| 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 | /* |
| 73 | * @brief |
| 74 | * Initialization routines |
| 75 | */ |
| 76 | |
| 77 | /* |
| 78 | * @brief |
| 79 | * result = numerator / denominator |
| 80 | */ |
| 81 | struct fixed31_32 dc_fixpt_from_fraction(long long numerator, long long denominator); |
| 82 | |
| 83 | /* |
| 84 | * @brief |
| 85 | * result = arg |
| 86 | */ |
| 87 | static inline struct fixed31_32 dc_fixpt_from_int(int arg) |
| 88 | { |
| 89 | struct fixed31_32 res; |
| 90 | |
| 91 | res.value = (long long) arg << FIXED31_32_BITS_PER_FRACTIONAL_PART; |
| 92 | |
| 93 | return res; |
| 94 | } |
| 95 | |
| 96 | /* |
| 97 | * @brief |
| 98 | * Unary operators |
| 99 | */ |
| 100 | |
| 101 | /* |
| 102 | * @brief |
| 103 | * result = -arg |
| 104 | */ |
| 105 | static inline struct fixed31_32 dc_fixpt_neg(struct fixed31_32 arg) |
| 106 | { |
| 107 | struct fixed31_32 res; |
| 108 | |
| 109 | res.value = -arg.value; |
| 110 | |
| 111 | return res; |
| 112 | } |
| 113 | |
| 114 | /* |
| 115 | * @brief |
| 116 | * result = abs(arg) := (arg >= 0) ? arg : -arg |
| 117 | */ |
| 118 | static inline struct fixed31_32 dc_fixpt_abs(struct fixed31_32 arg) |
| 119 | { |
| 120 | if (arg.value < 0) |
| 121 | return dc_fixpt_neg(arg); |
| 122 | else |
| 123 | return arg; |
| 124 | } |
| 125 | |
| 126 | /* |
| 127 | * @brief |
| 128 | * Binary relational operators |
| 129 | */ |
| 130 | |
| 131 | /* |
| 132 | * @brief |
| 133 | * result = arg1 < arg2 |
| 134 | */ |
| 135 | static inline bool dc_fixpt_lt(struct fixed31_32 arg1, struct fixed31_32 arg2) |
| 136 | { |
| 137 | return arg1.value < arg2.value; |
| 138 | } |
| 139 | |
| 140 | /* |
| 141 | * @brief |
| 142 | * result = arg1 <= arg2 |
| 143 | */ |
| 144 | static inline bool dc_fixpt_le(struct fixed31_32 arg1, struct fixed31_32 arg2) |
| 145 | { |
| 146 | return arg1.value <= arg2.value; |
| 147 | } |
| 148 | |
| 149 | /* |
| 150 | * @brief |
| 151 | * result = arg1 == arg2 |
| 152 | */ |
| 153 | static inline bool dc_fixpt_eq(struct fixed31_32 arg1, struct fixed31_32 arg2) |
| 154 | { |
| 155 | return arg1.value == arg2.value; |
| 156 | } |
| 157 | |
| 158 | /* |
| 159 | * @brief |
| 160 | * result = min(arg1, arg2) := (arg1 <= arg2) ? arg1 : arg2 |
| 161 | */ |
| 162 | static inline struct fixed31_32 dc_fixpt_min(struct fixed31_32 arg1, struct fixed31_32 arg2) |
| 163 | { |
| 164 | if (arg1.value <= arg2.value) |
| 165 | return arg1; |
| 166 | else |
| 167 | return arg2; |
| 168 | } |
| 169 | |
| 170 | /* |
| 171 | * @brief |
| 172 | * result = max(arg1, arg2) := (arg1 <= arg2) ? arg2 : arg1 |
| 173 | */ |
| 174 | static inline struct fixed31_32 dc_fixpt_max(struct fixed31_32 arg1, struct fixed31_32 arg2) |
| 175 | { |
| 176 | if (arg1.value <= arg2.value) |
| 177 | return arg2; |
| 178 | else |
| 179 | return arg1; |
| 180 | } |
| 181 | |
| 182 | /* |
| 183 | * @brief |
| 184 | * | min_value, when arg <= min_value |
| 185 | * result = | arg, when min_value < arg < max_value |
| 186 | * | max_value, when arg >= max_value |
| 187 | */ |
| 188 | static inline struct fixed31_32 dc_fixpt_clamp( |
| 189 | struct fixed31_32 arg, |
| 190 | struct fixed31_32 min_value, |
| 191 | struct fixed31_32 max_value) |
| 192 | { |
| 193 | if (dc_fixpt_le(arg, min_value)) |
| 194 | return min_value; |
| 195 | else if (dc_fixpt_le(max_value, arg)) |
| 196 | return max_value; |
| 197 | else |
| 198 | return arg; |
| 199 | } |
| 200 | |
| 201 | /* |
| 202 | * @brief |
| 203 | * Binary shift operators |
| 204 | */ |
| 205 | |
| 206 | /* |
| 207 | * @brief |
| 208 | * result = arg << shift |
| 209 | */ |
| 210 | static inline struct fixed31_32 dc_fixpt_shl(struct fixed31_32 arg, unsigned char shift) |
| 211 | { |
| 212 | ASSERT(((arg.value >= 0) && (arg.value <= LLONG_MAX >> shift)) || |
| 213 | ((arg.value < 0) && (arg.value >= ~(LLONG_MAX >> shift)))); |
| 214 | |
| 215 | arg.value = arg.value << shift; |
| 216 | |
| 217 | return arg; |
| 218 | } |
| 219 | |
| 220 | /* |
| 221 | * @brief |
| 222 | * result = arg >> shift |
| 223 | */ |
| 224 | static inline struct fixed31_32 dc_fixpt_shr(struct fixed31_32 arg, unsigned char shift) |
| 225 | { |
| 226 | bool negative = arg.value < 0; |
| 227 | |
| 228 | if (negative) |
| 229 | arg.value = -arg.value; |
| 230 | arg.value = arg.value >> shift; |
| 231 | if (negative) |
| 232 | arg.value = -arg.value; |
| 233 | return arg; |
| 234 | } |
| 235 | |
| 236 | /* |
| 237 | * @brief |
| 238 | * Binary additive operators |
| 239 | */ |
| 240 | |
| 241 | /* |
| 242 | * @brief |
| 243 | * result = arg1 + arg2 |
| 244 | */ |
| 245 | static inline struct fixed31_32 dc_fixpt_add(struct fixed31_32 arg1, struct fixed31_32 arg2) |
| 246 | { |
| 247 | struct fixed31_32 res; |
| 248 | |
| 249 | ASSERT(((arg1.value >= 0) && (LLONG_MAX - arg1.value >= arg2.value)) || |
| 250 | ((arg1.value < 0) && (LLONG_MIN - arg1.value <= arg2.value))); |
| 251 | |
| 252 | res.value = arg1.value + arg2.value; |
| 253 | |
| 254 | return res; |
| 255 | } |
| 256 | |
| 257 | /* |
| 258 | * @brief |
| 259 | * result = arg1 + arg2 |
| 260 | */ |
| 261 | static inline struct fixed31_32 dc_fixpt_add_int(struct fixed31_32 arg1, int arg2) |
| 262 | { |
| 263 | return dc_fixpt_add(arg1, dc_fixpt_from_int(arg2)); |
| 264 | } |
| 265 | |
| 266 | /* |
| 267 | * @brief |
| 268 | * result = arg1 - arg2 |
| 269 | */ |
| 270 | static inline struct fixed31_32 dc_fixpt_sub(struct fixed31_32 arg1, struct fixed31_32 arg2) |
| 271 | { |
| 272 | struct fixed31_32 res; |
| 273 | |
| 274 | ASSERT(((arg2.value >= 0) && (LLONG_MIN + arg2.value <= arg1.value)) || |
| 275 | ((arg2.value < 0) && (LLONG_MAX + arg2.value >= arg1.value))); |
| 276 | |
| 277 | res.value = arg1.value - arg2.value; |
| 278 | |
| 279 | return res; |
| 280 | } |
| 281 | |
| 282 | /* |
| 283 | * @brief |
| 284 | * result = arg1 - arg2 |
| 285 | */ |
| 286 | static inline struct fixed31_32 dc_fixpt_sub_int(struct fixed31_32 arg1, int arg2) |
| 287 | { |
| 288 | return dc_fixpt_sub(arg1, dc_fixpt_from_int(arg2)); |
| 289 | } |
| 290 | |
| 291 | |
| 292 | /* |
| 293 | * @brief |
| 294 | * Binary multiplicative operators |
| 295 | */ |
| 296 | |
| 297 | /* |
| 298 | * @brief |
| 299 | * result = arg1 * arg2 |
| 300 | */ |
| 301 | struct fixed31_32 dc_fixpt_mul(struct fixed31_32 arg1, struct fixed31_32 arg2); |
| 302 | |
| 303 | |
| 304 | /* |
| 305 | * @brief |
| 306 | * result = arg1 * arg2 |
| 307 | */ |
| 308 | static inline struct fixed31_32 dc_fixpt_mul_int(struct fixed31_32 arg1, int arg2) |
| 309 | { |
| 310 | return dc_fixpt_mul(arg1, dc_fixpt_from_int(arg2)); |
| 311 | } |
| 312 | |
| 313 | /* |
| 314 | * @brief |
| 315 | * result = square(arg) := arg * arg |
| 316 | */ |
| 317 | struct fixed31_32 dc_fixpt_sqr(struct fixed31_32 arg); |
| 318 | |
| 319 | /* |
| 320 | * @brief |
| 321 | * result = arg1 / arg2 |
| 322 | */ |
| 323 | static inline struct fixed31_32 dc_fixpt_div_int(struct fixed31_32 arg1, long long arg2) |
| 324 | { |
| 325 | return dc_fixpt_from_fraction(arg1.value, dc_fixpt_from_int((int)arg2).value); |
| 326 | } |
| 327 | |
| 328 | /* |
| 329 | * @brief |
| 330 | * result = arg1 / arg2 |
| 331 | */ |
| 332 | static inline struct fixed31_32 dc_fixpt_div(struct fixed31_32 arg1, struct fixed31_32 arg2) |
| 333 | { |
| 334 | return dc_fixpt_from_fraction(arg1.value, arg2.value); |
| 335 | } |
| 336 | |
| 337 | /* |
| 338 | * @brief |
| 339 | * Reciprocal function |
| 340 | */ |
| 341 | |
| 342 | /* |
| 343 | * @brief |
| 344 | * result = reciprocal(arg) := 1 / arg |
| 345 | * |
| 346 | * @note |
| 347 | * No special actions taken in case argument is zero. |
| 348 | */ |
| 349 | struct fixed31_32 dc_fixpt_recip(struct fixed31_32 arg); |
| 350 | |
| 351 | /* |
| 352 | * @brief |
| 353 | * Trigonometric functions |
| 354 | */ |
| 355 | |
| 356 | /* |
| 357 | * @brief |
| 358 | * result = sinc(arg) := sin(arg) / arg |
| 359 | * |
| 360 | * @note |
| 361 | * Argument specified in radians, |
| 362 | * internally it's normalized to [-2pi...2pi] range. |
| 363 | */ |
| 364 | struct fixed31_32 dc_fixpt_sinc(struct fixed31_32 arg); |
| 365 | |
| 366 | /* |
| 367 | * @brief |
| 368 | * result = sin(arg) |
| 369 | * |
| 370 | * @note |
| 371 | * Argument specified in radians, |
| 372 | * internally it's normalized to [-2pi...2pi] range. |
| 373 | */ |
| 374 | struct fixed31_32 dc_fixpt_sin(struct fixed31_32 arg); |
| 375 | |
| 376 | /* |
| 377 | * @brief |
| 378 | * result = cos(arg) |
| 379 | * |
| 380 | * @note |
| 381 | * Argument specified in radians |
| 382 | * and should be in [-2pi...2pi] range - |
| 383 | * passing arguments outside that range |
| 384 | * will cause incorrect result! |
| 385 | */ |
| 386 | struct fixed31_32 dc_fixpt_cos(struct fixed31_32 arg); |
| 387 | |
| 388 | /* |
| 389 | * @brief |
| 390 | * Transcendent functions |
| 391 | */ |
| 392 | |
| 393 | /* |
| 394 | * @brief |
| 395 | * result = exp(arg) |
| 396 | * |
| 397 | * @note |
| 398 | * Currently, function is verified for abs(arg) <= 1. |
| 399 | */ |
| 400 | struct fixed31_32 dc_fixpt_exp(struct fixed31_32 arg); |
| 401 | |
| 402 | /* |
| 403 | * @brief |
| 404 | * result = log(arg) |
| 405 | * |
| 406 | * @note |
| 407 | * Currently, abs(arg) should be less than 1. |
| 408 | * No normalization is done. |
| 409 | * Currently, no special actions taken |
| 410 | * in case of invalid argument(s). Take care! |
| 411 | */ |
| 412 | struct fixed31_32 dc_fixpt_log(struct fixed31_32 arg); |
| 413 | |
| 414 | /* |
| 415 | * @brief |
| 416 | * Power function |
| 417 | */ |
| 418 | |
| 419 | /* |
| 420 | * @brief |
| 421 | * result = pow(arg1, arg2) |
| 422 | * |
| 423 | * @note |
| 424 | * Currently, abs(arg1) should be less than 1. Take care! |
| 425 | */ |
| 426 | static inline struct fixed31_32 dc_fixpt_pow(struct fixed31_32 arg1, struct fixed31_32 arg2) |
| 427 | { |
| 428 | if (arg1.value == 0) |
| 429 | return arg2.value == 0 ? dc_fixpt_one : dc_fixpt_zero; |
| 430 | |
| 431 | return dc_fixpt_exp( |
| 432 | dc_fixpt_mul( |
| 433 | dc_fixpt_log(arg1), |
| 434 | arg2)); |
| 435 | } |
| 436 | |
| 437 | /* |
| 438 | * @brief |
| 439 | * Rounding functions |
| 440 | */ |
| 441 | |
| 442 | /* |
| 443 | * @brief |
| 444 | * result = floor(arg) := greatest integer lower than or equal to arg |
| 445 | */ |
| 446 | static inline int dc_fixpt_floor(struct fixed31_32 arg) |
| 447 | { |
| 448 | unsigned long long arg_value = arg.value > 0 ? arg.value : -arg.value; |
| 449 | |
| 450 | if (arg.value >= 0) |
| 451 | return (int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART); |
| 452 | else |
| 453 | return -(int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART); |
| 454 | } |
| 455 | |
| 456 | /* |
| 457 | * @brief |
| 458 | * result = round(arg) := integer nearest to arg |
| 459 | */ |
| 460 | static inline int dc_fixpt_round(struct fixed31_32 arg) |
| 461 | { |
| 462 | unsigned long long arg_value = arg.value > 0 ? arg.value : -arg.value; |
| 463 | |
| 464 | const long long summand = dc_fixpt_half.value; |
| 465 | |
| 466 | ASSERT(LLONG_MAX - (long long)arg_value >= summand); |
| 467 | |
| 468 | arg_value += summand; |
| 469 | |
| 470 | if (arg.value >= 0) |
| 471 | return (int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART); |
| 472 | else |
| 473 | return -(int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART); |
| 474 | } |
| 475 | |
| 476 | /* |
| 477 | * @brief |
| 478 | * result = ceil(arg) := lowest integer greater than or equal to arg |
| 479 | */ |
| 480 | static inline int dc_fixpt_ceil(struct fixed31_32 arg) |
| 481 | { |
| 482 | unsigned long long arg_value = arg.value > 0 ? arg.value : -arg.value; |
| 483 | |
| 484 | const long long summand = dc_fixpt_one.value - |
| 485 | dc_fixpt_epsilon.value; |
| 486 | |
| 487 | ASSERT(LLONG_MAX - (long long)arg_value >= summand); |
| 488 | |
| 489 | arg_value += summand; |
| 490 | |
| 491 | if (arg.value >= 0) |
| 492 | return (int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART); |
| 493 | else |
| 494 | return -(int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART); |
| 495 | } |
| 496 | |
| 497 | /* the following two function are used in scaler hw programming to convert fixed |
| 498 | * point value to format 2 bits from integer part and 19 bits from fractional |
| 499 | * part. The same applies for u0d19, 0 bits from integer part and 19 bits from |
| 500 | * fractional |
| 501 | */ |
| 502 | |
| 503 | unsigned int dc_fixpt_u4d19(struct fixed31_32 arg); |
| 504 | |
| 505 | unsigned int dc_fixpt_u3d19(struct fixed31_32 arg); |
| 506 | |
| 507 | unsigned int dc_fixpt_u2d19(struct fixed31_32 arg); |
| 508 | |
| 509 | unsigned int dc_fixpt_u0d19(struct fixed31_32 arg); |
| 510 | |
| 511 | unsigned int dc_fixpt_clamp_u0d14(struct fixed31_32 arg); |
| 512 | |
| 513 | unsigned int dc_fixpt_clamp_u0d10(struct fixed31_32 arg); |
| 514 | |
| 515 | int dc_fixpt_s4d19(struct fixed31_32 arg); |
| 516 | |
| 517 | static inline struct fixed31_32 dc_fixpt_truncate(struct fixed31_32 arg, unsigned int frac_bits) |
| 518 | { |
| 519 | bool negative = arg.value < 0; |
| 520 | |
| 521 | if (frac_bits >= FIXED31_32_BITS_PER_FRACTIONAL_PART) { |
| 522 | ASSERT(frac_bits == FIXED31_32_BITS_PER_FRACTIONAL_PART); |
| 523 | return arg; |
| 524 | } |
| 525 | |
| 526 | if (negative) |
| 527 | arg.value = -arg.value; |
| 528 | arg.value &= (~0ULL) << (FIXED31_32_BITS_PER_FRACTIONAL_PART - frac_bits); |
| 529 | if (negative) |
| 530 | arg.value = -arg.value; |
| 531 | return arg; |
| 532 | } |
| 533 | |
| 534 | #endif |