23e6278ed9
rounding) has better spread. Implement fp16_sin() to go along with fp16_cos(). In the rendering loop, switch from addition to subtraction so the center of the pattern will be a trough rather than a peak. This is completely arbitrary, of course, but looks better to me.
156 lines
4.7 KiB
C
156 lines
4.7 KiB
C
/*-
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* Copyright (c) 2015 Dag-Erling Smørgrav
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*
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* $FreeBSD$
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*/
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#ifdef _KERNEL
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#include <sys/libkern.h>
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#else
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#include <stdio.h>
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#include <strings.h>
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#endif
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#include "fp16.h"
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/*
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* Compute the quare root of x, using Newton's method with 2^(log2(x)/2)
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* as the initial estimate.
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*/
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fp16_t
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fp16_sqrt(fp16_t x)
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{
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fp16_t y, delta;
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signed int log2x;
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/* special case */
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if (x == 0)
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return (0);
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/* shift toward 0 by half the logarithm */
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log2x = flsl(x) - 1;
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if (log2x >= 16) {
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y = x >> (log2x - 16) / 2;
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} else {
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#if 0
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y = x << (16 - log2x) / 2;
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#else
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/* XXX for now, return 0 for anything < 1 */
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return (0);
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#endif
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}
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while (y > 0) {
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/* delta = y^2 / 2y */
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delta = fp16_div(fp16_sub(fp16_mul(y, y), x), y * 2);
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if (delta == 0)
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break;
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y = fp16_sub(y, delta);
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}
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return (y);
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}
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static fp16_t fp16_sin_table[256] = {
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0, 402, 804, 1206, 1608, 2010, 2412, 2814,
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3215, 3617, 4018, 4420, 4821, 5222, 5622, 6023,
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6423, 6823, 7223, 7623, 8022, 8421, 8819, 9218,
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9616, 10013, 10410, 10807, 11204, 11600, 11995, 12390,
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12785, 13179, 13573, 13966, 14359, 14751, 15142, 15533,
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15923, 16313, 16702, 17091, 17479, 17866, 18253, 18638,
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19024, 19408, 19792, 20175, 20557, 20938, 21319, 21699,
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22078, 22456, 22833, 23210, 23586, 23960, 24334, 24707,
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25079, 25450, 25820, 26189, 26557, 26925, 27291, 27656,
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28020, 28383, 28745, 29105, 29465, 29824, 30181, 30538,
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30893, 31247, 31600, 31952, 32302, 32651, 32999, 33346,
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33692, 34036, 34379, 34721, 35061, 35400, 35738, 36074,
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36409, 36743, 37075, 37406, 37736, 38064, 38390, 38716,
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39039, 39362, 39682, 40002, 40319, 40636, 40950, 41263,
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41575, 41885, 42194, 42501, 42806, 43110, 43412, 43712,
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44011, 44308, 44603, 44897, 45189, 45480, 45768, 46055,
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46340, 46624, 46906, 47186, 47464, 47740, 48015, 48288,
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48558, 48828, 49095, 49360, 49624, 49886, 50146, 50403,
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50660, 50914, 51166, 51416, 51665, 51911, 52155, 52398,
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52639, 52877, 53114, 53348, 53581, 53811, 54040, 54266,
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54491, 54713, 54933, 55152, 55368, 55582, 55794, 56004,
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56212, 56417, 56621, 56822, 57022, 57219, 57414, 57606,
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57797, 57986, 58172, 58356, 58538, 58718, 58895, 59070,
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59243, 59414, 59583, 59749, 59913, 60075, 60235, 60392,
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60547, 60700, 60850, 60998, 61144, 61288, 61429, 61568,
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61705, 61839, 61971, 62100, 62228, 62353, 62475, 62596,
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62714, 62829, 62942, 63053, 63162, 63268, 63371, 63473,
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63571, 63668, 63762, 63854, 63943, 64030, 64115, 64197,
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64276, 64353, 64428, 64501, 64571, 64638, 64703, 64766,
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64826, 64884, 64939, 64992, 65043, 65091, 65136, 65179,
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65220, 65258, 65294, 65327, 65358, 65386, 65412, 65436,
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65457, 65475, 65491, 65505, 65516, 65524, 65531, 65534,
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};
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/*
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* Compute the sine of theta.
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*/
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fp16_t
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fp16_sin(fp16_t theta)
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{
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unsigned int i;
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i = 1024 * (theta % FP16_2PI) / FP16_2PI;
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switch (i / 256) {
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case 0:
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return (fp16_sin_table[i % 256]);
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case 1:
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return (fp16_sin_table[255 - i % 256]);
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case 2:
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return (-fp16_sin_table[i % 256]);
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case 3:
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return (-fp16_sin_table[255 - i % 256]);
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default:
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/* inconceivable! */
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return (0);
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}
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}
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/*
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* Compute the cosine of theta.
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*/
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fp16_t
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fp16_cos(fp16_t theta)
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{
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unsigned int i;
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i = 1024 * (theta % FP16_2PI) / FP16_2PI;
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switch (i / 256) {
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case 0:
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return (fp16_sin_table[255 - i % 256]);
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case 1:
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return (-fp16_sin_table[i % 256]);
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case 2:
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return (-fp16_sin_table[255 - i % 256]);
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case 3:
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return (fp16_sin_table[i % 256]);
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default:
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/* inconceivable! */
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return (0);
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}
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}
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