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