Frodo4/Src/FixPoint.h

/*
 *  FixPoint.h - Provides fixed point arithmetic (for use in SID.cpp)
 *
 *  (C) 1997 Andreas Dehmel
 *
 *  Frodo (C) 1994-1997,2002-2005 Christian Bauer
 *
 *  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 2 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, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

/*
 *  You need to define FIXPOINT_PREC (number of fractional bits) and
 *  ldSINTAB (ld of the size of the sinus table) as well M_PI
 *  _before_ including this file.
 *  Requires at least 32bit ints!
 */


#define FIXPOINT_BITS   32
// Sign-bit
#define FIXPOINT_SIGN   (1<<(FIXPOINT_BITS-1))


/*
 *  Elementary functions for the FixPoint class
 */

// Multiplies two fixpoint numbers, result is a fixpoint number.
static inline int fixmult(int x, int y)
{
  register unsigned int a,b;
  register bool sign;

  sign = (x ^ y) < 0;
  if (x < 0) {x = -x;}
  if (y < 0) {y = -y;}
  // a, b : integer part; x, y : fractional part. All unsigned now (for shift right)!!!
  a = (((unsigned int)x) >> FIXPOINT_PREC); x &= ~(a << FIXPOINT_PREC);
  b = (((unsigned int)y) >> FIXPOINT_PREC); y &= ~(b << FIXPOINT_PREC);
  x = ((a*b) << FIXPOINT_PREC) + (a*y + b*x) +
      ((unsigned int)((x*y) + (1 << (FIXPOINT_PREC-1))) >> FIXPOINT_PREC);
#ifdef FIXPOINT_SIGN
  if (x < 0) {x ^= FIXPOINT_SIGN;}
#endif
  if (sign) {x = -x;}
  return(x);
}


// Multiplies a fixpoint number with an integer, result is a 32 bit (!) integer in
// contrast to using the standard member-functions which can provide only (32-FIXPOINT_PREC)
// valid bits.
static inline int intmult(int x, int y) // x is fixpoint, y integer
{
  register unsigned int i,j;
  register bool sign;

  sign = (x ^ y) < 0;
  if (x < 0) {x = -x;}
  if (y < 0) {y = -y;}
  i = (((unsigned int)x) >> 16); x &= ~(i << 16);       // split both into 16.16 parts
  j = (((unsigned int)y) >> 16); y &= ~(j << 16);
#if FIXPOINT_PREC <= 16
  // This '32' is independent of the number of bits used, it's due to the 16 bit shift
  i = ((i*j) << (32 - FIXPOINT_PREC)) + ((i*y + j*x) << (16 - FIXPOINT_PREC)) +
      ((unsigned int)(x*y + (1 << (FIXPOINT_PREC - 1))) >> FIXPOINT_PREC);
#else
  {
    register unsigned int h;

    h = (i*y + j*x);
    i = ((i*j) << (32 - FIXPOINT_PREC)) + (h >> (FIXPOINT_PREC - 16));
    h &= ((1 << (FIXPOINT_PREC - 16)) - 1); x *= y;
    i += (x >> FIXPOINT_PREC); x &= ((1 << FIXPOINT_PREC) - 1);
    i += (((h + (x >> 16)) + (1 << (FIXPOINT_PREC - 17))) >> (FIXPOINT_PREC - 16));
  }
#endif
#ifdef FIXPOINT_SIGN
  if (i < 0) {i ^= FIXPOINT_SIGN;}
#endif
  if (sign) {i = -i;}
  return(i);
}


// Computes the product of a fixpoint number with itself.
static inline int fixsquare(int x)
{
  register unsigned int a;

  if (x < 0) {x = -x;}
  a = (((unsigned int)x) >> FIXPOINT_PREC); x &= ~(a << FIXPOINT_PREC);
  x = ((a*a) << FIXPOINT_PREC) + ((a*x) << 1) +
      ((unsigned int)((x*x) + (1 << (FIXPOINT_PREC-1))) >> FIXPOINT_PREC);
#ifdef FIXPOINT_SIGN
  if (x < 0) {x ^= FIXPOINT_SIGN;}
#endif
  return(x);
}


// Computes the square root of a fixpoint number.
static inline int fixsqrt(int x)
{
  register int test, step;

  if (x < 0) return(-1); if (x == 0) return(0);
  step = (x <= (1<<FIXPOINT_PREC)) ? (1<<FIXPOINT_PREC) : (1<<((FIXPOINT_BITS - 2 + FIXPOINT_PREC)>>1));
  test = 0;
  while (step != 0)
  {
    register int h;

    h = fixsquare(test + step);
    if (h <= x) {test += step;}
    if (h == x) break;
    step >>= 1;
  }
  return(test);
}


// Divides a fixpoint number by another fixpoint number, yielding a fixpoint result.
static inline int fixdiv(int x, int y)
{
  register int res, mask;
  register bool sign;

  sign = (x ^ y) < 0;
  if (x < 0) {x = -x;}
  if (y < 0) {y = -y;}
  mask = (1<<FIXPOINT_PREC); res = 0;
  while (x > y) {y <<= 1; mask <<= 1;}
  while (mask != 0)
  {
    if (x >= y) {res |= mask; x -= y;}
    mask >>= 1; y >>= 1;
  }
#ifdef FIXPOINT_SIGN
  if (res < 0) {res ^= FIXPOINT_SIGN;}
#endif
  if (sign) {res = -res;}
  return(res);
}


/*
 *  The C++ Fixpoint class. By no means exhaustive...
 *  Since it contains only one int data, variables of type FixPoint can be
 *  passed directly rather than as a reference.
 */

class FixPoint
{
private:
  int x;

public:
  FixPoint(void);
  FixPoint(int y);
  ~FixPoint(void);

  // conversions
  int Value(void);
  int round(void);
  operator int(void);

  // unary operators
  FixPoint sqrt(void);
  FixPoint sqr(void);
  FixPoint abs(void);
  FixPoint operator+(void);
  FixPoint operator-(void);
  FixPoint operator++(void);
  FixPoint operator--(void);

  // binary operators
  int imul(int y);
  FixPoint operator=(FixPoint y);
  FixPoint operator=(int y);
  FixPoint operator+(FixPoint y);
  FixPoint operator+(int y);
  FixPoint operator-(FixPoint y);
  FixPoint operator-(int y);
  FixPoint operator/(FixPoint y);
  FixPoint operator/(int y);
  FixPoint operator*(FixPoint y);
  FixPoint operator*(int y);
  FixPoint operator+=(FixPoint y);
  FixPoint operator+=(int y);
  FixPoint operator-=(FixPoint y);
  FixPoint operator-=(int y);
  FixPoint operator*=(FixPoint y);
  FixPoint operator*=(int y);
  FixPoint operator/=(FixPoint y);
  FixPoint operator/=(int y);
  FixPoint operator<<(int y);
  FixPoint operator>>(int y);
  FixPoint operator<<=(int y);
  FixPoint operator>>=(int y);

  // conditional operators
  bool operator<(FixPoint y);
  bool operator<(int y);
  bool operator<=(FixPoint y);
  bool operator<=(int y);
  bool operator>(FixPoint y);
  bool operator>(int y);
  bool operator>=(FixPoint y);
  bool operator>=(int y);
  bool operator==(FixPoint y);
  bool operator==(int y);
  bool operator!=(FixPoint y);
  bool operator!=(int y);
};


/*
 *  int gets treated differently according to the case:
 *
 *  a) Equations (=) or condition checks (==, <, <= ...): raw int (i.e. no conversion)
 *  b) As an argument for an arithmetic operation: conversion to fixpoint by shifting
 *
 *  Otherwise loading meaningful values into FixPoint variables would be very awkward.
 */

FixPoint::FixPoint(void) {x = 0;}

FixPoint::FixPoint(int y) {x = y;}

FixPoint::~FixPoint(void) {;}

inline int FixPoint::Value(void) {return(x);}

inline int FixPoint::round(void) {return((x + (1 << (FIXPOINT_PREC-1))) >> FIXPOINT_PREC);}

inline FixPoint::operator int(void) {return(x);}


// unary operators
inline FixPoint FixPoint::sqrt(void) {return(fixsqrt(x));}

inline FixPoint FixPoint::sqr(void) {return(fixsquare(x));}

inline FixPoint FixPoint::abs(void) {return((x < 0) ? -x : x);}

inline FixPoint FixPoint::operator+(void) {return(x);}

inline FixPoint FixPoint::operator-(void) {return(-x);}

inline FixPoint FixPoint::operator++(void) {x += (1 << FIXPOINT_PREC); return x;}

inline FixPoint FixPoint::operator--(void) {x -= (1 << FIXPOINT_PREC); return x;}


// binary operators
inline int FixPoint::imul(int y) {return(intmult(x,y));}

inline FixPoint FixPoint::operator=(FixPoint y) {x = y.Value(); return x;}

inline FixPoint FixPoint::operator=(int y) {x = y; return x;}

inline FixPoint FixPoint::operator+(FixPoint y) {return(x + y.Value());}

inline FixPoint FixPoint::operator+(int y) {return(x + (y << FIXPOINT_PREC));}

inline FixPoint FixPoint::operator-(FixPoint y) {return(x - y.Value());}

inline FixPoint FixPoint::operator-(int y) {return(x - (y << FIXPOINT_PREC));}

inline FixPoint FixPoint::operator/(FixPoint y) {return(fixdiv(x,y.Value()));}

inline FixPoint FixPoint::operator/(int y) {return(x/y);}

inline FixPoint FixPoint::operator*(FixPoint y) {return(fixmult(x,y.Value()));}

inline FixPoint FixPoint::operator*(int y) {return(x*y);}

inline FixPoint FixPoint::operator+=(FixPoint y) {x += y.Value(); return x;}

inline FixPoint FixPoint::operator+=(int y) {x += (y << FIXPOINT_PREC); return x;}

inline FixPoint FixPoint::operator-=(FixPoint y) {x -= y.Value(); return x;}

inline FixPoint FixPoint::operator-=(int y) {x -= (y << FIXPOINT_PREC); return x;}

inline FixPoint FixPoint::operator*=(FixPoint y) {x = fixmult(x,y.Value()); return x;}

inline FixPoint FixPoint::operator*=(int y) {x *= y; return x;}

inline FixPoint FixPoint::operator/=(FixPoint y) {x = fixdiv(x,y.Value()); return x;}

inline FixPoint FixPoint::operator/=(int y) {x /= y; return x;}

inline FixPoint FixPoint::operator<<(int y) {return(x << y);}

inline FixPoint FixPoint::operator>>(int y) {return(x >> y);}

inline FixPoint FixPoint::operator<<=(int y) {x <<= y; return x;}

inline FixPoint FixPoint::operator>>=(int y) {x >>= y; return x;}


// conditional operators
inline bool FixPoint::operator<(FixPoint y) {return(x < y.Value());}

inline bool FixPoint::operator<(int y) {return(x < y);}

inline bool FixPoint::operator<=(FixPoint y) {return(x <= y.Value());}

inline bool FixPoint::operator<=(int y) {return(x <= y);}

inline bool FixPoint::operator>(FixPoint y) {return(x > y.Value());}

inline bool FixPoint::operator>(int y) {return(x > y);}

inline bool FixPoint::operator>=(FixPoint y) {return(x >= y.Value());}

inline bool FixPoint::operator>=(int y) {return(x >= y);}

inline bool FixPoint::operator==(FixPoint y) {return(x == y.Value());}

inline bool FixPoint::operator==(int y) {return(x == y);}

inline bool FixPoint::operator!=(FixPoint y) {return(x != y.Value());}

inline bool FixPoint::operator!=(int y) {return(x != y);}


/*
 *  In case the first argument is an int (i.e. member-operators not applicable):
 *  Not supported: things like int/FixPoint. The same difference in conversions
 *  applies as mentioned above.
 */


// binary operators
inline FixPoint operator+(int x, FixPoint y) {return((x << FIXPOINT_PREC) + y.Value());}

inline FixPoint operator-(int x, FixPoint y) {return((x << FIXPOINT_PREC) - y.Value());}

inline FixPoint operator*(int x, FixPoint y) {return(x*y.Value());}


// conditional operators
inline bool operator==(int x, FixPoint y) {return(x == y.Value());}

inline bool operator!=(int x, FixPoint y) {return(x != y.Value());}

inline bool operator<(int x, FixPoint y) {return(x < y.Value());}

inline bool operator<=(int x, FixPoint y) {return(x <= y.Value());}

inline bool operator>(int x, FixPoint y) {return(x > y.Value());}

inline bool operator>=(int x, FixPoint y) {return(x >= y.Value());}


/*
 *  For more convenient creation of constant fixpoint numbers from constant floats.
 */

#define FixNo(n)        (FixPoint)((int)(n*(1<<FIXPOINT_PREC)))


/*
 *  Stuff re. the sinus table used with fixpoint arithmetic
 */


// define as global variable
FixPoint SinTable[(1<<ldSINTAB)];


#define FIXPOINT_SIN_COS_GENERIC \
  if (angle >= 3*(1<<ldSINTAB)) {return(-SinTable[(1<<(ldSINTAB+2)) - angle]);}\
  if (angle >= 2*(1<<ldSINTAB)) {return(-SinTable[angle - 2*(1<<ldSINTAB)]);}\
  if (angle >= (1<<ldSINTAB)) {return(SinTable[2*(1<<ldSINTAB) - angle]);}\
  return(SinTable[angle]);


// sin and cos: angle is fixpoint number 0 <= angle <= 2 (*PI)
static inline FixPoint fixsin(FixPoint x)
{
  int angle = x;

  angle = (angle >> (FIXPOINT_PREC - ldSINTAB - 1)) & ((1<<(ldSINTAB+2))-1);
  FIXPOINT_SIN_COS_GENERIC
}


static inline FixPoint fixcos(FixPoint x)
{
  int angle = x;

  // cos(x) = sin(x+PI/2)
  angle = (angle + (1<<(FIXPOINT_PREC-1)) >> (FIXPOINT_PREC - ldSINTAB - 1)) & ((1<<(ldSINTAB+2))-1);
  FIXPOINT_SIN_COS_GENERIC
}


static inline void InitFixSinTab(void)
{
  int i;
  float step;

  for (i=0, step=0; i<(1<<ldSINTAB); i++, step+=0.5/(1<<ldSINTAB))
  {
    SinTable[i] = FixNo(sin(M_PI * step));
  }
}
Revision:	1.5
Committed:	2005-06-27T19:55:48Z (19 years, 5 months ago) by cebix
Content type:	text/plain
Branch:	MAIN
CVS Tags:	VERSION_4_2, HEAD
Changes since 1.4:	+1 -1 lines
Log Message:	updated copyright dates
#	Content
1	/*
2	* FixPoint.h - Provides fixed point arithmetic (for use in SID.cpp)
3	*
4	* (C) 1997 Andreas Dehmel
5	*
6	* Frodo (C) 1994-1997,2002-2005 Christian Bauer
7	*
8	* This program is free software; you can redistribute it and/or modify
9	* it under the terms of the GNU General Public License as published by
10	* the Free Software Foundation; either version 2 of the License, or
11	* (at your option) any later version.
12	*
13	* This program is distributed in the hope that it will be useful,
14	* but WITHOUT ANY WARRANTY; without even the implied warranty of
15	* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16	* GNU General Public License for more details.
17	*
18	* You should have received a copy of the GNU General Public License
19	* along with this program; if not, write to the Free Software
20	* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
21	*/
22
23	/*
24	* You need to define FIXPOINT_PREC (number of fractional bits) and
25	* ldSINTAB (ld of the size of the sinus table) as well M_PI
26	* _before_ including this file.
27	* Requires at least 32bit ints!
28	*/
29
30
31	#define FIXPOINT_BITS 32
32	// Sign-bit
33	#define FIXPOINT_SIGN (1<<(FIXPOINT_BITS-1))
34
35
36	/*
37	* Elementary functions for the FixPoint class
38	*/
39
40	// Multiplies two fixpoint numbers, result is a fixpoint number.
41	static inline int fixmult(int x, int y)
42	{
43	register unsigned int a,b;
44	register bool sign;
45
46	sign = (x ^ y) < 0;
47	if (x < 0) {x = -x;}
48	if (y < 0) {y = -y;}
49	// a, b : integer part; x, y : fractional part. All unsigned now (for shift right)!!!
50	a = (((unsigned int)x) >> FIXPOINT_PREC); x &= ~(a << FIXPOINT_PREC);
51	b = (((unsigned int)y) >> FIXPOINT_PREC); y &= ~(b << FIXPOINT_PREC);
52	x = ((ab) << FIXPOINT_PREC) + (ay + b*x) +
53	((unsigned int)((x*y) + (1 << (FIXPOINT_PREC-1))) >> FIXPOINT_PREC);
54	#ifdef FIXPOINT_SIGN
55	if (x < 0) {x ^= FIXPOINT_SIGN;}
56	#endif
57	if (sign) {x = -x;}
58	return(x);
59	}
60
61
62	// Multiplies a fixpoint number with an integer, result is a 32 bit (!) integer in
63	// contrast to using the standard member-functions which can provide only (32-FIXPOINT_PREC)
64	// valid bits.
65	static inline int intmult(int x, int y) // x is fixpoint, y integer
66	{
67	register unsigned int i,j;
68	register bool sign;
69
70	sign = (x ^ y) < 0;
71	if (x < 0) {x = -x;}
72	if (y < 0) {y = -y;}
73	i = (((unsigned int)x) >> 16); x &= ~(i << 16); // split both into 16.16 parts
74	j = (((unsigned int)y) >> 16); y &= ~(j << 16);
75	#if FIXPOINT_PREC <= 16
76	// This '32' is independent of the number of bits used, it's due to the 16 bit shift
77	i = ((ij) << (32 - FIXPOINT_PREC)) + ((iy + j*x) << (16 - FIXPOINT_PREC)) +
78	((unsigned int)(x*y + (1 << (FIXPOINT_PREC - 1))) >> FIXPOINT_PREC);
79	#else
80	{
81	register unsigned int h;
82
83	h = (iy + jx);
84	i = ((i*j) << (32 - FIXPOINT_PREC)) + (h >> (FIXPOINT_PREC - 16));
85	h &= ((1 << (FIXPOINT_PREC - 16)) - 1); x *= y;
86	i += (x >> FIXPOINT_PREC); x &= ((1 << FIXPOINT_PREC) - 1);
87	i += (((h + (x >> 16)) + (1 << (FIXPOINT_PREC - 17))) >> (FIXPOINT_PREC - 16));
88	}
89	#endif
90	#ifdef FIXPOINT_SIGN
91	if (i < 0) {i ^= FIXPOINT_SIGN;}
92	#endif
93	if (sign) {i = -i;}
94	return(i);
95	}
96
97
98	// Computes the product of a fixpoint number with itself.
99	static inline int fixsquare(int x)
100	{
101	register unsigned int a;
102
103	if (x < 0) {x = -x;}
104	a = (((unsigned int)x) >> FIXPOINT_PREC); x &= ~(a << FIXPOINT_PREC);
105	x = ((aa) << FIXPOINT_PREC) + ((ax) << 1) +
106	((unsigned int)((x*x) + (1 << (FIXPOINT_PREC-1))) >> FIXPOINT_PREC);
107	#ifdef FIXPOINT_SIGN
108	if (x < 0) {x ^= FIXPOINT_SIGN;}
109	#endif
110	return(x);
111	}
112
113
114	// Computes the square root of a fixpoint number.
115	static inline int fixsqrt(int x)
116	{
117	register int test, step;
118
119	if (x < 0) return(-1); if (x == 0) return(0);
120	step = (x <= (1<<FIXPOINT_PREC)) ? (1<<FIXPOINT_PREC) : (1<<((FIXPOINT_BITS - 2 + FIXPOINT_PREC)>>1));
121	test = 0;
122	while (step != 0)
123	{
124	register int h;
125
126	h = fixsquare(test + step);
127	if (h <= x) {test += step;}
128	if (h == x) break;
129	step >>= 1;
130	}
131	return(test);
132	}
133
134
135	// Divides a fixpoint number by another fixpoint number, yielding a fixpoint result.
136	static inline int fixdiv(int x, int y)
137	{
138	register int res, mask;
139	register bool sign;
140
141	sign = (x ^ y) < 0;
142	if (x < 0) {x = -x;}
143	if (y < 0) {y = -y;}
144	mask = (1<<FIXPOINT_PREC); res = 0;
145	while (x > y) {y <<= 1; mask <<= 1;}
146	while (mask != 0)
147	{
148	if (x >= y) {res \|= mask; x -= y;}
149	mask >>= 1; y >>= 1;
150	}
151	#ifdef FIXPOINT_SIGN
152	if (res < 0) {res ^= FIXPOINT_SIGN;}
153	#endif
154	if (sign) {res = -res;}
155	return(res);
156	}
157
158
159
160
161
162	/*
163	* The C++ Fixpoint class. By no means exhaustive...
164	* Since it contains only one int data, variables of type FixPoint can be
165	* passed directly rather than as a reference.
166	*/
167
168	class FixPoint
169	{
170	private:
171	int x;
172
173	public:
174	FixPoint(void);
175	FixPoint(int y);
176	~FixPoint(void);
177
178	// conversions
179	int Value(void);
180	int round(void);
181	operator int(void);
182
183	// unary operators
184	FixPoint sqrt(void);
185	FixPoint sqr(void);
186	FixPoint abs(void);
187	FixPoint operator+(void);
188	FixPoint operator-(void);
189	FixPoint operator++(void);
190	FixPoint operator--(void);
191
192	// binary operators
193	int imul(int y);
194	FixPoint operator=(FixPoint y);
195	FixPoint operator=(int y);
196	FixPoint operator+(FixPoint y);
197	FixPoint operator+(int y);
198	FixPoint operator-(FixPoint y);
199	FixPoint operator-(int y);
200	FixPoint operator/(FixPoint y);
201	FixPoint operator/(int y);
202	FixPoint operator*(FixPoint y);
203	FixPoint operator*(int y);
204	FixPoint operator+=(FixPoint y);
205	FixPoint operator+=(int y);
206	FixPoint operator-=(FixPoint y);
207	FixPoint operator-=(int y);
208	FixPoint operator*=(FixPoint y);
209	FixPoint operator*=(int y);
210	FixPoint operator/=(FixPoint y);
211	FixPoint operator/=(int y);
212	FixPoint operator<<(int y);
213	FixPoint operator>>(int y);
214	FixPoint operator<<=(int y);
215	FixPoint operator>>=(int y);
216
217	// conditional operators
218	bool operator<(FixPoint y);
219	bool operator<(int y);
220	bool operator<=(FixPoint y);
221	bool operator<=(int y);
222	bool operator>(FixPoint y);
223	bool operator>(int y);
224	bool operator>=(FixPoint y);
225	bool operator>=(int y);
226	bool operator==(FixPoint y);
227	bool operator==(int y);
228	bool operator!=(FixPoint y);
229	bool operator!=(int y);
230	};
231
232
233	/*
234	* int gets treated differently according to the case:
235	*
236	* a) Equations (=) or condition checks (==, <, <= ...): raw int (i.e. no conversion)
237	* b) As an argument for an arithmetic operation: conversion to fixpoint by shifting
238	*
239	* Otherwise loading meaningful values into FixPoint variables would be very awkward.
240	*/
241
242	FixPoint::FixPoint(void) {x = 0;}
243
244	FixPoint::FixPoint(int y) {x = y;}
245
246	FixPoint::~FixPoint(void) {;}
247
248	inline int FixPoint::Value(void) {return(x);}
249
250	inline int FixPoint::round(void) {return((x + (1 << (FIXPOINT_PREC-1))) >> FIXPOINT_PREC);}
251
252	inline FixPoint::operator int(void) {return(x);}
253
254
255	// unary operators
256	inline FixPoint FixPoint::sqrt(void) {return(fixsqrt(x));}
257
258	inline FixPoint FixPoint::sqr(void) {return(fixsquare(x));}
259
260	inline FixPoint FixPoint::abs(void) {return((x < 0) ? -x : x);}
261
262	inline FixPoint FixPoint::operator+(void) {return(x);}
263
264	inline FixPoint FixPoint::operator-(void) {return(-x);}
265
266	inline FixPoint FixPoint::operator++(void) {x += (1 << FIXPOINT_PREC); return x;}
267
268	inline FixPoint FixPoint::operator--(void) {x -= (1 << FIXPOINT_PREC); return x;}
269
270
271	// binary operators
272	inline int FixPoint::imul(int y) {return(intmult(x,y));}
273
274	inline FixPoint FixPoint::operator=(FixPoint y) {x = y.Value(); return x;}
275
276	inline FixPoint FixPoint::operator=(int y) {x = y; return x;}
277
278	inline FixPoint FixPoint::operator+(FixPoint y) {return(x + y.Value());}
279
280	inline FixPoint FixPoint::operator+(int y) {return(x + (y << FIXPOINT_PREC));}
281
282	inline FixPoint FixPoint::operator-(FixPoint y) {return(x - y.Value());}
283
284	inline FixPoint FixPoint::operator-(int y) {return(x - (y << FIXPOINT_PREC));}
285
286	inline FixPoint FixPoint::operator/(FixPoint y) {return(fixdiv(x,y.Value()));}
287
288	inline FixPoint FixPoint::operator/(int y) {return(x/y);}
289
290	inline FixPoint FixPoint::operator*(FixPoint y) {return(fixmult(x,y.Value()));}
291
292	inline FixPoint FixPoint::operator(int y) {return(xy);}
293
294	inline FixPoint FixPoint::operator+=(FixPoint y) {x += y.Value(); return x;}
295
296	inline FixPoint FixPoint::operator+=(int y) {x += (y << FIXPOINT_PREC); return x;}
297
298	inline FixPoint FixPoint::operator-=(FixPoint y) {x -= y.Value(); return x;}
299
300	inline FixPoint FixPoint::operator-=(int y) {x -= (y << FIXPOINT_PREC); return x;}
301
302	inline FixPoint FixPoint::operator*=(FixPoint y) {x = fixmult(x,y.Value()); return x;}
303
304	inline FixPoint FixPoint::operator=(int y) {x = y; return x;}
305
306	inline FixPoint FixPoint::operator/=(FixPoint y) {x = fixdiv(x,y.Value()); return x;}
307
308	inline FixPoint FixPoint::operator/=(int y) {x /= y; return x;}
309
310	inline FixPoint FixPoint::operator<<(int y) {return(x << y);}
311
312	inline FixPoint FixPoint::operator>>(int y) {return(x >> y);}
313
314	inline FixPoint FixPoint::operator<<=(int y) {x <<= y; return x;}
315
316	inline FixPoint FixPoint::operator>>=(int y) {x >>= y; return x;}
317
318
319	// conditional operators
320	inline bool FixPoint::operator<(FixPoint y) {return(x < y.Value());}
321
322	inline bool FixPoint::operator<(int y) {return(x < y);}
323
324	inline bool FixPoint::operator<=(FixPoint y) {return(x <= y.Value());}
325
326	inline bool FixPoint::operator<=(int y) {return(x <= y);}
327
328	inline bool FixPoint::operator>(FixPoint y) {return(x > y.Value());}
329
330	inline bool FixPoint::operator>(int y) {return(x > y);}
331
332	inline bool FixPoint::operator>=(FixPoint y) {return(x >= y.Value());}
333
334	inline bool FixPoint::operator>=(int y) {return(x >= y);}
335
336	inline bool FixPoint::operator==(FixPoint y) {return(x == y.Value());}
337
338	inline bool FixPoint::operator==(int y) {return(x == y);}
339
340	inline bool FixPoint::operator!=(FixPoint y) {return(x != y.Value());}
341
342	inline bool FixPoint::operator!=(int y) {return(x != y);}
343
344
345
346	/*
347	* In case the first argument is an int (i.e. member-operators not applicable):
348	* Not supported: things like int/FixPoint. The same difference in conversions
349	* applies as mentioned above.
350	*/
351
352
353	// binary operators
354	inline FixPoint operator+(int x, FixPoint y) {return((x << FIXPOINT_PREC) + y.Value());}
355
356	inline FixPoint operator-(int x, FixPoint y) {return((x << FIXPOINT_PREC) - y.Value());}
357
358	inline FixPoint operator(int x, FixPoint y) {return(xy.Value());}
359
360
361	// conditional operators
362	inline bool operator==(int x, FixPoint y) {return(x == y.Value());}
363
364	inline bool operator!=(int x, FixPoint y) {return(x != y.Value());}
365
366	inline bool operator<(int x, FixPoint y) {return(x < y.Value());}
367
368	inline bool operator<=(int x, FixPoint y) {return(x <= y.Value());}
369
370	inline bool operator>(int x, FixPoint y) {return(x > y.Value());}
371
372	inline bool operator>=(int x, FixPoint y) {return(x >= y.Value());}
373
374
375
376	/*
377	* For more convenient creation of constant fixpoint numbers from constant floats.
378	*/
379
380	#define FixNo(n) (FixPoint)((int)(n*(1<<FIXPOINT_PREC)))
381
382
383
384
385
386
387	/*
388	* Stuff re. the sinus table used with fixpoint arithmetic
389	*/
390
391
392	// define as global variable
393	FixPoint SinTable[(1<<ldSINTAB)];
394
395
396	#define FIXPOINT_SIN_COS_GENERIC \
397	if (angle >= 3*(1<<ldSINTAB)) {return(-SinTable[(1<<(ldSINTAB+2)) - angle]);}\
398	if (angle >= 2(1<<ldSINTAB)) {return(-SinTable[angle - 2(1<<ldSINTAB)]);}\
399	if (angle >= (1<<ldSINTAB)) {return(SinTable[2*(1<<ldSINTAB) - angle]);}\
400	return(SinTable[angle]);
401
402
403	// sin and cos: angle is fixpoint number 0 <= angle <= 2 (*PI)
404	static inline FixPoint fixsin(FixPoint x)
405	{
406	int angle = x;
407
408	angle = (angle >> (FIXPOINT_PREC - ldSINTAB - 1)) & ((1<<(ldSINTAB+2))-1);
409	FIXPOINT_SIN_COS_GENERIC
410	}
411
412
413	static inline FixPoint fixcos(FixPoint x)
414	{
415	int angle = x;
416
417	// cos(x) = sin(x+PI/2)
418	angle = (angle + (1<<(FIXPOINT_PREC-1)) >> (FIXPOINT_PREC - ldSINTAB - 1)) & ((1<<(ldSINTAB+2))-1);
419	FIXPOINT_SIN_COS_GENERIC
420	}
421
422
423
424	static inline void InitFixSinTab(void)
425	{
426	int i;
427	float step;
428
429	for (i=0, step=0; i<(1<<ldSINTAB); i++, step+=0.5/(1<<ldSINTAB))
430	{
431	SinTable[i] = FixNo(sin(M_PI * step));
432	}
433	}