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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#include "dm_services.h"
27#include "include/fixed31_32.h"
28
29static inline unsigned long long abs_i64(
30 long long arg)
31{
32 if (arg > 0)
33 return (unsigned long long)arg;
34 else
35 return (unsigned long long)(-arg);
36}
37
38/*
39 * @brief
40 * result = dividend / divisor
41 * *remainder = dividend % divisor
42 */
43static inline unsigned long long complete_integer_division_u64(
44 unsigned long long dividend,
45 unsigned long long divisor,
46 unsigned long long *remainder)
47{
48 unsigned long long result;
49
50 ASSERT(divisor);
51
52 result = div64_u64_rem(dividend, divisor, remainder);
53
54 return result;
55}
56
57
58#define FRACTIONAL_PART_MASK \
59 ((1ULL << FIXED31_32_BITS_PER_FRACTIONAL_PART) - 1)
60
61#define GET_INTEGER_PART(x) \
62 ((x) >> FIXED31_32_BITS_PER_FRACTIONAL_PART)
63
64#define GET_FRACTIONAL_PART(x) \
65 (FRACTIONAL_PART_MASK & (x))
66
67struct fixed31_32 dc_fixpt_from_fraction(long long numerator, long long denominator)
68{
69 struct fixed31_32 res;
70
71 bool arg1_negative = numerator < 0;
72 bool arg2_negative = denominator < 0;
73
74 unsigned long long arg1_value = arg1_negative ? -numerator : numerator;
75 unsigned long long arg2_value = arg2_negative ? -denominator : denominator;
76
77 unsigned long long remainder;
78
79 /* determine integer part */
80
81 unsigned long long res_value = complete_integer_division_u64(
82 arg1_value, arg2_value, &remainder);
83
84 ASSERT(res_value <= LONG_MAX);
85
86 /* determine fractional part */
87 {
88 unsigned int i = FIXED31_32_BITS_PER_FRACTIONAL_PART;
89
90 do {
91 remainder <<= 1;
92
93 res_value <<= 1;
94
95 if (remainder >= arg2_value) {
96 res_value |= 1;
97 remainder -= arg2_value;
98 }
99 } while (--i != 0);
100 }
101
102 /* round up LSB */
103 {
104 unsigned long long summand = (remainder << 1) >= arg2_value;
105
106 ASSERT(res_value <= LLONG_MAX - summand);
107
108 res_value += summand;
109 }
110
111 res.value = (long long)res_value;
112
113 if (arg1_negative ^ arg2_negative)
114 res.value = -res.value;
115
116 return res;
117}
118
119struct fixed31_32 dc_fixpt_mul(struct fixed31_32 arg1, struct fixed31_32 arg2)
120{
121 struct fixed31_32 res;
122
123 bool arg1_negative = arg1.value < 0;
124 bool arg2_negative = arg2.value < 0;
125
126 unsigned long long arg1_value = arg1_negative ? -arg1.value : arg1.value;
127 unsigned long long arg2_value = arg2_negative ? -arg2.value : arg2.value;
128
129 unsigned long long arg1_int = GET_INTEGER_PART(arg1_value);
130 unsigned long long arg2_int = GET_INTEGER_PART(arg2_value);
131
132 unsigned long long arg1_fra = GET_FRACTIONAL_PART(arg1_value);
133 unsigned long long arg2_fra = GET_FRACTIONAL_PART(arg2_value);
134
135 unsigned long long tmp;
136
137 res.value = arg1_int * arg2_int;
138
139 ASSERT(res.value <= LONG_MAX);
140
141 res.value <<= FIXED31_32_BITS_PER_FRACTIONAL_PART;
142
143 tmp = arg1_int * arg2_fra;
144
145 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
146
147 res.value += tmp;
148
149 tmp = arg2_int * arg1_fra;
150
151 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
152
153 res.value += tmp;
154
155 tmp = arg1_fra * arg2_fra;
156
157 tmp = (tmp >> FIXED31_32_BITS_PER_FRACTIONAL_PART) +
158 (tmp >= (unsigned long long)dc_fixpt_half.value);
159
160 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
161
162 res.value += tmp;
163
164 if (arg1_negative ^ arg2_negative)
165 res.value = -res.value;
166
167 return res;
168}
169
170struct fixed31_32 dc_fixpt_sqr(struct fixed31_32 arg)
171{
172 struct fixed31_32 res;
173
174 unsigned long long arg_value = abs_i64(arg.value);
175
176 unsigned long long arg_int = GET_INTEGER_PART(arg_value);
177
178 unsigned long long arg_fra = GET_FRACTIONAL_PART(arg_value);
179
180 unsigned long long tmp;
181
182 res.value = arg_int * arg_int;
183
184 ASSERT(res.value <= LONG_MAX);
185
186 res.value <<= FIXED31_32_BITS_PER_FRACTIONAL_PART;
187
188 tmp = arg_int * arg_fra;
189
190 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
191
192 res.value += tmp;
193
194 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
195
196 res.value += tmp;
197
198 tmp = arg_fra * arg_fra;
199
200 tmp = (tmp >> FIXED31_32_BITS_PER_FRACTIONAL_PART) +
201 (tmp >= (unsigned long long)dc_fixpt_half.value);
202
203 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
204
205 res.value += tmp;
206
207 return res;
208}
209
210struct fixed31_32 dc_fixpt_recip(struct fixed31_32 arg)
211{
212 /*
213 * @note
214 * Good idea to use Newton's method
215 */
216
217 ASSERT(arg.value);
218
219 return dc_fixpt_from_fraction(
220 dc_fixpt_one.value,
221 arg.value);
222}
223
224struct fixed31_32 dc_fixpt_sinc(struct fixed31_32 arg)
225{
226 struct fixed31_32 square;
227
228 struct fixed31_32 res = dc_fixpt_one;
229
230 int n = 27;
231
232 struct fixed31_32 arg_norm = arg;
233
234 if (dc_fixpt_le(
235 dc_fixpt_two_pi,
236 dc_fixpt_abs(arg))) {
237 arg_norm = dc_fixpt_sub(
238 arg_norm,
239 dc_fixpt_mul_int(
240 dc_fixpt_two_pi,
241 (int)div64_s64(
242 arg_norm.value,
243 dc_fixpt_two_pi.value)));
244 }
245
246 square = dc_fixpt_sqr(arg_norm);
247
248 do {
249 res = dc_fixpt_sub(
250 dc_fixpt_one,
251 dc_fixpt_div_int(
252 dc_fixpt_mul(
253 square,
254 res),
255 n * (n - 1)));
256
257 n -= 2;
258 } while (n > 2);
259
260 if (arg.value != arg_norm.value)
261 res = dc_fixpt_div(
262 dc_fixpt_mul(res, arg_norm),
263 arg);
264
265 return res;
266}
267
268struct fixed31_32 dc_fixpt_sin(struct fixed31_32 arg)
269{
270 return dc_fixpt_mul(
271 arg,
272 dc_fixpt_sinc(arg));
273}
274
275struct fixed31_32 dc_fixpt_cos(struct fixed31_32 arg)
276{
277 /* TODO implement argument normalization */
278
279 const struct fixed31_32 square = dc_fixpt_sqr(arg);
280
281 struct fixed31_32 res = dc_fixpt_one;
282
283 int n = 26;
284
285 do {
286 res = dc_fixpt_sub(
287 dc_fixpt_one,
288 dc_fixpt_div_int(
289 dc_fixpt_mul(
290 square,
291 res),
292 n * (n - 1)));
293
294 n -= 2;
295 } while (n != 0);
296
297 return res;
298}
299
300/*
301 * @brief
302 * result = exp(arg),
303 * where abs(arg) < 1
304 *
305 * Calculated as Taylor series.
306 */
307static struct fixed31_32 fixed31_32_exp_from_taylor_series(struct fixed31_32 arg)
308{
309 unsigned int n = 9;
310
311 struct fixed31_32 res = dc_fixpt_from_fraction(
312 n + 2,
313 n + 1);
314 /* TODO find correct res */
315
316 ASSERT(dc_fixpt_lt(arg, dc_fixpt_one));
317
318 do
319 res = dc_fixpt_add(
320 dc_fixpt_one,
321 dc_fixpt_div_int(
322 dc_fixpt_mul(
323 arg,
324 res),
325 n));
326 while (--n != 1);
327
328 return dc_fixpt_add(
329 dc_fixpt_one,
330 dc_fixpt_mul(
331 arg,
332 res));
333}
334
335struct fixed31_32 dc_fixpt_exp(struct fixed31_32 arg)
336{
337 /*
338 * @brief
339 * Main equation is:
340 * exp(x) = exp(r + m * ln(2)) = (1 << m) * exp(r),
341 * where m = round(x / ln(2)), r = x - m * ln(2)
342 */
343
344 if (dc_fixpt_le(
345 dc_fixpt_ln2_div_2,
346 dc_fixpt_abs(arg))) {
347 int m = dc_fixpt_round(
348 dc_fixpt_div(
349 arg,
350 dc_fixpt_ln2));
351
352 struct fixed31_32 r = dc_fixpt_sub(
353 arg,
354 dc_fixpt_mul_int(
355 dc_fixpt_ln2,
356 m));
357
358 ASSERT(m != 0);
359
360 ASSERT(dc_fixpt_lt(
361 dc_fixpt_abs(r),
362 dc_fixpt_one));
363
364 if (m > 0)
365 return dc_fixpt_shl(
366 fixed31_32_exp_from_taylor_series(r),
367 (unsigned char)m);
368 else
369 return dc_fixpt_div_int(
370 fixed31_32_exp_from_taylor_series(r),
371 1LL << -m);
372 } else if (arg.value != 0)
373 return fixed31_32_exp_from_taylor_series(arg);
374 else
375 return dc_fixpt_one;
376}
377
378struct fixed31_32 dc_fixpt_log(struct fixed31_32 arg)
379{
380 struct fixed31_32 res = dc_fixpt_neg(dc_fixpt_one);
381 /* TODO improve 1st estimation */
382
383 struct fixed31_32 error;
384
385 ASSERT(arg.value > 0);
386 /* TODO if arg is negative, return NaN */
387 /* TODO if arg is zero, return -INF */
388
389 do {
390 struct fixed31_32 res1 = dc_fixpt_add(
391 dc_fixpt_sub(
392 res,
393 dc_fixpt_one),
394 dc_fixpt_div(
395 arg,
396 dc_fixpt_exp(res)));
397
398 error = dc_fixpt_sub(
399 res,
400 res1);
401
402 res = res1;
403 /* TODO determine max_allowed_error based on quality of exp() */
404 } while (abs_i64(error.value) > 100ULL);
405
406 return res;
407}
408
409
410/* this function is a generic helper to translate fixed point value to
411 * specified integer format that will consist of integer_bits integer part and
412 * fractional_bits fractional part. For example it is used in
413 * dc_fixpt_u2d19 to receive 2 bits integer part and 19 bits fractional
414 * part in 32 bits. It is used in hw programming (scaler)
415 */
416
417static inline unsigned int ux_dy(
418 long long value,
419 unsigned int integer_bits,
420 unsigned int fractional_bits)
421{
422 /* 1. create mask of integer part */
423 unsigned int result = (1 << integer_bits) - 1;
424 /* 2. mask out fractional part */
425 unsigned int fractional_part = FRACTIONAL_PART_MASK & value;
426 /* 3. shrink fixed point integer part to be of integer_bits width*/
427 result &= GET_INTEGER_PART(value);
428 /* 4. make space for fractional part to be filled in after integer */
429 result <<= fractional_bits;
430 /* 5. shrink fixed point fractional part to of fractional_bits width*/
431 fractional_part >>= FIXED31_32_BITS_PER_FRACTIONAL_PART - fractional_bits;
432 /* 6. merge the result */
433 return result | fractional_part;
434}
435
436static inline unsigned int clamp_ux_dy(
437 long long value,
438 unsigned int integer_bits,
439 unsigned int fractional_bits,
440 unsigned int min_clamp)
441{
442 unsigned int truncated_val = ux_dy(value, integer_bits, fractional_bits);
443
444 if (value >= (1LL << (integer_bits + FIXED31_32_BITS_PER_FRACTIONAL_PART)))
445 return (1 << (integer_bits + fractional_bits)) - 1;
446 else if (truncated_val > min_clamp)
447 return truncated_val;
448 else
449 return min_clamp;
450}
451
452unsigned int dc_fixpt_u4d19(struct fixed31_32 arg)
453{
454 return ux_dy(arg.value, 4, 19);
455}
456
457unsigned int dc_fixpt_u3d19(struct fixed31_32 arg)
458{
459 return ux_dy(arg.value, 3, 19);
460}
461
462unsigned int dc_fixpt_u2d19(struct fixed31_32 arg)
463{
464 return ux_dy(arg.value, 2, 19);
465}
466
467unsigned int dc_fixpt_u0d19(struct fixed31_32 arg)
468{
469 return ux_dy(arg.value, 0, 19);
470}
471
472unsigned int dc_fixpt_clamp_u0d14(struct fixed31_32 arg)
473{
474 return clamp_ux_dy(arg.value, 0, 14, 1);
475}
476
477unsigned int dc_fixpt_clamp_u0d10(struct fixed31_32 arg)
478{
479 return clamp_ux_dy(arg.value, 0, 10, 1);
480}
481
482int dc_fixpt_s4d19(struct fixed31_32 arg)
483{
484 if (arg.value < 0)
485 return -(int)ux_dy(dc_fixpt_abs(arg).value, 4, 19);
486 else
487 return ux_dy(arg.value, 4, 19);
488}
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#include "dm_services.h"
27#include "include/fixed31_32.h"
28
29static inline uint64_t abs_i64(
30 int64_t arg)
31{
32 if (arg > 0)
33 return (uint64_t)arg;
34 else
35 return (uint64_t)(-arg);
36}
37
38/*
39 * @brief
40 * result = dividend / divisor
41 * *remainder = dividend % divisor
42 */
43static inline uint64_t complete_integer_division_u64(
44 uint64_t dividend,
45 uint64_t divisor,
46 uint64_t *remainder)
47{
48 uint64_t result;
49
50 ASSERT(divisor);
51
52 result = div64_u64_rem(dividend, divisor, remainder);
53
54 return result;
55}
56
57
58#define FRACTIONAL_PART_MASK \
59 ((1ULL << FIXED31_32_BITS_PER_FRACTIONAL_PART) - 1)
60
61#define GET_INTEGER_PART(x) \
62 ((x) >> FIXED31_32_BITS_PER_FRACTIONAL_PART)
63
64#define GET_FRACTIONAL_PART(x) \
65 (FRACTIONAL_PART_MASK & (x))
66
67struct fixed31_32 dal_fixed31_32_from_fraction(
68 int64_t numerator,
69 int64_t denominator)
70{
71 struct fixed31_32 res;
72
73 bool arg1_negative = numerator < 0;
74 bool arg2_negative = denominator < 0;
75
76 uint64_t arg1_value = arg1_negative ? -numerator : numerator;
77 uint64_t arg2_value = arg2_negative ? -denominator : denominator;
78
79 uint64_t remainder;
80
81 /* determine integer part */
82
83 uint64_t res_value = complete_integer_division_u64(
84 arg1_value, arg2_value, &remainder);
85
86 ASSERT(res_value <= LONG_MAX);
87
88 /* determine fractional part */
89 {
90 uint32_t i = FIXED31_32_BITS_PER_FRACTIONAL_PART;
91
92 do {
93 remainder <<= 1;
94
95 res_value <<= 1;
96
97 if (remainder >= arg2_value) {
98 res_value |= 1;
99 remainder -= arg2_value;
100 }
101 } while (--i != 0);
102 }
103
104 /* round up LSB */
105 {
106 uint64_t summand = (remainder << 1) >= arg2_value;
107
108 ASSERT(res_value <= LLONG_MAX - summand);
109
110 res_value += summand;
111 }
112
113 res.value = (int64_t)res_value;
114
115 if (arg1_negative ^ arg2_negative)
116 res.value = -res.value;
117
118 return res;
119}
120
121struct fixed31_32 dal_fixed31_32_from_int_nonconst(
122 int64_t arg)
123{
124 struct fixed31_32 res;
125
126 ASSERT((LONG_MIN <= arg) && (arg <= LONG_MAX));
127
128 res.value = arg << FIXED31_32_BITS_PER_FRACTIONAL_PART;
129
130 return res;
131}
132
133struct fixed31_32 dal_fixed31_32_shl(
134 struct fixed31_32 arg,
135 uint8_t shift)
136{
137 struct fixed31_32 res;
138
139 ASSERT(((arg.value >= 0) && (arg.value <= LLONG_MAX >> shift)) ||
140 ((arg.value < 0) && (arg.value >= LLONG_MIN >> shift)));
141
142 res.value = arg.value << shift;
143
144 return res;
145}
146
147struct fixed31_32 dal_fixed31_32_add(
148 struct fixed31_32 arg1,
149 struct fixed31_32 arg2)
150{
151 struct fixed31_32 res;
152
153 ASSERT(((arg1.value >= 0) && (LLONG_MAX - arg1.value >= arg2.value)) ||
154 ((arg1.value < 0) && (LLONG_MIN - arg1.value <= arg2.value)));
155
156 res.value = arg1.value + arg2.value;
157
158 return res;
159}
160
161struct fixed31_32 dal_fixed31_32_sub(
162 struct fixed31_32 arg1,
163 struct fixed31_32 arg2)
164{
165 struct fixed31_32 res;
166
167 ASSERT(((arg2.value >= 0) && (LLONG_MIN + arg2.value <= arg1.value)) ||
168 ((arg2.value < 0) && (LLONG_MAX + arg2.value >= arg1.value)));
169
170 res.value = arg1.value - arg2.value;
171
172 return res;
173}
174
175struct fixed31_32 dal_fixed31_32_mul(
176 struct fixed31_32 arg1,
177 struct fixed31_32 arg2)
178{
179 struct fixed31_32 res;
180
181 bool arg1_negative = arg1.value < 0;
182 bool arg2_negative = arg2.value < 0;
183
184 uint64_t arg1_value = arg1_negative ? -arg1.value : arg1.value;
185 uint64_t arg2_value = arg2_negative ? -arg2.value : arg2.value;
186
187 uint64_t arg1_int = GET_INTEGER_PART(arg1_value);
188 uint64_t arg2_int = GET_INTEGER_PART(arg2_value);
189
190 uint64_t arg1_fra = GET_FRACTIONAL_PART(arg1_value);
191 uint64_t arg2_fra = GET_FRACTIONAL_PART(arg2_value);
192
193 uint64_t tmp;
194
195 res.value = arg1_int * arg2_int;
196
197 ASSERT(res.value <= LONG_MAX);
198
199 res.value <<= FIXED31_32_BITS_PER_FRACTIONAL_PART;
200
201 tmp = arg1_int * arg2_fra;
202
203 ASSERT(tmp <= (uint64_t)(LLONG_MAX - res.value));
204
205 res.value += tmp;
206
207 tmp = arg2_int * arg1_fra;
208
209 ASSERT(tmp <= (uint64_t)(LLONG_MAX - res.value));
210
211 res.value += tmp;
212
213 tmp = arg1_fra * arg2_fra;
214
215 tmp = (tmp >> FIXED31_32_BITS_PER_FRACTIONAL_PART) +
216 (tmp >= (uint64_t)dal_fixed31_32_half.value);
217
218 ASSERT(tmp <= (uint64_t)(LLONG_MAX - res.value));
219
220 res.value += tmp;
221
222 if (arg1_negative ^ arg2_negative)
223 res.value = -res.value;
224
225 return res;
226}
227
228struct fixed31_32 dal_fixed31_32_sqr(
229 struct fixed31_32 arg)
230{
231 struct fixed31_32 res;
232
233 uint64_t arg_value = abs_i64(arg.value);
234
235 uint64_t arg_int = GET_INTEGER_PART(arg_value);
236
237 uint64_t arg_fra = GET_FRACTIONAL_PART(arg_value);
238
239 uint64_t tmp;
240
241 res.value = arg_int * arg_int;
242
243 ASSERT(res.value <= LONG_MAX);
244
245 res.value <<= FIXED31_32_BITS_PER_FRACTIONAL_PART;
246
247 tmp = arg_int * arg_fra;
248
249 ASSERT(tmp <= (uint64_t)(LLONG_MAX - res.value));
250
251 res.value += tmp;
252
253 ASSERT(tmp <= (uint64_t)(LLONG_MAX - res.value));
254
255 res.value += tmp;
256
257 tmp = arg_fra * arg_fra;
258
259 tmp = (tmp >> FIXED31_32_BITS_PER_FRACTIONAL_PART) +
260 (tmp >= (uint64_t)dal_fixed31_32_half.value);
261
262 ASSERT(tmp <= (uint64_t)(LLONG_MAX - res.value));
263
264 res.value += tmp;
265
266 return res;
267}
268
269struct fixed31_32 dal_fixed31_32_recip(
270 struct fixed31_32 arg)
271{
272 /*
273 * @note
274 * Good idea to use Newton's method
275 */
276
277 ASSERT(arg.value);
278
279 return dal_fixed31_32_from_fraction(
280 dal_fixed31_32_one.value,
281 arg.value);
282}
283
284struct fixed31_32 dal_fixed31_32_sinc(
285 struct fixed31_32 arg)
286{
287 struct fixed31_32 square;
288
289 struct fixed31_32 res = dal_fixed31_32_one;
290
291 int32_t n = 27;
292
293 struct fixed31_32 arg_norm = arg;
294
295 if (dal_fixed31_32_le(
296 dal_fixed31_32_two_pi,
297 dal_fixed31_32_abs(arg))) {
298 arg_norm = dal_fixed31_32_sub(
299 arg_norm,
300 dal_fixed31_32_mul_int(
301 dal_fixed31_32_two_pi,
302 (int32_t)div64_s64(
303 arg_norm.value,
304 dal_fixed31_32_two_pi.value)));
305 }
306
307 square = dal_fixed31_32_sqr(arg_norm);
308
309 do {
310 res = dal_fixed31_32_sub(
311 dal_fixed31_32_one,
312 dal_fixed31_32_div_int(
313 dal_fixed31_32_mul(
314 square,
315 res),
316 n * (n - 1)));
317
318 n -= 2;
319 } while (n > 2);
320
321 if (arg.value != arg_norm.value)
322 res = dal_fixed31_32_div(
323 dal_fixed31_32_mul(res, arg_norm),
324 arg);
325
326 return res;
327}
328
329struct fixed31_32 dal_fixed31_32_sin(
330 struct fixed31_32 arg)
331{
332 return dal_fixed31_32_mul(
333 arg,
334 dal_fixed31_32_sinc(arg));
335}
336
337struct fixed31_32 dal_fixed31_32_cos(
338 struct fixed31_32 arg)
339{
340 /* TODO implement argument normalization */
341
342 const struct fixed31_32 square = dal_fixed31_32_sqr(arg);
343
344 struct fixed31_32 res = dal_fixed31_32_one;
345
346 int32_t n = 26;
347
348 do {
349 res = dal_fixed31_32_sub(
350 dal_fixed31_32_one,
351 dal_fixed31_32_div_int(
352 dal_fixed31_32_mul(
353 square,
354 res),
355 n * (n - 1)));
356
357 n -= 2;
358 } while (n != 0);
359
360 return res;
361}
362
363/*
364 * @brief
365 * result = exp(arg),
366 * where abs(arg) < 1
367 *
368 * Calculated as Taylor series.
369 */
370static struct fixed31_32 fixed31_32_exp_from_taylor_series(
371 struct fixed31_32 arg)
372{
373 uint32_t n = 9;
374
375 struct fixed31_32 res = dal_fixed31_32_from_fraction(
376 n + 2,
377 n + 1);
378 /* TODO find correct res */
379
380 ASSERT(dal_fixed31_32_lt(arg, dal_fixed31_32_one));
381
382 do
383 res = dal_fixed31_32_add(
384 dal_fixed31_32_one,
385 dal_fixed31_32_div_int(
386 dal_fixed31_32_mul(
387 arg,
388 res),
389 n));
390 while (--n != 1);
391
392 return dal_fixed31_32_add(
393 dal_fixed31_32_one,
394 dal_fixed31_32_mul(
395 arg,
396 res));
397}
398
399struct fixed31_32 dal_fixed31_32_exp(
400 struct fixed31_32 arg)
401{
402 /*
403 * @brief
404 * Main equation is:
405 * exp(x) = exp(r + m * ln(2)) = (1 << m) * exp(r),
406 * where m = round(x / ln(2)), r = x - m * ln(2)
407 */
408
409 if (dal_fixed31_32_le(
410 dal_fixed31_32_ln2_div_2,
411 dal_fixed31_32_abs(arg))) {
412 int32_t m = dal_fixed31_32_round(
413 dal_fixed31_32_div(
414 arg,
415 dal_fixed31_32_ln2));
416
417 struct fixed31_32 r = dal_fixed31_32_sub(
418 arg,
419 dal_fixed31_32_mul_int(
420 dal_fixed31_32_ln2,
421 m));
422
423 ASSERT(m != 0);
424
425 ASSERT(dal_fixed31_32_lt(
426 dal_fixed31_32_abs(r),
427 dal_fixed31_32_one));
428
429 if (m > 0)
430 return dal_fixed31_32_shl(
431 fixed31_32_exp_from_taylor_series(r),
432 (uint8_t)m);
433 else
434 return dal_fixed31_32_div_int(
435 fixed31_32_exp_from_taylor_series(r),
436 1LL << -m);
437 } else if (arg.value != 0)
438 return fixed31_32_exp_from_taylor_series(arg);
439 else
440 return dal_fixed31_32_one;
441}
442
443struct fixed31_32 dal_fixed31_32_log(
444 struct fixed31_32 arg)
445{
446 struct fixed31_32 res = dal_fixed31_32_neg(dal_fixed31_32_one);
447 /* TODO improve 1st estimation */
448
449 struct fixed31_32 error;
450
451 ASSERT(arg.value > 0);
452 /* TODO if arg is negative, return NaN */
453 /* TODO if arg is zero, return -INF */
454
455 do {
456 struct fixed31_32 res1 = dal_fixed31_32_add(
457 dal_fixed31_32_sub(
458 res,
459 dal_fixed31_32_one),
460 dal_fixed31_32_div(
461 arg,
462 dal_fixed31_32_exp(res)));
463
464 error = dal_fixed31_32_sub(
465 res,
466 res1);
467
468 res = res1;
469 /* TODO determine max_allowed_error based on quality of exp() */
470 } while (abs_i64(error.value) > 100ULL);
471
472 return res;
473}
474
475struct fixed31_32 dal_fixed31_32_pow(
476 struct fixed31_32 arg1,
477 struct fixed31_32 arg2)
478{
479 return dal_fixed31_32_exp(
480 dal_fixed31_32_mul(
481 dal_fixed31_32_log(arg1),
482 arg2));
483}
484
485int32_t dal_fixed31_32_floor(
486 struct fixed31_32 arg)
487{
488 uint64_t arg_value = abs_i64(arg.value);
489
490 if (arg.value >= 0)
491 return (int32_t)GET_INTEGER_PART(arg_value);
492 else
493 return -(int32_t)GET_INTEGER_PART(arg_value);
494}
495
496int32_t dal_fixed31_32_round(
497 struct fixed31_32 arg)
498{
499 uint64_t arg_value = abs_i64(arg.value);
500
501 const int64_t summand = dal_fixed31_32_half.value;
502
503 ASSERT(LLONG_MAX - (int64_t)arg_value >= summand);
504
505 arg_value += summand;
506
507 if (arg.value >= 0)
508 return (int32_t)GET_INTEGER_PART(arg_value);
509 else
510 return -(int32_t)GET_INTEGER_PART(arg_value);
511}
512
513int32_t dal_fixed31_32_ceil(
514 struct fixed31_32 arg)
515{
516 uint64_t arg_value = abs_i64(arg.value);
517
518 const int64_t summand = dal_fixed31_32_one.value -
519 dal_fixed31_32_epsilon.value;
520
521 ASSERT(LLONG_MAX - (int64_t)arg_value >= summand);
522
523 arg_value += summand;
524
525 if (arg.value >= 0)
526 return (int32_t)GET_INTEGER_PART(arg_value);
527 else
528 return -(int32_t)GET_INTEGER_PART(arg_value);
529}
530
531/* this function is a generic helper to translate fixed point value to
532 * specified integer format that will consist of integer_bits integer part and
533 * fractional_bits fractional part. For example it is used in
534 * dal_fixed31_32_u2d19 to receive 2 bits integer part and 19 bits fractional
535 * part in 32 bits. It is used in hw programming (scaler)
536 */
537
538static inline uint32_t ux_dy(
539 int64_t value,
540 uint32_t integer_bits,
541 uint32_t fractional_bits)
542{
543 /* 1. create mask of integer part */
544 uint32_t result = (1 << integer_bits) - 1;
545 /* 2. mask out fractional part */
546 uint32_t fractional_part = FRACTIONAL_PART_MASK & value;
547 /* 3. shrink fixed point integer part to be of integer_bits width*/
548 result &= GET_INTEGER_PART(value);
549 /* 4. make space for fractional part to be filled in after integer */
550 result <<= fractional_bits;
551 /* 5. shrink fixed point fractional part to of fractional_bits width*/
552 fractional_part >>= FIXED31_32_BITS_PER_FRACTIONAL_PART - fractional_bits;
553 /* 6. merge the result */
554 return result | fractional_part;
555}
556
557static inline uint32_t clamp_ux_dy(
558 int64_t value,
559 uint32_t integer_bits,
560 uint32_t fractional_bits,
561 uint32_t min_clamp)
562{
563 uint32_t truncated_val = ux_dy(value, integer_bits, fractional_bits);
564
565 if (value >= (1LL << (integer_bits + FIXED31_32_BITS_PER_FRACTIONAL_PART)))
566 return (1 << (integer_bits + fractional_bits)) - 1;
567 else if (truncated_val > min_clamp)
568 return truncated_val;
569 else
570 return min_clamp;
571}
572
573uint32_t dal_fixed31_32_u2d19(
574 struct fixed31_32 arg)
575{
576 return ux_dy(arg.value, 2, 19);
577}
578
579uint32_t dal_fixed31_32_u0d19(
580 struct fixed31_32 arg)
581{
582 return ux_dy(arg.value, 0, 19);
583}
584
585uint32_t dal_fixed31_32_clamp_u0d14(
586 struct fixed31_32 arg)
587{
588 return clamp_ux_dy(arg.value, 0, 14, 1);
589}
590
591uint32_t dal_fixed31_32_clamp_u0d10(
592 struct fixed31_32 arg)
593{
594 return clamp_ux_dy(arg.value, 0, 10, 1);
595}
596
597int32_t dal_fixed31_32_s4d19(
598 struct fixed31_32 arg)
599{
600 if (arg.value < 0)
601 return -(int32_t)ux_dy(dal_fixed31_32_abs(arg).value, 4, 19);
602 else
603 return ux_dy(arg.value, 4, 19);
604}