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/****************************************************************************
* include/fixedmath.h
*
* Copyright (C) 2008, 2017 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.
*
****************************************************************************/
#ifndef __INCLUDE_FIXEDMATH_H
#define __INCLUDE_FIXEDMATH_H
/****************************************************************************
* Included Files
****************************************************************************/
#include <nuttx/compiler.h>
#include <stdint.h>
/****************************************************************************
* Pre-processor Definitions
****************************************************************************/
/* Common numbers */
#define b8HUNDRED 0x6400 /* 100 */
#define b8TEN 0x0a00 /* 10 */
#define b8ONE 0x0100 /* 1 */
#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 */
#define b8MIN 0x8000 /* Min value of b8_t */
#define ub8MIN 0x0000 /* Min value of ub8_t */
#define b16THOUSAND 0x03e80000 /* 1000 */
#define b16HUNDRED 0x00640000 /* 100 */
#define b16TEN 0x000a0000 /* 10 */
#define b16ONE 0x00010000 /* 1 */
#define b16HALF 0x00008000 /* 0.5 */
#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 */
#define b16MIN 0x80000000 /* Min value of b16_t */
#define ub16MIN 0x00000000 /* Min value of ub16_t */
#define b32MILLION 0x000f424000000000LL /* 1000000 */
#define b32THOUSAND 0x000003e800000000LL /* 1000 */
#define b32HUNDRED 0x0000006400000000LL /* 100 */
#define b32TEN 0x0000000a00000000LL /* 10 */
#define b32ONE 0x0000000100000000LL /* 1 */
#define b32HALF 0x0000000080000000LL /* 0.5 */
#define b32ONETENTH 0x000000001999999aLL /* 0.1 */
#define b32ONEHUNDRTH 0x00000000028f5c29LL /* 0.01 */
#define b32ONETHOUSTH 0x0000000000418937LL /* 0.001 */
#define b32ONETENTHOU 0x0000000000068db9LL /* 0.0001 */
#define b32HALFPI 0x00000001921eb9ffLL /* 1.57078134990 */
#define b32PI 0x00000003243f6b4fLL /* 3.14159269980 */
#define b32TWOPI 0x00000006487ae7fdLL /* 6.28312539984 */
#define b32MAX 0x7fffffffffffffffLL /* Max value of b16_t */
#define ub32MAX 0xffffffffffffffffLL /* Max value of ub16_t */
#define b32MIN 0x8000000000000000LL /* Min value of b16_t */
#define ub32MIN 0x0000000000000000LL /* Min value of ub16_t */
/* Conversions between b32, b16, and b8 ***********************************/
#define b8tob16(b) (((b16_t)(b)) << 8)
#define ub8toub16(b) (((ub16_t)(b)) << 8)
#define b16tob8(b) (b8_t)(((b)+0x0080)>>8)
#define ub16toub8(b) (ub8_t)(((b)+0x0080)>>8)
#ifdef CONFIG_HAVE_LONG_LONG
# define b8tob32(b) (((b32_t)(b)) << 24)
# define ub8toub32(b) (((ub32_t)(b)) << 24)
# define b16tob32(b) (((b32_t)(b)) << 16)
# define ub16toub32(b) (((ub32_t)(b)) << 16)
# define b32tob16(b) (b16_t)(((b) + 0x0000000000008000)>>16)
# define ub32toub16(b) (ub16_t)(((b) + 0x0000000000008000)>>16)
# define b32tob8(b) (b8_t)(((b) + 0x0000000000000080)>>8)
#endif
/* 16-bit values with 8 bits of precision *********************************/
/* Conversions */
#define b8toi(a) ((a) >> 8) /* Conversion to integer */
#define ub8toi(a) ((a) >> 8) /* Conversion to unsigned integer */
#define itob8(i) (((b8_t)(i)) << 8) /* Conversion from integer */
#define uitoub8(i) (((ub8_t)(i)) << 8) /* Conversion from unsigned integer */
#define b8tof(b) (((float)(b))/256.0f) /* Conversion to float */
#define ftob8(f) (b8_t)(((f)*256.0f)) /* Conversion from float */
#define b8trunc(a) ((a) & 0xff00) /* Truncate to integer b8 */
#define b8round(a) (((a)+0x0080) & 0xff00) /* Round to integer b8 */
#define b8frac(a) ((a) & 0x00ff) /* Take fractional part */
/* Operators */
#define ub8inv(b) (0x8000/((b)>>1)) /* Inversion (b8=b15/b7) */
#define b8inv(b) (0x4000/((b)>>2)) /* Inversion (b8=b14/b6) */
#define b8addb8(a,b) ((a)+(b)) /* Addition */
#define b8addi(a,i) ((a)+itob8(i)) /* Add integer from b16 */
#define b8subb8(a,b) ((a)-(b)) /* Subtraction */
#define b8subi(a,i) ((a)-itob8(i)) /* Subtract integer from b8 */
#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 */
#define b8idiv(i,j) (((i)<<8)/j) /* Division of integer, b8 result */
/* 32-bit values with 16 bits of precision ********************************/
/* Conversions */
#define b16toi(a) ((a) >> 16) /* Conversion to integer */
#define ub16toi(a) ((a) >> 16) /* Conversion to unsgined integer */
#define itob16(i) (((b16_t)(i)) << 16) /* Conversion from integer */
#define uitoub16(i) (((ub16_t)(i)) << 16) /* Conversion from unsigned integer */
#define b16tof(b) (((float)(b))/65536.0f) /* Conversion to float */
#define ftob16(f) (b16_t)(((f)*65536.0f)) /* Conversion from float */
#define b16tod(b) (((double)(b))/65536.0) /* Conversion to double */
#define dtob16(f) (b16_t)(((f)*65536.0)) /* Conversion from double */
#define b16trunc(a) ((a) & 0xffff0000) /* Truncate to integer */
#define b16round(a) (((a)+0x00008000) & 0xffff0000)
#define b16frac(a) ((a) & 0x0000ffff) /* Take fractional part */
/* Operators */
#define ub16inv(b) (0x80000000/((b)>>1)) /* Inversion (b16=b31/b15) */
#define b16inv(b) (0x40000000/((b)>>2)) /* Inversion (b16=b30/b14) */
#define b16addb16(a,b) ((a)+(b)) /* Addition */
#define b16addi(a,i) ((a)+itob16(i)) /* Add integer to b16 */
#define b16subb16(a,b) ((a)-(b)) /* Subtraction */
#define b16subi(a,i) ((a)-itob16(i)) /* Subtract integer from b16 */
#define b16muli(a,i) ((a)*(i)) /* Simple multiplication by integer */
#define b16divi(a,i) ((a)/(i)) /* Simple division by integer*/
#define b16idiv(i,j) (((i)<<16)/j) /* Division of integer, b16 result */
#ifdef CONFIG_HAVE_LONG_LONG
/* Multiplication operators */
# define b16mulb16(a,b) b32tob16((b32_t)(a)*(b32_t)(b))
# define ub16mulub16(a,b) ub32toub16((ub32_t)(a)*(ub32_t)(b))
/* Square operators */
# define b16sqr(a) b16mulb16(a,a)
# define ub16sqr(a) ub16mulub16(a,a)
/* Division operators */
# define b16divb16(a,b) (b16_t)(b16tob32(a)/(b32_t)(b))
# define ub16divub16(a,b) (ub16_t)(ub16toub32(a)/(ub32_t)(b))
/* Square root operators */
# define ub16sqrtub16(a) ub32sqrtub16(ub16toub32(a))
#else
# define ub16sqrtub16(a) ub8toub16(ub16sqrtub8(a))
#endif
/* 64-bit values with 32 bits of precision ********************************/
#ifdef CONFIG_HAVE_LONG_LONG
/* Conversions */
#define b32toi(a) ((a) >> 32) /* Conversion to integer */
#define itob32(i) (((b32_t)(i)) << 32) /* Conversion from integer */
#define uitoub32(i) (((ub32_t)(i)) << 32) /* Conversion from unsigned integer */
#define b32tod(b) (((double)(b))/b32ONE) /* Conversion to double */
#define dtob32(f) (b32_t)(((f)*(double)b32ONE)) /* Conversion from double */
#define b32trunc(a) ((a) & 0xffffffff00000000) /* Truncate to integer */
#define b32round(a) (((a)+0x0000000080000000) & 0xffffffff00000000)
#define b32frac(a) ((a) & 0x00000000ffffffff) /* Take fractional part */
#endif
/****************************************************************************
* Public Types
****************************************************************************/
typedef int16_t b8_t;
typedef uint16_t ub8_t;
typedef int32_t b16_t;
typedef uint32_t ub16_t;
#ifdef CONFIG_HAVE_LONG_LONG
typedef int64_t b32_t;
typedef uint64_t ub32_t;
#endif
/****************************************************************************
* Public Functions
****************************************************************************/
#undef EXTERN
#if defined(__cplusplus)
#define EXTERN extern "C"
extern "C"
{
#else
#define EXTERN extern
#endif
#ifndef CONFIG_HAVE_LONG_LONG
/* Multiplication operators */
b16_t b16mulb16(b16_t m1, b16_t m2);
ub16_t ub16mulub16(ub16_t m1, ub16_t m2);
/* Square operators */
b16_t b16sqr(b16_t a);
ub16_t ub16sqr(ub16_t a);
/* Division operators */
b16_t b16divb16(b16_t num, b16_t denom);
ub16_t ub16divub16(ub16_t num, ub16_t denom);
#endif
/* Trigonometric Functions */
b16_t b16sin(b16_t rad);
b16_t b16cos(b16_t rad);
b16_t b16atan2(b16_t y, b16_t x);
/* Square root operators */
#ifdef CONFIG_HAVE_LONG_LONG
ub16_t ub32sqrtub16(ub32_t a);
#endif
ub8_t ub16sqrtub8(ub16_t a);
#undef EXTERN
#if defined(__cplusplus)
}
#endif
#endif /* __INCLUDE_FIXEDMATH_H */