 1.504632769052528e-36,
	7.5231638452626401e-37, 3.76158192263132e-37, 1.88079096131566e-37, 9.4039548065783001e-38,
	4.70197740328915e-38, 2.350988701644575e-38, 1.1754943508222875e-38, 5.8774717541114375e-39,
	2.9387358770557188e-39, 1.4693679385278594e-39, 7.3468396926392969e-40, 3.6734198463196485e-40,
	1.8367099231598242e-40, 9.1835496157991212e-41, 4.5917748078995606e-41, 2.2958874039497803e-41,
	1.1479437019748901e-41, 5.7397185098744507e-42, 2.8698592549372254e-42, 1.4349296274686127e-42,
	7.1746481373430634e-43, 3.5873240686715317e-43, 1.7936620343357659e-43, 8.9683101716788293e-44,
	4.4841550858394146e-44, 2.2420775429197073e-44, 1.1210387714598537e-44, 5.6051938572992683e-45,
	2.8025969286496341e-45, 1.4012984643248171e-45, 7.0064923216240854e-46, 3.5032461608120427e-46,
	1.7516230804060213e-46, 8.7581154020301067e-47, 4.3790577010150533e-47, 2.1895288505075267e-47,
	1.0947644252537633e-47, 5.4738221262688167e-48, 2.7369110631344083e-48, 1.3684555315672042e-48,
	6.8422776578360209e-49, 3.4211388289180104e-49, 1.7105694144590052e-49, 8.5528470722950261e-50,
	4.276423536147513e-50, 2.1382117680737565e-50, 1.0691058840368783e-50, 5.3455294201843913e-51,
	2.6727647100921956e-51, 1.3363823550460978e-51, 6.6819117752304891e-52, 3.3409558876152446e-52,
	1.6704779438076223e-52, 8.3523897190381114e-53, 4.1761948595190557e-53, 2.0880974297595278e-53,
	1.0440487148797639e-53, 5.2202435743988196e-54, 2.6101217871994098e-54, 1.3050608935997049e-54,
	6.5253044679985245e-55, 3.2626522339992623e-55, 1.6313261169996311e-55, 8.1566305849981557e-56,
	4.0783152924990778e-56, 2.0391576462495389e-56, 1.0195788231247695e-56, 5.0978941156238473e-57,
	2.5489470578119236e-57, 1.2744735289059618e-57, 6.3723676445298091e-58, 3.1861838222649046e-58,
	1.5930919111324523e-58, 7.9654595556622614e-59, 3.9827297778311307e-59, 1.9913648889155653e-59,
	9.9568244445778267e-60, 4.9784122222889134e-60, 2.4892061111444567e-60, 1.2446030555722283e-60,
	6.2230152778611417e-61, 3.1115076389305709e-61, 1.5557538194652854e-61, 7.7787690973264271e-62,
	3.8893845486632136e-62, 1.9446922743316068e-62, 9.7234613716580339e-63, 4.861730685829017e-63,
	2.4308653429145085e-63, 1.2154326714572542e-63, 6.0771633572862712e-64, 3.0385816786431356e-64,
	1.5192908393215678e-64, 7.596454196607839e-65, 3.7982270983039195e-65, 1.8991135491519597e-65,
	9.4955677457597987e-66, 4.7477838728798994e-66, 2.3738919364399497e-66, 1.1869459682199748e-66,
	5.9347298410998742e-67, 2.9673649205499371e-67, 1.4836824602749686e-67, 7.4184123013748428e-68,
	3.7092061506874214e-68, 1.8546030753437107e-68, 9.2730153767185535e-69, 4.6365076883592767e-69,
	2.3182538441796384e-69, 1.1591269220898192e-69, 5.7956346104490959e-70, 2.897817305224548e-70,
	1.448908652612274e-70, 7.2445432630613699e-71, 3.6222716315306849e-71, 1.8111358157653425e-71,
	9.0556790788267124e-72, 4.5278395394133562e-72, 2.2639197697066781e-72, 1.131959884853339e-72,
	5.6597994242666952e-73, 2.8298997121333476e-73, 1.4149498560666738e-73, 7.074749280333369e-74,
	3.5373746401666845e-74, 1.7686873200833423e-74, 8.8434366004167113e-75, 4.4217183002083556e-75,
	2.2108591501041778e-75, 1.1054295750520889e-75, 5.5271478752604446e-76, 2.7635739376302223e-76,
	1.3817869688151111e-76, 6.9089348440755557e-77, 3.4544674220377779e-77, 1.7272337110188889e-77
	};

	} /* namespace datasketches */

	#endif