| 1 | // SPDX-License-Identifier: MIT |
| 2 | // |
| 3 | // Copyright 2024 Advanced Micro Devices, Inc. |
| 4 | |
| 5 | #include "spl_fixpt31_32.h" |
| 6 | |
| 7 | static const struct spl_fixed31_32 spl_fixpt_two_pi = { 26986075409LL }; |
| 8 | static const struct spl_fixed31_32 spl_fixpt_ln2 = { 2977044471LL }; |
| 9 | static const struct spl_fixed31_32 spl_fixpt_ln2_div_2 = { 1488522236LL }; |
| 10 | |
| 11 | static inline unsigned long long abs_i64( |
| 12 | long long arg) |
| 13 | { |
| 14 | if (arg > 0) |
| 15 | return (unsigned long long)arg; |
| 16 | else |
| 17 | return (unsigned long long)(-arg); |
| 18 | } |
| 19 | |
| 20 | /* |
| 21 | * @brief |
| 22 | * result = dividend / divisor |
| 23 | * *remainder = dividend % divisor |
| 24 | */ |
| 25 | static inline unsigned long long spl_complete_integer_division_u64( |
| 26 | unsigned long long dividend, |
| 27 | unsigned long long divisor, |
| 28 | unsigned long long *remainder) |
| 29 | { |
| 30 | unsigned long long result; |
| 31 | |
| 32 | result = spl_div64_u64_rem(dividend, divisor, remainder); |
| 33 | |
| 34 | return result; |
| 35 | } |
| 36 | |
| 37 | |
| 38 | #define FRACTIONAL_PART_MASK \ |
| 39 | ((1ULL << FIXED31_32_BITS_PER_FRACTIONAL_PART) - 1) |
| 40 | |
| 41 | #define GET_INTEGER_PART(x) \ |
| 42 | ((x) >> FIXED31_32_BITS_PER_FRACTIONAL_PART) |
| 43 | |
| 44 | #define GET_FRACTIONAL_PART(x) \ |
| 45 | (FRACTIONAL_PART_MASK & (x)) |
| 46 | |
| 47 | struct spl_fixed31_32 spl_fixpt_from_fraction(long long numerator, long long denominator) |
| 48 | { |
| 49 | struct spl_fixed31_32 res; |
| 50 | |
| 51 | bool arg1_negative = numerator < 0; |
| 52 | bool arg2_negative = denominator < 0; |
| 53 | |
| 54 | unsigned long long arg1_value = arg1_negative ? -numerator : numerator; |
| 55 | unsigned long long arg2_value = arg2_negative ? -denominator : denominator; |
| 56 | |
| 57 | unsigned long long remainder; |
| 58 | |
| 59 | /* determine integer part */ |
| 60 | |
| 61 | unsigned long long res_value = spl_complete_integer_division_u64( |
| 62 | dividend: arg1_value, divisor: arg2_value, remainder: &remainder); |
| 63 | |
| 64 | SPL_ASSERT(res_value <= (unsigned long long)LONG_MAX); |
| 65 | |
| 66 | /* determine fractional part */ |
| 67 | { |
| 68 | unsigned int i = FIXED31_32_BITS_PER_FRACTIONAL_PART; |
| 69 | |
| 70 | do { |
| 71 | remainder <<= 1; |
| 72 | |
| 73 | res_value <<= 1; |
| 74 | |
| 75 | if (remainder >= arg2_value) { |
| 76 | res_value |= 1; |
| 77 | remainder -= arg2_value; |
| 78 | } |
| 79 | } while (--i != 0); |
| 80 | } |
| 81 | |
| 82 | /* round up LSB */ |
| 83 | { |
| 84 | unsigned long long summand = (remainder << 1) >= arg2_value; |
| 85 | |
| 86 | SPL_ASSERT(res_value <= (unsigned long long)LLONG_MAX - summand); |
| 87 | |
| 88 | res_value += summand; |
| 89 | } |
| 90 | |
| 91 | res.value = (long long)res_value; |
| 92 | |
| 93 | if (arg1_negative ^ arg2_negative) |
| 94 | res.value = -res.value; |
| 95 | |
| 96 | return res; |
| 97 | } |
| 98 | |
| 99 | struct spl_fixed31_32 spl_fixpt_mul(struct spl_fixed31_32 arg1, struct spl_fixed31_32 arg2) |
| 100 | { |
| 101 | struct spl_fixed31_32 res; |
| 102 | |
| 103 | bool arg1_negative = arg1.value < 0; |
| 104 | bool arg2_negative = arg2.value < 0; |
| 105 | |
| 106 | unsigned long long arg1_value = arg1_negative ? -arg1.value : arg1.value; |
| 107 | unsigned long long arg2_value = arg2_negative ? -arg2.value : arg2.value; |
| 108 | |
| 109 | unsigned long long arg1_int = GET_INTEGER_PART(arg1_value); |
| 110 | unsigned long long arg2_int = GET_INTEGER_PART(arg2_value); |
| 111 | |
| 112 | unsigned long long arg1_fra = GET_FRACTIONAL_PART(arg1_value); |
| 113 | unsigned long long arg2_fra = GET_FRACTIONAL_PART(arg2_value); |
| 114 | |
| 115 | unsigned long long tmp; |
| 116 | |
| 117 | res.value = arg1_int * arg2_int; |
| 118 | |
| 119 | SPL_ASSERT(res.value <= (long long)LONG_MAX); |
| 120 | |
| 121 | res.value <<= FIXED31_32_BITS_PER_FRACTIONAL_PART; |
| 122 | |
| 123 | tmp = arg1_int * arg2_fra; |
| 124 | |
| 125 | SPL_ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value)); |
| 126 | |
| 127 | res.value += tmp; |
| 128 | |
| 129 | tmp = arg2_int * arg1_fra; |
| 130 | |
| 131 | SPL_ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value)); |
| 132 | |
| 133 | res.value += tmp; |
| 134 | |
| 135 | tmp = arg1_fra * arg2_fra; |
| 136 | |
| 137 | tmp = (tmp >> FIXED31_32_BITS_PER_FRACTIONAL_PART) + |
| 138 | (tmp >= (unsigned long long)spl_fixpt_half.value); |
| 139 | |
| 140 | SPL_ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value)); |
| 141 | |
| 142 | res.value += tmp; |
| 143 | |
| 144 | if (arg1_negative ^ arg2_negative) |
| 145 | res.value = -res.value; |
| 146 | |
| 147 | return res; |
| 148 | } |
| 149 | |
| 150 | struct spl_fixed31_32 spl_fixpt_sqr(struct spl_fixed31_32 arg) |
| 151 | { |
| 152 | struct spl_fixed31_32 res; |
| 153 | |
| 154 | unsigned long long arg_value = abs_i64(arg: arg.value); |
| 155 | |
| 156 | unsigned long long arg_int = GET_INTEGER_PART(arg_value); |
| 157 | |
| 158 | unsigned long long arg_fra = GET_FRACTIONAL_PART(arg_value); |
| 159 | |
| 160 | unsigned long long tmp; |
| 161 | |
| 162 | res.value = arg_int * arg_int; |
| 163 | |
| 164 | SPL_ASSERT(res.value <= (long long)LONG_MAX); |
| 165 | |
| 166 | res.value <<= FIXED31_32_BITS_PER_FRACTIONAL_PART; |
| 167 | |
| 168 | tmp = arg_int * arg_fra; |
| 169 | |
| 170 | SPL_ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value)); |
| 171 | |
| 172 | res.value += tmp; |
| 173 | |
| 174 | SPL_ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value)); |
| 175 | |
| 176 | res.value += tmp; |
| 177 | |
| 178 | tmp = arg_fra * arg_fra; |
| 179 | |
| 180 | tmp = (tmp >> FIXED31_32_BITS_PER_FRACTIONAL_PART) + |
| 181 | (tmp >= (unsigned long long)spl_fixpt_half.value); |
| 182 | |
| 183 | SPL_ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value)); |
| 184 | |
| 185 | res.value += tmp; |
| 186 | |
| 187 | return res; |
| 188 | } |
| 189 | |
| 190 | struct spl_fixed31_32 spl_fixpt_recip(struct spl_fixed31_32 arg) |
| 191 | { |
| 192 | /* |
| 193 | * @note |
| 194 | * Good idea to use Newton's method |
| 195 | */ |
| 196 | |
| 197 | return spl_fixpt_from_fraction( |
| 198 | numerator: spl_fixpt_one.value, |
| 199 | denominator: arg.value); |
| 200 | } |
| 201 | |
| 202 | struct spl_fixed31_32 spl_fixpt_sinc(struct spl_fixed31_32 arg) |
| 203 | { |
| 204 | struct spl_fixed31_32 square; |
| 205 | |
| 206 | struct spl_fixed31_32 res = spl_fixpt_one; |
| 207 | |
| 208 | int n = 27; |
| 209 | |
| 210 | struct spl_fixed31_32 arg_norm = arg; |
| 211 | |
| 212 | if (spl_fixpt_le( |
| 213 | arg1: spl_fixpt_two_pi, |
| 214 | arg2: spl_fixpt_abs(arg))) { |
| 215 | arg_norm = spl_fixpt_sub( |
| 216 | arg1: arg_norm, |
| 217 | arg2: spl_fixpt_mul_int( |
| 218 | arg1: spl_fixpt_two_pi, |
| 219 | arg2: (int)spl_div64_s64( |
| 220 | dividend: arg_norm.value, |
| 221 | divisor: spl_fixpt_two_pi.value))); |
| 222 | } |
| 223 | |
| 224 | square = spl_fixpt_sqr(arg: arg_norm); |
| 225 | |
| 226 | do { |
| 227 | res = spl_fixpt_sub( |
| 228 | arg1: spl_fixpt_one, |
| 229 | arg2: spl_fixpt_div_int( |
| 230 | arg1: spl_fixpt_mul( |
| 231 | arg1: square, |
| 232 | arg2: res), |
| 233 | arg2: n * (n - 1))); |
| 234 | |
| 235 | n -= 2; |
| 236 | } while (n > 2); |
| 237 | |
| 238 | if (arg.value != arg_norm.value) |
| 239 | res = spl_fixpt_div( |
| 240 | arg1: spl_fixpt_mul(arg1: res, arg2: arg_norm), |
| 241 | arg2: arg); |
| 242 | |
| 243 | return res; |
| 244 | } |
| 245 | |
| 246 | struct spl_fixed31_32 spl_fixpt_sin(struct spl_fixed31_32 arg) |
| 247 | { |
| 248 | return spl_fixpt_mul( |
| 249 | arg1: arg, |
| 250 | arg2: spl_fixpt_sinc(arg)); |
| 251 | } |
| 252 | |
| 253 | struct spl_fixed31_32 spl_fixpt_cos(struct spl_fixed31_32 arg) |
| 254 | { |
| 255 | /* TODO implement argument normalization */ |
| 256 | |
| 257 | const struct spl_fixed31_32 square = spl_fixpt_sqr(arg); |
| 258 | |
| 259 | struct spl_fixed31_32 res = spl_fixpt_one; |
| 260 | |
| 261 | int n = 26; |
| 262 | |
| 263 | do { |
| 264 | res = spl_fixpt_sub( |
| 265 | arg1: spl_fixpt_one, |
| 266 | arg2: spl_fixpt_div_int( |
| 267 | arg1: spl_fixpt_mul( |
| 268 | arg1: square, |
| 269 | arg2: res), |
| 270 | arg2: n * (n - 1))); |
| 271 | |
| 272 | n -= 2; |
| 273 | } while (n != 0); |
| 274 | |
| 275 | return res; |
| 276 | } |
| 277 | |
| 278 | /* |
| 279 | * @brief |
| 280 | * result = exp(arg), |
| 281 | * where abs(arg) < 1 |
| 282 | * |
| 283 | * Calculated as Taylor series. |
| 284 | */ |
| 285 | static struct spl_fixed31_32 spl_fixed31_32_exp_from_taylor_series(struct spl_fixed31_32 arg) |
| 286 | { |
| 287 | unsigned int n = 9; |
| 288 | |
| 289 | struct spl_fixed31_32 res = spl_fixpt_from_fraction( |
| 290 | numerator: n + 2, |
| 291 | denominator: n + 1); |
| 292 | /* TODO find correct res */ |
| 293 | |
| 294 | SPL_ASSERT(spl_fixpt_lt(arg, spl_fixpt_one)); |
| 295 | |
| 296 | do |
| 297 | res = spl_fixpt_add( |
| 298 | arg1: spl_fixpt_one, |
| 299 | arg2: spl_fixpt_div_int( |
| 300 | arg1: spl_fixpt_mul( |
| 301 | arg1: arg, |
| 302 | arg2: res), |
| 303 | arg2: n)); |
| 304 | while (--n != 1); |
| 305 | |
| 306 | return spl_fixpt_add( |
| 307 | arg1: spl_fixpt_one, |
| 308 | arg2: spl_fixpt_mul( |
| 309 | arg1: arg, |
| 310 | arg2: res)); |
| 311 | } |
| 312 | |
| 313 | struct spl_fixed31_32 spl_fixpt_exp(struct spl_fixed31_32 arg) |
| 314 | { |
| 315 | /* |
| 316 | * @brief |
| 317 | * Main equation is: |
| 318 | * exp(x) = exp(r + m * ln(2)) = (1 << m) * exp(r), |
| 319 | * where m = round(x / ln(2)), r = x - m * ln(2) |
| 320 | */ |
| 321 | |
| 322 | if (spl_fixpt_le( |
| 323 | arg1: spl_fixpt_ln2_div_2, |
| 324 | arg2: spl_fixpt_abs(arg))) { |
| 325 | int m = spl_fixpt_round( |
| 326 | arg: spl_fixpt_div( |
| 327 | arg1: arg, |
| 328 | arg2: spl_fixpt_ln2)); |
| 329 | |
| 330 | struct spl_fixed31_32 r = spl_fixpt_sub( |
| 331 | arg1: arg, |
| 332 | arg2: spl_fixpt_mul_int( |
| 333 | arg1: spl_fixpt_ln2, |
| 334 | arg2: m)); |
| 335 | |
| 336 | SPL_ASSERT(m != 0); |
| 337 | |
| 338 | SPL_ASSERT(spl_fixpt_lt( |
| 339 | spl_fixpt_abs(r), |
| 340 | spl_fixpt_one)); |
| 341 | |
| 342 | if (m > 0) |
| 343 | return spl_fixpt_shl( |
| 344 | arg: spl_fixed31_32_exp_from_taylor_series(arg: r), |
| 345 | shift: (unsigned int)m); |
| 346 | else |
| 347 | return spl_fixpt_div_int( |
| 348 | arg1: spl_fixed31_32_exp_from_taylor_series(arg: r), |
| 349 | arg2: 1LL << -m); |
| 350 | } else if (arg.value != 0) |
| 351 | return spl_fixed31_32_exp_from_taylor_series(arg); |
| 352 | else |
| 353 | return spl_fixpt_one; |
| 354 | } |
| 355 | |
| 356 | struct spl_fixed31_32 spl_fixpt_log(struct spl_fixed31_32 arg) |
| 357 | { |
| 358 | struct spl_fixed31_32 res = spl_fixpt_neg(arg: spl_fixpt_one); |
| 359 | /* TODO improve 1st estimation */ |
| 360 | |
| 361 | struct spl_fixed31_32 error; |
| 362 | |
| 363 | SPL_ASSERT(arg.value > 0); |
| 364 | /* TODO if arg is negative, return NaN */ |
| 365 | /* TODO if arg is zero, return -INF */ |
| 366 | |
| 367 | do { |
| 368 | struct spl_fixed31_32 res1 = spl_fixpt_add( |
| 369 | arg1: spl_fixpt_sub( |
| 370 | arg1: res, |
| 371 | arg2: spl_fixpt_one), |
| 372 | arg2: spl_fixpt_div( |
| 373 | arg1: arg, |
| 374 | arg2: spl_fixpt_exp(arg: res))); |
| 375 | |
| 376 | error = spl_fixpt_sub( |
| 377 | arg1: res, |
| 378 | arg2: res1); |
| 379 | |
| 380 | res = res1; |
| 381 | /* TODO determine max_allowed_error based on quality of exp() */ |
| 382 | } while (abs_i64(arg: error.value) > 100ULL); |
| 383 | |
| 384 | return res; |
| 385 | } |
| 386 | |
| 387 | |
| 388 | /* this function is a generic helper to translate fixed point value to |
| 389 | * specified integer format that will consist of integer_bits integer part and |
| 390 | * fractional_bits fractional part. For example it is used in |
| 391 | * spl_fixpt_u2d19 to receive 2 bits integer part and 19 bits fractional |
| 392 | * part in 32 bits. It is used in hw programming (scaler) |
| 393 | */ |
| 394 | |
| 395 | static inline unsigned int spl_ux_dy( |
| 396 | long long value, |
| 397 | unsigned int integer_bits, |
| 398 | unsigned int fractional_bits) |
| 399 | { |
| 400 | /* 1. create mask of integer part */ |
| 401 | unsigned int result = (1 << integer_bits) - 1; |
| 402 | /* 2. mask out fractional part */ |
| 403 | unsigned int fractional_part = FRACTIONAL_PART_MASK & value; |
| 404 | /* 3. shrink fixed point integer part to be of integer_bits width*/ |
| 405 | result &= GET_INTEGER_PART(value); |
| 406 | /* 4. make space for fractional part to be filled in after integer */ |
| 407 | result <<= fractional_bits; |
| 408 | /* 5. shrink fixed point fractional part to of fractional_bits width*/ |
| 409 | fractional_part >>= FIXED31_32_BITS_PER_FRACTIONAL_PART - fractional_bits; |
| 410 | /* 6. merge the result */ |
| 411 | return result | fractional_part; |
| 412 | } |
| 413 | |
| 414 | static inline unsigned int spl_clamp_ux_dy( |
| 415 | long long value, |
| 416 | unsigned int integer_bits, |
| 417 | unsigned int fractional_bits, |
| 418 | unsigned int min_clamp) |
| 419 | { |
| 420 | unsigned int truncated_val = spl_ux_dy(value, integer_bits, fractional_bits); |
| 421 | |
| 422 | if (value >= (1LL << (integer_bits + FIXED31_32_BITS_PER_FRACTIONAL_PART))) |
| 423 | return (1 << (integer_bits + fractional_bits)) - 1; |
| 424 | else if (truncated_val > min_clamp) |
| 425 | return truncated_val; |
| 426 | else |
| 427 | return min_clamp; |
| 428 | } |
| 429 | |
| 430 | unsigned int spl_fixpt_u4d19(struct spl_fixed31_32 arg) |
| 431 | { |
| 432 | return spl_ux_dy(value: arg.value, integer_bits: 4, fractional_bits: 19); |
| 433 | } |
| 434 | |
| 435 | unsigned int spl_fixpt_u3d19(struct spl_fixed31_32 arg) |
| 436 | { |
| 437 | return spl_ux_dy(value: arg.value, integer_bits: 3, fractional_bits: 19); |
| 438 | } |
| 439 | |
| 440 | unsigned int spl_fixpt_u2d19(struct spl_fixed31_32 arg) |
| 441 | { |
| 442 | return spl_ux_dy(value: arg.value, integer_bits: 2, fractional_bits: 19); |
| 443 | } |
| 444 | |
| 445 | unsigned int spl_fixpt_u0d19(struct spl_fixed31_32 arg) |
| 446 | { |
| 447 | return spl_ux_dy(value: arg.value, integer_bits: 0, fractional_bits: 19); |
| 448 | } |
| 449 | |
| 450 | unsigned int spl_fixpt_clamp_u0d14(struct spl_fixed31_32 arg) |
| 451 | { |
| 452 | return spl_clamp_ux_dy(value: arg.value, integer_bits: 0, fractional_bits: 14, min_clamp: 1); |
| 453 | } |
| 454 | |
| 455 | unsigned int spl_fixpt_clamp_u0d10(struct spl_fixed31_32 arg) |
| 456 | { |
| 457 | return spl_clamp_ux_dy(value: arg.value, integer_bits: 0, fractional_bits: 10, min_clamp: 1); |
| 458 | } |
| 459 | |
| 460 | int spl_fixpt_s4d19(struct spl_fixed31_32 arg) |
| 461 | { |
| 462 | if (arg.value < 0) |
| 463 | return -(int)spl_ux_dy(value: spl_fixpt_abs(arg).value, integer_bits: 4, fractional_bits: 19); |
| 464 | else |
| 465 | return spl_ux_dy(value: arg.value, integer_bits: 4, fractional_bits: 19); |
| 466 | } |
| 467 | |
| 468 | struct spl_fixed31_32 spl_fixpt_from_ux_dy(unsigned int value, |
| 469 | unsigned int integer_bits, |
| 470 | unsigned int fractional_bits) |
| 471 | { |
| 472 | struct spl_fixed31_32 fixpt_value = spl_fixpt_zero; |
| 473 | struct spl_fixed31_32 fixpt_int_value = spl_fixpt_zero; |
| 474 | long long frac_mask = ((long long)1 << (long long)integer_bits) - 1; |
| 475 | |
| 476 | fixpt_value.value = (long long)value << (FIXED31_32_BITS_PER_FRACTIONAL_PART - fractional_bits); |
| 477 | frac_mask = frac_mask << fractional_bits; |
| 478 | fixpt_int_value.value = value & frac_mask; |
| 479 | fixpt_int_value.value <<= (FIXED31_32_BITS_PER_FRACTIONAL_PART - fractional_bits); |
| 480 | fixpt_value.value |= fixpt_int_value.value; |
| 481 | return fixpt_value; |
| 482 | } |
| 483 | |
| 484 | struct spl_fixed31_32 spl_fixpt_from_int_dy(unsigned int int_value, |
| 485 | unsigned int frac_value, |
| 486 | unsigned int integer_bits, |
| 487 | unsigned int fractional_bits) |
| 488 | { |
| 489 | struct spl_fixed31_32 fixpt_value = spl_fixpt_from_int(arg: int_value); |
| 490 | |
| 491 | fixpt_value.value |= (long long)frac_value << (FIXED31_32_BITS_PER_FRACTIONAL_PART - fractional_bits); |
| 492 | return fixpt_value; |
| 493 | } |
| 494 | |