rational.c

   1 /*
   2   rational.c: Coded by Tadayoshi Funaba 2008
   3
   4   This implementation is based on Keiju Ishitsuka's Rational library
   5   which is written in ruby.
   6 */
   7
   8 #include "ruby.h"
   9 #include <math.h>
  10 #include <float.h>
  11
  12 #define NDEBUG
  13 #include <assert.h>
  14
  15 #ifdef HAVE_IEEEFP_H
  16 #include <ieeefp.h>
  17 #endif
  18
  19 #ifndef RATIONAL_NAME
  20 #define RATIONAL_NAME "Rational"
  21 #endif
  22
  23 #define ZERO INT2FIX(0)
  24 #define ONE INT2FIX(1)
  25 #define TWO INT2FIX(2)
  26
  27 VALUE rb_cRational;
  28
  29 static ID id_Unify, id_abs, id_cmp, id_convert, id_equal_p,
  30   id_expt, id_floor, id_format, id_idiv, id_inspect, id_negate, id_new,
  31   id_new_bang, id_to_f, id_to_i, id_to_s, id_truncate;
  32
  33 #define f_boolcast(x) ((x) ? Qtrue : Qfalse)
  34
  35 #define binop(n,op) \
  36 inline static VALUE \
  37 f_##n(VALUE x, VALUE y)\
  38 {\
  39   return rb_funcall(x, op, 1, y);\
  40 }
  41
  42 #define fun1(n) \
  43 inline static VALUE \
  44 f_##n(VALUE x)\
  45 {\
  46     return rb_funcall(x, id_##n, 0);\
  47 }
  48
  49 #define fun2(n) \
  50 inline static VALUE \
  51 f_##n(VALUE x, VALUE y)\
  52 {\
  53     return rb_funcall(x, id_##n, 1, y);\
  54 }
  55
  56 inline static VALUE
  57 f_add(VALUE x, VALUE y)
  58 {
  59     if (FIXNUM_P(y)) {
  60         if (FIX2LONG(y) == 0)
  61             return x;
  62     }
  63     else if (FIXNUM_P(x)) {
  64         if (FIX2LONG(x) == 0)
  65             return y;
  66     }
  67     return rb_funcall(x, '+', 1, y);
  68 }
  69
  70 inline static VALUE
  71 f_cmp(VALUE x, VALUE y)
  72 {
  73     if (FIXNUM_P(x) && FIXNUM_P(y)) {
  74         long c = FIX2LONG(x) - FIX2LONG(y);
  75         if (c > 0)
  76             c = 1;
  77         else if (c < 0)
  78             c = -1;
  79         return INT2FIX(c);
  80     }
  81     return rb_funcall(x, id_cmp, 1, y);
  82 }
  83
  84 inline static VALUE
  85 f_div(VALUE x, VALUE y)
  86 {
  87     if (FIXNUM_P(y) && FIX2LONG(y) == 1)
  88         return x;
  89     return rb_funcall(x, '/', 1, y);
  90 }
  91
  92 inline static VALUE
  93 f_gt_p(VALUE x, VALUE y)
  94 {
  95     if (FIXNUM_P(x) && FIXNUM_P(y))
  96         return f_boolcast(FIX2LONG(x) > FIX2LONG(y));
  97     return rb_funcall(x, '>', 1, y);
  98 }
  99
 100 inline static VALUE
 101 f_lt_p(VALUE x, VALUE y)
 102 {
 103     if (FIXNUM_P(x) && FIXNUM_P(y))
 104         return f_boolcast(FIX2LONG(x) < FIX2LONG(y));
 105     return rb_funcall(x, '<', 1, y);
 106 }
 107
 108 binop(mod, '%')
 109
 110 inline static VALUE
 111 f_mul(VALUE x, VALUE y)
 112 {
 113     if (FIXNUM_P(y)) {
 114         long _iy = FIX2LONG(y);
 115         if (_iy == 0) {
 116             if (TYPE(x) == T_FLOAT)
 117                 return rb_float_new(0.0);
 118             else
 119                 return ZERO;
 120         }
 121         else if (_iy == 1)
 122             return x;
 123     }
 124     else if (FIXNUM_P(x)) {
 125         long _ix = FIX2LONG(x);
 126         if (_ix == 0) {
 127             if (TYPE(y) == T_FLOAT)
 128                 return rb_float_new(0.0);
 129             else
 130                 return ZERO;
 131         }
 132         else if (_ix == 1)
 133             return y;
 134     }
 135     return rb_funcall(x, '*', 1, y);
 136 }
 137
 138 inline static VALUE
 139 f_sub(VALUE x, VALUE y)
 140 {
 141     if (FIXNUM_P(y))
 142         if (FIX2LONG(y) == 0)
 143             return x;
 144     return rb_funcall(x, '-', 1, y);
 145 }
 146
 147 binop(xor, '^')
 148
 149 fun1(abs)
 150 fun1(floor)
 151 fun1(inspect)
 152 fun1(negate)
 153 fun1(to_f)
 154 fun1(to_i)
 155 fun1(to_s)
 156 fun1(truncate)
 157
 158 inline static VALUE
 159 f_equal_p(VALUE x, VALUE y)
 160 {
 161     if (FIXNUM_P(x) && FIXNUM_P(y))
 162         return f_boolcast(FIX2LONG(x) == FIX2LONG(y));
 163     return rb_funcall(x, id_equal_p, 1, y);
 164 }
 165
 166 fun2(expt)
 167 fun2(idiv)
 168
 169 inline static VALUE
 170 f_negative_p(VALUE x)
 171 {
 172     if (FIXNUM_P(x))
 173         return f_boolcast(FIX2LONG(x) < 0);
 174     return rb_funcall(x, '<', 1, ZERO);
 175 }
 176
 177 inline static VALUE
 178 f_zero_p(VALUE x)
 179 {
 180     if (FIXNUM_P(x))
 181         return f_boolcast(FIX2LONG(x) == 0);
 182     return rb_funcall(x, id_equal_p, 1, ZERO);
 183 }
 184
 185 inline static VALUE
 186 f_one_p(VALUE x)
 187 {
 188     if (FIXNUM_P(x))
 189         return f_boolcast(FIX2LONG(x) == 1);
 190     return rb_funcall(x, id_equal_p, 1, ONE);
 191 }
 192
 193 inline static VALUE
 194 f_kind_of_p(VALUE x, VALUE c)
 195 {
 196     return rb_obj_is_kind_of(x, c);
 197 }
 198
 199 inline static VALUE
 200 k_numeric_p(VALUE x)
 201 {
 202     return f_kind_of_p(x, rb_cNumeric);
 203 }
 204
 205 inline static VALUE
 206 k_integer_p(VALUE x)
 207 {
 208     return f_kind_of_p(x, rb_cInteger);
 209 }
 210
 211 inline static VALUE
 212 k_float_p(VALUE x)
 213 {
 214     return f_kind_of_p(x, rb_cFloat);
 215 }
 216
 217 inline static VALUE
 218 k_rational_p(VALUE x)
 219 {
 220     return f_kind_of_p(x, rb_cRational);
 221 }
 222
 223 #ifndef NDEBUG
 224 #define f_gcd f_gcd_orig
 225 #endif
 226
 227 inline static long
 228 i_gcd(long x, long y)
 229 {
 230     long b;
 231
 232     if (x < 0)
 233         x = -x;
 234     if (y < 0)
 235         y = -y;
 236
 237     if (x == 0)
 238         return y;
 239     if (y == 0)
 240         return x;
 241
 242     b = 0;
 243     while ((x & 1) == 0 && (y & 1) == 0) {
 244         b += 1;
 245         x >>= 1;
 246         y >>= 1;
 247     }
 248
 249     while ((x & 1) == 0)
 250         x >>= 1;
 251
 252     while ((y & 1) == 0)
 253         y >>= 1;
 254
 255     while (x != y) {
 256         if (y > x) {
 257             long t;
 258             t = x;
 259             x = y;
 260             y = t;
 261         }
 262         x -= y;
 263         while ((x & 1) == 0)
 264             x >>= 1;
 265     }
 266
 267     return x << b;
 268 }
 269
 270 inline static VALUE
 271 f_gcd(VALUE x, VALUE y)
 272 {
 273     VALUE z;
 274
 275     if (FIXNUM_P(x) && FIXNUM_P(y))
 276         return LONG2NUM(i_gcd(FIX2LONG(x), FIX2LONG(y)));
 277
 278     if (f_negative_p(x))
 279         x = f_negate(x);
 280     if (f_negative_p(y))
 281         y = f_negate(y);
 282
 283     if (f_zero_p(x))
 284         return y;
 285     if (f_zero_p(y))
 286         return x;
 287
 288     for (;;) {
 289         if (FIXNUM_P(x)) {
 290             if (FIX2LONG(x) == 0)
 291                 return y;
 292             if (FIXNUM_P(y))
 293                 return LONG2NUM(i_gcd(FIX2LONG(x), FIX2LONG(y)));
 294         }
 295         z = x;
 296         x = f_mod(y, x);
 297         y = z;
 298     }
 299     /* NOTREACHED */
 300 }
 301
 302 #ifndef NDEBUG
 303 #undef f_gcd
 304
 305 inline static VALUE
 306 f_gcd(VALUE x, VALUE y)
 307 {
 308     VALUE r = f_gcd_orig(x, y);
 309     if (!f_zero_p(r)) {
 310         assert(f_zero_p(f_mod(x, r)));
 311         assert(f_zero_p(f_mod(y, r)));
 312     }
 313     return r;
 314 }
 315 #endif
 316
 317 inline static VALUE
 318 f_lcm(VALUE x, VALUE y)
 319 {
 320     if (f_zero_p(x) || f_zero_p(y))
 321         return ZERO;
 322     return f_abs(f_mul(f_div(x, f_gcd(x, y)), y));
 323 }
 324
 325 #define get_dat1(x) \
 326     struct RRational *dat;\
 327     dat = ((struct RRational *)(x))
 328
 329 #define get_dat2(x,y) \
 330     struct RRational *adat, *bdat;\
 331     adat = ((struct RRational *)(x));\
 332     bdat = ((struct RRational *)(y))
 333
 334 inline static VALUE
 335 nurat_s_new_internal(VALUE klass, VALUE num, VALUE den)
 336 {
 337     NEWOBJ(obj, struct RRational);
 338     OBJSETUP(obj, klass, T_RATIONAL);
 339
 340     obj->num = num;
 341     obj->den = den;
 342
 343     return (VALUE)obj;
 344 }
 345
 346 static VALUE
 347 nurat_s_alloc(VALUE klass)
 348 {
 349     return nurat_s_new_internal(klass, ZERO, ONE);
 350 }
 351
 352 static VALUE
 353 nurat_s_new_bang(int argc, VALUE *argv, VALUE klass)
 354 {
 355     VALUE num, den;
 356
 357     switch (rb_scan_args(argc, argv, "11", &num, &den)) {
 358       case 1:
 359         if (!k_integer_p(num))
 360             num = f_to_i(num);
 361         den = ONE;
 362         break;
 363       default:
 364         if (!k_integer_p(num))
 365             num = f_to_i(num);
 366         if (!k_integer_p(den))
 367             den = f_to_i(den);
 368
 369         switch (FIX2INT(f_cmp(den, ZERO))) {
 370           case -1:
 371             num = f_negate(num);
 372             den = f_negate(den);
 373             break;
 374           case 0:
 375             rb_raise(rb_eZeroDivError, "devided by zero");
 376             break;
 377         }
 378         break;
 379     }
 380
 381     return nurat_s_new_internal(klass, num, den);
 382 }
 383
 384 inline static VALUE
 385 f_rational_new_bang1(VALUE klass, VALUE x)
 386 {
 387     return nurat_s_new_internal(klass, x, ONE);
 388 }
 389
 390 inline static VALUE
 391 f_rational_new_bang2(VALUE klass, VALUE x, VALUE y)
 392 {
 393     assert(!f_negative_p(y));
 394     assert(!f_zero_p(y));
 395     return nurat_s_new_internal(klass, x, y);
 396 }
 397
 398 #define f_unify_p(klass) rb_const_defined(klass, id_Unify)
 399
 400 inline static void
 401 nurat_int_check(VALUE num)
 402 {
 403     switch (TYPE(num)) {
 404       case T_FIXNUM:
 405       case T_BIGNUM:
 406         break;
 407       default:
 408         rb_raise(rb_eArgError, "not an integer");
 409     }
 410 }
 411
 412 inline static VALUE
 413 nurat_s_canonicalize_internal(VALUE klass, VALUE num, VALUE den)
 414 {
 415     VALUE gcd;
 416
 417     switch (FIX2INT(f_cmp(den, ZERO))) {
 418       case -1:
 419         num = f_negate(num);
 420         den = f_negate(den);
 421         break;
 422       case 0:
 423         rb_raise(rb_eZeroDivError, "devided by zero");
 424         break;
 425     }
 426
 427     gcd = f_gcd(num, den);
 428     num = f_idiv(num, gcd);
 429     den = f_idiv(den, gcd);
 430
 431     if (f_one_p(den) && f_unify_p(klass))
 432         return num;
 433     return nurat_s_new_internal(klass, num, den);
 434 }
 435
 436 inline static VALUE
 437 nurat_s_canonicalize_internal_no_reduce(VALUE klass, VALUE num, VALUE den)
 438 {
 439     switch (FIX2INT(f_cmp(den, ZERO))) {
 440       case -1:
 441         num = f_negate(num);
 442         den = f_negate(den);
 443         break;
 444       case 0:
 445         rb_raise(rb_eZeroDivError, "devided by zero");
 446         break;
 447     }
 448
 449     if (f_equal_p(den, ONE) && f_unify_p(klass))
 450         return num;
 451     return nurat_s_new_internal(klass, num, den);
 452 }
 453
 454 #if 0
 455 static VALUE
 456 nurat_s_canonicalize(int argc, VALUE *argv, VALUE klass)
 457 {
 458     VALUE num, den;
 459
 460     if (rb_scan_args(argc, argv, "11", &num, &den) == 1) {
 461         den = ONE;
 462     }
 463
 464     nurat_int_check(num);
 465     nurat_int_check(den);
 466
 467     return nurat_s_canonicalize_internal(klass, num, den);
 468 }
 469 #endif
 470
 471 static VALUE
 472 nurat_s_new(int argc, VALUE *argv, VALUE klass)
 473 {
 474     VALUE num, den;
 475
 476     if (rb_scan_args(argc, argv, "11", &num, &den) == 1)
 477         den = ONE;
 478
 479     nurat_int_check(num);
 480     nurat_int_check(den);
 481
 482     return nurat_s_canonicalize_internal(klass, num, den);
 483 }
 484
 485 inline static VALUE
 486 f_rational_new1(VALUE klass, VALUE x)
 487 {
 488     assert(!k_rational_p(x));
 489     return nurat_s_canonicalize_internal(klass, x, ONE);
 490 }
 491
 492 inline static VALUE
 493 f_rational_new2(VALUE klass, VALUE x, VALUE y)
 494 {
 495     assert(!k_rational_p(x));
 496     assert(!k_rational_p(y));
 497     return nurat_s_canonicalize_internal(klass, x, y);
 498 }
 499
 500 inline static VALUE
 501 f_rational_new_no_reduce1(VALUE klass, VALUE x)
 502 {
 503     assert(!k_rational_p(x));
 504     return nurat_s_canonicalize_internal_no_reduce(klass, x, ONE);
 505 }
 506
 507 inline static VALUE
 508 f_rational_new_no_reduce2(VALUE klass, VALUE x, VALUE y)
 509 {
 510     assert(!k_rational_p(x));
 511     assert(!k_rational_p(y));
 512     return nurat_s_canonicalize_internal_no_reduce(klass, x, y);
 513 }
 514
 515 static VALUE
 516 nurat_f_rational(int argc, VALUE *argv, VALUE klass)
 517 {
 518     return rb_funcall2(rb_cRational, id_convert, argc, argv);
 519 }
 520
 521 static VALUE
 522 nurat_numerator(VALUE self)
 523 {
 524     get_dat1(self);
 525     return dat->num;
 526 }
 527
 528 static VALUE
 529 nurat_denominator(VALUE self)
 530 {
 531     get_dat1(self);
 532     return dat->den;
 533 }
 534
 535 #ifndef NDEBUG
 536 #define f_imul f_imul_orig
 537 #endif
 538
 539 inline static VALUE
 540 f_imul(long a, long b)
 541 {
 542     VALUE r;
 543     long c;
 544
 545     if (a == 0 || b == 0)
 546         return ZERO;
 547     else if (a == 1)
 548         return LONG2NUM(b);
 549     else if (b == 1)
 550         return LONG2NUM(a);
 551
 552     c = a * b;
 553     r = LONG2NUM(c);
 554     if (NUM2LONG(r) != c || (c / a) != b)
 555         r = rb_big_mul(rb_int2big(a), rb_int2big(b));
 556     return r;
 557 }
 558
 559 #ifndef NDEBUG
 560 #undef f_imul
 561
 562 inline static VALUE
 563 f_imul(long x, long y)
 564 {
 565     VALUE r = f_imul_orig(x, y);
 566     assert(f_equal_p(r, f_mul(LONG2NUM(x), LONG2NUM(y))));
 567     return r;
 568 }
 569 #endif
 570
 571 inline static VALUE
 572 f_addsub(VALUE self, VALUE anum, VALUE aden, VALUE bnum, VALUE bden, int k)
 573 {
 574     VALUE num, den;
 575
 576     if (FIXNUM_P(anum) && FIXNUM_P(aden) &&
 577         FIXNUM_P(bnum) && FIXNUM_P(bden)) {
 578         long an = FIX2LONG(anum);
 579         long ad = FIX2LONG(aden);
 580         long bn = FIX2LONG(bnum);
 581         long bd = FIX2LONG(bden);
 582         long ig = i_gcd(ad, bd);
 583
 584         VALUE g = LONG2NUM(ig);
 585         VALUE a = f_imul(an, bd / ig);
 586         VALUE b = f_imul(bn, ad / ig);
 587         VALUE c;
 588
 589         if (k == '+')
 590             c = f_add(a, b);
 591         else
 592             c = f_sub(a, b);
 593
 594         b = f_idiv(aden, g);
 595         g = f_gcd(c, g);
 596         num = f_idiv(c, g);
 597         a = f_idiv(bden, g);
 598         den = f_mul(a, b);
 599     }
 600     else {
 601         VALUE g = f_gcd(aden, bden);
 602         VALUE a = f_mul(anum, f_idiv(bden, g));
 603         VALUE b = f_mul(bnum, f_idiv(aden, g));
 604         VALUE c;
 605
 606         if (k == '+')
 607             c = f_add(a, b);
 608         else
 609             c = f_sub(a, b);
 610
 611         b = f_idiv(aden, g);
 612         g = f_gcd(c, g);
 613         num = f_idiv(c, g);
 614         a = f_idiv(bden, g);
 615         den = f_mul(a, b);
 616     }
 617     return f_rational_new_no_reduce2(CLASS_OF(self), num, den);
 618 }
 619
 620 static VALUE
 621 nurat_add(VALUE self, VALUE other)
 622 {
 623     switch (TYPE(other)) {
 624       case T_FIXNUM:
 625       case T_BIGNUM:
 626         {
 627             get_dat1(self);
 628
 629             return f_addsub(self,
 630                             dat->num, dat->den,
 631                             other, ONE, '+');
 632         }
 633       case T_FLOAT:
 634         return f_add(f_to_f(self), other);
 635       case T_RATIONAL:
 636         {
 637             get_dat2(self, other);
 638
 639             return f_addsub(self,
 640                             adat->num, adat->den,
 641                             bdat->num, bdat->den, '+');
 642         }
 643       default:
 644         return rb_num_coerce_bin(self, other, '+');
 645     }
 646 }
 647
 648 static VALUE
 649 nurat_sub(VALUE self, VALUE other)
 650 {
 651     switch (TYPE(other)) {
 652       case T_FIXNUM:
 653       case T_BIGNUM:
 654         {
 655             get_dat1(self);
 656
 657             return f_addsub(self,
 658                             dat->num, dat->den,
 659                             other, ONE, '-');
 660         }
 661       case T_FLOAT:
 662         return f_sub(f_to_f(self), other);
 663       case T_RATIONAL:
 664         {
 665             get_dat2(self, other);
 666
 667             return f_addsub(self,
 668                             adat->num, adat->den,
 669                             bdat->num, bdat->den, '-');
 670         }
 671       default:
 672         return rb_num_coerce_bin(self, other, '-');
 673     }
 674 }
 675
 676 inline static VALUE
 677 f_muldiv(VALUE self, VALUE anum, VALUE aden, VALUE bnum, VALUE bden, int k)
 678 {
 679     VALUE num, den;
 680
 681     if (k == '/') {
 682         VALUE t;
 683
 684         if (f_negative_p(bnum)) {
 685             anum = f_negate(anum);
 686             bnum = f_negate(bnum);
 687         }
 688         t = bnum;
 689         bnum = bden;
 690         bden = t;
 691     }
 692
 693     if (FIXNUM_P(anum) && FIXNUM_P(aden) &&
 694         FIXNUM_P(bnum) && FIXNUM_P(bden)) {
 695         long an = FIX2LONG(anum);
 696         long ad = FIX2LONG(aden);
 697         long bn = FIX2LONG(bnum);
 698         long bd = FIX2LONG(bden);
 699         long g1 = i_gcd(an, bd);
 700         long g2 = i_gcd(ad, bn);
 701
 702         num = f_imul(an / g1, bn / g2);
 703         den = f_imul(ad / g2, bd / g1);
 704     }
 705     else {
 706         VALUE g1 = f_gcd(anum, bden);
 707         VALUE g2 = f_gcd(aden, bnum);
 708
 709         num = f_mul(f_idiv(anum, g1), f_idiv(bnum, g2));
 710         den = f_mul(f_idiv(aden, g2), f_idiv(bden, g1));
 711     }
 712     return f_rational_new_no_reduce2(CLASS_OF(self), num, den);
 713 }
 714
 715 static VALUE
 716 nurat_mul(VALUE self, VALUE other)
 717 {
 718     switch (TYPE(other)) {
 719       case T_FIXNUM:
 720       case T_BIGNUM:
 721         {
 722             get_dat1(self);
 723
 724             return f_muldiv(self,
 725                             dat->num, dat->den,
 726                             other, ONE, '*');
 727         }
 728       case T_FLOAT:
 729         return f_mul(f_to_f(self), other);
 730       case T_RATIONAL:
 731         {
 732             get_dat2(self, other);
 733
 734             return f_muldiv(self,
 735                             adat->num, adat->den,
 736                             bdat->num, bdat->den, '*');
 737         }
 738       default:
 739         return rb_num_coerce_bin(self, other, '*');
 740     }
 741 }
 742
 743 static VALUE
 744 nurat_div(VALUE self, VALUE other)
 745 {
 746     switch (TYPE(other)) {
 747       case T_FIXNUM:
 748       case T_BIGNUM:
 749         if (f_zero_p(other))
 750             rb_raise(rb_eZeroDivError, "devided by zero");
 751         {
 752             get_dat1(self);
 753
 754             return f_muldiv(self,
 755                             dat->num, dat->den,
 756                             other, ONE, '/');
 757         }
 758       case T_FLOAT:
 759         return rb_funcall(f_to_f(self), '/', 1, other);
 760       case T_RATIONAL:
 761         if (f_zero_p(other))
 762             rb_raise(rb_eZeroDivError, "devided by zero");
 763         {
 764             get_dat2(self, other);
 765
 766             return f_muldiv(self,
 767                             adat->num, adat->den,
 768                             bdat->num, bdat->den, '/');
 769         }
 770       default:
 771         return rb_num_coerce_bin(self, other, '/');
 772     }
 773 }
 774
 775 static VALUE
 776 nurat_fdiv(VALUE self, VALUE other)
 777 {
 778     return f_div(f_to_f(self), other);
 779 }
 780
 781 static VALUE
 782 nurat_expt(VALUE self, VALUE other)
 783 {
 784     if (f_zero_p(other))
 785         return f_rational_new_bang1(CLASS_OF(self), ONE);
 786
 787     if (k_rational_p(other)) {
 788         get_dat1(other);
 789
 790         if (f_one_p(dat->den))
 791             other = dat->num; /* good? */
 792     }
 793
 794     switch (TYPE(other)) {
 795       case T_FIXNUM:
 796       case T_BIGNUM:
 797         {
 798             VALUE num, den;
 799
 800             get_dat1(self);
 801
 802             switch (FIX2INT(f_cmp(other, ZERO))) {
 803               case 1:
 804                 num = f_expt(dat->num, other);
 805                 den = f_expt(dat->den, other);
 806                 break;
 807               case -1:
 808                 num = f_expt(dat->den, f_negate(other));
 809                 den = f_expt(dat->num, f_negate(other));
 810                 break;
 811               default:
 812                 num = ONE;
 813                 den = ONE;
 814                 break;
 815             }
 816             return f_rational_new2(CLASS_OF(self), num, den);
 817         }
 818       case T_FLOAT:
 819       case T_RATIONAL:
 820         return f_expt(f_to_f(self), other);
 821       default:
 822         return rb_num_coerce_bin(self, other, id_expt);
 823     }
 824 }
 825
 826 static VALUE
 827 nurat_cmp(VALUE self, VALUE other)
 828 {
 829     switch (TYPE(other)) {
 830       case T_FIXNUM:
 831       case T_BIGNUM:
 832         {
 833             get_dat1(self);
 834
 835             if (FIXNUM_P(dat->den) && FIX2LONG(dat->den) == 1)
 836                 return f_cmp(dat->num, other);
 837             return f_cmp(self, f_rational_new_bang1(CLASS_OF(self), other));
 838         }
 839       case T_FLOAT:
 840         return f_cmp(f_to_f(self), other);
 841       case T_RATIONAL:
 842         {
 843             VALUE num1, num2;
 844
 845             get_dat2(self, other);
 846
 847             if (FIXNUM_P(adat->num) && FIXNUM_P(adat->den) &&
 848                 FIXNUM_P(bdat->num) && FIXNUM_P(bdat->den)) {
 849                 num1 = f_imul(FIX2LONG(adat->num), FIX2LONG(bdat->den));
 850                 num2 = f_imul(FIX2LONG(bdat->num), FIX2LONG(adat->den));
 851             }
 852             else {
 853                 num1 = f_mul(adat->num, bdat->den);
 854                 num2 = f_mul(bdat->num, adat->den);
 855             }
 856             return f_cmp(f_sub(num1, num2), ZERO);
 857         }
 858       default:
 859         return rb_num_coerce_bin(self, other, id_cmp);
 860     }
 861 }
 862
 863 static VALUE
 864 nurat_equal_p(VALUE self, VALUE other)
 865 {
 866     switch (TYPE(other)) {
 867       case T_FIXNUM:
 868       case T_BIGNUM:
 869         {
 870             get_dat1(self);
 871
 872             if (f_zero_p(dat->num) && f_zero_p(other))
 873                 return Qtrue;
 874
 875             if (!FIXNUM_P(dat->den))
 876                 return Qfalse;
 877             if (FIX2LONG(dat->den) != 1)
 878                 return Qfalse;
 879             if (f_equal_p(dat->num, other))
 880                 return Qtrue;
 881             return Qfalse;
 882         }
 883       case T_FLOAT:
 884         return f_equal_p(f_to_f(self), other);
 885       case T_RATIONAL:
 886         {
 887             get_dat2(self, other);
 888
 889             if (f_zero_p(adat->num) && f_zero_p(bdat->num))
 890                 return Qtrue;
 891
 892             return f_boolcast(f_equal_p(adat->num, bdat->num) &&
 893                               f_equal_p(adat->den, bdat->den));
 894         }
 895       default:
 896         return f_equal_p(other, self);
 897     }
 898 }
 899
 900 static VALUE
 901 nurat_coerce(VALUE self, VALUE other)
 902 {
 903     switch (TYPE(other)) {
 904       case T_FIXNUM:
 905       case T_BIGNUM:
 906         return rb_assoc_new(f_rational_new_bang1(CLASS_OF(self), other), self);
 907       case T_FLOAT:
 908         return rb_assoc_new(other, f_to_f(self));
 909     }
 910
 911     rb_raise(rb_eTypeError, "%s can't be coerced into %s",
 912              rb_obj_classname(other), rb_obj_classname(self));
 913     return Qnil;
 914 }
 915
 916 static VALUE
 917 nurat_idiv(VALUE self, VALUE other)
 918 {
 919     return f_floor(f_div(self, other));
 920 }
 921
 922 static VALUE
 923 nurat_mod(VALUE self, VALUE other)
 924 {
 925     VALUE val = f_floor(f_div(self, other));
 926     return f_sub(self, f_mul(other, val));
 927 }
 928
 929 static VALUE
 930 nurat_divmod(VALUE self, VALUE other)
 931 {
 932     VALUE val = f_floor(f_div(self, other));
 933     return rb_assoc_new(val, f_sub(self, f_mul(other, val)));
 934 }
 935
 936 #if 0
 937 static VALUE
 938 nurat_quot(VALUE self, VALUE other)
 939 {
 940     return f_truncate(f_div(self, other));
 941 }
 942 #endif
 943
 944 static VALUE
 945 nurat_rem(VALUE self, VALUE other)
 946 {
 947     VALUE val = f_truncate(f_div(self, other));
 948     return f_sub(self, f_mul(other, val));
 949 }
 950
 951 #if 0
 952 static VALUE
 953 nurat_quotrem(VALUE self, VALUE other)
 954 {
 955     VALUE val = f_truncate(f_div(self, other));
 956     return rb_assoc_new(val, f_sub(self, f_mul(other, val)));
 957 }
 958 #endif
 959
 960 static VALUE
 961 nurat_abs(VALUE self)
 962 {
 963     if (!f_negative_p(self))
 964         return self;
 965     return f_negate(self);
 966 }
 967
 968 #if 0
 969 static VALUE
 970 nurat_true(VALUE self)
 971 {
 972     return Qtrue;
 973 }
 974 #endif
 975
 976 static VALUE
 977 nurat_floor(VALUE self)
 978 {
 979     get_dat1(self);
 980     return f_idiv(dat->num, dat->den);
 981 }
 982
 983 static VALUE
 984 nurat_ceil(VALUE self)
 985 {
 986     get_dat1(self);
 987     return f_negate(f_idiv(f_negate(dat->num), dat->den));
 988 }
 989
 990 static VALUE
 991 nurat_truncate(VALUE self)
 992 {
 993     get_dat1(self);
 994     if (f_negative_p(dat->num))
 995         return f_negate(f_idiv(f_negate(dat->num), dat->den));
 996     return f_idiv(dat->num, dat->den);
 997 }
 998
 999 static VALUE
1000 nurat_round(VALUE self)
1001 {
1002     get_dat1(self);
1003
1004     if (f_negative_p(dat->num)) {
1005         VALUE num, den;
1006
1007         num = f_negate(dat->num);
1008         num = f_add(f_mul(num, TWO), dat->den);
1009         den = f_mul(dat->den, TWO);
1010         return f_negate(f_idiv(num, den));
1011     }
1012     else {
1013         VALUE num = f_add(f_mul(dat->num, TWO), dat->den);
1014         VALUE den = f_mul(dat->den, TWO);
1015         return f_idiv(num, den);
1016     }
1017 }
1018
1019 #define f_size(x) rb_funcall(x, rb_intern("size"), 0)
1020 #define f_rshift(x,y) rb_funcall(x, rb_intern(">>"), 1, y)
1021
1022 inline static long
1023 i_ilog2(VALUE x)
1024 {
1025     long q, r, fx;
1026
1027     assert(!f_lt_p(x, ONE));
1028
1029     q = (NUM2LONG(f_size(x)) - sizeof(long)) * 8 + 1;
1030
1031     if (q > 0)
1032         x = f_rshift(x, LONG2NUM(q));
1033
1034     fx = NUM2LONG(x);
1035
1036     r = -1;
1037     while (fx) {
1038         fx >>= 1;
1039         r += 1;
1040     }
1041
1042     return q + r;
1043 }
1044
1045 static VALUE
1046 nurat_to_f(VALUE self)
1047 {
1048     VALUE num, den;
1049     int minus = 0;
1050     long nl, dl, ml, ne, de;
1051     int e;
1052     double f;
1053
1054     {
1055         get_dat1(self);
1056
1057         if (f_zero_p(dat->num))
1058             return rb_float_new(0.0);
1059
1060         num = dat->num;
1061         den = dat->den;
1062     }
1063
1064     if (f_negative_p(num)) {
1065         num = f_negate(num);
1066         minus = 1;
1067     }
1068
1069     nl = i_ilog2(num);
1070     dl = i_ilog2(den);
1071     ml = (long)(log(DBL_MAX) / log(2.0) - 1); /* should be a static */
1072
1073     ne = 0;
1074     if (nl > ml) {
1075         ne = nl - ml;
1076         num = f_rshift(num, LONG2NUM(ne));
1077     }
1078
1079     de = 0;
1080     if (dl > ml) {
1081         de = dl - ml;
1082         den = f_rshift(den, LONG2NUM(de));
1083     }
1084
1085     e = (int)(ne - de);
1086
1087     if ((e > DBL_MAX_EXP) || (e < DBL_MIN_EXP)) {
1088         rb_warning("%s out of Float range", rb_obj_classname(self));
1089         return rb_float_new(e > 0 ? HUGE_VAL : 0.0);
1090     }
1091
1092     f = NUM2DBL(num) / NUM2DBL(den);
1093     if (minus)
1094         f = -f;
1095     f = ldexp(f, e);
1096
1097     if (isinf(f) || isnan(f))
1098         rb_warning("%s out of Float range", rb_obj_classname(self));
1099
1100     return rb_float_new(f);
1101 }
1102
1103 static VALUE
1104 nurat_to_r(VALUE self)
1105 {
1106     return self;
1107 }
1108
1109 static VALUE
1110 nurat_hash(VALUE self)
1111 {
1112     get_dat1(self);
1113     return f_xor(dat->num, dat->den);
1114 }
1115
1116 static VALUE
1117 nurat_to_s(VALUE self)
1118 {
1119     get_dat1(self);
1120
1121     if (f_one_p(dat->den))
1122         return f_to_s(dat->num);
1123     return rb_funcall(rb_mKernel, id_format, 3,
1124                       rb_str_new2("%d/%d"), dat->num, dat->den);
1125 }
1126
1127 static VALUE
1128 nurat_inspect(VALUE self)
1129 {
1130     get_dat1(self);
1131     return rb_funcall(rb_mKernel, id_format, 3,
1132                       rb_str_new2("Rational(%d, %d)"), dat->num, dat->den);
1133 }
1134
1135 static VALUE
1136 nurat_marshal_dump(VALUE self)
1137 {
1138     get_dat1(self);
1139     return rb_assoc_new(dat->num, dat->den);
1140 }
1141
1142 static VALUE
1143 nurat_marshal_load(VALUE self, VALUE a)
1144 {
1145     get_dat1(self);
1146     dat->num = RARRAY_PTR(a)[0];
1147     dat->den = RARRAY_PTR(a)[1];
1148
1149     if (f_zero_p(dat->den))
1150         rb_raise(rb_eZeroDivError, "devided by zero");
1151
1152     return self;
1153 }
1154
1155 /* --- */
1156
1157 VALUE
1158 rb_gcd(VALUE self, VALUE other)
1159 {
1160     nurat_int_check(other);
1161     return f_gcd(self, other);
1162 }
1163
1164 VALUE
1165 rb_lcm(VALUE self, VALUE other)
1166 {
1167     nurat_int_check(other);
1168     return f_lcm(self, other);
1169 }
1170
1171 VALUE
1172 rb_gcdlcm(VALUE self, VALUE other)
1173 {
1174     nurat_int_check(other);
1175     return rb_assoc_new(f_gcd(self, other), f_lcm(self, other));
1176 }
1177
1178 VALUE
1179 rb_rational_raw(VALUE x, VALUE y)
1180 {
1181     return nurat_s_new_internal(rb_cRational, x, y);
1182 }
1183
1184 VALUE
1185 rb_rational_new(VALUE x, VALUE y)
1186 {
1187     return nurat_s_canonicalize_internal(rb_cRational, x, y);
1188 }
1189
1190 static VALUE nurat_s_convert(int argc, VALUE *argv, VALUE klass);
1191
1192 VALUE
1193 rb_Rational(VALUE x, VALUE y)
1194 {
1195     VALUE a[2];
1196     a[0] = x;
1197     a[1] = y;
1198     return nurat_s_convert(2, a, rb_cRational);
1199 }
1200
1201 static VALUE
1202 nilclass_to_r(VALUE self)
1203 {
1204     return rb_rational_new1(INT2FIX(0));
1205 }
1206
1207 static VALUE
1208 integer_to_r(VALUE self)
1209 {
1210     return rb_rational_new1(self);
1211 }
1212
1213 static VALUE
1214 float_decode(VALUE self)
1215 {
1216     double f;
1217     int n;
1218
1219     f = frexp(RFLOAT_VALUE(self), &n);
1220     f = ldexp(f, DBL_MANT_DIG);
1221     n -= DBL_MANT_DIG;
1222     return rb_assoc_new(f_to_i(rb_float_new(f)), INT2FIX(n));
1223 }
1224
1225 static VALUE
1226 float_to_r(VALUE self)
1227 {
1228     VALUE a = float_decode(self);
1229     return f_mul(RARRAY_PTR(a)[0],
1230                  f_expt(INT2FIX(FLT_RADIX), RARRAY_PTR(a)[1]));
1231 }
1232
1233 static VALUE rat_pat, an_e_pat, a_dot_pat, underscores_pat, an_underscore;
1234
1235 #define DIGITS "(?:\\d(?:_\\d|\\d)*)"
1236 #define NUMERATOR "(?:" DIGITS "?\\.)?" DIGITS "(?:[eE][-+]?" DIGITS ")?"
1237 #define DENOMINATOR "[-+]?" DIGITS
1238 #define PATTERN "\\A([-+])?(" NUMERATOR ")(?:\\/(" DENOMINATOR "))?"
1239
1240 static void
1241 make_patterns(void)
1242 {
1243     static const char rat_pat_source[] = PATTERN;
1244     static const char an_e_pat_source[] = "[eE]";
1245     static const char a_dot_pat_source[] = "\\.";
1246     static const char underscores_pat_source[] = "_+";
1247
1248     if (rat_pat) return;
1249
1250     rat_pat = rb_reg_new(rat_pat_source, sizeof rat_pat_source - 1, 0);
1251     rb_global_variable(&rat_pat);
1252
1253     an_e_pat = rb_reg_new(an_e_pat_source, sizeof an_e_pat_source - 1, 0);
1254     rb_global_variable(&an_e_pat);
1255
1256     a_dot_pat = rb_reg_new(a_dot_pat_source, sizeof a_dot_pat_source - 1, 0);
1257     rb_global_variable(&a_dot_pat);
1258
1259     underscores_pat = rb_reg_new(underscores_pat_source,
1260                                  sizeof underscores_pat_source - 1, 0);
1261     rb_global_variable(&underscores_pat);
1262
1263     an_underscore = rb_str_new2("_");
1264     rb_global_variable(&an_underscore);
1265 }
1266
1267 #define id_strip rb_intern("strip")
1268 #define f_strip(x) rb_funcall(x, id_strip, 0)
1269
1270 #define id_match rb_intern("match")
1271 #define f_match(x,y) rb_funcall(x, id_match, 1, y)
1272
1273 #define id_aref rb_intern("[]")
1274 #define f_aref(x,y) rb_funcall(x, id_aref, 1, y)
1275
1276 #define id_post_match rb_intern("post_match")
1277 #define f_post_match(x) rb_funcall(x, id_post_match, 0)
1278
1279 #define id_split rb_intern("split")
1280 #define f_split(x,y) rb_funcall(x, id_split, 1, y)
1281
1282 #include <ctype.h>
1283
1284 static VALUE
1285 string_to_r_internal(VALUE self)
1286 {
1287     VALUE s, m;
1288
1289     s = f_strip(self);
1290
1291     if (RSTRING_LEN(s) == 0)
1292         return rb_assoc_new(Qnil, self);
1293
1294     m = f_match(rat_pat, s);
1295
1296     if (!NIL_P(m)) {
1297         VALUE v, ifp, exp, ip, fp;
1298         VALUE si = f_aref(m, INT2FIX(1));
1299         VALUE nu = f_aref(m, INT2FIX(2));
1300         VALUE de = f_aref(m, INT2FIX(3));
1301         VALUE re = f_post_match(m);
1302
1303         {
1304             VALUE a;
1305
1306             a = f_split(nu, an_e_pat);
1307             ifp = RARRAY_PTR(a)[0];
1308             if (RARRAY_LEN(a) != 2)
1309                 exp = Qnil;
1310             else
1311                 exp = RARRAY_PTR(a)[1];
1312
1313             a = f_split(ifp, a_dot_pat);
1314             ip = RARRAY_PTR(a)[0];
1315             if (RARRAY_LEN(a) != 2)
1316                 fp = Qnil;
1317             else
1318                 fp = RARRAY_PTR(a)[1];
1319         }
1320
1321         v = rb_rational_new1(f_to_i(ip));
1322
1323         if (!NIL_P(fp)) {
1324             char *p = StringValuePtr(fp);
1325             long count = 0;
1326             VALUE l;
1327
1328             while (*p) {
1329                 if (rb_isdigit(*p))
1330                     count++;
1331                 p++;
1332             }
1333
1334             l = f_expt(INT2FIX(10), LONG2NUM(count));
1335             v = f_mul(v, l);
1336             v = f_add(v, f_to_i(fp));
1337             v = f_div(v, l);
1338         }
1339         if (!NIL_P(exp))
1340             v = f_mul(v, f_expt(INT2FIX(10), f_to_i(exp)));
1341         if (!NIL_P(si) && *StringValuePtr(si) == '-')
1342             v = f_negate(v);
1343         if (!NIL_P(de))
1344             v = f_div(v, f_to_i(de));
1345
1346         return rb_assoc_new(v, re);
1347     }
1348     return rb_assoc_new(Qnil, self);
1349 }
1350
1351 static VALUE
1352 string_to_r_strict(VALUE self)
1353 {
1354     VALUE a = string_to_r_internal(self);
1355     if (NIL_P(RARRAY_PTR(a)[0]) || RSTRING_LEN(RARRAY_PTR(a)[1]) > 0) {
1356         VALUE s = f_inspect(self);
1357         rb_raise(rb_eArgError, "invalid value for Rational: %s",
1358                  StringValuePtr(s));
1359     }
1360     return RARRAY_PTR(a)[0];
1361 }
1362
1363 #define id_gsub rb_intern("gsub")
1364 #define f_gsub(x,y,z) rb_funcall(x, id_gsub, 2, y, z)
1365
1366 static VALUE
1367 string_to_r(VALUE self)
1368 {
1369     VALUE s, a, backref;
1370
1371     backref = rb_backref_get();
1372     rb_match_busy(backref);
1373
1374     s = f_gsub(self, underscores_pat, an_underscore);
1375     a = string_to_r_internal(s);
1376
1377     rb_backref_set(backref);
1378
1379     if (!NIL_P(RARRAY_PTR(a)[0]))
1380         return RARRAY_PTR(a)[0];
1381     return rb_rational_new1(INT2FIX(0));
1382 }
1383
1384 #define id_to_r rb_intern("to_r")
1385 #define f_to_r(x) rb_funcall(x, id_to_r, 0)
1386
1387 static VALUE
1388 nurat_s_convert(int argc, VALUE *argv, VALUE klass)
1389 {
1390     VALUE a1, a2, backref;
1391
1392     rb_scan_args(argc, argv, "02", &a1, &a2);
1393
1394     switch (TYPE(a1)) {
1395       case T_COMPLEX:
1396         if (k_float_p(RCOMPLEX(a1)->image) || !f_zero_p(RCOMPLEX(a1)->image)) {
1397             VALUE s = f_to_s(a1);
1398             rb_raise(rb_eRangeError, "can't accept %s",
1399                      StringValuePtr(s));
1400         }
1401         a1 = RCOMPLEX(a1)->real;
1402     }
1403
1404     switch (TYPE(a2)) {
1405       case T_COMPLEX:
1406         if (k_float_p(RCOMPLEX(a2)->image) || !f_zero_p(RCOMPLEX(a2)->image)) {
1407             VALUE s = f_to_s(a2);
1408             rb_raise(rb_eRangeError, "can't accept %s",
1409                      StringValuePtr(s));
1410         }
1411         a2 = RCOMPLEX(a2)->real;
1412     }
1413
1414     backref = rb_backref_get();
1415     rb_match_busy(backref);
1416
1417     switch (TYPE(a1)) {
1418       case T_FIXNUM:
1419       case T_BIGNUM:
1420         break;
1421       case T_FLOAT:
1422         a1 = f_to_r(a1);
1423         break;
1424       case T_STRING:
1425         a1 = string_to_r_strict(a1);
1426         break;
1427     }
1428
1429     switch (TYPE(a2)) {
1430       case T_FIXNUM:
1431       case T_BIGNUM:
1432         break;
1433       case T_FLOAT:
1434         a2 = f_to_r(a2);
1435         break;
1436       case T_STRING:
1437         a2 = string_to_r_strict(a2);
1438         break;
1439     }
1440
1441     rb_backref_set(backref);
1442
1443     switch (TYPE(a1)) {
1444       case T_RATIONAL:
1445         if (NIL_P(a2) || f_zero_p(a2))
1446             return a1;
1447         return f_div(a1, a2);
1448     }
1449
1450     switch (TYPE(a2)) {
1451       case T_RATIONAL:
1452         return f_div(a1, a2);
1453     }
1454
1455     {
1456         VALUE argv2[2];
1457         argv2[0] = a1;
1458         argv2[1] = a2;
1459         return nurat_s_new(argc, argv2, klass);
1460     }
1461 }
1462
1463 static VALUE
1464 nurat_s_induced_from(VALUE klass, VALUE n)
1465 {
1466     return f_to_r(n);
1467 }
1468
1469 void
1470 Init_Rational(void)
1471 {
1472 #undef rb_intern
1473 #define rb_intern(str) rb_intern_const(str)
1474
1475     assert(fprintf(stderr, "assert() is now active\n"));
1476
1477     id_Unify = rb_intern("Unify");
1478     id_abs = rb_intern("abs");
1479     id_cmp = rb_intern("<=>");
1480     id_convert = rb_intern("convert");
1481     id_equal_p = rb_intern("==");
1482     id_expt = rb_intern("**");
1483     id_floor = rb_intern("floor");
1484     id_format = rb_intern("format");
1485     id_idiv = rb_intern("div");
1486     id_inspect = rb_intern("inspect");
1487     id_negate = rb_intern("-@");
1488     id_new = rb_intern("new");
1489     id_new_bang = rb_intern("new!");
1490     id_to_f = rb_intern("to_f");
1491     id_to_i = rb_intern("to_i");
1492     id_to_s = rb_intern("to_s");
1493     id_truncate = rb_intern("truncate");
1494
1495     rb_cRational = rb_define_class(RATIONAL_NAME, rb_cNumeric);
1496
1497     rb_define_alloc_func(rb_cRational, nurat_s_alloc);
1498     rb_funcall(rb_cRational, rb_intern("private_class_method"), 1,
1499                ID2SYM(rb_intern("allocate")));
1500
1501     rb_define_singleton_method(rb_cRational, "new!", nurat_s_new_bang, -1);
1502     rb_funcall(rb_cRational, rb_intern("private_class_method"), 1,
1503                ID2SYM(rb_intern("new!")));
1504
1505     rb_define_singleton_method(rb_cRational, "new", nurat_s_new, -1);
1506     rb_funcall(rb_cRational, rb_intern("private_class_method"), 1,
1507                ID2SYM(rb_intern("new")));
1508
1509     rb_define_global_function(RATIONAL_NAME, nurat_f_rational, -1);
1510
1511     rb_define_method(rb_cRational, "numerator", nurat_numerator, 0);
1512     rb_define_method(rb_cRational, "denominator", nurat_denominator, 0);
1513
1514     rb_define_method(rb_cRational, "+", nurat_add, 1);
1515     rb_define_method(rb_cRational, "-", nurat_sub, 1);
1516     rb_define_method(rb_cRational, "*", nurat_mul, 1);
1517     rb_define_method(rb_cRational, "/", nurat_div, 1);
1518     rb_define_method(rb_cRational, "quo", nurat_div, 1);
1519     rb_define_method(rb_cRational, "fdiv", nurat_fdiv, 1);
1520     rb_define_method(rb_cRational, "**", nurat_expt, 1);
1521
1522     rb_define_method(rb_cRational, "<=>", nurat_cmp, 1);
1523     rb_define_method(rb_cRational, "==", nurat_equal_p, 1);
1524     rb_define_method(rb_cRational, "coerce", nurat_coerce, 1);
1525
1526     rb_define_method(rb_cRational, "div", nurat_idiv, 1);
1527 #if NUBY
1528     rb_define_method(rb_cRational, "//", nurat_idiv, 1);
1529 #endif
1530     rb_define_method(rb_cRational, "modulo", nurat_mod, 1);
1531     rb_define_method(rb_cRational, "%", nurat_mod, 1);
1532     rb_define_method(rb_cRational, "divmod", nurat_divmod, 1);
1533
1534 #if 0
1535     rb_define_method(rb_cRational, "quot", nurat_quot, 1);
1536 #endif
1537     rb_define_method(rb_cRational, "remainder", nurat_rem, 1);
1538 #if 0
1539     rb_define_method(rb_cRational, "quotrem", nurat_quotrem, 1);
1540 #endif
1541
1542     rb_define_method(rb_cRational, "abs", nurat_abs, 0);
1543
1544 #if 0
1545     rb_define_method(rb_cRational, "rational?", nurat_true, 0);
1546     rb_define_method(rb_cRational, "exact?", nurat_true, 0);
1547 #endif
1548
1549     rb_define_method(rb_cRational, "floor", nurat_floor, 0);
1550     rb_define_method(rb_cRational, "ceil", nurat_ceil, 0);
1551     rb_define_method(rb_cRational, "truncate", nurat_truncate, 0);
1552     rb_define_method(rb_cRational, "round", nurat_round, 0);
1553
1554     rb_define_method(rb_cRational, "to_i", nurat_truncate, 0);
1555     rb_define_method(rb_cRational, "to_f", nurat_to_f, 0);
1556     rb_define_method(rb_cRational, "to_r", nurat_to_r, 0);
1557
1558     rb_define_method(rb_cRational, "hash", nurat_hash, 0);
1559
1560     rb_define_method(rb_cRational, "to_s", nurat_to_s, 0);
1561     rb_define_method(rb_cRational, "inspect", nurat_inspect, 0);
1562
1563     rb_define_method(rb_cRational, "marshal_dump", nurat_marshal_dump, 0);
1564     rb_define_method(rb_cRational, "marshal_load", nurat_marshal_load, 1);
1565
1566     /* --- */
1567
1568     rb_define_method(rb_cInteger, "gcd", rb_gcd, 1);
1569     rb_define_method(rb_cInteger, "lcm", rb_lcm, 1);
1570     rb_define_method(rb_cInteger, "gcdlcm", rb_gcdlcm, 1);
1571
1572     rb_define_method(rb_cNilClass, "to_r", nilclass_to_r, 0);
1573     rb_define_method(rb_cInteger, "to_r", integer_to_r, 0);
1574     rb_define_method(rb_cFloat, "to_r", float_to_r, 0);
1575
1576     make_patterns();
1577
1578     rb_define_method(rb_cString, "to_r", string_to_r, 0);
1579
1580     rb_define_singleton_method(rb_cRational, "convert", nurat_s_convert, -1);
1581     rb_funcall(rb_cRational, rb_intern("private_class_method"), 1,
1582                ID2SYM(rb_intern("convert")));
1583
1584     rb_include_module(rb_cRational, rb_mPrecision);
1585     rb_define_singleton_method(rb_cRational, "induced_from",
1586                                nurat_s_induced_from, 1);
1587 }