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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 const struct fixed31_32 dc_fixpt_two_pi = { 26986075409LL };
30static const struct fixed31_32 dc_fixpt_ln2 = { 2977044471LL };
31static const struct fixed31_32 dc_fixpt_ln2_div_2 = { 1488522236LL };
32
33static inline unsigned long long abs_i64(
34 long long arg)
35{
36 if (arg > 0)
37 return (unsigned long long)arg;
38 else
39 return (unsigned long long)(-arg);
40}
41
42/*
43 * @brief
44 * result = dividend / divisor
45 * *remainder = dividend % divisor
46 */
47static inline unsigned long long complete_integer_division_u64(
48 unsigned long long dividend,
49 unsigned long long divisor,
50 unsigned long long *remainder)
51{
52 unsigned long long result;
53
54 ASSERT(divisor);
55
56 result = div64_u64_rem(dividend, divisor, remainder);
57
58 return result;
59}
60
61
62#define FRACTIONAL_PART_MASK \
63 ((1ULL << FIXED31_32_BITS_PER_FRACTIONAL_PART) - 1)
64
65#define GET_INTEGER_PART(x) \
66 ((x) >> FIXED31_32_BITS_PER_FRACTIONAL_PART)
67
68#define GET_FRACTIONAL_PART(x) \
69 (FRACTIONAL_PART_MASK & (x))
70
71struct fixed31_32 dc_fixpt_from_fraction(long long numerator, long long denominator)
72{
73 struct fixed31_32 res;
74
75 bool arg1_negative = numerator < 0;
76 bool arg2_negative = denominator < 0;
77
78 unsigned long long arg1_value = arg1_negative ? -numerator : numerator;
79 unsigned long long arg2_value = arg2_negative ? -denominator : denominator;
80
81 unsigned long long remainder;
82
83 /* determine integer part */
84
85 unsigned long long res_value = complete_integer_division_u64(
86 arg1_value, arg2_value, &remainder);
87
88 ASSERT(res_value <= LONG_MAX);
89
90 /* determine fractional part */
91 {
92 unsigned int i = FIXED31_32_BITS_PER_FRACTIONAL_PART;
93
94 do {
95 remainder <<= 1;
96
97 res_value <<= 1;
98
99 if (remainder >= arg2_value) {
100 res_value |= 1;
101 remainder -= arg2_value;
102 }
103 } while (--i != 0);
104 }
105
106 /* round up LSB */
107 {
108 unsigned long long summand = (remainder << 1) >= arg2_value;
109
110 ASSERT(res_value <= LLONG_MAX - summand);
111
112 res_value += summand;
113 }
114
115 res.value = (long long)res_value;
116
117 if (arg1_negative ^ arg2_negative)
118 res.value = -res.value;
119
120 return res;
121}
122
123struct fixed31_32 dc_fixpt_mul(struct fixed31_32 arg1, struct fixed31_32 arg2)
124{
125 struct fixed31_32 res;
126
127 bool arg1_negative = arg1.value < 0;
128 bool arg2_negative = arg2.value < 0;
129
130 unsigned long long arg1_value = arg1_negative ? -arg1.value : arg1.value;
131 unsigned long long arg2_value = arg2_negative ? -arg2.value : arg2.value;
132
133 unsigned long long arg1_int = GET_INTEGER_PART(arg1_value);
134 unsigned long long arg2_int = GET_INTEGER_PART(arg2_value);
135
136 unsigned long long arg1_fra = GET_FRACTIONAL_PART(arg1_value);
137 unsigned long long arg2_fra = GET_FRACTIONAL_PART(arg2_value);
138
139 unsigned long long tmp;
140
141 res.value = arg1_int * arg2_int;
142
143 ASSERT(res.value <= LONG_MAX);
144
145 res.value <<= FIXED31_32_BITS_PER_FRACTIONAL_PART;
146
147 tmp = arg1_int * arg2_fra;
148
149 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
150
151 res.value += tmp;
152
153 tmp = arg2_int * arg1_fra;
154
155 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
156
157 res.value += tmp;
158
159 tmp = arg1_fra * arg2_fra;
160
161 tmp = (tmp >> FIXED31_32_BITS_PER_FRACTIONAL_PART) +
162 (tmp >= (unsigned long long)dc_fixpt_half.value);
163
164 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
165
166 res.value += tmp;
167
168 if (arg1_negative ^ arg2_negative)
169 res.value = -res.value;
170
171 return res;
172}
173
174struct fixed31_32 dc_fixpt_sqr(struct fixed31_32 arg)
175{
176 struct fixed31_32 res;
177
178 unsigned long long arg_value = abs_i64(arg.value);
179
180 unsigned long long arg_int = GET_INTEGER_PART(arg_value);
181
182 unsigned long long arg_fra = GET_FRACTIONAL_PART(arg_value);
183
184 unsigned long long tmp;
185
186 res.value = arg_int * arg_int;
187
188 ASSERT(res.value <= LONG_MAX);
189
190 res.value <<= FIXED31_32_BITS_PER_FRACTIONAL_PART;
191
192 tmp = arg_int * arg_fra;
193
194 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
195
196 res.value += tmp;
197
198 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
199
200 res.value += tmp;
201
202 tmp = arg_fra * arg_fra;
203
204 tmp = (tmp >> FIXED31_32_BITS_PER_FRACTIONAL_PART) +
205 (tmp >= (unsigned long long)dc_fixpt_half.value);
206
207 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
208
209 res.value += tmp;
210
211 return res;
212}
213
214struct fixed31_32 dc_fixpt_recip(struct fixed31_32 arg)
215{
216 /*
217 * @note
218 * Good idea to use Newton's method
219 */
220
221 ASSERT(arg.value);
222
223 return dc_fixpt_from_fraction(
224 dc_fixpt_one.value,
225 arg.value);
226}
227
228struct fixed31_32 dc_fixpt_sinc(struct fixed31_32 arg)
229{
230 struct fixed31_32 square;
231
232 struct fixed31_32 res = dc_fixpt_one;
233
234 int n = 27;
235
236 struct fixed31_32 arg_norm = arg;
237
238 if (dc_fixpt_le(
239 dc_fixpt_two_pi,
240 dc_fixpt_abs(arg))) {
241 arg_norm = dc_fixpt_sub(
242 arg_norm,
243 dc_fixpt_mul_int(
244 dc_fixpt_two_pi,
245 (int)div64_s64(
246 arg_norm.value,
247 dc_fixpt_two_pi.value)));
248 }
249
250 square = dc_fixpt_sqr(arg_norm);
251
252 do {
253 res = dc_fixpt_sub(
254 dc_fixpt_one,
255 dc_fixpt_div_int(
256 dc_fixpt_mul(
257 square,
258 res),
259 n * (n - 1)));
260
261 n -= 2;
262 } while (n > 2);
263
264 if (arg.value != arg_norm.value)
265 res = dc_fixpt_div(
266 dc_fixpt_mul(res, arg_norm),
267 arg);
268
269 return res;
270}
271
272struct fixed31_32 dc_fixpt_sin(struct fixed31_32 arg)
273{
274 return dc_fixpt_mul(
275 arg,
276 dc_fixpt_sinc(arg));
277}
278
279struct fixed31_32 dc_fixpt_cos(struct fixed31_32 arg)
280{
281 /* TODO implement argument normalization */
282
283 const struct fixed31_32 square = dc_fixpt_sqr(arg);
284
285 struct fixed31_32 res = dc_fixpt_one;
286
287 int n = 26;
288
289 do {
290 res = dc_fixpt_sub(
291 dc_fixpt_one,
292 dc_fixpt_div_int(
293 dc_fixpt_mul(
294 square,
295 res),
296 n * (n - 1)));
297
298 n -= 2;
299 } while (n != 0);
300
301 return res;
302}
303
304/*
305 * @brief
306 * result = exp(arg),
307 * where abs(arg) < 1
308 *
309 * Calculated as Taylor series.
310 */
311static struct fixed31_32 fixed31_32_exp_from_taylor_series(struct fixed31_32 arg)
312{
313 unsigned int n = 9;
314
315 struct fixed31_32 res = dc_fixpt_from_fraction(
316 n + 2,
317 n + 1);
318 /* TODO find correct res */
319
320 ASSERT(dc_fixpt_lt(arg, dc_fixpt_one));
321
322 do
323 res = dc_fixpt_add(
324 dc_fixpt_one,
325 dc_fixpt_div_int(
326 dc_fixpt_mul(
327 arg,
328 res),
329 n));
330 while (--n != 1);
331
332 return dc_fixpt_add(
333 dc_fixpt_one,
334 dc_fixpt_mul(
335 arg,
336 res));
337}
338
339struct fixed31_32 dc_fixpt_exp(struct fixed31_32 arg)
340{
341 /*
342 * @brief
343 * Main equation is:
344 * exp(x) = exp(r + m * ln(2)) = (1 << m) * exp(r),
345 * where m = round(x / ln(2)), r = x - m * ln(2)
346 */
347
348 if (dc_fixpt_le(
349 dc_fixpt_ln2_div_2,
350 dc_fixpt_abs(arg))) {
351 int m = dc_fixpt_round(
352 dc_fixpt_div(
353 arg,
354 dc_fixpt_ln2));
355
356 struct fixed31_32 r = dc_fixpt_sub(
357 arg,
358 dc_fixpt_mul_int(
359 dc_fixpt_ln2,
360 m));
361
362 ASSERT(m != 0);
363
364 ASSERT(dc_fixpt_lt(
365 dc_fixpt_abs(r),
366 dc_fixpt_one));
367
368 if (m > 0)
369 return dc_fixpt_shl(
370 fixed31_32_exp_from_taylor_series(r),
371 (unsigned char)m);
372 else
373 return dc_fixpt_div_int(
374 fixed31_32_exp_from_taylor_series(r),
375 1LL << -m);
376 } else if (arg.value != 0)
377 return fixed31_32_exp_from_taylor_series(arg);
378 else
379 return dc_fixpt_one;
380}
381
382struct fixed31_32 dc_fixpt_log(struct fixed31_32 arg)
383{
384 struct fixed31_32 res = dc_fixpt_neg(dc_fixpt_one);
385 /* TODO improve 1st estimation */
386
387 struct fixed31_32 error;
388
389 ASSERT(arg.value > 0);
390 /* TODO if arg is negative, return NaN */
391 /* TODO if arg is zero, return -INF */
392
393 do {
394 struct fixed31_32 res1 = dc_fixpt_add(
395 dc_fixpt_sub(
396 res,
397 dc_fixpt_one),
398 dc_fixpt_div(
399 arg,
400 dc_fixpt_exp(res)));
401
402 error = dc_fixpt_sub(
403 res,
404 res1);
405
406 res = res1;
407 /* TODO determine max_allowed_error based on quality of exp() */
408 } while (abs_i64(error.value) > 100ULL);
409
410 return res;
411}
412
413
414/* this function is a generic helper to translate fixed point value to
415 * specified integer format that will consist of integer_bits integer part and
416 * fractional_bits fractional part. For example it is used in
417 * dc_fixpt_u2d19 to receive 2 bits integer part and 19 bits fractional
418 * part in 32 bits. It is used in hw programming (scaler)
419 */
420
421static inline unsigned int ux_dy(
422 long long value,
423 unsigned int integer_bits,
424 unsigned int fractional_bits)
425{
426 /* 1. create mask of integer part */
427 unsigned int result = (1 << integer_bits) - 1;
428 /* 2. mask out fractional part */
429 unsigned int fractional_part = FRACTIONAL_PART_MASK & value;
430 /* 3. shrink fixed point integer part to be of integer_bits width*/
431 result &= GET_INTEGER_PART(value);
432 /* 4. make space for fractional part to be filled in after integer */
433 result <<= fractional_bits;
434 /* 5. shrink fixed point fractional part to of fractional_bits width*/
435 fractional_part >>= FIXED31_32_BITS_PER_FRACTIONAL_PART - fractional_bits;
436 /* 6. merge the result */
437 return result | fractional_part;
438}
439
440static inline unsigned int clamp_ux_dy(
441 long long value,
442 unsigned int integer_bits,
443 unsigned int fractional_bits,
444 unsigned int min_clamp)
445{
446 unsigned int truncated_val = ux_dy(value, integer_bits, fractional_bits);
447
448 if (value >= (1LL << (integer_bits + FIXED31_32_BITS_PER_FRACTIONAL_PART)))
449 return (1 << (integer_bits + fractional_bits)) - 1;
450 else if (truncated_val > min_clamp)
451 return truncated_val;
452 else
453 return min_clamp;
454}
455
456unsigned int dc_fixpt_u4d19(struct fixed31_32 arg)
457{
458 return ux_dy(arg.value, 4, 19);
459}
460
461unsigned int dc_fixpt_u3d19(struct fixed31_32 arg)
462{
463 return ux_dy(arg.value, 3, 19);
464}
465
466unsigned int dc_fixpt_u2d19(struct fixed31_32 arg)
467{
468 return ux_dy(arg.value, 2, 19);
469}
470
471unsigned int dc_fixpt_u0d19(struct fixed31_32 arg)
472{
473 return ux_dy(arg.value, 0, 19);
474}
475
476unsigned int dc_fixpt_clamp_u0d14(struct fixed31_32 arg)
477{
478 return clamp_ux_dy(arg.value, 0, 14, 1);
479}
480
481unsigned int dc_fixpt_clamp_u0d10(struct fixed31_32 arg)
482{
483 return clamp_ux_dy(arg.value, 0, 10, 1);
484}
485
486int dc_fixpt_s4d19(struct fixed31_32 arg)
487{
488 if (arg.value < 0)
489 return -(int)ux_dy(dc_fixpt_abs(arg).value, 4, 19);
490 else
491 return ux_dy(arg.value, 4, 19);
492}
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}