1 /*- 2 * Copyright (c) 2015 Dag-Erling Smørgrav 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 1. Redistributions of source code must retain the above copyright 9 * notice, this list of conditions and the following disclaimer. 10 * 2. Redistributions in binary form must reproduce the above copyright 11 * notice, this list of conditions and the following disclaimer in the 12 * documentation and/or other materials provided with the distribution. 13 * 14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 24 * SUCH DAMAGE. 25 */ 26 27 #ifdef _KERNEL 28 #include <sys/libkern.h> 29 #else 30 #include <stdio.h> 31 #include <strings.h> 32 #endif 33 34 #include "fp16.h" 35 36 /* 37 * Compute the quare root of x, using Newton's method with 2^(log2(x)/2) 38 * as the initial estimate. 39 */ 40 fp16_t 41 fp16_sqrt(fp16_t x) 42 { 43 fp16_t y, delta; 44 signed int log2x; 45 46 /* special case */ 47 if (x == 0) 48 return (0); 49 50 /* shift toward 0 by half the logarithm */ 51 log2x = flsl(x) - 1; 52 if (log2x >= 16) { 53 y = x >> (log2x - 16) / 2; 54 } else { 55 #if 0 56 y = x << (16 - log2x) / 2; 57 #else 58 /* XXX for now, return 0 for anything < 1 */ 59 return (0); 60 #endif 61 } 62 while (y > 0) { 63 /* delta = y^2 / 2y */ 64 delta = fp16_div(fp16_sub(fp16_mul(y, y), x), y * 2); 65 if (delta == 0) 66 break; 67 y = fp16_sub(y, delta); 68 } 69 return (y); 70 } 71 72 static fp16_t fp16_sin_table[256] = { 73 0, 402, 804, 1206, 1608, 2010, 2412, 2814, 74 3215, 3617, 4018, 4420, 4821, 5222, 5622, 6023, 75 6423, 6823, 7223, 7623, 8022, 8421, 8819, 9218, 76 9616, 10013, 10410, 10807, 11204, 11600, 11995, 12390, 77 12785, 13179, 13573, 13966, 14359, 14751, 15142, 15533, 78 15923, 16313, 16702, 17091, 17479, 17866, 18253, 18638, 79 19024, 19408, 19792, 20175, 20557, 20938, 21319, 21699, 80 22078, 22456, 22833, 23210, 23586, 23960, 24334, 24707, 81 25079, 25450, 25820, 26189, 26557, 26925, 27291, 27656, 82 28020, 28383, 28745, 29105, 29465, 29824, 30181, 30538, 83 30893, 31247, 31600, 31952, 32302, 32651, 32999, 33346, 84 33692, 34036, 34379, 34721, 35061, 35400, 35738, 36074, 85 36409, 36743, 37075, 37406, 37736, 38064, 38390, 38716, 86 39039, 39362, 39682, 40002, 40319, 40636, 40950, 41263, 87 41575, 41885, 42194, 42501, 42806, 43110, 43412, 43712, 88 44011, 44308, 44603, 44897, 45189, 45480, 45768, 46055, 89 46340, 46624, 46906, 47186, 47464, 47740, 48015, 48288, 90 48558, 48828, 49095, 49360, 49624, 49886, 50146, 50403, 91 50660, 50914, 51166, 51416, 51665, 51911, 52155, 52398, 92 52639, 52877, 53114, 53348, 53581, 53811, 54040, 54266, 93 54491, 54713, 54933, 55152, 55368, 55582, 55794, 56004, 94 56212, 56417, 56621, 56822, 57022, 57219, 57414, 57606, 95 57797, 57986, 58172, 58356, 58538, 58718, 58895, 59070, 96 59243, 59414, 59583, 59749, 59913, 60075, 60235, 60392, 97 60547, 60700, 60850, 60998, 61144, 61288, 61429, 61568, 98 61705, 61839, 61971, 62100, 62228, 62353, 62475, 62596, 99 62714, 62829, 62942, 63053, 63162, 63268, 63371, 63473, 100 63571, 63668, 63762, 63854, 63943, 64030, 64115, 64197, 101 64276, 64353, 64428, 64501, 64571, 64638, 64703, 64766, 102 64826, 64884, 64939, 64992, 65043, 65091, 65136, 65179, 103 65220, 65258, 65294, 65327, 65358, 65386, 65412, 65436, 104 65457, 65475, 65491, 65505, 65516, 65524, 65531, 65534, 105 }; 106 107 /* 108 * Compute the sine of theta. 109 */ 110 fp16_t 111 fp16_sin(fp16_t theta) 112 { 113 unsigned int i; 114 115 i = 1024 * (theta % FP16_2PI) / FP16_2PI; 116 switch (i / 256) { 117 case 0: 118 return (fp16_sin_table[i % 256]); 119 case 1: 120 return (fp16_sin_table[255 - i % 256]); 121 case 2: 122 return (-fp16_sin_table[i % 256]); 123 case 3: 124 return (-fp16_sin_table[255 - i % 256]); 125 default: 126 /* inconceivable! */ 127 return (0); 128 } 129 } 130 131 /* 132 * Compute the cosine of theta. 133 */ 134 fp16_t 135 fp16_cos(fp16_t theta) 136 { 137 unsigned int i; 138 139 i = 1024 * (theta % FP16_2PI) / FP16_2PI; 140 switch (i / 256) { 141 case 0: 142 return (fp16_sin_table[255 - i % 256]); 143 case 1: 144 return (-fp16_sin_table[i % 256]); 145 case 2: 146 return (-fp16_sin_table[255 - i % 256]); 147 case 3: 148 return (fp16_sin_table[i % 256]); 149 default: 150 /* inconceivable! */ 151 return (0); 152 } 153 } 154