fixedptc.h

Go to the documentation of this file.

#ifndef _FIXEDPTC_H_
#define _FIXEDPTC_H_

#include <stdint.h>

/*
 * fixedptc.h is a 32-bit or 64-bit fixed point numeric library.
 *
 * The symbol FIXEDPT_BITS, if defined before this library header file
 * is included, determines the number of bits in the data type (its "width").
 * The default width is 32-bit (FIXEDPT_BITS=32) and it can be used
 * on any recent C99 compiler. The 64-bit precision (FIXEDPT_BITS=64) is
 * available on compilers which implement 128-bit "long long" types. This
 * precision has been tested on GCC 4.2+.
 *
 * The FIXEDPT_WBITS symbols governs how many bits are dedicated to the
 * "whole" part of the number (to the left of the decimal point). The larger
 * this width is, the larger the numbers which can be stored in the fixedpt
 * number. The rest of the bits (available in the FIXEDPT_FBITS symbol) are
 * dedicated to the fraction part of the number (to the right of the decimal
 * point).
 *
 * Since the number of bits in both cases is relatively low, many complex
 * functions (more complex than div & mul) take a large hit on the precision
 * of the end result because errors in precision accumulate.
 * This loss of precision can be lessened by increasing the number of
 * bits dedicated to the fraction part, but at the loss of range.
 *
 * Adventurous users might utilize this library to build two data types:
 * one which has the range, and one which has the precision, and carefully
 * convert between them (including adding two number of each type to produce
 * a simulated type with a larger range and precision).
 *
 * The ideas and algorithms have been cherry-picked from a large number
 * of previous implementations available on the Internet.
 * Tim Hartrick has contributed cleanup and 64-bit support patches.
 *
 * == Special notes for the 32-bit precision ==
 * Signed 32-bit fixed point numeric library for the 24.8 format.
 * The specific limits are -8388608.999... to 8388607.999... and the
 * most precise number is 0.00390625. In practice, you should not count
 * on working with numbers larger than a million or to the precision
 * of more than 2 decimal places. Make peace with the fact that PI
 * is 3.14 here. :)
 */

/*-
 * Copyright (c) 2010-2012 Ivan Voras <ivoras@freebsd.org>
 * Copyright (c) 2012 Tim Hartrick <tim@edgecast.com>
 *
 * 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.
 */

#ifndef FIXEDPT_BITS
#define FIXEDPT_BITS  32
#endif

#if FIXEDPT_BITS == 32
typedef int32_t fixedpt;
typedef int64_t fixedptd;
typedef uint32_t fixedptu;
typedef uint64_t fixedptud;
#elif FIXEDPT_BITS == 64
typedef int64_t fixedpt;
//typedef long long __int128_t;
typedef __int128_t fixedptd;
typedef uint64_t fixedptu;
//typedef unsigned long long __uint128_t;
typedef __uint128_t fixedptud;
#else
#error "FIXEDPT_BITS must be equal to 32 or 64"
#endif

#ifndef FIXEDPT_WBITS
#define FIXEDPT_WBITS 16
#endif

#if FIXEDPT_WBITS >= FIXEDPT_BITS
#error "FIXEDPT_WBITS must be less than or equal to FIXEDPT_BITS"
#endif

#define FIXEDPT_VCSID "$Id$"

#define FIXEDPT_FBITS (FIXEDPT_BITS - FIXEDPT_WBITS)
#define FIXEDPT_FMASK (((fixedpt)1 << FIXEDPT_FBITS) - 1)

#define fixedpt_rconst(R) ((fixedpt)((R) * FIXEDPT_ONE + ((R) >= 0 ? 0.5 : -0.5)))
#define fixedpt_fromint(I) ((fixedptd)(I) << FIXEDPT_FBITS)
#define fixedpt_toint(F) ((F) >> FIXEDPT_FBITS)
#define fixedpt_add(A,B) ((A) + (B))
#define fixedpt_sub(A,B) ((A) - (B))
#define fixedpt_xmul(A,B)           \
  ((fixedpt)(((fixedptd)(A) * (fixedptd)(B)) >> FIXEDPT_FBITS))
#define fixedpt_xdiv(A,B)           \
  ((fixedpt)(((fixedptd)(A) << FIXEDPT_FBITS) / (fixedptd)(B)))
#define fixedpt_fracpart(A) ((fixedpt)(A) & FIXEDPT_FMASK)

#define FIXEDPT_ONE ((fixedpt)((fixedpt)1 << FIXEDPT_FBITS))
#define FIXEDPT_ONE_HALF (FIXEDPT_ONE >> 1)
#define FIXEDPT_TWO (FIXEDPT_ONE + FIXEDPT_ONE)
#define FIXEDPT_PI  fixedpt_rconst(3.14159265358979323846)
#define FIXEDPT_TWO_PI  fixedpt_rconst(2 * 3.14159265358979323846)
#define FIXEDPT_HALF_PI fixedpt_rconst(3.14159265358979323846 / 2)
#define FIXEDPT_E fixedpt_rconst(2.7182818284590452354)

#define fixedpt_abs(A) ((A) < 0 ? -(A) : (A))

/* Multiplies two fixedpt numbers, returns the result. */
fixedpt fixedpt_mul(fixedpt A, fixedpt B);

/* Divides two fixedpt numbers, returns the result. */
fixedpt fixedpt_div(fixedpt A, fixedpt B);

//fixedpt fixedpt_mod(fixedpt A, fixedpt B);

/*
 * Note: adding and substracting fixedpt numbers can be done by using
 * the regular integer operators + and -.
 */

void fixedpt_str(fixedpt A, char *str, int max_dec);

/* Converts the given fixedpt number into a string, using a static
 * (non-threadsafe) string buffer */
char* fixedpt_cstr(const fixedpt A, const int max_dec);

/* Returns the square root of the given number, or -1 in case of error */
fixedpt fixedpt_sqrt(fixedpt A);

/* Returns the sine of the given fixedpt number.
 * Note: the loss of precision is extraordinary! */
fixedpt fixedpt_sin(fixedpt fp);

/* Returns the cosine of the given fixedpt number */
fixedpt fixedpt_cos(fixedpt A);

/* Returns the tangens of the given fixedpt number */
fixedpt fixedpt_tan(fixedpt A);

/* Returns the value exp(x), i.e. e^x of the given fixedpt number. */
fixedpt fixedpt_exp(fixedpt fp);

/* Returns the natural logarithm of the given fixedpt number. */
fixedpt fixedpt_ln(fixedpt x);

/* Returns the logarithm of the given base of the given fixedpt number */
fixedpt fixedpt_log(fixedpt x, fixedpt base);


/* Return the power value (n^exp) of the given fixedpt numbers */
fixedpt fixedpt_pow(fixedpt n, fixedpt exp);

void fixedpt_print(fixedpt A);
void fixedpt_print_file(fixedpt A);

#endif