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arm_common_tables.c
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/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. February 2012
* $Revision: V1.1.0
*
* Project: CMSIS DSP Library
* Title: arm_common_tables.c
*
* Description: This file has common tables like fft twiddle factors,
* Bitreverse, reciprocal etc which are used across different functions
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.1.0 2012/02/15
* Updated with more optimizations, bug fixes and minor API changes.
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_common_tables.h"
/**
* @ingroup groupTransforms
*/
/**
* @addtogroup CFFT_CIFFT Complex FFT Tables
* @{
*/
/**
* \par
* Pseudo code for Generation of Bit reversal Table is
* \par
* <pre>for(l=1;l <= N/4;l++)
* {
* for(i=0;i<logN2;i++)
* {
* a[i]=l&(1<<i);
* }
* for(j=0; j<logN2; j++)
* {
* if (a[j]!=0)
* y[l]+=(1<<((logN2-1)-j));
* }
* y[l] = y[l] >> 1;
* } </pre>
* \par
* where N = 4096 logN2 = 12
* \par
* N is the maximum FFT Size supported
*/
/*
* @brief Table for bit reversal process
*/
const uint16_t armBitRevTable[1024] = {
0x400, 0x200, 0x600, 0x100, 0x500, 0x300, 0x700, 0x80, 0x480, 0x280, 0x680,
0x180, 0x580, 0x380, 0x780, 0x40, 0x440, 0x240, 0x640, 0x140, 0x540, 0x340,
0x740, 0xc0, 0x4c0, 0x2c0, 0x6c0, 0x1c0, 0x5c0, 0x3c0, 0x7c0, 0x20, 0x420,
0x220, 0x620, 0x120, 0x520, 0x320, 0x720, 0xa0, 0x4a0, 0x2a0, 0x6a0, 0x1a0,
0x5a0, 0x3a0, 0x7a0, 0x60, 0x460, 0x260, 0x660, 0x160, 0x560, 0x360, 0x760,
0xe0, 0x4e0, 0x2e0, 0x6e0, 0x1e0, 0x5e0, 0x3e0, 0x7e0, 0x10, 0x410, 0x210,
0x610, 0x110, 0x510, 0x310, 0x710, 0x90, 0x490, 0x290, 0x690, 0x190, 0x590,
0x390, 0x790, 0x50, 0x450, 0x250, 0x650, 0x150, 0x550, 0x350, 0x750, 0xd0,
0x4d0, 0x2d0, 0x6d0, 0x1d0, 0x5d0, 0x3d0, 0x7d0, 0x30, 0x430, 0x230, 0x630,
0x130, 0x530, 0x330, 0x730, 0xb0, 0x4b0, 0x2b0, 0x6b0, 0x1b0, 0x5b0, 0x3b0,
0x7b0, 0x70, 0x470, 0x270, 0x670, 0x170, 0x570, 0x370, 0x770, 0xf0, 0x4f0,
0x2f0, 0x6f0, 0x1f0, 0x5f0, 0x3f0, 0x7f0, 0x8, 0x408, 0x208, 0x608, 0x108,
0x508, 0x308, 0x708, 0x88, 0x488, 0x288, 0x688, 0x188, 0x588, 0x388, 0x788,
0x48, 0x448, 0x248, 0x648, 0x148, 0x548, 0x348, 0x748, 0xc8, 0x4c8, 0x2c8,
0x6c8, 0x1c8, 0x5c8, 0x3c8, 0x7c8, 0x28, 0x428, 0x228, 0x628, 0x128, 0x528,
0x328, 0x728, 0xa8, 0x4a8, 0x2a8, 0x6a8, 0x1a8, 0x5a8, 0x3a8, 0x7a8, 0x68,
0x468, 0x268, 0x668, 0x168, 0x568, 0x368, 0x768, 0xe8, 0x4e8, 0x2e8, 0x6e8,
0x1e8, 0x5e8, 0x3e8, 0x7e8, 0x18, 0x418, 0x218, 0x618, 0x118, 0x518, 0x318,
0x718, 0x98, 0x498, 0x298, 0x698, 0x198, 0x598, 0x398, 0x798, 0x58, 0x458,
0x258, 0x658, 0x158, 0x558, 0x358, 0x758, 0xd8, 0x4d8, 0x2d8, 0x6d8, 0x1d8,
0x5d8, 0x3d8, 0x7d8, 0x38, 0x438, 0x238, 0x638, 0x138, 0x538, 0x338, 0x738,
0xb8, 0x4b8, 0x2b8, 0x6b8, 0x1b8, 0x5b8, 0x3b8, 0x7b8, 0x78, 0x478, 0x278,
0x678, 0x178, 0x578, 0x378, 0x778, 0xf8, 0x4f8, 0x2f8, 0x6f8, 0x1f8, 0x5f8,
0x3f8, 0x7f8, 0x4, 0x404, 0x204, 0x604, 0x104, 0x504, 0x304, 0x704, 0x84,
0x484, 0x284, 0x684, 0x184, 0x584, 0x384, 0x784, 0x44, 0x444, 0x244, 0x644,
0x144, 0x544, 0x344, 0x744, 0xc4, 0x4c4, 0x2c4, 0x6c4, 0x1c4, 0x5c4, 0x3c4,
0x7c4, 0x24, 0x424, 0x224, 0x624, 0x124, 0x524, 0x324, 0x724, 0xa4, 0x4a4,
0x2a4, 0x6a4, 0x1a4, 0x5a4, 0x3a4, 0x7a4, 0x64, 0x464, 0x264, 0x664, 0x164,
0x564, 0x364, 0x764, 0xe4, 0x4e4, 0x2e4, 0x6e4, 0x1e4, 0x5e4, 0x3e4, 0x7e4,
0x14, 0x414, 0x214, 0x614, 0x114, 0x514, 0x314, 0x714, 0x94, 0x494, 0x294,
0x694, 0x194, 0x594, 0x394, 0x794, 0x54, 0x454, 0x254, 0x654, 0x154, 0x554,
0x354, 0x754, 0xd4, 0x4d4, 0x2d4, 0x6d4, 0x1d4, 0x5d4, 0x3d4, 0x7d4, 0x34,
0x434, 0x234, 0x634, 0x134, 0x534, 0x334, 0x734, 0xb4, 0x4b4, 0x2b4, 0x6b4,
0x1b4, 0x5b4, 0x3b4, 0x7b4, 0x74, 0x474, 0x274, 0x674, 0x174, 0x574, 0x374,
0x774, 0xf4, 0x4f4, 0x2f4, 0x6f4, 0x1f4, 0x5f4, 0x3f4, 0x7f4, 0xc, 0x40c,
0x20c, 0x60c, 0x10c, 0x50c, 0x30c, 0x70c, 0x8c, 0x48c, 0x28c, 0x68c, 0x18c,
0x58c, 0x38c, 0x78c, 0x4c, 0x44c, 0x24c, 0x64c, 0x14c, 0x54c, 0x34c, 0x74c,
0xcc, 0x4cc, 0x2cc, 0x6cc, 0x1cc, 0x5cc, 0x3cc, 0x7cc, 0x2c, 0x42c, 0x22c,
0x62c, 0x12c, 0x52c, 0x32c, 0x72c, 0xac, 0x4ac, 0x2ac, 0x6ac, 0x1ac, 0x5ac,
0x3ac, 0x7ac, 0x6c, 0x46c, 0x26c, 0x66c, 0x16c, 0x56c, 0x36c, 0x76c, 0xec,
0x4ec, 0x2ec, 0x6ec, 0x1ec, 0x5ec, 0x3ec, 0x7ec, 0x1c, 0x41c, 0x21c, 0x61c,
0x11c, 0x51c, 0x31c, 0x71c, 0x9c, 0x49c, 0x29c, 0x69c, 0x19c, 0x59c, 0x39c,
0x79c, 0x5c, 0x45c, 0x25c, 0x65c, 0x15c, 0x55c, 0x35c, 0x75c, 0xdc, 0x4dc,
0x2dc, 0x6dc, 0x1dc, 0x5dc, 0x3dc, 0x7dc, 0x3c, 0x43c, 0x23c, 0x63c, 0x13c,
0x53c, 0x33c, 0x73c, 0xbc, 0x4bc, 0x2bc, 0x6bc, 0x1bc, 0x5bc, 0x3bc, 0x7bc,
0x7c, 0x47c, 0x27c, 0x67c, 0x17c, 0x57c, 0x37c, 0x77c, 0xfc, 0x4fc, 0x2fc,
0x6fc, 0x1fc, 0x5fc, 0x3fc, 0x7fc, 0x2, 0x402, 0x202, 0x602, 0x102, 0x502,
0x302, 0x702, 0x82, 0x482, 0x282, 0x682, 0x182, 0x582, 0x382, 0x782, 0x42,
0x442, 0x242, 0x642, 0x142, 0x542, 0x342, 0x742, 0xc2, 0x4c2, 0x2c2, 0x6c2,
0x1c2, 0x5c2, 0x3c2, 0x7c2, 0x22, 0x422, 0x222, 0x622, 0x122, 0x522, 0x322,
0x722, 0xa2, 0x4a2, 0x2a2, 0x6a2, 0x1a2, 0x5a2, 0x3a2, 0x7a2, 0x62, 0x462,
0x262, 0x662, 0x162, 0x562, 0x362, 0x762, 0xe2, 0x4e2, 0x2e2, 0x6e2, 0x1e2,
0x5e2, 0x3e2, 0x7e2, 0x12, 0x412, 0x212, 0x612, 0x112, 0x512, 0x312, 0x712,
0x92, 0x492, 0x292, 0x692, 0x192, 0x592, 0x392, 0x792, 0x52, 0x452, 0x252,
0x652, 0x152, 0x552, 0x352, 0x752, 0xd2, 0x4d2, 0x2d2, 0x6d2, 0x1d2, 0x5d2,
0x3d2, 0x7d2, 0x32, 0x432, 0x232, 0x632, 0x132, 0x532, 0x332, 0x732, 0xb2,
0x4b2, 0x2b2, 0x6b2, 0x1b2, 0x5b2, 0x3b2, 0x7b2, 0x72, 0x472, 0x272, 0x672,
0x172, 0x572, 0x372, 0x772, 0xf2, 0x4f2, 0x2f2, 0x6f2, 0x1f2, 0x5f2, 0x3f2,
0x7f2, 0xa, 0x40a, 0x20a, 0x60a, 0x10a, 0x50a, 0x30a, 0x70a, 0x8a, 0x48a,
0x28a, 0x68a, 0x18a, 0x58a, 0x38a, 0x78a, 0x4a, 0x44a, 0x24a, 0x64a, 0x14a,
0x54a, 0x34a, 0x74a, 0xca, 0x4ca, 0x2ca, 0x6ca, 0x1ca, 0x5ca, 0x3ca, 0x7ca,
0x2a, 0x42a, 0x22a, 0x62a, 0x12a, 0x52a, 0x32a, 0x72a, 0xaa, 0x4aa, 0x2aa,
0x6aa, 0x1aa, 0x5aa, 0x3aa, 0x7aa, 0x6a, 0x46a, 0x26a, 0x66a, 0x16a, 0x56a,
0x36a, 0x76a, 0xea, 0x4ea, 0x2ea, 0x6ea, 0x1ea, 0x5ea, 0x3ea, 0x7ea, 0x1a,
0x41a, 0x21a, 0x61a, 0x11a, 0x51a, 0x31a, 0x71a, 0x9a, 0x49a, 0x29a, 0x69a,
0x19a, 0x59a, 0x39a, 0x79a, 0x5a, 0x45a, 0x25a, 0x65a, 0x15a, 0x55a, 0x35a,
0x75a, 0xda, 0x4da, 0x2da, 0x6da, 0x1da, 0x5da, 0x3da, 0x7da, 0x3a, 0x43a,
0x23a, 0x63a, 0x13a, 0x53a, 0x33a, 0x73a, 0xba, 0x4ba, 0x2ba, 0x6ba, 0x1ba,
0x5ba, 0x3ba, 0x7ba, 0x7a, 0x47a, 0x27a, 0x67a, 0x17a, 0x57a, 0x37a, 0x77a,
0xfa, 0x4fa, 0x2fa, 0x6fa, 0x1fa, 0x5fa, 0x3fa, 0x7fa, 0x6, 0x406, 0x206,
0x606, 0x106, 0x506, 0x306, 0x706, 0x86, 0x486, 0x286, 0x686, 0x186, 0x586,
0x386, 0x786, 0x46, 0x446, 0x246, 0x646, 0x146, 0x546, 0x346, 0x746, 0xc6,
0x4c6, 0x2c6, 0x6c6, 0x1c6, 0x5c6, 0x3c6, 0x7c6, 0x26, 0x426, 0x226, 0x626,
0x126, 0x526, 0x326, 0x726, 0xa6, 0x4a6, 0x2a6, 0x6a6, 0x1a6, 0x5a6, 0x3a6,
0x7a6, 0x66, 0x466, 0x266, 0x666, 0x166, 0x566, 0x366, 0x766, 0xe6, 0x4e6,
0x2e6, 0x6e6, 0x1e6, 0x5e6, 0x3e6, 0x7e6, 0x16, 0x416, 0x216, 0x616, 0x116,
0x516, 0x316, 0x716, 0x96, 0x496, 0x296, 0x696, 0x196, 0x596, 0x396, 0x796,
0x56, 0x456, 0x256, 0x656, 0x156, 0x556, 0x356, 0x756, 0xd6, 0x4d6, 0x2d6,
0x6d6, 0x1d6, 0x5d6, 0x3d6, 0x7d6, 0x36, 0x436, 0x236, 0x636, 0x136, 0x536,
0x336, 0x736, 0xb6, 0x4b6, 0x2b6, 0x6b6, 0x1b6, 0x5b6, 0x3b6, 0x7b6, 0x76,
0x476, 0x276, 0x676, 0x176, 0x576, 0x376, 0x776, 0xf6, 0x4f6, 0x2f6, 0x6f6,
0x1f6, 0x5f6, 0x3f6, 0x7f6, 0xe, 0x40e, 0x20e, 0x60e, 0x10e, 0x50e, 0x30e,
0x70e, 0x8e, 0x48e, 0x28e, 0x68e, 0x18e, 0x58e, 0x38e, 0x78e, 0x4e, 0x44e,
0x24e, 0x64e, 0x14e, 0x54e, 0x34e, 0x74e, 0xce, 0x4ce, 0x2ce, 0x6ce, 0x1ce,
0x5ce, 0x3ce, 0x7ce, 0x2e, 0x42e, 0x22e, 0x62e, 0x12e, 0x52e, 0x32e, 0x72e,
0xae, 0x4ae, 0x2ae, 0x6ae, 0x1ae, 0x5ae, 0x3ae, 0x7ae, 0x6e, 0x46e, 0x26e,
0x66e, 0x16e, 0x56e, 0x36e, 0x76e, 0xee, 0x4ee, 0x2ee, 0x6ee, 0x1ee, 0x5ee,
0x3ee, 0x7ee, 0x1e, 0x41e, 0x21e, 0x61e, 0x11e, 0x51e, 0x31e, 0x71e, 0x9e,
0x49e, 0x29e, 0x69e, 0x19e, 0x59e, 0x39e, 0x79e, 0x5e, 0x45e, 0x25e, 0x65e,
0x15e, 0x55e, 0x35e, 0x75e, 0xde, 0x4de, 0x2de, 0x6de, 0x1de, 0x5de, 0x3de,
0x7de, 0x3e, 0x43e, 0x23e, 0x63e, 0x13e, 0x53e, 0x33e, 0x73e, 0xbe, 0x4be,
0x2be, 0x6be, 0x1be, 0x5be, 0x3be, 0x7be, 0x7e, 0x47e, 0x27e, 0x67e, 0x17e,
0x57e, 0x37e, 0x77e, 0xfe, 0x4fe, 0x2fe, 0x6fe, 0x1fe, 0x5fe, 0x3fe, 0x7fe,
0x1};
/*
* @brief Floating-point Twiddle factors Table Generation
*/
/**
* \par
* Example code for Floating-point Twiddle factors Generation:
* \par
* <pre>for(i = 0; i< 3N/4; i++)
* {
* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
* } </pre>
* \par
* where N = 4096 and PI = 3.14159265358979
* \par
* Cos and Sin values are in interleaved fashion
*
*/
const float32_t twiddleCoef[6144] = {
1.000000000000000000f, 0.000000000000000000f, 0.999998823451701880f,
0.001533980186284766f, 0.999995293809576190f, 0.003067956762965976f,
0.999989411081928400f, 0.004601926120448571f, 0.999981175282601110f,
0.006135884649154475f, 0.999970586430974140f, 0.007669828739531097f,
0.999957644551963900f, 0.009203754782059819f, 0.999942349676023910f,
0.010737659167264491f, 0.999924701839144500f, 0.012271538285719925f,
0.999904701082852900f, 0.013805388528060391f, 0.999882347454212560f,
0.015339206284988100f, 0.999857641005823860f, 0.016872987947281710f,
0.999830581795823400f, 0.018406729905804820f, 0.999801169887884260f,
0.019940428551514441f, 0.999769405351215280f, 0.021474080275469508f,
0.999735288260561680f, 0.023007681468839369f, 0.999698818696204250f,
0.024541228522912288f, 0.999659996743959220f, 0.026074717829103901f,
0.999618822495178640f, 0.027608145778965740f, 0.999575296046749220f,
0.029141508764193722f, 0.999529417501093140f, 0.030674803176636626f,
0.999481186966166950f, 0.032208025408304586f, 0.999430604555461730f,
0.033741171851377580f, 0.999377670388002850f, 0.035274238898213947f,
0.999322384588349540f, 0.036807222941358832f, 0.999264747286594420f,
0.038340120373552694f, 0.999204758618363890f, 0.039872927587739811f,
0.999142418724816910f, 0.041405640977076739f, 0.999077727752645360f,
0.042938256934940820f, 0.999010685854073380f, 0.044470771854938668f,
0.998941293186856870f, 0.046003182130914623f, 0.998869549914283560f,
0.047535484156959303f, 0.998795456205172410f, 0.049067674327418015f,
0.998719012233872940f, 0.050599749036899282f, 0.998640218180265270f,
0.052131704680283324f, 0.998559074229759310f, 0.053663537652730520f,
0.998475580573294770f, 0.055195244349689934f, 0.998389737407340160f,
0.056726821166907748f, 0.998301544933892890f, 0.058258264500435752f,
0.998211003360478190f, 0.059789570746639868f, 0.998118112900149180f,
0.061320736302208578f, 0.998022873771486240f, 0.062851757564161406f,
0.997925286198596000f, 0.064382630929857465f, 0.997825350411111640f,
0.065913352797003805f, 0.997723066644191640f, 0.067443919563664051f,
0.997618435138519550f, 0.068974327628266746f, 0.997511456140303450f,
0.070504573389613856f, 0.997402129901275300f, 0.072034653246889332f,
0.997290456678690210f, 0.073564563599667426f, 0.997176436735326190f,
0.075094300847921305f, 0.997060070339482960f, 0.076623861392031492f,
0.996941357764982160f, 0.078153241632794232f, 0.996820299291165670f,
0.079682437971430126f, 0.996696895202896060f, 0.081211446809592441f,
0.996571145790554840f, 0.082740264549375692f, 0.996443051350042630f,
0.084268887593324071f, 0.996312612182778000f, 0.085797312344439894f,
0.996179828595696980f, 0.087325535206192059f, 0.996044700901251970f,
0.088853552582524600f, 0.995907229417411720f, 0.090381360877864983f,
0.995767414467659820f, 0.091908956497132724f, 0.995625256380994310f,
0.093436335845747787f, 0.995480755491926940f, 0.094963495329638992f,
0.995333912140482280f, 0.096490431355252593f, 0.995184726672196930f,
0.098017140329560604f, 0.995033199438118630f, 0.099543618660069319f,
0.994879330794805620f, 0.101069862754827820f, 0.994723121104325700f,
0.102595869022436280f, 0.994564570734255420f, 0.104121633872054590f,
0.994403680057679100f, 0.105647153713410620f, 0.994240449453187900f,
0.107172424956808840f, 0.994074879304879370f, 0.108697444013138720f,
0.993906970002356060f, 0.110222207293883060f, 0.993736721940724600f,
0.111746711211126590f, 0.993564135520595300f, 0.113270952177564350f,
0.993389211148080650f, 0.114794926606510080f, 0.993211949234794500f,
0.116318630911904750f, 0.993032350197851410f, 0.117842061508324980f,
0.992850414459865100f, 0.119365214810991350f, 0.992666142448948020f,
0.120888087235777080f, 0.992479534598709970f, 0.122410675199216200f,
0.992290591348257370f, 0.123932975118512160f, 0.992099313142191800f,
0.125454983411546230f, 0.991905700430609330f, 0.126976696496885870f,
0.991709753669099530f, 0.128498110793793170f, 0.991511473318743900f,
0.130019222722233350f, 0.991310859846115440f, 0.131540028702883120f,
0.991107913723276890f, 0.133060525157139060f, 0.990902635427780010f,
0.134580708507126170f, 0.990695025442664630f, 0.136100575175706200f,
0.990485084256457090f, 0.137620121586486040f, 0.990272812363169110f,
0.139139344163826200f, 0.990058210262297120f, 0.140658239332849210f,
0.989841278458820530f, 0.142176803519448030f, 0.989622017463200890f,
0.143695033150294470f, 0.989400427791380380f, 0.145212924652847460f,
0.989176509964781010f, 0.146730474455361750f, 0.988950264510302990f,
0.148247678986896030f, 0.988721691960323780f, 0.149764534677321510f,
0.988490792852696590f, 0.151281037957330220f, 0.988257567730749460f,
0.152797185258443440f, 0.988022017143283530f, 0.154312973013020100f,
0.987784141644572180f, 0.155828397654265230f, 0.987543941794359230f,
0.157343455616238250f, 0.987301418157858430f, 0.158858143333861450f,
0.987056571305750970f, 0.160372457242928280f, 0.986809401814185530f,
0.161886393780111830f, 0.986559910264775410f, 0.163399949382973230f,
0.986308097244598670f, 0.164913120489969890f, 0.986053963346195440f,
0.166425903540464100f, 0.985797509167567480f, 0.167938294974731170f,
0.985538735312176060f, 0.169450291233967960f, 0.985277642388941220f,
0.170961888760301220f, 0.985014231012239840f, 0.172473083996795950f,
0.984748501801904210f, 0.173983873387463820f, 0.984480455383220930f,
0.175494253377271430f, 0.984210092386929030f, 0.177004220412148750f,
0.983937413449218920f, 0.178513770938997510f, 0.983662419211730250f,
0.180022901405699510f, 0.983385110321551180f, 0.181531608261124970f,
0.983105487431216290f, 0.183039887955140950f, 0.982823551198705240f,
0.184547736938619620f, 0.982539302287441240f, 0.186055151663446630f,
0.982252741366289370f, 0.187562128582529600f, 0.981963869109555240f,
0.189068664149806190f, 0.981672686196983110f, 0.190574754820252740f,
0.981379193313754560f, 0.192080397049892440f, 0.981083391150486710f,
0.193585587295803610f, 0.980785280403230430f, 0.195090322016128250f,
0.980484861773469380f, 0.196594597670080220f, 0.980182135968117430f,
0.198098410717953560f, 0.979877103699517640f, 0.199601757621130970f,
0.979569765685440520f, 0.201104634842091900f, 0.979260122649082020f,
0.202607038844421130f, 0.978948175319062200f, 0.204108966092816870f,
0.978633924429423210f, 0.205610413053099240f, 0.978317370719627650f,
0.207111376192218560f, 0.977998514934557140f, 0.208611851978263490f,
0.977677357824509930f, 0.210111836880469610f, 0.977353900145199960f,
0.211611327369227550f, 0.977028142657754390f, 0.213110319916091360f,
0.976700086128711840f, 0.214608810993786760f, 0.976369731330021140f,
0.216106797076219520f, 0.976037079039039020f, 0.217604274638483640f,
0.975702130038528570f, 0.219101240156869800f, 0.975364885116656980f,
0.220597690108873510f, 0.975025345066994120f, 0.222093620973203510f,
0.974683510688510670f, 0.223589029229789990f, 0.974339382785575860f,
0.225083911359792830f, 0.973992962167955830f, 0.226578263845610000f,
0.973644249650811980f, 0.228072083170885730f, 0.973293246054698250f,
0.229565365820518870f, 0.972939952205560180f, 0.231058108280671110f,
0.972584368934732210f, 0.232550307038775240f, 0.972226497078936270f,
0.234041958583543430f, 0.971866337480279400f, 0.235533059404975490f,
0.971503890986251780f, 0.237023605994367200f, 0.971139158449725090f,
0.238513594844318420f, 0.970772140728950350f, 0.240003022448741500f,
0.970402838687555500f, 0.241491885302869330f, 0.970031253194543970f,
0.242980179903263870f, 0.969657385124292450f, 0.244467902747824150f,
0.969281235356548530f, 0.245955050335794590f, 0.968902804776428870f,
0.247441619167773270f, 0.968522094274417380f, 0.248927605745720150f,
0.968139104746362440f, 0.250413006572965220f, 0.967753837093475510f,
0.251897818154216970f, 0.967366292222328510f, 0.253382036995570160f,
0.966976471044852070f, 0.254865659604514570f, 0.966584374478333120f,
0.256348682489942910f, 0.966190003445412500f, 0.257831102162158990f,
0.965793358874083680f, 0.259312915132886230f, 0.965394441697689400f,
0.260794117915275510f, 0.964993252854920320f, 0.262274707023913590f,
0.964589793289812760f, 0.263754678974831350f, 0.964184063951745830f,
0.265234030285511790f, 0.963776065795439840f, 0.266712757474898370f,
0.963365799780954050f, 0.268190857063403180f, 0.962953266873683880f,
0.269668325572915090f, 0.962538468044359160f, 0.271145159526808010f,
0.962121404269041580f, 0.272621355449948980f, 0.961702076529122540f,
0.274096909868706380f, 0.961280485811320640f, 0.275571819310958140f,
0.960856633107679660f, 0.277046080306099900f, 0.960430519415565790f,
0.278519689385053060f, 0.960002145737665960f, 0.279992643080273220f,
0.959571513081984520f, 0.281464937925757940f, 0.959138622461841890f,
0.282936570457055390f, 0.958703474895871600f, 0.284407537211271880f,
0.958266071408017670f, 0.285877834727080620f, 0.957826413027532910f,
0.287347459544729510f, 0.957384500788975860f, 0.288816408206049480f,
0.956940335732208820f, 0.290284677254462330f, 0.956493918902395100f,
0.291752263234989260f, 0.956045251349996410f, 0.293219162694258630f,
0.955594334130771110f, 0.294685372180514330f, 0.955141168305770780f,
0.296150888243623790f, 0.954685754941338340f, 0.297615707435086200f,
0.954228095109105670f, 0.299079826308040480f, 0.953768189885990330f,
0.300543241417273450f, 0.953306040354193860f, 0.302005949319228080f,
0.952841647601198720f, 0.303467946572011320f, 0.952375012719765880f,
0.304929229735402370f, 0.951906136807932350f, 0.306389795370860920f,
0.951435020969008340f, 0.307849640041534870f, 0.950961666311575080f,
0.309308760312268730f, 0.950486073949481700f, 0.310767152749611470f,
0.950008245001843000f, 0.312224813921824880f, 0.949528180593036670f,
0.313681740398891520f, 0.949045881852700560f, 0.315137928752522440f,
0.948561349915730270f, 0.316593375556165850f, 0.948074585922276230f,
0.318048077385014950f, 0.947585591017741090f, 0.319502030816015690f,
0.947094366352777220f, 0.320955232427875210f, 0.946600913083283530f,
0.322407678801069850f, 0.946105232370403450f, 0.323859366517852850f,
0.945607325380521280f, 0.325310292162262930f, 0.945107193285260610f,
0.326760452320131730f, 0.944604837261480260f, 0.328209843579092500f,
0.944100258491272660f, 0.329658462528587490f, 0.943593458161960390f,
0.331106305759876430f, 0.943084437466093490f, 0.332553369866044220f,
0.942573197601446870f, 0.333999651442009380f, 0.942059739771017310f,
0.335445147084531600f, 0.941544065183020810f, 0.336889853392220050f,
0.941026175050889260f, 0.338333766965541130f, 0.940506070593268300f,
0.339776884406826850f, 0.939983753034014050f, 0.341219202320282360f,
0.939459223602189920f, 0.342660717311994380f, 0.938932483532064600f,
0.344101425989938810f, 0.938403534063108060f, 0.345541324963989090f,
0.937872376439989890f, 0.346980410845923680f, 0.937339011912574960f,
0.348418680249434560f, 0.936803441735921560f, 0.349856129790134920f,
0.936265667170278260f, 0.351292756085567090f, 0.935725689481080370f,
0.352728555755210730f, 0.935183509938947610f, 0.354163525420490340f,
0.934639129819680780f, 0.355597661704783850f, 0.934092550404258980f,
0.357030961233429980f, 0.933543772978836170f, 0.358463420633736540f,
0.932992798834738960f, 0.359895036534988110f, 0.932439629268462360f,
0.361325805568454280f, 0.931884265581668150f, 0.362755724367397230f,
0.931326709081180430f, 0.364184789567079890f, 0.930766961078983710f,
0.365612997804773850f, 0.930205022892219070f, 0.367040345719767180f,
0.929640895843181330f, 0.368466829953372320f, 0.929074581259315860f,
0.369892447148934100f, 0.928506080473215590f, 0.371317193951837540f,
0.927935394822617890f, 0.372741067009515760f, 0.927362525650401110f,
0.374164062971457930f, 0.926787474304581750f, 0.375586178489217220f,
0.926210242138311380f, 0.377007410216418260f, 0.925630830509872720f,
0.378427754808765560f, 0.925049240782677580f, 0.379847208924051160f,
0.924465474325262600f, 0.381265769222162380f, 0.923879532511286740f,
0.382683432365089780f, 0.923291416719527640f, 0.384100195016935040f,
0.922701128333878630f, 0.385516053843918850f, 0.922108668743345180f,
0.386931005514388580f, 0.921514039342042010f, 0.388345046698826250f,
0.920917241529189520f, 0.389758174069856410f, 0.920318276709110590f,
0.391170384302253870f, 0.919717146291227360f, 0.392581674072951470f,
0.919113851690057770f, 0.393992040061048100f, 0.918508394325212250f,
0.395401478947816350f, 0.917900775621390500f, 0.396809987416710310f,
0.917290997008377910f, 0.398217562153373560f, 0.916679059921042700f,
0.399624199845646790f, 0.916064965799331720f, 0.401029897183575620f,
0.915448716088267830f, 0.402434650859418430f, 0.914830312237946200f,
0.403838457567654070f, 0.914209755703530690f, 0.405241314004989860f,
0.913587047945250810f, 0.406643216870369030f, 0.912962190428398210f,
0.408044162864978690f, 0.912335184623322750f, 0.409444148692257590f,
0.911706032005429880f, 0.410843171057903910f, 0.911074734055176360f,
0.412241226669882890f, 0.910441292258067250f, 0.413638312238434500f,
0.909805708104652220f, 0.415034424476081630f, 0.909167983090522380f,
0.416429560097637150f, 0.908528118716306120f, 0.417823715820212270f,
0.907886116487666260f, 0.419216888363223910f, 0.907241977915295820f,
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