jas_fix.h
1 /*
2  * Copyright (c) 1999-2000 Image Power, Inc. and the University of
3  * British Columbia.
4  * Copyright (c) 2001-2002 Michael David Adams.
5  * All rights reserved.
6  */
7 
8 /* __START_OF_JASPER_LICENSE__
9  *
10  * JasPer License Version 2.0
11  *
12  * Copyright (c) 2001-2006 Michael David Adams
13  * Copyright (c) 1999-2000 Image Power, Inc.
14  * Copyright (c) 1999-2000 The University of British Columbia
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16  * All rights reserved.
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61  * __END_OF_JASPER_LICENSE__
62  */
63 
64 /*
65  * Fixed-Point Number Class
66  *
67  * $Id$
68  */
69 
70 #ifndef JAS_FIX_H
71 #define JAS_FIX_H
72 
73 /******************************************************************************\
74 * Includes.
75 \******************************************************************************/
76 
77 /* The configuration header file should be included first. */
78 #include <jasper/jas_config.h>
79 
80 #include <stdio.h>
81 #include <stdlib.h>
82 #include <math.h>
83 
84 #include <jasper/jas_types.h>
85 #include <jasper/jas_debug.h>
86 
87 #ifdef __cplusplus
88 extern "C" {
89 #endif
90 
91 /******************************************************************************\
92 * Constants.
93 \******************************************************************************/
94 
95 /* The representation of the value zero. */
96 #define JAS_FIX_ZERO(fix_t, fracbits) \
97  JAS_CAST(fix_t, 0)
98 
99 /* The representation of the value one. */
100 #define JAS_FIX_ONE(fix_t, fracbits) \
101  (JAS_CAST(fix_t, 1) << (fracbits))
102 
103 /* The representation of the value one half. */
104 #define JAS_FIX_HALF(fix_t, fracbits) \
105  (JAS_CAST(fix_t, 1) << ((fracbits) - 1))
106 
107 /******************************************************************************\
108 * Conversion operations.
109 \******************************************************************************/
110 
111 /* Convert an int to a fixed-point number. */
112 #define JAS_INTTOFIX(fix_t, fracbits, x) \
113  JAS_CAST(fix_t, (x) << (fracbits))
114 
115 /* Convert a fixed-point number to an int. */
116 #define JAS_FIXTOINT(fix_t, fracbits, x) \
117  JAS_CAST(int, (x) >> (fracbits))
118 
119 /* Convert a fixed-point number to a double. */
120 #define JAS_FIXTODBL(fix_t, fracbits, x) \
121  (JAS_CAST(double, x) / (JAS_CAST(fix_t, 1) << (fracbits)))
122 
123 /* Convert a double to a fixed-point number. */
124 #define JAS_DBLTOFIX(fix_t, fracbits, x) \
125  JAS_CAST(fix_t, ((x) * JAS_CAST(double, JAS_CAST(fix_t, 1) << (fracbits))))
126 
127 /******************************************************************************\
128 * Basic arithmetic operations.
129 * All other arithmetic operations are synthesized from these basic operations.
130 * There are three macros for each type of arithmetic operation.
131 * One macro always performs overflow/underflow checking, one never performs
132 * overflow/underflow checking, and one is generic with its behavior
133 * depending on compile-time flags.
134 * Only the generic macros should be invoked directly by application code.
135 \******************************************************************************/
136 
137 /* Calculate the sum of two fixed-point numbers. */
138 #if !defined(DEBUG_OVERFLOW)
139 #define JAS_FIX_ADD JAS_FIX_ADD_FAST
140 #else
141 #define JAS_FIX_ADD JAS_FIX_ADD_OFLOW
142 #endif
143 
144 /* Calculate the sum of two fixed-point numbers without overflow checking. */
145 #define JAS_FIX_ADD_FAST(fix_t, fracbits, x, y) ((x) + (y))
146 
147 /* Calculate the sum of two fixed-point numbers with overflow checking. */
148 #define JAS_FIX_ADD_OFLOW(fix_t, fracbits, x, y) \
149  ((x) >= 0) ? \
150  (((y) >= 0) ? ((x) + (y) >= 0 || JAS_FIX_OFLOW(), (x) + (y)) : \
151  ((x) + (y))) : \
152  (((y) >= 0) ? ((x) + (y)) : ((x) + (y) < 0 || JAS_FIX_OFLOW(), \
153  (x) + (y)))
154 
155 /* Calculate the product of two fixed-point numbers. */
156 #if !defined(DEBUG_OVERFLOW)
157 #define JAS_FIX_MUL JAS_FIX_MUL_FAST
158 #else
159 #define JAS_FIX_MUL JAS_FIX_MUL_OFLOW
160 #endif
161 
162 /* Calculate the product of two fixed-point numbers without overflow
163  checking. */
164 #define JAS_FIX_MUL_FAST(fix_t, fracbits, bigfix_t, x, y) \
165  JAS_CAST(fix_t, (JAS_CAST(bigfix_t, x) * JAS_CAST(bigfix_t, y)) >> \
166  (fracbits))
167 
168 /* Calculate the product of two fixed-point numbers with overflow
169  checking. */
170 #define JAS_FIX_MUL_OFLOW(fix_t, fracbits, bigfix_t, x, y) \
171  ((JAS_CAST(bigfix_t, x) * JAS_CAST(bigfix_t, y) >> (fracbits)) == \
172  JAS_CAST(fix_t, (JAS_CAST(bigfix_t, x) * JAS_CAST(bigfix_t, y) >> \
173  (fracbits))) ? \
174  JAS_CAST(fix_t, (JAS_CAST(bigfix_t, x) * JAS_CAST(bigfix_t, y) >> \
175  (fracbits))) : JAS_FIX_OFLOW())
176 
177 /* Calculate the product of a fixed-point number and an int. */
178 #if !defined(DEBUG_OVERFLOW)
179 #define JAS_FIX_MULBYINT JAS_FIX_MULBYINT_FAST
180 #else
181 #define JAS_FIX_MULBYINT JAS_FIX_MULBYINT_OFLOW
182 #endif
183 
184 /* Calculate the product of a fixed-point number and an int without overflow
185  checking. */
186 #define JAS_FIX_MULBYINT_FAST(fix_t, fracbits, x, y) \
187  JAS_CAST(fix_t, ((x) * (y)))
188 
189 /* Calculate the product of a fixed-point number and an int with overflow
190  checking. */
191 #define JAS_FIX_MULBYINT_OFLOW(fix_t, fracbits, x, y) \
192  JAS_FIX_MULBYINT_FAST(fix_t, fracbits, x, y)
193 
194 /* Calculate the quotient of two fixed-point numbers. */
195 #if !defined(DEBUG_OVERFLOW)
196 #define JAS_FIX_DIV JAS_FIX_DIV_FAST
197 #else
198 #define JAS_FIX_DIV JAS_FIX_DIV_UFLOW
199 #endif
200 
201 /* Calculate the quotient of two fixed-point numbers without underflow
202  checking. */
203 #define JAS_FIX_DIV_FAST(fix_t, fracbits, bigfix_t, x, y) \
204  JAS_CAST(fix_t, (JAS_CAST(bigfix_t, x) << (fracbits)) / (y))
205 
206 /* Calculate the quotient of two fixed-point numbers with underflow
207  checking. */
208 #define JAS_FIX_DIV_UFLOW(fix_t, fracbits, bigfix_t, x, y) \
209  JAS_FIX_DIV_FAST(fix_t, fracbits, bigfix_t, x, y)
210 
211 /* Negate a fixed-point number. */
212 #if !defined(DEBUG_OVERFLOW)
213 #define JAS_FIX_NEG JAS_FIX_NEG_FAST
214 #else
215 #define JAS_FIX_NEG JAS_FIX_NEG_OFLOW
216 #endif
217 
218 /* Negate a fixed-point number without overflow checking. */
219 #define JAS_FIX_NEG_FAST(fix_t, fracbits, x) \
220  (-(x))
221 
222 /* Negate a fixed-point number with overflow checking. */
223 /* Yes, overflow is actually possible for two's complement representations,
224  although highly unlikely to occur. */
225 #define JAS_FIX_NEG_OFLOW(fix_t, fracbits, x) \
226  (((x) < 0) ? (-(x) > 0 || JAS_FIX_OFLOW(), -(x)) : (-(x)))
227 
228 /* Perform an arithmetic shift left of a fixed-point number. */
229 #if !defined(DEBUG_OVERFLOW)
230 #define JAS_FIX_ASL JAS_FIX_ASL_FAST
231 #else
232 #define JAS_FIX_ASL JAS_FIX_ASL_OFLOW
233 #endif
234 
235 /* Perform an arithmetic shift left of a fixed-point number without overflow
236  checking. */
237 #define JAS_FIX_ASL_FAST(fix_t, fracbits, x, n) \
238  ((x) << (n))
239 
240 /* Perform an arithmetic shift left of a fixed-point number with overflow
241  checking. */
242 #define JAS_FIX_ASL_OFLOW(fix_t, fracbits, x, n) \
243  ((((x) << (n)) >> (n)) == (x) || JAS_FIX_OFLOW(), (x) << (n))
244 
245 /* Perform an arithmetic shift right of a fixed-point number. */
246 #if !defined(DEBUG_OVERFLOW)
247 #define JAS_FIX_ASR JAS_FIX_ASR_FAST
248 #else
249 #define JAS_FIX_ASR JAS_FIX_ASR_UFLOW
250 #endif
251 
252 /* Perform an arithmetic shift right of a fixed-point number without underflow
253  checking. */
254 #define JAS_FIX_ASR_FAST(fix_t, fracbits, x, n) \
255  ((x) >> (n))
256 
257 /* Perform an arithmetic shift right of a fixed-point number with underflow
258  checking. */
259 #define JAS_FIX_ASR_UFLOW(fix_t, fracbits, x, n) \
260  JAS_FIX_ASR_FAST(fix_t, fracbits, x, n)
261 
262 /******************************************************************************\
263 * Other basic arithmetic operations.
264 \******************************************************************************/
265 
266 /* Calculate the difference between two fixed-point numbers. */
267 #define JAS_FIX_SUB(fix_t, fracbits, x, y) \
268  JAS_FIX_ADD(fix_t, fracbits, x, JAS_FIX_NEG(fix_t, fracbits, y))
269 
270 /* Add one fixed-point number to another. */
271 #define JAS_FIX_PLUSEQ(fix_t, fracbits, x, y) \
272  ((x) = JAS_FIX_ADD(fix_t, fracbits, x, y))
273 
274 /* Subtract one fixed-point number from another. */
275 #define JAS_FIX_MINUSEQ(fix_t, fracbits, x, y) \
276  ((x) = JAS_FIX_SUB(fix_t, fracbits, x, y))
277 
278 /* Multiply one fixed-point number by another. */
279 #define JAS_FIX_MULEQ(fix_t, fracbits, bigfix_t, x, y) \
280  ((x) = JAS_FIX_MUL(fix_t, fracbits, bigfix_t, x, y))
281 
282 /******************************************************************************\
283 * Miscellaneous operations.
284 \******************************************************************************/
285 
286 /* Calculate the absolute value of a fixed-point number. */
287 #define JAS_FIX_ABS(fix_t, fracbits, x) \
288  (((x) >= 0) ? (x) : (JAS_FIX_NEG(fix_t, fracbits, x)))
289 
290 /* Is a fixed-point number an integer? */
291 #define JAS_FIX_ISINT(fix_t, fracbits, x) \
292  (JAS_FIX_FLOOR(fix_t, fracbits, x) == (x))
293 
294 /* Get the sign of a fixed-point number. */
295 #define JAS_FIX_SGN(fix_t, fracbits, x) \
296  ((x) >= 0 ? 1 : (-1))
297 
298 /******************************************************************************\
299 * Relational operations.
300 \******************************************************************************/
301 
302 /* Compare two fixed-point numbers. */
303 #define JAS_FIX_CMP(fix_t, fracbits, x, y) \
304  ((x) > (y) ? 1 : (((x) == (y)) ? 0 : (-1)))
305 
306 /* Less than. */
307 #define JAS_FIX_LT(fix_t, fracbits, x, y) \
308  ((x) < (y))
309 
310 /* Less than or equal. */
311 #define JAS_FIX_LTE(fix_t, fracbits, x, y) \
312  ((x) <= (y))
313 
314 /* Greater than. */
315 #define JAS_FIX_GT(fix_t, fracbits, x, y) \
316  ((x) > (y))
317 
318 /* Greater than or equal. */
319 #define JAS_FIX_GTE(fix_t, fracbits, x, y) \
320  ((x) >= (y))
321 
322 /******************************************************************************\
323 * Rounding functions.
324 \******************************************************************************/
325 
326 /* Round a fixed-point number to the nearest integer. */
327 #define JAS_FIX_ROUND(fix_t, fracbits, x) \
328  (((x) < 0) ? JAS_FIX_FLOOR(fix_t, fracbits, JAS_FIX_ADD(fix_t, fracbits, \
329  (x), JAS_FIX_HALF(fix_t, fracbits))) : \
330  JAS_FIX_NEG(fix_t, fracbits, JAS_FIX_FLOOR(fix_t, fracbits, \
331  JAS_FIX_ADD(fix_t, fracbits, (-(x)), JAS_FIX_HALF(fix_t, fracbits)))))
332 
333 /* Round a fixed-point number to the nearest integer in the direction of
334  negative infinity (i.e., the floor function). */
335 #define JAS_FIX_FLOOR(fix_t, fracbits, x) \
336  ((x) & (~((JAS_CAST(fix_t, 1) << (fracbits)) - 1)))
337 
338 /* Round a fixed-point number to the nearest integer in the direction
339  of zero. */
340 #define JAS_FIX_TRUNC(fix_t, fracbits, x) \
341  (((x) >= 0) ? JAS_FIX_FLOOR(fix_t, fracbits, x) : \
342  JAS_FIX_CEIL(fix_t, fracbits, x))
343 
344 /******************************************************************************\
345 * The below macros are for internal library use only. Do not invoke them
346 * directly in application code.
347 \******************************************************************************/
348 
349 /* Handle overflow. */
350 #define JAS_FIX_OFLOW() \
351  jas_eprintf("overflow error: file %s, line %d\n", __FILE__, __LINE__)
352 
353 /* Handle underflow. */
354 #define JAS_FIX_UFLOW() \
355  jas_eprintf("underflow error: file %s, line %d\n", __FILE__, __LINE__)
356 
357 #ifdef __cplusplus
358 }
359 #endif
360 
361 #endif