FIX/Source/fix.h

/*

Copyright (C) 2015-2018 Night Dive Studios, LLC.

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <http://www.gnu.org/licenses/>.

*/
/*
 * $Source: r:/prj/lib/src/fix/RCS/fix.h $
 * $Revision: 1.41 $
 * $Author: jaemz $
 * $Date: 1994/08/18 18:10:21 $
 *
 * Code, prototypes and types for fixed-point routines.
 *
 * $Log: fix.h $
 * Revision 1.41  1994/08/18  18:10:21  jaemz
 * Added sloppy_sqrt
 *
 * Revision 1.40  1994/08/11  12:11:14  dfan
 * multiple source directories
 *
 * Revision 1.39  1994/03/16  10:29:25  lmfeeney
 * ,
 * added extern fn fix_pow
 *
 * Revision 1.38  1994/03/16  10:29:25  dfan
 * fix_safe_pyth_dist etc.
 * also conversions to and from degrees
 *
 * Revision 1.37  1994/01/22  19:05:46  dc
 * fast_fix_mul_int
 *
 * Revision 1.36  1994/01/22  19:04:22  dc
 * shrd not shr\shl\or for fix_mul
 * neat
 *
 * Revision 1.34  1993/11/11  13:50:46  rex
 * Changed fix_from_float() to much simpler macro, added atofix() and atofix24()
 *
 * Revision 1.33  1993/11/05  13:56:16  dfan
 * 2pi was wrong.
 *
 * Revision 1.32  1993/11/04  11:13:42  dfan
 * long_fast_pyth_dist
 *
 * Revision 1.31  1993/09/17  13:03:36  dfan
 * fast_pyth_dist
 *
 * Revision 1.30  1993/08/17  15:10:04  kaboom
 * Added fix_cint and fix_fint macros.
 *
 * Revision 1.29  1993/07/30  12:42:58  dfan
 * fix_exp
 *
 * Revision 1.28  1993/07/07  12:26:58  xemu
 * fixed a numerical error in fixang_to_fixrad
 *
 * Revision 1.27  1993/07/02  15:10:01  xemu
 * conversion from fixed-point radians to fixangs
 *
 * Revision 1.26  1993/06/27  02:30:47  dc
 * added char return to fix_sprint prototypes, added fix_sprint_hex prototypes
 *
 * Revision 1.25  1993/06/07  10:29:36  jak
 * Reversed #pragma and C decls for some functions
 * so that C++ parser will be happy.
 *
 * Revision 1.24  1993/06/05  07:38:36  mahk
 * Added abs, sgn, FIXANG_PI
 *
 * Revision 1.23  1993/04/19  13:31:42  dfan
 * individual sin & cos functions
 *
 * Revision 1.22  1993/04/14  17:13:23  jaemz
 * Added FIX_MIN and FIX_MAX
 *
 * Revision 1.21  1993/04/14  16:57:23  jaemz
 * Added floor and ceil
 *
 * Revision 1.20  1993/04/07  10:15:06  matt
 * Removed include of math.h, which seemed unneccesary.
 *
 * Revision 1.19  1993/03/15  16:55:45  matt
 * Added include of "types.h"
 *
 * Revision 1.18  1993/03/03  14:46:59  dfan
 * fix_from_float: short should have been ushort to prevent nasty sign-extend
 *
 * Revision 1.17  1993/03/03  11:50:53  dfan
 * float conversion
 *
 * Revision 1.16  1993/02/16  10:44:33  matt
 * Added parens around macro args
 *
 *
 * Revision 1.15  1993/02/15  12:15:29  dfan
 * more fix24 functions
 *
 * Revision 1.14  1993/02/15  11:40:22  dfan
 * fix24 support
 *
 * Revision 1.13  1993/02/04  16:25:33  matt
 * Added new fix_mul_div() function
 *
 * Revision 1.12  1993/01/29  11:10:45  dfan
 * hey, fix_sqrt returns a 32-bit value
 *
 * Revision 1.11  1993/01/29  10:42:34  dfan
 * type in fix_sqrt pragma
 *
 * Revision 1.10  1993/01/27  16:47:16  dfan
 * sqrt functions
 * by the way, the arctrig functions did work after all
 *
 * Revision 1.9  1993/01/22  15:52:36  dfan
 * Asin, acos, and atan2 do work after all
 *
 * Revision 1.8  1993/01/22  09:57:19  dfan
 * Added lots of functions, including trig ones
 * Arctrig doesn't work yet
 *
 * Revision 1.7  1992/10/14  23:37:46  kaboom
 * Added fix_rint macro to round & take integer part.
 *
 * Revision 1.6  1992/10/13  22:34:24  kaboom
 * Added #ifdef __FIX_H clause around body of file.
 *
 * Revision 1.5  1992/09/16  19:52:06  kaboom
 * Modified the fix_int macro not to round off before converting fix to int.
 * Added fix_trunc to remove fractional part, fix_frac to return fractional
 * part.
 *
 * Revision 1.4  1992/09/16  19:28:26  kaboom
 * Changed fix_mul and fix_div to be inline assembly-language functions
 * instead of called functions.  That makes this the only file in the
 * fixed-point math library and fix.asm is obsolete.
 *
 * Revision 1.3  1992/09/15  14:08:22  kaboom
 * Made typedef for fixed point variables.  Added fix_make macro.
 *
 * Revision 1.2  1992/08/24  17:27:17  kaboom
 * Added RCS keywords and header at top of file.
 *
 * Revision 1.1  1992/08/24  17:27:17  kaboom
 * Initial revision.
 */

#ifndef __FIX_H
#define __FIX_H

#include <stdbool.h>
#include <stdint.h>
#include <stdlib.h>

#include "lg_types.h"

#if defined(__cplusplus)
extern "C" {
#endif

// Globals
extern int gOVResult;

///////////////////////////////
//
// First some math functions that don't use fixes.
//
/*  @@@ Change this
// Returns 0 if x < 0
#pragma aux long_sqrt parm [eax] value [ax] modify [eax ebx ecx edx esi edi]
*/
int long_sqrt(int x);

//////////////////////////////
//
// fix.c
//

int long_fast_pyth_dist(int a, int b);

//========================================
//
// Now for fixes themselves.  Macros.
//
//========================================

/* these functions operate on fixed-point numbers with one bit of sign, 15
   bits of integer, and 16 bits of fraction.  thus, a rational number a is
   represented as a 32-bit number as a*2^16. */

typedef int32_t fix;
typedef fix fix16;

// define min and max
#define FIX_MAX (0x7fffffff)
#define FIX_MIN (0x80000000)

// A fixang (fixed-point angle) can be converted to radians by multiplying
// by 2 * PI and dividing by 2^16.
//
// 0x0000 -> 0
// 0x4000 -> PI/2
// 0x8000 -> PI
// 0xc000 -> 3PI/2
//

#define FIXANG_PI 0x8000
#define fix_2pi fix_make(6, 18559) // that's 6 + 18559/65536 = 6.28319

typedef uint16_t fixang;

/* makes a fixed point number with integral part a and fractional part b. */
#define fix_make(a, b) (int32_t)((((uint32_t)(a)) << 16) | (b))

#define FIX_UNIT fix_make(1, 0)

/* lops off the fractional part of a fixed point number. */
#define fix_trunc(n) ((n)&0xffff0000)

/* Does a floor */
#define fix_floor(n) ((n)&0xffff0000)

/* Does a ceil */
#define fix_ceil(n) (((n) + 65535) & 0xffff0000)

/* round a fix to the nearest integer, leaving in fix format. */
#define fix_round(n) (((n) + 32768) & 0xffff0000)

/* returns the integral part of a fixed point number. */
#define fix_int(n) ((int16_t)((n) >> 16))

// Absolute value and signum
#define fix_abs(n) (((n) < 0) ? -(n) : (n))
#define fix_sgn(n) (((n) < 0) ? -FIX_UNIT : (((n) == 0) ? 0 : FIX_UNIT))

/* converts the floor of n to an integer. */
#define fix_fint(n) ((n) >> 16)

/* converts the ceiling of n to an integer. */
#define fix_cint(n) (((n) + 0xffff) >> 16)

/* returns the integral part of a fixed point number rounded up. */
// #define fix_rint(n) (fix_int (fix_round (n)))
// the following macro does it all explictly to avoid the spurious & in
// fix_round
#define fix_rint(n) (((n) + 0x8000) >> 16)

/* returns the fractional part of a fixed point number. */
#define fix_frac(n) ((uint16_t)((n)&0xffff))

// fixrad_to_fixang converts a fixed-point in radians to a fixang
// fixang_to_fixrad converts a fixang to a fixed point radians
// degrees_to_fixang converts an integer number of degrees to a fixang
// fixang_to_degrees converts a fixang to an integer number of degrees

#define fixrad_to_fixang(fixradian) (fix_frac(fix_div((fixradian), fix_2pi)))
#define fixang_to_fixrad(ang) fix_div(fix_mul(ang, fix_2pi), 0x10000)
#define degrees_to_fixang(d) ((fixang)(((d)*FIXANG_PI) / 180))
#define fixang_to_degrees(ang) (((int)(ang)*180) / FIXANG_PI)

// turns a fixed point into a float.
#define fix_float(n) ((float)(fix_int(n)) + (float)(fix_frac(n)) / 65536.0)

// makes a fixed point from a float.
#define fix_from_float(n) ((fix)(65536.0 * (n)))

//========================================
//
// Multiplication and division.
//
//========================================

// For Mac version: The PowerPC version uses two assembly language routines
// to do the multiply and divide.
fix fix_mul(fix a, fix b);
fix fix_mul_asm_safe(fix a, fix b);
fix fix_div(fix a, fix b);
fix fix_div_int(fix a, fix b);
fix fix_div_safe_cint(fix a, fix b);
fix fix_mul_div(fix m0, fix m1, fix d);
fix fast_fix_mul_int(fix a, fix b);
#define fast_fix_mul fix_mul

//========================================
//
//  Square rooty kind of stuff.
//
//========================================

// Returns sqrt (a^2 + b^2)
fix fix_pyth_dist(fix a, fix b);

// Returns approximately sqrt (a^2 + b^2)
// Is never off by more than 12% (it's worst at 45 deg)
fix fix_fast_pyth_dist(fix a, fix b);

// pyth_dist with less fear of overflow.  Either number
// can be up to 0x2fffffff.
fix fix_safe_pyth_dist(fix a, fix b);

// Now in FIX_SQRT.C
// Returns 0 if x < 0
fix fix_sqrt(fix x);

int32_t quad_sqrt(int32_t hi, uint32_t lo);

//========================================
//
//  Trigonometric functions.
//
//========================================

// Computes sin and cos of theta
void fix_sincos(fixang theta, fix *sin, fix *cos);

fix fix_sin(fixang theta);

fix fix_cos(fixang theta);

// Computes sin and cos of theta
// Faster than fix_sincos() but not as accurate (does not interpolate)
void fix_fastsincos(fixang theta, fix *sin, fix *cos);

fix fix_fastsin(fixang theta);

fix fix_fastcos(fixang theta);

// Computes the arcsin of x
fixang fix_asin(fix x);

// Computes the arccos of x
fixang fix_acos(fix x);

// Computes the atan of y/x, in the correct quadrant and everything
fixang fix_atan2(fix y, fix x);

#if defined(__cplusplus)
}
#endif

/* fixpoint x ^ y */
extern fix fix_pow(fix x, fix y);

//////////////////////////////
//
// f_exp.c

// Computes e to the x
//
fix fix_exp(fix x);

//////////////////////////////
//
// fix24 - 24 bits integer, 8 bits fraction
//

typedef int32_t fix24;

#define fix24_make(a, b) ((((int32_t)(a)) << 8) | (b))
#define fix24_trunc(n) ((n)&0xffffff00)
#define fix24_round(n) (((n) + 128) & 0xffffff00)
#define fix24_int(n) ((n) >> 8)
#define fix24_frac(n) ((n)&0xff)
#define fix24_float(n) ((float)(fix24_int(n)) + (float)(fix24_frac(n)) / 256.0)

#define fix24_from_fix16(n) ((n) >> 8)
#define fix16_from_fix24(n) ((n) << 8)

// For Mac version: The PowerPC version uses an assembly language routine
// to do the multiply.
fix24 fix24_mul(fix24 a, fix24 b);
fix24 fix24_div(fix24 a, fix24 b);

// Wide (64-bit) fix functions

// 64-bit fix type (high 32 bit - integer, low 32 bit - fractional)
typedef int64_t fix64;

#define fix64_make(a, b) ((((int64_t)(a)) << 32) | (b))
#define fix64_int(n) ((int32_t)((n) >> 32))
#define fix64_frac(n) ((uint32_t)((n) & 0xffffffff))
#define fix64_to_fix(n) (fix64_int(n) << 16 | fix64_frac(n) >> 16)

// fix64 algebraic functions
/**
 * Divide two numbers. There no divide by zero check!
 * @param a dividend
 * @param b divisor
 * @return int32_t result of division
 */
extern int32_t fix64_div(int64_t a, int32_t b);

/**
 * Multiply two numbers.
 * @param a number
 * @param b number
 * @return result of multiplication
 */
extern int64_t fix64_mul(int32_t a, int32_t b);

//============================================
//
//  Other multiply/div/add variants used by 2D and 3D.
//
//============================================
extern fix fix_mul_3_3_3(fix a, fix b);
extern fix fix_mul_3_32_16(fix a, fix b);
extern fix fix_mul_3_16_20(fix a, fix b);
extern fix fix_mul_16_32_20(fix a, fix b);

extern fix fix_div_16_16_3(fix a, fix b);

#define fix_mul_div_3_16_16_3 fix_mul_div

extern fix fix_div_16_16_3(fix a, fix b);
extern fix fix_mul_3_3_3(fix a, fix b);
extern fix fix_mul_3_32_16(fix a, fix b);
extern fix fix_mul_3_16_20(fix a, fix b);
extern fix fix_mul_16_32_20(fix a, fix b);

#define fix_div_16_3_16 fix_div_16_16_3
#define fix_div_3_3_16 fix_div
#define fix_mul_3_16_16 fix_mul_3_3_3

#define fix_sal(a, b) ((a) << (b))
#define fix_sar(a, b) ((a) >> (b))

#define fix_3_16(a) ((a) >> 13)

#define FIX_UNIT_3 0x20000000

#endif /* !__fix24_H */