From 8fe09c85b6f068809ae454a47a2329bea21b80b4 Mon Sep 17 00:00:00 2001 From: Dennis Luxen Date: Sun, 18 May 2014 14:00:42 +0200 Subject: [PATCH] move atan2 lookup into trig header --- DataStructures/Coordinate.cpp | 5 +- Util/ComputeAngle.h | 756 +------------------------------- Util/TrigonometryTables.h | 789 ++++++++++++++++++++++++++++++++++ 3 files changed, 793 insertions(+), 757 deletions(-) create mode 100644 Util/TrigonometryTables.h diff --git a/DataStructures/Coordinate.cpp b/DataStructures/Coordinate.cpp index b4d06cacf..61afb4c20 100644 --- a/DataStructures/Coordinate.cpp +++ b/DataStructures/Coordinate.cpp @@ -29,6 +29,7 @@ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. #include "../Util/MercatorUtil.h" #include "../Util/SimpleLogger.h" #include "../Util/StringUtil.h" +#include "../Util/TrigonometryTables.h" #include @@ -339,7 +340,7 @@ double FixedPointCoordinate::GetBearing(const FixedPointCoordinate &A, const Fix const double y = sin(delta_long) * cos(lat2); const double x = cos(lat1) * sin(lat2) - sin(lat1) * cos(lat2) * cos(delta_long); - double result = RadianToDegree(atan2(y, x)); + double result = RadianToDegree(atan2_lookup(y, x)); while (result < 0.) { result += 360.; @@ -361,7 +362,7 @@ double FixedPointCoordinate::GetBearing(const FixedPointCoordinate &other) const const double y = std::sin(delta_long) * std::cos(lat2); const double x = std::cos(lat1) * std::sin(lat2) - std::sin(lat1) * std::cos(lat2) * std::cos(delta_long); - double result = RadianToDegree(std::atan2(y, x)); + double result = RadianToDegree(atan2_lookup(y, x)); while (result < 0.) { diff --git a/Util/ComputeAngle.h b/Util/ComputeAngle.h index 89a7348e6..02f678a07 100644 --- a/Util/ComputeAngle.h +++ b/Util/ComputeAngle.h @@ -28,767 +28,13 @@ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. #ifndef COMPUTE_ANGLE_H #define COMPUTE_ANGLE_H +#include "TrigonometryTables.h" #include "../Util/MercatorUtil.h" #include #include #include -constexpr unsigned short atan_table[4096] = { -0x0000, 0x0014, 0x0028, 0x003d, 0x0051, 0x0065, -0x007a, 0x008e, 0x00a3, 0x00b7, 0x00cb, 0x00e0, -0x00f4, 0x0108, 0x011d, 0x0131, 0x0146, 0x015a, -0x016e, 0x0183, 0x0197, 0x01ab, 0x01c0, 0x01d4, -0x01e9, 0x01fd, 0x0211, 0x0226, 0x023a, 0x024e, -0x0263, 0x0277, 0x028c, 0x02a0, 0x02b4, 0x02c9, -0x02dd, 0x02f1, 0x0306, 0x031a, 0x032f, 0x0343, -0x0357, 0x036c, 0x0380, 0x0394, 0x03a9, 0x03bd, -0x03d2, 0x03e6, 0x03fa, 0x040f, 0x0423, 0x0437, -0x044c, 0x0460, 0x0475, 0x0489, 0x049d, 0x04b2, -0x04c6, 0x04da, 0x04ef, 0x0503, 0x0517, 0x052c, -0x0540, 0x0555, 0x0569, 0x057d, 0x0592, 0x05a6, -0x05ba, 0x05cf, 0x05e3, 0x05f8, 0x060c, 0x0620, -0x0635, 0x0649, 0x065d, 0x0672, 0x0686, 0x069b, -0x06af, 0x06c3, 0x06d8, 0x06ec, 0x0700, 0x0715, -0x0729, 0x073d, 0x0752, 0x0766, 0x077b, 0x078f, -0x07a3, 0x07b8, 0x07cc, 0x07e0, 0x07f5, 0x0809, -0x081d, 0x0832, 0x0846, 0x085b, 0x086f, 0x0883, -0x0898, 0x08ac, 0x08c0, 0x08d5, 0x08e9, 0x08fd, -0x0912, 0x0926, 0x093b, 0x094f, 0x0963, 0x0978, -0x098c, 0x09a0, 0x09b5, 0x09c9, 0x09dd, 0x09f2, -0x0a06, 0x0a1a, 0x0a2f, 0x0a43, 0x0a58, 0x0a6c, -0x0a80, 0x0a95, 0x0aa9, 0x0abd, 0x0ad2, 0x0ae6, -0x0afa, 0x0b0f, 0x0b23, 0x0b37, 0x0b4c, 0x0b60, -0x0b75, 0x0b89, 0x0b9d, 0x0bb2, 0x0bc6, 0x0bda, -0x0bef, 0x0c03, 0x0c17, 0x0c2c, 0x0c40, 0x0c54, -0x0c69, 0x0c7d, 0x0c91, 0x0ca6, 0x0cba, 0x0cce, -0x0ce3, 0x0cf7, 0x0d0b, 0x0d20, 0x0d34, 0x0d48, -0x0d5d, 0x0d71, 0x0d86, 0x0d9a, 0x0dae, 0x0dc3, -0x0dd7, 0x0deb, 0x0e00, 0x0e14, 0x0e28, 0x0e3d, -0x0e51, 0x0e65, 0x0e7a, 0x0e8e, 0x0ea2, 0x0eb7, -0x0ecb, 0x0edf, 0x0ef4, 0x0f08, 0x0f1c, 0x0f31, -0x0f45, 0x0f59, 0x0f6e, 0x0f82, 0x0f96, 0x0fab, -0x0fbf, 0x0fd3, 0x0fe8, 0x0ffc, 0x1010, 0x1025, -0x1039, 0x104d, 0x1062, 0x1076, 0x108a, 0x109e, -0x10b3, 0x10c7, 0x10db, 0x10f0, 0x1104, 0x1118, -0x112d, 0x1141, 0x1155, 0x116a, 0x117e, 0x1192, -0x11a7, 0x11bb, 0x11cf, 0x11e4, 0x11f8, 0x120c, -0x1221, 0x1235, 0x1249, 0x125d, 0x1272, 0x1286, -0x129a, 0x12af, 0x12c3, 0x12d7, 0x12ec, 0x1300, 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-0xe812, 0xe81d, 0xe829, 0xe835, 0xe840, 0xe84c, -0xe858, 0xe863, 0xe86f, 0xe87b, 0xe886, 0xe892, -0xe89e, 0xe8a9, 0xe8b5, 0xe8c0, 0xe8cc, 0xe8d8, -0xe8e3, 0xe8ef, 0xe8fb, 0xe906, 0xe912, 0xe91d, -0xe929, 0xe935, 0xe940, 0xe94c, 0xe958, 0xe963, -0xe96f, 0xe97a, 0xe986, 0xe991, 0xe99d, 0xe9a9, -0xe9b4, 0xe9c0, 0xe9cb, 0xe9d7, 0xe9e3, 0xe9ee, -0xe9fa, 0xea05, 0xea11, 0xea1c, 0xea28, 0xea33, -0xea3f, 0xea4a, 0xea56, 0xea62, 0xea6d, 0xea79, -0xea84, 0xea90, 0xea9b, 0xeaa7, 0xeab2, 0xeabe, -0xeac9, 0xead5, 0xeae0, 0xeaec, 0xeaf7, 0xeb03, -0xeb0e, 0xeb1a, 0xeb25, 0xeb31, 0xeb3c, 0xeb48, -0xeb53, 0xeb5f, 0xeb6a, 0xeb76, 0xeb81, 0xeb8d, -0xeb98, 0xeba3, 0xebaf, 0xebba, 0xebc6, 0xebd1, -0xebdd, 0xebe8, 0xebf4, 0xebff, 0xec0a, 0xec16, -0xec21, 0xec2d, 0xec38, 0xec44, 0xec4f, 0xec5a, -0xec66, 0xec71, 0xec7d, 0xec88, 0xec93, 0xec9f, -0xecaa, 0xecb6, 0xecc1, 0xeccc, 0xecd8, 0xece3, -0xecef, 0xecfa, 0xed05, 0xed11, 0xed1c, 0xed27, -0xed33, 0xed3e, 0xed4a, 0xed55, 0xed60, 0xed6c, -0xed77, 0xed82, 0xed8e, 0xed99, 0xeda4, 0xedb0, -0xedbb, 0xedc6, 0xedd2, 0xeddd, 0xede8, 0xedf4, -0xedff, 0xee0a, 0xee15, 0xee21, 0xee2c, 0xee37, -0xee43, 0xee4e, 0xee59, 0xee65, 0xee70, 0xee7b, -0xee86, 0xee92, 0xee9d, 0xeea8, 0xeeb3, 0xeebf, -0xeeca, 0xeed5, 0xeee1, 0xeeec, 0xeef7, 0xef02, -0xef0e, 0xef19, 0xef24, 0xef2f, 0xef3a, 0xef46, -0xef51, 0xef5c, 0xef67, 0xef73, 0xef7e, 0xef89, -0xef94, 0xef9f, 0xefab, 0xefb6, 0xefc1, 0xefcc, -0xefd7, 0xefe3, 0xefee, 0xeff9, 0xf004, 0xf00f, -0xf01b, 0xf026, 0xf031, 0xf03c, 0xf047, 0xf052, -0xf05e, 0xf069, 0xf074, 0xf07f, 0xf08a, 0xf095, -0xf0a1, 0xf0ac, 0xf0b7, 0xf0c2, 0xf0cd, 0xf0d8, -0xf0e3, 0xf0ef, 0xf0fa, 0xf105, 0xf110, 0xf11b, -0xf126, 0xf131, 0xf13c, 0xf147, 0xf153, 0xf15e, -0xf169, 0xf174, 0xf17f, 0xf18a, 0xf195, 0xf1a0, -0xf1ab, 0xf1b6, 0xf1c2, 0xf1cd, 0xf1d8, 0xf1e3, -0xf1ee, 0xf1f9, 0xf204, 0xf20f, 0xf21a, 0xf225, -0xf230, 0xf23b, 0xf246, 0xf251, 0xf25c, 0xf267, -0xf272, 0xf27d, 0xf288, 0xf293, 0xf29f, 0xf2aa, -0xf2b5, 0xf2c0, 0xf2cb, 0xf2d6, 0xf2e1, 0xf2ec, -0xf2f7, 0xf302, 0xf30d, 0xf318, 0xf323, 0xf32e, -0xf339, 0xf344, 0xf34f, 0xf35a, 0xf364, 0xf36f, -0xf37a, 0xf385, 0xf390, 0xf39b, 0xf3a6, 0xf3b1, -0xf3bc, 0xf3c7, 0xf3d2, 0xf3dd, 0xf3e8, 0xf3f3, -0xf3fe, 0xf409, 0xf414, 0xf41f, 0xf42a, 0xf435, -0xf43f, 0xf44a, 0xf455, 0xf460, 0xf46b, 0xf476, -0xf481, 0xf48c, 0xf497, 0xf4a2, 0xf4ad, 0xf4b7, -0xf4c2, 0xf4cd, 0xf4d8, 0xf4e3, 0xf4ee, 0xf4f9, -0xf504, 0xf50f, 0xf519, 0xf524, 0xf52f, 0xf53a, -0xf545, 0xf550, 0xf55b, 0xf565, 0xf570, 0xf57b, -0xf586, 0xf591, 0xf59c, 0xf5a6, 0xf5b1, 0xf5bc, -0xf5c7, 0xf5d2, 0xf5dd, 0xf5e7, 0xf5f2, 0xf5fd, -0xf608, 0xf613, 0xf61d, 0xf628, 0xf633, 0xf63e, -0xf649, 0xf653, 0xf65e, 0xf669, 0xf674, 0xf67f, -0xf689, 0xf694, 0xf69f, 0xf6aa, 0xf6b4, 0xf6bf, -0xf6ca, 0xf6d5, 0xf6e0, 0xf6ea, 0xf6f5, 0xf700, -0xf70b, 0xf715, 0xf720, 0xf72b, 0xf736, 0xf740, -0xf74b, 0xf756, 0xf760, 0xf76b, 0xf776, 0xf781, -0xf78b, 0xf796, 0xf7a1, 0xf7ab, 0xf7b6, 0xf7c1, -0xf7cc, 0xf7d6, 0xf7e1, 0xf7ec, 0xf7f6, 0xf801, -0xf80c, 0xf816, 0xf821, 0xf82c, 0xf836, 0xf841, -0xf84c, 0xf856, 0xf861, 0xf86c, 0xf876, 0xf881, -0xf88c, 0xf896, 0xf8a1, 0xf8ac, 0xf8b6, 0xf8c1, -0xf8cc, 0xf8d6, 0xf8e1, 0xf8ec, 0xf8f6, 0xf901, -0xf90b, 0xf916, 0xf921, 0xf92b, 0xf936, 0xf941, -0xf94b, 0xf956, 0xf960, 0xf96b, 0xf976, 0xf980, -0xf98b, 0xf995, 0xf9a0, 0xf9aa, 0xf9b5, 0xf9c0, -0xf9ca, 0xf9d5, 0xf9df, 0xf9ea, 0xf9f4, 0xf9ff, -0xfa0a, 0xfa14, 0xfa1f, 0xfa29, 0xfa34, 0xfa3e, -0xfa49, 0xfa53, 0xfa5e, 0xfa69, 0xfa73, 0xfa7e, -0xfa88, 0xfa93, 0xfa9d, 0xfaa8, 0xfab2, 0xfabd, -0xfac7, 0xfad2, 0xfadc, 0xfae7, 0xfaf1, 0xfafc, -0xfb06, 0xfb11, 0xfb1b, 0xfb26, 0xfb30, 0xfb3b, -0xfb45, 0xfb50, 0xfb5a, 0xfb65, 0xfb6f, 0xfb7a, -0xfb84, 0xfb8f, 0xfb99, 0xfba4, 0xfbae, 0xfbb8, -0xfbc3, 0xfbcd, 0xfbd8, 0xfbe2, 0xfbed, 0xfbf7, -0xfc02, 0xfc0c, 0xfc16, 0xfc21, 0xfc2b, 0xfc36, -0xfc40, 0xfc4b, 0xfc55, 0xfc5f, 0xfc6a, 0xfc74, -0xfc7f, 0xfc89, 0xfc93, 0xfc9e, 0xfca8, 0xfcb3, -0xfcbd, 0xfcc7, 0xfcd2, 0xfcdc, 0xfce7, 0xfcf1, -0xfcfb, 0xfd06, 0xfd10, 0xfd1a, 0xfd25, 0xfd2f, -0xfd3a, 0xfd44, 0xfd4e, 0xfd59, 0xfd63, 0xfd6d, -0xfd78, 0xfd82, 0xfd8c, 0xfd97, 0xfda1, 0xfdab, -0xfdb6, 0xfdc0, 0xfdca, 0xfdd5, 0xfddf, 0xfde9, -0xfdf4, 0xfdfe, 0xfe08, 0xfe13, 0xfe1d, 0xfe27, -0xfe32, 0xfe3c, 0xfe46, 0xfe50, 0xfe5b, 0xfe65, -0xfe6f, 0xfe7a, 0xfe84, 0xfe8e, 0xfe98, 0xfea3, -0xfead, 0xfeb7, 0xfec1, 0xfecc, 0xfed6, 0xfee0, -0xfeeb, 0xfef5, 0xfeff, 0xff09, 0xff14, 0xff1e, -0xff28, 0xff32, 0xff3c, 0xff47, 0xff51, 0xff5b, -0xff65, 0xff70, 0xff7a, 0xff84, 0xff8e, 0xff98, -0xffa3, 0xffad, 0xffb7, 0xffc1, 0xffcc, 0xffd6, -0xffe0, 0xffea, 0xfff4, 0xffff -}; - -// max value is pi/4 -constexpr double SCALING_FACTOR = 4. / M_PI * 0xFFFF; - -inline double atan2_lookup(double y, double x) -{ - if (std::abs(x) < std::numeric_limits::epsilon()) - { - if (y >= 0.) - { - return M_PI / 2.; - } - else - { - return -M_PI / 2.; - } - } - - unsigned octant = 0; - - if (x < 0.) - { - octant = 1; - x = -x; - } - if (y < 0.) - { - octant |= 2; - y = -y; - } - - double t = y / x; - if (t > 1.0) - { - octant |= 4; - t = 1.0 / t; - } - - double angle = atan_table[(unsigned)(t * 4095)] / SCALING_FACTOR; - - switch (octant) - { - case 0: - break; - case 1: - angle = M_PI - angle; - break; - case 2: - angle = -angle; - break; - case 3: - angle = -M_PI + angle; - break; - case 4: - angle = M_PI / 2.0 - angle; - break; - case 5: - angle = M_PI / 2.0 + angle; - break; - case 6: - angle = -M_PI / 2.0 + angle; - break; - case 7: - angle = -M_PI / 2.0 - angle; - break; - } - - return angle; -} - /* Get angle of line segment (A,C)->(C,B), atan2 magic, formerly cosine theorem*/ template inline static double GetAngleBetweenThreeFixedPointCoordinates(const CoordinateT &A, diff --git a/Util/TrigonometryTables.h b/Util/TrigonometryTables.h new file mode 100644 index 000000000..665a397f8 --- /dev/null +++ b/Util/TrigonometryTables.h @@ -0,0 +1,789 @@ +/* + +Copyright (c) 2013, Project OSRM, Dennis Luxen, others +All rights reserved. + +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. + +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 HOLDER 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. + +*/ + +#ifndef TRIGONOMETRY_TABLES_H +#define TRIGONOMETRY_TABLES_H + +#include + +#include + +constexpr unsigned short atan_table[4096] = { +0x0000, 0x0014, 0x0028, 0x003d, 0x0051, 0x0065, +0x007a, 0x008e, 0x00a3, 0x00b7, 0x00cb, 0x00e0, +0x00f4, 0x0108, 0x011d, 0x0131, 0x0146, 0x015a, +0x016e, 0x0183, 0x0197, 0x01ab, 0x01c0, 0x01d4, +0x01e9, 0x01fd, 0x0211, 0x0226, 0x023a, 0x024e, +0x0263, 0x0277, 0x028c, 0x02a0, 0x02b4, 0x02c9, +0x02dd, 0x02f1, 0x0306, 0x031a, 0x032f, 0x0343, +0x0357, 0x036c, 0x0380, 0x0394, 0x03a9, 0x03bd, +0x03d2, 0x03e6, 0x03fa, 0x040f, 0x0423, 0x0437, +0x044c, 0x0460, 0x0475, 0x0489, 0x049d, 0x04b2, +0x04c6, 0x04da, 0x04ef, 0x0503, 0x0517, 0x052c, +0x0540, 0x0555, 0x0569, 0x057d, 0x0592, 0x05a6, +0x05ba, 0x05cf, 0x05e3, 0x05f8, 0x060c, 0x0620, +0x0635, 0x0649, 0x065d, 0x0672, 0x0686, 0x069b, +0x06af, 0x06c3, 0x06d8, 0x06ec, 0x0700, 0x0715, +0x0729, 0x073d, 0x0752, 0x0766, 0x077b, 0x078f, +0x07a3, 0x07b8, 0x07cc, 0x07e0, 0x07f5, 0x0809, +0x081d, 0x0832, 0x0846, 0x085b, 0x086f, 0x0883, +0x0898, 0x08ac, 0x08c0, 0x08d5, 0x08e9, 0x08fd, +0x0912, 0x0926, 0x093b, 0x094f, 0x0963, 0x0978, +0x098c, 0x09a0, 0x09b5, 0x09c9, 0x09dd, 0x09f2, +0x0a06, 0x0a1a, 0x0a2f, 0x0a43, 0x0a58, 0x0a6c, +0x0a80, 0x0a95, 0x0aa9, 0x0abd, 0x0ad2, 0x0ae6, +0x0afa, 0x0b0f, 0x0b23, 0x0b37, 0x0b4c, 0x0b60, +0x0b75, 0x0b89, 0x0b9d, 0x0bb2, 0x0bc6, 0x0bda, +0x0bef, 0x0c03, 0x0c17, 0x0c2c, 0x0c40, 0x0c54, +0x0c69, 0x0c7d, 0x0c91, 0x0ca6, 0x0cba, 0x0cce, +0x0ce3, 0x0cf7, 0x0d0b, 0x0d20, 0x0d34, 0x0d48, +0x0d5d, 0x0d71, 0x0d86, 0x0d9a, 0x0dae, 0x0dc3, +0x0dd7, 0x0deb, 0x0e00, 0x0e14, 0x0e28, 0x0e3d, +0x0e51, 0x0e65, 0x0e7a, 0x0e8e, 0x0ea2, 0x0eb7, +0x0ecb, 0x0edf, 0x0ef4, 0x0f08, 0x0f1c, 0x0f31, +0x0f45, 0x0f59, 0x0f6e, 0x0f82, 0x0f96, 0x0fab, +0x0fbf, 0x0fd3, 0x0fe8, 0x0ffc, 0x1010, 0x1025, +0x1039, 0x104d, 0x1062, 0x1076, 0x108a, 0x109e, +0x10b3, 0x10c7, 0x10db, 0x10f0, 0x1104, 0x1118, +0x112d, 0x1141, 0x1155, 0x116a, 0x117e, 0x1192, +0x11a7, 0x11bb, 0x11cf, 0x11e4, 0x11f8, 0x120c, +0x1221, 0x1235, 0x1249, 0x125d, 0x1272, 0x1286, +0x129a, 0x12af, 0x12c3, 0x12d7, 0x12ec, 0x1300, +0x1314, 0x1329, 0x133d, 0x1351, 0x1365, 0x137a, +0x138e, 0x13a2, 0x13b7, 0x13cb, 0x13df, 0x13f4, +0x1408, 0x141c, 0x1431, 0x1445, 0x1459, 0x146d, +0x1482, 0x1496, 0x14aa, 0x14bf, 0x14d3, 0x14e7, +0x14fb, 0x1510, 0x1524, 0x1538, 0x154d, 0x1561, +0x1575, 0x1589, 0x159e, 0x15b2, 0x15c6, 0x15db, +0x15ef, 0x1603, 0x1617, 0x162c, 0x1640, 0x1654, +0x1669, 0x167d, 0x1691, 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0xf9ea, 0xf9f4, 0xf9ff, +0xfa0a, 0xfa14, 0xfa1f, 0xfa29, 0xfa34, 0xfa3e, +0xfa49, 0xfa53, 0xfa5e, 0xfa69, 0xfa73, 0xfa7e, +0xfa88, 0xfa93, 0xfa9d, 0xfaa8, 0xfab2, 0xfabd, +0xfac7, 0xfad2, 0xfadc, 0xfae7, 0xfaf1, 0xfafc, +0xfb06, 0xfb11, 0xfb1b, 0xfb26, 0xfb30, 0xfb3b, +0xfb45, 0xfb50, 0xfb5a, 0xfb65, 0xfb6f, 0xfb7a, +0xfb84, 0xfb8f, 0xfb99, 0xfba4, 0xfbae, 0xfbb8, +0xfbc3, 0xfbcd, 0xfbd8, 0xfbe2, 0xfbed, 0xfbf7, +0xfc02, 0xfc0c, 0xfc16, 0xfc21, 0xfc2b, 0xfc36, +0xfc40, 0xfc4b, 0xfc55, 0xfc5f, 0xfc6a, 0xfc74, +0xfc7f, 0xfc89, 0xfc93, 0xfc9e, 0xfca8, 0xfcb3, +0xfcbd, 0xfcc7, 0xfcd2, 0xfcdc, 0xfce7, 0xfcf1, +0xfcfb, 0xfd06, 0xfd10, 0xfd1a, 0xfd25, 0xfd2f, +0xfd3a, 0xfd44, 0xfd4e, 0xfd59, 0xfd63, 0xfd6d, +0xfd78, 0xfd82, 0xfd8c, 0xfd97, 0xfda1, 0xfdab, +0xfdb6, 0xfdc0, 0xfdca, 0xfdd5, 0xfddf, 0xfde9, +0xfdf4, 0xfdfe, 0xfe08, 0xfe13, 0xfe1d, 0xfe27, +0xfe32, 0xfe3c, 0xfe46, 0xfe50, 0xfe5b, 0xfe65, +0xfe6f, 0xfe7a, 0xfe84, 0xfe8e, 0xfe98, 0xfea3, +0xfead, 0xfeb7, 0xfec1, 0xfecc, 0xfed6, 0xfee0, +0xfeeb, 0xfef5, 0xfeff, 0xff09, 0xff14, 0xff1e, +0xff28, 0xff32, 0xff3c, 0xff47, 0xff51, 0xff5b, +0xff65, 0xff70, 0xff7a, 0xff84, 0xff8e, 0xff98, +0xffa3, 0xffad, 0xffb7, 0xffc1, 0xffcc, 0xffd6, +0xffe0, 0xffea, 0xfff4, 0xffff +}; + +// max value is pi/4 +constexpr double SCALING_FACTOR = 4. / M_PI * 0xFFFF; + +inline double atan2_lookup(double y, double x) +{ + if (std::abs(x) < std::numeric_limits::epsilon()) + { + if (y >= 0.) + { + return M_PI / 2.; + } + else + { + return -M_PI / 2.; + } + } + + unsigned octant = 0; + + if (x < 0.) + { + octant = 1; + x = -x; + } + if (y < 0.) + { + octant |= 2; + y = -y; + } + + double t = y / x; + if (t > 1.0) + { + octant |= 4; + t = 1.0 / t; + } + + double angle = atan_table[(unsigned)(t * 4095)] / SCALING_FACTOR; + + switch (octant) + { + case 0: + break; + case 1: + angle = M_PI - angle; + break; + case 2: + angle = -angle; + break; + case 3: + angle = -M_PI + angle; + break; + case 4: + angle = M_PI / 2.0 - angle; + break; + case 5: + angle = M_PI / 2.0 + angle; + break; + case 6: + angle = -M_PI / 2.0 + angle; + break; + case 7: + angle = -M_PI / 2.0 - angle; + break; + } + return angle; +} + +#endif // TRIGONOMETRY_TABLES_H