summaryrefslogtreecommitdiff
path: root/numeric.c
blob: 8381762cd6be60d74098d8f33024d3f93e2d773f (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
/************************************************

  numeric.c -

  $Author: matz $
  $Date: 1995/01/10 10:42:42 $
  created at: Fri Aug 13 18:33:09 JST 1993

  Copyright (C) 1995 Yukihiro Matsumoto

************************************************/

#include "ruby.h"
#include "env.h"
#include <math.h>

static ID coerce;
static ID to_i;

VALUE C_Numeric;
VALUE C_Float;
VALUE C_Integer;
VALUE C_Fixnum;

double big2dbl();

VALUE
float_new(d)
    double d;
{
    NEWOBJ(flt, struct RFloat);
    OBJSETUP(flt, C_Float, T_FLOAT);

    flt->value = d;
    return (VALUE)flt;
}

static
num_coerce_bin(x, y)
    VALUE x, y;
{
    return rb_funcall(rb_funcall(y, coerce, 1, x),
		      the_env->last_func, 1, y);
}

static VALUE
Fnum_uplus(num)
    VALUE num;
{
    return num;
}

static VALUE
Fnum_uminus(num)
    VALUE num;
{
    return rb_funcall(rb_funcall(num, coerce, 1, INT2FIX(0)), 1, num);
}

static VALUE
Fnum_dot2(left, right)
    VALUE left, right;
{
    Need_Fixnum(left);
    Need_Fixnum(right);
    return range_new(left, right);
}

static VALUE
Fnum_next(num)
    VALUE num;
{
    num = rb_funcall(num, rb_intern("to_i"), 0);
    return rb_funcall(num, '+', 1, INT2FIX(1));
}

VALUE
Fnum_upto(from, to)
    VALUE from, to;
{
    int i, end;

    end = NUM2INT(to);
    for (i = NUM2INT(from); i <= end; i++) {
	rb_yield(INT2FIX(i));
    }

    return from;
}

static VALUE
Fnum_downto(from, to)
    VALUE from, to;
{
    int i, end;

    end = NUM2INT(to);
    for (i=NUM2INT(from); i >= end; i--) {
	rb_yield(INT2FIX(i));
    }

    return from;
}

static VALUE
Fnum_step(from, to, step)
    VALUE from, to;
{
    int i, end, diff;

    end = NUM2INT(to);
    diff = NUM2INT(step);

    if (diff == 0) {
	Fail("step cannot be 0");
    }
    else if (diff > 0) {
	for (i=NUM2INT(from); i <= end; i+=diff) {
	    rb_yield(INT2FIX(i));
	}
    }
    else {
	for (i=NUM2INT(from); i >= end; i+=diff) {
	    rb_yield(INT2FIX(i));
	}
    }
    return from;
}

static VALUE
Fnum_dotimes(num)
    VALUE num;
{
    int i, end;

    end = NUM2INT(num);
    for (i=0; i<end; i++) {
	rb_yield(INT2FIX(i));
    }
    return num;
}

static VALUE
Fnum_divmod(x, y)
    VALUE x, y;
{
    VALUE div, mod;

    div = rb_funcall(x, '/', 1, y);
    if (TYPE(div) == T_FLOAT) {
	double d = floor(RFLOAT(div)->value);

	if (RFLOAT(div)->value > d) {
	    div = float_new(d);
	}
    }
    mod = rb_funcall(x, '%', 1, y);
    return assoc_new(div, mod);
}

static VALUE
Fnum_is_int(num)
    VALUE num;
{
    return FALSE;
}

static VALUE
Fflo_to_s(flt)
    struct RFloat *flt;
{
    char buf[32];

    sprintf(buf, "%g", flt->value);

    return str_new2(buf);
}

static VALUE
Fflo_coerce(x, y)
    VALUE x, y;
{
    switch (TYPE(y)) {
      case T_FIXNUM:
	return float_new((double)FIX2INT(y));
      case T_FLOAT:
	return y;
      case T_BIGNUM:
	return Fbig_to_f(y);
      default:
	Fail("can't coerce %s to Float", rb_class2name(CLASS_OF(y)));
    }
    /* not reached */
    return Qnil;
}

static VALUE
Fflo_uminus(flt)
    struct RFloat *flt;
{
    return float_new(-flt->value);
}

static VALUE
Fflo_plus(x, y)
    struct RFloat *x, *y;
{
    switch (TYPE(y)) {
      case T_FIXNUM:
	return float_new(x->value + (double)FIX2INT(y));
      case T_BIGNUM:
	return float_new(x->value + big2dbl(y));
      case T_FLOAT:
	return float_new(x->value + y->value);
      case T_STRING:
	return Fstr_plus(obj_as_string(x), y);
      default:
	return num_coerce_bin(x, y);
    }
}

static VALUE
Fflo_minus(x, y)
    struct RFloat *x, *y;
{
    switch (TYPE(y)) {
      case T_FIXNUM:
	return float_new(x->value - (double)FIX2INT(y));
      case T_BIGNUM:
	return float_new(x->value - big2dbl(y));
      case T_FLOAT:
	return float_new(x->value - y->value);
      default:
	return num_coerce_bin(x, y);
    }
}

static VALUE
Fflo_mul(x, y)
    struct RFloat *x, *y;
{
    switch (TYPE(y)) {
      case T_FIXNUM:
	return float_new(x->value * (double)FIX2INT(y));
      case T_BIGNUM:
	return float_new(x->value * big2dbl(y));
      case T_FLOAT:
	return float_new(x->value * y->value);
      case T_STRING:
	return Fstr_times(y, INT2FIX((int)x->value));
      default:
	return num_coerce_bin(x, y);
    }
}

static VALUE
Fflo_div(x, y)
    struct RFloat *x, *y;
{
    int f_y;
    double d;

    switch (TYPE(y)) {
      case T_FIXNUM:
	f_y = FIX2INT(y);
	if (f_y == 0) Fail("devided by 0");
	return float_new(x->value / (double)f_y);
      case T_BIGNUM:
	d = big2dbl(y);
	if (d == 0.0) Fail("devided by 0");
	return float_new(x->value + d);
      case T_FLOAT:
	if (y->value == 0.0) Fail("devided by 0");
	return float_new(x->value / y->value);
      default:
	return num_coerce_bin(x, y);
    }
}

static VALUE
Fflo_mod(x, y)
    struct RFloat *x, *y;
{
    double value;

    switch (TYPE(y)) {
      case T_FIXNUM:
	value = (double)FIX2INT(y);
	break;
      case T_BIGNUM:
	value = big2dbl(y);
	break;
      case T_FLOAT:
	value = y->value;
	break;
      default:
	return num_coerce_bin(x, y);
    }
#ifdef HAVE_FMOD
    {
	value = fmod(x->value, value);
    }
#else
    {
	double value1 = x->value;
	double value2;

	modf(value1/value, &value2);
	value = value1 - value2 * value;
    }
#endif

    return float_new(value);
}

Fflo_pow(x, y)
    struct RFloat *x, *y;
{
    switch (TYPE(y)) {
      case T_FIXNUM:
        return float_new(pow(x->value, (double)FIX2INT(y)));
      case T_BIGNUM:
	return float_new(pow(x->value, big2dbl(y)));
      case T_FLOAT:
        return float_new(pow(x->value, y->value));
      default:
        return num_coerce_bin(x, y);
    }
}

static VALUE
Fflo_eq(x, y)
    struct RFloat *x, *y;
{
    switch (TYPE(y)) {
      case T_NIL:
	return Qnil;
      case T_FIXNUM:
	if (x->value == FIX2INT(y)) return TRUE;
	return FALSE;
      case T_BIGNUM:
	return float_new(x->value == big2dbl(y));
      case T_FLOAT:
	return (x->value == y->value)?TRUE:FALSE;
      default:
	return num_coerce_bin(x, y);
    }
}

static VALUE
Fflo_hash(num)
    struct RFloat *num;
{
    double d;
    char *c;
    int i, hash;

    d = num->value;
    c = (char*)&d;
    for (hash=0, i=0; i<sizeof(double);i++) {
	hash += c[i] * 971;
    }
    if (hash < 0) hash = -hash;
    return INT2FIX(hash);
}

static VALUE
Fflo_cmp(x, y)
    struct RFloat *x, *y;
{
    double a, b;

    a = x->value;
    switch (TYPE(y)) {
      case T_FIXNUM:
	b = (double)FIX2INT(y);
	break;

      case T_BIGNUM:
	b = big2dbl(y);
	break;

      case T_FLOAT:
	b = y->value;
	break;

      default:
	return num_coerce_bin(x, y);
    }
    if (a == b) return INT2FIX(0);
    if (a > b) return INT2FIX(1);
    return INT2FIX(-1);
}

static VALUE
Fflo_to_i(num)
    struct RFloat *num;
{
    double f = num->value;
    int val;

    if (!FIXABLE(f)) {
	return dbl2big(f);
    }
    val = f;
    return INT2FIX(val);
}

static VALUE
Fflo_to_f(num)
    VALUE num;
{
    return num;
}

static VALUE
Fflo_abs(flt)
    struct RFloat *flt;
{
    double val = fabs(flt->value);
    return float_new(val);
}

static VALUE
to_integer(val)
    VALUE val;
{
    return rb_funcall(val, to_i, 0);
}

static VALUE
fail_to_integer(val)
    VALUE val;
{
    Fail("failed to convert %s into integer", rb_class2name(CLASS_OF(val)));
}

int
num2int(val)
    VALUE val;
{
    if (val == Qnil) return 0;

    switch (TYPE(val)) {
      case T_FIXNUM:
	return FIX2INT(val);
	break;

      case T_FLOAT:
	if (RFLOAT(val)->value <= (double) LONG_MAX
	    && RFLOAT(val)->value >= (double) LONG_MIN) {
	    return (int)(RFLOAT(val)->value);
	}
	else {
	    Fail("float %g out of rang of integer", RFLOAT(val)->value);
	}
	break;

      case T_BIGNUM:
	return big2int(val);

      default:
	val = rb_resque(to_integer, val, fail_to_integer, val);
	return NUM2INT(val);
    }
}

VALUE
num2fix(val)
    VALUE val;
{
    int v;

    if (val == Qnil) return INT2FIX(0);
    switch (TYPE(val)) {
      case T_FIXNUM:
	return val;

      case T_FLOAT:
      case T_BIGNUM:
      default:
	v = num2int(val);
	if (!FIXABLE(v))
	    Fail("integer %d out of rang of Fixnum", v);
	return INT2FIX(v);
    }
}

static VALUE
Fint_is_int(num)
    VALUE num;
{
    return TRUE;
}

static VALUE
Fint_chr(num)
    VALUE num;
{
    char c;
    int i = NUM2INT(num);

    if (i < 0 || 0xff < i)
	Fail("%d out of char range", i);
    c = i;
    return str_new(&c, 1);
}

static VALUE
Ffix_uminus(num)
    VALUE num;
{
    return int2inum(-FIX2INT(num));
}

VALUE
fix2str(x, base)
    VALUE x;
    int base;
{
    char fmt[3], buf[12];

    fmt[0] = '%'; fmt[2] = '\0';
    if (base == 10) fmt[1] = 'd';
    else if (base == 16) fmt[1] = 'x';
    else if (base == 8) fmt[1] = 'o';
    else Fail("fixnum cannot treat base %d", base);

    sprintf(buf, fmt, FIX2INT(x));
    return str_new2(buf);
}

VALUE
Ffix_to_s(in)
    VALUE in;
{
    return fix2str(in, 10);
}

static VALUE
Ffix_plus(x, y)
    VALUE x;
    struct RFloat *y;
{
    switch (TYPE(y)) {
      case T_FIXNUM:
	{
	    int a, b, c;
	    VALUE r;

	    a = FIX2INT(x);
	    b = FIX2INT(y);
	    c = a + b;
	    r = INT2FIX(c);

	    if (FIX2INT(r) != c) {
		r = Fbig_plus(int2big(a), int2big(b));
	    }
	    return r;
	}
      case T_FLOAT:
	return float_new((double)FIX2INT(x) + y->value);
      default:
	return num_coerce_bin(x, y);
    }
}

static VALUE
Ffix_minus(x, y)
    VALUE x;
    struct RFloat *y;
{
    switch (TYPE(y)) {
      case T_FIXNUM:
	{
	    int a, b, c;
	    VALUE r;

	    a = FIX2INT(x);
	    b = FIX2INT(y);
	    c = a - b;
	    r = INT2FIX(c);

	    if (FIX2INT(r) != c) {
		r = Fbig_minus(int2big(a), int2big(b));
	    }
	    return r;
	}
      case T_FLOAT:
	return float_new((double)FIX2INT(x) - y->value);
      default:
	return num_coerce_bin(x, y);
    }
}

static VALUE
Ffix_mul(x, y)
    VALUE x;
    struct RFloat *y;
{
    switch (TYPE(y)) {
      case T_FIXNUM:
	{
	    int a = FIX2INT(x), b = FIX2INT(y);
	    int c = a * b;
	    VALUE r = INT2FIX(c);

	    if (FIX2INT(r) != c) {
		r = Fbig_mul(int2big(a), int2big(b));
	    }
	    return r;
	}
      case T_FLOAT:
	return float_new((double)FIX2INT(x) * y->value);
      default:
	return num_coerce_bin(x, y);
    }
}

static VALUE
Ffix_div(x, y)
    VALUE x;
    struct RFloat *y;
{
    int i;

    if (TYPE(y) == T_FIXNUM) {
	i = FIX2INT(y);
	if (i == 0) Fail("devided by 0");
	i = FIX2INT(x)/i;
	return INT2FIX(i);
    }
    return num_coerce_bin(x, y);
}

static VALUE
Ffix_mod(x, y)
    VALUE x, y;
{
    int mod, i;

    if (TYPE(y) == T_FIXNUM) {
	i = FIX2INT(y);
	if (i == 0) Fail("devided by 0");
	i = FIX2INT(x)%i;
	return INT2FIX(i);
    }
    return num_coerce_bin(x, y);
}

static VALUE
Ffix_pow(x, y)
    VALUE x, y;
{
    extern double pow();

    if (FIXNUM_P(y)) {
	int a, b;

	b = FIX2INT(y);
	if (b == 0) return INT2FIX(1);
	a = FIX2INT(x);
	if (b > 0) {
	    return Fbig_pow(int2big(a), y);
	}
	return float_new(pow((double)a, (double)b));
    }
    else if (NIL_P(y)) {
	return INT2FIX(1);
    }
    return num_coerce_bin(x, y);
}

static VALUE
Ffix_equal(x, y)
    VALUE x, y;
{
    if (FIXNUM_P(y)) {
	return (FIX2INT(x) == FIX2INT(y))?TRUE:FALSE;
    }
    else if (NIL_P(y)) {
	return Qnil;
    }
    else {
	return num_coerce_bin(x, y);
    }
}

static VALUE
Ffix_cmp(x, y)
    VALUE x, y;
{
    if (FIXNUM_P(y)) {
	int a = FIX2INT(x), b = FIX2INT(y);

	if (a == b) return INT2FIX(0);
	if (a > b) return INT2FIX(1);
	return INT2FIX(-1);
    }
    else {
	return num_coerce_bin(x, y);
    }
}

static VALUE
Ffix_gt(x, y)
    VALUE x, y;
{
    if (FIXNUM_P(y)) {
	int a = FIX2INT(x), b = FIX2INT(y);

	if (a > b) return TRUE;
	return FALSE;
    }
    else {
	return num_coerce_bin(x, y);
    }
}

static VALUE
Ffix_ge(x, y)
    VALUE x, y;
{
    if (FIXNUM_P(y)) {
	int a = FIX2INT(x), b = FIX2INT(y);

	if (a >= b) return TRUE;
	return FALSE;
    }
    else {
	return num_coerce_bin(x, y);
    }
}

static VALUE
Ffix_lt(x, y)
    VALUE x, y;
{
    if (FIXNUM_P(y)) {
	int a = FIX2INT(x), b = FIX2INT(y);

	if (a < b) return TRUE;
	return FALSE;
    }
    else {
	return num_coerce_bin(x, y);
    }
}

static VALUE
Ffix_le(x, y)
    VALUE x, y;
{
    if (FIXNUM_P(y)) {
	int a = FIX2INT(x), b = FIX2INT(y);

	if (a <= b) return TRUE;
	return FALSE;
    }
    else {
	return num_coerce_bin(x, y);
    }
}

static VALUE
Ffix_dot2(left, right)
    VALUE left, right;
{
    Need_Fixnum(right);
    return range_new(left, right);
}

static VALUE
Ffix_rev(num)
    VALUE num;
{
    unsigned long val = FIX2UINT(num);

    val = ~val;
    return INT2FIX(val);
}

static VALUE
Ffix_and(x, y)
    VALUE x, y;
{
    long val;

    if (TYPE(y) == T_BIGNUM) {
	return Fbig_and(y, x);
    }
    val = NUM2INT(x) & NUM2INT(y);
    return int2inum(val);
}

static VALUE
Ffix_or(x, y)
    VALUE x, y;
{
    long val;

    if (TYPE(y) == T_BIGNUM) {
	return Fbig_or(y, x);
    }
    val = NUM2INT(x) | NUM2INT(y);
    return INT2FIX(val);
}

static VALUE
Ffix_xor(x, y)
    VALUE x, y;
{
    long val;

    if (TYPE(y) == T_BIGNUM) {
	return Fbig_xor(y, x);
    }
    val = NUM2INT(x) ^ NUM2INT(y);
    return INT2FIX(val);
}

static VALUE
Ffix_lshift(x, y)
    VALUE x, y;
{
    long val, width;

    val = NUM2INT(x);
    width = NUM2INT(y);
    if (width > (sizeof(VALUE)*CHAR_BIT-1)
	|| (unsigned)val>>(sizeof(VALUE)*CHAR_BIT-width) > 0) {
	return Fbig_lshift(int2big(val), y);
    }
    val = val << width;
    return int2inum(val);
}

static VALUE
Ffix_rshift(x, y)
    VALUE x, y;
{
    long val;

    val = RSHIFT(NUM2INT(x), NUM2INT(y));
    return INT2FIX(val);
}

static VALUE
Ffix_aref(fix, idx)
    VALUE fix, idx;
{
    unsigned long val = FIX2INT(fix);
    int i = FIX2INT(idx);

    if (i < 0 || sizeof(VALUE)*CHAR_BIT-1 < i)
	return INT2FIX(0);
    if (val & (1<<i))
	return INT2FIX(1);
    return INT2FIX(0);
}

static VALUE
Ffix_to_i(num)
    VALUE num;
{
    return num;
}

static VALUE
Ffix_to_f(num)
    VALUE num;
{
    double val;

    val = (double)FIX2INT(num);

    return float_new(val);
}

static VALUE
Ffix_class(fix)
    VALUE fix;
{
    return C_Fixnum;
}

static
Ffix_abs(fix)
    VALUE fix;
{
    int i = FIX2INT(fix);

    if (fix < 0) i = -i;

    return int2inum(fix);
}

static VALUE
Ffix_id2name(fix)
    VALUE fix;
{
    char *name = rb_id2name(FIX2UINT(fix));
    if (name) return str_new2(name);
    return Qnil;
}

static VALUE
Ffix_next(fix)
    VALUE fix;
{
    int i = FIX2INT(fix) + 1;

    return int2inum(i);
}

extern VALUE M_Comparable;
extern Fkrn_inspect();

Init_Numeric()
{
    coerce = rb_intern("coerce");
    to_i = rb_intern("to_i");

    C_Numeric = rb_define_class("Numeric", C_Object);

    rb_undef_method(CLASS_OF(C_Numeric), "new");
    rb_undef_method(C_Numeric, "clone");

    rb_include_module(C_Numeric, M_Comparable);
    rb_define_method(C_Numeric, "+@", Fnum_uplus, 0);
    rb_define_method(C_Numeric, "-@", Fnum_uminus, 0);
    rb_define_method(C_Numeric, "..", Fnum_dot2, 1);
    rb_define_method(C_Numeric, "divmod", Fnum_divmod, 1);

    rb_define_method(C_Numeric, "next", Fnum_next, 0);
    rb_define_method(C_Numeric, "upto", Fnum_upto, 1);
    rb_define_method(C_Numeric, "downto", Fnum_downto, 1);
    rb_define_method(C_Numeric, "step", Fnum_step, 2);
    rb_define_method(C_Numeric, "times", Fnum_dotimes, 0);
    rb_define_method(C_Numeric, "is_integer", Fnum_is_int, 0);
    rb_define_method(C_Numeric, "_inspect", Fkrn_inspect, 0);

    C_Integer = rb_define_class("Integer", C_Numeric);
    rb_define_method(C_Integer, "is_integer", Fint_is_int, 0);
    rb_define_method(C_Integer, "chr", Fint_chr, 0);

    C_Fixnum = rb_define_class("Fixnum", C_Integer);

    rb_define_method(C_Fixnum, "to_s", Ffix_to_s, 0);
    rb_define_method(C_Fixnum, "class", Ffix_class, 0);

    rb_define_method(C_Fixnum, "id2name", Ffix_id2name, 0);

    rb_define_method(C_Fixnum, "-@", Ffix_uminus, 0);
    rb_define_method(C_Fixnum, "+", Ffix_plus, 1);
    rb_define_method(C_Fixnum, "-", Ffix_minus, 1);
    rb_define_method(C_Fixnum, "*", Ffix_mul, 1);
    rb_define_method(C_Fixnum, "/", Ffix_div, 1);
    rb_define_method(C_Fixnum, "%", Ffix_mod, 1);
    rb_define_method(C_Fixnum, "**", Ffix_pow, 1);

    rb_define_method(C_Fixnum, "abs", Ffix_abs, 0);

    rb_define_method(C_Fixnum, "==", Ffix_equal, 1);
    rb_define_method(C_Fixnum, "<=>", Ffix_cmp, 1);
    rb_define_method(C_Fixnum, ">",  Ffix_gt, 1);
    rb_define_method(C_Fixnum, ">=", Ffix_ge, 1);
    rb_define_method(C_Fixnum, "<",  Ffix_lt, 1);
    rb_define_method(C_Fixnum, "<=", Ffix_le, 1);
    rb_define_method(C_Fixnum, "..", Ffix_dot2, 1);

    rb_define_method(C_Fixnum, "~", Ffix_rev, 0);
    rb_define_method(C_Fixnum, "&", Ffix_and, 1);
    rb_define_method(C_Fixnum, "|", Ffix_or,  1);
    rb_define_method(C_Fixnum, "^", Ffix_xor, 1);
    rb_define_method(C_Fixnum, "[]", Ffix_aref, 1);

    rb_define_method(C_Fixnum, "<<", Ffix_lshift, 1);
    rb_define_method(C_Fixnum, ">>", Ffix_rshift, 1);

    rb_define_method(C_Fixnum, "to_i", Ffix_to_i, 0);
    rb_define_method(C_Fixnum, "to_f", Ffix_to_f, 0);

    rb_define_method(C_Fixnum, "next", Ffix_next, 0);

    C_Float  = rb_define_class("Float", C_Numeric);

    rb_define_method(C_Float, "to_s", Fflo_to_s, 0);
    rb_define_method(C_Float, "coerce", Fflo_coerce, 1);
    rb_define_method(C_Float, "-@", Fflo_uminus, 0);
    rb_define_method(C_Float, "+", Fflo_plus, 1);
    rb_define_method(C_Float, "-", Fflo_minus, 1);
    rb_define_method(C_Float, "*", Fflo_mul, 1);
    rb_define_method(C_Float, "/", Fflo_div, 1);
    rb_define_method(C_Float, "%", Fflo_mod, 1);
    rb_define_method(C_Float, "**", Fflo_pow, 1);
    rb_define_method(C_Float, "==", Fflo_eq, 1);
    rb_define_method(C_Float, "<=>", Fflo_cmp, 1);
    rb_define_method(C_Float, "hash", Fflo_hash, 0);
    rb_define_method(C_Float, "to_i", Fflo_to_i, 0);
    rb_define_method(C_Float, "to_f", Fflo_to_f, 0);
    rb_define_method(C_Float, "abs", Fflo_abs, 0);
}