include/a/complex.h

   1 /*!
   2  @file complex.h
   3  @brief complex number
   4 */
   5
   6 #ifndef LIBA_COMPLEX_H
   7 #define LIBA_COMPLEX_H
   8
   9 #include "a.h"
  10
  11 /*!
  12  @ingroup A
  13  @addtogroup A_COMPLEX complex number
  14  @{
  15 */
  16
  17 // clang-format off
  18 /*! format constants for the fprintf family of functions */
  19 #define A_COMPLEX_PRI(RF, RC, IF, IC) "(" A_FLOAT_PRI(RF, RC) "," A_FLOAT_PRI(IF, IC) ")"
  20 /*! constructs a complex number constant from real and imaginary parts */
  21 #if !defined __cplusplus
  22 #define A_COMPLEX_C(R, I) (a_complex){A_FLOAT_C(R), A_FLOAT_C(I)}
  23 #else /* !__cplusplus */
  24 #define A_COMPLEX_C(R, I) {A_FLOAT_C(R), A_FLOAT_C(I)}
  25 #endif /* __cplusplus */
  26 /*! constructs a complex number from real and imaginary parts */
  27 #if !defined __cplusplus
  28 #define a_complex_c(r, i) (a_complex){a_float_c(r), a_float_c(i)}
  29 #else /* !__cplusplus */
  30 #define a_complex_c(r, i) {a_float_c(r), a_float_c(i)}
  31 #endif /* __cplusplus */
  32 // clang-format on
  33
  34 /*!
  35  @brief instance structure for complex number
  36 */
  37 typedef struct a_complex
  38 {
  39     a_float real; //!< real part of complex number
  40     a_float imag; //!< imaginary part of complex number
  41 } a_complex;
  42
  43 #if defined(__cplusplus)
  44 extern "C" {
  45 #endif /* __cplusplus */
  46 #if defined(LIBA_COMPLEX_C)
  47 #undef A_INTERN
  48 #define A_INTERN A_INLINE
  49 #endif /* LIBA_COMPLEX_C */
  50
  51 /*!
  52  @brief constructs a complex number from real and imaginary parts
  53  @param _z = \f$ (\rm{Re},\rm{Im}) \f$
  54  @param real real part of complex number
  55  @param imag imaginary part of complex number
  56 */
  57 static A_INLINE void a_complex_rect(a_complex *_z, a_float real, a_float imag)
  58 {
  59     _z->real = real;
  60     _z->imag = imag;
  61 }
  62
  63 /*!
  64  @brief constructs a complex number from polar form
  65  @param _z = \f$ (\rho\cos\theta,\rho\sin\theta{i}) \f$
  66  @param rho a distance from a reference point
  67  @param theta an angle from a reference direction
  68 */
  69 A_EXTERN void a_complex_polar(a_complex *_z, a_float rho, a_float theta);
  70
  71 /*!
  72  @brief parse a string into a complex number
  73  @param _z points to an instance structure for complex number
  74  @param str complex number string to be parsed
  75  @return number of parsed characters
  76 */
  77 A_EXTERN unsigned int a_complex_parse(a_complex *_z, char const *str);
  78
  79 /*!
  80  @brief complex number x is equal to complex number y
  81  @param x complex number on the left
  82  @param y complex number on the right
  83  @return result of comparison
  84 */
  85 A_EXTERN a_bool a_complex_eq(a_complex x, a_complex y);
  86
  87 /*!
  88  @brief complex number x is not equal to complex number y
  89  @param x complex number on the left
  90  @param y complex number on the right
  91  @return result of comparison
  92 */
  93 A_EXTERN a_bool a_complex_ne(a_complex x, a_complex y);
  94
  95 /* Properties of complex numbers */
  96
  97 /*!
  98  @brief computes the natural logarithm of magnitude of a complex number
  99  @param z a complex number
 100  @return = \f$ \log\left|x\right| \f$
 101 */
 102 A_EXTERN a_float a_complex_logabs(a_complex z);
 103
 104 /*!
 105  @brief computes the squared magnitude of a complex number
 106  @param z a complex number
 107  @return = \f$ a^2+b^2 \f$
 108 */
 109 A_EXTERN a_float a_complex_abs2(a_complex z);
 110
 111 /*!
 112  @brief computes the magnitude of a complex number
 113  @param z a complex number
 114  @return = \f$ \sqrt{a^2+b^2} \f$
 115 */
 116 A_EXTERN a_float a_complex_abs(a_complex z);
 117
 118 /*!
 119  @brief computes the phase angle of a complex number
 120  @param z a complex number
 121  @return = \f$ \arctan\frac{b}{a} \f$
 122 */
 123 A_EXTERN a_float a_complex_arg(a_complex z);
 124
 125 /* Complex arithmetic operators */
 126
 127 /*!
 128  @brief computes the projection on Riemann sphere
 129  @param _z = \f$ z \f$ or \f$ (\inf,\rm{copysign}(0,b)i) \f$
 130  @param z a complex number
 131 */
 132 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 133 A_EXTERN void a_complex_proj(a_complex *_z, a_complex z);
 134 #endif /* A_HAVE_INLINE */
 135 A_EXTERN void a_complex_proj_(a_complex *_z);
 136 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 137 A_INTERN void a_complex_proj(a_complex *_z, a_complex z)
 138 {
 139     a_complex_proj_(&z);
 140     *_z = z;
 141 }
 142 #endif /* A_HAVE_INLINE */
 143
 144 /*!
 145  @brief computes the complex conjugate
 146  @param _z = \f$ (a,-b{i}) \f$
 147  @param z a complex number
 148 */
 149 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 150 A_EXTERN void a_complex_conj(a_complex *_z, a_complex z);
 151 #endif /* A_HAVE_INLINE */
 152 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 153 A_INTERN void a_complex_conj(a_complex *_z, a_complex z)
 154 {
 155     _z->real = +z.real;
 156     _z->imag = -z.imag;
 157 }
 158 #endif /* A_HAVE_INLINE */
 159 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 160 A_EXTERN void a_complex_conj_(a_complex *_z);
 161 #endif /* A_HAVE_INLINE */
 162 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 163 A_INTERN void a_complex_conj_(a_complex *_z)
 164 {
 165     _z->imag = -_z->imag;
 166 }
 167 #endif /* A_HAVE_INLINE */
 168
 169 /*!
 170  @brief computes the complex negative
 171  @param _z = \f$ (-a,-b{i}) \f$
 172  @param z a complex number
 173 */
 174 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 175 A_EXTERN void a_complex_neg(a_complex *_z, a_complex z);
 176 #endif /* A_HAVE_INLINE */
 177 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 178 A_INTERN void a_complex_neg(a_complex *_z, a_complex z)
 179 {
 180     _z->real = -z.real;
 181     _z->imag = -z.imag;
 182 }
 183 #endif /* A_HAVE_INLINE */
 184 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 185 A_EXTERN void a_complex_neg_(a_complex *_z);
 186 #endif /* A_HAVE_INLINE */
 187 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 188 A_INTERN void a_complex_neg_(a_complex *_z)
 189 {
 190     _z->real = -_z->real;
 191     _z->imag = -_z->imag;
 192 }
 193 #endif /* A_HAVE_INLINE */
 194
 195 /*!
 196  @brief addition of complex numbers \f[ (a+b i)+(c+d i)=(a+c)+(b+d)i \f]
 197  @param _z = \f$ x + y \f$
 198  @param x complex number on the left
 199  @param y complex number on the right
 200 */
 201 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 202 A_EXTERN void a_complex_add(a_complex *_z, a_complex x, a_complex y);
 203 #endif /* A_HAVE_INLINE */
 204 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 205 A_INTERN void a_complex_add(a_complex *_z, a_complex x, a_complex y)
 206 {
 207     _z->real = x.real + y.real;
 208     _z->imag = x.imag + y.imag;
 209 }
 210 #endif /* A_HAVE_INLINE */
 211 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 212 A_EXTERN void a_complex_add_(a_complex *_z, a_complex z);
 213 #endif /* A_HAVE_INLINE */
 214 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 215 A_INTERN void a_complex_add_(a_complex *_z, a_complex z)
 216 {
 217     _z->real += z.real;
 218     _z->imag += z.imag;
 219 }
 220 #endif /* A_HAVE_INLINE */
 221 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 222 A_EXTERN void a_complex_add_real(a_complex *_z, a_complex x, a_float y);
 223 #endif /* A_HAVE_INLINE */
 224 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 225 A_INTERN void a_complex_add_real(a_complex *_z, a_complex x, a_float y)
 226 {
 227     _z->real = x.real + y;
 228     _z->imag = x.imag;
 229 }
 230 #endif /* A_HAVE_INLINE */
 231 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 232 A_EXTERN void a_complex_add_real_(a_complex *_z, a_float x);
 233 #endif /* A_HAVE_INLINE */
 234 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 235 A_INTERN void a_complex_add_real_(a_complex *_z, a_float x)
 236 {
 237     _z->real += x;
 238 }
 239 #endif /* A_HAVE_INLINE */
 240 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 241 A_EXTERN void a_complex_add_imag(a_complex *_z, a_complex x, a_float y);
 242 #endif /* A_HAVE_INLINE */
 243 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 244 A_INTERN void a_complex_add_imag(a_complex *_z, a_complex x, a_float y)
 245 {
 246     _z->real = x.real;
 247     _z->imag = x.imag + y;
 248 }
 249 #endif /* A_HAVE_INLINE */
 250 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 251 A_EXTERN void a_complex_add_imag_(a_complex *_z, a_float x);
 252 #endif /* A_HAVE_INLINE */
 253 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 254 A_INTERN void a_complex_add_imag_(a_complex *_z, a_float x)
 255 {
 256     _z->imag += x;
 257 }
 258 #endif /* A_HAVE_INLINE */
 259
 260 /*!
 261  @brief subtraction of complex numbers \f[ (a+b i)-(c+d i)=(a-c)+(b-d)i \f]
 262  @param _z = \f$ x - y \f$
 263  @param x complex number on the left
 264  @param y complex number on the right
 265 */
 266 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 267 A_EXTERN void a_complex_sub(a_complex *_z, a_complex x, a_complex y);
 268 #endif /* A_HAVE_INLINE */
 269 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 270 A_INTERN void a_complex_sub(a_complex *_z, a_complex x, a_complex y)
 271 {
 272     _z->real = x.real - y.real;
 273     _z->imag = x.imag - y.imag;
 274 }
 275 #endif /* A_HAVE_INLINE */
 276 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 277 A_EXTERN void a_complex_sub_(a_complex *_z, a_complex z);
 278 #endif /* A_HAVE_INLINE */
 279 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 280 A_INTERN void a_complex_sub_(a_complex *_z, a_complex z)
 281 {
 282     _z->real -= z.real;
 283     _z->imag -= z.imag;
 284 }
 285 #endif /* A_HAVE_INLINE */
 286 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 287 A_EXTERN void a_complex_sub_real(a_complex *_z, a_complex x, a_float y);
 288 #endif /* A_HAVE_INLINE */
 289 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 290 A_INTERN void a_complex_sub_real(a_complex *_z, a_complex x, a_float y)
 291 {
 292     _z->real = x.real - y;
 293     _z->imag = x.imag;
 294 }
 295 #endif /* A_HAVE_INLINE */
 296 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 297 A_EXTERN void a_complex_sub_real_(a_complex *_z, a_float x);
 298 #endif /* A_HAVE_INLINE */
 299 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 300 A_INTERN void a_complex_sub_real_(a_complex *_z, a_float x)
 301 {
 302     _z->real -= x;
 303 }
 304 #endif /* A_HAVE_INLINE */
 305 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 306 A_EXTERN void a_complex_sub_imag(a_complex *_z, a_complex x, a_float y);
 307 #endif /* A_HAVE_INLINE */
 308 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 309 A_INTERN void a_complex_sub_imag(a_complex *_z, a_complex x, a_float y)
 310 {
 311     _z->real = x.real;
 312     _z->imag = x.imag - y;
 313 }
 314 #endif /* A_HAVE_INLINE */
 315 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 316 A_EXTERN void a_complex_sub_imag_(a_complex *_z, a_float x);
 317 #endif /* A_HAVE_INLINE */
 318 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 319 A_INTERN void a_complex_sub_imag_(a_complex *_z, a_float x)
 320 {
 321     _z->imag -= x;
 322 }
 323 #endif /* A_HAVE_INLINE */
 324
 325 /*!
 326  @brief multiplication of complex numbers \f[ (a+b i)(c+d i)=a c+b c i+a d i+b d i^{2}=(a c-b d)+(b c+a d) i \f]
 327  @param _z = \f$ x \times y \f$
 328  @param x complex number on the left
 329  @param y complex number on the right
 330 */
 331 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 332 A_EXTERN void a_complex_mul(a_complex *_z, a_complex x, a_complex y);
 333 #endif /* A_HAVE_INLINE */
 334 A_EXTERN void a_complex_mul_(a_complex *_z, a_complex z);
 335 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 336 A_INTERN void a_complex_mul(a_complex *_z, a_complex x, a_complex y)
 337 {
 338     a_complex_mul_(&x, y);
 339     *_z = x;
 340 }
 341 #endif /* A_HAVE_INLINE */
 342 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 343 A_EXTERN void a_complex_mul_real(a_complex *_z, a_complex x, a_float y);
 344 #endif /* A_HAVE_INLINE */
 345 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 346 A_INTERN void a_complex_mul_real(a_complex *_z, a_complex x, a_float y)
 347 {
 348     _z->real = x.real * y;
 349     _z->imag = x.imag * y;
 350 }
 351 #endif /* A_HAVE_INLINE */
 352 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 353 A_EXTERN void a_complex_mul_real_(a_complex *_z, a_float x);
 354 #endif /* A_HAVE_INLINE */
 355 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 356 A_INTERN void a_complex_mul_real_(a_complex *_z, a_float x)
 357 {
 358     _z->real *= x;
 359     _z->imag *= x;
 360 }
 361 #endif /* A_HAVE_INLINE */
 362 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 363 A_EXTERN void a_complex_mul_imag(a_complex *_z, a_complex x, a_float y);
 364 #endif /* A_HAVE_INLINE */
 365 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 366 A_INTERN void a_complex_mul_imag(a_complex *_z, a_complex x, a_float y)
 367 {
 368     _z->real = -x.imag * y;
 369     _z->imag = x.real * y;
 370 }
 371 #endif /* A_HAVE_INLINE */
 372 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 373 A_EXTERN void a_complex_mul_imag_(a_complex *_z, a_float x);
 374 #endif /* A_HAVE_INLINE */
 375 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 376 A_INTERN void a_complex_mul_imag_(a_complex *_z, a_float x)
 377 {
 378     a_float const real = _z->real;
 379     _z->real = -_z->imag * x;
 380     _z->imag = real * x;
 381 }
 382 #endif /* A_HAVE_INLINE */
 383
 384 /*!
 385  @brief division of complex numbers \f[ \frac{(a+b i)}{(c+d i)}=\frac{(a+b i)(c-d i)}{(c+d i)(c-d i)}=\frac{a c+b c i-a d i-b d i^{2}}{c^{2}-(d i)^{2}}=\frac{(a c+b d)+(b c-a d) i}{c^{2}+d^{2}}=\left(\frac{a c+b d}{c^{2}+d^{2}}\right)+\left(\frac{b c-a d}{c^{2}+d^{2}}\right) i \f]
 386  @param _z = \f$ x \div y \f$
 387  @param x complex number on the left
 388  @param y complex number on the right
 389 */
 390 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 391 A_EXTERN void a_complex_div(a_complex *_z, a_complex x, a_complex y);
 392 #endif /* A_HAVE_INLINE */
 393 A_EXTERN void a_complex_div_(a_complex *_z, a_complex z);
 394 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 395 A_INTERN void a_complex_div(a_complex *_z, a_complex x, a_complex y)
 396 {
 397     a_complex_div_(&x, y);
 398     *_z = x;
 399 }
 400 #endif /* A_HAVE_INLINE */
 401 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 402 A_EXTERN void a_complex_div_real(a_complex *_z, a_complex x, a_float y);
 403 #endif /* A_HAVE_INLINE */
 404 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 405 A_INTERN void a_complex_div_real(a_complex *_z, a_complex x, a_float y)
 406 {
 407     _z->real = x.real / y;
 408     _z->imag = x.imag / y;
 409 }
 410 #endif /* A_HAVE_INLINE */
 411 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 412 A_EXTERN void a_complex_div_real_(a_complex *_z, a_float x);
 413 #endif /* A_HAVE_INLINE */
 414 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 415 A_INTERN void a_complex_div_real_(a_complex *_z, a_float x)
 416 {
 417     _z->real /= x;
 418     _z->imag /= x;
 419 }
 420 #endif /* A_HAVE_INLINE */
 421 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 422 A_EXTERN void a_complex_div_imag(a_complex *_z, a_complex x, a_float y);
 423 #endif /* A_HAVE_INLINE */
 424 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 425 A_INTERN void a_complex_div_imag(a_complex *_z, a_complex x, a_float y)
 426 {
 427     _z->real = -x.imag / y;
 428     _z->imag = x.real / y;
 429 }
 430 #endif /* A_HAVE_INLINE */
 431 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 432 A_EXTERN void a_complex_div_imag_(a_complex *_z, a_float x);
 433 #endif /* A_HAVE_INLINE */
 434 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 435 A_INTERN void a_complex_div_imag_(a_complex *_z, a_float x)
 436 {
 437     a_float const real = _z->real;
 438     _z->real = -_z->imag / x;
 439     _z->imag = real / x;
 440 }
 441 #endif /* A_HAVE_INLINE */
 442
 443 /*!
 444  @brief inverse of a complex number \f[ \frac{a-bi}{a^2+b^2}=\left(\frac{a}{a^2+b^2}\right)-\left(\frac{b}{a^2+b^2}\right)i \f]
 445  @param _z inverse or reciprocal \f$ \frac{1}{z} \f$
 446  @param z a complex number
 447 */
 448 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 449 A_EXTERN void a_complex_inv(a_complex *_z, a_complex z);
 450 #endif /* A_HAVE_INLINE */
 451 A_EXTERN void a_complex_inv_(a_complex *_z);
 452 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 453 A_INTERN void a_complex_inv(a_complex *_z, a_complex z)
 454 {
 455     a_complex_inv_(&z);
 456     *_z = z;
 457 }
 458 #endif /* A_HAVE_INLINE */
 459
 460 /* Elementary Complex Functions */
 461
 462 /*!
 463  @brief computes the complex square root
 464  @param _z = \f$ \sqrt{z} \f$
 465  @param z a complex number
 466 */
 467 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 468 A_EXTERN void a_complex_sqrt(a_complex *_z, a_complex z);
 469 #endif /* A_HAVE_INLINE */
 470 A_EXTERN void a_complex_sqrt_(a_complex *_z);
 471 A_EXTERN void a_complex_sqrt_real(a_complex *_z, a_float x);
 472 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 473 A_INTERN void a_complex_sqrt(a_complex *_z, a_complex z)
 474 {
 475     a_complex_sqrt_(&z);
 476     *_z = z;
 477 }
 478 #endif /* A_HAVE_INLINE */
 479
 480 /*!
 481  @brief complex number z raised to complex power a
 482  @param _z = \f$ z^a \f$
 483  @param z a complex number
 484  @param a a complex number
 485 */
 486 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 487 A_EXTERN void a_complex_pow(a_complex *_z, a_complex z, a_complex a);
 488 #endif /* A_HAVE_INLINE */
 489 A_EXTERN void a_complex_pow_(a_complex *_z, a_complex a);
 490 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 491 A_INTERN void a_complex_pow(a_complex *_z, a_complex z, a_complex a)
 492 {
 493     a_complex_pow_(&z, a);
 494     *_z = z;
 495 }
 496 #endif /* A_HAVE_INLINE */
 497
 498 /*!
 499  @brief complex number z raised to real power a
 500  @param _z = \f$ z^a \f$
 501  @param z a complex number
 502  @param a a real number
 503 */
 504 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 505 A_EXTERN void a_complex_pow_real(a_complex *_z, a_complex z, a_float a);
 506 #endif /* A_HAVE_INLINE */
 507 A_EXTERN void a_complex_pow_real_(a_complex *_z, a_float a);
 508 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 509 A_INTERN void a_complex_pow_real(a_complex *_z, a_complex z, a_float a)
 510 {
 511     a_complex_pow_real_(&z, a);
 512     *_z = z;
 513 }
 514 #endif /* A_HAVE_INLINE */
 515
 516 /*!
 517  @brief computes the complex base-e exponential
 518  @param _z = \f$ e^z \f$
 519  @param z a complex number
 520 */
 521 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 522 A_EXTERN void a_complex_exp(a_complex *_z, a_complex z);
 523 #endif /* A_HAVE_INLINE */
 524 A_EXTERN void a_complex_exp_(a_complex *_z);
 525 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 526 A_INTERN void a_complex_exp(a_complex *_z, a_complex z)
 527 {
 528     a_complex_exp_(&z);
 529     *_z = z;
 530 }
 531 #endif /* A_HAVE_INLINE */
 532
 533 /*!
 534  @brief computes the complex natural logarithm
 535  @param _z = \f$ \ln{z} \f$
 536  @param z a complex number
 537 */
 538 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 539 A_EXTERN void a_complex_log(a_complex *_z, a_complex z);
 540 #endif /* A_HAVE_INLINE */
 541 A_EXTERN void a_complex_log_(a_complex *_z);
 542 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 543 A_INTERN void a_complex_log(a_complex *_z, a_complex z)
 544 {
 545     a_complex_log_(&z);
 546     *_z = z;
 547 }
 548 #endif /* A_HAVE_INLINE */
 549
 550 /*!
 551  @brief computes the complex base-2 logarithm
 552  @param _z = \f$ \log_{2}{z} \f$
 553  @param z a complex number
 554 */
 555 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 556 A_EXTERN void a_complex_log2(a_complex *_z, a_complex z);
 557 #endif /* A_HAVE_INLINE */
 558 A_EXTERN void a_complex_log2_(a_complex *_z);
 559 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 560 A_INTERN void a_complex_log2(a_complex *_z, a_complex z)
 561 {
 562     a_complex_log2_(&z);
 563     *_z = z;
 564 }
 565 #endif /* A_HAVE_INLINE */
 566
 567 /*!
 568  @brief computes the complex base-10 logarithm
 569  @param _z = \f$ \lg{z} \f$
 570  @param z a complex number
 571 */
 572 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 573 A_EXTERN void a_complex_log10(a_complex *_z, a_complex z);
 574 #endif /* A_HAVE_INLINE */
 575 A_EXTERN void a_complex_log10_(a_complex *_z);
 576 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 577 A_INTERN void a_complex_log10(a_complex *_z, a_complex z)
 578 {
 579     a_complex_log10_(&z);
 580     *_z = z;
 581 }
 582 #endif /* A_HAVE_INLINE */
 583
 584 /*!
 585  @brief computes the complex base-b logarithm
 586  @param _z = \f$ \log_{b}{z} \f$
 587  @param z a complex number
 588  @param b a complex number
 589 */
 590 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 591 A_EXTERN void a_complex_logb(a_complex *_z, a_complex z, a_complex b);
 592 #endif /* A_HAVE_INLINE */
 593 A_EXTERN void a_complex_logb_(a_complex *_z, a_complex b);
 594 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 595 A_INTERN void a_complex_logb(a_complex *_z, a_complex z, a_complex b)
 596 {
 597     a_complex_logb_(&z, b);
 598     *_z = z;
 599 }
 600 #endif /* A_HAVE_INLINE */
 601
 602 /* Complex Trigonometric Functions */
 603
 604 /*!
 605  @brief computes the complex sine \f[ \sin(z)=\frac{\exp(z{i})-\exp(-z{i})}{2{i}} \f]
 606  @param _z = \f$ \sin(z) \f$
 607  @param z a complex number
 608 */
 609 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 610 A_EXTERN void a_complex_sin(a_complex *_z, a_complex z);
 611 #endif /* A_HAVE_INLINE */
 612 A_EXTERN void a_complex_sin_(a_complex *_z);
 613 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 614 A_INTERN void a_complex_sin(a_complex *_z, a_complex z)
 615 {
 616     a_complex_sin_(&z);
 617     *_z = z;
 618 }
 619 #endif /* A_HAVE_INLINE */
 620
 621 /*!
 622  @brief computes the complex cosine \f[ \cos(z)=\frac{\exp(z{i})+\exp(-z{i})}{2} \f]
 623  @param _z = \f$ \cos(z) \f$
 624  @param z a complex number
 625 */
 626 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 627 A_EXTERN void a_complex_cos(a_complex *_z, a_complex z);
 628 #endif /* A_HAVE_INLINE */
 629 A_EXTERN void a_complex_cos_(a_complex *_z);
 630 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 631 A_INTERN void a_complex_cos(a_complex *_z, a_complex z)
 632 {
 633     a_complex_cos_(&z);
 634     *_z = z;
 635 }
 636 #endif /* A_HAVE_INLINE */
 637
 638 /*!
 639  @brief computes the complex tangent \f[ \tan(z)=\frac{\sin(z)}{\cos(z)} \f]
 640  @param _z = \f$ \tan(z) \f$
 641  @param z a complex number
 642 */
 643 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 644 A_EXTERN void a_complex_tan(a_complex *_z, a_complex z);
 645 #endif /* A_HAVE_INLINE */
 646 A_EXTERN void a_complex_tan_(a_complex *_z);
 647 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 648 A_INTERN void a_complex_tan(a_complex *_z, a_complex z)
 649 {
 650     a_complex_tan_(&z);
 651     *_z = z;
 652 }
 653 #endif /* A_HAVE_INLINE */
 654
 655 /*!
 656  @brief computes the complex secant \f[ \sec(z)=\frac{1}{\cos(z)} \f]
 657  @param _z = \f$ \sec(z) \f$
 658  @param z a complex number
 659 */
 660 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 661 A_EXTERN void a_complex_sec(a_complex *_z, a_complex z);
 662 #endif /* A_HAVE_INLINE */
 663 A_EXTERN void a_complex_sec_(a_complex *_z);
 664 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 665 A_INTERN void a_complex_sec(a_complex *_z, a_complex z)
 666 {
 667     a_complex_sec_(&z);
 668     *_z = z;
 669 }
 670 #endif /* A_HAVE_INLINE */
 671
 672 /*!
 673  @brief computes the complex cosecant \f[ \csc(z)=\frac{1}{\sin(z)} \f]
 674  @param _z = \f$ \csc(z) \f$
 675  @param z a complex number
 676 */
 677 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 678 A_EXTERN void a_complex_csc(a_complex *_z, a_complex z);
 679 #endif /* A_HAVE_INLINE */
 680 A_EXTERN void a_complex_csc_(a_complex *_z);
 681 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 682 A_INTERN void a_complex_csc(a_complex *_z, a_complex z)
 683 {
 684     a_complex_csc_(&z);
 685     *_z = z;
 686 }
 687 #endif /* A_HAVE_INLINE */
 688
 689 /*!
 690  @brief computes the complex cotangent \f[ \cot(z)=\frac{1}{\tan(z)} \f]
 691  @param _z = \f$ \cot(z) \f$
 692  @param z a complex number
 693 */
 694 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 695 A_EXTERN void a_complex_cot(a_complex *_z, a_complex z);
 696 #endif /* A_HAVE_INLINE */
 697 A_EXTERN void a_complex_cot_(a_complex *_z);
 698 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 699 A_INTERN void a_complex_cot(a_complex *_z, a_complex z)
 700 {
 701     a_complex_cot_(&z);
 702     *_z = z;
 703 }
 704 #endif /* A_HAVE_INLINE */
 705
 706 /* Inverse Complex Trigonometric Functions */
 707
 708 /*!
 709  @brief computes the complex arc sine
 710  @param _z = \f$ \arcsin(z) \f$
 711  @param z a complex number
 712 */
 713 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 714 A_EXTERN void a_complex_asin(a_complex *_z, a_complex z);
 715 #endif /* A_HAVE_INLINE */
 716 A_EXTERN void a_complex_asin_(a_complex *_z);
 717 A_EXTERN void a_complex_asin_real(a_complex *_z, a_float x);
 718 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 719 A_INTERN void a_complex_asin(a_complex *_z, a_complex z)
 720 {
 721     a_complex_asin_(&z);
 722     *_z = z;
 723 }
 724 #endif /* A_HAVE_INLINE */
 725
 726 /*!
 727  @brief computes the complex arc cosine
 728  @param _z = \f$ \arccos(z) \f$
 729  @param z a complex number
 730 */
 731 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 732 A_EXTERN void a_complex_acos(a_complex *_z, a_complex z);
 733 #endif /* A_HAVE_INLINE */
 734 A_EXTERN void a_complex_acos_(a_complex *_z);
 735 A_EXTERN void a_complex_acos_real(a_complex *_z, a_float x);
 736 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 737 A_INTERN void a_complex_acos(a_complex *_z, a_complex z)
 738 {
 739     a_complex_acos_(&z);
 740     *_z = z;
 741 }
 742 #endif /* A_HAVE_INLINE */
 743
 744 /*!
 745  @brief computes the complex arc tangent
 746  @param _z = \f$ \arctan(z) \f$
 747  @param z a complex number
 748 */
 749 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 750 A_EXTERN void a_complex_atan(a_complex *_z, a_complex z);
 751 #endif /* A_HAVE_INLINE */
 752 A_EXTERN void a_complex_atan_(a_complex *_z);
 753 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 754 A_INTERN void a_complex_atan(a_complex *_z, a_complex z)
 755 {
 756     a_complex_atan_(&z);
 757     *_z = z;
 758 }
 759 #endif /* A_HAVE_INLINE */
 760
 761 /*!
 762  @brief computes the complex arc secant \f[ \mathrm{arcsec}(z)=\mathrm{arccos}(\frac{1}{z}) \f]
 763  @param _z = \f$ \mathrm{arcsec}(z) \f$
 764  @param z a complex number
 765 */
 766 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 767 A_EXTERN void a_complex_asec(a_complex *_z, a_complex z);
 768 #endif /* A_HAVE_INLINE */
 769 A_EXTERN void a_complex_asec_(a_complex *_z);
 770 A_EXTERN void a_complex_asec_real(a_complex *_z, a_float x);
 771 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 772 A_INTERN void a_complex_asec(a_complex *_z, a_complex z)
 773 {
 774     a_complex_asec_(&z);
 775     *_z = z;
 776 }
 777 #endif /* A_HAVE_INLINE */
 778
 779 /*!
 780  @brief computes the complex arc cosecant \f[ \mathrm{arccsc}(z)=\mathrm{arcsin}(\frac{1}{z}) \f]
 781  @param _z = \f$ \mathrm{arccsc}(z) \f$
 782  @param z a complex number
 783 */
 784 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 785 A_EXTERN void a_complex_acsc(a_complex *_z, a_complex z);
 786 #endif /* A_HAVE_INLINE */
 787 A_EXTERN void a_complex_acsc_(a_complex *_z);
 788 A_EXTERN void a_complex_acsc_real(a_complex *_z, a_float x);
 789 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 790 A_INTERN void a_complex_acsc(a_complex *_z, a_complex z)
 791 {
 792     a_complex_acsc_(&z);
 793     *_z = z;
 794 }
 795 #endif /* A_HAVE_INLINE */
 796
 797 /*!
 798  @brief computes the complex arc cotangent \f[ \mathrm{arccot}(z)=\mathrm{arctan}(\frac{1}{z}) \f]
 799  @param _z = \f$ \mathrm{arccot}(z) \f$
 800  @param z a complex number
 801 */
 802 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 803 A_EXTERN void a_complex_acot(a_complex *_z, a_complex z);
 804 #endif /* A_HAVE_INLINE */
 805 A_EXTERN void a_complex_acot_(a_complex *_z);
 806 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 807 A_INTERN void a_complex_acot(a_complex *_z, a_complex z)
 808 {
 809     a_complex_acot_(&z);
 810     *_z = z;
 811 }
 812 #endif /* A_HAVE_INLINE */
 813
 814 /* Complex Hyperbolic Functions */
 815
 816 /*!
 817  @brief computes the complex hyperbolic sine \f[ \sinh(z)=\frac{\exp(z)-\exp(-z)}{2} \f]
 818  @param _z = \f$ \sinh(z) \f$
 819  @param z a complex number
 820 */
 821 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 822 A_EXTERN void a_complex_sinh(a_complex *_z, a_complex z);
 823 #endif /* A_HAVE_INLINE */
 824 A_EXTERN void a_complex_sinh_(a_complex *_z);
 825 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 826 A_INTERN void a_complex_sinh(a_complex *_z, a_complex z)
 827 {
 828     a_complex_sinh_(&z);
 829     *_z = z;
 830 }
 831 #endif /* A_HAVE_INLINE */
 832
 833 /*!
 834  @brief computes the complex hyperbolic cosine \f[ \cosh(z)=\frac{\exp(z)+\exp(-z)}{2} \f]
 835  @param _z = \f$ \cosh(z) \f$
 836  @param z a complex number
 837 */
 838 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 839 A_EXTERN void a_complex_cosh(a_complex *_z, a_complex z);
 840 #endif /* A_HAVE_INLINE */
 841 A_EXTERN void a_complex_cosh_(a_complex *_z);
 842 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 843 A_INTERN void a_complex_cosh(a_complex *_z, a_complex z)
 844 {
 845     a_complex_cosh_(&z);
 846     *_z = z;
 847 }
 848 #endif /* A_HAVE_INLINE */
 849
 850 /*!
 851  @brief computes the complex hyperbolic tangent \f[ \tanh(z)=\frac{\sinh(z)}{\cosh(z)} \f]
 852  @param _z = \f$ \tanh(z) \f$
 853  @param z a complex number
 854 */
 855 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 856 A_EXTERN void a_complex_tanh(a_complex *_z, a_complex z);
 857 #endif /* A_HAVE_INLINE */
 858 A_EXTERN void a_complex_tanh_(a_complex *_z);
 859 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 860 A_INTERN void a_complex_tanh(a_complex *_z, a_complex z)
 861 {
 862     a_complex_tanh_(&z);
 863     *_z = z;
 864 }
 865 #endif /* A_HAVE_INLINE */
 866
 867 /*!
 868  @brief computes the complex hyperbolic secant \f[ \mathrm{sech}(z)=\frac{1}{\cosh(z)} \f]
 869  @param _z = \f$ \mathrm{sech}(z) \f$
 870  @param z a complex number
 871 */
 872 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 873 A_EXTERN void a_complex_sech(a_complex *_z, a_complex z);
 874 #endif /* A_HAVE_INLINE */
 875 A_EXTERN void a_complex_sech_(a_complex *_z);
 876 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 877 A_INTERN void a_complex_sech(a_complex *_z, a_complex z)
 878 {
 879     a_complex_sech_(&z);
 880     *_z = z;
 881 }
 882 #endif /* A_HAVE_INLINE */
 883
 884 /*!
 885  @brief computes the complex hyperbolic cosecant \f[ \mathrm{csch}(z)=\frac{1}{\sinh(z)} \f]
 886  @param _z = \f$ \mathrm{csch}(z) \f$
 887  @param z a complex number
 888 */
 889 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 890 A_EXTERN void a_complex_csch(a_complex *_z, a_complex z);
 891 #endif /* A_HAVE_INLINE */
 892 A_EXTERN void a_complex_csch_(a_complex *_z);
 893 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 894 A_INTERN void a_complex_csch(a_complex *_z, a_complex z)
 895 {
 896     a_complex_csch_(&z);
 897     *_z = z;
 898 }
 899 #endif /* A_HAVE_INLINE */
 900
 901 /*!
 902  @brief computes the complex hyperbolic cotangent \f[ \mathrm{coth}(z)=\frac{1}{\tanh(z)} \f]
 903  @param _z = \f$ \mathrm{coth}(z) \f$
 904  @param z a complex number
 905 */
 906 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 907 A_EXTERN void a_complex_coth(a_complex *_z, a_complex z);
 908 #endif /* A_HAVE_INLINE */
 909 A_EXTERN void a_complex_coth_(a_complex *_z);
 910 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 911 A_INTERN void a_complex_coth(a_complex *_z, a_complex z)
 912 {
 913     a_complex_coth_(&z);
 914     *_z = z;
 915 }
 916 #endif /* A_HAVE_INLINE */
 917
 918 /* Inverse Complex Hyperbolic Functions */
 919
 920 /*!
 921  @brief computes the complex arc hyperbolic sine
 922  @param _z = \f$ \mathrm{arcsinh}(z) \f$
 923  @param z a complex number
 924 */
 925 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 926 A_EXTERN void a_complex_asinh(a_complex *_z, a_complex z);
 927 #endif /* A_HAVE_INLINE */
 928 A_EXTERN void a_complex_asinh_(a_complex *_z);
 929 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 930 A_INTERN void a_complex_asinh(a_complex *_z, a_complex z)
 931 {
 932     a_complex_asinh_(&z);
 933     *_z = z;
 934 }
 935 #endif /* A_HAVE_INLINE */
 936
 937 /*!
 938  @brief computes the complex arc hyperbolic cosine \f[ \mathrm{arccosh}(z)=\log(z-\sqrt{z^2-1}) \f]
 939  @param _z = \f$ \mathrm{arccosh}(z) \f$
 940  @param z a complex number
 941 */
 942 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 943 A_EXTERN void a_complex_acosh(a_complex *_z, a_complex z);
 944 #endif /* A_HAVE_INLINE */
 945 A_EXTERN void a_complex_acosh_(a_complex *_z);
 946 A_EXTERN void a_complex_acosh_real(a_complex *_z, a_float x);
 947 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 948 A_INTERN void a_complex_acosh(a_complex *_z, a_complex z)
 949 {
 950     a_complex_acosh_(&z);
 951     *_z = z;
 952 }
 953 #endif /* A_HAVE_INLINE */
 954
 955 /*!
 956  @brief computes the complex arc hyperbolic tangent
 957  @param _z = \f$ \mathrm{arctanh}(z) \f$
 958  @param z a complex number
 959 */
 960 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 961 A_EXTERN void a_complex_atanh(a_complex *_z, a_complex z);
 962 #endif /* A_HAVE_INLINE */
 963 A_EXTERN void a_complex_atanh_(a_complex *_z);
 964 A_EXTERN void a_complex_atanh_real(a_complex *_z, a_float x);
 965 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 966 A_INTERN void a_complex_atanh(a_complex *_z, a_complex z)
 967 {
 968     a_complex_atanh_(&z);
 969     *_z = z;
 970 }
 971 #endif /* A_HAVE_INLINE */
 972
 973 /*!
 974  @brief computes the complex arc hyperbolic secant \f[ \mathrm{arcsech}(z)=\mathrm{arccosh}(\frac{1}{z}) \f]
 975  @param _z = \f$ \mathrm{arcsech}(z) \f$
 976  @param z a complex number
 977 */
 978 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 979 A_EXTERN void a_complex_asech(a_complex *_z, a_complex z);
 980 #endif /* A_HAVE_INLINE */
 981 A_EXTERN void a_complex_asech_(a_complex *_z);
 982 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
 983 A_INTERN void a_complex_asech(a_complex *_z, a_complex z)
 984 {
 985     a_complex_asech_(&z);
 986     *_z = z;
 987 }
 988 #endif /* A_HAVE_INLINE */
 989
 990 /*!
 991  @brief computes the complex arc hyperbolic cosecant \f[ \mathrm{arccsch}(z)=\mathrm{arcsinh}(\frac{1}{z}) \f]
 992  @param _z = \f$ \mathrm{arccsch}(z) \f$
 993  @param z a complex number
 994 */
 995 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
 996 A_EXTERN void a_complex_acsch(a_complex *_z, a_complex z);
 997 #endif /* A_HAVE_INLINE */
 998 A_EXTERN void a_complex_acsch_(a_complex *_z);
 999 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
1000 A_INTERN void a_complex_acsch(a_complex *_z, a_complex z)
1001 {
1002     a_complex_acsch_(&z);
1003     *_z = z;
1004 }
1005 #endif /* A_HAVE_INLINE */
1006
1007 /*!
1008  @brief computes the complex arc hyperbolic cotangent \f[ \mathrm{arccoth}(z)=\mathrm{arctanh}(\frac{1}{z}) \f]
1009  @param _z = \f$ \mathrm{arccoth}(z) \f$
1010  @param z a complex number
1011 */
1012 #if !defined A_HAVE_INLINE || defined(LIBA_COMPLEX_C)
1013 A_EXTERN void a_complex_acoth(a_complex *_z, a_complex z);
1014 #endif /* A_HAVE_INLINE */
1015 A_EXTERN void a_complex_acoth_(a_complex *_z);
1016 #if defined(A_HAVE_INLINE) || defined(LIBA_COMPLEX_C)
1017 A_INTERN void a_complex_acoth(a_complex *_z, a_complex z)
1018 {
1019     a_complex_acoth_(&z);
1020     *_z = z;
1021 }
1022 #endif /* A_HAVE_INLINE */
1023
1024 #if defined(LIBA_COMPLEX_C)
1025 #undef A_INTERN
1026 #define A_INTERN static A_INLINE
1027 #endif /* LIBA_COMPLEX_C */
1028 #if defined(__cplusplus)
1029 } /* extern "C" */
1030 #endif /* __cplusplus */
1031
1032 /*! @} A_COMPLEX */
1033
1034 #endif /* a/complex.h */