gszauer/trigapproximations.cpp

## trigapproximations.cpp
// Trig approximations from: http://www.ganssle.com/approx.htm

#include <windows.h>
#include <cmath>
#include <iostream>
#include <iomanip>


#define WINDOW_WIDTH 800
#define WINDOW_HEIGHT 600
#define WINDOW_CLASS "GDI_Sample"
#define WINDOW_TITLE "Double Buffered GDI Sample"


#if 1
const int num_floats = 10000;
const float rando_floats[] = {
	6.9084, 2.3504, 5.9393, 2.1995, 6.9788, 4.5800, 1.2876, 3.7013, 1.9697, 2.7241, 7.9970, 2.3300, 7.4100, 7.6173, 6.6112, 1.2391, 7.8210, 4.4060, 6.1480, 5.6367, 0.3375, 2.7864, 2.0000, 2.5421, 6.4652, 7.3482, 7.5172, 3.7798, 4.2308, 1.9803, 6.1153, 2.9707, 0.0472, 4.5240, 1.6795, 1.7698, 2.8173, 6.6781, 5.5801, 5.2696, 4.0168, 2.6126, 4.8747, 3.3826, 3.3805, 5.5582, 3.1856, 5.5784, 6.7845, 4.6369, 0.0974, 4.6771, 6.1472, 6.7081, 3.5568, 3.2700, 1.7868, 5.8658, 0.9733, 5.2559, 7.4211, 3.1177, 1.8397, 3.7930, 4.0191, 5.8022, 7.5109, 7.8512, 2.5062, 2.7670, 6.0232, 0.1724, 0.7736, 1.5016, 3.9123, 4.8226, 2.9712, 5.8571, 6.2498, 7.8077, 2.7280, 3.5722, 6.7691, 2.6042, 5.4155, 4.1252, 0.7980, 1.8713, 0.6663, 0.1796, 4.0968, 1.1130, 4.0558, 6.4572, 0.5161, 5.8781, 4.9736, 2.7062, 0.0663, 2.3662, 5.3852, 6.0000, 6.7477, 3.3608, 7.9006, 7.9385, 6.7156, 3.3028, 6.0332, 7.1317, 6.4910, 5.1567, 7.1540, 0.3170, 5.9579, 1.2700, 4.7792, 3.9701, 3.9484, 4.9030, 1.6672, 6.4814, 2.1437, 2.8824, 3.6666, 0.1099, 3.4336, 0.6839, 6.2936, 5.2740, 2.9189, 3.6685, 2.3864, 0.5644, 4.5368, 5.7800, 5.0096, 7.9859, 3.7357, 4.8956, 7.6202, 1.0903, 3.8846, 0.2869, 2.7718, 2.6730, 7.5658, 1.4093, 0.6238, 4.9548, 5.8408, 3.6572, 2.0209, 6.9424, 2.8576, 5.8263, 2.6573, 6.1259, 7.6424, 1.3909, 7.9008, 1.3421, 0.3613, 4.5996, 0.6480, 0.3192, 4.2864, 2.5159, 7.3168, 2.4910, 0.3599, 4.3626, 1.9689, 5.3904, 5.3859, 1.3032, 2.7957, 4.5157, 4.0436, 0.2658, 5.8818, 0.6516, 2.5576, 7.0912, 5.4708, 5.3082, 6.9799, 6.1880, 2.8000, 6.7294, 0.1005, 4.2100, 1.4102, 0.7881, 4.5280, 2.0744, 4.8993, 3.1822, 1.5646, 1.4406, 0.5660, 3.4572, 3.1336, 6.9154, 2.1643, 7.0176, 6.9640, 2.3492, 5.1240, 0.4699, 4.8285, 7.4047, 1.6012, 7.6404, 7.1432, 7.0300, 4.1464, 5.9459, 2.6955, 1.8738, 6.8444, 7.5487, 4.4960, 4.8697, 1.0032, 3.5624, 1.4587, 5.4314, 3.2115, 5.9787, 1.1923, 6.9602, 0.8226, 7.5288, 6.0303, 6.0276, 2.6214, 2.2432, 4.2800, 0.8287, 3.0364, 5.2872, 4.0118, 3.5202, 4.6080, 0.8404, 6.9952, 0.1756, 3.8337, 6.6387, 0.7860, 7.0632, 6.4522, 3.9792, 3.0393, 3.5510, 5.4460, 0.4154, 5.6676, 0.0876, 1.1853, 5.3723, 3.0764, 5.1228, 2.9087, 5.7966, 6.6157, 6.2671, 3.4255, 3.1701, 1.0846, 4.0804, 6.8460, 7.5992, 1.4338, 6.6349, 0.2019, 5.3499, 5.5132, 5.7672, 4.8868, 6.4586, 5.4582, 0.2452, 2.8516, 1.4202, 3.8380, 2.1376, 3.3741, 1.5763, 5.0530, 5.4554, 4.4543, 2.4195, 0.5250, 3.8868, 5.7545, 2.3565, 2.3665, 3.3252, 3.6468, 6.1778, 4.5187, 6.4279, 2.4445, 2.4811, 2.7029, 3.8953, 3.8504, 5.8432, 2.8327, 7.9493, 5.4044, 0.7016, 7.8289, 2.2453, 5.0201, 2.1568, 6.2203, 4.6280, 5.0117, 6.1196, 1.8308, 2.8756, 6.5035, 4.5096, 0.0968, 2.8974, 3.4845, 1.6640, 4.3239, 3.1774, 0.2272, 0.6837, 1.7579, 7.4527, 1.5621, 5.3519, 6.7796, 1.2269, 1.0723, 2.6572, 2.0776, 4.0596, 1.3232, 5.8615, 5.7372, 6.0761, 2.5930, 7.9360, 3.6361, 1.0130, 0.1084, 5.2825, 7.4289, 3.6800, 0.6135, 7.2821, 5.5604, 6.9334, 6.6464, 1.9784, 2.5324, 1.4004, 4.2479, 4.0002, 7.8367, 0.3812, 1.7926, 2.1284, 4.2556, 2.9091, 4.4428, 1.4005, 3.7640, 2.4541, 2.9934, 6.5049, 4.0605, 1.1920, 2.0153, 6.6861, 7.6456, 3.2406, 7.9372, 1.4405, 6.0259, 5.5092, 1.2033, 7.4240, 6.0920, 5.5829, 5.3668, 3.7608, 5.8665, 5.7191, 4.8791, 0.4224, 0.0424, 4.8499, 3.3728, 3.6364, 0.7954, 4.2334, 3.3851, 7.2456, 4.9787, 3.8035, 2.9326, 0.5616, 7.4564, 7.6565, 1.0776, 2.5736, 0.7036, 5.3272, 1.6532, 1.9889, 2.2111, 3.1240, 3.9384, 4.4145, 1.6754, 6.0161, 5.5692, 1.2398, 7.3015, 1.4595, 7.2931, 4.4245, 1.5604, 5.6226, 4.9672, 4.0494, 0.9008, 7.6817, 1.5705, 0.2357, 5.2941, 4.0224, 2.9376, 3.9533, 4.2603, 5.0578, 4.5048, 6.3822, 0.0160, 3.9049, 6.0782, 1.9427, 7.5437, 5.9302, 4.3033, 2.4970, 2.1124, 2.5280, 3.6237, 0.8052, 5.0748, 3.8349, 7.1546, 6.7792, 2.0377, 3.4805, 6.3911, 7.2185, 6.6497, 2.0272, 0.7786, 4.2602, 6.1494, 6.7072, 7.6984, 2.5869, 1.2116, 3.8957, 6.2549, 5.5687, 3.8530, 2.2429, 0.6960, 2.4225, 3.7944, 2.5542, 1.2816, 0.9071, 5.8552, 4.2337, 5.9669, 5.7718, 6.8684, 3.9196, 0.2918, 1.5005, 0.2273, 3.4040, 7.2410, 5.8140, 4.6949, 0.9121, 4.9735, 6.7266, 4.3410, 0.0433, 0.9068, 0.5588, 2.1484, 3.0909, 3.3224, 5.2196, 2.5677, 5.9411, 6.9876, 4.5656, 0.7910, 5.2672, 3.2989, 3.2829, 5.9777, 1.6117, 1.9447, 2.0389, 2.5644, 2.5329, 3.7555, 0.9654, 3.7528, 1.8475, 2.5178, 2.2598, 0.3136, 4.2136, 5.7356, 3.6390, 2.6310, 6.0544, 1.7326, 5.9521, 4.6783, 2.7676, 7.4298, 1.2780, 3.6000, 2.1162, 2.3473, 2.5261, 5.0563, 0.7340, 2.0088, 4.7571, 2.2182, 5.8806, 2.4408, 4.7242, 1.8988, 7.3134, 0.8473, 4.0477, 2.4208, 4.4778, 7.6529, 6.8486, 4.4848, 3.6134, 2.7042, 5.4713, 2.5632, 0.1579, 2.7286, 2.7487, 3.1368, 4.2754, 3.2141, 7.1377, 3.4728, 7.9376, 3.9520, 7.9060, 4.5305, 2.0141, 4.1248, 0.5096, 7.3273, 3.1528, 6.5360, 7.4264, 7.9586, 2.4440, 1.0268, 7.4501, 6.5085, 2.4566, 7.6633, 3.5725, 2.4488, 7.0418, 5.7929, 6.2378, 3.8862, 1.9089, 6.1759, 2.4712, 6.3763, 7.3368, 7.0958, 7.0874, 1.6122, 5.3936, 1.2778, 4.7960, 6.5130, 6.0245, 7.6673, 5.4848, 4.7676, 7.9749, 1.3024, 7.4741, 3.3870, 5.0617, 0.8494, 7.3640, 5.2059, 4.7387, 3.7948, 5.3240, 0.7865, 0.0145, 3.6281, 7.8125, 0.6139, 2.4323, 6.9200, 6.3290, 2.6729, 0.2566, 3.2037, 0.6576, 4.1986, 6.1204, 7.9690, 5.3632, 0.4708, 0.3581, 3.1380, 5.5049, 6.5256, 7.4260, 1.6372, 3.8707, 2.1246, 0.5197, 3.1905, 4.6415, 5.7936, 2.4888, 4.8348, 0.7171, 4.0711, 4.7035, 6.6752, 5.3088, 7.1875, 0.5373, 7.4780, 3.7230, 6.4387, 0.5676, 7.9262, 7.7706, 5.2400, 7.5844, 7.1364, 5.4951, 4.2756, 0.6303, 4.8820, 0.8360, 6.1582, 4.4828, 2.7327, 1.0767, 2.5857, 6.6065, 5.9269, 0.7656, 1.3166, 1.3798, 7.8177, 4.9008, 2.8802, 0.8336, 2.9000, 3.2052, 1.1055, 2.2614, 6.7842, 0.1697, 5.0048, 2.2100, 2.4616, 2.1796, 0.0526, 6.5840, 4.3395, 2.3500, 7.6695, 6.3067, 2.5539, 2.3982, 4.3363, 0.2127, 3.1204, 6.9211, 3.4080, 2.7198, 5.7051, 3.7856, 0.2555, 5.3116, 7.3469, 1.0321, 3.6129, 7.0187, 3.3012, 2.4277, 7.7366, 3.5593, 0.5592, 4.7463, 5.4871, 1.2811, 1.9072, 0.8284, 7.6339, 5.5649, 0.5890, 7.4039, 3.4202, 7.9349, 3.8083, 3.6248, 7.3131, 4.1484, 5.3214, 2.6802, 4.6297, 2.7936, 5.3988, 6.7708, 2.2494, 6.2114, 3.4828, 5.7085, 3.8900, 6.7624, 6.0684, 4.2090, 4.9419, 2.1929, 3.3233, 0.1242, 5.2360, 1.5728, 2.7688, 7.9892, 6.1548, 6.6778, 2.1468, 0.2695, 7.6664, 5.9232, 6.0291, 0.9595, 2.3097, 2.2584, 6.7190, 1.8930, 4.0331, 4.2566, 0.1282, 6.4232, 5.7772, 1.2547, 1.4663, 7.2552, 3.0988, 0.5364, 4.3420, 4.9725, 0.5227, 2.3160, 7.1593, 2.2104, 0.1538, 3.3136, 0.0879, 0.2268, 4.2217, 6.5187, 6.1510, 5.4715, 1.4739, 0.5235, 4.6210, 7.0038, 4.8701, 3.9902, 1.5534, 5.9494, 2.7750, 7.2218, 6.5275, 7.4020, 6.5165, 2.3648, 2.3400, 5.2632, 1.9063, 2.3749, 2.8801, 2.8251, 0.8746, 3.7982, 2.6891, 5.5711, 0.7525, 7.7588, 6.5339, 5.9344, 1.5248, 2.5976, 2.7150, 6.0124, 7.4841, 7.9635, 4.7531, 3.9036, 4.2821, 3.1920, 6.5449, 3.4940, 0.8757, 6.8546, 4.2495, 3.8029, 3.4406, 1.5625, 6.4137, 3.8046, 6.8628, 0.1776, 1.9396, 0.6532, 1.5135, 5.3135, 3.8652, 2.1236, 6.7060, 1.8559, 0.6578, 0.0288, 2.9500, 5.8886, 7.4580, 2.0190, 2.4482, 5.0170, 7.1498, 3.5582, 7.6468, 6.6579, 3.4345, 4.7807, 7.1816, 4.6681, 7.3450, 1.2560, 0.4264, 0.0988, 5.1477, 7.7408, 1.8656, 6.2184, 2.9601, 2.3192, 7.1924, 7.3805, 6.6338, 1.1155, 5.9406, 1.0839, 6.8488, 7.8440, 4.9525, 1.8653, 3.4800, 6.0628, 0.8503, 4.8132, 6.0675, 5.6032, 3.6124, 3.9378, 3.4613, 4.4206, 5.2020, 6.5051, 3.9746, 7.0738, 7.7039, 0.9475, 5.2024, 0.4460, 4.0230, 1.0498, 6.8790, 5.0954, 4.3688, 0.0579, 1.5060, 7.5666, 4.5581, 1.0632, 4.7764, 6.7044, 1.4392, 4.3548, 3.3248, 7.2307, 1.4125, 6.0656, 2.6928, 6.1314, 3.8828, 7.1228, 2.7944, 0.8643, 7.5105, 2.6291, 7.7028, 7.7900, 6.9062, 7.1068, 1.2096, 5.9925, 5.5771, 7.4319, 6.8058, 5.4069, 7.5201, 4.3338, 2.1575, 7.5843, 1.2349, 6.5488, 7.0432, 3.8830, 4.9863, 1.7722, 6.5116, 0.9726, 6.2924, 5.8801, 1.4267, 4.9243, 7.7263, 3.7668, 1.8711, 1.0099, 3.5256, 4.2713, 5.7590, 7.3030, 2.5636, 3.2022, 3.5140, 2.2378, 2.9125, 7.2977, 7.7995, 4.5452, 3.7109, 0.1353, 2.9218, 4.6255, 5.1640, 7.2028, 5.4680, 6.9258, 0.9144, 4.5075, 4.8073, 0.6566, 4.5084, 1.7126, 7.1717, 6.1732, 1.9380, 0.7073, 4.5638, 6.2000, 3.8410, 0.2443, 6.7154, 2.9200, 7.6831, 5.5980, 6.2822, 3.3203, 3.1051, 5.2432, 7.0362, 6.2711, 7.0526, 7.1975, 3.8572, 1.5468, 3.9781, 6.6240, 3.3217, 4.0948, 0.9286, 7.0991, 3.0108, 7.2689, 3.8587, 5.5623, 0.2027, 3.6368, 0.0010, 1.5764, 7.5836, 7.8608, 7.5849, 3.0207, 7.8802, 7.7114, 5.5389, 0.1184, 4.5518, 2.1239, 1.0543, 5.1985, 0.2674, 7.3331, 7.7043, 5.0352, 7.3058, 5.3836, 4.0054, 6.8913, 7.2248, 3.6997, 6.8976, 6.7995, 4.1713, 6.9872, 6.3782, 3.2728, 6.2877, 6.6532, 7.5848, 6.6651, 2.7143, 7.4311, 5.7382, 4.7733, 2.3591, 7.7889, 5.5198, 6.4484, 2.9765, 0.9576, 4.0088, 0.8117, 3.1960, 7.0248, 1.7414, 1.2355, 0.7471, 7.3841, 7.9584, 5.7200, 7.4815, 3.5565, 7.0080, 3.2398, 5.8232, 0.2831, 1.3388, 5.9008, 4.0912, 4.4140, 3.5812, 6.2451, 3.2612, 1.5917, 5.2047, 7.4908, 7.4442, 2.8806, 0.1755, 3.7591, 0.7599, 1.6556, 7.6088, 4.1696, 2.1202, 4.6328, 6.6044, 3.3940, 2.5435, 3.9866, 3.7252, 0.5342, 7.0544, 3.5472, 6.3619, 4.1232, 2.2255, 3.0552, 7.2593, 0.1524, 2.4115, 4.1663, 1.7693, 1.8469, 2.6506, 6.4632, 2.5339, 0.3842, 6.4324, 2.6829, 6.4840, 0.3276, 1.6189, 3.6853, 0.3723, 6.6436, 0.9761, 4.5121, 3.4625, 3.7312, 0.9524, 7.5328, 3.3208, 6.4496, 0.5576, 3.6430, 3.2962, 6.0647, 0.0636, 3.0145, 0.7641, 3.7508, 6.1062, 5.8854, 2.9300, 3.1474, 2.0487, 1.2496, 6.5371, 5.6622, 1.4151, 3.7755, 1.6951, 3.5764, 4.9542, 2.6969, 7.1912, 7.8203, 4.9232, 4.6200, 4.5892, 1.2128, 3.6821, 1.1574, 4.4619, 1.7278, 2.7539, 7.9956, 1.3067, 3.8135, 1.9099, 0.0523, 0.1696, 1.4981, 3.8686, 0.9680, 4.8313, 4.6916, 0.2617, 4.9999, 6.7270, 0.9291, 0.1190, 3.6454, 4.3806, 4.0452, 0.7444, 4.3136, 6.6594, 6.9706, 6.6868, 7.4025, 4.4097, 4.8531, 4.6524, 3.9393, 3.6397, 7.4877, 3.0394, 5.8194, 6.2051, 7.6235, 2.4220, 6.2710, 7.7192, 7.9259, 5.8960, 5.3438, 3.5736, 2.3736, 3.7104, 4.3736, 2.0457, 7.3725, 4.7461, 2.1755, 0.8789, 3.2911, 0.4676, 3.3015, 6.8944, 3.7300, 4.9800, 5.4142, 7.4139, 2.4429, 0.3317, 6.5580, 1.9414, 2.6403, 4.3637, 6.7428, 6.2721, 0.3794, 1.2533, 5.6627, 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7.3723, 1.6200, 5.5896, 4.6789, 2.5356, 7.0911, 0.1529, 1.2095, 1.0248, 1.3509, 1.6330, 1.9362, 1.1312, 3.3051, 4.9321, 1.6252, 4.1629, 2.4539, 5.3791, 5.8192, 5.8724, 3.4044, 3.6931, 5.4241, 7.0465, 1.9163, 7.9292, 3.5947, 1.2192, 7.4588, 2.8788, 6.8505, 5.0768, 3.2896, 2.1756, 5.3665, 6.3532, 1.8919, 1.1996, 4.2539, 0.5428, 0.9665, 0.4028, 7.6996, 7.1792, 2.0183, 3.1711, 5.9500, 1.5827, 5.3158, 2.6820, 2.2508, 3.5752, 3.6609, 4.6611, 6.3318, 6.4485, 1.0063, 3.8421, 0.3196, 3.2020, 7.8220, 2.3505, 1.2167, 4.7344, 4.5054, 7.4748, 4.9821, 2.1777, 6.2208, 3.5859, 6.0067, 2.6844, 4.7124, 4.9209, 5.7664, 7.8364, 2.5258, 2.8288, 3.2586, 2.9701, 5.1701, 0.4489, 4.5388, 6.2379, 1.3680, 2.1237, 2.5378, 0.9164, 1.9755, 4.0426, 1.8324, 1.0027, 3.0948, 1.0468, 1.5243, 7.2206, 0.0510, 1.0305, 3.5628, 1.4737, 0.1853, 3.5473, 4.5294, 1.1599, 2.7775, 7.8900, 7.4933, 2.2355, 0.5212, 5.8044, 5.6460, 0.3350, 4.1814, 0.3732, 6.2152, 2.5822, 6.1660, 6.7159, 7.9330, 0.9464, 5.5492, 5.8125, 2.6157, 6.4888, 4.4236, 5.5918, 1.7521, 2.9196, 3.2045, 7.1368, 2.8960, 1.2711, 0.0976, 4.9639, 2.8921, 1.6796, 7.0382, 0.8880, 3.7657, 5.3580, 2.9501, 7.9341, 0.1719, 5.9564, 4.4323, 7.7297, 7.8618, 0.5513, 7.6882, 3.4774, 6.4038, 2.1198, 2.8594, 5.8616, 4.5750, 0.4444, 2.8722, 4.9792, 2.7662, 6.9091, 5.5867, 4.9246, 3.7048, 6.9420, 6.8867, 2.4872, 5.4232, 2.8698, 7.1892, 3.5972, 5.2108, 6.8608, 6.3268, 1.8676, 7.3810, 6.0234, 3.0168, 3.8884, 3.0662, 4.5917, 6.2197, 1.8657, 4.4198, 1.6094, 2.7340, 7.2147, 6.2322, 7.2499, 1.5680, 5.1533, 6.9677, 1.5615, 6.7645, 3.5572, 7.2377, 7.8604, 6.8528, 3.8746, 0.5132, 3.4685, 2.8645, 5.3572, 2.5327, 4.9444, 6.8969, 4.9103, 6.2994, 6.7324, 4.9048, 3.4144, 2.7852, 6.5362, 4.8901, 5.7574, 4.6095, 7.5315, 0.1582, 5.8420, 6.5048, 6.7459, 1.4549, 0.5182, 2.3184, 0.4079, 3.9272, 0.2470, 1.3528, 5.0368, 3.7976, 3.7020, 7.4428, 5.6441, 7.5553, 2.0499, 1.3895, 4.6107, 3.1954, 4.8152, 5.4112, 2.9955, 0.0429, 0.2080, 1.6177, 0.7240, 2.9418, 5.1472, 2.0909, 6.0214, 6.9164
};

#define math_min(a, b) ((a) < (b) ? (a) : (b))
#define math_max(a, b) ((a) > (b) ? (a) : (b))

struct Timer {
	LARGE_INTEGER frequency;
	LARGE_INTEGER start;
	LARGE_INTEGER end;
	double interval;
};

inline Timer TimerInit() {
	Timer result = { 0 };
	if (::QueryPerformanceFrequency(&result.frequency) == FALSE) {
		std::cout << "Could not create timer\n";
	}
	return result;
}

inline void TimerStart(Timer& timer) {
	if (::QueryPerformanceCounter(&timer.start) == FALSE) {
		std::cout << "could not start timer\n";
	}
}

inline double TimerStop(Timer& timer) { // In seconds
	if (::QueryPerformanceCounter(&timer.end) == FALSE) {
		std::cout << "Could not end timer\n";
	}

	timer.interval = static_cast<double>(timer.end.QuadPart - timer.start.QuadPart) / timer.frequency.QuadPart;
	return timer.interval;
}
#else
#include "MyMath.h"
#include "RandoFloat.h"
#include "Timer.h"
#endif

struct WindowData {
    HWND hwnd;
    HDC hdcDisplay; // Front Buffer DC
    HDC hdcMemory;  // Back Buffer DC
    HINSTANCE hInstance; // Window instance
};

// This is sample data, can we move it into an appropriate struct? Or at least on the bottom into the lifecycle stuff

typedef double  (*MathFunction )(double val);

void* Initialize(const WindowData& window) {
	return (void*) (& window);
}

void Shutdown(void* userData) {
}

void Update(void* userData, float deltatTime) {
}

//
double power(double base, int exp) {
	if (exp < 0) {
		if (base == 0) {
			return -0; // Error!!
		}
		return 1 / (base * power(base, (-exp) - 1));
	}
	if (exp == 0) {
		return 1;
	}
	if (exp == 1) {
		return base;
	}
	return base * power(base, exp - 1);
}

int fact(int n) {
	return n <= 0 ? 1 : n * fact(n - 1);
}

double cos_121s(double x) {
	const double c1 = 0.99999999999925182;
	const double c2 = -0.49999999997024012;
	const double c3 = 0.041666666473384543;
	const double c4 = -0.001388888418000423;
	const double c5 = 0.0000248010406484558;
	const double c6 = -0.0000002752469638432;
	const double c7 = 0.0000000019907856854;

	double x2 = x * x;
	return (c1 + x2 * (c2 + x2 * (c3 + x2 * (c4 + x2 * (c5 + x2 * (c6 + c7 * x2))))));
}

double cos_121(double x) {
	double const pi = 3.1415926535897932384626433;	// pi
	double const twopi = 2.0 * pi;			// pi times 2
	double const two_over_pi = 2.0 / pi;		// 2/pi

	x = fmod(x, twopi);				// Get rid of values > 2* pi
	if (x < 0)x = -x;					// cos(-x) = cos(x)
	int quad = int(x * two_over_pi);			// Get quadrant # (0 to 3) we're in
	if (quad < 0) {
		quad = -quad;
	}

	switch (quad) {
	case 0: return  cos_121s(x);
	case 1: return -cos_121s(pi - x);
	case 2: return -cos_121s(x - pi);
	case 3: return  cos_121s(twopi - x);
	}
}

double sine(double rad) {
	{
		const double pi = 3.14159265358979323846;
		const double twoPi = 6.28318530717958623200;
		const double invTwoPi = 0.15915494309189534561;

		// Range reduction (-2pi to 2pi)
		int k = (int)((double)rad * invTwoPi);
		double x = (double)rad - (double)k * twoPi;

		// Range reduce to (-pi/2 to pi/2)
		x = math_min(x, pi - x);
		x = math_max(x, -pi - x);
		x = math_min(x, pi - x);

		rad = x;
	}

#if 0
	const int TERMS = 5;
	double sin = 0;
	for (int i = 0; i < TERMS; i++) { // That's Taylor series!!
		sin += power(-1, i) * power(rad, 2 * i + 1) / (double)fact(2 * i + 1);
	}
	return sin;
#else
	double const pi = 3.1415926535897932384626433;	// pi
	double const halfpi = pi / 2.0;			// pi divided by 2

	return cos_121(halfpi - rad);
#endif
}

double cosine(double rad) {
	const int TERMS = 6;
	double flip = 1.0f;
	{
		const double pi = 3.14159265358979323846;
		const double twoPi = 6.28318530717958623200;
		const double invTwoPi = 0.15915494309189534561;
		const double halfPi = 1.57079632679489655800;

		// Range reduction (-2pi to 2pi)
		int k = (int)((double)rad * invTwoPi);
		double x = (double)rad - (double)k * twoPi;

		// Range reduce -pi to pi
		if (x < -pi) {
			x = pi - (-pi - x);
		}
		else if (x > pi) {
			x = -pi + (x - pi);
		}

		// Range reduce to -pi/2 to pi/2
		if (x < -halfPi) {
			x = -(x + pi);
			flip = -1.0f;
		}
		else if (x > halfPi) {
			flip = -1.0f;
			x = -(pi - x);
		}

		rad = x;
	}

#if 0
	double cos = 0;
	for (int i = 0; i < TERMS; i++) { // That's also Taylor series!!
		cos += power(-1, i) * power(rad, 2 * i) / (double)fact(2 * i);
	}
	return cos * flip;
#else
	return cos_121(rad) * flip;
#endif
}

double tan_82s(double x) {
	const double c1 = 211.849369664121;
	const double c2 = -12.5288887278448;
	const double c3 = 269.7350131214121;
	const double c4 = -71.4145309347748;

	double x2 = x * x;
	return (x * (c1 + c2 * x2) / (c3 + x2 * (c4 + x2)));
}

double tan_82(double x) {
	const double pi = 3.1415926535897932384626433;	// pi
	const double four_over_pi = 4.0 / pi;		// 4/pi, used in tan routines
	const double twoPi = 6.28318530717958623200;
	const double invTwoPi = 0.15915494309189534561;
	const double qtrpi = pi / 4.0;			// pi/4.0, used in tan routines
	const double halfpi = pi / 2.0;			// pi divided by 2
	const double threehalfpi = 3.0 * pi / 2.0;  		// pi times 3/2, used in tan routines
	const double twopi = 2.0 * pi;			// pi times 2
	const double halfPi = 1.57079632679489655800;

	// Range reduction (-2pi to 2pi)
	int k = (int)((double)x * invTwoPi);
	x = (double)x - (double)k * twoPi;

	// Range reduce to 0 to 2 pi
	if (x < 0.0) {
		x = twoPi - (- x);
	}

	// 0 to pi
	if (x > pi) {
		x = x - pi;
	}

	// 0 to pi / 2
	double flip = 1.0f;
	if (x > halfPi) {
		x = (halfPi - (x - halfPi));
		flip = -flip;
	}

	int octant = int(x * four_over_pi);			// Get octant # (0 to 7)
	if (octant < 0) {
		octant = -octant;
	}
	switch (octant) {
	case 0: return      tan_82s(x					* four_over_pi) * flip;
	case 1: return  1.0 / tan_82s((halfpi - x)		* four_over_pi) * flip;
	case 2: return -1.0 / tan_82s((x - halfpi)		* four_over_pi) * flip;
	case 3: return -tan_82s((pi - x)				* four_over_pi) * flip;
	case 4: return      tan_82s((x - pi)			* four_over_pi) * flip;
	case 5: return  1.0 / tan_82s((threehalfpi - x) * four_over_pi) * flip;
	case 6: return -1.0 / tan_82s((x - threehalfpi) * four_over_pi) * flip;
	case 7: return -tan_82s((twopi - x)				* four_over_pi) * flip;
	}
	return 0;
}

double tangent(double rad) {
#if 1
	double denom = 0.0f;
	return sine(rad) / cosine(rad);
#else
	return tan_82(rad);
#endif
}
//

void Render(void* userData, HDC backBuffer, RECT client) {
	WindowData& window = *(WindowData*)userData;

	COLORREF bgColor = RGB(30, 30, 30);
	HBRUSH bgBrush = CreateSolidBrush(bgColor);
	HBRUSH oldBrush = (HBRUSH)SelectObject(backBuffer, bgBrush);
	FillRect(backBuffer, &client, bgBrush);
	SelectObject(backBuffer, oldBrush);
	DeleteObject(bgBrush);

	int middle = (client.bottom - client.top) / 2;
	int width = (client.right - client.left);
	int height = (client.bottom - client.top);

	float xAxisLength = 14.0f;
	float xAxisValue = -7.0f;
	float xAxisStep = xAxisLength / (float)width;

	float yAxisScale = 150.0f;
	float yAxisValue = 0.0f;

	HGDIOBJ ogPen = SelectObject(backBuffer, GetStockObject(DC_PEN));

	SetDCPenColor(backBuffer, RGB(180, 20, 20));
	MoveToEx(backBuffer, width / 2, 0, (LPPOINT)NULL);
	LineTo(backBuffer, width / 2, height);

	const double pi = (3.14159265358979323846 / 14.0) * (double)width;
	const double halfPi = ((3.14159265358979323846 / 2.0) / 14.0) * (double)width;

	SetDCPenColor(backBuffer, RGB(20, 180, 20));
	MoveToEx(backBuffer, (double)(width / 2) - pi, 0, (LPPOINT)NULL);
	LineTo(backBuffer, (double)(width / 2) - pi, height);
	MoveToEx(backBuffer, (double)(width / 2) + pi, 0, (LPPOINT)NULL);
	LineTo(backBuffer, (double)(width / 2) + pi, height);

	SetDCPenColor(backBuffer, RGB(20, 20, 180));
	MoveToEx(backBuffer, (double)(width / 2) - halfPi, 0, (LPPOINT)NULL);
	LineTo(backBuffer, (double)(width / 2) - halfPi, height);
	MoveToEx(backBuffer, (double)(width / 2) + halfPi, 0, (LPPOINT)NULL);
	LineTo(backBuffer, (double)(width / 2) + halfPi, height);

#if 1
	MathFunction baseFun = std::tan;
	MathFunction compFun = tangent;
#elif 0
	MathFunction baseFun = std::sin;
	MathFunction compFun = sine;
#elif 0
	MathFunction baseFun = std::cos;
	MathFunction compFun = cosine;
#endif

	SetDCPenColor(backBuffer, RGB(255, 255, 255));
	if (true) { // sin
		xAxisValue = -7.0f;
		yAxisValue = baseFun(xAxisValue)* yAxisScale + (float)middle;
		MoveToEx(backBuffer, 0, yAxisValue, (LPPOINT)NULL);
		xAxisValue += xAxisStep;

		for (int x = 1; x < width; ++x) {
			yAxisValue = baseFun(xAxisValue) * yAxisScale + (float)middle;
			LineTo(backBuffer, x, yAxisValue);
			xAxisValue += xAxisStep;
			if (xAxisValue > xAxisLength) {
				std::cout << "Error, bad axis\n";
			}
		}
	}

	SetDCPenColor(backBuffer, RGB(0, 0, 0));
	{ // sin
		xAxisValue = -7.0f;
		yAxisValue = compFun(xAxisValue) * yAxisScale + (float)middle;
		MoveToEx(backBuffer, 0, yAxisValue, (LPPOINT)NULL);
		xAxisValue += xAxisStep;

		for (int x = 1; x < width; ++x) {
			yAxisValue = compFun(xAxisValue) * yAxisScale + (float)middle;
			LineTo(backBuffer, x, yAxisValue);
			xAxisValue += xAxisStep;
			if (xAxisValue > xAxisLength) {
				std::cout << "Error, bad axis\n";
			}
		}
	}

	SelectObject(backBuffer, ogPen);
}

LRESULT CALLBACK WndProc(HWND hwnd, UINT iMsg, WPARAM wParam, LPARAM lParam);
int WINAPI WinMain(HINSTANCE hInstance, HINSTANCE hPrevInstance, PSTR szCmdLine, int iCmdShow) {
	WNDCLASSA wndclass;
	wndclass.style = CS_HREDRAW | CS_VREDRAW;
	wndclass.lpfnWndProc = WndProc;
	wndclass.cbClsExtra = 0;
	wndclass.cbWndExtra = 0;
	wndclass.hInstance = hInstance;
	wndclass.hIcon = LoadIcon(NULL, IDI_APPLICATION);
	wndclass.hCursor = LoadCursor(NULL, IDC_ARROW);
	wndclass.hbrBackground = (HBRUSH)(COLOR_BTNFACE + 1);
	wndclass.lpszMenuName = 0;
	wndclass.lpszClassName = WINDOW_CLASS;
	RegisterClassA(&wndclass);

	RECT rClient;
	SetRect(&rClient, 0, 0, WINDOW_WIDTH, WINDOW_HEIGHT);
	AdjustWindowRect(&rClient, WS_OVERLAPPEDWINDOW | WS_VISIBLE, FALSE);

	const char* title_a = WINDOW_TITLE;
	wchar_t title_w[64] = { 0 };
	for (int i = 0; i < 63 && title_a[i] != 0; title_w[i] = title_a[i], ++i);

	HWND hwnd = CreateWindowA(WINDOW_CLASS, (char*)title_w, WS_OVERLAPPEDWINDOW | WS_VISIBLE,
		(GetSystemMetrics(SM_CXSCREEN) / 2) - ((rClient.right - rClient.left) / 2),
		(GetSystemMetrics(SM_CYSCREEN) / 2) - ((rClient.right - rClient.left) / 2),
		(rClient.right - rClient.left), (rClient.bottom - rClient.top), NULL, NULL, hInstance, 0);

	WindowData windowData = { 0 };
	windowData.hwnd = hwnd;
	windowData.hInstance = hInstance;
	HBITMAP hbmBackBuffer; // Back Buffer Bitmap
	HBITMAP hbmOld; // For restoring previous state
	{ // Create back buffer
		windowData.hdcDisplay = GetDC(hwnd);
		windowData.hdcMemory = CreateCompatibleDC(windowData.hdcDisplay);
		hbmBackBuffer = CreateCompatibleBitmap(windowData.hdcDisplay, GetSystemMetrics(SM_CXSCREEN), GetSystemMetrics(SM_CYSCREEN));
		hbmOld = (HBITMAP)SelectObject(windowData.hdcMemory, hbmBackBuffer);
	}

	LONG_PTR lptr = (LONG_PTR)(&windowData);
	SetWindowLongPtrA(hwnd, GWLP_USERDATA, lptr);

	ShowWindow(hwnd, SW_NORMAL);
	void* userData = Initialize(windowData);

	MSG msg;
	bool running = true;
	bool quit = false;

	LARGE_INTEGER timerFrequency;
	LARGE_INTEGER thisTick;
	LARGE_INTEGER lastTick;
	LARGE_INTEGER timerStart;
	LONGLONG timeDelta;

	if (!QueryPerformanceFrequency(&timerFrequency)) {
		OutputDebugStringA("WinMain: QueryPerformanceFrequency failed\n");
	}

	QueryPerformanceCounter(&thisTick);
	lastTick = thisTick;
	while (!quit) {
		while (PeekMessage(&msg, NULL, 0, 0, PM_REMOVE)) {
			if (msg.message == WM_QUIT) {
				quit = true;
				break;
			}
			else if (msg.message == WM_DESTROY) {
				Shutdown(userData);
				{ // Destroy back buffer
					SelectObject(windowData.hdcMemory, hbmOld);
					DeleteObject(hbmBackBuffer);
					DeleteDC(windowData.hdcMemory);
					ReleaseDC(hwnd, windowData.hdcDisplay);
				}
				running = false;
			}
			TranslateMessage(&msg);
			DispatchMessage(&msg);
		}
		if (running) {
			RECT clientRect = {};
			GetClientRect(hwnd, &clientRect);

			QueryPerformanceCounter(&thisTick);
			timeDelta = thisTick.QuadPart - lastTick.QuadPart;
			double deltaTime = (double)timeDelta * 1000.0 / (double)timerFrequency.QuadPart;
			Update(userData, (float)deltaTime);
			Render(userData, windowData.hdcMemory, clientRect);
			lastTick = thisTick;

			InvalidateRect(hwnd, NULL, false);
			Sleep(1);
		}
	}

	return (int)msg.wParam;
}

LRESULT CALLBACK WndProc(HWND hwnd, UINT iMsg, WPARAM wParam, LPARAM lParam) {
	switch (iMsg) {
	case WM_CLOSE:
		DestroyWindow(hwnd);
		break;
	case WM_DESTROY:
		PostQuitMessage(0);
		break;
	case WM_ERASEBKGND:
		return TRUE;
	case WM_PAINT:
	{
		LONG_PTR lptr = GetWindowLongPtrA(hwnd, GWLP_USERDATA);
		WindowData* windowData = (WindowData*)lptr;

		RECT rClient = {};
		GetClientRect(hwnd, &rClient);
		BitBlt(windowData->hdcDisplay, 0, 0, rClient.right - rClient.left, rClient.bottom - rClient.top, windowData->hdcMemory, 0, 0, SRCCOPY);
		ValidateRect(hwnd, NULL);
	}
	return TRUE;
	}
	return DefWindowProc(hwnd, iMsg, wParam, lParam);
}

void TestRange(const char* name, MathFunction stock, MathFunction test) {
	std::cout << "Testing: " << name << "\n";

	const int loop_min = -100000;
	const int loop_max = 100000;
	const float max_delta = 0.00009f;

	Timer stopwatch = TimerInit();
	double time = 0.0f;
	int err_max = 100;

	int errCount = 0;
	float total = 0.0f;
	TimerStart(stopwatch);
	for (int i = loop_min; i < loop_max; ++i) {
		float result = stock((float)i);
		if (result != result) {
			//std::cout << "stock nan at: " << i << "\n";
			errCount += 1;
			if (errCount == err_max) {
				//std::cout << "Too many errors, stopping\n";
				break;
			}
		}
		total += result;
	}
	time = TimerStop(stopwatch) * 1000.0;
	std::cout << "stock(" << loop_min << " - " << loop_max << "): " << time << "ms [" << total << "]\n";

	errCount = 0;
	total = 0.0f;
	TimerStart(stopwatch);
	for (int i = loop_min; i < loop_max; ++i) {
		float result = stock((float)i);
		if (result != result) {
			std::cout << "mine nan at: " << i << "\n";
			errCount += 1;
			if (errCount == err_max) {
				std::cout << "Too many errors, stopping\n";
				break;
			}
		}
		total += result;
	}
	time = TimerStop(stopwatch) * 1000.0;
	std::cout << "2nd(" << loop_min << " - " << loop_max << "): " << time << "ms [" << total << "]\n";

	errCount = 0;
	total = 0.0f;
	TimerStart(stopwatch);
	for (int i = loop_min; i < loop_max; ++i) {
		float result = test((float)i);
		if (result != result) {
			std::cout << "mine nan at: " << i << "\n";
			errCount += 1;
			if (errCount == err_max) {
				std::cout << "Too many errors, stopping\n";
				break;
			}
		}
		total += result;
	}
	time = TimerStop(stopwatch) * 1000.0;
	std::cout << "mine(" << loop_min << " - " << loop_max << "): " << time << "ms [" << total << "]\n";

	errCount = 0;
	for (int i = loop_min; i < loop_max; ++i) {
		float result1 = stock((float)i);
		float result2 = test((float)i);
		float delta = 0.0f;
		//std::cout << i << ": " << result1 << " / " << result2 << "\n";
		if (result1 > result2) {
			delta = result1 - result2;
		}
		else if (result2 > result1) {
			delta = result2 - result1;
		}

		if (delta > max_delta || result2 != result2) {
			std::cout << "divergence at: " << i << ", with delta: " << delta << "\n";

			errCount += 1;
			if (errCount == err_max) {
				std::cout << "Too many errors, stopping\n";
				break;
			}
		}
	}

	errCount = 0;
	for (int i = 0; i < num_floats; ++i) {
		float result1 = stock(rando_floats[i]);
		float result2 = test(rando_floats[i]);
		float delta = 0.0f;
		//std::cout << i << ": " << result1 << " / " << result2 << "\n";
		if (result1 > result2) {
			delta = result1 - result2;
		}
		else if (result2 > result1) {
			delta = result2 - result1;
		}

		if (delta > max_delta || result2 != result2) {
			std::cout << "divergence at: " << i << ", with delta: " << delta << "\n";

			errCount += 1;
			if (errCount == err_max) {
				std::cout << "Too many errors, stopping\n";
				break;
			}
		}
	}

	std::cout << "\n";
}

int main(int argc, char** argv) {
	/*
	double twoPi = 3.14159265358979323846 / 2.0;
	std::cout << std::fixed << std::setprecision(20);
	std::cout << "double      " << twoPi << std::endl;
	*/
	//TestRange("cos", std::cos, cosine);

	double pi = 3.14159265358979323846;
	double neinty = 90.0 * (pi / 180); // Also bad at 270
	std::cout << "Tan 90: " << std::tan(neinty) << " / " << tangent(neinty) << "\n";
	std::cout << "Cos 90: " << std::cos(neinty) << " / " << cosine(neinty) << "\n";

	TestRange("sin", std::sin, sine);
	TestRange("cos", std::cos, cosine);
	TestRange("tan", std::tan, tangent);
	std::cout << "\nDone with tests\n";

	return WinMain(GetModuleHandle(NULL), NULL, GetCommandLineA(), SW_SHOWDEFAULT);
}