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/****************************************************************************
* lib/math/lib_fixedmath.c
*
* Copyright (C) 2008-2009, 2011 Gregory Nutt. All rights reserved.
* Author: Gregory Nutt <gnutt@nuttx.org>
*
* 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 <nuttx/config.h>
#include <stdint.h>
#include <stdbool.h>
#include <fixedmath.h>
#ifndef CONFIG_HAVE_LONG_LONG
/****************************************************************************
* Pre-processor Definitions
****************************************************************************/
/****************************************************************************
* Private Type Declarations
****************************************************************************/
/****************************************************************************
* Private Function Prototypes
****************************************************************************/
/****************************************************************************
* Public Data
****************************************************************************/
/****************************************************************************
* Private Data
****************************************************************************/
/****************************************************************************
* Name: fixsign
****************************************************************************/
static void fixsign(b16_t *parg1, b16_t *parg2, bool *pnegate)
{
bool negate = false;
b16_t arg;
arg = *parg1;
if (arg < 0)
{
*parg1 = -arg;
negate = true;
}
arg = *parg2;
if (arg < 0)
{
*parg2 = -arg;
negate ^= true;
}
*pnegate = negate;
}
/****************************************************************************
* Name: adjustsign
****************************************************************************/
static b16_t adjustsign(b16_t result, bool negate)
{
/* If the product is negative, then we overflowed */
if (result < 0)
{
if (result)
{
return b16MIN;
}
else
{
return b16MAX;
}
}
/* correct the sign of the result */
if (negate)
{
return -result;
}
return result;
}
/****************************************************************************
* Public Functions
****************************************************************************/
/****************************************************************************
* Name: b16mulb16
****************************************************************************/
b16_t b16mulb16(b16_t m1, b16_t m2)
{
bool negate;
b16_t product;
fixsign(&m1, &m2, &negate);
product = (b16_t)ub16mulub16((ub16_t)m1, (ub16_t)m2);
return adjustsign(product, negate);
}
/****************************************************************************
* Name: ub16mulub16
**************************************************************************/
ub16_t ub16mulub16(ub16_t m1, ub16_t m2)
{
/* Let:
*
* m1 = m1i*2**16 + m1f (b16)
* m2 = m2i*2**16 + m2f (b16)
*
* Then:
*
* m1*m2 = (m1i*m2i)*2**32 + (m1i*m2f + m2i*m1f)*2**16 + m1f*m2f (b32)
* = (m1i*m2i)*2**16 + (m1i*m2f + m2i*m1f) + m1f*m2f*2**-16 (b16)
* = a*2**16 + b + c*2**-16
*/
uint32_t m1i = ((uint32_t)m1 >> 16);
uint32_t m2i = ((uint32_t)m1 >> 16);
uint32_t m1f = ((uint32_t)m1 & 0x0000ffff);
uint32_t m2f = ((uint32_t)m2 & 0x0000ffff);
return (m1i*m2i << 16) + m1i*m2f + m2i*m1f + (((m1f*m2f) + b16HALF) >> 16);
}
/****************************************************************************
* Name: b16sqr
**************************************************************************/
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 = (b16_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_t mi = ((uint32_t)a >> 16);
uint32_t mf = ((uint32_t)a & 0x0000ffff);
return (mi*mi << 16) + (mi*mf << 1) + ((mf*mf + b16HALF) >> 16);
}
/****************************************************************************
* Name: b16divb16
**************************************************************************/
b16_t b16divb16(b16_t num, b16_t denom)
{
bool negate;
b16_t quotient;
fixsign(&num, &denom, &negate);
quotient = (b16_t)ub16divub16((ub16_t)num, (ub16_t)denom);
return adjustsign(quotient, negate);
}
/****************************************************************************
* Name: ub16divub16
**************************************************************************/
ub16_t ub16divub16(ub16_t num, ub16_t denom)
{
uint32_t term1;
uint32_t numf;
uint32_t product;
/* Let:
*
* num = numi*2**16 + numf (b16)
* den = deni*2**16 + denf (b16)
*
* Then:
*
* num/den = numi*2**16 / den + numf / den (b0)
* = numi*2**32 / den + numf*2**16 /den (b16)
*/
/* Check for overflow in the first part of the quotient */
term1 = ((uint32_t)num & 0xffff0000) / denom;
if (term1 >= 0x00010000)
{
return ub16MAX; /* Will overflow */
}
/* Finish the division */
numf = num - term1 * denom;
term1 <<= 16;
product = term1 + (numf + (denom >> 1)) / denom;
/* Check for overflow */
if (product < term1)
{
return ub16MAX; /* Overflowed */
}
return product;
}
#endif
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