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| 1 | /* GATE PROJECT LICENSE: | ||
| 2 | +----------------------------------------------------------------------------+ | ||
| 3 | | Copyright (c) 2018-2026, Stefan Meislinger <sm@opengate.at> | | ||
| 4 | | All rights reserved. | | ||
| 5 | | | | ||
| 6 | | Redistribution and use in source and binary forms, with or without | | ||
| 7 | | modification, are permitted provided that the following conditions are met:| | ||
| 8 | | | | ||
| 9 | | 1. Redistributions of source code must retain the above copyright notice, | | ||
| 10 | | this list of conditions and the following disclaimer. | | ||
| 11 | | 2. Redistributions in binary form must reproduce the above copyright | | ||
| 12 | | notice, this list of conditions and the following disclaimer in the | | ||
| 13 | | documentation and/or other materials provided with the distribution. | | ||
| 14 | | | | ||
| 15 | | THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"| | ||
| 16 | | AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | | ||
| 17 | | IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | | ||
| 18 | | ARE DISCLAIMED.IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE | | ||
| 19 | | LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR | | ||
| 20 | | CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF | | ||
| 21 | | SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS | | ||
| 22 | | INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN | | ||
| 23 | | CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | | ||
| 24 | | ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF | | ||
| 25 | | THE POSSIBILITY OF SUCH DAMAGE. | | ||
| 26 | +----------------------------------------------------------------------------+ | ||
| 27 | */ | ||
| 28 | |||
| 29 | #include "gate/mathematics.h" | ||
| 30 | |||
| 31 | #if defined(GATE_SYS_EFI) | ||
| 32 | //# define GATE_CORE_MATH_EFI_IMPL 1 | ||
| 33 | # define GATE_CORE_MATH_STD_IMPL 1 | ||
| 34 | #else | ||
| 35 | # define GATE_CORE_MATH_STD_IMPL 1 | ||
| 36 | #endif | ||
| 37 | |||
| 38 | /***************************** | ||
| 39 | * Generic implementations * | ||
| 40 | *****************************/ | ||
| 41 | |||
| 42 | #include <stdarg.h> | ||
| 43 | #include <float.h> | ||
| 44 | |||
| 45 | ✗ | void gate_decimal_init(gate_decimal_t* deci, gate_int32_t int_num, gate_uint32_t micro_num) | |
| 46 | { | ||
| 47 | ✗ | deci->value = (gate_decimal_primitive_t)(int_num * GATE_DECIMAL_FACTOR); | |
| 48 | ✗ | deci->value += (gate_decimal_primitive_t)(micro_num % GATE_DECIMAL_FACTOR); | |
| 49 | ✗ | } | |
| 50 | ✗ | gate_int32_t gate_decimal_get_int(gate_decimal_t const* deci) | |
| 51 | { | ||
| 52 | ✗ | return (gate_int32_t)(deci->value / GATE_DECIMAL_FACTOR); | |
| 53 | } | ||
| 54 | ✗ | gate_uint32_t gate_decimal_get_micro(gate_decimal_t const* deci) | |
| 55 | { | ||
| 56 | ✗ | if (deci->value < 0) | |
| 57 | { | ||
| 58 | ✗ | return (gate_uint32_t)((-deci->value) % GATE_DECIMAL_FACTOR); | |
| 59 | } | ||
| 60 | else | ||
| 61 | { | ||
| 62 | ✗ | return (gate_uint32_t)(deci->value % GATE_DECIMAL_FACTOR); | |
| 63 | } | ||
| 64 | } | ||
| 65 | ✗ | gate_real32_t gate_decimal_get_float(gate_decimal_t const* micro) | |
| 66 | { | ||
| 67 | ✗ | return (gate_real32_t)micro->value / (gate_real32_t)GATE_DECIMAL_FACTOR; | |
| 68 | } | ||
| 69 | |||
| 70 | ✗ | int gate_decimal_compare(gate_decimal_t const* a, gate_decimal_t const* b) | |
| 71 | { | ||
| 72 | ✗ | if (a->value < b->value) | |
| 73 | { | ||
| 74 | ✗ | return -1; | |
| 75 | } | ||
| 76 | ✗ | else if (a->value > b->value) | |
| 77 | { | ||
| 78 | ✗ | return 1; | |
| 79 | } | ||
| 80 | ✗ | return 0; | |
| 81 | } | ||
| 82 | |||
| 83 | |||
| 84 | ✗ | void gate_decimal_add_int(gate_decimal_t* deci, gate_int32_t value) | |
| 85 | { | ||
| 86 | ✗ | deci->value += (gate_decimal_primitive_t)value * GATE_DECIMAL_FACTOR; | |
| 87 | ✗ | } | |
| 88 | ✗ | void gate_decimal_sub_int(gate_decimal_t* deci, gate_int32_t value) | |
| 89 | { | ||
| 90 | ✗ | deci->value -= (gate_decimal_primitive_t)value * GATE_DECIMAL_FACTOR; | |
| 91 | ✗ | } | |
| 92 | ✗ | void gate_decimal_mul_int(gate_decimal_t* deci, gate_int32_t value) | |
| 93 | { | ||
| 94 | ✗ | deci->value *= (gate_decimal_primitive_t)value; | |
| 95 | ✗ | } | |
| 96 | ✗ | void gate_decimal_div_int(gate_decimal_t* deci, gate_int32_t value) | |
| 97 | { | ||
| 98 | ✗ | deci->value /= (gate_decimal_primitive_t)value; | |
| 99 | ✗ | } | |
| 100 | |||
| 101 | ✗ | void gate_decimal_add_dec(gate_decimal_t* deci, gate_decimal_t const* ptr_value) | |
| 102 | { | ||
| 103 | ✗ | deci->value += ptr_value->value; | |
| 104 | ✗ | } | |
| 105 | ✗ | void gate_decimal_sub_dec(gate_decimal_t* deci, gate_decimal_t const* ptr_value) | |
| 106 | { | ||
| 107 | ✗ | deci->value -= ptr_value->value; | |
| 108 | ✗ | } | |
| 109 | ✗ | void gate_decimal_mul_dec(gate_decimal_t* deci, gate_decimal_t const* ptr_value) | |
| 110 | { | ||
| 111 | ✗ | deci->value *= ptr_value->value; | |
| 112 | ✗ | deci->value /= (gate_decimal_primitive_t)GATE_DECIMAL_FACTOR; | |
| 113 | ✗ | } | |
| 114 | ✗ | void gate_decimal_div_dec(gate_decimal_t* deci, gate_decimal_t const* ptr_value) | |
| 115 | { | ||
| 116 | ✗ | gate_int64_t r = deci->value % ptr_value->value; | |
| 117 | ✗ | deci->value /= ptr_value->value; | |
| 118 | ✗ | deci->value *= (gate_decimal_primitive_t)GATE_DECIMAL_FACTOR; | |
| 119 | ✗ | deci->value += (gate_decimal_primitive_t)(r * GATE_DECIMAL_FACTOR / ptr_value->value); | |
| 120 | ✗ | } | |
| 121 | |||
| 122 | ✗ | void gate_decimal_add_flt(gate_decimal_t* deci, gate_real32_t value) | |
| 123 | { | ||
| 124 | ✗ | deci->value += (gate_decimal_primitive_t)(value * (gate_real32_t)GATE_DECIMAL_FACTOR); | |
| 125 | ✗ | } | |
| 126 | ✗ | void gate_decimal_sub_flt(gate_decimal_t* deci, gate_real32_t value) | |
| 127 | { | ||
| 128 | ✗ | deci->value -= (gate_decimal_primitive_t)(value * (gate_real32_t)GATE_DECIMAL_FACTOR); | |
| 129 | ✗ | } | |
| 130 | ✗ | void gate_decimal_mul_flt(gate_decimal_t* deci, gate_real32_t value) | |
| 131 | { | ||
| 132 | ✗ | deci->value = (gate_decimal_primitive_t)((gate_real32_t)deci->value * value); | |
| 133 | ✗ | } | |
| 134 | ✗ | void gate_decimal_div_flt(gate_decimal_t* deci, gate_real32_t value) | |
| 135 | { | ||
| 136 | ✗ | deci->value = (gate_decimal_primitive_t)((gate_real32_t)deci->value / value); | |
| 137 | ✗ | } | |
| 138 | ✗ | void gate_decimal_sqrt(gate_decimal_t* deci) | |
| 139 | { | ||
| 140 | static gate_decimal_t n2 = GATE_DECIMAL_INIT(2, 0); | ||
| 141 | ✗ | gate_decimal_t a = GATE_DECIMAL_INIT(1255, 0); | |
| 142 | gate_decimal_t b; | ||
| 143 | unsigned n; | ||
| 144 | |||
| 145 | ✗ | if (gate_decimal_compare(deci, &n2) < 0) | |
| 146 | { | ||
| 147 | ✗ | return; | |
| 148 | } | ||
| 149 | |||
| 150 | ✗ | for (n = 0; n < 8; ++n) | |
| 151 | { | ||
| 152 | ✗ | b.value = (deci->value / a.value) * GATE_DECIMAL_FACTOR; | |
| 153 | ✗ | a.value = (a.value + b.value) / 2; | |
| 154 | } | ||
| 155 | ✗ | deci->value = a.value; | |
| 156 | } | ||
| 157 | |||
| 158 | |||
| 159 | 470 | gate_bool_t gate_math_iszero(gate_real64_t num) | |
| 160 | { | ||
| 161 |
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470 | if (num < 0.0) |
| 162 | { | ||
| 163 | 20 | return (-num < DBL_EPSILON) ? true : false; | |
| 164 | } | ||
| 165 | else | ||
| 166 | { | ||
| 167 | 450 | return (num < DBL_EPSILON) ? true : false; | |
| 168 | } | ||
| 169 | } | ||
| 170 | 2214 | gate_bool_t gate_math_iszerof(gate_real32_t num) | |
| 171 | { | ||
| 172 |
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2214 | if (num < 0.0f) |
| 173 | { | ||
| 174 | 4 | return (-num < FLT_EPSILON) ? true : false; | |
| 175 | } | ||
| 176 | else | ||
| 177 | { | ||
| 178 | 2210 | return (num < FLT_EPSILON) ? true : false; | |
| 179 | } | ||
| 180 | } | ||
| 181 | |||
| 182 | 360 | gate_bool_t gate_math_isnan(gate_real64_t num) | |
| 183 | { | ||
| 184 | 360 | volatile gate_real64_t tmp = num; | |
| 185 | 360 | return (tmp != num) ? true : false; | |
| 186 | } | ||
| 187 | 3 | gate_bool_t gate_math_isnanf(gate_real32_t num) | |
| 188 | { | ||
| 189 | 3 | volatile gate_real32_t tmp = num; | |
| 190 | 3 | return (tmp != num) ? true : false; | |
| 191 | } | ||
| 192 | |||
| 193 | 360 | int gate_math_isinfinite(gate_real64_t num) | |
| 194 | { | ||
| 195 | #if defined(DBL_MAX) | ||
| 196 |
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360 | if (num > DBL_MAX) |
| 197 | { | ||
| 198 | 1 | return 1; | |
| 199 | } | ||
| 200 |
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|
359 | else if (num < -DBL_MAX) |
| 201 | { | ||
| 202 | ✗ | return -1; | |
| 203 | } | ||
| 204 | 359 | return 0; | |
| 205 | #else | ||
| 206 | #define gate_math_infinite_pos (1.0 / 0.0) | ||
| 207 | #define gate_math_infinite_neg (-1.0 / 0.0) | ||
| 208 | if (num == gate_math_infinite_pos) | ||
| 209 | { | ||
| 210 | return 1; | ||
| 211 | } | ||
| 212 | else if (num == gate_math_infinite_neg) | ||
| 213 | { | ||
| 214 | return -1; | ||
| 215 | } | ||
| 216 | return 0; | ||
| 217 | #endif | ||
| 218 | } | ||
| 219 | 3 | int gate_math_isinfinitef(gate_real32_t num) | |
| 220 | { | ||
| 221 | #if defined(FLT_MAX) | ||
| 222 |
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3 | if (num > FLT_MAX) |
| 223 | { | ||
| 224 | 1 | return 1; | |
| 225 | } | ||
| 226 |
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2 | else if (num < -FLT_MAX) |
| 227 | { | ||
| 228 | ✗ | return -1; | |
| 229 | } | ||
| 230 | 2 | return 0; | |
| 231 | #else | ||
| 232 | static gate_real32_t const gate_math_infinite_pos = 1.0f / 0.0f; | ||
| 233 | static gate_real32_t const gate_math_infinite_neg = -1.0f / 0.0f; | ||
| 234 | if (num == gate_math_infinite_pos) | ||
| 235 | { | ||
| 236 | return 1; | ||
| 237 | } | ||
| 238 | else if (num == gate_math_infinite_neg) | ||
| 239 | { | ||
| 240 | return -1; | ||
| 241 | } | ||
| 242 | return 0; | ||
| 243 | #endif | ||
| 244 | |||
| 245 | } | ||
| 246 | |||
| 247 | 4 | int gate_math_signum_i8(gate_int8_t num) | |
| 248 | { | ||
| 249 |
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4 | return (num < 0) ? -1 : ((num == 0) ? 0 : 1); |
| 250 | } | ||
| 251 | 4 | int gate_math_signum_i16(gate_int16_t num) | |
| 252 | { | ||
| 253 |
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4 | return (num < 0) ? -1 : ((num == 0) ? 0 : 1); |
| 254 | } | ||
| 255 | 4 | int gate_math_signum_i32(gate_int32_t num) | |
| 256 | { | ||
| 257 |
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4 | return (num < 0) ? -1 : ((num == 0) ? 0 : 1); |
| 258 | } | ||
| 259 | 4 | int gate_math_signum_i64(gate_int64_t num) | |
| 260 | { | ||
| 261 |
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4 | return (num < 0) ? -1 : ((num == 0) ? 0 : 1); |
| 262 | } | ||
| 263 | 4 | int gate_math_signum_r32(gate_real32_t num) | |
| 264 | { | ||
| 265 |
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4 | return gate_math_iszerof(num) ? 0 : ((num < 0.0f) ? -1 : 1); |
| 266 | } | ||
| 267 | 4 | int gate_math_signum_r64(gate_real64_t num) | |
| 268 | { | ||
| 269 |
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4 | return gate_math_iszero(num) ? 0 : ((num < 0.0) ? -1 : 1); |
| 270 | } | ||
| 271 | |||
| 272 | |||
| 273 | 3 | gate_int8_t gate_math_abs_i8(gate_int8_t num) | |
| 274 | { | ||
| 275 | 3 | return num < 0 ? -num : num; | |
| 276 | } | ||
| 277 | 819 | gate_int16_t gate_math_abs_i16(gate_int16_t num) | |
| 278 | { | ||
| 279 | 819 | return num < 0 ? -num : num; | |
| 280 | } | ||
| 281 | 166 | gate_int32_t gate_math_abs_i32(gate_int32_t num) | |
| 282 | { | ||
| 283 | 166 | return num < 0 ? -num : num; | |
| 284 | } | ||
| 285 | 3 | gate_int64_t gate_math_abs_i64(gate_int64_t num) | |
| 286 | { | ||
| 287 | 3 | return num < 0 ? -num : num; | |
| 288 | } | ||
| 289 | 6 | gate_real32_t gate_math_abs_r32(gate_real32_t num) | |
| 290 | { | ||
| 291 |
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6 | return num < 0.0f ? -num : num; |
| 292 | } | ||
| 293 | 7 | gate_real64_t gate_math_abs_r64(gate_real64_t num) | |
| 294 | { | ||
| 295 |
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7 | return num < 0.0 ? -num : num; |
| 296 | } | ||
| 297 | |||
| 298 | #define gate_math_min_type(type, va_type, count) \ | ||
| 299 | type ret = 0; \ | ||
| 300 | type tmp; \ | ||
| 301 | va_list vl; \ | ||
| 302 | if(count != 0) \ | ||
| 303 | { \ | ||
| 304 | va_start(vl, count); \ | ||
| 305 | ret = (type)va_arg(vl, va_type); \ | ||
| 306 | while(--count) \ | ||
| 307 | { \ | ||
| 308 | tmp = (type)va_arg(vl, va_type); \ | ||
| 309 | if(tmp < ret) \ | ||
| 310 | { \ | ||
| 311 | ret = tmp; \ | ||
| 312 | } \ | ||
| 313 | } \ | ||
| 314 | va_end(vl); \ | ||
| 315 | } \ | ||
| 316 | return ret | ||
| 317 | |||
| 318 | #define gate_math_max_type(type, va_type, count) \ | ||
| 319 | type ret = 0; \ | ||
| 320 | type tmp; \ | ||
| 321 | va_list vl; \ | ||
| 322 | if(count != 0) \ | ||
| 323 | { \ | ||
| 324 | va_start(vl, count); \ | ||
| 325 | ret = (type)va_arg(vl, va_type); \ | ||
| 326 | while(--count) \ | ||
| 327 | { \ | ||
| 328 | tmp = (type)va_arg(vl, va_type); \ | ||
| 329 | if(tmp > ret) \ | ||
| 330 | { \ | ||
| 331 | ret = tmp; \ | ||
| 332 | } \ | ||
| 333 | } \ | ||
| 334 | va_end(vl); \ | ||
| 335 | } \ | ||
| 336 | return ret | ||
| 337 | |||
| 338 | |||
| 339 | 1 | gate_int16_t gate_math_min_i16(gate_size_t count, ...) | |
| 340 | { | ||
| 341 |
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3 | gate_math_min_type(gate_int16_t, int, count); |
| 342 | } | ||
| 343 | 1 | gate_int32_t gate_math_min_i32(gate_size_t count, ...) | |
| 344 | { | ||
| 345 |
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3 | gate_math_min_type(gate_int32_t, gate_int32_t, count); |
| 346 | } | ||
| 347 | 1 | gate_int64_t gate_math_min_i64(gate_size_t count, ...) | |
| 348 | { | ||
| 349 |
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3 | gate_math_min_type(gate_int64_t, gate_int64_t, count); |
| 350 | } | ||
| 351 | 1 | gate_real32_t gate_math_min_r32(gate_size_t count, ...) | |
| 352 | { | ||
| 353 |
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3 | gate_math_min_type(gate_real32_t, gate_real64_t, count); |
| 354 | } | ||
| 355 | 1 | gate_real64_t gate_math_min_r64(gate_size_t count, ...) | |
| 356 | { | ||
| 357 |
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3 | gate_math_min_type(gate_real64_t, gate_real64_t, count); |
| 358 | } | ||
| 359 | |||
| 360 | 273 | gate_int16_t gate_math_max_i16(gate_size_t count, ...) | |
| 361 | { | ||
| 362 |
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819 | gate_math_max_type(gate_int16_t, int, count); |
| 363 | } | ||
| 364 | 1 | gate_int32_t gate_math_max_i32(gate_size_t count, ...) | |
| 365 | { | ||
| 366 |
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3 | gate_math_max_type(gate_int32_t, gate_int32_t, count); |
| 367 | } | ||
| 368 | 1 | gate_int64_t gate_math_max_i64(gate_size_t count, ...) | |
| 369 | { | ||
| 370 |
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3 | gate_math_max_type(gate_int64_t, gate_int64_t, count); |
| 371 | } | ||
| 372 | 1 | gate_real32_t gate_math_max_r32(gate_size_t count, ...) | |
| 373 | { | ||
| 374 |
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3 | gate_math_max_type(gate_real32_t, gate_real64_t, count); |
| 375 | } | ||
| 376 | 1 | gate_real64_t gate_math_max_r64(gate_size_t count, ...) | |
| 377 | { | ||
| 378 |
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3 | gate_math_max_type(gate_real64_t, gate_real64_t, count); |
| 379 | } | ||
| 380 | 7 | gate_uint8_t gate_math_decimal_length(gate_real64_t value) | |
| 381 | { | ||
| 382 | 7 | gate_uint8_t len = 0; | |
| 383 | 7 | gate_real64_t factor = 1.0; | |
| 384 | gate_real64_t test_value; | ||
| 385 | gate_real64_t diff; | ||
| 386 | |||
| 387 |
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7 | if (value < 0.0) |
| 388 | { | ||
| 389 | ✗ | value = -value; | |
| 390 | } | ||
| 391 | |||
| 392 |
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30 | while (len < 20) |
| 393 | { | ||
| 394 | 30 | test_value = value * factor; | |
| 395 | 30 | diff = (test_value - ((gate_real64_t)(gate_int64_t)test_value)); | |
| 396 |
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30 | if (gate_math_iszero(diff)) |
| 397 | { | ||
| 398 | 7 | break; | |
| 399 | } | ||
| 400 | 23 | factor *= 10.0; | |
| 401 | 23 | ++len; | |
| 402 | } | ||
| 403 | 7 | return len; | |
| 404 | } | ||
| 405 | |||
| 406 | 21 | gate_real64_t gate_math_deg2rad(gate_real64_t value) | |
| 407 | { | ||
| 408 | 21 | return value * GATE_MATH_CONST_PI / 180.0; | |
| 409 | } | ||
| 410 | 11 | gate_real64_t gate_math_rad2deg(gate_real64_t value) | |
| 411 | { | ||
| 412 | 11 | return value * 180.0 / GATE_MATH_CONST_PI; | |
| 413 | } | ||
| 414 | |||
| 415 | 1 | gate_int64_t gate_math_pow_i64(gate_int64_t base, gate_uint16_t exp) | |
| 416 | { | ||
| 417 | gate_uint8_t n; | ||
| 418 | 1 | gate_int64_t ret = 1; | |
| 419 |
2/2✓ Branch 0 taken 19 times.
✓ Branch 1 taken 1 times.
|
20 | for (n = 0; n != exp; ++n) |
| 420 | { | ||
| 421 | 19 | ret *= base; | |
| 422 | } | ||
| 423 | 1 | return ret; | |
| 424 | } | ||
| 425 | |||
| 426 | ✗ | gate_real64_t gate_math_pow_iexp(gate_real64_t base, gate_uint16_t exp) | |
| 427 | { | ||
| 428 | gate_uint16_t n; | ||
| 429 | ✗ | gate_real64_t ret = 1.0; | |
| 430 | ✗ | for (n = 0; n != exp; ++n) | |
| 431 | { | ||
| 432 | ✗ | ret *= base; | |
| 433 | } | ||
| 434 | ✗ | return ret; | |
| 435 | } | ||
| 436 | |||
| 437 | 5 | gate_real64_t gate_math_acosh(gate_real64_t value) | |
| 438 | { | ||
| 439 | 5 | return gate_math_log(value + gate_math_sqrt(value * value - 1.0)); | |
| 440 | } | ||
| 441 | 6 | gate_real64_t gate_math_asinh(gate_real64_t value) | |
| 442 | { | ||
| 443 | 6 | return gate_math_log(value + gate_math_sqrt(value * value + 1.0)); | |
| 444 | } | ||
| 445 | 6 | gate_real64_t gate_math_atanh(gate_real64_t value) | |
| 446 | { | ||
| 447 | 6 | return gate_math_log((1.0 + value) / (1.0 - value)) / 2.0; | |
| 448 | } | ||
| 449 | |||
| 450 | |||
| 451 | |||
| 452 | |||
| 453 | |||
| 454 | |||
| 455 | |||
| 456 | #if defined(GATE_CORE_MATH_STD_IMPL) | ||
| 457 | |||
| 458 | #include <math.h> | ||
| 459 | |||
| 460 | 40 | gate_real64_t gate_math_cos(gate_real64_t value) | |
| 461 | { | ||
| 462 | 40 | return cos(value); | |
| 463 | } | ||
| 464 | 9 | gate_real64_t gate_math_sin(gate_real64_t value) | |
| 465 | { | ||
| 466 | 9 | return sin(value); | |
| 467 | } | ||
| 468 | 9 | gate_real64_t gate_math_tan(gate_real64_t value) | |
| 469 | { | ||
| 470 | 9 | return tan(value); | |
| 471 | } | ||
| 472 | 6 | gate_real64_t gate_math_acos(gate_real64_t value) | |
| 473 | { | ||
| 474 | 6 | return acos(value); | |
| 475 | } | ||
| 476 | 9 | gate_real64_t gate_math_asin(gate_real64_t value) | |
| 477 | { | ||
| 478 | 9 | return asin(value); | |
| 479 | } | ||
| 480 | 12 | gate_real64_t gate_math_atan(gate_real64_t value) | |
| 481 | { | ||
| 482 | 12 | return atan(value); | |
| 483 | } | ||
| 484 | 2 | gate_real64_t gate_math_atan2(gate_real64_t y, gate_real64_t x) | |
| 485 | { | ||
| 486 | 2 | return atan2(y, x); | |
| 487 | } | ||
| 488 | 6 | gate_real64_t gate_math_cosh(gate_real64_t value) | |
| 489 | { | ||
| 490 | 6 | return cosh(value); | |
| 491 | } | ||
| 492 | 6 | gate_real64_t gate_math_sinh(gate_real64_t value) | |
| 493 | { | ||
| 494 | 6 | return sinh(value); | |
| 495 | } | ||
| 496 | 6 | gate_real64_t gate_math_tanh(gate_real64_t value) | |
| 497 | { | ||
| 498 | 6 | return tanh(value); | |
| 499 | } | ||
| 500 | |||
| 501 | 9 | gate_real64_t gate_math_exp(gate_real64_t value) | |
| 502 | { | ||
| 503 | 9 | return exp(value); | |
| 504 | } | ||
| 505 | 2 | gate_real64_t gate_math_frexp(gate_real64_t value, int* exp) | |
| 506 | { | ||
| 507 | 2 | return frexp(value, exp); | |
| 508 | } | ||
| 509 | ✗ | gate_real64_t gate_math_ldexp(gate_real64_t value, int exp) | |
| 510 | { | ||
| 511 | ✗ | return ldexp(value, exp); | |
| 512 | } | ||
| 513 | 24 | gate_real64_t gate_math_log(gate_real64_t value) | |
| 514 | { | ||
| 515 | 24 | return log(value); | |
| 516 | } | ||
| 517 | 2 | gate_real64_t gate_math_log2(gate_real64_t value) | |
| 518 | { | ||
| 519 | static const gate_real64_t log2inverse = 1.4426950408889634; | ||
| 520 | 2 | return log(value) * log2inverse; | |
| 521 | } | ||
| 522 | 6 | gate_real64_t gate_math_log10(gate_real64_t value) | |
| 523 | { | ||
| 524 | 6 | return log10(value); | |
| 525 | } | ||
| 526 | 2 | gate_real64_t gate_math_modf(gate_real64_t value, double* intpart) | |
| 527 | { | ||
| 528 | 2 | return modf(value, intpart); | |
| 529 | } | ||
| 530 | |||
| 531 | 2 | gate_real64_t gate_math_pow(gate_real64_t base, gate_real64_t exp) | |
| 532 | { | ||
| 533 | 2 | return pow(base, exp); | |
| 534 | } | ||
| 535 | 21 | gate_real64_t gate_math_sqrt(gate_real64_t value) | |
| 536 | { | ||
| 537 | 21 | return sqrt(value); | |
| 538 | } | ||
| 539 | |||
| 540 | 7 | gate_real64_t gate_math_ceil(gate_real64_t value) | |
| 541 | { | ||
| 542 | 7 | return ceil(value); | |
| 543 | } | ||
| 544 | 9 | gate_real64_t gate_math_floor(gate_real64_t value) | |
| 545 | { | ||
| 546 | 9 | return floor(value); | |
| 547 | } | ||
| 548 | |||
| 549 | |||
| 550 | #endif /* GATE_CORE_MATH_STD_IMPL */ | ||
| 551 | |||
| 552 | |||
| 553 | |||
| 554 | #if defined(GATE_CORE_MATH_EFI_IMPL) | ||
| 555 | |||
| 556 | static gate_real64_t normalize_angle(gate_real64_t angle) | ||
| 557 | { | ||
| 558 | while (angle <= -GATE_MATH_CONST_PI) | ||
| 559 | { | ||
| 560 | angle += GATE_MATH_CONST_PI; | ||
| 561 | } | ||
| 562 | while (angle > GATE_MATH_CONST_PI) | ||
| 563 | { | ||
| 564 | angle -= GATE_MATH_CONST_PI; | ||
| 565 | } | ||
| 566 | return angle; | ||
| 567 | } | ||
| 568 | |||
| 569 | gate_real64_t gate_math_cos(gate_real64_t value) | ||
| 570 | { | ||
| 571 | static gate_real64_t const n2 = 2.0; | ||
| 572 | static gate_real64_t const n4 = 24.0; | ||
| 573 | static gate_real64_t const n6 = 720.0; | ||
| 574 | static gate_real64_t const n8 = 40320.0; | ||
| 575 | static gate_real64_t const n10 = 3628800.0; | ||
| 576 | static gate_real64_t const n12 = 479001600.0; | ||
| 577 | gate_real64_t const x = normalize_angle(value); | ||
| 578 | gate_real64_t const x2 = x * x; | ||
| 579 | gate_real64_t const x4 = x2 * x * x; | ||
| 580 | gate_real64_t const x6 = x4 * x * x; | ||
| 581 | gate_real64_t const x8 = x6 * x * x; | ||
| 582 | gate_real64_t const x10 = x8 * x * x; | ||
| 583 | gate_real64_t const x12 = x10 * x * x; | ||
| 584 | |||
| 585 | return 1 - x2 / n2 + x4 / n4 - x6 / n6 + x8 / n8 - x10 / n10 + x12 / n12; | ||
| 586 | } | ||
| 587 | |||
| 588 | |||
| 589 | |||
| 590 | gate_real64_t gate_math_sin(gate_real64_t value) | ||
| 591 | { | ||
| 592 | static gate_real64_t const n3 = 6.0; | ||
| 593 | static gate_real64_t const n5 = 120.0; | ||
| 594 | static gate_real64_t const n7 = 5040.0; | ||
| 595 | static gate_real64_t const n9 = 362880.0; | ||
| 596 | static gate_real64_t const n11 = 39916800.0; | ||
| 597 | static gate_real64_t const n13 = 6227020800.0; | ||
| 598 | gate_real64_t const x = normalize_angle(value); | ||
| 599 | gate_real64_t const x3 = x * x * x; | ||
| 600 | gate_real64_t const x5 = x3 * x * x; | ||
| 601 | gate_real64_t const x7 = x5 * x * x; | ||
| 602 | gate_real64_t const x9 = x7 * x * x; | ||
| 603 | gate_real64_t const x11 = x9 * x * x; | ||
| 604 | gate_real64_t const x13 = x11 * x * x; | ||
| 605 | |||
| 606 | return x - x3 / n3 + x5 / n5 - x7 / n7 + x9 / n9 - x11 / n11 + x13 / n13; | ||
| 607 | } | ||
| 608 | gate_real64_t gate_math_tan(gate_real64_t value) | ||
| 609 | { | ||
| 610 | return gate_math_sin(value) / gate_math_cos(value); | ||
| 611 | } | ||
| 612 | |||
| 613 | gate_real64_t gate_math_asin(gate_real64_t value) | ||
| 614 | { | ||
| 615 | /* https://de.wikipedia.org/wiki/Arkussinus_und_Arkuskosinus#Reihenentwicklungen */ | ||
| 616 | |||
| 617 | static double const ret_0_96 = 1.2870022176; | ||
| 618 | /*static double const ret_1_00 = GATE_MATH_CONST_PI * 0.5;*/ | ||
| 619 | static double const diff_1_00 = GATE_MATH_CONST_PI * 0.5 - 1.2870022176; | ||
| 620 | double ret = value; | ||
| 621 | |||
| 622 | if (value > 0.96) | ||
| 623 | { | ||
| 624 | /* iterative solution becomes unstable for value > 0.96 | ||
| 625 | just apply a quick and dirty linear patch */ | ||
| 626 | double factor = (value - 0.96) / (1.00 - 0.96); | ||
| 627 | ret = ret_0_96 + diff_1_00 * factor; | ||
| 628 | } | ||
| 629 | else | ||
| 630 | { | ||
| 631 | static unsigned const n_max = 107; /* quite OK up to 0.96 */ | ||
| 632 | unsigned n; | ||
| 633 | double x = value; | ||
| 634 | double a = 1; | ||
| 635 | double b = 1; | ||
| 636 | for (n = 3; n != n_max; n += 2) | ||
| 637 | { | ||
| 638 | x *= value * value; | ||
| 639 | a *= ((double)n - 2.0); | ||
| 640 | b *= ((double)n - 1.0); | ||
| 641 | ret += a * x / (b * (double)n); | ||
| 642 | } | ||
| 643 | } | ||
| 644 | |||
| 645 | return ret; | ||
| 646 | } | ||
| 647 | gate_real64_t gate_math_acos(gate_real64_t value) | ||
| 648 | { | ||
| 649 | /* https://stackoverflow.com/questions/3380628/fast-arc-cos-algorithm/20914630 */ | ||
| 650 | /* return (-0.69813170079773212 * value * value - 0.87266462599716477) * value + 1.5707963267948966; */ | ||
| 651 | return GATE_MATH_CONST_PI * 0.5 - gate_math_asin(value); | ||
| 652 | } | ||
| 653 | gate_real64_t gate_math_atan(gate_real64_t value) | ||
| 654 | { | ||
| 655 | gate_real64_t ret; | ||
| 656 | ret = gate_math_asin(value / gate_math_sqrt(1 + value * value)); | ||
| 657 | return ret; | ||
| 658 | } | ||
| 659 | gate_real64_t gate_math_atan2(gate_real64_t y, gate_real64_t x) | ||
| 660 | { | ||
| 661 | /* TODO */ | ||
| 662 | return 0.0; | ||
| 663 | } | ||
| 664 | gate_real64_t gate_math_sinh(gate_real64_t value) | ||
| 665 | { | ||
| 666 | return 0.5 * (gate_math_exp(value) - gate_math_exp(-value)); | ||
| 667 | } | ||
| 668 | gate_real64_t gate_math_cosh(gate_real64_t value) | ||
| 669 | { | ||
| 670 | return 0.5 * (gate_math_exp(value) + gate_math_exp(-value)); | ||
| 671 | } | ||
| 672 | gate_real64_t gate_math_tanh(gate_real64_t value) | ||
| 673 | { | ||
| 674 | return gate_math_sinh(value) / gate_math_cosh(value); | ||
| 675 | } | ||
| 676 | |||
| 677 | gate_real64_t gate_math_exp(gate_real64_t value) | ||
| 678 | { | ||
| 679 | /* https://www.pseudorandom.com/implementing-exp */ | ||
| 680 | gate_real64_t x0, tn; | ||
| 681 | gate_int64_t i, n; | ||
| 682 | |||
| 683 | if (gate_math_iszero(value)) | ||
| 684 | { | ||
| 685 | return 1.0; | ||
| 686 | } | ||
| 687 | x0 = gate_math_abs_r64(value); | ||
| 688 | tn = 1.0; | ||
| 689 | n = 12; | ||
| 690 | n *= (gate_int64_t)gate_math_ceil(x0 * GATE_MATH_CONST_E); | ||
| 691 | for (i = n; i > 0; i--) | ||
| 692 | { | ||
| 693 | tn = tn * (x0 / i) + 1.0; | ||
| 694 | } | ||
| 695 | |||
| 696 | if (value < 0.0) | ||
| 697 | { | ||
| 698 | tn = 1.0 / tn; | ||
| 699 | } | ||
| 700 | return tn; | ||
| 701 | } | ||
| 702 | gate_real64_t gate_math_frexp(gate_real64_t value, int* exp) | ||
| 703 | { | ||
| 704 | /* TODO */ | ||
| 705 | return 0.0; | ||
| 706 | } | ||
| 707 | gate_real64_t gate_math_ldexp(gate_real64_t value, int exp) | ||
| 708 | { | ||
| 709 | /* TODO */ | ||
| 710 | return 0.0; | ||
| 711 | } | ||
| 712 | |||
| 713 | static unsigned msb(unsigned v) | ||
| 714 | { | ||
| 715 | unsigned ret = 0; | ||
| 716 | while (v >>= 1) | ||
| 717 | { | ||
| 718 | ret++; | ||
| 719 | } | ||
| 720 | return ret; | ||
| 721 | } | ||
| 722 | |||
| 723 | static float log_n(float value) | ||
| 724 | { | ||
| 725 | /* https://stackoverflow.com/questions/9799041/efficient-implementation-of-natural-logarithm-ln-and-exponentiation */ | ||
| 726 | int log2; | ||
| 727 | float divisor, x, result; | ||
| 728 | |||
| 729 | log2 = msb((int)value); // See: https://stackoverflow.com/a/4970859/6630230 | ||
| 730 | divisor = (float)(1 << log2); | ||
| 731 | x = value / divisor; | ||
| 732 | result = -1.7417939f + (2.8212026f + (-1.4699568f + (0.44717955f - 0.056570851f * x) * x) * x) * x; | ||
| 733 | result += ((float)log2) * 0.69314718f; | ||
| 734 | |||
| 735 | return result; | ||
| 736 | } | ||
| 737 | |||
| 738 | |||
| 739 | gate_real64_t gate_math_log(gate_real64_t value) | ||
| 740 | { | ||
| 741 | return (gate_real64_t)log_n((float)value); | ||
| 742 | } | ||
| 743 | gate_real64_t gate_math_log10(gate_real64_t value) | ||
| 744 | { | ||
| 745 | return gate_math_log(value) / gate_math_log(10.0); | ||
| 746 | } | ||
| 747 | gate_real64_t gate_math_modf(gate_real64_t value, gate_real64_t* intpart) | ||
| 748 | { | ||
| 749 | gate_real64_t ret; | ||
| 750 | gate_uint64_t ui; | ||
| 751 | if (value < 0.0) | ||
| 752 | { | ||
| 753 | ui = (gate_uint64_t)-value; | ||
| 754 | ret = -value - (gate_real64_t)ui; | ||
| 755 | if (intpart) | ||
| 756 | { | ||
| 757 | *intpart = -((gate_real64_t)ui); | ||
| 758 | } | ||
| 759 | } | ||
| 760 | else | ||
| 761 | { | ||
| 762 | ui = (gate_uint64_t)value; | ||
| 763 | ret = value - (gate_real64_t)ui; | ||
| 764 | if (intpart) | ||
| 765 | { | ||
| 766 | *intpart = (gate_real64_t)ui; | ||
| 767 | } | ||
| 768 | } | ||
| 769 | return ret; | ||
| 770 | } | ||
| 771 | |||
| 772 | gate_real64_t gate_math_pow(gate_real64_t base, gate_real64_t exp) | ||
| 773 | { | ||
| 774 | if (exp < 0.0) | ||
| 775 | { | ||
| 776 | return 1.0 / gate_math_pow_iexp(base, (gate_uint16_t)-exp); | ||
| 777 | } | ||
| 778 | else | ||
| 779 | { | ||
| 780 | return gate_math_pow_iexp(base, (gate_uint16_t)exp); | ||
| 781 | } | ||
| 782 | return 0.0; | ||
| 783 | } | ||
| 784 | |||
| 785 | union f_rsqrt_helper | ||
| 786 | { | ||
| 787 | float f; | ||
| 788 | gate_uint32_t i; | ||
| 789 | }; | ||
| 790 | |||
| 791 | |||
| 792 | union d_rsqrt_helper | ||
| 793 | { | ||
| 794 | double d; | ||
| 795 | gate_uint64_t i; | ||
| 796 | }; | ||
| 797 | |||
| 798 | /* https://en.wikipedia.org/wiki/Fast_inverse_square_root */ | ||
| 799 | /* https://stackoverflow.com/questions/11644441/fast-inverse-square-root-on-x64/11644533 */ | ||
| 800 | static float f_rsqrt(float number) | ||
| 801 | { | ||
| 802 | static const float threehalfs = 1.5F; | ||
| 803 | const float x2 = number * 0.5F; | ||
| 804 | |||
| 805 | union f_rsqrt_helper conv; | ||
| 806 | conv.f = number; | ||
| 807 | conv.i = 0x5f3759df - (conv.i >> 1); | ||
| 808 | conv.f *= threehalfs - (x2 * conv.f * conv.f); | ||
| 809 | return conv.f; | ||
| 810 | } | ||
| 811 | |||
| 812 | static double d_rsqrt(double number) | ||
| 813 | { | ||
| 814 | double y = number; | ||
| 815 | double x2 = y * 0.5; | ||
| 816 | |||
| 817 | union d_rsqrt_helper conv; | ||
| 818 | conv.d = y; | ||
| 819 | conv.i = 0x5fe6eb50c7b537a9 - (conv.i >> 1); | ||
| 820 | y = conv.d; | ||
| 821 | y = y * (1.5 - (x2 * y * y)); | ||
| 822 | y = y * (1.5 - (x2 * y * y)); | ||
| 823 | return y; | ||
| 824 | } | ||
| 825 | |||
| 826 | |||
| 827 | gate_real64_t gate_math_sqrt(gate_real64_t value) | ||
| 828 | { | ||
| 829 | double num = gate_math_abs_r64((double)value); | ||
| 830 | return (gate_real64_t)(1.0 / d_rsqrt(num)); | ||
| 831 | } | ||
| 832 | |||
| 833 | gate_real64_t gate_math_ceil(gate_real64_t value) | ||
| 834 | { | ||
| 835 | gate_int64_t i = (gate_int64_t)value; | ||
| 836 | gate_real64_t diff = value - (gate_real64_t)i; | ||
| 837 | if (!gate_math_iszero(diff)) | ||
| 838 | { | ||
| 839 | if (value >= 0.0) | ||
| 840 | { | ||
| 841 | i = (gate_int64_t)(value + 1.0); | ||
| 842 | } | ||
| 843 | else | ||
| 844 | { | ||
| 845 | i = -(gate_int64_t)(-value); | ||
| 846 | } | ||
| 847 | } | ||
| 848 | return (gate_real64_t)i; | ||
| 849 | } | ||
| 850 | gate_real64_t gate_math_floor(gate_real64_t value) | ||
| 851 | { | ||
| 852 | gate_int64_t i = (gate_int64_t)value; | ||
| 853 | gate_real64_t diff = value - (gate_real64_t)i; | ||
| 854 | if (!gate_math_iszero(diff)) | ||
| 855 | { | ||
| 856 | if (value >= 0.0) | ||
| 857 | { | ||
| 858 | i = (gate_int64_t)(value); | ||
| 859 | } | ||
| 860 | else | ||
| 861 | { | ||
| 862 | i = -(gate_int64_t)(-value + 1.0); | ||
| 863 | } | ||
| 864 | } | ||
| 865 | return (gate_real64_t)i; | ||
| 866 | } | ||
| 867 | |||
| 868 | #endif /* GATE_CORE_MATH_EFI_IMPL */ | ||
| 869 | |||
| 870 |