1 /*
2 * Copyright 2012-15 Advanced Micro Devices, Inc.
3 *
4 * Permission is hereby granted, free of charge, to any person obtaining a
5 * copy of this software and associated documentation files (the "Software"),
6 * to deal in the Software without restriction, including without limitation
7 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
8 * and/or sell copies of the Software, and to permit persons to whom the
9 * Software is furnished to do so, subject to the following conditions:
10 *
11 * The above copyright notice and this permission notice shall be included in
12 * all copies or substantial portions of the Software.
13 *
14 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
15 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
16 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
17 * THE COPYRIGHT HOLDER(S) OR AUTHOR(S) BE LIABLE FOR ANY CLAIM, DAMAGES OR
18 * OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
19 * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
20 * OTHER DEALINGS IN THE SOFTWARE.
21 *
22 * Authors: AMD
23 *
24 */
25
26 #ifndef __DAL_FIXED31_32_H__
27 #define __DAL_FIXED31_32_H__
28
29 #ifndef LLONG_MAX
30 #define LLONG_MAX 9223372036854775807ll
31 #endif
32 #ifndef LLONG_MIN
33 #define LLONG_MIN (-LLONG_MAX - 1ll)
34 #endif
35
36 #define FIXED31_32_BITS_PER_FRACTIONAL_PART 32
37 #ifndef LLONG_MIN
38 #define LLONG_MIN (1LL<<63)
39 #endif
40 #ifndef LLONG_MAX
41 #define LLONG_MAX (-1LL>>1)
42 #endif
43
44 /*
45 * @brief
46 * Arithmetic operations on real numbers
47 * represented as fixed-point numbers.
48 * There are: 1 bit for sign,
49 * 31 bit for integer part,
50 * 32 bits for fractional part.
51 *
52 * @note
53 * Currently, overflows and underflows are asserted;
54 * no special result returned.
55 */
56
57 struct fixed31_32 {
58 long long value;
59 };
60
61
62 /*
63 * @brief
64 * Useful constants
65 */
66
67 static const struct fixed31_32 dc_fixpt_zero = { 0 };
68 static const struct fixed31_32 dc_fixpt_epsilon = { 1LL };
69 static const struct fixed31_32 dc_fixpt_half = { 0x80000000LL };
70 static const struct fixed31_32 dc_fixpt_one = { 0x100000000LL };
71
72 static const struct fixed31_32 dc_fixpt_pi = { 13493037705LL };
73 static const struct fixed31_32 dc_fixpt_two_pi = { 26986075409LL };
74 static const struct fixed31_32 dc_fixpt_e = { 11674931555LL };
75 static const struct fixed31_32 dc_fixpt_ln2 = { 2977044471LL };
76 static const struct fixed31_32 dc_fixpt_ln2_div_2 = { 1488522236LL };
77
78 /*
79 * @brief
80 * Initialization routines
81 */
82
83 /*
84 * @brief
85 * result = numerator / denominator
86 */
87 struct fixed31_32 dc_fixpt_from_fraction(long long numerator, long long denominator);
88
89 /*
90 * @brief
91 * result = arg
92 */
dc_fixpt_from_int(int arg)93 static inline struct fixed31_32 dc_fixpt_from_int(int arg)
94 {
95 struct fixed31_32 res;
96
97 res.value = (long long) arg << FIXED31_32_BITS_PER_FRACTIONAL_PART;
98
99 return res;
100 }
101
102 /*
103 * @brief
104 * Unary operators
105 */
106
107 /*
108 * @brief
109 * result = -arg
110 */
dc_fixpt_neg(struct fixed31_32 arg)111 static inline struct fixed31_32 dc_fixpt_neg(struct fixed31_32 arg)
112 {
113 struct fixed31_32 res;
114
115 res.value = -arg.value;
116
117 return res;
118 }
119
120 /*
121 * @brief
122 * result = abs(arg) := (arg >= 0) ? arg : -arg
123 */
dc_fixpt_abs(struct fixed31_32 arg)124 static inline struct fixed31_32 dc_fixpt_abs(struct fixed31_32 arg)
125 {
126 if (arg.value < 0)
127 return dc_fixpt_neg(arg);
128 else
129 return arg;
130 }
131
132 /*
133 * @brief
134 * Binary relational operators
135 */
136
137 /*
138 * @brief
139 * result = arg1 < arg2
140 */
dc_fixpt_lt(struct fixed31_32 arg1,struct fixed31_32 arg2)141 static inline bool dc_fixpt_lt(struct fixed31_32 arg1, struct fixed31_32 arg2)
142 {
143 return arg1.value < arg2.value;
144 }
145
146 /*
147 * @brief
148 * result = arg1 <= arg2
149 */
dc_fixpt_le(struct fixed31_32 arg1,struct fixed31_32 arg2)150 static inline bool dc_fixpt_le(struct fixed31_32 arg1, struct fixed31_32 arg2)
151 {
152 return arg1.value <= arg2.value;
153 }
154
155 /*
156 * @brief
157 * result = arg1 == arg2
158 */
dc_fixpt_eq(struct fixed31_32 arg1,struct fixed31_32 arg2)159 static inline bool dc_fixpt_eq(struct fixed31_32 arg1, struct fixed31_32 arg2)
160 {
161 return arg1.value == arg2.value;
162 }
163
164 /*
165 * @brief
166 * result = min(arg1, arg2) := (arg1 <= arg2) ? arg1 : arg2
167 */
dc_fixpt_min(struct fixed31_32 arg1,struct fixed31_32 arg2)168 static inline struct fixed31_32 dc_fixpt_min(struct fixed31_32 arg1, struct fixed31_32 arg2)
169 {
170 if (arg1.value <= arg2.value)
171 return arg1;
172 else
173 return arg2;
174 }
175
176 /*
177 * @brief
178 * result = max(arg1, arg2) := (arg1 <= arg2) ? arg2 : arg1
179 */
dc_fixpt_max(struct fixed31_32 arg1,struct fixed31_32 arg2)180 static inline struct fixed31_32 dc_fixpt_max(struct fixed31_32 arg1, struct fixed31_32 arg2)
181 {
182 if (arg1.value <= arg2.value)
183 return arg2;
184 else
185 return arg1;
186 }
187
188 /*
189 * @brief
190 * | min_value, when arg <= min_value
191 * result = | arg, when min_value < arg < max_value
192 * | max_value, when arg >= max_value
193 */
dc_fixpt_clamp(struct fixed31_32 arg,struct fixed31_32 min_value,struct fixed31_32 max_value)194 static inline struct fixed31_32 dc_fixpt_clamp(
195 struct fixed31_32 arg,
196 struct fixed31_32 min_value,
197 struct fixed31_32 max_value)
198 {
199 if (dc_fixpt_le(arg, min_value))
200 return min_value;
201 else if (dc_fixpt_le(max_value, arg))
202 return max_value;
203 else
204 return arg;
205 }
206
207 /*
208 * @brief
209 * Binary shift operators
210 */
211
212 /*
213 * @brief
214 * result = arg << shift
215 */
dc_fixpt_shl(struct fixed31_32 arg,unsigned char shift)216 static inline struct fixed31_32 dc_fixpt_shl(struct fixed31_32 arg, unsigned char shift)
217 {
218 ASSERT(((arg.value >= 0) && (arg.value <= LLONG_MAX >> shift)) ||
219 ((arg.value < 0) && (arg.value >= ~(LLONG_MAX >> shift))));
220
221 arg.value = arg.value << shift;
222
223 return arg;
224 }
225
226 /*
227 * @brief
228 * result = arg >> shift
229 */
dc_fixpt_shr(struct fixed31_32 arg,unsigned char shift)230 static inline struct fixed31_32 dc_fixpt_shr(struct fixed31_32 arg, unsigned char shift)
231 {
232 bool negative = arg.value < 0;
233
234 if (negative)
235 arg.value = -arg.value;
236 arg.value = arg.value >> shift;
237 if (negative)
238 arg.value = -arg.value;
239 return arg;
240 }
241
242 /*
243 * @brief
244 * Binary additive operators
245 */
246
247 /*
248 * @brief
249 * result = arg1 + arg2
250 */
dc_fixpt_add(struct fixed31_32 arg1,struct fixed31_32 arg2)251 static inline struct fixed31_32 dc_fixpt_add(struct fixed31_32 arg1, struct fixed31_32 arg2)
252 {
253 struct fixed31_32 res;
254
255 ASSERT(((arg1.value >= 0) && (LLONG_MAX - arg1.value >= arg2.value)) ||
256 ((arg1.value < 0) && (LLONG_MIN - arg1.value <= arg2.value)));
257
258 res.value = arg1.value + arg2.value;
259
260 return res;
261 }
262
263 /*
264 * @brief
265 * result = arg1 + arg2
266 */
dc_fixpt_add_int(struct fixed31_32 arg1,int arg2)267 static inline struct fixed31_32 dc_fixpt_add_int(struct fixed31_32 arg1, int arg2)
268 {
269 return dc_fixpt_add(arg1, dc_fixpt_from_int(arg2));
270 }
271
272 /*
273 * @brief
274 * result = arg1 - arg2
275 */
dc_fixpt_sub(struct fixed31_32 arg1,struct fixed31_32 arg2)276 static inline struct fixed31_32 dc_fixpt_sub(struct fixed31_32 arg1, struct fixed31_32 arg2)
277 {
278 struct fixed31_32 res;
279
280 ASSERT(((arg2.value >= 0) && (LLONG_MIN + arg2.value <= arg1.value)) ||
281 ((arg2.value < 0) && (LLONG_MAX + arg2.value >= arg1.value)));
282
283 res.value = arg1.value - arg2.value;
284
285 return res;
286 }
287
288 /*
289 * @brief
290 * result = arg1 - arg2
291 */
dc_fixpt_sub_int(struct fixed31_32 arg1,int arg2)292 static inline struct fixed31_32 dc_fixpt_sub_int(struct fixed31_32 arg1, int arg2)
293 {
294 return dc_fixpt_sub(arg1, dc_fixpt_from_int(arg2));
295 }
296
297
298 /*
299 * @brief
300 * Binary multiplicative operators
301 */
302
303 /*
304 * @brief
305 * result = arg1 * arg2
306 */
307 struct fixed31_32 dc_fixpt_mul(struct fixed31_32 arg1, struct fixed31_32 arg2);
308
309
310 /*
311 * @brief
312 * result = arg1 * arg2
313 */
dc_fixpt_mul_int(struct fixed31_32 arg1,int arg2)314 static inline struct fixed31_32 dc_fixpt_mul_int(struct fixed31_32 arg1, int arg2)
315 {
316 return dc_fixpt_mul(arg1, dc_fixpt_from_int(arg2));
317 }
318
319 /*
320 * @brief
321 * result = square(arg) := arg * arg
322 */
323 struct fixed31_32 dc_fixpt_sqr(struct fixed31_32 arg);
324
325 /*
326 * @brief
327 * result = arg1 / arg2
328 */
dc_fixpt_div_int(struct fixed31_32 arg1,long long arg2)329 static inline struct fixed31_32 dc_fixpt_div_int(struct fixed31_32 arg1, long long arg2)
330 {
331 return dc_fixpt_from_fraction(arg1.value, dc_fixpt_from_int(arg2).value);
332 }
333
334 /*
335 * @brief
336 * result = arg1 / arg2
337 */
dc_fixpt_div(struct fixed31_32 arg1,struct fixed31_32 arg2)338 static inline struct fixed31_32 dc_fixpt_div(struct fixed31_32 arg1, struct fixed31_32 arg2)
339 {
340 return dc_fixpt_from_fraction(arg1.value, arg2.value);
341 }
342
343 /*
344 * @brief
345 * Reciprocal function
346 */
347
348 /*
349 * @brief
350 * result = reciprocal(arg) := 1 / arg
351 *
352 * @note
353 * No special actions taken in case argument is zero.
354 */
355 struct fixed31_32 dc_fixpt_recip(struct fixed31_32 arg);
356
357 /*
358 * @brief
359 * Trigonometric functions
360 */
361
362 /*
363 * @brief
364 * result = sinc(arg) := sin(arg) / arg
365 *
366 * @note
367 * Argument specified in radians,
368 * internally it's normalized to [-2pi...2pi] range.
369 */
370 struct fixed31_32 dc_fixpt_sinc(struct fixed31_32 arg);
371
372 /*
373 * @brief
374 * result = sin(arg)
375 *
376 * @note
377 * Argument specified in radians,
378 * internally it's normalized to [-2pi...2pi] range.
379 */
380 struct fixed31_32 dc_fixpt_sin(struct fixed31_32 arg);
381
382 /*
383 * @brief
384 * result = cos(arg)
385 *
386 * @note
387 * Argument specified in radians
388 * and should be in [-2pi...2pi] range -
389 * passing arguments outside that range
390 * will cause incorrect result!
391 */
392 struct fixed31_32 dc_fixpt_cos(struct fixed31_32 arg);
393
394 /*
395 * @brief
396 * Transcendent functions
397 */
398
399 /*
400 * @brief
401 * result = exp(arg)
402 *
403 * @note
404 * Currently, function is verified for abs(arg) <= 1.
405 */
406 struct fixed31_32 dc_fixpt_exp(struct fixed31_32 arg);
407
408 /*
409 * @brief
410 * result = log(arg)
411 *
412 * @note
413 * Currently, abs(arg) should be less than 1.
414 * No normalization is done.
415 * Currently, no special actions taken
416 * in case of invalid argument(s). Take care!
417 */
418 struct fixed31_32 dc_fixpt_log(struct fixed31_32 arg);
419
420 /*
421 * @brief
422 * Power function
423 */
424
425 /*
426 * @brief
427 * result = pow(arg1, arg2)
428 *
429 * @note
430 * Currently, abs(arg1) should be less than 1. Take care!
431 */
dc_fixpt_pow(struct fixed31_32 arg1,struct fixed31_32 arg2)432 static inline struct fixed31_32 dc_fixpt_pow(struct fixed31_32 arg1, struct fixed31_32 arg2)
433 {
434 return dc_fixpt_exp(
435 dc_fixpt_mul(
436 dc_fixpt_log(arg1),
437 arg2));
438 }
439
440 /*
441 * @brief
442 * Rounding functions
443 */
444
445 /*
446 * @brief
447 * result = floor(arg) := greatest integer lower than or equal to arg
448 */
dc_fixpt_floor(struct fixed31_32 arg)449 static inline int dc_fixpt_floor(struct fixed31_32 arg)
450 {
451 unsigned long long arg_value = arg.value > 0 ? arg.value : -arg.value;
452
453 if (arg.value >= 0)
454 return (int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
455 else
456 return -(int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
457 }
458
459 /*
460 * @brief
461 * result = round(arg) := integer nearest to arg
462 */
dc_fixpt_round(struct fixed31_32 arg)463 static inline int dc_fixpt_round(struct fixed31_32 arg)
464 {
465 unsigned long long arg_value = arg.value > 0 ? arg.value : -arg.value;
466
467 const long long summand = dc_fixpt_half.value;
468
469 ASSERT(LLONG_MAX - (long long)arg_value >= summand);
470
471 arg_value += summand;
472
473 if (arg.value >= 0)
474 return (int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
475 else
476 return -(int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
477 }
478
479 /*
480 * @brief
481 * result = ceil(arg) := lowest integer greater than or equal to arg
482 */
dc_fixpt_ceil(struct fixed31_32 arg)483 static inline int dc_fixpt_ceil(struct fixed31_32 arg)
484 {
485 unsigned long long arg_value = arg.value > 0 ? arg.value : -arg.value;
486
487 const long long summand = dc_fixpt_one.value -
488 dc_fixpt_epsilon.value;
489
490 ASSERT(LLONG_MAX - (long long)arg_value >= summand);
491
492 arg_value += summand;
493
494 if (arg.value >= 0)
495 return (int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
496 else
497 return -(int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
498 }
499
500 /* the following two function are used in scaler hw programming to convert fixed
501 * point value to format 2 bits from integer part and 19 bits from fractional
502 * part. The same applies for u0d19, 0 bits from integer part and 19 bits from
503 * fractional
504 */
505
506 unsigned int dc_fixpt_u3d19(struct fixed31_32 arg);
507
508 unsigned int dc_fixpt_u2d19(struct fixed31_32 arg);
509
510 unsigned int dc_fixpt_u0d19(struct fixed31_32 arg);
511
512 unsigned int dc_fixpt_clamp_u0d14(struct fixed31_32 arg);
513
514 unsigned int dc_fixpt_clamp_u0d10(struct fixed31_32 arg);
515
516 int dc_fixpt_s4d19(struct fixed31_32 arg);
517
dc_fixpt_truncate(struct fixed31_32 arg,unsigned int frac_bits)518 static inline struct fixed31_32 dc_fixpt_truncate(struct fixed31_32 arg, unsigned int frac_bits)
519 {
520 bool negative = arg.value < 0;
521
522 if (frac_bits >= FIXED31_32_BITS_PER_FRACTIONAL_PART) {
523 ASSERT(frac_bits == FIXED31_32_BITS_PER_FRACTIONAL_PART);
524 return arg;
525 }
526
527 if (negative)
528 arg.value = -arg.value;
529 arg.value &= (~0LL) << (FIXED31_32_BITS_PER_FRACTIONAL_PART - frac_bits);
530 if (negative)
531 arg.value = -arg.value;
532 return arg;
533 }
534
535 #endif
536
