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/* ----------------------------------------------------------------------
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
*
* $Date: 19. March 2015
* $Revision: V.1.4.5
*
* 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
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* - Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* - Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
* - Neither the name of ARM LIMITED nor the names of its contributors
* may be used to endorse or promote products derived from this
* software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
* -------------------------------------------------------------------- */
#include "arm_math.h"
#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< N/; i++)
* {
* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
* } </pre>
* \par
* where N = 16 and PI = 3.14159265358979
* \par
* Cos and Sin values are in interleaved fashion
*
*/
const float32_t twiddleCoef_16[32] = {
1.000000000f, 0.000000000f,
0.923879533f, 0.382683432f,
0.707106781f, 0.707106781f,
0.382683432f, 0.923879533f,
0.000000000f, 1.000000000f,
-0.382683432f, 0.923879533f,
-0.707106781f, 0.707106781f,
-0.923879533f, 0.382683432f,
-1.000000000f, 0.000000000f,
-0.923879533f, -0.382683432f,
-0.707106781f, -0.707106781f,
-0.382683432f, -0.923879533f,
-0.000000000f, -1.000000000f,
0.382683432f, -0.923879533f,
0.707106781f, -0.707106781f,
0.923879533f, -0.382683432f
};
/**
* \par
* Example code for Floating-point Twiddle factors Generation:
* \par
* <pre>for(i = 0; i< N/; i++)
* {
* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
* } </pre>
* \par
* where N = 32 and PI = 3.14159265358979
* \par
* Cos and Sin values are in interleaved fashion
*
*/
const float32_t twiddleCoef_32[64] = {
1.000000000f, 0.000000000f,
0.980785280f, 0.195090322f,
0.923879533f, 0.382683432f,
0.831469612f, 0.555570233f,
0.707106781f, 0.707106781f,
0.555570233f, 0.831469612f,
0.382683432f, 0.923879533f,
0.195090322f, 0.980785280f,
0.000000000f, 1.000000000f,
-0.195090322f, 0.980785280f,
-0.382683432f, 0.923879533f,
-0.555570233f, 0.831469612f,
-0.707106781f, 0.707106781f,
-0.831469612f, 0.555570233f,
-0.923879533f, 0.382683432f,
-0.980785280f, 0.195090322f,
-1.000000000f, 0.000000000f,
-0.980785280f, -0.195090322f,
-0.923879533f, -0.382683432f,
-0.831469612f, -0.555570233f,
-0.707106781f, -0.707106781f,
-0.555570233f, -0.831469612f,
-0.382683432f, -0.923879533f,
-0.195090322f, -0.980785280f,
-0.000000000f, -1.000000000f,
0.195090322f, -0.980785280f,
0.382683432f, -0.923879533f,
0.555570233f, -0.831469612f,
0.707106781f, -0.707106781f,
0.831469612f, -0.555570233f,
0.923879533f, -0.382683432f,
0.980785280f, -0.195090322f
};
/**
* \par
* Example code for Floating-point Twiddle factors Generation:
* \par
* <pre>for(i = 0; i< N/; i++)
* {
* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
* } </pre>
* \par
* where N = 64 and PI = 3.14159265358979
* \par
* Cos and Sin values are in interleaved fashion
*
*/
const float32_t twiddleCoef_64[128] = {
1.000000000f, 0.000000000f,
0.995184727f, 0.098017140f,
0.980785280f, 0.195090322f,
0.956940336f, 0.290284677f,
0.923879533f, 0.382683432f,
0.881921264f, 0.471396737f,
0.831469612f, 0.555570233f,
0.773010453f, 0.634393284f,
0.707106781f, 0.707106781f,
0.634393284f, 0.773010453f,
0.555570233f, 0.831469612f,
0.471396737f, 0.881921264f,
0.382683432f, 0.923879533f,
0.290284677f, 0.956940336f,
0.195090322f, 0.980785280f,
0.098017140f, 0.995184727f,
0.000000000f, 1.000000000f,
-0.098017140f, 0.995184727f,
-0.195090322f, 0.980785280f,
-0.290284677f, 0.956940336f,
-0.382683432f, 0.923879533f,
-0.471396737f, 0.881921264f,
-0.555570233f, 0.831469612f,
-0.634393284f, 0.773010453f,
-0.707106781f, 0.707106781f,
-0.773010453f, 0.634393284f,
-0.831469612f, 0.555570233f,
-0.881921264f, 0.471396737f,
-0.923879533f, 0.382683432f,
-0.956940336f, 0.290284677f,
-0.980785280f, 0.195090322f,
-0.995184727f, 0.098017140f,
-1.000000000f, 0.000000000f,
-0.995184727f, -0.098017140f,
-0.980785280f, -0.195090322f,
-0.956940336f, -0.290284677f,
-0.923879533f, -0.382683432f,
-0.881921264f, -0.471396737f,
-0.831469612f, -0.555570233f,
-0.773010453f, -0.634393284f,
-0.707106781f, -0.707106781f,
-0.634393284f, -0.773010453f,
-0.555570233f, -0.831469612f,
-0.471396737f, -0.881921264f,
-0.382683432f, -0.923879533f,
-0.290284677f, -0.956940336f,
-0.195090322f, -0.980785280f,
-0.098017140f, -0.995184727f,
-0.000000000f, -1.000000000f,
0.098017140f, -0.995184727f,
0.195090322f, -0.980785280f,
0.290284677f, -0.956940336f,
0.382683432f, -0.923879533f,
0.471396737f, -0.881921264f,
0.555570233f, -0.831469612f,
0.634393284f, -0.773010453f,
0.707106781f, -0.707106781f,
0.773010453f, -0.634393284f,
0.831469612f, -0.555570233f,
0.881921264f, -0.471396737f,
0.923879533f, -0.382683432f,
0.956940336f, -0.290284677f,
0.980785280f, -0.195090322f,
0.995184727f, -0.098017140f
};
/**
* \par
* Example code for Floating-point Twiddle factors Generation:
* \par
* <pre>for(i = 0; i< N/; i++)
* {
* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
* } </pre>
* \par
* where N = 128 and PI = 3.14159265358979
* \par
* Cos and Sin values are in interleaved fashion
*
*/
const float32_t twiddleCoef_128[256] = {
1.000000000f , 0.000000000f ,
0.998795456f , 0.049067674f ,
0.995184727f , 0.098017140f ,
0.989176510f , 0.146730474f ,
0.980785280f , 0.195090322f ,
0.970031253f , 0.242980180f ,
0.956940336f , 0.290284677f ,
0.941544065f , 0.336889853f ,
0.923879533f , 0.382683432f ,
0.903989293f , 0.427555093f ,
0.881921264f , 0.471396737f ,
0.857728610f , 0.514102744f ,
0.831469612f , 0.555570233f ,
0.803207531f , 0.595699304f ,
0.773010453f , 0.634393284f ,
0.740951125f , 0.671558955f ,
0.707106781f , 0.707106781f ,
0.671558955f , 0.740951125f ,
0.634393284f , 0.773010453f ,
0.595699304f , 0.803207531f ,
0.555570233f , 0.831469612f ,
0.514102744f , 0.857728610f ,
0.471396737f , 0.881921264f ,
0.427555093f , 0.903989293f ,
0.382683432f , 0.923879533f ,
0.336889853f , 0.941544065f ,
0.290284677f , 0.956940336f ,
0.242980180f , 0.970031253f ,
0.195090322f , 0.980785280f ,
0.146730474f , 0.989176510f ,
0.098017140f , 0.995184727f ,
0.049067674f , 0.998795456f ,
0.000000000f , 1.000000000f ,
-0.049067674f , 0.998795456f ,
-0.098017140f , 0.995184727f ,
-0.146730474f , 0.989176510f ,
-0.195090322f , 0.980785280f ,
-0.242980180f , 0.970031253f ,
-0.290284677f , 0.956940336f ,
-0.336889853f , 0.941544065f ,
-0.382683432f , 0.923879533f ,
-0.427555093f , 0.903989293f ,
-0.471396737f , 0.881921264f ,
-0.514102744f , 0.857728610f ,
-0.555570233f , 0.831469612f ,
-0.595699304f , 0.803207531f ,
-0.634393284f , 0.773010453f ,
-0.671558955f , 0.740951125f ,
-0.707106781f , 0.707106781f ,
-0.740951125f , 0.671558955f ,
-0.773010453f , 0.634393284f ,
-0.803207531f , 0.595699304f ,
-0.831469612f , 0.555570233f ,
-0.857728610f , 0.514102744f ,
-0.881921264f , 0.471396737f ,
-0.903989293f , 0.427555093f ,
-0.923879533f , 0.382683432f ,
-0.941544065f , 0.336889853f ,
-0.956940336f , 0.290284677f ,
-0.970031253f , 0.242980180f ,
-0.980785280f , 0.195090322f ,
-0.989176510f , 0.146730474f ,
-0.995184727f , 0.098017140f ,
-0.998795456f , 0.049067674f ,
-1.000000000f , 0.000000000f ,
-0.998795456f , -0.049067674f ,
-0.995184727f , -0.098017140f ,
-0.989176510f , -0.146730474f ,
-0.980785280f , -0.195090322f ,
-0.970031253f , -0.242980180f ,
-0.956940336f , -0.290284677f ,
-0.941544065f , -0.336889853f ,
-0.923879533f , -0.382683432f ,
-0.903989293f , -0.427555093f ,
-0.881921264f , -0.471396737f ,
-0.857728610f , -0.514102744f ,
-0.831469612f , -0.555570233f ,
-0.803207531f , -0.595699304f ,
-0.773010453f , -0.634393284f ,
-0.740951125f , -0.671558955f ,
-0.707106781f , -0.707106781f ,
-0.671558955f , -0.740951125f ,
-0.634393284f , -0.773010453f ,
-0.595699304f , -0.803207531f ,
-0.555570233f , -0.831469612f ,
-0.514102744f , -0.857728610f ,
-0.471396737f , -0.881921264f ,
-0.427555093f , -0.903989293f ,
-0.382683432f , -0.923879533f ,
-0.336889853f , -0.941544065f ,
-0.290284677f , -0.956940336f ,
-0.242980180f , -0.970031253f ,
-0.195090322f , -0.980785280f ,
-0.146730474f , -0.989176510f ,
-0.098017140f , -0.995184727f ,
-0.049067674f , -0.998795456f ,
-0.000000000f , -1.000000000f ,
0.049067674f , -0.998795456f ,
0.098017140f , -0.995184727f ,
0.146730474f , -0.989176510f ,
0.195090322f , -0.980785280f ,
0.242980180f , -0.970031253f ,
0.290284677f , -0.956940336f ,
0.336889853f , -0.941544065f ,
0.382683432f , -0.923879533f ,
0.427555093f , -0.903989293f ,
0.471396737f , -0.881921264f ,
0.514102744f , -0.857728610f ,
0.555570233f , -0.831469612f ,
0.595699304f , -0.803207531f ,
0.634393284f , -0.773010453f ,
0.671558955f , -0.740951125f ,
0.707106781f , -0.707106781f ,
0.740951125f , -0.671558955f ,
0.773010453f , -0.634393284f ,
0.803207531f , -0.595699304f ,
0.831469612f , -0.555570233f ,
0.857728610f , -0.514102744f ,
0.881921264f , -0.471396737f ,
0.903989293f , -0.427555093f ,
0.923879533f , -0.382683432f ,
0.941544065f , -0.336889853f ,
0.956940336f , -0.290284677f ,
0.970031253f , -0.242980180f ,
0.980785280f , -0.195090322f ,
0.989176510f , -0.146730474f ,
0.995184727f , -0.098017140f ,
0.998795456f , -0.049067674f
};
/**
* \par
* Example code for Floating-point Twiddle factors Generation:
* \par
* <pre>for(i = 0; i< N/; i++)
* {
* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
* } </pre>
* \par
* where N = 256 and PI = 3.14159265358979
* \par
* Cos and Sin values are in interleaved fashion
*
*/
const float32_t twiddleCoef_256[512] = {
1.000000000f, 0.000000000f,
0.999698819f, 0.024541229f,
0.998795456f, 0.049067674f,
0.997290457f, 0.073564564f,
0.995184727f, 0.098017140f,
0.992479535f, 0.122410675f,
0.989176510f, 0.146730474f,
0.985277642f, 0.170961889f,
0.980785280f, 0.195090322f,
0.975702130f, 0.219101240f,
0.970031253f, 0.242980180f,
0.963776066f, 0.266712757f,
0.956940336f, 0.290284677f,
0.949528181f, 0.313681740f,
0.941544065f, 0.336889853f,
0.932992799f, 0.359895037f,
0.923879533f, 0.382683432f,
0.914209756f, 0.405241314f,
0.903989293f, 0.427555093f,
0.893224301f, 0.449611330f,
0.881921264f, 0.471396737f,
0.870086991f, 0.492898192f,
0.857728610f, 0.514102744f,
0.844853565f, 0.534997620f,
0.831469612f, 0.555570233f,
0.817584813f, 0.575808191f,
0.803207531f, 0.595699304f,
0.788346428f, 0.615231591f,
0.773010453f, 0.634393284f,
0.757208847f, 0.653172843f,
0.740951125f, 0.671558955f,
0.724247083f, 0.689540545f,
0.707106781f, 0.707106781f,
0.689540545f, 0.724247083f,
0.671558955f, 0.740951125f,
0.653172843f, 0.757208847f,
0.634393284f, 0.773010453f,
0.615231591f, 0.788346428f,
0.595699304f, 0.803207531f,
0.575808191f, 0.817584813f,
0.555570233f, 0.831469612f,
0.534997620f, 0.844853565f,
0.514102744f, 0.857728610f,
0.492898192f, 0.870086991f,
0.471396737f, 0.881921264f,
0.449611330f, 0.893224301f,
0.427555093f, 0.903989293f,
0.405241314f, 0.914209756f,
0.382683432f, 0.923879533f,
0.359895037f, 0.932992799f,
0.336889853f, 0.941544065f,
0.313681740f, 0.949528181f,
0.290284677f, 0.956940336f,
0.266712757f, 0.963776066f,
0.242980180f, 0.970031253f,
0.219101240f, 0.975702130f,
0.195090322f, 0.980785280f,
0.170961889f, 0.985277642f,
0.146730474f, 0.989176510f,
0.122410675f, 0.992479535f,
0.098017140f, 0.995184727f,
0.073564564f, 0.997290457f,
0.049067674f, 0.998795456f,
0.024541229f, 0.999698819f,
0.000000000f, 1.000000000f,
-0.024541229f, 0.999698819f,
-0.049067674f, 0.998795456f,
-0.073564564f, 0.997290457f,
-0.098017140f, 0.995184727f,
-0.122410675f, 0.992479535f,
-0.146730474f, 0.989176510f,
-0.170961889f, 0.985277642f,
-0.195090322f, 0.980785280f,
-0.219101240f, 0.975702130f,
-0.242980180f, 0.970031253f,
-0.266712757f, 0.963776066f,
-0.290284677f, 0.956940336f,
-0.313681740f, 0.949528181f,
-0.336889853f, 0.941544065f,
-0.359895037f, 0.932992799f,
-0.382683432f, 0.923879533f,
-0.405241314f, 0.914209756f,
-0.427555093f, 0.903989293f,
-0.449611330f, 0.893224301f,
-0.471396737f, 0.881921264f,
-0.492898192f, 0.870086991f,
-0.514102744f, 0.857728610f,
-0.534997620f, 0.844853565f,
-0.555570233f, 0.831469612f,
-0.575808191f, 0.817584813f,
-0.595699304f, 0.803207531f,
-0.615231591f, 0.788346428f,
-0.634393284f, 0.773010453f,
-0.653172843f, 0.757208847f,
-0.671558955f, 0.740951125f,
-0.689540545f, 0.724247083f,
-0.707106781f, 0.707106781f,
-0.724247083f, 0.689540545f,
-0.740951125f, 0.671558955f,
-0.757208847f, 0.653172843f,
-0.773010453f, 0.634393284f,
-0.788346428f, 0.615231591f,
-0.803207531f, 0.595699304f,
-0.817584813f, 0.575808191f,
-0.831469612f, 0.555570233f,
-0.844853565f, 0.534997620f,
-0.857728610f, 0.514102744f,
-0.870086991f, 0.492898192f,
-0.881921264f, 0.471396737f,
-0.893224301f, 0.449611330f,
-0.903989293f, 0.427555093f,
-0.914209756f, 0.405241314f,
-0.923879533f, 0.382683432f,
-0.932992799f, 0.359895037f,
-0.941544065f, 0.336889853f,
-0.949528181f, 0.313681740f,
-0.956940336f, 0.290284677f,
-0.963776066f, 0.266712757f,
-0.970031253f, 0.242980180f,
-0.975702130f, 0.219101240f,
-0.980785280f, 0.195090322f,
-0.985277642f, 0.170961889f,
-0.989176510f, 0.146730474f,
-0.992479535f, 0.122410675f,
-0.995184727f, 0.098017140f,
-0.997290457f, 0.073564564f,
-0.998795456f, 0.049067674f,
-0.999698819f, 0.024541229f,
-1.000000000f, 0.000000000f,
-0.999698819f, -0.024541229f,
-0.998795456f, -0.049067674f,
-0.997290457f, -0.073564564f,
-0.995184727f, -0.098017140f,
-0.992479535f, -0.122410675f,
-0.989176510f, -0.146730474f,
-0.985277642f, -0.170961889f,
-0.980785280f, -0.195090322f,
-0.975702130f, -0.219101240f,
-0.970031253f, -0.242980180f,
-0.963776066f, -0.266712757f,
-0.956940336f, -0.290284677f,
-0.949528181f, -0.313681740f,
-0.941544065f, -0.336889853f,
-0.932992799f, -0.359895037f,
-0.923879533f, -0.382683432f,
-0.914209756f, -0.405241314f,
-0.903989293f, -0.427555093f,
-0.893224301f, -0.449611330f,
-0.881921264f, -0.471396737f,
-0.870086991f, -0.492898192f,
-0.857728610f, -0.514102744f,
-0.844853565f, -0.534997620f,
-0.831469612f, -0.555570233f,
-0.817584813f, -0.575808191f,
-0.803207531f, -0.595699304f,
-0.788346428f, -0.615231591f,
-0.773010453f, -0.634393284f,
-0.757208847f, -0.653172843f,
-0.740951125f, -0.671558955f,
-0.724247083f, -0.689540545f,
-0.707106781f, -0.707106781f,
-0.689540545f, -0.724247083f,
-0.671558955f, -0.740951125f,
-0.653172843f, -0.757208847f,
-0.634393284f, -0.773010453f,
-0.615231591f, -0.788346428f,
-0.595699304f, -0.803207531f,
-0.575808191f, -0.817584813f,
-0.555570233f, -0.831469612f,
-0.534997620f, -0.844853565f,
-0.514102744f, -0.857728610f,
-0.492898192f, -0.870086991f,
-0.471396737f, -0.881921264f,
-0.449611330f, -0.893224301f,
-0.427555093f, -0.903989293f,
-0.405241314f, -0.914209756f,
-0.382683432f, -0.923879533f,
-0.359895037f, -0.932992799f,
-0.336889853f, -0.941544065f,
-0.313681740f, -0.949528181f,
-0.290284677f, -0.956940336f,
-0.266712757f, -0.963776066f,
-0.242980180f, -0.970031253f,
-0.219101240f, -0.975702130f,
-0.195090322f, -0.980785280f,
-0.170961889f, -0.985277642f,
-0.146730474f, -0.989176510f,
-0.122410675f, -0.992479535f,
-0.098017140f, -0.995184727f,
-0.073564564f, -0.997290457f,
-0.049067674f, -0.998795456f,
-0.024541229f, -0.999698819f,
-0.000000000f, -1.000000000f,
0.024541229f, -0.999698819f,
0.049067674f, -0.998795456f,
0.073564564f, -0.997290457f,
0.098017140f, -0.995184727f,
0.122410675f, -0.992479535f,
0.146730474f, -0.989176510f,
0.170961889f, -0.985277642f,
0.195090322f, -0.980785280f,
0.219101240f, -0.975702130f,
0.242980180f, -0.970031253f,
0.266712757f, -0.963776066f,
0.290284677f, -0.956940336f,
0.313681740f, -0.949528181f,
0.336889853f, -0.941544065f,
0.359895037f, -0.932992799f,
0.382683432f, -0.923879533f,
0.405241314f, -0.914209756f,
0.427555093f, -0.903989293f,
0.449611330f, -0.893224301f,
0.471396737f, -0.881921264f,
0.492898192f, -0.870086991f,
0.514102744f, -0.857728610f,
0.534997620f, -0.844853565f,
0.555570233f, -0.831469612f,
0.575808191f, -0.817584813f,
0.595699304f, -0.803207531f,
0.615231591f, -0.788346428f,
0.634393284f, -0.773010453f,
0.653172843f, -0.757208847f,
0.671558955f, -0.740951125f,
0.689540545f, -0.724247083f,
0.707106781f, -0.707106781f,
0.724247083f, -0.689540545f,
0.740951125f, -0.671558955f,
0.757208847f, -0.653172843f,
0.773010453f, -0.634393284f,
0.788346428f, -0.615231591f,
0.803207531f, -0.595699304f,
0.817584813f, -0.575808191f,
0.831469612f, -0.555570233f,
0.844853565f, -0.534997620f,
0.857728610f, -0.514102744f,
0.870086991f, -0.492898192f,
0.881921264f, -0.471396737f,
0.893224301f, -0.449611330f,
0.903989293f, -0.427555093f,
0.914209756f, -0.405241314f,
0.923879533f, -0.382683432f,
0.932992799f, -0.359895037f,
0.941544065f, -0.336889853f,
0.949528181f, -0.313681740f,
0.956940336f, -0.290284677f,
0.963776066f, -0.266712757f,
0.970031253f, -0.242980180f,
0.975702130f, -0.219101240f,
0.980785280f, -0.195090322f,
0.985277642f, -0.170961889f,
0.989176510f, -0.146730474f,
0.992479535f, -0.122410675f,
0.995184727f, -0.098017140f,
0.997290457f, -0.073564564f,
0.998795456f, -0.049067674f,
0.999698819f, -0.024541229f
};
/**
* \par
* Example code for Floating-point Twiddle factors Generation:
* \par
* <pre>for(i = 0; i< N/; i++)
* {
* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
* } </pre>
* \par
* where N = 512 and PI = 3.14159265358979
* \par
* Cos and Sin values are in interleaved fashion
*
*/
const float32_t twiddleCoef_512[1024] = {
1.000000000f, 0.000000000f,
0.999924702f, 0.012271538f,
0.999698819f, 0.024541229f,
0.999322385f, 0.036807223f,
0.998795456f, 0.049067674f,
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0.624859488f, -0.780737229f,
0.634393284f, -0.773010453f,
0.643831543f, -0.765167266f,
0.653172843f, -0.757208847f,
0.662415778f, -0.749136395f,
0.671558955f, -0.740951125f,
0.680600998f, -0.732654272f,
0.689540545f, -0.724247083f,
0.698376249f, -0.715730825f,
0.707106781f, -0.707106781f,
0.715730825f, -0.698376249f,
0.724247083f, -0.689540545f,
0.732654272f, -0.680600998f,
0.740951125f, -0.671558955f,
0.749136395f, -0.662415778f,
0.757208847f, -0.653172843f,
0.765167266f, -0.643831543f,
0.773010453f, -0.634393284f,
0.780737229f, -0.624859488f,
0.788346428f, -0.615231591f,
0.795836905f, -0.605511041f,
0.803207531f, -0.595699304f,
0.810457198f, -0.585797857f,
0.817584813f, -0.575808191f,
0.824589303f, -0.565731811f,
0.831469612f, -0.555570233f,
0.838224706f, -0.545324988f,
0.844853565f, -0.534997620f,
0.851355193f, -0.524589683f,
0.857728610f, -0.514102744f,
0.863972856f, -0.503538384f,
0.870086991f, -0.492898192f,
0.876070094f, -0.482183772f,
0.881921264f, -0.471396737f,
0.887639620f, -0.460538711f,
0.893224301f, -0.449611330f,
0.898674466f, -0.438616239f,
0.903989293f, -0.427555093f,
0.909167983f, -0.416429560f,
0.914209756f, -0.405241314f,
0.919113852f, -0.393992040f,
0.923879533f, -0.382683432f,
0.928506080f, -0.371317194f,
0.932992799f, -0.359895037f,
0.937339012f, -0.348418680f,
0.941544065f, -0.336889853f,
0.945607325f, -0.325310292f,
0.949528181f, -0.313681740f,
0.953306040f, -0.302005949f,
0.956940336f, -0.290284677f,
0.960430519f, -0.278519689f,
0.963776066f, -0.266712757f,
0.966976471f, -0.254865660f,
0.970031253f, -0.242980180f,
0.972939952f, -0.231058108f,
0.975702130f, -0.219101240f,
0.978317371f, -0.207111376f,
0.980785280f, -0.195090322f,
0.983105487f, -0.183039888f,
0.985277642f, -0.170961889f,
0.987301418f, -0.158858143f,
0.989176510f, -0.146730474f,
0.990902635f, -0.134580709f,
0.992479535f, -0.122410675f,
0.993906970f, -0.110222207f,
0.995184727f, -0.098017140f,
0.996312612f, -0.085797312f,
0.997290457f, -0.073564564f,
0.998118113f, -0.061320736f,
0.998795456f, -0.049067674f,
0.999322385f, -0.036807223f,
0.999698819f, -0.024541229f,
0.999924702f, -0.012271538f
};
/**
* \par
* Example code for Floating-point Twiddle factors Generation:
* \par
* <pre>for(i = 0; i< N/; i++)
* {
* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
* } </pre>
* \par
* where N = 1024 and PI = 3.14159265358979
* \par
* Cos and Sin values are in interleaved fashion
*
*/
const float32_t twiddleCoef_1024[2048] = {
1.000000000f , 0.000000000f ,
0.999981175f , 0.006135885f ,
0.999924702f , 0.012271538f ,
0.999830582f , 0.018406730f ,
0.999698819f , 0.024541229f ,
0.999529418f , 0.030674803f ,
0.999322385f , 0.036807223f ,
0.999077728f , 0.042938257f ,
0.998795456f , 0.049067674f ,
0.998475581f , 0.055195244f ,
0.998118113f , 0.061320736f ,
0.997723067f , 0.067443920f ,
0.997290457f , 0.073564564f ,
0.996820299f , 0.079682438f ,
0.996312612f , 0.085797312f ,
0.995767414f , 0.091908956f ,
0.995184727f , 0.098017140f ,
0.994564571f , 0.104121634f ,
0.993906970f , 0.110222207f ,
0.993211949f , 0.116318631f ,
0.992479535f , 0.122410675f ,
0.991709754f , 0.128498111f ,
0.990902635f , 0.134580709f ,
0.990058210f , 0.140658239f ,
0.989176510f , 0.146730474f ,
0.988257568f , 0.152797185f ,
0.987301418f , 0.158858143f ,
0.986308097f , 0.164913120f ,
0.985277642f , 0.170961889f ,
0.984210092f , 0.177004220f ,
0.983105487f , 0.183039888f ,
0.981963869f , 0.189068664f ,
0.980785280f , 0.195090322f ,
0.979569766f , 0.201104635f ,
0.978317371f , 0.207111376f ,
0.977028143f , 0.213110320f ,
0.975702130f , 0.219101240f ,
0.974339383f , 0.225083911f ,
0.972939952f , 0.231058108f ,
0.971503891f , 0.237023606f ,
0.970031253f , 0.242980180f ,
0.968522094f , 0.248927606f ,
0.966976471f , 0.254865660f ,
0.965394442f , 0.260794118f ,
0.963776066f , 0.266712757f ,
0.962121404f , 0.272621355f ,
0.960430519f , 0.278519689f ,
0.958703475f , 0.284407537f ,
0.956940336f , 0.290284677f ,
0.955141168f , 0.296150888f ,
0.953306040f , 0.302005949f ,
0.951435021f , 0.307849640f ,
0.949528181f , 0.313681740f ,
0.947585591f , 0.319502031f ,
0.945607325f , 0.325310292f ,
0.943593458f , 0.331106306f ,
0.941544065f , 0.336889853f ,
0.939459224f , 0.342660717f ,
0.937339012f , 0.348418680f ,
0.935183510f , 0.354163525f ,
0.932992799f , 0.359895037f ,
0.930766961f , 0.365612998f ,
0.928506080f , 0.371317194f ,
0.926210242f , 0.377007410f ,
0.923879533f , 0.382683432f ,
0.921514039f , 0.388345047f ,
0.919113852f , 0.393992040f ,
0.916679060f , 0.399624200f ,
0.914209756f , 0.405241314f ,
0.911706032f , 0.410843171f ,
0.909167983f , 0.416429560f ,
0.906595705f , 0.422000271f ,
0.903989293f , 0.427555093f ,
0.901348847f , 0.433093819f ,
0.898674466f , 0.438616239f ,
0.895966250f , 0.444122145f ,
0.893224301f , 0.449611330f ,
0.890448723f , 0.455083587f ,
0.887639620f , 0.460538711f ,
0.884797098f , 0.465976496f ,
0.881921264f , 0.471396737f ,
0.879012226f , 0.476799230f ,
0.876070094f , 0.482183772f ,
0.873094978f , 0.487550160f ,
0.870086991f , 0.492898192f ,
0.867046246f , 0.498227667f ,
0.863972856f , 0.503538384f ,
0.860866939f , 0.508830143f ,
0.857728610f , 0.514102744f ,
0.854557988f , 0.519355990f ,
0.851355193f , 0.524589683f ,
0.848120345f , 0.529803625f ,
0.844853565f , 0.534997620f ,
0.841554977f , 0.540171473f ,
0.838224706f , 0.545324988f ,
0.834862875f , 0.550457973f ,
0.831469612f , 0.555570233f ,
0.828045045f , 0.560661576f ,
0.824589303f , 0.565731811f ,
0.821102515f , 0.570780746f ,
0.817584813f , 0.575808191f ,
0.814036330f , 0.580813958f ,
0.810457198f , 0.585797857f ,
0.806847554f , 0.590759702f ,
0.803207531f , 0.595699304f ,
0.799537269f , 0.600616479f ,
0.795836905f , 0.605511041f ,
0.792106577f , 0.610382806f ,
0.788346428f , 0.615231591f ,
0.784556597f , 0.620057212f ,
0.780737229f , 0.624859488f ,
0.776888466f , 0.629638239f ,
0.773010453f , 0.634393284f ,
0.769103338f , 0.639124445f ,
0.765167266f , 0.643831543f ,
0.761202385f , 0.648514401f ,
0.757208847f , 0.653172843f ,
0.753186799f , 0.657806693f ,
0.749136395f , 0.662415778f ,
0.745057785f , 0.666999922f ,
0.740951125f , 0.671558955f ,
0.736816569f , 0.676092704f ,
0.732654272f , 0.680600998f ,
0.728464390f , 0.685083668f ,
0.724247083f , 0.689540545f ,
0.720002508f , 0.693971461f ,
0.715730825f , 0.698376249f ,
0.711432196f , 0.702754744f ,
0.707106781f , 0.707106781f ,
0.702754744f , 0.711432196f ,
0.698376249f , 0.715730825f ,
0.693971461f , 0.720002508f ,
0.689540545f , 0.724247083f ,
0.685083668f , 0.728464390f ,
0.680600998f , 0.732654272f ,
0.676092704f , 0.736816569f ,
0.671558955f , 0.740951125f ,
0.666999922f , 0.745057785f ,
0.662415778f , 0.749136395f ,
0.657806693f , 0.753186799f ,
0.653172843f , 0.757208847f ,
0.648514401f , 0.761202385f ,
0.643831543f , 0.765167266f ,
0.639124445f , 0.769103338f ,
0.634393284f , 0.773010453f ,
0.629638239f , 0.776888466f ,
0.624859488f , 0.780737229f ,
0.620057212f , 0.784556597f ,
0.615231591f , 0.788346428f ,
0.610382806f , 0.792106577f ,
0.605511041f , 0.795836905f ,
0.600616479f , 0.799537269f ,
0.595699304f , 0.803207531f ,
0.590759702f , 0.806847554f ,
0.585797857f , 0.810457198f ,
0.580813958f , 0.814036330f ,
0.575808191f , 0.817584813f ,
0.570780746f , 0.821102515f ,
0.565731811f , 0.824589303f ,
0.560661576f , 0.828045045f ,
0.555570233f , 0.831469612f ,
0.550457973f , 0.834862875f ,
0.545324988f , 0.838224706f ,
0.540171473f , 0.841554977f ,
0.534997620f , 0.844853565f ,
0.529803625f , 0.848120345f ,
0.524589683f , 0.851355193f ,
0.519355990f , 0.854557988f ,
0.514102744f , 0.857728610f ,
0.508830143f , 0.860866939f ,
0.503538384f , 0.863972856f ,
0.498227667f , 0.867046246f ,
0.492898192f , 0.870086991f ,
0.487550160f , 0.873094978f ,
0.482183772f , 0.876070094f ,
0.476799230f , 0.879012226f ,
0.471396737f , 0.881921264f ,
0.465976496f , 0.884797098f ,
0.460538711f , 0.887639620f ,
0.455083587f , 0.890448723f ,
0.449611330f , 0.893224301f ,
0.444122145f , 0.895966250f ,
0.438616239f , 0.898674466f ,
0.433093819f , 0.901348847f ,
0.427555093f , 0.903989293f ,
0.422000271f , 0.906595705f ,
0.416429560f , 0.909167983f ,
0.410843171f , 0.911706032f ,
0.405241314f , 0.914209756f ,
0.399624200f , 0.916679060f ,
0.393992040f , 0.919113852f ,
0.388345047f , 0.921514039f ,
0.382683432f , 0.923879533f ,
0.377007410f , 0.926210242f ,
0.371317194f , 0.928506080f ,
0.365612998f , 0.930766961f ,
0.359895037f , 0.932992799f ,
0.354163525f , 0.935183510f ,
0.348418680f , 0.937339012f ,
0.342660717f , 0.939459224f ,
0.336889853f , 0.941544065f ,
0.331106306f , 0.943593458f ,
0.325310292f , 0.945607325f ,
0.319502031f , 0.947585591f ,
0.313681740f , 0.949528181f ,
0.307849640f , 0.951435021f ,
0.302005949f , 0.953306040f ,
0.296150888f , 0.955141168f ,
0.290284677f , 0.956940336f ,
0.284407537f , 0.958703475f ,
0.278519689f , 0.960430519f ,
0.272621355f , 0.962121404f ,
0.266712757f , 0.963776066f ,
0.260794118f , 0.965394442f ,
0.254865660f , 0.966976471f ,
0.248927606f , 0.968522094f ,
0.242980180f , 0.970031253f ,
0.237023606f , 0.971503891f ,
0.231058108f , 0.972939952f ,
0.225083911f , 0.974339383f ,
0.219101240f , 0.975702130f ,
0.213110320f , 0.977028143f ,
0.207111376f , 0.978317371f ,
0.201104635f , 0.979569766f ,
0.195090322f , 0.980785280f ,
0.189068664f , 0.981963869f ,
0.183039888f , 0.983105487f ,
0.177004220f , 0.984210092f ,
0.170961889f , 0.985277642f ,
0.164913120f , 0.986308097f ,
0.158858143f , 0.987301418f ,
0.152797185f , 0.988257568f ,
0.146730474f , 0.989176510f ,
0.140658239f , 0.990058210f ,
0.134580709f , 0.990902635f ,
0.128498111f , 0.991709754f ,
0.122410675f , 0.992479535f ,
0.116318631f , 0.993211949f ,
0.110222207f , 0.993906970f ,
0.104121634f , 0.994564571f ,
0.098017140f , 0.995184727f ,
0.091908956f , 0.995767414f ,
0.085797312f , 0.996312612f ,
0.079682438f , 0.996820299f ,
0.073564564f , 0.997290457f ,
0.067443920f , 0.997723067f ,
0.061320736f , 0.998118113f ,
0.055195244f , 0.998475581f ,
0.049067674f , 0.998795456f ,
0.042938257f , 0.999077728f ,
0.036807223f , 0.999322385f ,
0.030674803f , 0.999529418f ,
0.024541229f , 0.999698819f ,
0.018406730f , 0.999830582f ,
0.012271538f , 0.999924702f ,
0.006135885f , 0.999981175f ,
0.000000000f , 1.000000000f ,
-0.006135885f , 0.999981175f ,
-0.012271538f , 0.999924702f ,
-0.018406730f , 0.999830582f ,
-0.024541229f , 0.999698819f ,
-0.030674803f , 0.999529418f ,
-0.036807223f , 0.999322385f ,
-0.042938257f , 0.999077728f ,
-0.049067674f , 0.998795456f ,
-0.055195244f , 0.998475581f ,
-0.061320736f , 0.998118113f ,
-0.067443920f , 0.997723067f ,
-0.073564564f , 0.997290457f ,
-0.079682438f , 0.996820299f ,
-0.085797312f , 0.996312612f ,
-0.091908956f , 0.995767414f ,
-0.098017140f , 0.995184727f ,
-0.104121634f , 0.994564571f ,
-0.110222207f , 0.993906970f ,
-0.116318631f , 0.993211949f ,
-0.122410675f , 0.992479535f ,
-0.128498111f , 0.991709754f ,
-0.134580709f , 0.990902635f ,
-0.140658239f , 0.990058210f ,
-0.146730474f , 0.989176510f ,
-0.152797185f , 0.988257568f ,
-0.158858143f , 0.987301418f ,
-0.164913120f , 0.986308097f ,
-0.170961889f , 0.985277642f ,
-0.177004220f , 0.984210092f ,
-0.183039888f , 0.983105487f ,
-0.189068664f , 0.981963869f ,
-0.195090322f , 0.980785280f ,
-0.201104635f , 0.979569766f ,
-0.207111376f , 0.978317371f ,
-0.213110320f , 0.977028143f ,
-0.219101240f , 0.975702130f ,
-0.225083911f , 0.974339383f ,
-0.231058108f , 0.972939952f ,
-0.237023606f , 0.971503891f ,
-0.242980180f , 0.970031253f ,
-0.248927606f , 0.968522094f ,
-0.254865660f , 0.966976471f ,
-0.260794118f , 0.965394442f ,
-0.266712757f , 0.963776066f ,
-0.272621355f , 0.962121404f ,
-0.278519689f , 0.960430519f ,
-0.284407537f , 0.958703475f ,
-0.290284677f , 0.956940336f ,
-0.296150888f , 0.955141168f ,
-0.302005949f , 0.953306040f ,
-0.307849640f , 0.951435021f ,
-0.313681740f , 0.949528181f ,
-0.319502031f , 0.947585591f ,
-0.325310292f , 0.945607325f ,
-0.331106306f , 0.943593458f ,
-0.336889853f , 0.941544065f ,
-0.342660717f , 0.939459224f ,
-0.348418680f , 0.937339012f ,
-0.354163525f , 0.935183510f ,
-0.359895037f , 0.932992799f ,
-0.365612998f , 0.930766961f ,
-0.371317194f , 0.928506080f ,
-0.377007410f , 0.926210242f ,
-0.382683432f , 0.923879533f ,
-0.388345047f , 0.921514039f ,
-0.393992040f , 0.919113852f ,
-0.399624200f , 0.916679060f ,
-0.405241314f , 0.914209756f ,
-0.410843171f , 0.911706032f ,
-0.416429560f , 0.909167983f ,
-0.422000271f , 0.906595705f ,
-0.427555093f , 0.903989293f ,
-0.433093819f , 0.901348847f ,
-0.438616239f , 0.898674466f ,
-0.444122145f , 0.895966250f ,
-0.449611330f , 0.893224301f ,
-0.455083587f , 0.890448723f ,
-0.460538711f , 0.887639620f ,
-0.465976496f , 0.884797098f ,
-0.471396737f , 0.881921264f ,
-0.476799230f , 0.879012226f ,
-0.482183772f , 0.876070094f ,
-0.487550160f , 0.873094978f ,
-0.492898192f , 0.870086991f ,
-0.498227667f , 0.867046246f ,
-0.503538384f , 0.863972856f ,
-0.508830143f , 0.860866939f ,
-0.514102744f , 0.857728610f ,
-0.519355990f , 0.854557988f ,
-0.524589683f , 0.851355193f ,
-0.529803625f , 0.848120345f ,
-0.534997620f , 0.844853565f ,
-0.540171473f , 0.841554977f ,
-0.545324988f , 0.838224706f ,
-0.550457973f , 0.834862875f ,
-0.555570233f , 0.831469612f ,
-0.560661576f , 0.828045045f ,
-0.565731811f , 0.824589303f ,
-0.570780746f , 0.821102515f ,
-0.575808191f , 0.817584813f ,
-0.580813958f , 0.814036330f ,
-0.585797857f , 0.810457198f ,
-0.590759702f , 0.806847554f ,
-0.595699304f , 0.803207531f ,
-0.600616479f , 0.799537269f ,
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