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/*-
* Copyright (c) 2015 Dag-Erling Smørgrav
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. 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 AUTHOR 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 AUTHOR 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.
*
* $FreeBSD$
*/
#ifdef _KERNEL
#include <sys/libkern.h>
#else
#include <stdio.h>
#include <strings.h>
#endif
#include "fp16.h"
/*
* Compute the quare root of x, using Newton's method with 2^(log2(x)/2)
* as the initial estimate.
*/
fp16_t
fp16_sqrt(fp16_t x)
{
fp16_t y, delta;
signed int log2x;
/* special case */
if (x == 0)
return (0);
/* shift toward 0 by half the logarithm */
log2x = flsl(x) - 1;
if (log2x >= 16) {
y = x >> (log2x - 16) / 2;
} else {
#if 0
y = x << (16 - log2x) / 2;
#else
/* XXX for now, return 0 for anything < 1 */
return (0);
#endif
}
while (y > 0) {
/* delta = y^2 / 2y */
delta = fp16_div(fp16_sub(fp16_mul(y, y), x), y * 2);
if (delta == 0)
break;
y = fp16_sub(y, delta);
}
return (y);
}
static fp16_t fp16_sin_table[256] = {
0, 402, 804, 1206, 1608, 2010, 2412, 2814,
3215, 3617, 4018, 4420, 4821, 5222, 5622, 6023,
6423, 6823, 7223, 7623, 8022, 8421, 8819, 9218,
9616, 10013, 10410, 10807, 11204, 11600, 11995, 12390,
12785, 13179, 13573, 13966, 14359, 14751, 15142, 15533,
15923, 16313, 16702, 17091, 17479, 17866, 18253, 18638,
19024, 19408, 19792, 20175, 20557, 20938, 21319, 21699,
22078, 22456, 22833, 23210, 23586, 23960, 24334, 24707,
25079, 25450, 25820, 26189, 26557, 26925, 27291, 27656,
28020, 28383, 28745, 29105, 29465, 29824, 30181, 30538,
30893, 31247, 31600, 31952, 32302, 32651, 32999, 33346,
33692, 34036, 34379, 34721, 35061, 35400, 35738, 36074,
36409, 36743, 37075, 37406, 37736, 38064, 38390, 38716,
39039, 39362, 39682, 40002, 40319, 40636, 40950, 41263,
41575, 41885, 42194, 42501, 42806, 43110, 43412, 43712,
44011, 44308, 44603, 44897, 45189, 45480, 45768, 46055,
46340, 46624, 46906, 47186, 47464, 47740, 48015, 48288,
48558, 48828, 49095, 49360, 49624, 49886, 50146, 50403,
50660, 50914, 51166, 51416, 51665, 51911, 52155, 52398,
52639, 52877, 53114, 53348, 53581, 53811, 54040, 54266,
54491, 54713, 54933, 55152, 55368, 55582, 55794, 56004,
56212, 56417, 56621, 56822, 57022, 57219, 57414, 57606,
57797, 57986, 58172, 58356, 58538, 58718, 58895, 59070,
59243, 59414, 59583, 59749, 59913, 60075, 60235, 60392,
60547, 60700, 60850, 60998, 61144, 61288, 61429, 61568,
61705, 61839, 61971, 62100, 62228, 62353, 62475, 62596,
62714, 62829, 62942, 63053, 63162, 63268, 63371, 63473,
63571, 63668, 63762, 63854, 63943, 64030, 64115, 64197,
64276, 64353, 64428, 64501, 64571, 64638, 64703, 64766,
64826, 64884, 64939, 64992, 65043, 65091, 65136, 65179,
65220, 65258, 65294, 65327, 65358, 65386, 65412, 65436,
65457, 65475, 65491, 65505, 65516, 65524, 65531, 65534,
};
/*
* Compute the sine of theta.
*/
fp16_t
fp16_sin(fp16_t theta)
{
unsigned int i;
i = 1024 * (theta % FP16_2PI) / FP16_2PI;
switch (i / 256) {
case 0:
return (fp16_sin_table[i % 256]);
case 1:
return (fp16_sin_table[255 - i % 256]);
case 2:
return (-fp16_sin_table[i % 256]);
case 3:
return (-fp16_sin_table[255 - i % 256]);
default:
/* inconceivable! */
return (0);
}
}
/*
* Compute the cosine of theta.
*/
fp16_t
fp16_cos(fp16_t theta)
{
unsigned int i;
i = 1024 * (theta % FP16_2PI) / FP16_2PI;
switch (i / 256) {
case 0:
return (fp16_sin_table[255 - i % 256]);
case 1:
return (-fp16_sin_table[i % 256]);
case 2:
return (-fp16_sin_table[255 - i % 256]);
case 3:
return (fp16_sin_table[i % 256]);
default:
/* inconceivable! */
return (0);
}
}
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