fp16.c

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    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  * $FreeBSD$
   27  */
   28 
   29 #ifdef _KERNEL
   30 #include <sys/libkern.h>
   31 #else
   32 #include <stdio.h>
   33 #include <strings.h>
   34 #endif
   35 
   36 #include "fp16.h"
   37 
   38 /*
   39  * Compute the quare root of x, using Newton's method with 2^(log2(x)/2)
   40  * as the initial estimate.
   41  */
   42 fp16_t
   43 fp16_sqrt(fp16_t x)
   44 {
   45         fp16_t y, delta;
   46         signed int log2x;
   47 
   48         /* special case */
   49         if (x == 0)
   50                 return (0);
   51 
   52         /* shift toward 0 by half the logarithm */
   53         log2x = flsl(x) - 1;
   54         if (log2x >= 16) {
   55                 y = x >> (log2x - 16) / 2;
   56         } else {
   57 #if 0
   58                 y = x << (16 - log2x) / 2;
   59 #else
   60                 /* XXX for now, return 0 for anything < 1 */
   61                 return (0);
   62 #endif
   63         }
   64         while (y > 0) {
   65                 /* delta = y^2 / 2y */
   66                 delta = fp16_div(fp16_sub(fp16_mul(y, y), x), y * 2);
   67                 if (delta == 0)
   68                         break;
   69                 y = fp16_sub(y, delta);
   70         }
   71         return (y);
   72 }
   73 
   74 static fp16_t fp16_sin_table[256] = {
   75             0,    402,    804,   1206,   1608,   2010,   2412,   2814,
   76          3215,   3617,   4018,   4420,   4821,   5222,   5622,   6023,
   77          6423,   6823,   7223,   7623,   8022,   8421,   8819,   9218,
   78          9616,  10013,  10410,  10807,  11204,  11600,  11995,  12390,
   79         12785,  13179,  13573,  13966,  14359,  14751,  15142,  15533,
   80         15923,  16313,  16702,  17091,  17479,  17866,  18253,  18638,
   81         19024,  19408,  19792,  20175,  20557,  20938,  21319,  21699,
   82         22078,  22456,  22833,  23210,  23586,  23960,  24334,  24707,
   83         25079,  25450,  25820,  26189,  26557,  26925,  27291,  27656,
   84         28020,  28383,  28745,  29105,  29465,  29824,  30181,  30538,
   85         30893,  31247,  31600,  31952,  32302,  32651,  32999,  33346,
   86         33692,  34036,  34379,  34721,  35061,  35400,  35738,  36074,
   87         36409,  36743,  37075,  37406,  37736,  38064,  38390,  38716,
   88         39039,  39362,  39682,  40002,  40319,  40636,  40950,  41263,
   89         41575,  41885,  42194,  42501,  42806,  43110,  43412,  43712,
   90         44011,  44308,  44603,  44897,  45189,  45480,  45768,  46055,
   91         46340,  46624,  46906,  47186,  47464,  47740,  48015,  48288,
   92         48558,  48828,  49095,  49360,  49624,  49886,  50146,  50403,
   93         50660,  50914,  51166,  51416,  51665,  51911,  52155,  52398,
   94         52639,  52877,  53114,  53348,  53581,  53811,  54040,  54266,
   95         54491,  54713,  54933,  55152,  55368,  55582,  55794,  56004,
   96         56212,  56417,  56621,  56822,  57022,  57219,  57414,  57606,
   97         57797,  57986,  58172,  58356,  58538,  58718,  58895,  59070,
   98         59243,  59414,  59583,  59749,  59913,  60075,  60235,  60392,
   99         60547,  60700,  60850,  60998,  61144,  61288,  61429,  61568,
  100         61705,  61839,  61971,  62100,  62228,  62353,  62475,  62596,
  101         62714,  62829,  62942,  63053,  63162,  63268,  63371,  63473,
  102         63571,  63668,  63762,  63854,  63943,  64030,  64115,  64197,
  103         64276,  64353,  64428,  64501,  64571,  64638,  64703,  64766,
  104         64826,  64884,  64939,  64992,  65043,  65091,  65136,  65179,
  105         65220,  65258,  65294,  65327,  65358,  65386,  65412,  65436,
  106         65457,  65475,  65491,  65505,  65516,  65524,  65531,  65534,
  107 };
  108 
  109 /*
  110  * Compute the sine of theta.
  111  */
  112 fp16_t
  113 fp16_sin(fp16_t theta)
  114 {
  115         unsigned int i;
  116 
  117         i = 1024 * (theta % FP16_2PI) / FP16_2PI;
  118         switch (i / 256) {
  119         case 0:
  120                 return (fp16_sin_table[i % 256]);
  121         case 1:
  122                 return (fp16_sin_table[255 - i % 256]);
  123         case 2:
  124                 return (-fp16_sin_table[i % 256]);
  125         case 3:
  126                 return (-fp16_sin_table[255 - i % 256]);
  127         default:
  128                 /* inconceivable! */
  129                 return (0);
  130         }
  131 }
  132 
  133 /*
  134  * Compute the cosine of theta.
  135  */
  136 fp16_t
  137 fp16_cos(fp16_t theta)
  138 {
  139         unsigned int i;
  140 
  141         i = 1024 * (theta % FP16_2PI) / FP16_2PI;
  142         switch (i / 256) {
  143         case 0:
  144                 return (fp16_sin_table[255 - i % 256]);
  145         case 1:
  146                 return (-fp16_sin_table[i % 256]);
  147         case 2:
  148                 return (-fp16_sin_table[255 - i % 256]);
  149         case 3:
  150                 return (fp16_sin_table[i % 256]);
  151         default:
  152                 /* inconceivable! */
  153                 return (0);
  154         }
  155 }

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FreeBSD/Linux Kernel Cross Reference sys/dev/syscons/plasma/fp16.c

FreeBSD/Linux Kernel Cross Reference
sys/dev/syscons/plasma/fp16.c