lua/src/complex.h

   1 /***
   2  complex number
   3  @classmod a.complex
   4 */
   5
   6 #ifndef LUA_LIBA_COMPLEX_H
   7 #define LUA_LIBA_COMPLEX_H
   8
   9 #include "a.h"
  10
  11 /***
  12  complex number
  13  @field real real part of complex number
  14  @field imag imaginary part of complex number
  15  @field rho the magnitude of complex number
  16  @field theta the phase angle of complex number
  17  @table a.complex
  18 */
  19 #if defined(__cplusplus)
  20 extern "C" {
  21 #endif /* __cplusplus */
  22
  23 /***
  24  constructor for complex number from real and imaginary parts
  25  @tparam[opt] number|string|a.complex real real part of complex number
  26  @tparam[opt] number imag imaginary part of complex number
  27  @treturn a.complex complex number userdata
  28  @function new
  29 */
  30 int liba_complex_new(lua_State *L);
  31
  32 /***
  33  constructor for complex number from rectangular Cartesian components
  34  @tparam[opt] number real real part of complex number
  35  @tparam[opt] number imag imaginary part of complex number
  36  @treturn a.complex complex number userdata
  37  @function rect
  38 */
  39 int liba_complex_rect(lua_State *L);
  40
  41 /***
  42  constructor for complex number from polar form
  43  @tparam[opt] number rho a distance from a reference point
  44  @tparam[opt] number theta an angle from a reference direction
  45  @treturn a.complex complex number userdata
  46  @function polar
  47 */
  48 int liba_complex_polar(lua_State *L);
  49
  50 /***
  51  complex number self is equal to complex number that
  52  @tparam a.complex that complex number
  53  @treturn bool result of comparison
  54  @function eq
  55 */
  56 int liba_complex_eq(lua_State *L);
  57
  58 /***
  59  complex number self is not equal to complex number that
  60  @tparam a.complex that complex number
  61  @treturn bool result of comparison
  62  @function ne
  63 */
  64 int liba_complex_ne(lua_State *L);
  65
  66 /***
  67  computes the natural logarithm of magnitude of a complex number
  68  @treturn number log|z|
  69  @function logabs
  70 */
  71 int liba_complex_logabs(lua_State *L);
  72
  73 /***
  74  computes the squared magnitude of a complex number
  75  @treturn number a^2+b^2
  76  @function abs2
  77 */
  78 int liba_complex_abs2(lua_State *L);
  79
  80 /***
  81  computes the magnitude of a complex number
  82  @treturn number sqrt{a^2+b^2}
  83  @function abs
  84 */
  85 int liba_complex_abs(lua_State *L);
  86
  87 /***
  88  computes the phase angle of a complex number
  89  @treturn number arctan(b/a)
  90  @function arg
  91 */
  92 int liba_complex_arg(lua_State *L);
  93
  94 /***
  95  computes the projection on Riemann sphere
  96  @treturn a.complex complex number userdata
  97  @function proj
  98 */
  99 int liba_complex_proj(lua_State *L);
 100
 101 /***
 102  computes the complex conjugate
 103  @treturn a.complex complex number userdata
 104  @function conj
 105 */
 106 int liba_complex_conj(lua_State *L);
 107
 108 /***
 109  computes the complex negative
 110  @treturn a.complex complex number userdata
 111  @function unm
 112 */
 113 int liba_complex_neg(lua_State *L);
 114
 115 /***
 116  inverse of a complex number
 117  @treturn a.complex complex number userdata
 118  @function inv
 119 */
 120 int liba_complex_inv(lua_State *L);
 121
 122 /***
 123  addition of complex numbers
 124  @tparam a.complex z complex number userdata
 125  @treturn a.complex complex number userdata
 126  @function add
 127 */
 128 int liba_complex_add(lua_State *L);
 129
 130 /***
 131  subtraction of complex numbers
 132  @tparam a.complex z complex number userdata
 133  @treturn a.complex complex number userdata
 134  @function sub
 135 */
 136 int liba_complex_sub(lua_State *L);
 137
 138 /***
 139  multiplication of complex numbers
 140  @tparam a.complex z complex number userdata
 141  @treturn a.complex complex number userdata
 142  @function mul
 143 */
 144 int liba_complex_mul(lua_State *L);
 145
 146 /***
 147  division of complex numbers
 148  @tparam a.complex z complex number userdata
 149  @treturn a.complex complex number userdata
 150  @function div
 151 */
 152 int liba_complex_div(lua_State *L);
 153
 154 /***
 155  complex number z raised to complex power a
 156  @tparam a.complex a complex number userdata
 157  @treturn a.complex complex number userdata
 158  @function pow
 159 */
 160 int liba_complex_pow(lua_State *L);
 161
 162 /***
 163  computes the complex base-b logarithm
 164  @tparam a.complex b complex number userdata
 165  @treturn a.complex complex number userdata
 166  @function logb
 167 */
 168 int liba_complex_logb(lua_State *L);
 169
 170 /***
 171  computes the complex base-e exponential
 172  @treturn a.complex complex number userdata
 173  @function exp
 174 */
 175 int liba_complex_exp(lua_State *L);
 176
 177 /***
 178  computes the complex natural logarithm
 179  @treturn a.complex complex number userdata
 180  @function log
 181 */
 182 int liba_complex_log(lua_State *L);
 183
 184 /***
 185  computes the complex square root
 186  @treturn a.complex complex number userdata
 187  @function sqrt
 188 */
 189 int liba_complex_sqrt(lua_State *L);
 190
 191 /***
 192  computes the complex base-2 logarithm
 193  @treturn a.complex complex number userdata
 194  @function log2
 195 */
 196 int liba_complex_log2(lua_State *L);
 197
 198 /***
 199  computes the complex base-10 logarithm
 200  @treturn a.complex complex number userdata
 201  @function log10
 202 */
 203 int liba_complex_log10(lua_State *L);
 204
 205 /***
 206  computes the complex sine
 207  @treturn a.complex complex number userdata
 208  @function sin
 209 */
 210 int liba_complex_sin(lua_State *L);
 211
 212 /***
 213  computes the complex cosine
 214  @treturn a.complex complex number userdata
 215  @function cos
 216 */
 217 int liba_complex_cos(lua_State *L);
 218
 219 /***
 220  computes the complex tangent
 221  @treturn a.complex complex number userdata
 222  @function tan
 223 */
 224 int liba_complex_tan(lua_State *L);
 225
 226 /***
 227  computes the complex secant
 228  @treturn a.complex complex number userdata
 229  @function sec
 230 */
 231 int liba_complex_sec(lua_State *L);
 232
 233 /***
 234  computes the complex cosecant
 235  @treturn a.complex complex number userdata
 236  @function csc
 237 */
 238 int liba_complex_csc(lua_State *L);
 239
 240 /***
 241  computes the complex cotangent
 242  @treturn a.complex complex number userdata
 243  @function cot
 244 */
 245 int liba_complex_cot(lua_State *L);
 246
 247 /***
 248  computes the complex arc sine
 249  @treturn a.complex complex number userdata
 250  @function asin
 251 */
 252 int liba_complex_asin(lua_State *L);
 253
 254 /***
 255  computes the complex arc cosine
 256  @treturn a.complex complex number userdata
 257  @function acos
 258 */
 259 int liba_complex_acos(lua_State *L);
 260
 261 /***
 262  computes the complex arc tangent
 263  @treturn a.complex complex number userdata
 264  @function atan
 265 */
 266 int liba_complex_atan(lua_State *L);
 267
 268 /***
 269  computes the complex arc secant
 270  @treturn a.complex complex number userdata
 271  @function asec
 272 */
 273 int liba_complex_asec(lua_State *L);
 274
 275 /***
 276  computes the complex arc cosecant
 277  @treturn a.complex complex number userdata
 278  @function acsc
 279 */
 280 int liba_complex_acsc(lua_State *L);
 281
 282 /***
 283  computes the complex arc cotangent
 284  @treturn a.complex complex number userdata
 285  @function acot
 286 */
 287 int liba_complex_acot(lua_State *L);
 288
 289 /***
 290  computes the complex hyperbolic sine
 291  @treturn a.complex complex number userdata
 292  @function sinh
 293 */
 294 int liba_complex_sinh(lua_State *L);
 295
 296 /***
 297  computes the complex hyperbolic cosine
 298  @treturn a.complex complex number userdata
 299  @function cosh
 300 */
 301 int liba_complex_cosh(lua_State *L);
 302
 303 /***
 304  computes the complex hyperbolic tangent
 305  @treturn a.complex complex number userdata
 306  @function tanh
 307 */
 308 int liba_complex_tanh(lua_State *L);
 309
 310 /***
 311  computes the complex hyperbolic secant
 312  @treturn a.complex complex number userdata
 313  @function sech
 314 */
 315 int liba_complex_sech(lua_State *L);
 316
 317 /***
 318  computes the complex hyperbolic cosecant
 319  @treturn a.complex complex number userdata
 320  @function csch
 321 */
 322 int liba_complex_csch(lua_State *L);
 323
 324 /***
 325  computes the complex hyperbolic cotangent
 326  @treturn a.complex complex number userdata
 327  @function coth
 328 */
 329 int liba_complex_coth(lua_State *L);
 330
 331 /***
 332  computes the complex arc hyperbolic sine
 333  @treturn a.complex complex number userdata
 334  @function asinh
 335 */
 336 int liba_complex_asinh(lua_State *L);
 337
 338 /***
 339  computes the complex arc hyperbolic cosine
 340  @treturn a.complex complex number userdata
 341  @function acosh
 342 */
 343 int liba_complex_acosh(lua_State *L);
 344
 345 /***
 346  computes the complex arc hyperbolic tangent
 347  @treturn a.complex complex number userdata
 348  @function atanh
 349 */
 350 int liba_complex_atanh(lua_State *L);
 351
 352 /***
 353  computes the complex arc hyperbolic secant
 354  @treturn a.complex complex number userdata
 355  @function asech
 356 */
 357 int liba_complex_asech(lua_State *L);
 358
 359 /***
 360  computes the complex arc hyperbolic cosecant
 361  @treturn a.complex complex number userdata
 362  @function acsch
 363 */
 364 int liba_complex_acsch(lua_State *L);
 365
 366 /***
 367  computes the complex arc hyperbolic cotangent
 368  @treturn a.complex complex number userdata
 369  @function acoth
 370 */
 371 int liba_complex_acoth(lua_State *L);
 372
 373 #if defined(__cplusplus)
 374 } /* extern "C" */
 375 #endif /* __cplusplus */
 376
 377 #endif /* complex.h */