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Add fixed precision sin() and cos()

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git-svn-id: svn://svn.code.sf.net/p/nuttx/code/trunk@1342 42af7a65-404d-4744-a932-0658087f49c3
This commit is contained in:
patacongo 2008-11-29 01:19:35 +00:00
parent 63101c7916
commit 586f69da53
7 changed files with 244 additions and 3 deletions
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1
ChangeLog
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@ -590,4 +590,5 @@
0.3.20 2008-xx-xx Gregory Nutt <spudmonkey@racsa.co.cr>
* Initial release of a tiny windowing system for NuttX (not well tested at initial check-in)
* Add fixed precision sin() and cos() (not well tested at initial check-in)

1
Documentation/NuttX.html
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@ -1206,6 +1206,7 @@ buildroot-0.1.2 2007-11-06 &lt;spudmonkey@racsa.co.cr&gt
<pre><ul>
nuttx-0.3.20 2008-xx-xx Gregory Nutt &lt;spudmonkey@racsa.co.cr&gt;
* Initial release of a tiny windowing system for NuttX (not well tested at initial check-in)
* Add fixed precision sin() and cos() (not well tested at initial check-in)
pascal-0.1.3 2008-xx-xx Gregory Nutt &lt;spudmonkey@racsa.co.cr&gt;

22
include/fixedmath.h
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@ -54,6 +54,9 @@
#define b8HALF 0x0080 /* 0.5 */
#define b8ONETENTH 0x001a /* 0.1 (acutally 0.1015625) */
#define b8ONEHUNDRTH 0x0003 /* 0.01 (actualy 0.0117198765) */
#define b8HALFPI 0x0192 /* 1.5703125 */
#define b8PI 0x0324 /* 3.1406250 */
#define b8TWOPI 0x0648 /* 6.2812500 */
#define b8MAX 0x7fff /* Max value of b8_t */
#define ub8MAX 0xffff /* Max value of rb8_t */
@ -68,6 +71,9 @@
#define b16ONETENTH 0x0000199a /* 0.1 (actually 0.100006..) */
#define b16ONEHUNDRTH 0x0000028f /* 0.01 (actually 0.0099945..) */
#define b16ONETHOUSTH 0x00000042 /* 0.001 (actually 0.000100708..)*/
#define b16HALFPI 0x0001921f /* 1.57078552246 */
#define b16PI 0x0003243f /* 3.14158630371 */
#define b16TWOPI 0x0006487b /* 6.28312683105 */
#define b16MAX 0x7fffffff /* Max value of b16_t */
#define ub16MAX 0xffffffff /* Max value of ub16_t */
@ -84,6 +90,9 @@
#define b32ONEHUNDRTH 0x00000000028f5c29 /* 0.01 */
#define b32ONETHOUSTH 0x0000000000418937 /* 0.001 */
#define b32ONETENTHOU 0x0000000000068db9 /* 0.0001 */
#define b32HALFPI 0x00000001921eb9ff /* 1.57078134990 */
#define b32PI 0x00000003243f6b4f /* 3.14159269980 */
#define b32TWOPI 0x00000006487ae7fd /* 6.28312539984 */
#define b32MAX 0x7fffffffffffffff /* Max value of b16_t */
#define ub32MAX 0xffffffffffffffff /* Max value of ub16_t */
@ -131,6 +140,8 @@
#define b8mulb8(a,b) b16tob8((b16_t)(a)*(b16_t)(b) /* Muliplication */
#define ub8mulub8(a,b) ub16toub8((ub16_t)(a)*(ub16_t)(b) /* Muliplication */
#define b8muli(a,i) ((a)*(i)) /* Simple multiplication by integer */
#define b8sqr(a) b8mulb8(a,a) /* Square */
#define ub8sqr(a) ub8mulub8(a,a) /* Square */
#define b8divb8(a,b) b8tob16(a)/(b16_t)(b) /* Division */
#define ub8divub8(a,b) ub8toub16(a)/(ub16_t)(b) /* Division */
#define b8divi(a,i) ((a)/(i)) /* Simple division by integer */
@ -162,9 +173,11 @@
#define b16idiv(i,j) (((i)<<16)/j) /* Division of integer, b16 result */
#ifdef CONFIG_HAVE_LONG_LONG
# define b16mulb16(a,b) b32tob16((b32_t)(a)*(b32_t)(b) /* Muliplication */
# define b16mulb16(a,b) b32tob16((b32_t)(a)*(b32_t)(b)) /* Muliplication */
# define ub16mulub16(a,b) ub32toub16((ub32_t)(a)*(ub32_t)(b)
# define b16divb16(a,b) b16tob32(a)/(b32_t)(b) /* Division */
# define b16sqr(a) b16mulb16(a,a) /* Square */
# define ub16sqr(a) ub16mulub16(a,a) /* Square */
# define b16divb16(a,b) b16tob32(a)/(b32_t)(b) /* Division */
# define ub16divub16(a,b) ub16toub32(a)/(ub32_t)(b)
#endif
@ -196,10 +209,15 @@ extern "C" {
#ifndef CONFIG_HAVE_LONG_LONG
EXTERN b16_t b16mulb16(b16_t m1, b16_t m2);
EXTERN ub16_t ub16mulub16(ub16_t m1, ub16_t m2);
EXTERN b16_t b16sqr(b16_t a);
EXTERN ub16_t ub16sqr(ub16_t a);
EXTERN b16_t b16divb16(b16_t num, b16_t denom);
EXTERN ub16_t ub16divub16(ub16_t num, ub16_t denom);
#endif
EXTERN b16_t b16sin(b16_t rad);
EXTERN b16_t b16cos(b16_t rad);
#undef EXTERN
#if defined(__cplusplus)
}

2
lib/Makefile
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@ -71,7 +71,7 @@ endif
STDLIB_SRCS = lib_rand.c
MATH_SRCS = lib_rint.c lib_fixedmath.c
MATH_SRCS = lib_rint.c lib_fixedmath.c lib_b16sin.c lib_b16cos.c
UNISTD_SRCS = lib_getopt.c
ifneq ($(CONFIG_NFILE_DESCRIPTORS),0)

64
lib/lib_b16cos.c Normal file
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@ -0,0 +1,64 @@
/****************************************************************************
* lib/lib_b16cos.c
*
* Copyright (C) 2007, 2008 Gregory Nutt. All rights reserved.
* Author: Gregory Nutt <spudmonkey@racsa.co.cr>
*
* 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.
* 3. Neither the name NuttX nor the names of its contributors may be
* used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS 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
* COPYRIGHT OWNER 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.
*
****************************************************************************/
/****************************************************************************
* Included Files
****************************************************************************/
#include <fixedmath.h>
/****************************************************************************
* Pre-processor Definitions
****************************************************************************/
/****************************************************************************
* Global Functions
****************************************************************************/
/****************************************************************************
* Name: b16cos
****************************************************************************/
b16_t b16cos(b16_t rad)
{
/* Compute cosine: sin(rad + PI/2) = cos(rad) */
rad += b16HALFPI;
if (rad > b16PI)
{
rad -= b16TWOPI;
}
return b16sin(rad);
}

110
lib/lib_b16sin.c Normal file
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@ -0,0 +1,110 @@
/****************************************************************************
* lib/lib_b16sin.c
*
* Copyright (C) 2008 Gregory Nutt. All rights reserved.
* Author: Gregory Nutt <spudmonkey@racsa.co.cr>
*
* 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.
* 3. Neither the name NuttX nor the names of its contributors may be
* used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS 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
* COPYRIGHT OWNER 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.
*
****************************************************************************/
/****************************************************************************
* Included Files
****************************************************************************/
#include <fixedmath.h>
/****************************************************************************
* Pre-processor Definitions
****************************************************************************/
#define b16_P225 0x0000399a
#define b16_P405284735 0x000067c1
#define b16_1P27323954 0x000145f3
/****************************************************************************
* Global Functions
****************************************************************************/
/****************************************************************************
* Name: b16sin
* Ref: http://lab.polygonal.de/2007/07/18/fast-and-accurate-sinecosine-approximation/
****************************************************************************/
b16_t b16sin(b16_t rad)
{
b16_t tmp1;
b16_t tmp2;
b16_t tmp3;
/* Force angle into the good range */
if (rad < -b16PI)
{
rad += b16TWOPI;
}
else if (rad > b16PI)
{
rad -= b16TWOPI;
}
/* tmp1 = 1.27323954 * rad
* tmp2 = .405284735 * rad * rad
*/
tmp1 = b16mulb16(b16_1P27323954, rad);
tmp2 = b16mulb16(b16_P405284735, b16sqr(rad));
if (rad < 0)
{
/* tmp3 = 1.27323954 * rad + .405284735 * rad * rad */
tmp3 = tmp1 + tmp2;
}
else
{
/* tmp3 = 1.27323954 * rad - 0.405284735 * rad * rad */
tmp3 = tmp1 - tmp2;
}
/* tmp1 = tmp3*tmp3 */
tmp1 = b16sqr(tmp3);
if (tmp3 < 0)
{
/* tmp1 = tmp3 * -tmp3 */
tmp1 = -tmp1;
}
/* Return sin = .225 * (tmp3 * (+/-tmp3) - tmp3) + tmp3 */
return b16mulb16(b16_P225, (tmp1 - tmp3)) + tmp3;
}

47
lib/lib_fixedmath.c
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@ -161,6 +161,53 @@ ub16_t ub16mulub16(ub16_t m1, ub16_t m2)
return (m1i*m2i << 16) + m1i*m2f + m2i*m1f + (((m1f*m2f) + b16HALF) >> 16);
}
/****************************************************************************
* Name: b16divb16
**************************************************************************/
b16_t b16sqr(b16_t a)
{
b16_t sq;
/* The result is always positive. Just take the absolute value */
if (a < 0)
{
a = -a;
}
/* Overflow occurred if the result is negative */
sq = (bt_t)ub16sqr(a);
if (sq < 0)
{
sq = b16MAX;
}
return sq;
}
/****************************************************************************
* Name: b16divb16
**************************************************************************/
ub16_t ub16sqr(ub16_t a)
{
/* Let:
*
* m = mi*2**16 + mf (b16)
*
* Then:
*
* m*m = (mi*mi)*2**32 + 2*(m1*m2)*2**16 + mf*mf (b32)
* = (mi*mi)*2**16 + 2*(mi*mf) + mf*mf*2**-16 (b16)
*/
uint32 mi = ((uint32)m1 >> 16);
uint32 mf = ((uint32)m1 & 0x0000ffff);
return (mi*mi << 16) + (mi*mf << 1) (((mf*mf) + b16HALF) >> 16);
}
/****************************************************************************
* Name: b16divb16
**************************************************************************/