include/a/math.h

   1 /*!
   2  @file math.h
   3  @brief mathematical algorithm library
   4 */
   5
   6 #ifndef LIBA_MATH_H
   7 #define LIBA_MATH_H
   8
   9 #include "a.h"
  10 #include <math.h>
  11
  12 /*!
  13  @ingroup liba
  14  @addtogroup a_math mathematical algorithm library
  15  @{
  16 */
  17
  18 /*! \f$ e \f$ */
  19 #define A_E 2.71828182845904523536
  20 /*! \f$ \log_{2}{e}=\frac{1}{\ln{2}} \f$ */
  21 #define A_LOG2E 1.44269504088896340736
  22 /*! \f$ \lg{e}=\frac{1}{\ln{2}+\ln{5}} \f$ */
  23 #define A_LOG10E 0.434294481903251827651
  24 /*! \f$ \ln{2} \f$ */
  25 #define A_LN2 0.693147180559945309417
  26 /*! \f$ \frac{1}{\ln{2}} \f$ */
  27 #define A_LN1_2 3.32192809488736218171
  28 /*! \f$ \ln{10} \f$ */
  29 #define A_LN10 2.30258509299404568402
  30 /*! \f$ \frac{1}{\ln{10}} \f$ */
  31 #define A_LN1_10 0.434294481903251827651
  32 /*! \f$ \pi \f$ */
  33 #define A_PI 3.14159265358979323846
  34 /*! \f$ 2\pi \f$ */
  35 #define A_TAU 6.28318530717958647693
  36 /*! \f$ \frac{\pi}{2} \f$ */
  37 #define A_PI_2 1.57079632679489661923
  38 /*! \f$ \frac{\pi}{4} \f$ */
  39 #define A_PI_4 0.785398163397448309616
  40 /*! \f$ \frac{1}{\pi} \f$ */
  41 #define A_1_PI 0.318309886183790671538
  42 /*! \f$ \frac{2}{\pi} \f$ */
  43 #define A_2_PI 0.636619772367581343076
  44 /*! \f$ \frac{1}{2\pi} \f$ */
  45 #define A_1_TAU 0.159154943091895335769
  46 /*! \f$ \frac{2}{\sqrt{\pi}} \f$ */
  47 #define A_2_SQRTPI 1.12837916709551257390
  48 /*! \f$ \sqrt{2} \f$ */
  49 #define A_SQRT2 1.41421356237309504880
  50 /*! \f$ \frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2} \f$ */
  51 #define A_SQRT1_2 0.707106781186547524401
  52 /*! \f$ \sqrt{3} \f$ */
  53 #define A_SQRT3 1.73205080756887729352
  54 /*! \f$ \frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3} \f$ */
  55 #define A_SQRT1_3 0.57735026918962576450
  56
  57 #if defined(__cplusplus)
  58 extern "C" {
  59 #endif /* __cplusplus */
  60
  61 /*!
  62  @brief reciprocal of square-root, \f$ \frac{1}{\sqrt{x}} \f$
  63  @details http://en.wikipedia.org/wiki/Fast_inverse_square_root
  64  @param[in] x independent variable
  65  @return calculated result
  66 */
  67 A_EXTERN a_f32 a_f32_rsqrt(a_f32 x);
  68 A_EXTERN a_f64 a_f64_rsqrt(a_f64 x);
  69
  70 /*!
  71  @brief square root of an unsigned integer
  72  @param[in] x independent variable
  73  @return calculated result
  74 */
  75 A_EXTERN a_u16 a_u32_sqrt(a_u32 x);
  76 A_EXTERN a_u32 a_u64_sqrt(a_u64 x);
  77
  78 #if defined(__cplusplus)
  79 } /* extern "C" */
  80 #endif /* __cplusplus */
  81
  82 #define a_f32_modf A_F32_F(modf)
  83 #define a_f32_frexp A_F32_F(frexp)
  84 #define a_f32_ldexp A_F32_F(ldexp)
  85 #define a_f32_scalbn A_F32_F(scalbn)
  86 #define a_f32_scalbln A_F32_F(scalbln)
  87 #define a_f32_nextafter A_F32_F(nextafter)
  88 #define a_f32_nexttoward A_F32_F(nexttoward)
  89 #define a_f32_copysign A_F32_F(copysign)
  90
  91 #define a_f32_ma A_F32_F(fma)
  92 #define a_f32_nan A_F32_F(nan)
  93 #define a_f32_abs A_F32_F(fabs)
  94 #define a_f32_mod A_F32_F(fmod)
  95 #define a_f32_max A_F32_F(fmax)
  96 #define a_f32_min A_F32_F(fmin)
  97 #define a_f32_dim A_F32_F(fdim)
  98 #define a_f32_remquo A_F32_F(remquo)
  99 #define a_f32_remainder A_F32_F(remainder)
 100
 101 #define a_f32_exp A_F32_F(exp)
 102 #define a_f32_exp2 A_F32_F(exp2)
 103 #define a_f32_expm1 A_F32_F(expm1)
 104
 105 #define a_f32_log A_F32_F(log)
 106 #define a_f32_logb A_F32_F(logb)
 107 #define a_f32_log2 A_F32_F(log2)
 108 #define a_f32_log10 A_F32_F(log10)
 109 #define a_f32_log1p A_F32_F(log1p)
 110 #define a_f32_ilogb A_F32_F(ilogb)
 111
 112 #define a_f32_pow A_F32_F(pow)
 113 #define a_f32_sqrt A_F32_F(sqrt)
 114 #define a_f32_cbrt A_F32_F(cbrt)
 115 #define a_f32_hypot A_F32_F(hypot)
 116
 117 #define a_f32_sin A_F32_F(sin)
 118 #define a_f32_cos A_F32_F(cos)
 119 #define a_f32_tan A_F32_F(tan)
 120 #define a_f32_asin A_F32_F(asin)
 121 #define a_f32_acos A_F32_F(acos)
 122 #define a_f32_atan A_F32_F(atan)
 123 #define a_f32_atan2 A_F32_F(atan2)
 124
 125 #define a_f32_sinh A_F32_F(sinh)
 126 #define a_f32_cosh A_F32_F(cosh)
 127 #define a_f32_tanh A_F32_F(tanh)
 128 #define a_f32_asinh A_F32_F(asinh)
 129 #define a_f32_acosh A_F32_F(acosh)
 130 #define a_f32_atanh A_F32_F(atanh)
 131
 132 #define a_f32_erf A_F32_F(erf)
 133 #define a_f32_erfc A_F32_F(erfc)
 134 #define a_f32_tgamma A_F32_F(tgamma)
 135 #define a_f32_lgamma A_F32_F(lgamma)
 136
 137 #define a_f32_ceil A_F32_F(ceil)
 138 #define a_f32_floor A_F32_F(floor)
 139 #define a_f32_trunc A_F32_F(trunc)
 140 #define a_f32_round A_F32_F(round)
 141 #define a_f32_lround A_F32_F(lround)
 142 #define a_f32_llround A_F32_F(llround)
 143 #define a_f32_nearbyint A_F32_F(nearbyint)
 144 #define a_f32_rint A_F32_F(rint)
 145 #define a_f32_lrintt A_F32_F(lrint)
 146 #define a_f32_llrintt A_F32_F(llrint)
 147
 148 #define a_f64_modf A_F64_F(modf)
 149 #define a_f64_frexp A_F64_F(frexp)
 150 #define a_f64_ldexp A_F64_F(ldexp)
 151 #define a_f64_scalbn A_F64_F(scalbn)
 152 #define a_f64_scalbln A_F64_F(scalbln)
 153 #define a_f64_nextafter A_F64_F(nextafter)
 154 #define a_f64_nexttoward A_F64_F(nexttoward)
 155 #define a_f64_copysign A_F64_F(copysign)
 156
 157 #define a_f64_ma A_F64_F(fma)
 158 #define a_f64_nan A_F64_F(nan)
 159 #define a_f64_abs A_F64_F(fabs)
 160 #define a_f64_mod A_F64_F(fmod)
 161 #define a_f64_max A_F64_F(fmax)
 162 #define a_f64_min A_F64_F(fmin)
 163 #define a_f64_dim A_F64_F(fdim)
 164 #define a_f64_remquo A_F64_F(remquo)
 165 #define a_f64_remainder A_F64_F(remainder)
 166
 167 #define a_f64_exp A_F64_F(exp)
 168 #define a_f64_exp2 A_F64_F(exp2)
 169 #define a_f64_expm1 A_F64_F(expm1)
 170
 171 #define a_f64_log A_F64_F(log)
 172 #define a_f64_logb A_F64_F(logb)
 173 #define a_f64_log2 A_F64_F(log2)
 174 #define a_f64_log10 A_F64_F(log10)
 175 #define a_f64_log1p A_F64_F(log1p)
 176 #define a_f64_ilogb A_F64_F(ilogb)
 177
 178 #define a_f64_pow A_F64_F(pow)
 179 #define a_f64_sqrt A_F64_F(sqrt)
 180 #define a_f64_cbrt A_F64_F(cbrt)
 181 #define a_f64_hypot A_F64_F(hypot)
 182
 183 #define a_f64_sin A_F64_F(sin)
 184 #define a_f64_cos A_F64_F(cos)
 185 #define a_f64_tan A_F64_F(tan)
 186 #define a_f64_asin A_F64_F(asin)
 187 #define a_f64_acos A_F64_F(acos)
 188 #define a_f64_atan A_F64_F(atan)
 189 #define a_f64_atan2 A_F64_F(atan2)
 190
 191 #define a_f64_sinh A_F64_F(sinh)
 192 #define a_f64_cosh A_F64_F(cosh)
 193 #define a_f64_tanh A_F64_F(tanh)
 194 #define a_f64_asinh A_F64_F(asinh)
 195 #define a_f64_acosh A_F64_F(acosh)
 196 #define a_f64_atanh A_F64_F(atanh)
 197
 198 #define a_f64_erf A_F64_F(erf)
 199 #define a_f64_erfc A_F64_F(erfc)
 200 #define a_f64_tgamma A_F64_F(tgamma)
 201 #define a_f64_lgamma A_F64_F(lgamma)
 202
 203 #define a_f64_ceil A_F64_F(ceil)
 204 #define a_f64_floor A_F64_F(floor)
 205 #define a_f64_trunc A_F64_F(trunc)
 206 #define a_f64_round A_F64_F(round)
 207 #define a_f64_lround A_F64_F(lround)
 208 #define a_f64_llround A_F64_F(llround)
 209 #define a_f64_nearbyint A_F64_F(nearbyint)
 210 #define a_f64_rint A_F64_F(rint)
 211 #define a_f64_lrintt A_F64_F(lrint)
 212 #define a_f64_llrintt A_F64_F(llrint)
 213
 214 /*! @} a_math */
 215
 216 /*!
 217  @ingroup liba
 218  @addtogroup a_float floating-point number
 219  @{
 220 */
 221
 222 /*! \f$ e \f$ */
 223 #define A_FLOAT_E A_FLOAT_C(A_E)
 224 /*! \f$ \log_{2}{e}=\frac{1}{\ln{2}} \f$ */
 225 #define A_FLOAT_LOG2E A_FLOAT_C(A_LOG2E)
 226 /*! \f$ \lg{e}=\frac{1}{\ln{2}+\ln{5}} \f$ */
 227 #define A_FLOAT_LOG10E A_FLOAT_C(A_LOG10E)
 228 /*! \f$ \ln{2} \f$ */
 229 #define A_FLOAT_LN2 A_FLOAT_C(A_LN2)
 230 /*! \f$ \frac{1}{\ln{2}} \f$ */
 231 #define A_FLOAT_LN1_2 A_FLOAT_C(A_LN1_2)
 232 /*! \f$ \ln{10} \f$ */
 233 #define A_FLOAT_LN10 A_FLOAT_C(A_LN10)
 234 /*! \f$ \frac{1}{\ln{10}} \f$ */
 235 #define A_FLOAT_LN1_10 A_FLOAT_C(A_LN1_10)
 236 /*! \f$ \pi \f$ */
 237 #define A_FLOAT_PI A_FLOAT_C(A_PI)
 238 /*! \f$ 2\pi \f$ */
 239 #define A_FLOAT_TAU A_FLOAT_C(A_TAU)
 240 /*! \f$ \frac{\pi}{2} \f$ */
 241 #define A_FLOAT_PI_2 A_FLOAT_C(A_PI_2)
 242 /*! \f$ \frac{\pi}{4} \f$ */
 243 #define A_FLOAT_PI_4 A_FLOAT_C(A_PI_4)
 244 /*! \f$ \frac{1}{\pi} \f$ */
 245 #define A_FLOAT_1_PI A_FLOAT_C(A_1_PI)
 246 /*! \f$ \frac{2}{\pi} \f$ */
 247 #define A_FLOAT_2_PI A_FLOAT_C(A_2_PI)
 248 /*! \f$ \frac{1}{2\pi} \f$ */
 249 #define A_FLOAT_1_TAU A_FLOAT_C(A_1_TAU)
 250 /*! \f$ \frac{2}{\sqrt{\pi}} \f$ */
 251 #define A_FLOAT_2_SQRTPI A_FLOAT_C(A_2_SQRTPI)
 252 /*! \f$ \sqrt{2} \f$ */
 253 #define A_FLOAT_SQRT2 A_FLOAT_C(A_SQRT2)
 254 /*! \f$ \frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2} \f$ */
 255 #define A_FLOAT_SQRT1_2 A_FLOAT_C(A_SQRT1_2)
 256 /*! \f$ \sqrt{3} \f$ */
 257 #define A_FLOAT_SQRT3 A_FLOAT_C(A_SQRT3)
 258 /*! \f$ \frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3} \f$ */
 259 #define A_FLOAT_SQRT1_3 A_FLOAT_C(A_SQRT1_3)
 260
 261 #if defined(__cplusplus)
 262 extern "C" {
 263 #endif /* __cplusplus */
 264
 265 A_EXTERN a_float a_float_asinh(a_float x);
 266 A_EXTERN a_float a_float_acosh(a_float x);
 267 A_EXTERN a_float a_float_atanh(a_float x);
 268 A_EXTERN a_float a_float_expm1(a_float x);
 269 A_EXTERN a_float a_float_log1p(a_float x);
 270 A_EXTERN a_float a_float_atan2(a_float x, a_float y);
 271 A_EXTERN a_float a_float_hypot(a_float x, a_float y);
 272 A_EXTERN a_float a_float_hypot3(a_float x, a_float y, a_float z);
 273
 274 /*!
 275  @brief calculate the sum of a float array
 276  @param[in] p points to a float array
 277  @param[in] n number of a float array
 278  @return sum of a float array
 279 */
 280 A_EXTERN a_float a_float_sum(a_float const *p, a_size n);
 281
 282 /*!
 283  @brief calculate the absolute sum of a float array
 284  @param[in] p points to a float array
 285  @param[in] n number of a float array
 286  @return absolute sum of a float array
 287 */
 288 A_EXTERN a_float a_float_sum1(a_float const *p, a_size n);
 289
 290 /*!
 291  @brief calculate the sum of squares of a float array
 292  @param[in] p points to a float array
 293  @param[in] n number of a float array
 294  @return sum of squares of a float array
 295 */
 296 A_EXTERN a_float a_float_sum2(a_float const *p, a_size n);
 297
 298 /*!
 299  @brief calculate the mean of a float array
 300  @param[in] p points to a float array
 301  @param[in] n number of a float array
 302  @return mean of a float array
 303 */
 304 A_EXTERN a_float a_float_mean(a_float const *p, a_size n);
 305
 306 /*!
 307  @brief swap two different a_float blocks of the same size
 308  @param[in,out] lhs points to a_float block on the left
 309  @param[in,out] rhs points to a_float block on the right
 310  @param[in] n the number of a_float block being swapped
 311 */
 312 A_EXTERN A_NONULL((1, 2)) void a_float_swap(a_float *lhs, a_float *rhs, a_size n);
 313
 314 /*!
 315  @brief push an element into the front of a float array
 316  @param[in] p points to a float array
 317  @param[in] n number of a float array
 318  @param[in] x value
 319 */
 320 A_EXTERN void a_float_push_fore(a_float *p, a_size n, a_float x);
 321
 322 /*!
 323  @brief push an element into the end of a float array
 324  @param[in] p points to a float array
 325  @param[in] n number of a float array
 326  @param[in] x value
 327 */
 328 A_EXTERN void a_float_push_back(a_float *p, a_size n, a_float x);
 329
 330 /*!
 331  @brief push the elements into the front of a float array
 332  @param[in] block_p points to a float array
 333  @param[in] block_n number of a float array
 334  @param[in] cache_p points to a cache array
 335  @param[in] cache_n number of a cache array
 336 */
 337 A_EXTERN void a_float_push_fore_(a_float *block_p, a_size block_n,
 338                                  a_float const *cache_p, a_size cache_n);
 339
 340 /*!
 341  @brief push the elements into the end of a float array
 342  @param[in] block_p points to a float array
 343  @param[in] block_n number of a float array
 344  @param[in] cache_p points to a cache array
 345  @param[in] cache_n number of a cache array
 346 */
 347 A_EXTERN void a_float_push_back_(a_float *block_p, a_size block_n,
 348                                  a_float const *cache_p, a_size cache_n);
 349
 350 /*!
 351  @brief roll forward the elements of a float array circularly
 352  @param[in] p points to a float array
 353  @param[in] n number of a float array
 354 */
 355 A_EXTERN void a_float_roll_fore(a_float *p, a_size n);
 356
 357 /*!
 358  @brief roll backward the elements of a float array circularly
 359  @param[in] p points to a float array
 360  @param[in] n number of a float array
 361 */
 362 A_EXTERN void a_float_roll_back(a_float *p, a_size n);
 363
 364 /*!
 365  @brief roll forward the elements of a float array circularly
 366  @param[in] block_p points to a float array
 367  @param[in] block_n number of a float array
 368  @param[in] shift_p points to a shift array
 369  @param[in] shift_n number of a shift array
 370 */
 371 A_EXTERN void a_float_roll_fore_(a_float *block_p, a_size block_n,
 372                                  a_float *shift_p, a_size shift_n);
 373
 374 /*!
 375  @brief roll backward the elements of a float array circularly
 376  @param[in] block_p points to a float array
 377  @param[in] block_n number of a float array
 378  @param[in] shift_p points to a shift array
 379  @param[in] shift_n number of a shift array
 380 */
 381 A_EXTERN void a_float_roll_back_(a_float *block_p, a_size block_n,
 382                                  a_float *shift_p, a_size shift_n);
 383
 384 #if defined(__cplusplus)
 385 } /* extern "C" */
 386 #endif /* __cplusplus */
 387
 388 #define a_float_modf A_FLOAT_F(modf)
 389 #define a_float_frexp A_FLOAT_F(frexp)
 390 #define a_float_ldexp A_FLOAT_F(ldexp)
 391 #define a_float_scalbn A_FLOAT_F(scalbn)
 392 #define a_float_scalbln A_FLOAT_F(scalbln)
 393 #define a_float_nextafter A_FLOAT_F(nextafter)
 394 #define a_float_nexttoward A_FLOAT_F(nexttoward)
 395 #define a_float_copysign A_FLOAT_F(copysign)
 396
 397 #define a_float_ma A_FLOAT_F(fma)
 398 #define a_float_nan A_FLOAT_F(nan)
 399 #define a_float_abs A_FLOAT_F(fabs)
 400 #define a_float_mod A_FLOAT_F(fmod)
 401 #define a_float_max A_FLOAT_F(fmax)
 402 #define a_float_min A_FLOAT_F(fmin)
 403 #define a_float_dim A_FLOAT_F(fdim)
 404 #define a_float_remquo A_FLOAT_F(remquo)
 405 #define a_float_remainder A_FLOAT_F(remainder)
 406
 407 #define a_float_exp A_FLOAT_F(exp)
 408 #define a_float_exp2 A_FLOAT_F(exp2)
 409 #if defined(A_HAVE_EXPM1) && (A_HAVE_EXPM1 + 0 > 0)
 410 #define a_float_expm1 A_FLOAT_F(expm1)
 411 #endif /* A_HAVE_EXPM1 */
 412
 413 #define a_float_log A_FLOAT_F(log)
 414 #define a_float_logb A_FLOAT_F(logb)
 415 #define a_float_log2 A_FLOAT_F(log2)
 416 #define a_float_log10 A_FLOAT_F(log10)
 417 #if defined(A_HAVE_LOG1P) && (A_HAVE_LOG1P + 0 > 0)
 418 #define a_float_log1p A_FLOAT_F(log1p)
 419 #endif /* A_HAVE_LOG1P */
 420 #define a_float_ilogb A_FLOAT_F(ilogb)
 421
 422 #define a_float_pow A_FLOAT_F(pow)
 423 #define a_float_sqrt A_FLOAT_F(sqrt)
 424 #define a_float_cbrt A_FLOAT_F(cbrt)
 425 #if defined(A_HAVE_HYPOT) && (A_HAVE_HYPOT + 0 > 0)
 426 #define a_float_hypot A_FLOAT_F(hypot)
 427 #elif defined(_MSC_VER)
 428 #define a_float_hypot A_FLOAT_F(_hypot)
 429 #endif /* A_HAVE_HYPOT */
 430
 431 #define a_float_sin A_FLOAT_F(sin)
 432 #define a_float_cos A_FLOAT_F(cos)
 433 #define a_float_tan A_FLOAT_F(tan)
 434 #define a_float_asin A_FLOAT_F(asin)
 435 #define a_float_acos A_FLOAT_F(acos)
 436 #define a_float_atan A_FLOAT_F(atan)
 437 #if defined(A_HAVE_ATAN2) && (A_HAVE_ATAN2 + 0 > 0)
 438 #define a_float_atan2 A_FLOAT_F(atan2)
 439 #endif /* A_HAVE_ATAN2 */
 440
 441 #define a_float_sinh A_FLOAT_F(sinh)
 442 #define a_float_cosh A_FLOAT_F(cosh)
 443 #define a_float_tanh A_FLOAT_F(tanh)
 444 #if defined(A_HAVE_ASINH) && (A_HAVE_ASINH + 0 > 0)
 445 #define a_float_asinh A_FLOAT_F(asinh)
 446 #endif /* A_HAVE_ASINH */
 447 #if defined(A_HAVE_ACOSH) && (A_HAVE_ACOSH + 0 > 0)
 448 #define a_float_acosh A_FLOAT_F(acosh)
 449 #endif /* A_HAVE_ACOSH */
 450 #if defined(A_HAVE_ATANH) && (A_HAVE_ATANH + 0 > 0)
 451 #define a_float_atanh A_FLOAT_F(atanh)
 452 #endif /* A_HAVE_ATANH */
 453
 454 #define a_float_erf A_FLOAT_F(erf)
 455 #define a_float_erfc A_FLOAT_F(erfc)
 456 #define a_float_tgamma A_FLOAT_F(tgamma)
 457 #define a_float_lgamma A_FLOAT_F(lgamma)
 458
 459 #define a_float_ceil A_FLOAT_F(ceil)
 460 #define a_float_floor A_FLOAT_F(floor)
 461 #define a_float_trunc A_FLOAT_F(trunc)
 462 #define a_float_round A_FLOAT_F(round)
 463 #define a_float_lround A_FLOAT_F(lround)
 464 #define a_float_llround A_FLOAT_F(llround)
 465 #define a_float_nearbyint A_FLOAT_F(nearbyint)
 466 #define a_float_rint A_FLOAT_F(rint)
 467 #define a_float_lrintt A_FLOAT_F(lrint)
 468 #define a_float_llrintt A_FLOAT_F(llrint)
 469
 470 /*! @} a_float */
 471
 472 #endif /* a/math.h */