complex.c

   1 /*
   2   complex.c: Coded by Tadayoshi Funaba 2008
   3
   4   This implementation is based on Keiju Ishitsuka's Complex library
   5   which is written in ruby.
   6 */
   7
   8 #include "ruby.h"
   9 #include <math.h>
  10
  11 #define NDEBUG
  12 #include <assert.h>
  13
  14 #ifndef COMPLEX_NAME
  15 #define COMPLEX_NAME "Complex"
  16 #endif
  17
  18 #define ZERO INT2FIX(0)
  19 #define ONE INT2FIX(1)
  20 #define TWO INT2FIX(2)
  21
  22 VALUE rb_cComplex;
  23
  24 static ID id_Unify, id_abs, id_abs2, id_arg, id_atan2_bang, id_cmp,
  25   id_conjugate, id_convert, id_cos, id_denominator, id_divmod,
  26   id_equal_p, id_exact_p, id_exp_bang, id_expt, id_floor, id_format,
  27   id_hypot, id_idiv, id_inspect, id_log_bang, id_negate, id_new, id_new_bang,
  28   id_numerator, id_polar, id_quo, id_scalar_p, id_sin, id_sqrt, id_to_f,
  29   id_to_i, id_to_r, id_to_s, id_truncate;
  30
  31 #define f_boolcast(x) ((x) ? Qtrue : Qfalse)
  32
  33 #define binop(n,op) \
  34 inline static VALUE \
  35 f_##n(VALUE x, VALUE y)\
  36 {\
  37     return rb_funcall(x, op, 1, y);\
  38 }
  39
  40 #define fun1(n) \
  41 inline static VALUE \
  42 f_##n(VALUE x)\
  43 {\
  44     return rb_funcall(x, id_##n, 0);\
  45 }
  46
  47 #define fun2(n) \
  48 inline static VALUE \
  49 f_##n(VALUE x, VALUE y)\
  50 {\
  51     return rb_funcall(x, id_##n, 1, y);\
  52 }
  53
  54 #define math1(n) \
  55 inline static VALUE \
  56 m_##n(VALUE x)\
  57 {\
  58     return rb_funcall(rb_mMath, id_##n, 1, x);\
  59 }
  60
  61 #define math2(n) \
  62 inline static VALUE \
  63 m_##n(VALUE x, VALUE y)\
  64 {\
  65     return rb_funcall(rb_mMath, id_##n, 2, x, y);\
  66 }
  67
  68 inline static VALUE
  69 f_add(VALUE x, VALUE y)
  70 {
  71     if (FIXNUM_P(y)) {
  72         if (FIX2LONG(y) == 0)
  73             return x;
  74     }
  75     else if (FIXNUM_P(x)) {
  76         if (FIX2LONG(x) == 0)
  77             return y;
  78     }
  79     return rb_funcall(x, '+', 1, y);
  80 }
  81
  82 inline static VALUE
  83 f_cmp(VALUE x, VALUE y)
  84 {
  85     if (FIXNUM_P(x) && FIXNUM_P(y)) {
  86         long c = FIX2LONG(x) - FIX2LONG(y);
  87         if (c > 0)
  88             c = 1;
  89         else if (c < 0)
  90             c = -1;
  91         return INT2FIX(c);
  92     }
  93     return rb_funcall(x, id_cmp, 1, y);
  94 }
  95
  96 inline static VALUE
  97 f_div(VALUE x, VALUE y)
  98 {
  99     if (FIXNUM_P(y) && FIX2LONG(y) == 1)
 100         return x;
 101     return rb_funcall(x, '/', 1, y);
 102 }
 103
 104 inline static VALUE
 105 f_gt_p(VALUE x, VALUE y)
 106 {
 107     if (FIXNUM_P(x) && FIXNUM_P(y))
 108         return f_boolcast(FIX2LONG(x) > FIX2LONG(y));
 109     return rb_funcall(x, '>', 1, y);
 110 }
 111
 112 inline static VALUE
 113 f_lt_p(VALUE x, VALUE y)
 114 {
 115     if (FIXNUM_P(x) && FIXNUM_P(y))
 116         return f_boolcast(FIX2LONG(x) < FIX2LONG(y));
 117     return rb_funcall(x, '<', 1, y);
 118 }
 119
 120 binop(mod, '%')
 121
 122 inline static VALUE
 123 f_mul(VALUE x, VALUE y)
 124 {
 125     if (FIXNUM_P(y)) {
 126         long _iy = FIX2LONG(y);
 127         if (_iy == 0) {
 128             if (TYPE(x) == T_FLOAT)
 129                 return rb_float_new(0.0);
 130             else
 131                 return ZERO;
 132         }
 133         else if (_iy == 1)
 134             return x;
 135     }
 136     else if (FIXNUM_P(x)) {
 137         long _ix = FIX2LONG(x);
 138         if (_ix == 0) {
 139             if (TYPE(y) == T_FLOAT)
 140                 return rb_float_new(0.0);
 141             else
 142                 return ZERO;
 143         }
 144         else if (_ix == 1)
 145             return y;
 146     }
 147     return rb_funcall(x, '*', 1, y);
 148 }
 149
 150 inline static VALUE
 151 f_sub(VALUE x, VALUE y)
 152 {
 153     if (FIXNUM_P(y))
 154         if (FIX2LONG(y) == 0)
 155             return x;
 156     return rb_funcall(x, '-', 1, y);
 157 }
 158
 159 binop(xor, '^')
 160
 161 fun1(abs)
 162 fun1(abs2)
 163 fun1(arg)
 164 fun1(conjugate)
 165 fun1(denominator)
 166 fun1(exact_p)
 167 fun1(floor)
 168 fun1(inspect)
 169 fun1(negate)
 170 fun1(numerator)
 171 fun1(polar)
 172 fun1(scalar_p)
 173 fun1(to_f)
 174 fun1(to_i)
 175 fun1(to_r)
 176 fun1(to_s)
 177 fun1(truncate)
 178
 179 fun2(divmod)
 180
 181 inline static VALUE
 182 f_equal_p(VALUE x, VALUE y)
 183 {
 184     if (FIXNUM_P(x) && FIXNUM_P(y))
 185         return f_boolcast(FIX2LONG(x) == FIX2LONG(y));
 186     return rb_funcall(x, id_equal_p, 1, y);
 187 }
 188
 189 fun2(expt)
 190 fun2(idiv)
 191 fun2(quo)
 192
 193 inline static VALUE
 194 f_negative_p(VALUE x)
 195 {
 196     if (FIXNUM_P(x))
 197         return f_boolcast(FIX2LONG(x) < 0);
 198     return rb_funcall(x, '<', 1, ZERO);
 199 }
 200
 201 inline static VALUE
 202 f_zero_p(VALUE x)
 203 {
 204     if (FIXNUM_P(x))
 205         return f_boolcast(FIX2LONG(x) == 0);
 206     return rb_funcall(x, id_equal_p, 1, ZERO);
 207 }
 208
 209 inline static VALUE
 210 f_one_p(VALUE x)
 211 {
 212     if (FIXNUM_P(x))
 213         return f_boolcast(FIX2LONG(x) == 1);
 214     return rb_funcall(x, id_equal_p, 1, ONE);
 215 }
 216
 217 inline static VALUE
 218 f_kind_of_p(VALUE x, VALUE c)
 219 {
 220     return rb_obj_is_kind_of(x, c);
 221 }
 222
 223 inline static VALUE
 224 k_numeric_p(VALUE x)
 225 {
 226     return f_kind_of_p(x, rb_cNumeric);
 227 }
 228
 229 inline static VALUE
 230 k_integer_p(VALUE x)
 231 {
 232     return f_kind_of_p(x, rb_cInteger);
 233 }
 234
 235 inline static VALUE
 236 k_float_p(VALUE x)
 237 {
 238     return f_kind_of_p(x, rb_cFloat);
 239 }
 240
 241 inline static VALUE
 242 k_rational_p(VALUE x)
 243 {
 244     return f_kind_of_p(x, rb_cRational);
 245 }
 246
 247 inline static VALUE
 248 k_complex_p(VALUE x)
 249 {
 250     return f_kind_of_p(x, rb_cComplex);
 251 }
 252
 253 inline static VALUE
 254 f_generic_p(VALUE x)
 255 {
 256     switch (TYPE(x)) {
 257       case T_FIXNUM:
 258       case T_BIGNUM:
 259       case T_FLOAT:
 260       case T_RATIONAL:
 261         return Qtrue;
 262       default:
 263         return Qfalse;
 264     }
 265 }
 266
 267 static VALUE
 268 nucomp_s_generic_p(VALUE klass, VALUE x)
 269 {
 270     return f_generic_p(x);
 271 }
 272
 273 #define get_dat1(x) \
 274     struct RComplex *dat;\
 275     dat = ((struct RComplex *)(x))
 276
 277 #define get_dat2(x,y) \
 278     struct RComplex *adat, *bdat;\
 279     adat = ((struct RComplex *)(x));\
 280     bdat = ((struct RComplex *)(y))
 281
 282 inline static VALUE
 283 nucomp_s_new_internal(VALUE klass, VALUE real, VALUE image)
 284 {
 285     NEWOBJ(obj, struct RComplex);
 286     OBJSETUP(obj, klass, T_COMPLEX);
 287
 288     obj->real = real;
 289     obj->image = image;
 290
 291     return (VALUE)obj;
 292 }
 293
 294 static VALUE
 295 nucomp_s_alloc(VALUE klass)
 296 {
 297     return nucomp_s_new_internal(klass, ZERO, ZERO);
 298 }
 299
 300 static VALUE
 301 nucomp_s_new_bang(int argc, VALUE *argv, VALUE klass)
 302 {
 303     VALUE real, image;
 304
 305     switch (rb_scan_args(argc, argv, "11", &real, &image)) {
 306       case 1:
 307         if (!k_numeric_p(real))
 308             real = f_to_i(real);
 309         image = ZERO;
 310         break;
 311       default:
 312         if (!k_numeric_p(real))
 313             real = f_to_i(real);
 314         if (!k_numeric_p(image))
 315             image = f_to_i(image);
 316         break;
 317     }
 318
 319     return nucomp_s_new_internal(klass, real, image);
 320 }
 321
 322 inline static VALUE
 323 f_complex_new_bang1(VALUE klass, VALUE x)
 324 {
 325     return nucomp_s_new_internal(klass, x, ZERO);
 326 }
 327
 328 inline static VALUE
 329 f_complex_new_bang2(VALUE klass, VALUE x, VALUE y)
 330 {
 331     return nucomp_s_new_internal(klass, x, y);
 332 }
 333
 334 #define f_unify_p(klass) rb_const_defined(klass, id_Unify)
 335
 336 inline static void
 337 nucomp_real_check(VALUE num)
 338 {
 339     switch (TYPE(num)) {
 340       case T_FIXNUM:
 341       case T_BIGNUM:
 342       case T_FLOAT:
 343       case T_RATIONAL:
 344         break;
 345       default:
 346         rb_raise(rb_eArgError, "not a real");
 347     }
 348 }
 349
 350 inline static VALUE
 351 nucomp_s_canonicalize_internal(VALUE klass, VALUE real, VALUE image)
 352 {
 353 #define CL_CANON
 354 #ifdef CL_CANON
 355     if (f_zero_p(image) && f_unify_p(klass) &&
 356         !k_float_p(real) && !k_float_p(image))
 357         return real;
 358 #else
 359     if (f_zero_p(image) && f_unify_p(klass))
 360         return real;
 361 #endif
 362     else if (f_scalar_p(real) && f_scalar_p(image))
 363         return nucomp_s_new_internal(klass, real, image);
 364     else if (f_scalar_p(real)) {
 365         get_dat1(image);
 366
 367         return nucomp_s_new_internal(klass,
 368                                      f_sub(real, dat->image),
 369                                      f_add(ZERO, dat->real));
 370     }
 371     else if (f_scalar_p(image)) {
 372         get_dat1(real);
 373
 374         return nucomp_s_new_internal(klass,
 375                                      dat->real,
 376                                      f_add(dat->image, image));
 377     }
 378     else {
 379         get_dat2(real, image);
 380
 381         return nucomp_s_new_internal(klass,
 382                                      f_sub(adat->real, bdat->image),
 383                                      f_add(adat->image, bdat->real));
 384     }
 385 }
 386
 387 #if 0
 388 static VALUE
 389 nucomp_s_canonicalize(int argc, VALUE *argv, VALUE klass)
 390 {
 391     VALUE real, image;
 392
 393     switch (rb_scan_args(argc, argv, "11", &real, &image)) {
 394       case 1:
 395         image = ZERO;
 396         break;
 397     }
 398
 399     nucomp_real_check(real);
 400     nucomp_real_check(image);
 401
 402     return nucomp_s_canonicalize_internal(klass, real, image);
 403 }
 404 #endif
 405
 406 static VALUE
 407 nucomp_s_new(int argc, VALUE *argv, VALUE klass)
 408 {
 409     VALUE real, image;
 410
 411     switch (rb_scan_args(argc, argv, "11", &real, &image)) {
 412       case 1:
 413         image = ZERO;
 414         break;
 415     }
 416
 417     nucomp_real_check(real);
 418     nucomp_real_check(image);
 419
 420     return nucomp_s_canonicalize_internal(klass, real, image);
 421 }
 422
 423 inline static VALUE
 424 f_complex_new1(VALUE klass, VALUE x)
 425 {
 426     assert(!k_complex_p(x));
 427     return nucomp_s_canonicalize_internal(klass, x, ZERO);
 428 }
 429
 430 inline static VALUE
 431 f_complex_new2(VALUE klass, VALUE x, VALUE y)
 432 {
 433     assert(!k_complex_p(x));
 434     return nucomp_s_canonicalize_internal(klass, x, y);
 435 }
 436
 437 static VALUE
 438 nucomp_f_complex(int argc, VALUE *argv, VALUE klass)
 439 {
 440     return rb_funcall2(rb_cComplex, id_convert, argc, argv);
 441 }
 442
 443 extern VALUE math_atan2(VALUE obj, VALUE x, VALUE y);
 444 extern VALUE math_cos(VALUE obj, VALUE x);
 445 extern VALUE math_cosh(VALUE obj, VALUE x);
 446 extern VALUE math_exp(VALUE obj, VALUE x);
 447 extern VALUE math_hypot(VALUE obj, VALUE x, VALUE y);
 448 extern VALUE math_log(int argc, VALUE *argv);
 449 extern VALUE math_sin(VALUE obj, VALUE x);
 450 extern VALUE math_sinh(VALUE obj, VALUE x);
 451 extern VALUE math_sqrt(VALUE obj, VALUE x);
 452
 453 #define m_atan2_bang(x,y) math_atan2(Qnil,x,y)
 454 #define m_cos_bang(x) math_cos(Qnil,x)
 455 #define m_cosh_bang(x) math_cosh(Qnil,x)
 456 #define m_exp_bang(x) math_exp(Qnil,x)
 457 #define m_hypot(x,y) math_hypot(Qnil,x,y)
 458
 459 static VALUE
 460 m_log_bang(VALUE x)
 461 {
 462   return math_log(1, &x);
 463 }
 464
 465 #define m_sin_bang(x) math_sin(Qnil,x)
 466 #define m_sinh_bang(x) math_sinh(Qnil,x)
 467 #define m_sqrt_bang(x) math_sqrt(Qnil,x)
 468
 469 static VALUE
 470 m_cos(VALUE x)
 471 {
 472     get_dat1(x);
 473
 474     if (f_generic_p(x))
 475         return m_cos_bang(x);
 476     return f_complex_new2(rb_cComplex,
 477                           f_mul(m_cos_bang(dat->real),
 478                                 m_cosh_bang(dat->image)),
 479                           f_mul(f_negate(m_sin_bang(dat->real)),
 480                                 m_sinh_bang(dat->image)));
 481 }
 482
 483 static VALUE
 484 m_sin(VALUE x)
 485 {
 486     get_dat1(x);
 487
 488     if (f_generic_p(x))
 489         return m_sin_bang(x);
 490     return f_complex_new2(rb_cComplex,
 491                           f_mul(m_sin_bang(dat->real),
 492                                 m_cosh_bang(dat->image)),
 493                           f_mul(m_cos_bang(dat->real),
 494                                 m_sinh_bang(dat->image)));
 495 }
 496
 497 static VALUE
 498 m_sqrt(VALUE x)
 499 {
 500     if (f_generic_p(x)) {
 501         if (!f_negative_p(x))
 502             return m_sqrt_bang(x);
 503         return f_complex_new2(rb_cComplex, ZERO, m_sqrt_bang(f_negate(x)));
 504     }
 505     else {
 506         get_dat1(x);
 507
 508         if (f_negative_p(dat->image))
 509             return f_conjugate(m_sqrt(f_conjugate(x)));
 510         else {
 511             VALUE a = f_abs(x);
 512             return f_complex_new2(rb_cComplex,
 513                                   m_sqrt_bang(f_div(f_add(a, dat->real), TWO)),
 514                                   m_sqrt_bang(f_div(f_sub(a, dat->real), TWO)));
 515         }
 516     }
 517 }
 518
 519 static VALUE
 520 nucomp_s_polar(VALUE klass, VALUE abs, VALUE arg)
 521 {
 522     return f_complex_new2(klass,
 523                           f_mul(abs, m_cos(arg)),
 524                           f_mul(abs, m_sin(arg)));
 525 }
 526
 527 static VALUE
 528 nucomp_real(VALUE self)
 529 {
 530     get_dat1(self);
 531     return dat->real;
 532 }
 533
 534 static VALUE
 535 nucomp_image(VALUE self)
 536 {
 537     get_dat1(self);
 538     return dat->image;
 539 }
 540
 541 static VALUE
 542 nucomp_add(VALUE self, VALUE other)
 543 {
 544     switch (TYPE(other)) {
 545       case T_FIXNUM:
 546       case T_BIGNUM:
 547       case T_FLOAT:
 548       case T_RATIONAL:
 549         {
 550             get_dat1(self);
 551
 552             return f_complex_new2(CLASS_OF(self),
 553                                   f_add(dat->real, other), dat->image);
 554         }
 555       case T_COMPLEX:
 556         {
 557             VALUE real, image;
 558
 559             get_dat2(self, other);
 560
 561             real = f_add(adat->real, bdat->real);
 562             image = f_add(adat->image, bdat->image);
 563
 564             return f_complex_new2(CLASS_OF(self), real, image);
 565         }
 566       default:
 567         return rb_num_coerce_bin(self, other, '+');
 568     }
 569 }
 570
 571 static VALUE
 572 nucomp_sub(VALUE self, VALUE other)
 573 {
 574     switch (TYPE(other)) {
 575       case T_FIXNUM:
 576       case T_BIGNUM:
 577       case T_FLOAT:
 578       case T_RATIONAL:
 579         {
 580             get_dat1(self);
 581
 582             return f_complex_new2(CLASS_OF(self),
 583                                   f_sub(dat->real, other), dat->image);
 584         }
 585       case T_COMPLEX:
 586         {
 587             VALUE real, image;
 588
 589             get_dat2(self, other);
 590
 591             real = f_sub(adat->real, bdat->real);
 592             image = f_sub(adat->image, bdat->image);
 593
 594             return f_complex_new2(CLASS_OF(self), real, image);
 595         }
 596       default:
 597         return rb_num_coerce_bin(self, other, '-');
 598     }
 599 }
 600
 601 static VALUE
 602 nucomp_mul(VALUE self, VALUE other)
 603 {
 604     switch (TYPE(other)) {
 605       case T_FIXNUM:
 606       case T_BIGNUM:
 607       case T_FLOAT:
 608       case T_RATIONAL:
 609         {
 610             get_dat1(self);
 611
 612             return f_complex_new2(CLASS_OF(self),
 613                                   f_mul(dat->real, other),
 614                                   f_mul(dat->image, other));
 615         }
 616       case T_COMPLEX:
 617         {
 618             VALUE real, image;
 619
 620             get_dat2(self, other);
 621
 622             real = f_sub(f_mul(adat->real, bdat->real),
 623                          f_mul(adat->image, bdat->image));
 624             image = f_add(f_mul(adat->real, bdat->image),
 625                           f_mul(adat->image, bdat->real));
 626
 627             return f_complex_new2(CLASS_OF(self), real, image);
 628         }
 629       default:
 630         return rb_num_coerce_bin(self, other, '*');
 631     }
 632 }
 633
 634 static VALUE
 635 nucomp_div(VALUE self, VALUE other)
 636 {
 637     switch (TYPE(other)) {
 638       case T_FIXNUM:
 639       case T_BIGNUM:
 640       case T_FLOAT:
 641       case T_RATIONAL:
 642         {
 643             get_dat1(self);
 644
 645             return f_complex_new2(CLASS_OF(self),
 646                                   f_div(dat->real, other),
 647                                   f_div(dat->image, other));
 648         }
 649       case T_COMPLEX:
 650         {
 651             get_dat2(self, other);
 652
 653             if (TYPE(adat->real)  == T_FLOAT ||
 654                 TYPE(adat->image) == T_FLOAT ||
 655                 TYPE(bdat->real)  == T_FLOAT ||
 656                 TYPE(bdat->image) == T_FLOAT) {
 657                 VALUE magn = m_hypot(bdat->real, bdat->image);
 658                 VALUE tmp = f_complex_new_bang2(CLASS_OF(self),
 659                                                 f_div(bdat->real, magn),
 660                                                 f_div(bdat->image, magn));
 661                 return f_div(f_mul(self, f_conjugate(tmp)), magn);
 662             }
 663             return f_div(f_mul(self, f_conjugate(other)), f_abs2(other));
 664         }
 665       default:
 666         return rb_num_coerce_bin(self, other, '/');
 667     }
 668 }
 669
 670 static VALUE
 671 nucomp_quo(VALUE self, VALUE other)
 672 {
 673     get_dat1(self);
 674
 675     return f_div(f_complex_new2(CLASS_OF(self),
 676                                 f_quo(dat->real, ONE),
 677                                 f_quo(dat->image, ONE)), other);
 678 }
 679
 680 static VALUE
 681 nucomp_fdiv(VALUE self, VALUE other)
 682 {
 683     get_dat1(self);
 684
 685     return f_div(f_complex_new2(CLASS_OF(self),
 686                                 f_to_f(dat->real),
 687                                 f_to_f(dat->image)), other);
 688 }
 689
 690 static VALUE
 691 nucomp_expt(VALUE self, VALUE other)
 692 {
 693     if (f_zero_p(other))
 694         return f_complex_new_bang1(CLASS_OF(self), ONE);
 695
 696     if (k_rational_p(other) && f_one_p(f_denominator(other)))
 697         other = f_numerator(other); /* good? */
 698
 699     switch (TYPE(other)) {
 700       case T_FIXNUM:
 701       case T_BIGNUM:
 702         if (f_gt_p(other, ZERO)) {
 703             VALUE x, z, n;
 704
 705             x = self;
 706             z = x;
 707             n = f_sub(other, ONE);
 708
 709             while (!f_zero_p(n)) {
 710                 VALUE a;
 711
 712                 while (a = f_divmod(n, TWO),
 713                        f_zero_p(RARRAY_PTR(a)[1])) {
 714                     get_dat1(x);
 715
 716                     x = f_complex_new2(CLASS_OF(self),
 717                                        f_sub(f_mul(dat->real, dat->real),
 718                                              f_mul(dat->image, dat->image)),
 719                                        f_mul(f_mul(TWO, dat->real), dat->image));
 720                     n = RARRAY_PTR(a)[0];
 721                 }
 722                 z = f_mul(z, x);
 723                 n = f_sub(n, ONE);
 724             }
 725             return z;
 726         }
 727         return f_expt(f_div(f_to_r(ONE), self), f_negate(other));
 728       case T_FLOAT:
 729       case T_RATIONAL:
 730         {
 731             VALUE a, r, theta;
 732
 733             a = f_polar(self);
 734             r = RARRAY_PTR(a)[0];
 735             theta = RARRAY_PTR(a)[1];
 736             return nucomp_s_polar(CLASS_OF(self), f_expt(r, other),
 737                                   f_mul(theta, other));
 738         }
 739       case T_COMPLEX:
 740         {
 741             VALUE a, r, theta, ore, oim, nr, ntheta;
 742
 743             get_dat1(other);
 744
 745             a = f_polar(self);
 746             r = RARRAY_PTR(a)[0];
 747             theta = RARRAY_PTR(a)[1];
 748
 749             ore = dat->real;
 750             oim = dat->image;
 751             nr = m_exp_bang(f_sub(f_mul(ore, m_log_bang(r)),
 752                                   f_mul(oim, theta)));
 753             ntheta = f_add(f_mul(theta, ore), f_mul(oim, m_log_bang(r)));
 754             return nucomp_s_polar(CLASS_OF(self), nr, ntheta);
 755         }
 756       default:
 757         return rb_num_coerce_bin(self, other, id_expt);
 758     }
 759 }
 760
 761 static VALUE
 762 nucomp_equal_p(VALUE self, VALUE other)
 763 {
 764     switch (TYPE(other)) {
 765       case T_FIXNUM:
 766       case T_BIGNUM:
 767       case T_FLOAT:
 768       case T_RATIONAL:
 769         {
 770             get_dat1(self);
 771
 772             return f_boolcast(f_equal_p(dat->real, other) && f_zero_p(dat->image));
 773         }
 774       case T_COMPLEX:
 775         {
 776             get_dat2(self, other);
 777
 778             return f_boolcast(f_equal_p(adat->real, bdat->real) &&
 779                               f_equal_p(adat->image, bdat->image));
 780         }
 781       default:
 782         return f_equal_p(other, self);
 783     }
 784 }
 785
 786 static VALUE
 787 nucomp_coerce(VALUE self, VALUE other)
 788 {
 789     switch (TYPE(other)) {
 790       case T_FIXNUM:
 791       case T_BIGNUM:
 792       case T_FLOAT:
 793       case T_RATIONAL:
 794         return rb_assoc_new(f_complex_new_bang1(CLASS_OF(self), other), self);
 795     }
 796
 797     rb_raise(rb_eTypeError, "%s can't be coerced into %s",
 798              rb_obj_classname(other), rb_obj_classname(self));
 799     return Qnil;
 800 }
 801
 802 static VALUE
 803 nucomp_abs(VALUE self)
 804 {
 805     get_dat1(self);
 806     return m_hypot(dat->real, dat->image);
 807 }
 808
 809 static VALUE
 810 nucomp_abs2(VALUE self)
 811 {
 812     get_dat1(self);
 813     return f_add(f_mul(dat->real, dat->real),
 814                  f_mul(dat->image, dat->image));
 815 }
 816
 817 static VALUE
 818 nucomp_arg(VALUE self)
 819 {
 820     get_dat1(self);
 821     return m_atan2_bang(dat->image, dat->real);
 822 }
 823
 824 static VALUE
 825 nucomp_polar(VALUE self)
 826 {
 827     return rb_assoc_new(f_abs(self), f_arg(self));
 828 }
 829
 830 static VALUE
 831 nucomp_conjugate(VALUE self)
 832 {
 833     get_dat1(self);
 834     return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->image));
 835 }
 836
 837 #if 0
 838 static VALUE
 839 nucomp_real_p(VALUE self)
 840 {
 841     return Qfalse;
 842 }
 843
 844 static VALUE
 845 nucomp_complex_p(VALUE self)
 846 {
 847     return Qtrue;
 848 }
 849
 850 static VALUE
 851 nucomp_exact_p(VALUE self)
 852 {
 853     get_dat1(self);
 854     return f_boolcast(f_exact_p(dat->real) && f_exact_p(dat->image));
 855 }
 856
 857 static VALUE
 858 nucomp_inexact_p(VALUE self)
 859 {
 860     return f_boolcast(!nucomp_exact_p(self));
 861 }
 862 #endif
 863
 864 extern VALUE rb_lcm(VALUE x, VALUE y);
 865
 866 static VALUE
 867 nucomp_denominator(VALUE self)
 868 {
 869     get_dat1(self);
 870     return rb_lcm(f_denominator(dat->real), f_denominator(dat->image));
 871 }
 872
 873 static VALUE
 874 nucomp_numerator(VALUE self)
 875 {
 876     VALUE cd;
 877
 878     get_dat1(self);
 879
 880     cd = f_denominator(self);
 881     return f_complex_new2(CLASS_OF(self),
 882                           f_mul(f_numerator(dat->real),
 883                                 f_div(cd, f_denominator(dat->real))),
 884                           f_mul(f_numerator(dat->image),
 885                                 f_div(cd, f_denominator(dat->image))));
 886 }
 887
 888 static VALUE
 889 nucomp_hash(VALUE self)
 890 {
 891     get_dat1(self);
 892     return f_xor(dat->real, dat->image);
 893 }
 894
 895 #ifndef HAVE_SIGNBIT
 896 #ifdef signbit
 897 #define HAVE_SIGNBIT 1
 898 #endif
 899 #endif
 900
 901 inline static VALUE
 902 f_signbit(VALUE x)
 903 {
 904     switch (TYPE(x)) {
 905       case T_FLOAT:
 906 #ifdef HAVE_SIGNBIT
 907         return f_boolcast(signbit(RFLOAT_VALUE(x)));
 908 #else
 909         {
 910             char s[2];
 911
 912             (void)snprintf(s, sizeof s, "%.0f", RFLOAT_VALUE(x));
 913
 914             return f_boolcast(s[0] == '-');
 915         }
 916 #endif
 917     }
 918     return f_negative_p(x);
 919 }
 920
 921 inline static VALUE
 922 f_tzero_p(VALUE x)
 923 {
 924     return f_boolcast(f_zero_p(x) && !f_signbit(x));
 925 }
 926
 927 inline static VALUE
 928 f_tpositive_p(VALUE x)
 929 {
 930     return f_boolcast(!f_signbit(x));
 931 }
 932
 933 static VALUE
 934 nucomp_to_s(VALUE self)
 935 {
 936     VALUE s, rezero, impos;
 937
 938     get_dat1(self);
 939
 940     rezero = f_tzero_p(dat->real);
 941     impos = f_tpositive_p(dat->image);
 942
 943     if (rezero)
 944         s = rb_str_new2("");
 945     else {
 946         s = f_to_s(dat->real);
 947         rb_str_cat2(s, !impos ? "-" : "+");
 948     }
 949
 950     if (k_rational_p(dat->image) &&
 951         !f_one_p(f_denominator(dat->image))) {
 952         rb_str_cat2(s, "(");
 953         rb_str_concat(s, f_to_s(rezero ? dat->image : f_abs(dat->image)));
 954         rb_str_cat2(s, ")i");
 955     }
 956     else {
 957         rb_str_concat(s, f_to_s(rezero ? dat->image : f_abs(dat->image)));
 958         rb_str_cat2(s, "i");
 959     }
 960
 961     return s;
 962 }
 963
 964 static VALUE
 965 nucomp_inspect(VALUE self)
 966 {
 967     VALUE s;
 968
 969     get_dat1(self);
 970
 971     s = rb_str_new2("Complex(");
 972     rb_str_concat(s, f_inspect(dat->real));
 973     rb_str_cat2(s, ", ");
 974     rb_str_concat(s, f_inspect(dat->image));
 975     rb_str_cat2(s, ")");
 976
 977     return s;
 978 }
 979
 980 static VALUE
 981 nucomp_marshal_dump(VALUE self)
 982 {
 983     get_dat1(self);
 984     return rb_assoc_new(dat->real, dat->image);
 985 }
 986
 987 static VALUE
 988 nucomp_marshal_load(VALUE self, VALUE a)
 989 {
 990     get_dat1(self);
 991     dat->real = RARRAY_PTR(a)[0];
 992     dat->image = RARRAY_PTR(a)[1];
 993     return self;
 994 }
 995
 996 /* --- */
 997
 998 VALUE
 999 rb_complex_raw(VALUE x, VALUE y)
1000 {
1001     return nucomp_s_new_internal(rb_cComplex, x, y);
1002 }
1003
1004 VALUE
1005 rb_complex_new(VALUE x, VALUE y)
1006 {
1007     return nucomp_s_canonicalize_internal(rb_cComplex, x, y);
1008 }
1009
1010 static VALUE nucomp_s_convert(int argc, VALUE *argv, VALUE klass);
1011
1012 VALUE
1013 rb_Complex(VALUE x, VALUE y)
1014 {
1015     VALUE a[2];
1016     a[0] = x;
1017     a[1] = y;
1018     return nucomp_s_convert(2, a, rb_cComplex);
1019 }
1020
1021 static VALUE
1022 nucomp_scalar_p(VALUE self)
1023 {
1024     return Qfalse;
1025 }
1026
1027 static VALUE
1028 nucomp_to_i(VALUE self)
1029 {
1030     get_dat1(self);
1031
1032     if (k_float_p(dat->image) || !f_zero_p(dat->image)) {
1033         VALUE s = f_to_s(self);
1034         rb_raise(rb_eRangeError, "can't convert %s into Integer",
1035                  StringValuePtr(s));
1036     }
1037     return f_to_i(dat->real);
1038 }
1039
1040 static VALUE
1041 nucomp_to_f(VALUE self)
1042 {
1043     get_dat1(self);
1044
1045     if (k_float_p(dat->image) || !f_zero_p(dat->image)) {
1046         VALUE s = f_to_s(self);
1047         rb_raise(rb_eRangeError, "can't convert %s into Float",
1048                  StringValuePtr(s));
1049     }
1050     return f_to_f(dat->real);
1051 }
1052
1053 static VALUE
1054 nucomp_to_r(VALUE self)
1055 {
1056     get_dat1(self);
1057
1058     if (k_float_p(dat->image) || !f_zero_p(dat->image)) {
1059         VALUE s = f_to_s(self);
1060         rb_raise(rb_eRangeError, "can't convert %s into Rational",
1061                  StringValuePtr(s));
1062     }
1063     return f_to_r(dat->real);
1064 }
1065
1066 static VALUE
1067 nilclass_to_c(VALUE self)
1068 {
1069     return rb_complex_new1(INT2FIX(0));
1070 }
1071
1072 static VALUE
1073 numeric_to_c(VALUE self)
1074 {
1075     return rb_complex_new1(self);
1076 }
1077
1078 static VALUE comp_pat1, comp_pat2, a_slash, a_dot_and_an_e,
1079     null_string, underscores_pat, an_underscore;
1080
1081 #define DIGITS "(?:\\d(?:_\\d|\\d)*)"
1082 #define NUMERATOR "(?:" DIGITS "?\\.)?" DIGITS "(?:[eE][-+]?" DIGITS ")?"
1083 #define DENOMINATOR "[-+]?" DIGITS
1084 #define NUMBER "[-+]?" NUMERATOR "(?:\\/" DENOMINATOR ")?"
1085 #define NUMBERNOS NUMERATOR "(?:\\/" DENOMINATOR ")?"
1086 #define PATTERN1 "\\A((" NUMBER ")|\\((" NUMBER ")\\))?[iIjJ]"
1087 #define PATTERN2 "\\A(" NUMBER ")(([-+])(?:(" NUMBERNOS ")|\\((" NUMBER ")\\))?[iIjJ])?"
1088
1089 static void
1090 make_patterns(void)
1091 {
1092     static const char comp_pat1_source[] = PATTERN1;
1093     static const char comp_pat2_source[] = PATTERN2;
1094     static const char underscores_pat_source[] = "_+";
1095
1096     if (comp_pat1) return;
1097
1098     comp_pat1 = rb_reg_new(comp_pat1_source, sizeof comp_pat1_source - 1, 0);
1099     rb_global_variable(&comp_pat1);
1100
1101     comp_pat2 = rb_reg_new(comp_pat2_source, sizeof comp_pat2_source - 1, 0);
1102     rb_global_variable(&comp_pat2);
1103
1104     a_slash = rb_str_new2("/");
1105     rb_global_variable(&a_slash);
1106
1107     a_dot_and_an_e = rb_str_new2(".eE");
1108     rb_global_variable(&a_dot_and_an_e);
1109
1110     null_string = rb_str_new2("");
1111     rb_global_variable(&null_string);
1112
1113     underscores_pat = rb_reg_new(underscores_pat_source,
1114                                  sizeof underscores_pat_source - 1, 0);
1115     rb_global_variable(&underscores_pat);
1116
1117     an_underscore = rb_str_new2("_");
1118     rb_global_variable(&an_underscore);
1119 }
1120
1121 #define id_strip rb_intern("strip")
1122 #define f_strip(x) rb_funcall(x, id_strip, 0)
1123
1124 #define id_match rb_intern("match")
1125 #define f_match(x,y) rb_funcall(x, id_match, 1, y)
1126
1127 #define id_aref rb_intern("[]")
1128 #define f_aref(x,y) rb_funcall(x, id_aref, 1, y)
1129
1130 #define id_post_match rb_intern("post_match")
1131 #define f_post_match(x) rb_funcall(x, id_post_match, 0)
1132
1133 #define id_split rb_intern("split")
1134 #define f_split(x,y) rb_funcall(x, id_split, 1, y)
1135
1136 #define id_include_p rb_intern("include?")
1137 #define f_include_p(x,y) rb_funcall(x, id_include_p, 1, y)
1138
1139 #define id_count rb_intern("count")
1140 #define f_count(x,y) rb_funcall(x, id_count, 1, y)
1141
1142 #define id_gsub_bang rb_intern("gsub!")
1143 #define f_gsub_bang(x,y,z) rb_funcall(x, id_gsub_bang, 2, y, z)
1144
1145 static VALUE
1146 string_to_c_internal(VALUE self)
1147 {
1148     VALUE s;
1149
1150     s = f_strip(self);
1151
1152     if (RSTRING_LEN(s) == 0)
1153         return rb_assoc_new(Qnil, self);
1154
1155     {
1156         VALUE m, sr, si, re, r, i;
1157
1158         m = f_match(comp_pat1, s);
1159         if (!NIL_P(m)) {
1160             sr = Qnil;
1161             si = f_aref(m, INT2FIX(1));
1162             if (NIL_P(si))
1163                 si = rb_str_new2("1");
1164             else {
1165                 si = f_aref(m, INT2FIX(2));
1166                 if (NIL_P(si))
1167                     si = f_aref(m, INT2FIX(3));
1168             }
1169             re = f_post_match(m);
1170         }
1171         if (NIL_P(m)) {
1172             m = f_match(comp_pat2, s);
1173             if (NIL_P(m)) {
1174                 return rb_assoc_new(Qnil, self);
1175             }
1176             sr = f_aref(m, INT2FIX(1));
1177             if (NIL_P(f_aref(m, INT2FIX(2))))
1178                 si = Qnil;
1179             else {
1180                 VALUE t;
1181
1182                 si = f_aref(m, INT2FIX(3));
1183                 t = f_aref(m, INT2FIX(4));
1184                 if (NIL_P(t))
1185                     t = f_aref(m, INT2FIX(5));
1186                 if (NIL_P(t))
1187                     t = rb_str_new2("1");
1188                 rb_str_concat(si, t);
1189             }
1190             re = f_post_match(m);
1191         }
1192         r = INT2FIX(0);
1193         i = INT2FIX(0);
1194         if (!NIL_P(sr)) {
1195             if (f_include_p(sr, a_slash))
1196                 r = f_to_r(sr);
1197             else if (f_gt_p(f_count(sr, a_dot_and_an_e), INT2FIX(0)))
1198                 r = f_to_f(sr);
1199             else
1200                 r = f_to_i(sr);
1201         }
1202         if (!NIL_P(si)) {
1203             if (f_include_p(si, a_slash))
1204                 i = f_to_r(si);
1205             else if (f_gt_p(f_count(si, a_dot_and_an_e), INT2FIX(0)))
1206                 i = f_to_f(si);
1207             else
1208                 i = f_to_i(si);
1209         }
1210         return rb_assoc_new(rb_complex_new2(r, i), re);
1211     }
1212 }
1213
1214 static VALUE
1215 string_to_c_strict(VALUE self)
1216 {
1217     VALUE a = string_to_c_internal(self);
1218     if (NIL_P(RARRAY_PTR(a)[0]) || RSTRING_LEN(RARRAY_PTR(a)[1]) > 0) {
1219         VALUE s = f_inspect(self);
1220         rb_raise(rb_eArgError, "invalid value for Complex: %s",
1221                  StringValuePtr(s));
1222     }
1223     return RARRAY_PTR(a)[0];
1224 }
1225
1226 #define id_gsub rb_intern("gsub")
1227 #define f_gsub(x,y,z) rb_funcall(x, id_gsub, 2, y, z)
1228
1229 static VALUE
1230 string_to_c(VALUE self)
1231 {
1232     VALUE s, a, backref;
1233
1234     backref = rb_backref_get();
1235     rb_match_busy(backref);
1236
1237     s = f_gsub(self, underscores_pat, an_underscore);
1238     a = string_to_c_internal(s);
1239
1240     rb_backref_set(backref);
1241
1242     if (!NIL_P(RARRAY_PTR(a)[0]))
1243         return RARRAY_PTR(a)[0];
1244     return rb_complex_new1(INT2FIX(0));
1245 }
1246
1247 static VALUE
1248 nucomp_s_convert(int argc, VALUE *argv, VALUE klass)
1249 {
1250     VALUE a1, a2, backref;
1251
1252     rb_scan_args(argc, argv, "02", &a1, &a2);
1253
1254     backref = rb_backref_get();
1255     rb_match_busy(backref);
1256
1257     switch (TYPE(a1)) {
1258       case T_FIXNUM:
1259       case T_BIGNUM:
1260       case T_FLOAT:
1261         break;
1262       case T_STRING:
1263         a1 = string_to_c_strict(a1);
1264         break;
1265     }
1266
1267     switch (TYPE(a2)) {
1268       case T_FIXNUM:
1269       case T_BIGNUM:
1270       case T_FLOAT:
1271         break;
1272       case T_STRING:
1273         a2 = string_to_c_strict(a2);
1274         break;
1275     }
1276
1277     rb_backref_set(backref);
1278
1279     switch (TYPE(a1)) {
1280       case T_COMPLEX:
1281         {
1282             get_dat1(a1);
1283
1284             if (!k_float_p(dat->image) && f_zero_p(dat->image))
1285                 a1 = dat->real;
1286         }
1287     }
1288
1289     switch (TYPE(a2)) {
1290       case T_COMPLEX:
1291         {
1292             get_dat1(a2);
1293
1294             if (!k_float_p(dat->image) && f_zero_p(dat->image))
1295                 a2 = dat->real;
1296         }
1297     }
1298
1299     switch (TYPE(a1)) {
1300       case T_COMPLEX:
1301         if (NIL_P(a2) || f_zero_p(a2))
1302             return a1;
1303     }
1304
1305     {
1306         VALUE argv2[2];
1307         argv2[0] = a1;
1308         argv2[1] = a2;
1309         return nucomp_s_new(argc, argv2, klass);
1310     }
1311 }
1312
1313 /* --- */
1314
1315 #define id_Complex rb_intern("Complex")
1316
1317 static VALUE
1318 numeric_re(VALUE self)
1319 {
1320     return rb_Complex1(self);
1321 }
1322
1323 static VALUE
1324 numeric_im(VALUE self)
1325 {
1326     return rb_Complex2(ZERO, self);
1327 }
1328
1329 static VALUE
1330 numeric_real(VALUE self)
1331 {
1332     return self;
1333 }
1334
1335 static VALUE
1336 numeric_image(VALUE self)
1337 {
1338     return INT2FIX(0);
1339 }
1340
1341 #define id_PI rb_intern("PI")
1342
1343 static VALUE
1344 numeric_arg(VALUE self)
1345 {
1346     if (!f_negative_p(self))
1347         return INT2FIX(0);
1348     return rb_const_get(rb_mMath, id_PI);
1349 }
1350
1351 static VALUE
1352 numeric_polar(VALUE self)
1353 {
1354     return rb_assoc_new(f_abs(self), f_arg(self));
1355 }
1356
1357 static VALUE
1358 numeric_conjugate(VALUE self)
1359 {
1360     return self;
1361 }
1362
1363 void
1364 Init_Complex(void)
1365 {
1366 #undef rb_intern
1367
1368     assert(fprintf(stderr, "assert() is now active\n"));
1369
1370     id_Unify = rb_intern("Unify");
1371     id_abs = rb_intern("abs");
1372     id_abs2 = rb_intern("abs2");
1373     id_arg = rb_intern("arg");
1374     id_atan2_bang = rb_intern("atan2!");
1375     id_cmp = rb_intern("<=>");
1376     id_conjugate = rb_intern("conjugate");
1377     id_convert = rb_intern("convert");
1378     id_cos = rb_intern("cos");
1379     id_denominator = rb_intern("denominator");
1380     id_divmod = rb_intern("divmod");
1381     id_equal_p = rb_intern("==");
1382     id_exact_p = rb_intern("exact?");
1383     id_exp_bang = rb_intern("exp!");
1384     id_expt = rb_intern("**");
1385     id_floor = rb_intern("floor");
1386     id_format = rb_intern("format");
1387     id_hypot = rb_intern("hypot");
1388     id_idiv = rb_intern("div");
1389     id_inspect = rb_intern("inspect");
1390     id_log_bang = rb_intern("log!");
1391     id_negate = rb_intern("-@");
1392     id_new = rb_intern("new");
1393     id_new_bang = rb_intern("new!");
1394     id_numerator = rb_intern("numerator");
1395     id_polar = rb_intern("polar");
1396     id_quo = rb_intern("quo");
1397     id_scalar_p = rb_intern("scalar?");
1398     id_sin = rb_intern("sin");
1399     id_sqrt = rb_intern("sqrt");
1400     id_to_f = rb_intern("to_f");
1401     id_to_i = rb_intern("to_i");
1402     id_to_r = rb_intern("to_r");
1403     id_to_s = rb_intern("to_s");
1404     id_truncate = rb_intern("truncate");
1405
1406     rb_cComplex = rb_define_class(COMPLEX_NAME, rb_cNumeric);
1407
1408     rb_define_alloc_func(rb_cComplex, nucomp_s_alloc);
1409     rb_funcall(rb_cComplex, rb_intern("private_class_method"), 1,
1410                ID2SYM(rb_intern("allocate")));
1411
1412     rb_define_singleton_method(rb_cComplex, "generic?", nucomp_s_generic_p, 1);
1413
1414     rb_define_singleton_method(rb_cComplex, "new!", nucomp_s_new_bang, -1);
1415     rb_funcall(rb_cComplex, rb_intern("private_class_method"), 1,
1416                ID2SYM(rb_intern("new!")));
1417
1418     rb_define_singleton_method(rb_cComplex, "new", nucomp_s_new, -1);
1419     rb_funcall(rb_cComplex, rb_intern("private_class_method"), 1,
1420                ID2SYM(rb_intern("new")));
1421
1422 #if 0
1423     rb_define_singleton_method(rb_cComplex, "rect", nucomp_s_new, -1);
1424     rb_define_singleton_method(rb_cComplex, "rectangular", nucomp_s_new, -1);
1425 #endif
1426     rb_define_singleton_method(rb_cComplex, "polar", nucomp_s_polar, 2);
1427
1428     rb_define_global_function(COMPLEX_NAME, nucomp_f_complex, -1);
1429
1430     rb_undef_method(rb_cComplex, "<");
1431     rb_undef_method(rb_cComplex, "<=");
1432     rb_undef_method(rb_cComplex, "<=>");
1433     rb_undef_method(rb_cComplex, ">");
1434     rb_undef_method(rb_cComplex, ">=");
1435     rb_undef_method(rb_cComplex, "between?");
1436     rb_undef_method(rb_cComplex, "divmod");
1437     rb_undef_method(rb_cComplex, "floor");
1438     rb_undef_method(rb_cComplex, "ceil");
1439     rb_undef_method(rb_cComplex, "modulo");
1440     rb_undef_method(rb_cComplex, "round");
1441     rb_undef_method(rb_cComplex, "step");
1442     rb_undef_method(rb_cComplex, "truncate");
1443
1444 #if NUBY
1445     rb_undef_method(rb_cComplex, "//");
1446 #endif
1447
1448     rb_define_method(rb_cComplex, "real", nucomp_real, 0);
1449     rb_define_method(rb_cComplex, "image", nucomp_image, 0);
1450     rb_define_method(rb_cComplex, "imag", nucomp_image, 0);
1451
1452     rb_define_method(rb_cComplex, "+", nucomp_add, 1);
1453     rb_define_method(rb_cComplex, "-", nucomp_sub, 1);
1454     rb_define_method(rb_cComplex, "*", nucomp_mul, 1);
1455     rb_define_method(rb_cComplex, "/", nucomp_div, 1);
1456     rb_define_method(rb_cComplex, "quo", nucomp_quo, 1);
1457     rb_define_method(rb_cComplex, "fdiv", nucomp_fdiv, 1);
1458     rb_define_method(rb_cComplex, "**", nucomp_expt, 1);
1459
1460     rb_define_method(rb_cComplex, "==", nucomp_equal_p, 1);
1461     rb_define_method(rb_cComplex, "coerce", nucomp_coerce, 1);
1462
1463     rb_define_method(rb_cComplex, "abs", nucomp_abs, 0);
1464 #if 0
1465     rb_define_method(rb_cComplex, "magnitude", nucomp_abs, 0);
1466 #endif
1467     rb_define_method(rb_cComplex, "abs2", nucomp_abs2, 0);
1468     rb_define_method(rb_cComplex, "arg", nucomp_arg, 0);
1469     rb_define_method(rb_cComplex, "angle", nucomp_arg, 0);
1470     rb_define_method(rb_cComplex, "polar", nucomp_polar, 0);
1471     rb_define_method(rb_cComplex, "conjugate", nucomp_conjugate, 0);
1472     rb_define_method(rb_cComplex, "conj", nucomp_conjugate, 0);
1473 #if 0
1474     rb_define_method(rb_cComplex, "~", nucomp_conjugate, 0); /* gcc */
1475 #endif
1476
1477 #if 0
1478     rb_define_method(rb_cComplex, "real?", nucomp_real_p, 0);
1479     rb_define_method(rb_cComplex, "complex?", nucomp_complex_p, 0);
1480     rb_define_method(rb_cComplex, "exact?", nucomp_exact_p, 0);
1481     rb_define_method(rb_cComplex, "inexact?", nucomp_inexact_p, 0);
1482 #endif
1483
1484     rb_define_method(rb_cComplex, "numerator", nucomp_numerator, 0);
1485     rb_define_method(rb_cComplex, "denominator", nucomp_denominator, 0);
1486
1487     rb_define_method(rb_cComplex, "hash", nucomp_hash, 0);
1488
1489     rb_define_method(rb_cComplex, "to_s", nucomp_to_s, 0);
1490     rb_define_method(rb_cComplex, "inspect", nucomp_inspect, 0);
1491
1492     rb_define_method(rb_cComplex, "marshal_dump", nucomp_marshal_dump, 0);
1493     rb_define_method(rb_cComplex, "marshal_load", nucomp_marshal_load, 1);
1494
1495     /* --- */
1496
1497     rb_define_method(rb_cComplex, "scalar?", nucomp_scalar_p, 0);
1498     rb_define_method(rb_cComplex, "to_i", nucomp_to_i, 0);
1499     rb_define_method(rb_cComplex, "to_f", nucomp_to_f, 0);
1500     rb_define_method(rb_cComplex, "to_r", nucomp_to_r, 0);
1501     rb_define_method(rb_cNilClass, "to_c", nilclass_to_c, 0);
1502     rb_define_method(rb_cNumeric, "to_c", numeric_to_c, 0);
1503
1504     make_patterns();
1505
1506     rb_define_method(rb_cString, "to_c", string_to_c, 0);
1507
1508     rb_define_singleton_method(rb_cComplex, "convert", nucomp_s_convert, -1);
1509     rb_funcall(rb_cComplex, rb_intern("private_class_method"), 1,
1510                ID2SYM(rb_intern("convert")));
1511
1512     /* --- */
1513
1514     rb_define_method(rb_cNumeric, "re", numeric_re, 0);
1515     rb_define_method(rb_cNumeric, "im", numeric_im, 0);
1516     rb_define_method(rb_cNumeric, "real", numeric_real, 0);
1517     rb_define_method(rb_cNumeric, "image", numeric_image, 0);
1518     rb_define_method(rb_cNumeric, "imag", numeric_image, 0);
1519     rb_define_method(rb_cNumeric, "arg", numeric_arg, 0);
1520     rb_define_method(rb_cNumeric, "angle", numeric_arg, 0);
1521     rb_define_method(rb_cNumeric, "polar", numeric_polar, 0);
1522     rb_define_method(rb_cNumeric, "conjugate", numeric_conjugate, 0);
1523     rb_define_method(rb_cNumeric, "conj", numeric_conjugate, 0);
1524
1525     rb_define_const(rb_cComplex, "I",
1526                     f_complex_new_bang2(rb_cComplex, ZERO, ONE));
1527 }