Ruby  3.4.0dev (2024-12-06 revision 892c46283a5ea4179500d951c9d4866c0051f27b)
numeric.c (892c46283a5ea4179500d951c9d4866c0051f27b)
1 /**********************************************************************
2 
3  numeric.c -
4 
5  $Author$
6  created at: Fri Aug 13 18:33:09 JST 1993
7 
8  Copyright (C) 1993-2007 Yukihiro Matsumoto
9 
10 **********************************************************************/
11 
12 #include "ruby/internal/config.h"
13 
14 #include <assert.h>
15 #include <ctype.h>
16 #include <math.h>
17 #include <stdio.h>
18 
19 #ifdef HAVE_FLOAT_H
20 #include <float.h>
21 #endif
22 
23 #ifdef HAVE_IEEEFP_H
24 #include <ieeefp.h>
25 #endif
26 
27 #include "id.h"
28 #include "internal.h"
29 #include "internal/array.h"
30 #include "internal/compilers.h"
31 #include "internal/complex.h"
32 #include "internal/enumerator.h"
33 #include "internal/gc.h"
34 #include "internal/hash.h"
35 #include "internal/numeric.h"
36 #include "internal/object.h"
37 #include "internal/rational.h"
38 #include "internal/string.h"
39 #include "internal/util.h"
40 #include "internal/variable.h"
41 #include "ruby/encoding.h"
42 #include "ruby/util.h"
43 #include "builtin.h"
44 
45 /* use IEEE 64bit values if not defined */
46 #ifndef FLT_RADIX
47 #define FLT_RADIX 2
48 #endif
49 #ifndef DBL_MIN
50 #define DBL_MIN 2.2250738585072014e-308
51 #endif
52 #ifndef DBL_MAX
53 #define DBL_MAX 1.7976931348623157e+308
54 #endif
55 #ifndef DBL_MIN_EXP
56 #define DBL_MIN_EXP (-1021)
57 #endif
58 #ifndef DBL_MAX_EXP
59 #define DBL_MAX_EXP 1024
60 #endif
61 #ifndef DBL_MIN_10_EXP
62 #define DBL_MIN_10_EXP (-307)
63 #endif
64 #ifndef DBL_MAX_10_EXP
65 #define DBL_MAX_10_EXP 308
66 #endif
67 #ifndef DBL_DIG
68 #define DBL_DIG 15
69 #endif
70 #ifndef DBL_MANT_DIG
71 #define DBL_MANT_DIG 53
72 #endif
73 #ifndef DBL_EPSILON
74 #define DBL_EPSILON 2.2204460492503131e-16
75 #endif
76 
77 #ifndef USE_RB_INFINITY
78 #elif !defined(WORDS_BIGENDIAN) /* BYTE_ORDER == LITTLE_ENDIAN */
79 const union bytesequence4_or_float rb_infinity = {{0x00, 0x00, 0x80, 0x7f}};
80 #else
81 const union bytesequence4_or_float rb_infinity = {{0x7f, 0x80, 0x00, 0x00}};
82 #endif
83 
84 #ifndef USE_RB_NAN
85 #elif !defined(WORDS_BIGENDIAN) /* BYTE_ORDER == LITTLE_ENDIAN */
86 const union bytesequence4_or_float rb_nan = {{0x00, 0x00, 0xc0, 0x7f}};
87 #else
88 const union bytesequence4_or_float rb_nan = {{0x7f, 0xc0, 0x00, 0x00}};
89 #endif
90 
91 #ifndef HAVE_ROUND
92 double
93 round(double x)
94 {
95  double f;
96 
97  if (x > 0.0) {
98  f = floor(x);
99  x = f + (x - f >= 0.5);
100  }
101  else if (x < 0.0) {
102  f = ceil(x);
103  x = f - (f - x >= 0.5);
104  }
105  return x;
106 }
107 #endif
108 
109 static double
110 round_half_up(double x, double s)
111 {
112  double f, xs = x * s;
113 
114  f = round(xs);
115  if (s == 1.0) return f;
116  if (x > 0) {
117  if ((double)((f + 0.5) / s) <= x) f += 1;
118  x = f;
119  }
120  else {
121  if ((double)((f - 0.5) / s) >= x) f -= 1;
122  x = f;
123  }
124  return x;
125 }
126 
127 static double
128 round_half_down(double x, double s)
129 {
130  double f, xs = x * s;
131 
132  f = round(xs);
133  if (x > 0) {
134  if ((double)((f - 0.5) / s) >= x) f -= 1;
135  x = f;
136  }
137  else {
138  if ((double)((f + 0.5) / s) <= x) f += 1;
139  x = f;
140  }
141  return x;
142 }
143 
144 static double
145 round_half_even(double x, double s)
146 {
147  double u, v, us, vs, f, d, uf;
148 
149  v = modf(x, &u);
150  us = u * s;
151  vs = v * s;
152 
153  if (x > 0.0) {
154  f = floor(vs);
155  uf = us + f;
156  d = vs - f;
157  if (d > 0.5)
158  d = 1.0;
159  else if (d == 0.5 || ((double)((uf + 0.5) / s) <= x))
160  d = fmod(uf, 2.0);
161  else
162  d = 0.0;
163  x = f + d;
164  }
165  else if (x < 0.0) {
166  f = ceil(vs);
167  uf = us + f;
168  d = f - vs;
169  if (d > 0.5)
170  d = 1.0;
171  else if (d == 0.5 || ((double)((uf - 0.5) / s) >= x))
172  d = fmod(-uf, 2.0);
173  else
174  d = 0.0;
175  x = f - d;
176  }
177  return us + x;
178 }
179 
180 static VALUE fix_lshift(long, unsigned long);
181 static VALUE fix_rshift(long, unsigned long);
182 static VALUE int_pow(long x, unsigned long y);
183 static VALUE rb_int_floor(VALUE num, int ndigits);
184 static VALUE rb_int_ceil(VALUE num, int ndigits);
185 static VALUE flo_to_i(VALUE num);
186 static int float_round_overflow(int ndigits, int binexp);
187 static int float_round_underflow(int ndigits, int binexp);
188 
189 static ID id_coerce;
190 #define id_div idDiv
191 #define id_divmod idDivmod
192 #define id_to_i idTo_i
193 #define id_eq idEq
194 #define id_cmp idCmp
195 
199 
202 
203 static ID id_to, id_by;
204 
205 void
207 {
208  rb_raise(rb_eZeroDivError, "divided by 0");
209 }
210 
211 enum ruby_num_rounding_mode
212 rb_num_get_rounding_option(VALUE opts)
213 {
214  static ID round_kwds[1];
215  VALUE rounding;
216  VALUE str;
217  const char *s;
218 
219  if (!NIL_P(opts)) {
220  if (!round_kwds[0]) {
221  round_kwds[0] = rb_intern_const("half");
222  }
223  if (!rb_get_kwargs(opts, round_kwds, 0, 1, &rounding)) goto noopt;
224  if (SYMBOL_P(rounding)) {
225  str = rb_sym2str(rounding);
226  }
227  else if (NIL_P(rounding)) {
228  goto noopt;
229  }
230  else if (!RB_TYPE_P(str = rounding, T_STRING)) {
231  str = rb_check_string_type(rounding);
232  if (NIL_P(str)) goto invalid;
233  }
234  rb_must_asciicompat(str);
235  s = RSTRING_PTR(str);
236  switch (RSTRING_LEN(str)) {
237  case 2:
238  if (rb_memcicmp(s, "up", 2) == 0)
239  return RUBY_NUM_ROUND_HALF_UP;
240  break;
241  case 4:
242  if (rb_memcicmp(s, "even", 4) == 0)
243  return RUBY_NUM_ROUND_HALF_EVEN;
244  if (strncasecmp(s, "down", 4) == 0)
245  return RUBY_NUM_ROUND_HALF_DOWN;
246  break;
247  }
248  invalid:
249  rb_raise(rb_eArgError, "invalid rounding mode: % "PRIsVALUE, rounding);
250  }
251  noopt:
252  return RUBY_NUM_ROUND_DEFAULT;
253 }
254 
255 /* experimental API */
256 int
257 rb_num_to_uint(VALUE val, unsigned int *ret)
258 {
259 #define NUMERR_TYPE 1
260 #define NUMERR_NEGATIVE 2
261 #define NUMERR_TOOLARGE 3
262  if (FIXNUM_P(val)) {
263  long v = FIX2LONG(val);
264 #if SIZEOF_INT < SIZEOF_LONG
265  if (v > (long)UINT_MAX) return NUMERR_TOOLARGE;
266 #endif
267  if (v < 0) return NUMERR_NEGATIVE;
268  *ret = (unsigned int)v;
269  return 0;
270  }
271 
272  if (RB_BIGNUM_TYPE_P(val)) {
273  if (BIGNUM_NEGATIVE_P(val)) return NUMERR_NEGATIVE;
274 #if SIZEOF_INT < SIZEOF_LONG
275  /* long is 64bit */
276  return NUMERR_TOOLARGE;
277 #else
278  /* long is 32bit */
279  if (rb_absint_size(val, NULL) > sizeof(int)) return NUMERR_TOOLARGE;
280  *ret = (unsigned int)rb_big2ulong((VALUE)val);
281  return 0;
282 #endif
283  }
284  return NUMERR_TYPE;
285 }
286 
287 #define method_basic_p(klass) rb_method_basic_definition_p(klass, mid)
288 
289 static inline int
290 int_pos_p(VALUE num)
291 {
292  if (FIXNUM_P(num)) {
293  return FIXNUM_POSITIVE_P(num);
294  }
295  else if (RB_BIGNUM_TYPE_P(num)) {
296  return BIGNUM_POSITIVE_P(num);
297  }
298  rb_raise(rb_eTypeError, "not an Integer");
299 }
300 
301 static inline int
302 int_neg_p(VALUE num)
303 {
304  if (FIXNUM_P(num)) {
305  return FIXNUM_NEGATIVE_P(num);
306  }
307  else if (RB_BIGNUM_TYPE_P(num)) {
308  return BIGNUM_NEGATIVE_P(num);
309  }
310  rb_raise(rb_eTypeError, "not an Integer");
311 }
312 
313 int
314 rb_int_positive_p(VALUE num)
315 {
316  return int_pos_p(num);
317 }
318 
319 int
320 rb_int_negative_p(VALUE num)
321 {
322  return int_neg_p(num);
323 }
324 
325 int
326 rb_num_negative_p(VALUE num)
327 {
328  return rb_num_negative_int_p(num);
329 }
330 
331 static VALUE
332 num_funcall_op_0(VALUE x, VALUE arg, int recursive)
333 {
334  ID func = (ID)arg;
335  if (recursive) {
336  const char *name = rb_id2name(func);
337  if (ISALNUM(name[0])) {
338  rb_name_error(func, "%"PRIsVALUE".%"PRIsVALUE,
339  x, ID2SYM(func));
340  }
341  else if (name[0] && name[1] == '@' && !name[2]) {
342  rb_name_error(func, "%c%"PRIsVALUE,
343  name[0], x);
344  }
345  else {
346  rb_name_error(func, "%"PRIsVALUE"%"PRIsVALUE,
347  ID2SYM(func), x);
348  }
349  }
350  return rb_funcallv(x, func, 0, 0);
351 }
352 
353 static VALUE
354 num_funcall0(VALUE x, ID func)
355 {
356  return rb_exec_recursive(num_funcall_op_0, x, (VALUE)func);
357 }
358 
359 NORETURN(static void num_funcall_op_1_recursion(VALUE x, ID func, VALUE y));
360 
361 static void
362 num_funcall_op_1_recursion(VALUE x, ID func, VALUE y)
363 {
364  const char *name = rb_id2name(func);
365  if (ISALNUM(name[0])) {
366  rb_name_error(func, "%"PRIsVALUE".%"PRIsVALUE"(%"PRIsVALUE")",
367  x, ID2SYM(func), y);
368  }
369  else {
370  rb_name_error(func, "%"PRIsVALUE"%"PRIsVALUE"%"PRIsVALUE,
371  x, ID2SYM(func), y);
372  }
373 }
374 
375 static VALUE
376 num_funcall_op_1(VALUE y, VALUE arg, int recursive)
377 {
378  ID func = (ID)((VALUE *)arg)[0];
379  VALUE x = ((VALUE *)arg)[1];
380  if (recursive) {
381  num_funcall_op_1_recursion(x, func, y);
382  }
383  return rb_funcall(x, func, 1, y);
384 }
385 
386 static VALUE
387 num_funcall1(VALUE x, ID func, VALUE y)
388 {
389  VALUE args[2];
390  args[0] = (VALUE)func;
391  args[1] = x;
392  return rb_exec_recursive_paired(num_funcall_op_1, y, x, (VALUE)args);
393 }
394 
395 /*
396  * call-seq:
397  * coerce(other) -> array
398  *
399  * Returns a 2-element array containing two numeric elements,
400  * formed from the two operands +self+ and +other+,
401  * of a common compatible type.
402  *
403  * Of the Core and Standard Library classes,
404  * Integer, Rational, and Complex use this implementation.
405  *
406  * Examples:
407  *
408  * i = 2 # => 2
409  * i.coerce(3) # => [3, 2]
410  * i.coerce(3.0) # => [3.0, 2.0]
411  * i.coerce(Rational(1, 2)) # => [0.5, 2.0]
412  * i.coerce(Complex(3, 4)) # Raises RangeError.
413  *
414  * r = Rational(5, 2) # => (5/2)
415  * r.coerce(2) # => [(2/1), (5/2)]
416  * r.coerce(2.0) # => [2.0, 2.5]
417  * r.coerce(Rational(2, 3)) # => [(2/3), (5/2)]
418  * r.coerce(Complex(3, 4)) # => [(3+4i), ((5/2)+0i)]
419  *
420  * c = Complex(2, 3) # => (2+3i)
421  * c.coerce(2) # => [(2+0i), (2+3i)]
422  * c.coerce(2.0) # => [(2.0+0i), (2+3i)]
423  * c.coerce(Rational(1, 2)) # => [((1/2)+0i), (2+3i)]
424  * c.coerce(Complex(3, 4)) # => [(3+4i), (2+3i)]
425  *
426  * Raises an exception if any type conversion fails.
427  *
428  */
429 
430 static VALUE
431 num_coerce(VALUE x, VALUE y)
432 {
433  if (CLASS_OF(x) == CLASS_OF(y))
434  return rb_assoc_new(y, x);
435  x = rb_Float(x);
436  y = rb_Float(y);
437  return rb_assoc_new(y, x);
438 }
439 
440 NORETURN(static void coerce_failed(VALUE x, VALUE y));
441 static void
442 coerce_failed(VALUE x, VALUE y)
443 {
444  if (SPECIAL_CONST_P(y) || SYMBOL_P(y) || RB_FLOAT_TYPE_P(y)) {
445  y = rb_inspect(y);
446  }
447  else {
448  y = rb_obj_class(y);
449  }
450  rb_raise(rb_eTypeError, "%"PRIsVALUE" can't be coerced into %"PRIsVALUE,
451  y, rb_obj_class(x));
452 }
453 
454 static int
455 do_coerce(VALUE *x, VALUE *y, int err)
456 {
457  VALUE ary = rb_check_funcall(*y, id_coerce, 1, x);
458  if (UNDEF_P(ary)) {
459  if (err) {
460  coerce_failed(*x, *y);
461  }
462  return FALSE;
463  }
464  if (!err && NIL_P(ary)) {
465  return FALSE;
466  }
467  if (!RB_TYPE_P(ary, T_ARRAY) || RARRAY_LEN(ary) != 2) {
468  rb_raise(rb_eTypeError, "coerce must return [x, y]");
469  }
470 
471  *x = RARRAY_AREF(ary, 0);
472  *y = RARRAY_AREF(ary, 1);
473  return TRUE;
474 }
475 
476 VALUE
478 {
479  do_coerce(&x, &y, TRUE);
480  return rb_funcall(x, func, 1, y);
481 }
482 
483 VALUE
485 {
486  if (do_coerce(&x, &y, FALSE))
487  return rb_funcall(x, func, 1, y);
488  return Qnil;
489 }
490 
491 static VALUE
492 ensure_cmp(VALUE c, VALUE x, VALUE y)
493 {
494  if (NIL_P(c)) rb_cmperr(x, y);
495  return c;
496 }
497 
498 VALUE
500 {
501  VALUE x0 = x, y0 = y;
502 
503  if (!do_coerce(&x, &y, FALSE)) {
504  rb_cmperr(x0, y0);
506  }
507  return ensure_cmp(rb_funcall(x, func, 1, y), x0, y0);
508 }
509 
510 NORETURN(static VALUE num_sadded(VALUE x, VALUE name));
511 
512 /*
513  * :nodoc:
514  *
515  * Trap attempts to add methods to Numeric objects. Always raises a TypeError.
516  *
517  * Numerics should be values; singleton_methods should not be added to them.
518  */
519 
520 static VALUE
521 num_sadded(VALUE x, VALUE name)
522 {
523  ID mid = rb_to_id(name);
524  /* ruby_frame = ruby_frame->prev; */ /* pop frame for "singleton_method_added" */
527  "can't define singleton method \"%"PRIsVALUE"\" for %"PRIsVALUE,
528  rb_id2str(mid),
529  rb_obj_class(x));
530 
532 }
533 
534 #if 0
535 /*
536  * call-seq:
537  * clone(freeze: true) -> self
538  *
539  * Returns +self+.
540  *
541  * Raises an exception if the value for +freeze+ is neither +true+ nor +nil+.
542  *
543  * Related: Numeric#dup.
544  *
545  */
546 static VALUE
547 num_clone(int argc, VALUE *argv, VALUE x)
548 {
549  return rb_immutable_obj_clone(argc, argv, x);
550 }
551 #else
552 # define num_clone rb_immutable_obj_clone
553 #endif
554 
555 /*
556  * call-seq:
557  * i -> complex
558  *
559  * Returns <tt>Complex(0, self)</tt>:
560  *
561  * 2.i # => (0+2i)
562  * -2.i # => (0-2i)
563  * 2.0.i # => (0+2.0i)
564  * Rational(1, 2).i # => (0+(1/2)*i)
565  * Complex(3, 4).i # Raises NoMethodError.
566  *
567  */
568 
569 static VALUE
570 num_imaginary(VALUE num)
571 {
572  return rb_complex_new(INT2FIX(0), num);
573 }
574 
575 /*
576  * call-seq:
577  * -self -> numeric
578  *
579  * Unary Minus---Returns the receiver, negated.
580  */
581 
582 static VALUE
583 num_uminus(VALUE num)
584 {
585  VALUE zero;
586 
587  zero = INT2FIX(0);
588  do_coerce(&zero, &num, TRUE);
589 
590  return num_funcall1(zero, '-', num);
591 }
592 
593 /*
594  * call-seq:
595  * fdiv(other) -> float
596  *
597  * Returns the quotient <tt>self/other</tt> as a float,
598  * using method +/+ in the derived class of +self+.
599  * (\Numeric itself does not define method +/+.)
600  *
601  * Of the Core and Standard Library classes,
602  * only BigDecimal uses this implementation.
603  *
604  */
605 
606 static VALUE
607 num_fdiv(VALUE x, VALUE y)
608 {
609  return rb_funcall(rb_Float(x), '/', 1, y);
610 }
611 
612 /*
613  * call-seq:
614  * div(other) -> integer
615  *
616  * Returns the quotient <tt>self/other</tt> as an integer (via +floor+),
617  * using method +/+ in the derived class of +self+.
618  * (\Numeric itself does not define method +/+.)
619  *
620  * Of the Core and Standard Library classes,
621  * Only Float and Rational use this implementation.
622  *
623  */
624 
625 static VALUE
626 num_div(VALUE x, VALUE y)
627 {
628  if (rb_equal(INT2FIX(0), y)) rb_num_zerodiv();
629  return rb_funcall(num_funcall1(x, '/', y), rb_intern("floor"), 0);
630 }
631 
632 /*
633  * call-seq:
634  * self % other -> real_numeric
635  *
636  * Returns +self+ modulo +other+ as a real number.
637  *
638  * Of the Core and Standard Library classes,
639  * only Rational uses this implementation.
640  *
641  * For Rational +r+ and real number +n+, these expressions are equivalent:
642  *
643  * r % n
644  * r-n*(r/n).floor
645  * r.divmod(n)[1]
646  *
647  * See Numeric#divmod.
648  *
649  * Examples:
650  *
651  * r = Rational(1, 2) # => (1/2)
652  * r2 = Rational(2, 3) # => (2/3)
653  * r % r2 # => (1/2)
654  * r % 2 # => (1/2)
655  * r % 2.0 # => 0.5
656  *
657  * r = Rational(301,100) # => (301/100)
658  * r2 = Rational(7,5) # => (7/5)
659  * r % r2 # => (21/100)
660  * r % -r2 # => (-119/100)
661  * (-r) % r2 # => (119/100)
662  * (-r) %-r2 # => (-21/100)
663  *
664  */
665 
666 static VALUE
667 num_modulo(VALUE x, VALUE y)
668 {
669  VALUE q = num_funcall1(x, id_div, y);
670  return rb_funcall(x, '-', 1,
671  rb_funcall(y, '*', 1, q));
672 }
673 
674 /*
675  * call-seq:
676  * remainder(other) -> real_number
677  *
678  * Returns the remainder after dividing +self+ by +other+.
679  *
680  * Of the Core and Standard Library classes,
681  * only Float and Rational use this implementation.
682  *
683  * Examples:
684  *
685  * 11.0.remainder(4) # => 3.0
686  * 11.0.remainder(-4) # => 3.0
687  * -11.0.remainder(4) # => -3.0
688  * -11.0.remainder(-4) # => -3.0
689  *
690  * 12.0.remainder(4) # => 0.0
691  * 12.0.remainder(-4) # => 0.0
692  * -12.0.remainder(4) # => -0.0
693  * -12.0.remainder(-4) # => -0.0
694  *
695  * 13.0.remainder(4.0) # => 1.0
696  * 13.0.remainder(Rational(4, 1)) # => 1.0
697  *
698  * Rational(13, 1).remainder(4) # => (1/1)
699  * Rational(13, 1).remainder(-4) # => (1/1)
700  * Rational(-13, 1).remainder(4) # => (-1/1)
701  * Rational(-13, 1).remainder(-4) # => (-1/1)
702  *
703  */
704 
705 static VALUE
706 num_remainder(VALUE x, VALUE y)
707 {
708  if (!rb_obj_is_kind_of(y, rb_cNumeric)) {
709  do_coerce(&x, &y, TRUE);
710  }
711  VALUE z = num_funcall1(x, '%', y);
712 
713  if ((!rb_equal(z, INT2FIX(0))) &&
714  ((rb_num_negative_int_p(x) &&
715  rb_num_positive_int_p(y)) ||
716  (rb_num_positive_int_p(x) &&
717  rb_num_negative_int_p(y)))) {
718  if (RB_FLOAT_TYPE_P(y)) {
719  if (isinf(RFLOAT_VALUE(y))) {
720  return x;
721  }
722  }
723  return rb_funcall(z, '-', 1, y);
724  }
725  return z;
726 }
727 
728 /*
729  * call-seq:
730  * divmod(other) -> array
731  *
732  * Returns a 2-element array <tt>[q, r]</tt>, where
733  *
734  * q = (self/other).floor # Quotient
735  * r = self % other # Remainder
736  *
737  * Of the Core and Standard Library classes,
738  * only Rational uses this implementation.
739  *
740  * Examples:
741  *
742  * Rational(11, 1).divmod(4) # => [2, (3/1)]
743  * Rational(11, 1).divmod(-4) # => [-3, (-1/1)]
744  * Rational(-11, 1).divmod(4) # => [-3, (1/1)]
745  * Rational(-11, 1).divmod(-4) # => [2, (-3/1)]
746  *
747  * Rational(12, 1).divmod(4) # => [3, (0/1)]
748  * Rational(12, 1).divmod(-4) # => [-3, (0/1)]
749  * Rational(-12, 1).divmod(4) # => [-3, (0/1)]
750  * Rational(-12, 1).divmod(-4) # => [3, (0/1)]
751  *
752  * Rational(13, 1).divmod(4.0) # => [3, 1.0]
753  * Rational(13, 1).divmod(Rational(4, 11)) # => [35, (3/11)]
754  */
755 
756 static VALUE
757 num_divmod(VALUE x, VALUE y)
758 {
759  return rb_assoc_new(num_div(x, y), num_modulo(x, y));
760 }
761 
762 /*
763  * call-seq:
764  * abs -> numeric
765  *
766  * Returns the absolute value of +self+.
767  *
768  * 12.abs #=> 12
769  * (-34.56).abs #=> 34.56
770  * -34.56.abs #=> 34.56
771  *
772  */
773 
774 static VALUE
775 num_abs(VALUE num)
776 {
777  if (rb_num_negative_int_p(num)) {
778  return num_funcall0(num, idUMinus);
779  }
780  return num;
781 }
782 
783 /*
784  * call-seq:
785  * zero? -> true or false
786  *
787  * Returns +true+ if +zero+ has a zero value, +false+ otherwise.
788  *
789  * Of the Core and Standard Library classes,
790  * only Rational and Complex use this implementation.
791  *
792  */
793 
794 static VALUE
795 num_zero_p(VALUE num)
796 {
797  return rb_equal(num, INT2FIX(0));
798 }
799 
800 static bool
801 int_zero_p(VALUE num)
802 {
803  if (FIXNUM_P(num)) {
804  return FIXNUM_ZERO_P(num);
805  }
806  RUBY_ASSERT(RB_BIGNUM_TYPE_P(num));
807  return rb_bigzero_p(num);
808 }
809 
810 VALUE
811 rb_int_zero_p(VALUE num)
812 {
813  return RBOOL(int_zero_p(num));
814 }
815 
816 /*
817  * call-seq:
818  * nonzero? -> self or nil
819  *
820  * Returns +self+ if +self+ is not a zero value, +nil+ otherwise;
821  * uses method <tt>zero?</tt> for the evaluation.
822  *
823  * The returned +self+ allows the method to be chained:
824  *
825  * a = %w[z Bb bB bb BB a aA Aa AA A]
826  * a.sort {|a, b| (a.downcase <=> b.downcase).nonzero? || a <=> b }
827  * # => ["A", "a", "AA", "Aa", "aA", "BB", "Bb", "bB", "bb", "z"]
828  *
829  * Of the Core and Standard Library classes,
830  * Integer, Float, Rational, and Complex use this implementation.
831  *
832  * Related: #zero?
833  *
834  */
835 
836 static VALUE
837 num_nonzero_p(VALUE num)
838 {
839  if (RTEST(num_funcall0(num, rb_intern("zero?")))) {
840  return Qnil;
841  }
842  return num;
843 }
844 
845 /*
846  * call-seq:
847  * to_int -> integer
848  *
849  * Returns +self+ as an integer;
850  * converts using method +to_i+ in the derived class.
851  *
852  * Of the Core and Standard Library classes,
853  * only Rational and Complex use this implementation.
854  *
855  * Examples:
856  *
857  * Rational(1, 2).to_int # => 0
858  * Rational(2, 1).to_int # => 2
859  * Complex(2, 0).to_int # => 2
860  * Complex(2, 1) # Raises RangeError (non-zero imaginary part)
861  *
862  */
863 
864 static VALUE
865 num_to_int(VALUE num)
866 {
867  return num_funcall0(num, id_to_i);
868 }
869 
870 /*
871  * call-seq:
872  * positive? -> true or false
873  *
874  * Returns +true+ if +self+ is greater than 0, +false+ otherwise.
875  *
876  */
877 
878 static VALUE
879 num_positive_p(VALUE num)
880 {
881  const ID mid = '>';
882 
883  if (FIXNUM_P(num)) {
884  if (method_basic_p(rb_cInteger))
885  return RBOOL((SIGNED_VALUE)num > (SIGNED_VALUE)INT2FIX(0));
886  }
887  else if (RB_BIGNUM_TYPE_P(num)) {
888  if (method_basic_p(rb_cInteger))
889  return RBOOL(BIGNUM_POSITIVE_P(num) && !rb_bigzero_p(num));
890  }
891  return rb_num_compare_with_zero(num, mid);
892 }
893 
894 /*
895  * call-seq:
896  * negative? -> true or false
897  *
898  * Returns +true+ if +self+ is less than 0, +false+ otherwise.
899  *
900  */
901 
902 static VALUE
903 num_negative_p(VALUE num)
904 {
905  return RBOOL(rb_num_negative_int_p(num));
906 }
907 
908 
909 /********************************************************************
910  *
911  * Document-class: Float
912  *
913  * A \Float object represents a sometimes-inexact real number using the native
914  * architecture's double-precision floating point representation.
915  *
916  * Floating point has a different arithmetic and is an inexact number.
917  * So you should know its esoteric system. See following:
918  *
919  * - https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html
920  * - https://github.com/rdp/ruby_tutorials_core/wiki/Ruby-Talk-FAQ#-why-are-rubys-floats-imprecise
921  * - https://en.wikipedia.org/wiki/Floating_point#Accuracy_problems
922  *
923  * You can create a \Float object explicitly with:
924  *
925  * - A {floating-point literal}[rdoc-ref:syntax/literals.rdoc@Float+Literals].
926  *
927  * You can convert certain objects to Floats with:
928  *
929  * - \Method #Float.
930  *
931  * == What's Here
932  *
933  * First, what's elsewhere. \Class \Float:
934  *
935  * - Inherits from
936  * {class Numeric}[rdoc-ref:Numeric@What-27s+Here]
937  * and {class Object}[rdoc-ref:Object@What-27s+Here].
938  * - Includes {module Comparable}[rdoc-ref:Comparable@What-27s+Here].
939  *
940  * Here, class \Float provides methods for:
941  *
942  * - {Querying}[rdoc-ref:Float@Querying]
943  * - {Comparing}[rdoc-ref:Float@Comparing]
944  * - {Converting}[rdoc-ref:Float@Converting]
945  *
946  * === Querying
947  *
948  * - #finite?: Returns whether +self+ is finite.
949  * - #hash: Returns the integer hash code for +self+.
950  * - #infinite?: Returns whether +self+ is infinite.
951  * - #nan?: Returns whether +self+ is a NaN (not-a-number).
952  *
953  * === Comparing
954  *
955  * - #<: Returns whether +self+ is less than the given value.
956  * - #<=: Returns whether +self+ is less than or equal to the given value.
957  * - #<=>: Returns a number indicating whether +self+ is less than, equal
958  * to, or greater than the given value.
959  * - #== (aliased as #=== and #eql?): Returns whether +self+ is equal to
960  * the given value.
961  * - #>: Returns whether +self+ is greater than the given value.
962  * - #>=: Returns whether +self+ is greater than or equal to the given value.
963  *
964  * === Converting
965  *
966  * - #% (aliased as #modulo): Returns +self+ modulo the given value.
967  * - #*: Returns the product of +self+ and the given value.
968  * - #**: Returns the value of +self+ raised to the power of the given value.
969  * - #+: Returns the sum of +self+ and the given value.
970  * - #-: Returns the difference of +self+ and the given value.
971  * - #/: Returns the quotient of +self+ and the given value.
972  * - #ceil: Returns the smallest number greater than or equal to +self+.
973  * - #coerce: Returns a 2-element array containing the given value converted to a \Float
974  * and +self+
975  * - #divmod: Returns a 2-element array containing the quotient and remainder
976  * results of dividing +self+ by the given value.
977  * - #fdiv: Returns the \Float result of dividing +self+ by the given value.
978  * - #floor: Returns the greatest number smaller than or equal to +self+.
979  * - #next_float: Returns the next-larger representable \Float.
980  * - #prev_float: Returns the next-smaller representable \Float.
981  * - #quo: Returns the quotient from dividing +self+ by the given value.
982  * - #round: Returns +self+ rounded to the nearest value, to a given precision.
983  * - #to_i (aliased as #to_int): Returns +self+ truncated to an Integer.
984  * - #to_s (aliased as #inspect): Returns a string containing the place-value
985  * representation of +self+ in the given radix.
986  * - #truncate: Returns +self+ truncated to a given precision.
987  *
988  */
989 
990 VALUE
992 {
993  NEWOBJ_OF(flt, struct RFloat, rb_cFloat, T_FLOAT | (RGENGC_WB_PROTECTED_FLOAT ? FL_WB_PROTECTED : 0), sizeof(struct RFloat), 0);
994 
995 #if SIZEOF_DOUBLE <= SIZEOF_VALUE
996  flt->float_value = d;
997 #else
998  union {
999  double d;
1000  rb_float_value_type v;
1001  } u = {d};
1002  flt->float_value = u.v;
1003 #endif
1004  OBJ_FREEZE((VALUE)flt);
1005  return (VALUE)flt;
1006 }
1007 
1008 /*
1009  * call-seq:
1010  * to_s -> string
1011  *
1012  * Returns a string containing a representation of +self+;
1013  * depending of the value of +self+, the string representation
1014  * may contain:
1015  *
1016  * - A fixed-point number.
1017  * 3.14.to_s # => "3.14"
1018  * - A number in "scientific notation" (containing an exponent).
1019  * (10.1**50).to_s # => "1.644631821843879e+50"
1020  * - 'Infinity'.
1021  * (10.1**500).to_s # => "Infinity"
1022  * - '-Infinity'.
1023  * (-10.1**500).to_s # => "-Infinity"
1024  * - 'NaN' (indicating not-a-number).
1025  * (0.0/0.0).to_s # => "NaN"
1026  *
1027  */
1028 
1029 static VALUE
1030 flo_to_s(VALUE flt)
1031 {
1032  enum {decimal_mant = DBL_MANT_DIG-DBL_DIG};
1033  enum {float_dig = DBL_DIG+1};
1034  char buf[float_dig + roomof(decimal_mant, CHAR_BIT) + 10];
1035  double value = RFLOAT_VALUE(flt);
1036  VALUE s;
1037  char *p, *e;
1038  int sign, decpt, digs;
1039 
1040  if (isinf(value)) {
1041  static const char minf[] = "-Infinity";
1042  const int pos = (value > 0); /* skip "-" */
1043  return rb_usascii_str_new(minf+pos, strlen(minf)-pos);
1044  }
1045  else if (isnan(value))
1046  return rb_usascii_str_new2("NaN");
1047 
1048  p = ruby_dtoa(value, 0, 0, &decpt, &sign, &e);
1049  s = sign ? rb_usascii_str_new_cstr("-") : rb_usascii_str_new(0, 0);
1050  if ((digs = (int)(e - p)) >= (int)sizeof(buf)) digs = (int)sizeof(buf) - 1;
1051  memcpy(buf, p, digs);
1052  free(p);
1053  if (decpt > 0) {
1054  if (decpt < digs) {
1055  memmove(buf + decpt + 1, buf + decpt, digs - decpt);
1056  buf[decpt] = '.';
1057  rb_str_cat(s, buf, digs + 1);
1058  }
1059  else if (decpt <= DBL_DIG) {
1060  long len;
1061  char *ptr;
1062  rb_str_cat(s, buf, digs);
1063  rb_str_resize(s, (len = RSTRING_LEN(s)) + decpt - digs + 2);
1064  ptr = RSTRING_PTR(s) + len;
1065  if (decpt > digs) {
1066  memset(ptr, '0', decpt - digs);
1067  ptr += decpt - digs;
1068  }
1069  memcpy(ptr, ".0", 2);
1070  }
1071  else {
1072  goto exp;
1073  }
1074  }
1075  else if (decpt > -4) {
1076  long len;
1077  char *ptr;
1078  rb_str_cat(s, "0.", 2);
1079  rb_str_resize(s, (len = RSTRING_LEN(s)) - decpt + digs);
1080  ptr = RSTRING_PTR(s);
1081  memset(ptr += len, '0', -decpt);
1082  memcpy(ptr -= decpt, buf, digs);
1083  }
1084  else {
1085  goto exp;
1086  }
1087  return s;
1088 
1089  exp:
1090  if (digs > 1) {
1091  memmove(buf + 2, buf + 1, digs - 1);
1092  }
1093  else {
1094  buf[2] = '0';
1095  digs++;
1096  }
1097  buf[1] = '.';
1098  rb_str_cat(s, buf, digs + 1);
1099  rb_str_catf(s, "e%+03d", decpt - 1);
1100  return s;
1101 }
1102 
1103 /*
1104  * call-seq:
1105  * coerce(other) -> array
1106  *
1107  * Returns a 2-element array containing +other+ converted to a \Float
1108  * and +self+:
1109  *
1110  * f = 3.14 # => 3.14
1111  * f.coerce(2) # => [2.0, 3.14]
1112  * f.coerce(2.0) # => [2.0, 3.14]
1113  * f.coerce(Rational(1, 2)) # => [0.5, 3.14]
1114  * f.coerce(Complex(1, 0)) # => [1.0, 3.14]
1115  *
1116  * Raises an exception if a type conversion fails.
1117  *
1118  */
1119 
1120 static VALUE
1121 flo_coerce(VALUE x, VALUE y)
1122 {
1123  return rb_assoc_new(rb_Float(y), x);
1124 }
1125 
1126 VALUE
1127 rb_float_uminus(VALUE flt)
1128 {
1129  return DBL2NUM(-RFLOAT_VALUE(flt));
1130 }
1131 
1132 /*
1133  * call-seq:
1134  * self + other -> numeric
1135  *
1136  * Returns a new \Float which is the sum of +self+ and +other+:
1137  *
1138  * f = 3.14
1139  * f + 1 # => 4.140000000000001
1140  * f + 1.0 # => 4.140000000000001
1141  * f + Rational(1, 1) # => 4.140000000000001
1142  * f + Complex(1, 0) # => (4.140000000000001+0i)
1143  *
1144  */
1145 
1146 VALUE
1147 rb_float_plus(VALUE x, VALUE y)
1148 {
1149  if (FIXNUM_P(y)) {
1150  return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y));
1151  }
1152  else if (RB_BIGNUM_TYPE_P(y)) {
1153  return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y));
1154  }
1155  else if (RB_FLOAT_TYPE_P(y)) {
1156  return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y));
1157  }
1158  else {
1159  return rb_num_coerce_bin(x, y, '+');
1160  }
1161 }
1162 
1163 /*
1164  * call-seq:
1165  * self - other -> numeric
1166  *
1167  * Returns a new \Float which is the difference of +self+ and +other+:
1168  *
1169  * f = 3.14
1170  * f - 1 # => 2.14
1171  * f - 1.0 # => 2.14
1172  * f - Rational(1, 1) # => 2.14
1173  * f - Complex(1, 0) # => (2.14+0i)
1174  *
1175  */
1176 
1177 VALUE
1178 rb_float_minus(VALUE x, VALUE y)
1179 {
1180  if (FIXNUM_P(y)) {
1181  return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y));
1182  }
1183  else if (RB_BIGNUM_TYPE_P(y)) {
1184  return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y));
1185  }
1186  else if (RB_FLOAT_TYPE_P(y)) {
1187  return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y));
1188  }
1189  else {
1190  return rb_num_coerce_bin(x, y, '-');
1191  }
1192 }
1193 
1194 /*
1195  * call-seq:
1196  * self * other -> numeric
1197  *
1198  * Returns a new \Float which is the product of +self+ and +other+:
1199  *
1200  * f = 3.14
1201  * f * 2 # => 6.28
1202  * f * 2.0 # => 6.28
1203  * f * Rational(1, 2) # => 1.57
1204  * f * Complex(2, 0) # => (6.28+0.0i)
1205  */
1206 
1207 VALUE
1208 rb_float_mul(VALUE x, VALUE y)
1209 {
1210  if (FIXNUM_P(y)) {
1211  return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y));
1212  }
1213  else if (RB_BIGNUM_TYPE_P(y)) {
1214  return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y));
1215  }
1216  else if (RB_FLOAT_TYPE_P(y)) {
1217  return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y));
1218  }
1219  else {
1220  return rb_num_coerce_bin(x, y, '*');
1221  }
1222 }
1223 
1224 static double
1225 double_div_double(double x, double y)
1226 {
1227  if (LIKELY(y != 0.0)) {
1228  return x / y;
1229  }
1230  else if (x == 0.0) {
1231  return nan("");
1232  }
1233  else {
1234  double z = signbit(y) ? -1.0 : 1.0;
1235  return x * z * HUGE_VAL;
1236  }
1237 }
1238 
1239 VALUE
1240 rb_flo_div_flo(VALUE x, VALUE y)
1241 {
1242  double num = RFLOAT_VALUE(x);
1243  double den = RFLOAT_VALUE(y);
1244  double ret = double_div_double(num, den);
1245  return DBL2NUM(ret);
1246 }
1247 
1248 /*
1249  * call-seq:
1250  * self / other -> numeric
1251  *
1252  * Returns a new \Float which is the result of dividing +self+ by +other+:
1253  *
1254  * f = 3.14
1255  * f / 2 # => 1.57
1256  * f / 2.0 # => 1.57
1257  * f / Rational(2, 1) # => 1.57
1258  * f / Complex(2, 0) # => (1.57+0.0i)
1259  *
1260  */
1261 
1262 VALUE
1263 rb_float_div(VALUE x, VALUE y)
1264 {
1265  double num = RFLOAT_VALUE(x);
1266  double den;
1267  double ret;
1268 
1269  if (FIXNUM_P(y)) {
1270  den = FIX2LONG(y);
1271  }
1272  else if (RB_BIGNUM_TYPE_P(y)) {
1273  den = rb_big2dbl(y);
1274  }
1275  else if (RB_FLOAT_TYPE_P(y)) {
1276  den = RFLOAT_VALUE(y);
1277  }
1278  else {
1279  return rb_num_coerce_bin(x, y, '/');
1280  }
1281 
1282  ret = double_div_double(num, den);
1283  return DBL2NUM(ret);
1284 }
1285 
1286 /*
1287  * call-seq:
1288  * quo(other) -> numeric
1289  *
1290  * Returns the quotient from dividing +self+ by +other+:
1291  *
1292  * f = 3.14
1293  * f.quo(2) # => 1.57
1294  * f.quo(-2) # => -1.57
1295  * f.quo(Rational(2, 1)) # => 1.57
1296  * f.quo(Complex(2, 0)) # => (1.57+0.0i)
1297  *
1298  */
1299 
1300 static VALUE
1301 flo_quo(VALUE x, VALUE y)
1302 {
1303  return num_funcall1(x, '/', y);
1304 }
1305 
1306 static void
1307 flodivmod(double x, double y, double *divp, double *modp)
1308 {
1309  double div, mod;
1310 
1311  if (isnan(y)) {
1312  /* y is NaN so all results are NaN */
1313  if (modp) *modp = y;
1314  if (divp) *divp = y;
1315  return;
1316  }
1317  if (y == 0.0) rb_num_zerodiv();
1318  if ((x == 0.0) || (isinf(y) && !isinf(x)))
1319  mod = x;
1320  else {
1321 #ifdef HAVE_FMOD
1322  mod = fmod(x, y);
1323 #else
1324  double z;
1325 
1326  modf(x/y, &z);
1327  mod = x - z * y;
1328 #endif
1329  }
1330  if (isinf(x) && !isinf(y))
1331  div = x;
1332  else {
1333  div = (x - mod) / y;
1334  if (modp && divp) div = round(div);
1335  }
1336  if (y*mod < 0) {
1337  mod += y;
1338  div -= 1.0;
1339  }
1340  if (modp) *modp = mod;
1341  if (divp) *divp = div;
1342 }
1343 
1344 /*
1345  * Returns the modulo of division of x by y.
1346  * An error will be raised if y == 0.
1347  */
1348 
1349 double
1350 ruby_float_mod(double x, double y)
1351 {
1352  double mod;
1353  flodivmod(x, y, 0, &mod);
1354  return mod;
1355 }
1356 
1357 /*
1358  * call-seq:
1359  * self % other -> float
1360  *
1361  * Returns +self+ modulo +other+ as a float.
1362  *
1363  * For float +f+ and real number +r+, these expressions are equivalent:
1364  *
1365  * f % r
1366  * f-r*(f/r).floor
1367  * f.divmod(r)[1]
1368  *
1369  * See Numeric#divmod.
1370  *
1371  * Examples:
1372  *
1373  * 10.0 % 2 # => 0.0
1374  * 10.0 % 3 # => 1.0
1375  * 10.0 % 4 # => 2.0
1376  *
1377  * 10.0 % -2 # => 0.0
1378  * 10.0 % -3 # => -2.0
1379  * 10.0 % -4 # => -2.0
1380  *
1381  * 10.0 % 4.0 # => 2.0
1382  * 10.0 % Rational(4, 1) # => 2.0
1383  *
1384  */
1385 
1386 static VALUE
1387 flo_mod(VALUE x, VALUE y)
1388 {
1389  double fy;
1390 
1391  if (FIXNUM_P(y)) {
1392  fy = (double)FIX2LONG(y);
1393  }
1394  else if (RB_BIGNUM_TYPE_P(y)) {
1395  fy = rb_big2dbl(y);
1396  }
1397  else if (RB_FLOAT_TYPE_P(y)) {
1398  fy = RFLOAT_VALUE(y);
1399  }
1400  else {
1401  return rb_num_coerce_bin(x, y, '%');
1402  }
1403  return DBL2NUM(ruby_float_mod(RFLOAT_VALUE(x), fy));
1404 }
1405 
1406 static VALUE
1407 dbl2ival(double d)
1408 {
1409  if (FIXABLE(d)) {
1410  return LONG2FIX((long)d);
1411  }
1412  return rb_dbl2big(d);
1413 }
1414 
1415 /*
1416  * call-seq:
1417  * divmod(other) -> array
1418  *
1419  * Returns a 2-element array <tt>[q, r]</tt>, where
1420  *
1421  * q = (self/other).floor # Quotient
1422  * r = self % other # Remainder
1423  *
1424  * Examples:
1425  *
1426  * 11.0.divmod(4) # => [2, 3.0]
1427  * 11.0.divmod(-4) # => [-3, -1.0]
1428  * -11.0.divmod(4) # => [-3, 1.0]
1429  * -11.0.divmod(-4) # => [2, -3.0]
1430  *
1431  * 12.0.divmod(4) # => [3, 0.0]
1432  * 12.0.divmod(-4) # => [-3, 0.0]
1433  * -12.0.divmod(4) # => [-3, -0.0]
1434  * -12.0.divmod(-4) # => [3, -0.0]
1435  *
1436  * 13.0.divmod(4.0) # => [3, 1.0]
1437  * 13.0.divmod(Rational(4, 1)) # => [3, 1.0]
1438  *
1439  */
1440 
1441 static VALUE
1442 flo_divmod(VALUE x, VALUE y)
1443 {
1444  double fy, div, mod;
1445  volatile VALUE a, b;
1446 
1447  if (FIXNUM_P(y)) {
1448  fy = (double)FIX2LONG(y);
1449  }
1450  else if (RB_BIGNUM_TYPE_P(y)) {
1451  fy = rb_big2dbl(y);
1452  }
1453  else if (RB_FLOAT_TYPE_P(y)) {
1454  fy = RFLOAT_VALUE(y);
1455  }
1456  else {
1457  return rb_num_coerce_bin(x, y, id_divmod);
1458  }
1459  flodivmod(RFLOAT_VALUE(x), fy, &div, &mod);
1460  a = dbl2ival(div);
1461  b = DBL2NUM(mod);
1462  return rb_assoc_new(a, b);
1463 }
1464 
1465 /*
1466  * call-seq:
1467  * self ** other -> numeric
1468  *
1469  * Raises +self+ to the power of +other+:
1470  *
1471  * f = 3.14
1472  * f ** 2 # => 9.8596
1473  * f ** -2 # => 0.1014239928597509
1474  * f ** 2.1 # => 11.054834900588839
1475  * f ** Rational(2, 1) # => 9.8596
1476  * f ** Complex(2, 0) # => (9.8596+0i)
1477  *
1478  */
1479 
1480 VALUE
1481 rb_float_pow(VALUE x, VALUE y)
1482 {
1483  double dx, dy;
1484  if (y == INT2FIX(2)) {
1485  dx = RFLOAT_VALUE(x);
1486  return DBL2NUM(dx * dx);
1487  }
1488  else if (FIXNUM_P(y)) {
1489  dx = RFLOAT_VALUE(x);
1490  dy = (double)FIX2LONG(y);
1491  }
1492  else if (RB_BIGNUM_TYPE_P(y)) {
1493  dx = RFLOAT_VALUE(x);
1494  dy = rb_big2dbl(y);
1495  }
1496  else if (RB_FLOAT_TYPE_P(y)) {
1497  dx = RFLOAT_VALUE(x);
1498  dy = RFLOAT_VALUE(y);
1499  if (dx < 0 && dy != round(dy))
1500  return rb_dbl_complex_new_polar_pi(pow(-dx, dy), dy);
1501  }
1502  else {
1503  return rb_num_coerce_bin(x, y, idPow);
1504  }
1505  return DBL2NUM(pow(dx, dy));
1506 }
1507 
1508 /*
1509  * call-seq:
1510  * eql?(other) -> true or false
1511  *
1512  * Returns +true+ if +self+ and +other+ are the same type and have equal values.
1513  *
1514  * Of the Core and Standard Library classes,
1515  * only Integer, Rational, and Complex use this implementation.
1516  *
1517  * Examples:
1518  *
1519  * 1.eql?(1) # => true
1520  * 1.eql?(1.0) # => false
1521  * 1.eql?(Rational(1, 1)) # => false
1522  * 1.eql?(Complex(1, 0)) # => false
1523  *
1524  * \Method +eql?+ is different from <tt>==</tt> in that +eql?+ requires matching types,
1525  * while <tt>==</tt> does not.
1526  *
1527  */
1528 
1529 static VALUE
1530 num_eql(VALUE x, VALUE y)
1531 {
1532  if (TYPE(x) != TYPE(y)) return Qfalse;
1533 
1534  if (RB_BIGNUM_TYPE_P(x)) {
1535  return rb_big_eql(x, y);
1536  }
1537 
1538  return rb_equal(x, y);
1539 }
1540 
1541 /*
1542  * call-seq:
1543  * self <=> other -> zero or nil
1544  *
1545  * Returns zero if +self+ is the same as +other+, +nil+ otherwise.
1546  *
1547  * No subclass in the Ruby Core or Standard Library uses this implementation.
1548  *
1549  */
1550 
1551 static VALUE
1552 num_cmp(VALUE x, VALUE y)
1553 {
1554  if (x == y) return INT2FIX(0);
1555  return Qnil;
1556 }
1557 
1558 static VALUE
1559 num_equal(VALUE x, VALUE y)
1560 {
1561  VALUE result;
1562  if (x == y) return Qtrue;
1563  result = num_funcall1(y, id_eq, x);
1564  return RBOOL(RTEST(result));
1565 }
1566 
1567 /*
1568  * call-seq:
1569  * self == other -> true or false
1570  *
1571  * Returns +true+ if +other+ has the same value as +self+, +false+ otherwise:
1572  *
1573  * 2.0 == 2 # => true
1574  * 2.0 == 2.0 # => true
1575  * 2.0 == Rational(2, 1) # => true
1576  * 2.0 == Complex(2, 0) # => true
1577  *
1578  * <tt>Float::NAN == Float::NAN</tt> returns an implementation-dependent value.
1579  *
1580  * Related: Float#eql? (requires +other+ to be a \Float).
1581  *
1582  */
1583 
1584 VALUE
1585 rb_float_equal(VALUE x, VALUE y)
1586 {
1587  volatile double a, b;
1588 
1589  if (RB_INTEGER_TYPE_P(y)) {
1590  return rb_integer_float_eq(y, x);
1591  }
1592  else if (RB_FLOAT_TYPE_P(y)) {
1593  b = RFLOAT_VALUE(y);
1594 #if MSC_VERSION_BEFORE(1300)
1595  if (isnan(b)) return Qfalse;
1596 #endif
1597  }
1598  else {
1599  return num_equal(x, y);
1600  }
1601  a = RFLOAT_VALUE(x);
1602 #if MSC_VERSION_BEFORE(1300)
1603  if (isnan(a)) return Qfalse;
1604 #endif
1605  return RBOOL(a == b);
1606 }
1607 
1608 #define flo_eq rb_float_equal
1609 static VALUE rb_dbl_hash(double d);
1610 
1611 /*
1612  * call-seq:
1613  * hash -> integer
1614  *
1615  * Returns the integer hash value for +self+.
1616  *
1617  * See also Object#hash.
1618  */
1619 
1620 static VALUE
1621 flo_hash(VALUE num)
1622 {
1623  return rb_dbl_hash(RFLOAT_VALUE(num));
1624 }
1625 
1626 static VALUE
1627 rb_dbl_hash(double d)
1628 {
1629  return ST2FIX(rb_dbl_long_hash(d));
1630 }
1631 
1632 VALUE
1633 rb_dbl_cmp(double a, double b)
1634 {
1635  if (isnan(a) || isnan(b)) return Qnil;
1636  if (a == b) return INT2FIX(0);
1637  if (a > b) return INT2FIX(1);
1638  if (a < b) return INT2FIX(-1);
1639  return Qnil;
1640 }
1641 
1642 /*
1643  * call-seq:
1644  * self <=> other -> -1, 0, +1, or nil
1645  *
1646  * Returns a value that depends on the numeric relation
1647  * between +self+ and +other+:
1648  *
1649  * - -1, if +self+ is less than +other+.
1650  * - 0, if +self+ is equal to +other+.
1651  * - 1, if +self+ is greater than +other+.
1652  * - +nil+, if the two values are incommensurate.
1653  *
1654  * Examples:
1655  *
1656  * 2.0 <=> 2 # => 0
1657  * 2.0 <=> 2.0 # => 0
1658  * 2.0 <=> Rational(2, 1) # => 0
1659  * 2.0 <=> Complex(2, 0) # => 0
1660  * 2.0 <=> 1.9 # => 1
1661  * 2.0 <=> 2.1 # => -1
1662  * 2.0 <=> 'foo' # => nil
1663  *
1664  * This is the basis for the tests in the Comparable module.
1665  *
1666  * <tt>Float::NAN <=> Float::NAN</tt> returns an implementation-dependent value.
1667  *
1668  */
1669 
1670 static VALUE
1671 flo_cmp(VALUE x, VALUE y)
1672 {
1673  double a, b;
1674  VALUE i;
1675 
1676  a = RFLOAT_VALUE(x);
1677  if (isnan(a)) return Qnil;
1678  if (RB_INTEGER_TYPE_P(y)) {
1679  VALUE rel = rb_integer_float_cmp(y, x);
1680  if (FIXNUM_P(rel))
1681  return LONG2FIX(-FIX2LONG(rel));
1682  return rel;
1683  }
1684  else if (RB_FLOAT_TYPE_P(y)) {
1685  b = RFLOAT_VALUE(y);
1686  }
1687  else {
1688  if (isinf(a) && !UNDEF_P(i = rb_check_funcall(y, rb_intern("infinite?"), 0, 0))) {
1689  if (RTEST(i)) {
1690  int j = rb_cmpint(i, x, y);
1691  j = (a > 0.0) ? (j > 0 ? 0 : +1) : (j < 0 ? 0 : -1);
1692  return INT2FIX(j);
1693  }
1694  if (a > 0.0) return INT2FIX(1);
1695  return INT2FIX(-1);
1696  }
1697  return rb_num_coerce_cmp(x, y, id_cmp);
1698  }
1699  return rb_dbl_cmp(a, b);
1700 }
1701 
1702 int
1703 rb_float_cmp(VALUE x, VALUE y)
1704 {
1705  return NUM2INT(ensure_cmp(flo_cmp(x, y), x, y));
1706 }
1707 
1708 /*
1709  * call-seq:
1710  * self > other -> true or false
1711  *
1712  * Returns +true+ if +self+ is numerically greater than +other+:
1713  *
1714  * 2.0 > 1 # => true
1715  * 2.0 > 1.0 # => true
1716  * 2.0 > Rational(1, 2) # => true
1717  * 2.0 > 2.0 # => false
1718  *
1719  * <tt>Float::NAN > Float::NAN</tt> returns an implementation-dependent value.
1720  *
1721  */
1722 
1723 VALUE
1724 rb_float_gt(VALUE x, VALUE y)
1725 {
1726  double a, b;
1727 
1728  a = RFLOAT_VALUE(x);
1729  if (RB_INTEGER_TYPE_P(y)) {
1730  VALUE rel = rb_integer_float_cmp(y, x);
1731  if (FIXNUM_P(rel))
1732  return RBOOL(-FIX2LONG(rel) > 0);
1733  return Qfalse;
1734  }
1735  else if (RB_FLOAT_TYPE_P(y)) {
1736  b = RFLOAT_VALUE(y);
1737 #if MSC_VERSION_BEFORE(1300)
1738  if (isnan(b)) return Qfalse;
1739 #endif
1740  }
1741  else {
1742  return rb_num_coerce_relop(x, y, '>');
1743  }
1744 #if MSC_VERSION_BEFORE(1300)
1745  if (isnan(a)) return Qfalse;
1746 #endif
1747  return RBOOL(a > b);
1748 }
1749 
1750 /*
1751  * call-seq:
1752  * self >= other -> true or false
1753  *
1754  * Returns +true+ if +self+ is numerically greater than or equal to +other+:
1755  *
1756  * 2.0 >= 1 # => true
1757  * 2.0 >= 1.0 # => true
1758  * 2.0 >= Rational(1, 2) # => true
1759  * 2.0 >= 2.0 # => true
1760  * 2.0 >= 2.1 # => false
1761  *
1762  * <tt>Float::NAN >= Float::NAN</tt> returns an implementation-dependent value.
1763  *
1764  */
1765 
1766 static VALUE
1767 flo_ge(VALUE x, VALUE y)
1768 {
1769  double a, b;
1770 
1771  a = RFLOAT_VALUE(x);
1772  if (RB_TYPE_P(y, T_FIXNUM) || RB_BIGNUM_TYPE_P(y)) {
1773  VALUE rel = rb_integer_float_cmp(y, x);
1774  if (FIXNUM_P(rel))
1775  return RBOOL(-FIX2LONG(rel) >= 0);
1776  return Qfalse;
1777  }
1778  else if (RB_FLOAT_TYPE_P(y)) {
1779  b = RFLOAT_VALUE(y);
1780 #if MSC_VERSION_BEFORE(1300)
1781  if (isnan(b)) return Qfalse;
1782 #endif
1783  }
1784  else {
1785  return rb_num_coerce_relop(x, y, idGE);
1786  }
1787 #if MSC_VERSION_BEFORE(1300)
1788  if (isnan(a)) return Qfalse;
1789 #endif
1790  return RBOOL(a >= b);
1791 }
1792 
1793 /*
1794  * call-seq:
1795  * self < other -> true or false
1796  *
1797  * Returns +true+ if +self+ is numerically less than +other+:
1798  *
1799  * 2.0 < 3 # => true
1800  * 2.0 < 3.0 # => true
1801  * 2.0 < Rational(3, 1) # => true
1802  * 2.0 < 2.0 # => false
1803  *
1804  * <tt>Float::NAN < Float::NAN</tt> returns an implementation-dependent value.
1805  *
1806  */
1807 
1808 static VALUE
1809 flo_lt(VALUE x, VALUE y)
1810 {
1811  double a, b;
1812 
1813  a = RFLOAT_VALUE(x);
1814  if (RB_INTEGER_TYPE_P(y)) {
1815  VALUE rel = rb_integer_float_cmp(y, x);
1816  if (FIXNUM_P(rel))
1817  return RBOOL(-FIX2LONG(rel) < 0);
1818  return Qfalse;
1819  }
1820  else if (RB_FLOAT_TYPE_P(y)) {
1821  b = RFLOAT_VALUE(y);
1822 #if MSC_VERSION_BEFORE(1300)
1823  if (isnan(b)) return Qfalse;
1824 #endif
1825  }
1826  else {
1827  return rb_num_coerce_relop(x, y, '<');
1828  }
1829 #if MSC_VERSION_BEFORE(1300)
1830  if (isnan(a)) return Qfalse;
1831 #endif
1832  return RBOOL(a < b);
1833 }
1834 
1835 /*
1836  * call-seq:
1837  * self <= other -> true or false
1838  *
1839  * Returns +true+ if +self+ is numerically less than or equal to +other+:
1840  *
1841  * 2.0 <= 3 # => true
1842  * 2.0 <= 3.0 # => true
1843  * 2.0 <= Rational(3, 1) # => true
1844  * 2.0 <= 2.0 # => true
1845  * 2.0 <= 1.0 # => false
1846  *
1847  * <tt>Float::NAN <= Float::NAN</tt> returns an implementation-dependent value.
1848  *
1849  */
1850 
1851 static VALUE
1852 flo_le(VALUE x, VALUE y)
1853 {
1854  double a, b;
1855 
1856  a = RFLOAT_VALUE(x);
1857  if (RB_INTEGER_TYPE_P(y)) {
1858  VALUE rel = rb_integer_float_cmp(y, x);
1859  if (FIXNUM_P(rel))
1860  return RBOOL(-FIX2LONG(rel) <= 0);
1861  return Qfalse;
1862  }
1863  else if (RB_FLOAT_TYPE_P(y)) {
1864  b = RFLOAT_VALUE(y);
1865 #if MSC_VERSION_BEFORE(1300)
1866  if (isnan(b)) return Qfalse;
1867 #endif
1868  }
1869  else {
1870  return rb_num_coerce_relop(x, y, idLE);
1871  }
1872 #if MSC_VERSION_BEFORE(1300)
1873  if (isnan(a)) return Qfalse;
1874 #endif
1875  return RBOOL(a <= b);
1876 }
1877 
1878 /*
1879  * call-seq:
1880  * eql?(other) -> true or false
1881  *
1882  * Returns +true+ if +other+ is a \Float with the same value as +self+,
1883  * +false+ otherwise:
1884  *
1885  * 2.0.eql?(2.0) # => true
1886  * 2.0.eql?(1.0) # => false
1887  * 2.0.eql?(1) # => false
1888  * 2.0.eql?(Rational(2, 1)) # => false
1889  * 2.0.eql?(Complex(2, 0)) # => false
1890  *
1891  * <tt>Float::NAN.eql?(Float::NAN)</tt> returns an implementation-dependent value.
1892  *
1893  * Related: Float#== (performs type conversions).
1894  */
1895 
1896 VALUE
1897 rb_float_eql(VALUE x, VALUE y)
1898 {
1899  if (RB_FLOAT_TYPE_P(y)) {
1900  double a = RFLOAT_VALUE(x);
1901  double b = RFLOAT_VALUE(y);
1902 #if MSC_VERSION_BEFORE(1300)
1903  if (isnan(a) || isnan(b)) return Qfalse;
1904 #endif
1905  return RBOOL(a == b);
1906  }
1907  return Qfalse;
1908 }
1909 
1910 #define flo_eql rb_float_eql
1911 
1912 VALUE
1913 rb_float_abs(VALUE flt)
1914 {
1915  double val = fabs(RFLOAT_VALUE(flt));
1916  return DBL2NUM(val);
1917 }
1918 
1919 /*
1920  * call-seq:
1921  * nan? -> true or false
1922  *
1923  * Returns +true+ if +self+ is a NaN, +false+ otherwise.
1924  *
1925  * f = -1.0 #=> -1.0
1926  * f.nan? #=> false
1927  * f = 0.0/0.0 #=> NaN
1928  * f.nan? #=> true
1929  */
1930 
1931 static VALUE
1932 flo_is_nan_p(VALUE num)
1933 {
1934  double value = RFLOAT_VALUE(num);
1935 
1936  return RBOOL(isnan(value));
1937 }
1938 
1939 /*
1940  * call-seq:
1941  * infinite? -> -1, 1, or nil
1942  *
1943  * Returns:
1944  *
1945  * - 1, if +self+ is <tt>Infinity</tt>.
1946  * - -1 if +self+ is <tt>-Infinity</tt>.
1947  * - +nil+, otherwise.
1948  *
1949  * Examples:
1950  *
1951  * f = 1.0/0.0 # => Infinity
1952  * f.infinite? # => 1
1953  * f = -1.0/0.0 # => -Infinity
1954  * f.infinite? # => -1
1955  * f = 1.0 # => 1.0
1956  * f.infinite? # => nil
1957  * f = 0.0/0.0 # => NaN
1958  * f.infinite? # => nil
1959  *
1960  */
1961 
1962 VALUE
1963 rb_flo_is_infinite_p(VALUE num)
1964 {
1965  double value = RFLOAT_VALUE(num);
1966 
1967  if (isinf(value)) {
1968  return INT2FIX( value < 0 ? -1 : 1 );
1969  }
1970 
1971  return Qnil;
1972 }
1973 
1974 /*
1975  * call-seq:
1976  * finite? -> true or false
1977  *
1978  * Returns +true+ if +self+ is not +Infinity+, +-Infinity+, or +NaN+,
1979  * +false+ otherwise:
1980  *
1981  * f = 2.0 # => 2.0
1982  * f.finite? # => true
1983  * f = 1.0/0.0 # => Infinity
1984  * f.finite? # => false
1985  * f = -1.0/0.0 # => -Infinity
1986  * f.finite? # => false
1987  * f = 0.0/0.0 # => NaN
1988  * f.finite? # => false
1989  *
1990  */
1991 
1992 VALUE
1993 rb_flo_is_finite_p(VALUE num)
1994 {
1995  double value = RFLOAT_VALUE(num);
1996 
1997  return RBOOL(isfinite(value));
1998 }
1999 
2000 static VALUE
2001 flo_nextafter(VALUE flo, double value)
2002 {
2003  double x, y;
2004  x = NUM2DBL(flo);
2005  y = nextafter(x, value);
2006  return DBL2NUM(y);
2007 }
2008 
2009 /*
2010  * call-seq:
2011  * next_float -> float
2012  *
2013  * Returns the next-larger representable \Float.
2014  *
2015  * These examples show the internally stored values (64-bit hexadecimal)
2016  * for each \Float +f+ and for the corresponding <tt>f.next_float</tt>:
2017  *
2018  * f = 0.0 # 0x0000000000000000
2019  * f.next_float # 0x0000000000000001
2020  *
2021  * f = 0.01 # 0x3f847ae147ae147b
2022  * f.next_float # 0x3f847ae147ae147c
2023  *
2024  * In the remaining examples here, the output is shown in the usual way
2025  * (result +to_s+):
2026  *
2027  * 0.01.next_float # => 0.010000000000000002
2028  * 1.0.next_float # => 1.0000000000000002
2029  * 100.0.next_float # => 100.00000000000001
2030  *
2031  * f = 0.01
2032  * (0..3).each_with_index {|i| printf "%2d %-20a %s\n", i, f, f.to_s; f = f.next_float }
2033  *
2034  * Output:
2035  *
2036  * 0 0x1.47ae147ae147bp-7 0.01
2037  * 1 0x1.47ae147ae147cp-7 0.010000000000000002
2038  * 2 0x1.47ae147ae147dp-7 0.010000000000000004
2039  * 3 0x1.47ae147ae147ep-7 0.010000000000000005
2040  *
2041  * f = 0.0; 100.times { f += 0.1 }
2042  * f # => 9.99999999999998 # should be 10.0 in the ideal world.
2043  * 10-f # => 1.9539925233402755e-14 # the floating point error.
2044  * 10.0.next_float-10 # => 1.7763568394002505e-15 # 1 ulp (unit in the last place).
2045  * (10-f)/(10.0.next_float-10) # => 11.0 # the error is 11 ulp.
2046  * (10-f)/(10*Float::EPSILON) # => 8.8 # approximation of the above.
2047  * "%a" % 10 # => "0x1.4p+3"
2048  * "%a" % f # => "0x1.3fffffffffff5p+3" # the last hex digit is 5. 16 - 5 = 11 ulp.
2049  *
2050  * Related: Float#prev_float
2051  *
2052  */
2053 static VALUE
2054 flo_next_float(VALUE vx)
2055 {
2056  return flo_nextafter(vx, HUGE_VAL);
2057 }
2058 
2059 /*
2060  * call-seq:
2061  * float.prev_float -> float
2062  *
2063  * Returns the next-smaller representable \Float.
2064  *
2065  * These examples show the internally stored values (64-bit hexadecimal)
2066  * for each \Float +f+ and for the corresponding <tt>f.pev_float</tt>:
2067  *
2068  * f = 5e-324 # 0x0000000000000001
2069  * f.prev_float # 0x0000000000000000
2070  *
2071  * f = 0.01 # 0x3f847ae147ae147b
2072  * f.prev_float # 0x3f847ae147ae147a
2073  *
2074  * In the remaining examples here, the output is shown in the usual way
2075  * (result +to_s+):
2076  *
2077  * 0.01.prev_float # => 0.009999999999999998
2078  * 1.0.prev_float # => 0.9999999999999999
2079  * 100.0.prev_float # => 99.99999999999999
2080  *
2081  * f = 0.01
2082  * (0..3).each_with_index {|i| printf "%2d %-20a %s\n", i, f, f.to_s; f = f.prev_float }
2083  *
2084  * Output:
2085  *
2086  * 0 0x1.47ae147ae147bp-7 0.01
2087  * 1 0x1.47ae147ae147ap-7 0.009999999999999998
2088  * 2 0x1.47ae147ae1479p-7 0.009999999999999997
2089  * 3 0x1.47ae147ae1478p-7 0.009999999999999995
2090  *
2091  * Related: Float#next_float.
2092  *
2093  */
2094 static VALUE
2095 flo_prev_float(VALUE vx)
2096 {
2097  return flo_nextafter(vx, -HUGE_VAL);
2098 }
2099 
2100 VALUE
2101 rb_float_floor(VALUE num, int ndigits)
2102 {
2103  double number;
2104  number = RFLOAT_VALUE(num);
2105  if (number == 0.0) {
2106  return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0);
2107  }
2108  if (ndigits > 0) {
2109  int binexp;
2110  double f, mul, res;
2111  frexp(number, &binexp);
2112  if (float_round_overflow(ndigits, binexp)) return num;
2113  if (number > 0.0 && float_round_underflow(ndigits, binexp))
2114  return DBL2NUM(0.0);
2115  f = pow(10, ndigits);
2116  mul = floor(number * f);
2117  res = (mul + 1) / f;
2118  if (res > number)
2119  res = mul / f;
2120  return DBL2NUM(res);
2121  }
2122  else {
2123  num = dbl2ival(floor(number));
2124  if (ndigits < 0) num = rb_int_floor(num, ndigits);
2125  return num;
2126  }
2127 }
2128 
2129 static int
2130 flo_ndigits(int argc, VALUE *argv)
2131 {
2132  if (rb_check_arity(argc, 0, 1)) {
2133  return NUM2INT(argv[0]);
2134  }
2135  return 0;
2136 }
2137 
2138 /*
2139  * :markup: markdown
2140  *
2141  * call-seq:
2142  * floor(ndigits = 0) -> float or integer
2143  *
2144  * Returns a float or integer that is a "floor" value for `self`,
2145  * as specified by `ndigits`,
2146  * which must be an
2147  * [integer-convertible object](rdoc-ref:implicit_conversion.rdoc@Integer-Convertible+Objects).
2148  *
2149  * When `self` is zero,
2150  * returns a zero value:
2151  * a float if `ndigits` is positive,
2152  * an integer otherwise:
2153  *
2154  * ```
2155  * f = 0.0 # => 0.0
2156  * f.floor(20) # => 0.0
2157  * f.floor(0) # => 0
2158  * f.floor(-20) # => 0
2159  * ```
2160  *
2161  * When `self` is non-zero and `ndigits` is positive, returns a float with `ndigits`
2162  * digits after the decimal point (as available):
2163  *
2164  * ```
2165  * f = 12345.6789
2166  * f.floor(1) # => 12345.6
2167  * f.floor(3) # => 12345.678
2168  * f.floor(30) # => 12345.6789
2169  * f = -12345.6789
2170  * f.floor(1) # => -12345.7
2171  * f.floor(3) # => -12345.679
2172  * f.floor(30) # => -12345.6789
2173  * ```
2174  *
2175  * When `self` is non-zero and `ndigits` is non-positive,
2176  * returns an integer value based on a computed granularity:
2177  *
2178  * - The granularity is `10 ** ndigits.abs`.
2179  * - The returned value is the largest multiple of the granularity
2180  * that is less than or equal to `self`.
2181  *
2182  * Examples with positive `self`:
2183  *
2184  * | ndigits | Granularity | 12345.6789.floor(ndigits) |
2185  * |--------:|------------:|--------------------------:|
2186  * | 0 | 1 | 12345 |
2187  * | -1 | 10 | 12340 |
2188  * | -2 | 100 | 12300 |
2189  * | -3 | 1000 | 12000 |
2190  * | -4 | 10000 | 10000 |
2191  * | -5 | 100000 | 0 |
2192  *
2193  * Examples with negative `self`:
2194  *
2195  * | ndigits | Granularity | -12345.6789.floor(ndigits) |
2196  * |--------:|------------:|---------------------------:|
2197  * | 0 | 1 | -12346 |
2198  * | -1 | 10 | -12350 |
2199  * | -2 | 100 | -12400 |
2200  * | -3 | 1000 | -13000 |
2201  * | -4 | 10000 | -20000 |
2202  * | -5 | 100000 | -100000 |
2203  * | -6 | 1000000 | -1000000 |
2204  *
2205  * Note that the limited precision of floating-point arithmetic
2206  * may lead to surprising results:
2207  *
2208  * ```
2209  * (0.3 / 0.1).floor # => 2 # Not 3, (because (0.3 / 0.1) # => 2.9999999999999996, not 3.0)
2210  * ```
2211  *
2212  * Related: Float#ceil.
2213  *
2214  */
2215 
2216 static VALUE
2217 flo_floor(int argc, VALUE *argv, VALUE num)
2218 {
2219  int ndigits = flo_ndigits(argc, argv);
2220  return rb_float_floor(num, ndigits);
2221 }
2222 
2223 /*
2224  * :markup: markdown
2225  *
2226  * call-seq:
2227  * ceil(ndigits = 0) -> float or integer
2228  *
2229  * Returns a numeric that is a "ceiling" value for `self`,
2230  * as specified by the given `ndigits`,
2231  * which must be an
2232  * [integer-convertible object](rdoc-ref:implicit_conversion.rdoc@Integer-Convertible+Objects).
2233  *
2234  * When `ndigits` is positive, returns a Float with `ndigits`
2235  * decimal digits after the decimal point
2236  * (as available, but no fewer than 1):
2237  *
2238  * ```
2239  * f = 12345.6789
2240  * f.ceil(1) # => 12345.7
2241  * f.ceil(3) # => 12345.679
2242  * f.ceil(30) # => 12345.6789
2243  * f = -12345.6789
2244  * f.ceil(1) # => -12345.6
2245  * f.ceil(3) # => -12345.678
2246  * f.ceil(30) # => -12345.6789
2247  * f = 0.0
2248  * f.ceil(1) # => 0.0
2249  * f.ceil(100) # => 0.0
2250  * ```
2251  *
2252  * When `ndigits` is non-positive,
2253  * returns an Integer based on a computed granularity:
2254  *
2255  * - The granularity is `10 ** ndigits.abs`.
2256  * - The returned value is the largest multiple of the granularity
2257  * that is less than or equal to `self`.
2258  *
2259  * Examples with positive `self`:
2260  *
2261  * | ndigits | Granularity | 12345.6789.ceil(ndigits) |
2262  * |--------:|------------:|-------------------------:|
2263  * | 0 | 1 | 12346 |
2264  * | -1 | 10 | 12350 |
2265  * | -2 | 100 | 12400 |
2266  * | -3 | 1000 | 13000 |
2267  * | -4 | 10000 | 20000 |
2268  * | -5 | 100000 | 100000 |
2269  *
2270  * Examples with negative `self`:
2271  *
2272  * | ndigits | Granularity | -12345.6789.ceil(ndigits) |
2273  * |--------:|------------:|--------------------------:|
2274  * | 0 | 1 | -12345 |
2275  * | -1 | 10 | -12340 |
2276  * | -2 | 100 | -12300 |
2277  * | -3 | 1000 | -12000 |
2278  * | -4 | 10000 | -10000 |
2279  * | -5 | 100000 | 0 |
2280  *
2281  * When `self` is zero and `ndigits` is non-positive,
2282  * returns Integer zero:
2283  *
2284  * ```
2285  * 0.0.ceil(0) # => 0
2286  * 0.0.ceil(-1) # => 0
2287  * 0.0.ceil(-2) # => 0
2288  * ```
2289  *
2290  * Note that the limited precision of floating-point arithmetic
2291  * may lead to surprising results:
2292  *
2293  * ```
2294  * (2.1 / 0.7).ceil #=> 4 # Not 3 (because 2.1 / 0.7 # => 3.0000000000000004, not 3.0)
2295  * ```
2296  *
2297  * Related: Float#floor.
2298  *
2299  */
2300 
2301 static VALUE
2302 flo_ceil(int argc, VALUE *argv, VALUE num)
2303 {
2304  int ndigits = flo_ndigits(argc, argv);
2305  return rb_float_ceil(num, ndigits);
2306 }
2307 
2308 VALUE
2309 rb_float_ceil(VALUE num, int ndigits)
2310 {
2311  double number, f;
2312 
2313  number = RFLOAT_VALUE(num);
2314  if (number == 0.0) {
2315  return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0);
2316  }
2317  if (ndigits > 0) {
2318  int binexp;
2319  frexp(number, &binexp);
2320  if (float_round_overflow(ndigits, binexp)) return num;
2321  if (number < 0.0 && float_round_underflow(ndigits, binexp))
2322  return DBL2NUM(0.0);
2323  f = pow(10, ndigits);
2324  f = ceil(number * f) / f;
2325  return DBL2NUM(f);
2326  }
2327  else {
2328  num = dbl2ival(ceil(number));
2329  if (ndigits < 0) num = rb_int_ceil(num, ndigits);
2330  return num;
2331  }
2332 }
2333 
2334 static int
2335 int_round_zero_p(VALUE num, int ndigits)
2336 {
2337  long bytes;
2338  /* If 10**N / 2 > num, then return 0 */
2339  /* We have log_256(10) > 0.415241 and log_256(1/2) = -0.125, so */
2340  if (FIXNUM_P(num)) {
2341  bytes = sizeof(long);
2342  }
2343  else if (RB_BIGNUM_TYPE_P(num)) {
2344  bytes = rb_big_size(num);
2345  }
2346  else {
2347  bytes = NUM2LONG(rb_funcall(num, idSize, 0));
2348  }
2349  return (-0.415241 * ndigits - 0.125 > bytes);
2350 }
2351 
2352 static SIGNED_VALUE
2353 int_round_half_even(SIGNED_VALUE x, SIGNED_VALUE y)
2354 {
2355  SIGNED_VALUE z = +(x + y / 2) / y;
2356  if ((z * y - x) * 2 == y) {
2357  z &= ~1;
2358  }
2359  return z * y;
2360 }
2361 
2362 static SIGNED_VALUE
2363 int_round_half_up(SIGNED_VALUE x, SIGNED_VALUE y)
2364 {
2365  return (x + y / 2) / y * y;
2366 }
2367 
2368 static SIGNED_VALUE
2369 int_round_half_down(SIGNED_VALUE x, SIGNED_VALUE y)
2370 {
2371  return (x + y / 2 - 1) / y * y;
2372 }
2373 
2374 static int
2375 int_half_p_half_even(VALUE num, VALUE n, VALUE f)
2376 {
2377  return (int)rb_int_odd_p(rb_int_idiv(n, f));
2378 }
2379 
2380 static int
2381 int_half_p_half_up(VALUE num, VALUE n, VALUE f)
2382 {
2383  return int_pos_p(num);
2384 }
2385 
2386 static int
2387 int_half_p_half_down(VALUE num, VALUE n, VALUE f)
2388 {
2389  return int_neg_p(num);
2390 }
2391 
2392 /*
2393  * Assumes num is an \Integer, ndigits <= 0
2394  */
2395 static VALUE
2396 rb_int_round(VALUE num, int ndigits, enum ruby_num_rounding_mode mode)
2397 {
2398  VALUE n, f, h, r;
2399 
2400  if (int_round_zero_p(num, ndigits)) {
2401  return INT2FIX(0);
2402  }
2403 
2404  f = int_pow(10, -ndigits);
2405  if (FIXNUM_P(num) && FIXNUM_P(f)) {
2406  SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f);
2407  int neg = x < 0;
2408  if (neg) x = -x;
2409  x = ROUND_CALL(mode, int_round, (x, y));
2410  if (neg) x = -x;
2411  return LONG2NUM(x);
2412  }
2413  if (RB_FLOAT_TYPE_P(f)) {
2414  /* then int_pow overflow */
2415  return INT2FIX(0);
2416  }
2417  h = rb_int_idiv(f, INT2FIX(2));
2418  r = rb_int_modulo(num, f);
2419  n = rb_int_minus(num, r);
2420  r = rb_int_cmp(r, h);
2421  if (FIXNUM_POSITIVE_P(r) ||
2422  (FIXNUM_ZERO_P(r) && ROUND_CALL(mode, int_half_p, (num, n, f)))) {
2423  n = rb_int_plus(n, f);
2424  }
2425  return n;
2426 }
2427 
2428 static VALUE
2429 rb_int_floor(VALUE num, int ndigits)
2430 {
2431  VALUE f = int_pow(10, -ndigits);
2432  if (FIXNUM_P(num) && FIXNUM_P(f)) {
2433  SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f);
2434  int neg = x < 0;
2435  if (neg) x = -x + y - 1;
2436  x = x / y * y;
2437  if (neg) x = -x;
2438  return LONG2NUM(x);
2439  }
2440  else {
2441  bool neg = int_neg_p(num);
2442  if (neg) num = rb_int_minus(rb_int_plus(rb_int_uminus(num), f), INT2FIX(1));
2443  num = rb_int_mul(rb_int_div(num, f), f);
2444  if (neg) num = rb_int_uminus(num);
2445  return num;
2446  }
2447 }
2448 
2449 static VALUE
2450 rb_int_ceil(VALUE num, int ndigits)
2451 {
2452  VALUE f = int_pow(10, -ndigits);
2453  if (FIXNUM_P(num) && FIXNUM_P(f)) {
2454  SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f);
2455  int neg = x < 0;
2456  if (neg) x = -x;
2457  else x += y - 1;
2458  x = (x / y) * y;
2459  if (neg) x = -x;
2460  return LONG2NUM(x);
2461  }
2462  else {
2463  bool neg = int_neg_p(num);
2464  if (neg)
2465  num = rb_int_uminus(num);
2466  else
2467  num = rb_int_plus(num, rb_int_minus(f, INT2FIX(1)));
2468  num = rb_int_mul(rb_int_div(num, f), f);
2469  if (neg) num = rb_int_uminus(num);
2470  return num;
2471  }
2472 }
2473 
2474 VALUE
2475 rb_int_truncate(VALUE num, int ndigits)
2476 {
2477  VALUE f;
2478  VALUE m;
2479 
2480  if (int_round_zero_p(num, ndigits))
2481  return INT2FIX(0);
2482  f = int_pow(10, -ndigits);
2483  if (FIXNUM_P(num) && FIXNUM_P(f)) {
2484  SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f);
2485  int neg = x < 0;
2486  if (neg) x = -x;
2487  x = x / y * y;
2488  if (neg) x = -x;
2489  return LONG2NUM(x);
2490  }
2491  if (RB_FLOAT_TYPE_P(f)) {
2492  /* then int_pow overflow */
2493  return INT2FIX(0);
2494  }
2495  m = rb_int_modulo(num, f);
2496  if (int_neg_p(num)) {
2497  return rb_int_plus(num, rb_int_minus(f, m));
2498  }
2499  else {
2500  return rb_int_minus(num, m);
2501  }
2502 }
2503 
2504 /*
2505  * call-seq:
2506  * round(ndigits = 0, half: :up) -> integer or float
2507  *
2508  * Returns +self+ rounded to the nearest value with
2509  * a precision of +ndigits+ decimal digits.
2510  *
2511  * When +ndigits+ is non-negative, returns a float with +ndigits+
2512  * after the decimal point (as available):
2513  *
2514  * f = 12345.6789
2515  * f.round(1) # => 12345.7
2516  * f.round(3) # => 12345.679
2517  * f = -12345.6789
2518  * f.round(1) # => -12345.7
2519  * f.round(3) # => -12345.679
2520  *
2521  * When +ndigits+ is negative, returns an integer
2522  * with at least <tt>ndigits.abs</tt> trailing zeros:
2523  *
2524  * f = 12345.6789
2525  * f.round(0) # => 12346
2526  * f.round(-3) # => 12000
2527  * f = -12345.6789
2528  * f.round(0) # => -12346
2529  * f.round(-3) # => -12000
2530  *
2531  * If keyword argument +half+ is given,
2532  * and +self+ is equidistant from the two candidate values,
2533  * the rounding is according to the given +half+ value:
2534  *
2535  * - +:up+ or +nil+: round away from zero:
2536  *
2537  * 2.5.round(half: :up) # => 3
2538  * 3.5.round(half: :up) # => 4
2539  * (-2.5).round(half: :up) # => -3
2540  *
2541  * - +:down+: round toward zero:
2542  *
2543  * 2.5.round(half: :down) # => 2
2544  * 3.5.round(half: :down) # => 3
2545  * (-2.5).round(half: :down) # => -2
2546  *
2547  * - +:even+: round toward the candidate whose last nonzero digit is even:
2548  *
2549  * 2.5.round(half: :even) # => 2
2550  * 3.5.round(half: :even) # => 4
2551  * (-2.5).round(half: :even) # => -2
2552  *
2553  * Raises and exception if the value for +half+ is invalid.
2554  *
2555  * Related: Float#truncate.
2556  *
2557  */
2558 
2559 static VALUE
2560 flo_round(int argc, VALUE *argv, VALUE num)
2561 {
2562  double number, f, x;
2563  VALUE nd, opt;
2564  int ndigits = 0;
2565  enum ruby_num_rounding_mode mode;
2566 
2567  if (rb_scan_args(argc, argv, "01:", &nd, &opt)) {
2568  ndigits = NUM2INT(nd);
2569  }
2570  mode = rb_num_get_rounding_option(opt);
2571  number = RFLOAT_VALUE(num);
2572  if (number == 0.0) {
2573  return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0);
2574  }
2575  if (ndigits < 0) {
2576  return rb_int_round(flo_to_i(num), ndigits, mode);
2577  }
2578  if (ndigits == 0) {
2579  x = ROUND_CALL(mode, round, (number, 1.0));
2580  return dbl2ival(x);
2581  }
2582  if (isfinite(number)) {
2583  int binexp;
2584  frexp(number, &binexp);
2585  if (float_round_overflow(ndigits, binexp)) return num;
2586  if (float_round_underflow(ndigits, binexp)) return DBL2NUM(0);
2587  if (ndigits > 14) {
2588  /* In this case, pow(10, ndigits) may not be accurate. */
2589  return rb_flo_round_by_rational(argc, argv, num);
2590  }
2591  f = pow(10, ndigits);
2592  x = ROUND_CALL(mode, round, (number, f));
2593  return DBL2NUM(x / f);
2594  }
2595  return num;
2596 }
2597 
2598 static int
2599 float_round_overflow(int ndigits, int binexp)
2600 {
2601  enum {float_dig = DBL_DIG+2};
2602 
2603 /* Let `exp` be such that `number` is written as:"0.#{digits}e#{exp}",
2604  i.e. such that 10 ** (exp - 1) <= |number| < 10 ** exp
2605  Recall that up to float_dig digits can be needed to represent a double,
2606  so if ndigits + exp >= float_dig, the intermediate value (number * 10 ** ndigits)
2607  will be an integer and thus the result is the original number.
2608  If ndigits + exp <= 0, the result is 0 or "1e#{exp}", so
2609  if ndigits + exp < 0, the result is 0.
2610  We have:
2611  2 ** (binexp-1) <= |number| < 2 ** binexp
2612  10 ** ((binexp-1)/log_2(10)) <= |number| < 10 ** (binexp/log_2(10))
2613  If binexp >= 0, and since log_2(10) = 3.322259:
2614  10 ** (binexp/4 - 1) < |number| < 10 ** (binexp/3)
2615  floor(binexp/4) <= exp <= ceil(binexp/3)
2616  If binexp <= 0, swap the /4 and the /3
2617  So if ndigits + floor(binexp/(4 or 3)) >= float_dig, the result is number
2618  If ndigits + ceil(binexp/(3 or 4)) < 0 the result is 0
2619 */
2620  if (ndigits >= float_dig - (binexp > 0 ? binexp / 4 : binexp / 3 - 1)) {
2621  return TRUE;
2622  }
2623  return FALSE;
2624 }
2625 
2626 static int
2627 float_round_underflow(int ndigits, int binexp)
2628 {
2629  if (ndigits < - (binexp > 0 ? binexp / 3 + 1 : binexp / 4)) {
2630  return TRUE;
2631  }
2632  return FALSE;
2633 }
2634 
2635 /*
2636  * call-seq:
2637  * to_i -> integer
2638  *
2639  * Returns +self+ truncated to an Integer.
2640  *
2641  * 1.2.to_i # => 1
2642  * (-1.2).to_i # => -1
2643  *
2644  * Note that the limited precision of floating-point arithmetic
2645  * may lead to surprising results:
2646  *
2647  * (0.3 / 0.1).to_i # => 2 (!)
2648  *
2649  */
2650 
2651 static VALUE
2652 flo_to_i(VALUE num)
2653 {
2654  double f = RFLOAT_VALUE(num);
2655 
2656  if (f > 0.0) f = floor(f);
2657  if (f < 0.0) f = ceil(f);
2658 
2659  return dbl2ival(f);
2660 }
2661 
2662 /*
2663  * call-seq:
2664  * truncate(ndigits = 0) -> float or integer
2665  *
2666  * Returns +self+ truncated (toward zero) to
2667  * a precision of +ndigits+ decimal digits.
2668  *
2669  * When +ndigits+ is positive, returns a float with +ndigits+ digits
2670  * after the decimal point (as available):
2671  *
2672  * f = 12345.6789
2673  * f.truncate(1) # => 12345.6
2674  * f.truncate(3) # => 12345.678
2675  * f = -12345.6789
2676  * f.truncate(1) # => -12345.6
2677  * f.truncate(3) # => -12345.678
2678  *
2679  * When +ndigits+ is negative, returns an integer
2680  * with at least <tt>ndigits.abs</tt> trailing zeros:
2681  *
2682  * f = 12345.6789
2683  * f.truncate(0) # => 12345
2684  * f.truncate(-3) # => 12000
2685  * f = -12345.6789
2686  * f.truncate(0) # => -12345
2687  * f.truncate(-3) # => -12000
2688  *
2689  * Note that the limited precision of floating-point arithmetic
2690  * may lead to surprising results:
2691  *
2692  * (0.3 / 0.1).truncate #=> 2 (!)
2693  *
2694  * Related: Float#round.
2695  *
2696  */
2697 static VALUE
2698 flo_truncate(int argc, VALUE *argv, VALUE num)
2699 {
2700  if (signbit(RFLOAT_VALUE(num)))
2701  return flo_ceil(argc, argv, num);
2702  else
2703  return flo_floor(argc, argv, num);
2704 }
2705 
2706 /*
2707  * call-seq:
2708  * floor(ndigits = 0) -> float or integer
2709  *
2710  * Returns the largest float or integer that is less than or equal to +self+,
2711  * as specified by the given `ndigits`,
2712  * which must be an
2713  * {integer-convertible object}[rdoc-ref:implicit_conversion.rdoc@Integer-Convertible+Objects].
2714  *
2715  * Equivalent to <tt>self.to_f.floor(ndigits)</tt>.
2716  *
2717  * Related: #ceil, Float#floor.
2718  */
2719 
2720 static VALUE
2721 num_floor(int argc, VALUE *argv, VALUE num)
2722 {
2723  return flo_floor(argc, argv, rb_Float(num));
2724 }
2725 
2726 /*
2727  * call-seq:
2728  * ceil(ndigits = 0) -> float or integer
2729  *
2730  * Returns the smallest float or integer that is greater than or equal to +self+,
2731  * as specified by the given `ndigits`,
2732  * which must be an
2733  * {integer-convertible object}[rdoc-ref:implicit_conversion.rdoc@Integer-Convertible+Objects].
2734  *
2735  * Equivalent to <tt>self.to_f.ceil(ndigits)</tt>.
2736  *
2737  * Related: #floor, Float#ceil.
2738  */
2739 
2740 static VALUE
2741 num_ceil(int argc, VALUE *argv, VALUE num)
2742 {
2743  return flo_ceil(argc, argv, rb_Float(num));
2744 }
2745 
2746 /*
2747  * call-seq:
2748  * round(digits = 0) -> integer or float
2749  *
2750  * Returns +self+ rounded to the nearest value with
2751  * a precision of +digits+ decimal digits.
2752  *
2753  * \Numeric implements this by converting +self+ to a Float and
2754  * invoking Float#round.
2755  */
2756 
2757 static VALUE
2758 num_round(int argc, VALUE* argv, VALUE num)
2759 {
2760  return flo_round(argc, argv, rb_Float(num));
2761 }
2762 
2763 /*
2764  * call-seq:
2765  * truncate(digits = 0) -> integer or float
2766  *
2767  * Returns +self+ truncated (toward zero) to
2768  * a precision of +digits+ decimal digits.
2769  *
2770  * \Numeric implements this by converting +self+ to a Float and
2771  * invoking Float#truncate.
2772  */
2773 
2774 static VALUE
2775 num_truncate(int argc, VALUE *argv, VALUE num)
2776 {
2777  return flo_truncate(argc, argv, rb_Float(num));
2778 }
2779 
2780 double
2781 ruby_float_step_size(double beg, double end, double unit, int excl)
2782 {
2783  const double epsilon = DBL_EPSILON;
2784  double d, n, err;
2785 
2786  if (unit == 0) {
2787  return HUGE_VAL;
2788  }
2789  if (isinf(unit)) {
2790  return unit > 0 ? beg <= end : beg >= end;
2791  }
2792  n= (end - beg)/unit;
2793  err = (fabs(beg) + fabs(end) + fabs(end-beg)) / fabs(unit) * epsilon;
2794  if (err>0.5) err=0.5;
2795  if (excl) {
2796  if (n<=0) return 0;
2797  if (n<1)
2798  n = 0;
2799  else
2800  n = floor(n - err);
2801  d = +((n + 1) * unit) + beg;
2802  if (beg < end) {
2803  if (d < end)
2804  n++;
2805  }
2806  else if (beg > end) {
2807  if (d > end)
2808  n++;
2809  }
2810  }
2811  else {
2812  if (n<0) return 0;
2813  n = floor(n + err);
2814  d = +((n + 1) * unit) + beg;
2815  if (beg < end) {
2816  if (d <= end)
2817  n++;
2818  }
2819  else if (beg > end) {
2820  if (d >= end)
2821  n++;
2822  }
2823  }
2824  return n+1;
2825 }
2826 
2827 int
2828 ruby_float_step(VALUE from, VALUE to, VALUE step, int excl, int allow_endless)
2829 {
2830  if (RB_FLOAT_TYPE_P(from) || RB_FLOAT_TYPE_P(to) || RB_FLOAT_TYPE_P(step)) {
2831  double unit = NUM2DBL(step);
2832  double beg = NUM2DBL(from);
2833  double end = (allow_endless && NIL_P(to)) ? (unit < 0 ? -1 : 1)*HUGE_VAL : NUM2DBL(to);
2834  double n = ruby_float_step_size(beg, end, unit, excl);
2835  long i;
2836 
2837  if (isinf(unit)) {
2838  /* if unit is infinity, i*unit+beg is NaN */
2839  if (n) rb_yield(DBL2NUM(beg));
2840  }
2841  else if (unit == 0) {
2842  VALUE val = DBL2NUM(beg);
2843  for (;;)
2844  rb_yield(val);
2845  }
2846  else {
2847  for (i=0; i<n; i++) {
2848  double d = i*unit+beg;
2849  if (unit >= 0 ? end < d : d < end) d = end;
2850  rb_yield(DBL2NUM(d));
2851  }
2852  }
2853  return TRUE;
2854  }
2855  return FALSE;
2856 }
2857 
2858 VALUE
2859 ruby_num_interval_step_size(VALUE from, VALUE to, VALUE step, int excl)
2860 {
2861  if (FIXNUM_P(from) && FIXNUM_P(to) && FIXNUM_P(step)) {
2862  long delta, diff;
2863 
2864  diff = FIX2LONG(step);
2865  if (diff == 0) {
2866  return DBL2NUM(HUGE_VAL);
2867  }
2868  delta = FIX2LONG(to) - FIX2LONG(from);
2869  if (diff < 0) {
2870  diff = -diff;
2871  delta = -delta;
2872  }
2873  if (excl) {
2874  delta--;
2875  }
2876  if (delta < 0) {
2877  return INT2FIX(0);
2878  }
2879  return ULONG2NUM(delta / diff + 1UL);
2880  }
2881  else if (RB_FLOAT_TYPE_P(from) || RB_FLOAT_TYPE_P(to) || RB_FLOAT_TYPE_P(step)) {
2882  double n = ruby_float_step_size(NUM2DBL(from), NUM2DBL(to), NUM2DBL(step), excl);
2883 
2884  if (isinf(n)) return DBL2NUM(n);
2885  if (POSFIXABLE(n)) return LONG2FIX((long)n);
2886  return rb_dbl2big(n);
2887  }
2888  else {
2889  VALUE result;
2890  ID cmp = '>';
2891  switch (rb_cmpint(rb_num_coerce_cmp(step, INT2FIX(0), id_cmp), step, INT2FIX(0))) {
2892  case 0: return DBL2NUM(HUGE_VAL);
2893  case -1: cmp = '<'; break;
2894  }
2895  if (RTEST(rb_funcall(from, cmp, 1, to))) return INT2FIX(0);
2896  result = rb_funcall(rb_funcall(to, '-', 1, from), id_div, 1, step);
2897  if (!excl || RTEST(rb_funcall(to, cmp, 1, rb_funcall(from, '+', 1, rb_funcall(result, '*', 1, step))))) {
2898  result = rb_funcall(result, '+', 1, INT2FIX(1));
2899  }
2900  return result;
2901  }
2902 }
2903 
2904 static int
2905 num_step_negative_p(VALUE num)
2906 {
2907  const ID mid = '<';
2908  VALUE zero = INT2FIX(0);
2909  VALUE r;
2910 
2911  if (FIXNUM_P(num)) {
2912  if (method_basic_p(rb_cInteger))
2913  return (SIGNED_VALUE)num < 0;
2914  }
2915  else if (RB_BIGNUM_TYPE_P(num)) {
2916  if (method_basic_p(rb_cInteger))
2917  return BIGNUM_NEGATIVE_P(num);
2918  }
2919 
2920  r = rb_check_funcall(num, '>', 1, &zero);
2921  if (UNDEF_P(r)) {
2922  coerce_failed(num, INT2FIX(0));
2923  }
2924  return !RTEST(r);
2925 }
2926 
2927 static int
2928 num_step_extract_args(int argc, const VALUE *argv, VALUE *to, VALUE *step, VALUE *by)
2929 {
2930  VALUE hash;
2931 
2932  argc = rb_scan_args(argc, argv, "02:", to, step, &hash);
2933  if (!NIL_P(hash)) {
2934  ID keys[2];
2935  VALUE values[2];
2936  keys[0] = id_to;
2937  keys[1] = id_by;
2938  rb_get_kwargs(hash, keys, 0, 2, values);
2939  if (!UNDEF_P(values[0])) {
2940  if (argc > 0) rb_raise(rb_eArgError, "to is given twice");
2941  *to = values[0];
2942  }
2943  if (!UNDEF_P(values[1])) {
2944  if (argc > 1) rb_raise(rb_eArgError, "step is given twice");
2945  *by = values[1];
2946  }
2947  }
2948 
2949  return argc;
2950 }
2951 
2952 static int
2953 num_step_check_fix_args(int argc, VALUE *to, VALUE *step, VALUE by, int fix_nil, int allow_zero_step)
2954 {
2955  int desc;
2956  if (!UNDEF_P(by)) {
2957  *step = by;
2958  }
2959  else {
2960  /* compatibility */
2961  if (argc > 1 && NIL_P(*step)) {
2962  rb_raise(rb_eTypeError, "step must be numeric");
2963  }
2964  }
2965  if (!allow_zero_step && rb_equal(*step, INT2FIX(0))) {
2966  rb_raise(rb_eArgError, "step can't be 0");
2967  }
2968  if (NIL_P(*step)) {
2969  *step = INT2FIX(1);
2970  }
2971  desc = num_step_negative_p(*step);
2972  if (fix_nil && NIL_P(*to)) {
2973  *to = desc ? DBL2NUM(-HUGE_VAL) : DBL2NUM(HUGE_VAL);
2974  }
2975  return desc;
2976 }
2977 
2978 static int
2979 num_step_scan_args(int argc, const VALUE *argv, VALUE *to, VALUE *step, int fix_nil, int allow_zero_step)
2980 {
2981  VALUE by = Qundef;
2982  argc = num_step_extract_args(argc, argv, to, step, &by);
2983  return num_step_check_fix_args(argc, to, step, by, fix_nil, allow_zero_step);
2984 }
2985 
2986 static VALUE
2987 num_step_size(VALUE from, VALUE args, VALUE eobj)
2988 {
2989  VALUE to, step;
2990  int argc = args ? RARRAY_LENINT(args) : 0;
2991  const VALUE *argv = args ? RARRAY_CONST_PTR(args) : 0;
2992 
2993  num_step_scan_args(argc, argv, &to, &step, TRUE, FALSE);
2994 
2995  return ruby_num_interval_step_size(from, to, step, FALSE);
2996 }
2997 
2998 /*
2999  * call-seq:
3000  * step(to = nil, by = 1) {|n| ... } -> self
3001  * step(to = nil, by = 1) -> enumerator
3002  * step(to = nil, by: 1) {|n| ... } -> self
3003  * step(to = nil, by: 1) -> enumerator
3004  * step(by: 1, to: ) {|n| ... } -> self
3005  * step(by: 1, to: ) -> enumerator
3006  * step(by: , to: nil) {|n| ... } -> self
3007  * step(by: , to: nil) -> enumerator
3008  *
3009  * Generates a sequence of numbers; with a block given, traverses the sequence.
3010  *
3011  * Of the Core and Standard Library classes,
3012  * Integer, Float, and Rational use this implementation.
3013  *
3014  * A quick example:
3015  *
3016  * squares = []
3017  * 1.step(by: 2, to: 10) {|i| squares.push(i*i) }
3018  * squares # => [1, 9, 25, 49, 81]
3019  *
3020  * The generated sequence:
3021  *
3022  * - Begins with +self+.
3023  * - Continues at intervals of +by+ (which may not be zero).
3024  * - Ends with the last number that is within or equal to +to+;
3025  * that is, less than or equal to +to+ if +by+ is positive,
3026  * greater than or equal to +to+ if +by+ is negative.
3027  * If +to+ is +nil+, the sequence is of infinite length.
3028  *
3029  * If a block is given, calls the block with each number in the sequence;
3030  * returns +self+. If no block is given, returns an Enumerator::ArithmeticSequence.
3031  *
3032  * <b>Keyword Arguments</b>
3033  *
3034  * With keyword arguments +by+ and +to+,
3035  * their values (or defaults) determine the step and limit:
3036  *
3037  * # Both keywords given.
3038  * squares = []
3039  * 4.step(by: 2, to: 10) {|i| squares.push(i*i) } # => 4
3040  * squares # => [16, 36, 64, 100]
3041  * cubes = []
3042  * 3.step(by: -1.5, to: -3) {|i| cubes.push(i*i*i) } # => 3
3043  * cubes # => [27.0, 3.375, 0.0, -3.375, -27.0]
3044  * squares = []
3045  * 1.2.step(by: 0.2, to: 2.0) {|f| squares.push(f*f) }
3046  * squares # => [1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4.0]
3047  *
3048  * squares = []
3049  * Rational(6/5).step(by: 0.2, to: 2.0) {|r| squares.push(r*r) }
3050  * squares # => [1.0, 1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4.0]
3051  *
3052  * # Only keyword to given.
3053  * squares = []
3054  * 4.step(to: 10) {|i| squares.push(i*i) } # => 4
3055  * squares # => [16, 25, 36, 49, 64, 81, 100]
3056  * # Only by given.
3057  *
3058  * # Only keyword by given
3059  * squares = []
3060  * 4.step(by:2) {|i| squares.push(i*i); break if i > 10 }
3061  * squares # => [16, 36, 64, 100, 144]
3062  *
3063  * # No block given.
3064  * e = 3.step(by: -1.5, to: -3) # => (3.step(by: -1.5, to: -3))
3065  * e.class # => Enumerator::ArithmeticSequence
3066  *
3067  * <b>Positional Arguments</b>
3068  *
3069  * With optional positional arguments +to+ and +by+,
3070  * their values (or defaults) determine the step and limit:
3071  *
3072  * squares = []
3073  * 4.step(10, 2) {|i| squares.push(i*i) } # => 4
3074  * squares # => [16, 36, 64, 100]
3075  * squares = []
3076  * 4.step(10) {|i| squares.push(i*i) }
3077  * squares # => [16, 25, 36, 49, 64, 81, 100]
3078  * squares = []
3079  * 4.step {|i| squares.push(i*i); break if i > 10 } # => nil
3080  * squares # => [16, 25, 36, 49, 64, 81, 100, 121]
3081  *
3082  * <b>Implementation Notes</b>
3083  *
3084  * If all the arguments are integers, the loop operates using an integer
3085  * counter.
3086  *
3087  * If any of the arguments are floating point numbers, all are converted
3088  * to floats, and the loop is executed
3089  * <i>floor(n + n*Float::EPSILON) + 1</i> times,
3090  * where <i>n = (limit - self)/step</i>.
3091  *
3092  */
3093 
3094 static VALUE
3095 num_step(int argc, VALUE *argv, VALUE from)
3096 {
3097  VALUE to, step;
3098  int desc, inf;
3099 
3100  if (!rb_block_given_p()) {
3101  VALUE by = Qundef;
3102 
3103  num_step_extract_args(argc, argv, &to, &step, &by);
3104  if (!UNDEF_P(by)) {
3105  step = by;
3106  }
3107  if (NIL_P(step)) {
3108  step = INT2FIX(1);
3109  }
3110  else if (rb_equal(step, INT2FIX(0))) {
3111  rb_raise(rb_eArgError, "step can't be 0");
3112  }
3113  if ((NIL_P(to) || rb_obj_is_kind_of(to, rb_cNumeric)) &&
3114  rb_obj_is_kind_of(step, rb_cNumeric)) {
3115  return rb_arith_seq_new(from, ID2SYM(rb_frame_this_func()), argc, argv,
3116  num_step_size, from, to, step, FALSE);
3117  }
3118 
3119  return SIZED_ENUMERATOR_KW(from, 2, ((VALUE [2]){to, step}), num_step_size, FALSE);
3120  }
3121 
3122  desc = num_step_scan_args(argc, argv, &to, &step, TRUE, FALSE);
3123  if (rb_equal(step, INT2FIX(0))) {
3124  inf = 1;
3125  }
3126  else if (RB_FLOAT_TYPE_P(to)) {
3127  double f = RFLOAT_VALUE(to);
3128  inf = isinf(f) && (signbit(f) ? desc : !desc);
3129  }
3130  else inf = 0;
3131 
3132  if (FIXNUM_P(from) && (inf || FIXNUM_P(to)) && FIXNUM_P(step)) {
3133  long i = FIX2LONG(from);
3134  long diff = FIX2LONG(step);
3135 
3136  if (inf) {
3137  for (;; i += diff)
3138  rb_yield(LONG2FIX(i));
3139  }
3140  else {
3141  long end = FIX2LONG(to);
3142 
3143  if (desc) {
3144  for (; i >= end; i += diff)
3145  rb_yield(LONG2FIX(i));
3146  }
3147  else {
3148  for (; i <= end; i += diff)
3149  rb_yield(LONG2FIX(i));
3150  }
3151  }
3152  }
3153  else if (!ruby_float_step(from, to, step, FALSE, FALSE)) {
3154  VALUE i = from;
3155 
3156  if (inf) {
3157  for (;; i = rb_funcall(i, '+', 1, step))
3158  rb_yield(i);
3159  }
3160  else {
3161  ID cmp = desc ? '<' : '>';
3162 
3163  for (; !RTEST(rb_funcall(i, cmp, 1, to)); i = rb_funcall(i, '+', 1, step))
3164  rb_yield(i);
3165  }
3166  }
3167  return from;
3168 }
3169 
3170 static char *
3171 out_of_range_float(char (*pbuf)[24], VALUE val)
3172 {
3173  char *const buf = *pbuf;
3174  char *s;
3175 
3176  snprintf(buf, sizeof(*pbuf), "%-.10g", RFLOAT_VALUE(val));
3177  if ((s = strchr(buf, ' ')) != 0) *s = '\0';
3178  return buf;
3179 }
3180 
3181 #define FLOAT_OUT_OF_RANGE(val, type) do { \
3182  char buf[24]; \
3183  rb_raise(rb_eRangeError, "float %s out of range of "type, \
3184  out_of_range_float(&buf, (val))); \
3185 } while (0)
3186 
3187 #define LONG_MIN_MINUS_ONE ((double)LONG_MIN-1)
3188 #define LONG_MAX_PLUS_ONE (2*(double)(LONG_MAX/2+1))
3189 #define ULONG_MAX_PLUS_ONE (2*(double)(ULONG_MAX/2+1))
3190 #define LONG_MIN_MINUS_ONE_IS_LESS_THAN(n) \
3191  (LONG_MIN_MINUS_ONE == (double)LONG_MIN ? \
3192  LONG_MIN <= (n): \
3193  LONG_MIN_MINUS_ONE < (n))
3194 
3195 long
3197 {
3198  again:
3199  if (NIL_P(val)) {
3200  rb_raise(rb_eTypeError, "no implicit conversion from nil to integer");
3201  }
3202 
3203  if (FIXNUM_P(val)) return FIX2LONG(val);
3204 
3205  else if (RB_FLOAT_TYPE_P(val)) {
3206  if (RFLOAT_VALUE(val) < LONG_MAX_PLUS_ONE
3207  && LONG_MIN_MINUS_ONE_IS_LESS_THAN(RFLOAT_VALUE(val))) {
3208  return (long)RFLOAT_VALUE(val);
3209  }
3210  else {
3211  FLOAT_OUT_OF_RANGE(val, "integer");
3212  }
3213  }
3214  else if (RB_BIGNUM_TYPE_P(val)) {
3215  return rb_big2long(val);
3216  }
3217  else {
3218  val = rb_to_int(val);
3219  goto again;
3220  }
3221 }
3222 
3223 static unsigned long
3224 rb_num2ulong_internal(VALUE val, int *wrap_p)
3225 {
3226  again:
3227  if (NIL_P(val)) {
3228  rb_raise(rb_eTypeError, "no implicit conversion of nil into Integer");
3229  }
3230 
3231  if (FIXNUM_P(val)) {
3232  long l = FIX2LONG(val); /* this is FIX2LONG, intended */
3233  if (wrap_p)
3234  *wrap_p = l < 0;
3235  return (unsigned long)l;
3236  }
3237  else if (RB_FLOAT_TYPE_P(val)) {
3238  double d = RFLOAT_VALUE(val);
3239  if (d < ULONG_MAX_PLUS_ONE && LONG_MIN_MINUS_ONE_IS_LESS_THAN(d)) {
3240  if (wrap_p)
3241  *wrap_p = d <= -1.0; /* NUM2ULONG(v) uses v.to_int conceptually. */
3242  if (0 <= d)
3243  return (unsigned long)d;
3244  return (unsigned long)(long)d;
3245  }
3246  else {
3247  FLOAT_OUT_OF_RANGE(val, "integer");
3248  }
3249  }
3250  else if (RB_BIGNUM_TYPE_P(val)) {
3251  {
3252  unsigned long ul = rb_big2ulong(val);
3253  if (wrap_p)
3254  *wrap_p = BIGNUM_NEGATIVE_P(val);
3255  return ul;
3256  }
3257  }
3258  else {
3259  val = rb_to_int(val);
3260  goto again;
3261  }
3262 }
3263 
3264 unsigned long
3266 {
3267  return rb_num2ulong_internal(val, NULL);
3268 }
3269 
3270 void
3272 {
3273  rb_raise(rb_eRangeError, "integer %"PRIdVALUE " too %s to convert to 'int'",
3274  num, num < 0 ? "small" : "big");
3275 }
3276 
3277 #if SIZEOF_INT < SIZEOF_LONG
3278 static void
3279 check_int(long num)
3280 {
3281  if ((long)(int)num != num) {
3282  rb_out_of_int(num);
3283  }
3284 }
3285 
3286 static void
3287 check_uint(unsigned long num, int sign)
3288 {
3289  if (sign) {
3290  /* minus */
3291  if (num < (unsigned long)INT_MIN)
3292  rb_raise(rb_eRangeError, "integer %ld too small to convert to 'unsigned int'", (long)num);
3293  }
3294  else {
3295  /* plus */
3296  if (UINT_MAX < num)
3297  rb_raise(rb_eRangeError, "integer %lu too big to convert to 'unsigned int'", num);
3298  }
3299 }
3300 
3301 long
3302 rb_num2int(VALUE val)
3303 {
3304  long num = rb_num2long(val);
3305 
3306  check_int(num);
3307  return num;
3308 }
3309 
3310 long
3311 rb_fix2int(VALUE val)
3312 {
3313  long num = FIXNUM_P(val)?FIX2LONG(val):rb_num2long(val);
3314 
3315  check_int(num);
3316  return num;
3317 }
3318 
3319 unsigned long
3320 rb_num2uint(VALUE val)
3321 {
3322  int wrap;
3323  unsigned long num = rb_num2ulong_internal(val, &wrap);
3324 
3325  check_uint(num, wrap);
3326  return num;
3327 }
3328 
3329 unsigned long
3330 rb_fix2uint(VALUE val)
3331 {
3332  unsigned long num;
3333 
3334  if (!FIXNUM_P(val)) {
3335  return rb_num2uint(val);
3336  }
3337  num = FIX2ULONG(val);
3338 
3339  check_uint(num, FIXNUM_NEGATIVE_P(val));
3340  return num;
3341 }
3342 #else
3343 long
3345 {
3346  return rb_num2long(val);
3347 }
3348 
3349 long
3351 {
3352  return FIX2INT(val);
3353 }
3354 
3355 unsigned long
3357 {
3358  return rb_num2ulong(val);
3359 }
3360 
3361 unsigned long
3363 {
3364  return RB_FIX2ULONG(val);
3365 }
3366 #endif
3367 
3368 NORETURN(static void rb_out_of_short(SIGNED_VALUE num));
3369 static void
3370 rb_out_of_short(SIGNED_VALUE num)
3371 {
3372  rb_raise(rb_eRangeError, "integer %"PRIdVALUE " too %s to convert to 'short'",
3373  num, num < 0 ? "small" : "big");
3374 }
3375 
3376 static void
3377 check_short(long num)
3378 {
3379  if ((long)(short)num != num) {
3380  rb_out_of_short(num);
3381  }
3382 }
3383 
3384 static void
3385 check_ushort(unsigned long num, int sign)
3386 {
3387  if (sign) {
3388  /* minus */
3389  if (num < (unsigned long)SHRT_MIN)
3390  rb_raise(rb_eRangeError, "integer %ld too small to convert to 'unsigned short'", (long)num);
3391  }
3392  else {
3393  /* plus */
3394  if (USHRT_MAX < num)
3395  rb_raise(rb_eRangeError, "integer %lu too big to convert to 'unsigned short'", num);
3396  }
3397 }
3398 
3399 short
3401 {
3402  long num = rb_num2long(val);
3403 
3404  check_short(num);
3405  return num;
3406 }
3407 
3408 short
3410 {
3411  long num = FIXNUM_P(val)?FIX2LONG(val):rb_num2long(val);
3412 
3413  check_short(num);
3414  return num;
3415 }
3416 
3417 unsigned short
3419 {
3420  int wrap;
3421  unsigned long num = rb_num2ulong_internal(val, &wrap);
3422 
3423  check_ushort(num, wrap);
3424  return num;
3425 }
3426 
3427 unsigned short
3429 {
3430  unsigned long num;
3431 
3432  if (!FIXNUM_P(val)) {
3433  return rb_num2ushort(val);
3434  }
3435  num = FIX2ULONG(val);
3436 
3437  check_ushort(num, FIXNUM_NEGATIVE_P(val));
3438  return num;
3439 }
3440 
3441 VALUE
3443 {
3444  long v;
3445 
3446  if (FIXNUM_P(val)) return val;
3447 
3448  v = rb_num2long(val);
3449  if (!FIXABLE(v))
3450  rb_raise(rb_eRangeError, "integer %ld out of range of fixnum", v);
3451  return LONG2FIX(v);
3452 }
3453 
3454 #if HAVE_LONG_LONG
3455 
3456 #define LLONG_MIN_MINUS_ONE ((double)LLONG_MIN-1)
3457 #define LLONG_MAX_PLUS_ONE (2*(double)(LLONG_MAX/2+1))
3458 #define ULLONG_MAX_PLUS_ONE (2*(double)(ULLONG_MAX/2+1))
3459 #ifndef ULLONG_MAX
3460 #define ULLONG_MAX ((unsigned LONG_LONG)LLONG_MAX*2+1)
3461 #endif
3462 #define LLONG_MIN_MINUS_ONE_IS_LESS_THAN(n) \
3463  (LLONG_MIN_MINUS_ONE == (double)LLONG_MIN ? \
3464  LLONG_MIN <= (n): \
3465  LLONG_MIN_MINUS_ONE < (n))
3466 
3467 LONG_LONG
3468 rb_num2ll(VALUE val)
3469 {
3470  if (NIL_P(val)) {
3471  rb_raise(rb_eTypeError, "no implicit conversion from nil");
3472  }
3473 
3474  if (FIXNUM_P(val)) return (LONG_LONG)FIX2LONG(val);
3475 
3476  else if (RB_FLOAT_TYPE_P(val)) {
3477  double d = RFLOAT_VALUE(val);
3478  if (d < LLONG_MAX_PLUS_ONE && (LLONG_MIN_MINUS_ONE_IS_LESS_THAN(d))) {
3479  return (LONG_LONG)d;
3480  }
3481  else {
3482  FLOAT_OUT_OF_RANGE(val, "long long");
3483  }
3484  }
3485  else if (RB_BIGNUM_TYPE_P(val)) {
3486  return rb_big2ll(val);
3487  }
3488  else if (RB_TYPE_P(val, T_STRING)) {
3489  rb_raise(rb_eTypeError, "no implicit conversion from string");
3490  }
3491  else if (RB_TYPE_P(val, T_TRUE) || RB_TYPE_P(val, T_FALSE)) {
3492  rb_raise(rb_eTypeError, "no implicit conversion from boolean");
3493  }
3494 
3495  val = rb_to_int(val);
3496  return NUM2LL(val);
3497 }
3498 
3499 unsigned LONG_LONG
3500 rb_num2ull(VALUE val)
3501 {
3502  if (NIL_P(val)) {
3503  rb_raise(rb_eTypeError, "no implicit conversion of nil into Integer");
3504  }
3505  else if (FIXNUM_P(val)) {
3506  return (LONG_LONG)FIX2LONG(val); /* this is FIX2LONG, intended */
3507  }
3508  else if (RB_FLOAT_TYPE_P(val)) {
3509  double d = RFLOAT_VALUE(val);
3510  if (d < ULLONG_MAX_PLUS_ONE && LLONG_MIN_MINUS_ONE_IS_LESS_THAN(d)) {
3511  if (0 <= d)
3512  return (unsigned LONG_LONG)d;
3513  return (unsigned LONG_LONG)(LONG_LONG)d;
3514  }
3515  else {
3516  FLOAT_OUT_OF_RANGE(val, "unsigned long long");
3517  }
3518  }
3519  else if (RB_BIGNUM_TYPE_P(val)) {
3520  return rb_big2ull(val);
3521  }
3522  else {
3523  val = rb_to_int(val);
3524  return NUM2ULL(val);
3525  }
3526 }
3527 
3528 #endif /* HAVE_LONG_LONG */
3529 
3530 /********************************************************************
3531  *
3532  * Document-class: Integer
3533  *
3534  * An \Integer object represents an integer value.
3535  *
3536  * You can create an \Integer object explicitly with:
3537  *
3538  * - An {integer literal}[rdoc-ref:syntax/literals.rdoc@Integer+Literals].
3539  *
3540  * You can convert certain objects to Integers with:
3541  *
3542  * - \Method #Integer.
3543  *
3544  * An attempt to add a singleton method to an instance of this class
3545  * causes an exception to be raised.
3546  *
3547  * == What's Here
3548  *
3549  * First, what's elsewhere. \Class \Integer:
3550  *
3551  * - Inherits from
3552  * {class Numeric}[rdoc-ref:Numeric@What-27s+Here]
3553  * and {class Object}[rdoc-ref:Object@What-27s+Here].
3554  * - Includes {module Comparable}[rdoc-ref:Comparable@What-27s+Here].
3555  *
3556  * Here, class \Integer provides methods for:
3557  *
3558  * - {Querying}[rdoc-ref:Integer@Querying]
3559  * - {Comparing}[rdoc-ref:Integer@Comparing]
3560  * - {Converting}[rdoc-ref:Integer@Converting]
3561  * - {Other}[rdoc-ref:Integer@Other]
3562  *
3563  * === Querying
3564  *
3565  * - #allbits?: Returns whether all bits in +self+ are set.
3566  * - #anybits?: Returns whether any bits in +self+ are set.
3567  * - #nobits?: Returns whether no bits in +self+ are set.
3568  *
3569  * === Comparing
3570  *
3571  * - #<: Returns whether +self+ is less than the given value.
3572  * - #<=: Returns whether +self+ is less than or equal to the given value.
3573  * - #<=>: Returns a number indicating whether +self+ is less than, equal
3574  * to, or greater than the given value.
3575  * - #== (aliased as #===): Returns whether +self+ is equal to the given
3576  * value.
3577  * - #>: Returns whether +self+ is greater than the given value.
3578  * - #>=: Returns whether +self+ is greater than or equal to the given value.
3579  *
3580  * === Converting
3581  *
3582  * - ::sqrt: Returns the integer square root of the given value.
3583  * - ::try_convert: Returns the given value converted to an \Integer.
3584  * - #% (aliased as #modulo): Returns +self+ modulo the given value.
3585  * - #&: Returns the bitwise AND of +self+ and the given value.
3586  * - #*: Returns the product of +self+ and the given value.
3587  * - #**: Returns the value of +self+ raised to the power of the given value.
3588  * - #+: Returns the sum of +self+ and the given value.
3589  * - #-: Returns the difference of +self+ and the given value.
3590  * - #/: Returns the quotient of +self+ and the given value.
3591  * - #<<: Returns the value of +self+ after a leftward bit-shift.
3592  * - #>>: Returns the value of +self+ after a rightward bit-shift.
3593  * - #[]: Returns a slice of bits from +self+.
3594  * - #^: Returns the bitwise EXCLUSIVE OR of +self+ and the given value.
3595  * - #|: Returns the bitwise OR of +self+ and the given value.
3596  * - #ceil: Returns the smallest number greater than or equal to +self+.
3597  * - #chr: Returns a 1-character string containing the character
3598  * represented by the value of +self+.
3599  * - #digits: Returns an array of integers representing the base-radix digits
3600  * of +self+.
3601  * - #div: Returns the integer result of dividing +self+ by the given value.
3602  * - #divmod: Returns a 2-element array containing the quotient and remainder
3603  * results of dividing +self+ by the given value.
3604  * - #fdiv: Returns the Float result of dividing +self+ by the given value.
3605  * - #floor: Returns the greatest number smaller than or equal to +self+.
3606  * - #pow: Returns the modular exponentiation of +self+.
3607  * - #pred: Returns the integer predecessor of +self+.
3608  * - #remainder: Returns the remainder after dividing +self+ by the given value.
3609  * - #round: Returns +self+ rounded to the nearest value with the given precision.
3610  * - #succ (aliased as #next): Returns the integer successor of +self+.
3611  * - #to_f: Returns +self+ converted to a Float.
3612  * - #to_s (aliased as #inspect): Returns a string containing the place-value
3613  * representation of +self+ in the given radix.
3614  * - #truncate: Returns +self+ truncated to the given precision.
3615  *
3616  * === Other
3617  *
3618  * - #downto: Calls the given block with each integer value from +self+
3619  * down to the given value.
3620  * - #times: Calls the given block +self+ times with each integer
3621  * in <tt>(0..self-1)</tt>.
3622  * - #upto: Calls the given block with each integer value from +self+
3623  * up to the given value.
3624  *
3625  */
3626 
3627 VALUE
3628 rb_int_odd_p(VALUE num)
3629 {
3630  if (FIXNUM_P(num)) {
3631  return RBOOL(num & 2);
3632  }
3633  else {
3634  RUBY_ASSERT(RB_BIGNUM_TYPE_P(num));
3635  return rb_big_odd_p(num);
3636  }
3637 }
3638 
3639 static VALUE
3640 int_even_p(VALUE num)
3641 {
3642  if (FIXNUM_P(num)) {
3643  return RBOOL((num & 2) == 0);
3644  }
3645  else {
3646  RUBY_ASSERT(RB_BIGNUM_TYPE_P(num));
3647  return rb_big_even_p(num);
3648  }
3649 }
3650 
3651 VALUE
3652 rb_int_even_p(VALUE num)
3653 {
3654  return int_even_p(num);
3655 }
3656 
3657 /*
3658  * call-seq:
3659  * allbits?(mask) -> true or false
3660  *
3661  * Returns +true+ if all bits that are set (=1) in +mask+
3662  * are also set in +self+; returns +false+ otherwise.
3663  *
3664  * Example values:
3665  *
3666  * 0b1010101 self
3667  * 0b1010100 mask
3668  * 0b1010100 self & mask
3669  * true self.allbits?(mask)
3670  *
3671  * 0b1010100 self
3672  * 0b1010101 mask
3673  * 0b1010100 self & mask
3674  * false self.allbits?(mask)
3675  *
3676  * Related: Integer#anybits?, Integer#nobits?.
3677  *
3678  */
3679 
3680 static VALUE
3681 int_allbits_p(VALUE num, VALUE mask)
3682 {
3683  mask = rb_to_int(mask);
3684  return rb_int_equal(rb_int_and(num, mask), mask);
3685 }
3686 
3687 /*
3688  * call-seq:
3689  * anybits?(mask) -> true or false
3690  *
3691  * Returns +true+ if any bit that is set (=1) in +mask+
3692  * is also set in +self+; returns +false+ otherwise.
3693  *
3694  * Example values:
3695  *
3696  * 0b10000010 self
3697  * 0b11111111 mask
3698  * 0b10000010 self & mask
3699  * true self.anybits?(mask)
3700  *
3701  * 0b00000000 self
3702  * 0b11111111 mask
3703  * 0b00000000 self & mask
3704  * false self.anybits?(mask)
3705  *
3706  * Related: Integer#allbits?, Integer#nobits?.
3707  *
3708  */
3709 
3710 static VALUE
3711 int_anybits_p(VALUE num, VALUE mask)
3712 {
3713  mask = rb_to_int(mask);
3714  return RBOOL(!int_zero_p(rb_int_and(num, mask)));
3715 }
3716 
3717 /*
3718  * call-seq:
3719  * nobits?(mask) -> true or false
3720  *
3721  * Returns +true+ if no bit that is set (=1) in +mask+
3722  * is also set in +self+; returns +false+ otherwise.
3723  *
3724  * Example values:
3725  *
3726  * 0b11110000 self
3727  * 0b00001111 mask
3728  * 0b00000000 self & mask
3729  * true self.nobits?(mask)
3730  *
3731  * 0b00000001 self
3732  * 0b11111111 mask
3733  * 0b00000001 self & mask
3734  * false self.nobits?(mask)
3735  *
3736  * Related: Integer#allbits?, Integer#anybits?.
3737  *
3738  */
3739 
3740 static VALUE
3741 int_nobits_p(VALUE num, VALUE mask)
3742 {
3743  mask = rb_to_int(mask);
3744  return RBOOL(int_zero_p(rb_int_and(num, mask)));
3745 }
3746 
3747 /*
3748  * call-seq:
3749  * succ -> next_integer
3750  *
3751  * Returns the successor integer of +self+ (equivalent to <tt>self + 1</tt>):
3752  *
3753  * 1.succ #=> 2
3754  * -1.succ #=> 0
3755  *
3756  * Related: Integer#pred (predecessor value).
3757  */
3758 
3759 VALUE
3760 rb_int_succ(VALUE num)
3761 {
3762  if (FIXNUM_P(num)) {
3763  long i = FIX2LONG(num) + 1;
3764  return LONG2NUM(i);
3765  }
3766  if (RB_BIGNUM_TYPE_P(num)) {
3767  return rb_big_plus(num, INT2FIX(1));
3768  }
3769  return num_funcall1(num, '+', INT2FIX(1));
3770 }
3771 
3772 #define int_succ rb_int_succ
3773 
3774 /*
3775  * call-seq:
3776  * pred -> next_integer
3777  *
3778  * Returns the predecessor of +self+ (equivalent to <tt>self - 1</tt>):
3779  *
3780  * 1.pred #=> 0
3781  * -1.pred #=> -2
3782  *
3783  * Related: Integer#succ (successor value).
3784  *
3785  */
3786 
3787 static VALUE
3788 rb_int_pred(VALUE num)
3789 {
3790  if (FIXNUM_P(num)) {
3791  long i = FIX2LONG(num) - 1;
3792  return LONG2NUM(i);
3793  }
3794  if (RB_BIGNUM_TYPE_P(num)) {
3795  return rb_big_minus(num, INT2FIX(1));
3796  }
3797  return num_funcall1(num, '-', INT2FIX(1));
3798 }
3799 
3800 #define int_pred rb_int_pred
3801 
3802 VALUE
3803 rb_enc_uint_chr(unsigned int code, rb_encoding *enc)
3804 {
3805  int n;
3806  VALUE str;
3807  switch (n = rb_enc_codelen(code, enc)) {
3808  case ONIGERR_INVALID_CODE_POINT_VALUE:
3809  rb_raise(rb_eRangeError, "invalid codepoint 0x%X in %s", code, rb_enc_name(enc));
3810  break;
3811  case ONIGERR_TOO_BIG_WIDE_CHAR_VALUE:
3812  case 0:
3813  rb_raise(rb_eRangeError, "%u out of char range", code);
3814  break;
3815  }
3816  str = rb_enc_str_new(0, n, enc);
3817  rb_enc_mbcput(code, RSTRING_PTR(str), enc);
3818  if (rb_enc_precise_mbclen(RSTRING_PTR(str), RSTRING_END(str), enc) != n) {
3819  rb_raise(rb_eRangeError, "invalid codepoint 0x%X in %s", code, rb_enc_name(enc));
3820  }
3821  return str;
3822 }
3823 
3824 /* call-seq:
3825  * chr -> string
3826  * chr(encoding) -> string
3827  *
3828  * Returns a 1-character string containing the character
3829  * represented by the value of +self+, according to the given +encoding+.
3830  *
3831  * 65.chr # => "A"
3832  * 0.chr # => "\x00"
3833  * 255.chr # => "\xFF"
3834  * string = 255.chr(Encoding::UTF_8)
3835  * string.encoding # => Encoding::UTF_8
3836  *
3837  * Raises an exception if +self+ is negative.
3838  *
3839  * Related: Integer#ord.
3840  *
3841  */
3842 
3843 static VALUE
3844 int_chr(int argc, VALUE *argv, VALUE num)
3845 {
3846  char c;
3847  unsigned int i;
3848  rb_encoding *enc;
3849 
3850  if (rb_num_to_uint(num, &i) == 0) {
3851  }
3852  else if (FIXNUM_P(num)) {
3853  rb_raise(rb_eRangeError, "%ld out of char range", FIX2LONG(num));
3854  }
3855  else {
3856  rb_raise(rb_eRangeError, "bignum out of char range");
3857  }
3858 
3859  switch (argc) {
3860  case 0:
3861  if (0xff < i) {
3863  if (!enc) {
3864  rb_raise(rb_eRangeError, "%u out of char range", i);
3865  }
3866  goto decode;
3867  }
3868  c = (char)i;
3869  if (i < 0x80) {
3870  return rb_usascii_str_new(&c, 1);
3871  }
3872  else {
3873  return rb_str_new(&c, 1);
3874  }
3875  case 1:
3876  break;
3877  default:
3878  rb_error_arity(argc, 0, 1);
3879  }
3880  enc = rb_to_encoding(argv[0]);
3881  if (!enc) enc = rb_ascii8bit_encoding();
3882  decode:
3883  return rb_enc_uint_chr(i, enc);
3884 }
3885 
3886 /*
3887  * Fixnum
3888  */
3889 
3890 static VALUE
3891 fix_uminus(VALUE num)
3892 {
3893  return LONG2NUM(-FIX2LONG(num));
3894 }
3895 
3896 VALUE
3897 rb_int_uminus(VALUE num)
3898 {
3899  if (FIXNUM_P(num)) {
3900  return fix_uminus(num);
3901  }
3902  else {
3903  RUBY_ASSERT(RB_BIGNUM_TYPE_P(num));
3904  return rb_big_uminus(num);
3905  }
3906 }
3907 
3908 VALUE
3909 rb_fix2str(VALUE x, int base)
3910 {
3911  char buf[SIZEOF_VALUE*CHAR_BIT + 1], *const e = buf + sizeof buf, *b = e;
3912  long val = FIX2LONG(x);
3913  unsigned long u;
3914  int neg = 0;
3915 
3916  if (base < 2 || 36 < base) {
3917  rb_raise(rb_eArgError, "invalid radix %d", base);
3918  }
3919 #if SIZEOF_LONG < SIZEOF_VOIDP
3920 # if SIZEOF_VOIDP == SIZEOF_LONG_LONG
3921  if ((val >= 0 && (x & 0xFFFFFFFF00000000ull)) ||
3922  (val < 0 && (x & 0xFFFFFFFF00000000ull) != 0xFFFFFFFF00000000ull)) {
3923  rb_bug("Unnormalized Fixnum value %p", (void *)x);
3924  }
3925 # else
3926  /* should do something like above code, but currently ruby does not know */
3927  /* such platforms */
3928 # endif
3929 #endif
3930  if (val == 0) {
3931  return rb_usascii_str_new2("0");
3932  }
3933  if (val < 0) {
3934  u = 1 + (unsigned long)(-(val + 1)); /* u = -val avoiding overflow */
3935  neg = 1;
3936  }
3937  else {
3938  u = val;
3939  }
3940  do {
3941  *--b = ruby_digitmap[(int)(u % base)];
3942  } while (u /= base);
3943  if (neg) {
3944  *--b = '-';
3945  }
3946 
3947  return rb_usascii_str_new(b, e - b);
3948 }
3949 
3950 static VALUE rb_fix_to_s_static[10];
3951 
3952 VALUE
3953 rb_fix_to_s(VALUE x)
3954 {
3955  long i = FIX2LONG(x);
3956  if (i >= 0 && i < 10) {
3957  return rb_fix_to_s_static[i];
3958  }
3959  return rb_fix2str(x, 10);
3960 }
3961 
3962 /*
3963  * call-seq:
3964  * to_s(base = 10) -> string
3965  *
3966  * Returns a string containing the place-value representation of +self+
3967  * in radix +base+ (in 2..36).
3968  *
3969  * 12345.to_s # => "12345"
3970  * 12345.to_s(2) # => "11000000111001"
3971  * 12345.to_s(8) # => "30071"
3972  * 12345.to_s(10) # => "12345"
3973  * 12345.to_s(16) # => "3039"
3974  * 12345.to_s(36) # => "9ix"
3975  * 78546939656932.to_s(36) # => "rubyrules"
3976  *
3977  * Raises an exception if +base+ is out of range.
3978  */
3979 
3980 VALUE
3981 rb_int_to_s(int argc, VALUE *argv, VALUE x)
3982 {
3983  int base;
3984 
3985  if (rb_check_arity(argc, 0, 1))
3986  base = NUM2INT(argv[0]);
3987  else
3988  base = 10;
3989  return rb_int2str(x, base);
3990 }
3991 
3992 VALUE
3993 rb_int2str(VALUE x, int base)
3994 {
3995  if (FIXNUM_P(x)) {
3996  return rb_fix2str(x, base);
3997  }
3998  else if (RB_BIGNUM_TYPE_P(x)) {
3999  return rb_big2str(x, base);
4000  }
4001 
4002  return rb_any_to_s(x);
4003 }
4004 
4005 static VALUE
4006 fix_plus(VALUE x, VALUE y)
4007 {
4008  if (FIXNUM_P(y)) {
4009  return rb_fix_plus_fix(x, y);
4010  }
4011  else if (RB_BIGNUM_TYPE_P(y)) {
4012  return rb_big_plus(y, x);
4013  }
4014  else if (RB_FLOAT_TYPE_P(y)) {
4015  return DBL2NUM((double)FIX2LONG(x) + RFLOAT_VALUE(y));
4016  }
4017  else if (RB_TYPE_P(y, T_COMPLEX)) {
4018  return rb_complex_plus(y, x);
4019  }
4020  else {
4021  return rb_num_coerce_bin(x, y, '+');
4022  }
4023 }
4024 
4025 VALUE
4026 rb_fix_plus(VALUE x, VALUE y)
4027 {
4028  return fix_plus(x, y);
4029 }
4030 
4031 /*
4032  * call-seq:
4033  * self + numeric -> numeric_result
4034  *
4035  * Performs addition:
4036  *
4037  * 2 + 2 # => 4
4038  * -2 + 2 # => 0
4039  * -2 + -2 # => -4
4040  * 2 + 2.0 # => 4.0
4041  * 2 + Rational(2, 1) # => (4/1)
4042  * 2 + Complex(2, 0) # => (4+0i)
4043  *
4044  */
4045 
4046 VALUE
4047 rb_int_plus(VALUE x, VALUE y)
4048 {
4049  if (FIXNUM_P(x)) {
4050  return fix_plus(x, y);
4051  }
4052  else if (RB_BIGNUM_TYPE_P(x)) {
4053  return rb_big_plus(x, y);
4054  }
4055  return rb_num_coerce_bin(x, y, '+');
4056 }
4057 
4058 static VALUE
4059 fix_minus(VALUE x, VALUE y)
4060 {
4061  if (FIXNUM_P(y)) {
4062  return rb_fix_minus_fix(x, y);
4063  }
4064  else if (RB_BIGNUM_TYPE_P(y)) {
4065  x = rb_int2big(FIX2LONG(x));
4066  return rb_big_minus(x, y);
4067  }
4068  else if (RB_FLOAT_TYPE_P(y)) {
4069  return DBL2NUM((double)FIX2LONG(x) - RFLOAT_VALUE(y));
4070  }
4071  else {
4072  return rb_num_coerce_bin(x, y, '-');
4073  }
4074 }
4075 
4076 /*
4077  * call-seq:
4078  * self - numeric -> numeric_result
4079  *
4080  * Performs subtraction:
4081  *
4082  * 4 - 2 # => 2
4083  * -4 - 2 # => -6
4084  * -4 - -2 # => -2
4085  * 4 - 2.0 # => 2.0
4086  * 4 - Rational(2, 1) # => (2/1)
4087  * 4 - Complex(2, 0) # => (2+0i)
4088  *
4089  */
4090 
4091 VALUE
4092 rb_int_minus(VALUE x, VALUE y)
4093 {
4094  if (FIXNUM_P(x)) {
4095  return fix_minus(x, y);
4096  }
4097  else if (RB_BIGNUM_TYPE_P(x)) {
4098  return rb_big_minus(x, y);
4099  }
4100  return rb_num_coerce_bin(x, y, '-');
4101 }
4102 
4103 
4104 #define SQRT_LONG_MAX HALF_LONG_MSB
4105 /*tests if N*N would overflow*/
4106 #define FIT_SQRT_LONG(n) (((n)<SQRT_LONG_MAX)&&((n)>=-SQRT_LONG_MAX))
4107 
4108 static VALUE
4109 fix_mul(VALUE x, VALUE y)
4110 {
4111  if (FIXNUM_P(y)) {
4112  return rb_fix_mul_fix(x, y);
4113  }
4114  else if (RB_BIGNUM_TYPE_P(y)) {
4115  switch (x) {
4116  case INT2FIX(0): return x;
4117  case INT2FIX(1): return y;
4118  }
4119  return rb_big_mul(y, x);
4120  }
4121  else if (RB_FLOAT_TYPE_P(y)) {
4122  return DBL2NUM((double)FIX2LONG(x) * RFLOAT_VALUE(y));
4123  }
4124  else if (RB_TYPE_P(y, T_COMPLEX)) {
4125  return rb_complex_mul(y, x);
4126  }
4127  else {
4128  return rb_num_coerce_bin(x, y, '*');
4129  }
4130 }
4131 
4132 /*
4133  * call-seq:
4134  * self * numeric -> numeric_result
4135  *
4136  * Performs multiplication:
4137  *
4138  * 4 * 2 # => 8
4139  * 4 * -2 # => -8
4140  * -4 * 2 # => -8
4141  * 4 * 2.0 # => 8.0
4142  * 4 * Rational(1, 3) # => (4/3)
4143  * 4 * Complex(2, 0) # => (8+0i)
4144  */
4145 
4146 VALUE
4147 rb_int_mul(VALUE x, VALUE y)
4148 {
4149  if (FIXNUM_P(x)) {
4150  return fix_mul(x, y);
4151  }
4152  else if (RB_BIGNUM_TYPE_P(x)) {
4153  return rb_big_mul(x, y);
4154  }
4155  return rb_num_coerce_bin(x, y, '*');
4156 }
4157 
4158 static double
4159 fix_fdiv_double(VALUE x, VALUE y)
4160 {
4161  if (FIXNUM_P(y)) {
4162  long iy = FIX2LONG(y);
4163 #if SIZEOF_LONG * CHAR_BIT > DBL_MANT_DIG
4164  if ((iy < 0 ? -iy : iy) >= (1L << DBL_MANT_DIG)) {
4165  return rb_big_fdiv_double(rb_int2big(FIX2LONG(x)), rb_int2big(iy));
4166  }
4167 #endif
4168  return double_div_double(FIX2LONG(x), iy);
4169  }
4170  else if (RB_BIGNUM_TYPE_P(y)) {
4171  return rb_big_fdiv_double(rb_int2big(FIX2LONG(x)), y);
4172  }
4173  else if (RB_FLOAT_TYPE_P(y)) {
4174  return double_div_double(FIX2LONG(x), RFLOAT_VALUE(y));
4175  }
4176  else {
4177  return NUM2DBL(rb_num_coerce_bin(x, y, idFdiv));
4178  }
4179 }
4180 
4181 double
4182 rb_int_fdiv_double(VALUE x, VALUE y)
4183 {
4184  if (RB_INTEGER_TYPE_P(y) && !FIXNUM_ZERO_P(y)) {
4185  VALUE gcd = rb_gcd(x, y);
4186  if (!FIXNUM_ZERO_P(gcd) && gcd != INT2FIX(1)) {
4187  x = rb_int_idiv(x, gcd);
4188  y = rb_int_idiv(y, gcd);
4189  }
4190  }
4191  if (FIXNUM_P(x)) {
4192  return fix_fdiv_double(x, y);
4193  }
4194  else if (RB_BIGNUM_TYPE_P(x)) {
4195  return rb_big_fdiv_double(x, y);
4196  }
4197  else {
4198  return nan("");
4199  }
4200 }
4201 
4202 /*
4203  * call-seq:
4204  * fdiv(numeric) -> float
4205  *
4206  * Returns the Float result of dividing +self+ by +numeric+:
4207  *
4208  * 4.fdiv(2) # => 2.0
4209  * 4.fdiv(-2) # => -2.0
4210  * -4.fdiv(2) # => -2.0
4211  * 4.fdiv(2.0) # => 2.0
4212  * 4.fdiv(Rational(3, 4)) # => 5.333333333333333
4213  *
4214  * Raises an exception if +numeric+ cannot be converted to a Float.
4215  *
4216  */
4217 
4218 VALUE
4219 rb_int_fdiv(VALUE x, VALUE y)
4220 {
4221  if (RB_INTEGER_TYPE_P(x)) {
4222  return DBL2NUM(rb_int_fdiv_double(x, y));
4223  }
4224  return Qnil;
4225 }
4226 
4227 static VALUE
4228 fix_divide(VALUE x, VALUE y, ID op)
4229 {
4230  if (FIXNUM_P(y)) {
4231  if (FIXNUM_ZERO_P(y)) rb_num_zerodiv();
4232  return rb_fix_div_fix(x, y);
4233  }
4234  else if (RB_BIGNUM_TYPE_P(y)) {
4235  x = rb_int2big(FIX2LONG(x));
4236  return rb_big_div(x, y);
4237  }
4238  else if (RB_FLOAT_TYPE_P(y)) {
4239  if (op == '/') {
4240  double d = FIX2LONG(x);
4241  return rb_flo_div_flo(DBL2NUM(d), y);
4242  }
4243  else {
4244  VALUE v;
4245  if (RFLOAT_VALUE(y) == 0) rb_num_zerodiv();
4246  v = fix_divide(x, y, '/');
4247  return flo_floor(0, 0, v);
4248  }
4249  }
4250  else {
4251  if (RB_TYPE_P(y, T_RATIONAL) &&
4252  op == '/' && FIX2LONG(x) == 1)
4253  return rb_rational_reciprocal(y);
4254  return rb_num_coerce_bin(x, y, op);
4255  }
4256 }
4257 
4258 static VALUE
4259 fix_div(VALUE x, VALUE y)
4260 {
4261  return fix_divide(x, y, '/');
4262 }
4263 
4264 /*
4265  * call-seq:
4266  * self / numeric -> numeric_result
4267  *
4268  * Performs division; for integer +numeric+, truncates the result to an integer:
4269  *
4270  * 4 / 3 # => 1
4271  * 4 / -3 # => -2
4272  * -4 / 3 # => -2
4273  * -4 / -3 # => 1
4274  *
4275  * For other +numeric+, returns non-integer result:
4276  *
4277  * 4 / 3.0 # => 1.3333333333333333
4278  * 4 / Rational(3, 1) # => (4/3)
4279  * 4 / Complex(3, 0) # => ((4/3)+0i)
4280  *
4281  */
4282 
4283 VALUE
4284 rb_int_div(VALUE x, VALUE y)
4285 {
4286  if (FIXNUM_P(x)) {
4287  return fix_div(x, y);
4288  }
4289  else if (RB_BIGNUM_TYPE_P(x)) {
4290  return rb_big_div(x, y);
4291  }
4292  return Qnil;
4293 }
4294 
4295 static VALUE
4296 fix_idiv(VALUE x, VALUE y)
4297 {
4298  return fix_divide(x, y, id_div);
4299 }
4300 
4301 /*
4302  * call-seq:
4303  * div(numeric) -> integer
4304  *
4305  * Performs integer division; returns the integer result of dividing +self+
4306  * by +numeric+:
4307  *
4308  * 4.div(3) # => 1
4309  * 4.div(-3) # => -2
4310  * -4.div(3) # => -2
4311  * -4.div(-3) # => 1
4312  * 4.div(3.0) # => 1
4313  * 4.div(Rational(3, 1)) # => 1
4314  *
4315  * Raises an exception if +numeric+ does not have method +div+.
4316  *
4317  */
4318 
4319 VALUE
4320 rb_int_idiv(VALUE x, VALUE y)
4321 {
4322  if (FIXNUM_P(x)) {
4323  return fix_idiv(x, y);
4324  }
4325  else if (RB_BIGNUM_TYPE_P(x)) {
4326  return rb_big_idiv(x, y);
4327  }
4328  return num_div(x, y);
4329 }
4330 
4331 static VALUE
4332 fix_mod(VALUE x, VALUE y)
4333 {
4334  if (FIXNUM_P(y)) {
4335  if (FIXNUM_ZERO_P(y)) rb_num_zerodiv();
4336  return rb_fix_mod_fix(x, y);
4337  }
4338  else if (RB_BIGNUM_TYPE_P(y)) {
4339  x = rb_int2big(FIX2LONG(x));
4340  return rb_big_modulo(x, y);
4341  }
4342  else if (RB_FLOAT_TYPE_P(y)) {
4343  return DBL2NUM(ruby_float_mod((double)FIX2LONG(x), RFLOAT_VALUE(y)));
4344  }
4345  else {
4346  return rb_num_coerce_bin(x, y, '%');
4347  }
4348 }
4349 
4350 /*
4351  * call-seq:
4352  * self % other -> real_number
4353  *
4354  * Returns +self+ modulo +other+ as a real number.
4355  *
4356  * For integer +n+ and real number +r+, these expressions are equivalent:
4357  *
4358  * n % r
4359  * n-r*(n/r).floor
4360  * n.divmod(r)[1]
4361  *
4362  * See Numeric#divmod.
4363  *
4364  * Examples:
4365  *
4366  * 10 % 2 # => 0
4367  * 10 % 3 # => 1
4368  * 10 % 4 # => 2
4369  *
4370  * 10 % -2 # => 0
4371  * 10 % -3 # => -2
4372  * 10 % -4 # => -2
4373  *
4374  * 10 % 3.0 # => 1.0
4375  * 10 % Rational(3, 1) # => (1/1)
4376  *
4377  */
4378 VALUE
4379 rb_int_modulo(VALUE x, VALUE y)
4380 {
4381  if (FIXNUM_P(x)) {
4382  return fix_mod(x, y);
4383  }
4384  else if (RB_BIGNUM_TYPE_P(x)) {
4385  return rb_big_modulo(x, y);
4386  }
4387  return num_modulo(x, y);
4388 }
4389 
4390 /*
4391  * call-seq:
4392  * remainder(other) -> real_number
4393  *
4394  * Returns the remainder after dividing +self+ by +other+.
4395  *
4396  * Examples:
4397  *
4398  * 11.remainder(4) # => 3
4399  * 11.remainder(-4) # => 3
4400  * -11.remainder(4) # => -3
4401  * -11.remainder(-4) # => -3
4402  *
4403  * 12.remainder(4) # => 0
4404  * 12.remainder(-4) # => 0
4405  * -12.remainder(4) # => 0
4406  * -12.remainder(-4) # => 0
4407  *
4408  * 13.remainder(4.0) # => 1.0
4409  * 13.remainder(Rational(4, 1)) # => (1/1)
4410  *
4411  */
4412 
4413 static VALUE
4414 int_remainder(VALUE x, VALUE y)
4415 {
4416  if (FIXNUM_P(x)) {
4417  if (FIXNUM_P(y)) {
4418  VALUE z = fix_mod(x, y);
4419  RUBY_ASSERT(FIXNUM_P(z));
4420  if (z != INT2FIX(0) && (SIGNED_VALUE)(x ^ y) < 0)
4421  z = fix_minus(z, y);
4422  return z;
4423  }
4424  else if (!RB_BIGNUM_TYPE_P(y)) {
4425  return num_remainder(x, y);
4426  }
4427  x = rb_int2big(FIX2LONG(x));
4428  }
4429  else if (!RB_BIGNUM_TYPE_P(x)) {
4430  return Qnil;
4431  }
4432  return rb_big_remainder(x, y);
4433 }
4434 
4435 static VALUE
4436 fix_divmod(VALUE x, VALUE y)
4437 {
4438  if (FIXNUM_P(y)) {
4439  VALUE div, mod;
4440  if (FIXNUM_ZERO_P(y)) rb_num_zerodiv();
4441  rb_fix_divmod_fix(x, y, &div, &mod);
4442  return rb_assoc_new(div, mod);
4443  }
4444  else if (RB_BIGNUM_TYPE_P(y)) {
4445  x = rb_int2big(FIX2LONG(x));
4446  return rb_big_divmod(x, y);
4447  }
4448  else if (RB_FLOAT_TYPE_P(y)) {
4449  {
4450  double div, mod;
4451  volatile VALUE a, b;
4452 
4453  flodivmod((double)FIX2LONG(x), RFLOAT_VALUE(y), &div, &mod);
4454  a = dbl2ival(div);
4455  b = DBL2NUM(mod);
4456  return rb_assoc_new(a, b);
4457  }
4458  }
4459  else {
4460  return rb_num_coerce_bin(x, y, id_divmod);
4461  }
4462 }
4463 
4464 /*
4465  * call-seq:
4466  * divmod(other) -> array
4467  *
4468  * Returns a 2-element array <tt>[q, r]</tt>, where
4469  *
4470  * q = (self/other).floor # Quotient
4471  * r = self % other # Remainder
4472  *
4473  * Examples:
4474  *
4475  * 11.divmod(4) # => [2, 3]
4476  * 11.divmod(-4) # => [-3, -1]
4477  * -11.divmod(4) # => [-3, 1]
4478  * -11.divmod(-4) # => [2, -3]
4479  *
4480  * 12.divmod(4) # => [3, 0]
4481  * 12.divmod(-4) # => [-3, 0]
4482  * -12.divmod(4) # => [-3, 0]
4483  * -12.divmod(-4) # => [3, 0]
4484  *
4485  * 13.divmod(4.0) # => [3, 1.0]
4486  * 13.divmod(Rational(4, 1)) # => [3, (1/1)]
4487  *
4488  */
4489 VALUE
4490 rb_int_divmod(VALUE x, VALUE y)
4491 {
4492  if (FIXNUM_P(x)) {
4493  return fix_divmod(x, y);
4494  }
4495  else if (RB_BIGNUM_TYPE_P(x)) {
4496  return rb_big_divmod(x, y);
4497  }
4498  return Qnil;
4499 }
4500 
4501 /*
4502  * call-seq:
4503  * self ** numeric -> numeric_result
4504  *
4505  * Raises +self+ to the power of +numeric+:
4506  *
4507  * 2 ** 3 # => 8
4508  * 2 ** -3 # => (1/8)
4509  * -2 ** 3 # => -8
4510  * -2 ** -3 # => (-1/8)
4511  * 2 ** 3.3 # => 9.849155306759329
4512  * 2 ** Rational(3, 1) # => (8/1)
4513  * 2 ** Complex(3, 0) # => (8+0i)
4514  *
4515  */
4516 
4517 static VALUE
4518 int_pow(long x, unsigned long y)
4519 {
4520  int neg = x < 0;
4521  long z = 1;
4522 
4523  if (y == 0) return INT2FIX(1);
4524  if (y == 1) return LONG2NUM(x);
4525  if (neg) x = -x;
4526  if (y & 1)
4527  z = x;
4528  else
4529  neg = 0;
4530  y &= ~1;
4531  do {
4532  while (y % 2 == 0) {
4533  if (!FIT_SQRT_LONG(x)) {
4534  goto bignum;
4535  }
4536  x = x * x;
4537  y >>= 1;
4538  }
4539  {
4540  if (MUL_OVERFLOW_FIXNUM_P(x, z)) {
4541  goto bignum;
4542  }
4543  z = x * z;
4544  }
4545  } while (--y);
4546  if (neg) z = -z;
4547  return LONG2NUM(z);
4548 
4549  VALUE v;
4550  bignum:
4551  v = rb_big_pow(rb_int2big(x), LONG2NUM(y));
4552  if (RB_FLOAT_TYPE_P(v)) /* infinity due to overflow */
4553  return v;
4554  if (z != 1) v = rb_big_mul(rb_int2big(neg ? -z : z), v);
4555  return v;
4556 }
4557 
4558 VALUE
4559 rb_int_positive_pow(long x, unsigned long y)
4560 {
4561  return int_pow(x, y);
4562 }
4563 
4564 static VALUE
4565 fix_pow_inverted(VALUE x, VALUE minusb)
4566 {
4567  if (x == INT2FIX(0)) {
4568  rb_num_zerodiv();
4570  }
4571  else {
4572  VALUE y = rb_int_pow(x, minusb);
4573 
4574  if (RB_FLOAT_TYPE_P(y)) {
4575  double d = pow((double)FIX2LONG(x), RFLOAT_VALUE(y));
4576  return DBL2NUM(1.0 / d);
4577  }
4578  else {
4579  return rb_rational_raw(INT2FIX(1), y);
4580  }
4581  }
4582 }
4583 
4584 static VALUE
4585 fix_pow(VALUE x, VALUE y)
4586 {
4587  long a = FIX2LONG(x);
4588 
4589  if (FIXNUM_P(y)) {
4590  long b = FIX2LONG(y);
4591 
4592  if (a == 1) return INT2FIX(1);
4593  if (a == -1) return INT2FIX(b % 2 ? -1 : 1);
4594  if (b < 0) return fix_pow_inverted(x, fix_uminus(y));
4595  if (b == 0) return INT2FIX(1);
4596  if (b == 1) return x;
4597  if (a == 0) return INT2FIX(0);
4598  return int_pow(a, b);
4599  }
4600  else if (RB_BIGNUM_TYPE_P(y)) {
4601  if (a == 1) return INT2FIX(1);
4602  if (a == -1) return INT2FIX(int_even_p(y) ? 1 : -1);
4603  if (BIGNUM_NEGATIVE_P(y)) return fix_pow_inverted(x, rb_big_uminus(y));
4604  if (a == 0) return INT2FIX(0);
4605  x = rb_int2big(FIX2LONG(x));
4606  return rb_big_pow(x, y);
4607  }
4608  else if (RB_FLOAT_TYPE_P(y)) {
4609  double dy = RFLOAT_VALUE(y);
4610  if (dy == 0.0) return DBL2NUM(1.0);
4611  if (a == 0) {
4612  return DBL2NUM(dy < 0 ? HUGE_VAL : 0.0);
4613  }
4614  if (a == 1) return DBL2NUM(1.0);
4615  if (a < 0 && dy != round(dy))
4616  return rb_dbl_complex_new_polar_pi(pow(-(double)a, dy), dy);
4617  return DBL2NUM(pow((double)a, dy));
4618  }
4619  else {
4620  return rb_num_coerce_bin(x, y, idPow);
4621  }
4622 }
4623 
4624 /*
4625  * call-seq:
4626  * self ** numeric -> numeric_result
4627  *
4628  * Raises +self+ to the power of +numeric+:
4629  *
4630  * 2 ** 3 # => 8
4631  * 2 ** -3 # => (1/8)
4632  * -2 ** 3 # => -8
4633  * -2 ** -3 # => (-1/8)
4634  * 2 ** 3.3 # => 9.849155306759329
4635  * 2 ** Rational(3, 1) # => (8/1)
4636  * 2 ** Complex(3, 0) # => (8+0i)
4637  *
4638  */
4639 VALUE
4640 rb_int_pow(VALUE x, VALUE y)
4641 {
4642  if (FIXNUM_P(x)) {
4643  return fix_pow(x, y);
4644  }
4645  else if (RB_BIGNUM_TYPE_P(x)) {
4646  return rb_big_pow(x, y);
4647  }
4648  return Qnil;
4649 }
4650 
4651 VALUE
4652 rb_num_pow(VALUE x, VALUE y)
4653 {
4654  VALUE z = rb_int_pow(x, y);
4655  if (!NIL_P(z)) return z;
4656  if (RB_FLOAT_TYPE_P(x)) return rb_float_pow(x, y);
4657  if (SPECIAL_CONST_P(x)) return Qnil;
4658  switch (BUILTIN_TYPE(x)) {
4659  case T_COMPLEX:
4660  return rb_complex_pow(x, y);
4661  case T_RATIONAL:
4662  return rb_rational_pow(x, y);
4663  default:
4664  break;
4665  }
4666  return Qnil;
4667 }
4668 
4669 static VALUE
4670 fix_equal(VALUE x, VALUE y)
4671 {
4672  if (x == y) return Qtrue;
4673  if (FIXNUM_P(y)) return Qfalse;
4674  else if (RB_BIGNUM_TYPE_P(y)) {
4675  return rb_big_eq(y, x);
4676  }
4677  else if (RB_FLOAT_TYPE_P(y)) {
4678  return rb_integer_float_eq(x, y);
4679  }
4680  else {
4681  return num_equal(x, y);
4682  }
4683 }
4684 
4685 /*
4686  * call-seq:
4687  * self == other -> true or false
4688  *
4689  * Returns +true+ if +self+ is numerically equal to +other+; +false+ otherwise.
4690  *
4691  * 1 == 2 #=> false
4692  * 1 == 1.0 #=> true
4693  *
4694  * Related: Integer#eql? (requires +other+ to be an \Integer).
4695  */
4696 
4697 VALUE
4698 rb_int_equal(VALUE x, VALUE y)
4699 {
4700  if (FIXNUM_P(x)) {
4701  return fix_equal(x, y);
4702  }
4703  else if (RB_BIGNUM_TYPE_P(x)) {
4704  return rb_big_eq(x, y);
4705  }
4706  return Qnil;
4707 }
4708 
4709 static VALUE
4710 fix_cmp(VALUE x, VALUE y)
4711 {
4712  if (x == y) return INT2FIX(0);
4713  if (FIXNUM_P(y)) {
4714  if (FIX2LONG(x) > FIX2LONG(y)) return INT2FIX(1);
4715  return INT2FIX(-1);
4716  }
4717  else if (RB_BIGNUM_TYPE_P(y)) {
4718  VALUE cmp = rb_big_cmp(y, x);
4719  switch (cmp) {
4720  case INT2FIX(+1): return INT2FIX(-1);
4721  case INT2FIX(-1): return INT2FIX(+1);
4722  }
4723  return cmp;
4724  }
4725  else if (RB_FLOAT_TYPE_P(y)) {
4726  return rb_integer_float_cmp(x, y);
4727  }
4728  else {
4729  return rb_num_coerce_cmp(x, y, id_cmp);
4730  }
4731 }
4732 
4733 /*
4734  * call-seq:
4735  * self <=> other -> -1, 0, +1, or nil
4736  *
4737  * Returns:
4738  *
4739  * - -1, if +self+ is less than +other+.
4740  * - 0, if +self+ is equal to +other+.
4741  * - 1, if +self+ is greater then +other+.
4742  * - +nil+, if +self+ and +other+ are incomparable.
4743  *
4744  * Examples:
4745  *
4746  * 1 <=> 2 # => -1
4747  * 1 <=> 1 # => 0
4748  * 1 <=> 0 # => 1
4749  * 1 <=> 'foo' # => nil
4750  *
4751  * 1 <=> 1.0 # => 0
4752  * 1 <=> Rational(1, 1) # => 0
4753  * 1 <=> Complex(1, 0) # => 0
4754  *
4755  * This method is the basis for comparisons in module Comparable.
4756  *
4757  */
4758 
4759 VALUE
4760 rb_int_cmp(VALUE x, VALUE y)
4761 {
4762  if (FIXNUM_P(x)) {
4763  return fix_cmp(x, y);
4764  }
4765  else if (RB_BIGNUM_TYPE_P(x)) {
4766  return rb_big_cmp(x, y);
4767  }
4768  else {
4769  rb_raise(rb_eNotImpError, "need to define '<=>' in %s", rb_obj_classname(x));
4770  }
4771 }
4772 
4773 static VALUE
4774 fix_gt(VALUE x, VALUE y)
4775 {
4776  if (FIXNUM_P(y)) {
4777  return RBOOL(FIX2LONG(x) > FIX2LONG(y));
4778  }
4779  else if (RB_BIGNUM_TYPE_P(y)) {
4780  return RBOOL(rb_big_cmp(y, x) == INT2FIX(-1));
4781  }
4782  else if (RB_FLOAT_TYPE_P(y)) {
4783  return RBOOL(rb_integer_float_cmp(x, y) == INT2FIX(1));
4784  }
4785  else {
4786  return rb_num_coerce_relop(x, y, '>');
4787  }
4788 }
4789 
4790 /*
4791  * call-seq:
4792  * self > other -> true or false
4793  *
4794  * Returns +true+ if the value of +self+ is greater than that of +other+:
4795  *
4796  * 1 > 0 # => true
4797  * 1 > 1 # => false
4798  * 1 > 2 # => false
4799  * 1 > 0.5 # => true
4800  * 1 > Rational(1, 2) # => true
4801  *
4802  * Raises an exception if the comparison cannot be made.
4803  *
4804  */
4805 
4806 VALUE
4807 rb_int_gt(VALUE x, VALUE y)
4808 {
4809  if (FIXNUM_P(x)) {
4810  return fix_gt(x, y);
4811  }
4812  else if (RB_BIGNUM_TYPE_P(x)) {
4813  return rb_big_gt(x, y);
4814  }
4815  return Qnil;
4816 }
4817 
4818 static VALUE
4819 fix_ge(VALUE x, VALUE y)
4820 {
4821  if (FIXNUM_P(y)) {
4822  return RBOOL(FIX2LONG(x) >= FIX2LONG(y));
4823  }
4824  else if (RB_BIGNUM_TYPE_P(y)) {
4825  return RBOOL(rb_big_cmp(y, x) != INT2FIX(+1));
4826  }
4827  else if (RB_FLOAT_TYPE_P(y)) {
4828  VALUE rel = rb_integer_float_cmp(x, y);
4829  return RBOOL(rel == INT2FIX(1) || rel == INT2FIX(0));
4830  }
4831  else {
4832  return rb_num_coerce_relop(x, y, idGE);
4833  }
4834 }
4835 
4836 /*
4837  * call-seq:
4838  * self >= real -> true or false
4839  *
4840  * Returns +true+ if the value of +self+ is greater than or equal to
4841  * that of +other+:
4842  *
4843  * 1 >= 0 # => true
4844  * 1 >= 1 # => true
4845  * 1 >= 2 # => false
4846  * 1 >= 0.5 # => true
4847  * 1 >= Rational(1, 2) # => true
4848  *
4849  * Raises an exception if the comparison cannot be made.
4850  *
4851  */
4852 
4853 VALUE
4854 rb_int_ge(VALUE x, VALUE y)
4855 {
4856  if (FIXNUM_P(x)) {
4857  return fix_ge(x, y);
4858  }
4859  else if (RB_BIGNUM_TYPE_P(x)) {
4860  return rb_big_ge(x, y);
4861  }
4862  return Qnil;
4863 }
4864 
4865 static VALUE
4866 fix_lt(VALUE x, VALUE y)
4867 {
4868  if (FIXNUM_P(y)) {
4869  return RBOOL(FIX2LONG(x) < FIX2LONG(y));
4870  }
4871  else if (RB_BIGNUM_TYPE_P(y)) {
4872  return RBOOL(rb_big_cmp(y, x) == INT2FIX(+1));
4873  }
4874  else if (RB_FLOAT_TYPE_P(y)) {
4875  return RBOOL(rb_integer_float_cmp(x, y) == INT2FIX(-1));
4876  }
4877  else {
4878  return rb_num_coerce_relop(x, y, '<');
4879  }
4880 }
4881 
4882 /*
4883  * call-seq:
4884  * self < other -> true or false
4885  *
4886  * Returns +true+ if the value of +self+ is less than that of +other+:
4887  *
4888  * 1 < 0 # => false
4889  * 1 < 1 # => false
4890  * 1 < 2 # => true
4891  * 1 < 0.5 # => false
4892  * 1 < Rational(1, 2) # => false
4893  *
4894  * Raises an exception if the comparison cannot be made.
4895  *
4896  */
4897 
4898 static VALUE
4899 int_lt(VALUE x, VALUE y)
4900 {
4901  if (FIXNUM_P(x)) {
4902  return fix_lt(x, y);
4903  }
4904  else if (RB_BIGNUM_TYPE_P(x)) {
4905  return rb_big_lt(x, y);
4906  }
4907  return Qnil;
4908 }
4909 
4910 static VALUE
4911 fix_le(VALUE x, VALUE y)
4912 {
4913  if (FIXNUM_P(y)) {
4914  return RBOOL(FIX2LONG(x) <= FIX2LONG(y));
4915  }
4916  else if (RB_BIGNUM_TYPE_P(y)) {
4917  return RBOOL(rb_big_cmp(y, x) != INT2FIX(-1));
4918  }
4919  else if (RB_FLOAT_TYPE_P(y)) {
4920  VALUE rel = rb_integer_float_cmp(x, y);
4921  return RBOOL(rel == INT2FIX(-1) || rel == INT2FIX(0));
4922  }
4923  else {
4924  return rb_num_coerce_relop(x, y, idLE);
4925  }
4926 }
4927 
4928 /*
4929  * call-seq:
4930  * self <= real -> true or false
4931  *
4932  * Returns +true+ if the value of +self+ is less than or equal to
4933  * that of +other+:
4934  *
4935  * 1 <= 0 # => false
4936  * 1 <= 1 # => true
4937  * 1 <= 2 # => true
4938  * 1 <= 0.5 # => false
4939  * 1 <= Rational(1, 2) # => false
4940  *
4941  * Raises an exception if the comparison cannot be made.
4942  *
4943  */
4944 
4945 static VALUE
4946 int_le(VALUE x, VALUE y)
4947 {
4948  if (FIXNUM_P(x)) {
4949  return fix_le(x, y);
4950  }
4951  else if (RB_BIGNUM_TYPE_P(x)) {
4952  return rb_big_le(x, y);
4953  }
4954  return Qnil;
4955 }
4956 
4957 static VALUE
4958 fix_comp(VALUE num)
4959 {
4960  return ~num | FIXNUM_FLAG;
4961 }
4962 
4963 VALUE
4964 rb_int_comp(VALUE num)
4965 {
4966  if (FIXNUM_P(num)) {
4967  return fix_comp(num);
4968  }
4969  else if (RB_BIGNUM_TYPE_P(num)) {
4970  return rb_big_comp(num);
4971  }
4972  return Qnil;
4973 }
4974 
4975 static VALUE
4976 num_funcall_bit_1(VALUE y, VALUE arg, int recursive)
4977 {
4978  ID func = (ID)((VALUE *)arg)[0];
4979  VALUE x = ((VALUE *)arg)[1];
4980  if (recursive) {
4981  num_funcall_op_1_recursion(x, func, y);
4982  }
4983  return rb_check_funcall(x, func, 1, &y);
4984 }
4985 
4986 VALUE
4988 {
4989  VALUE ret, args[3];
4990 
4991  args[0] = (VALUE)func;
4992  args[1] = x;
4993  args[2] = y;
4994  do_coerce(&args[1], &args[2], TRUE);
4995  ret = rb_exec_recursive_paired(num_funcall_bit_1,
4996  args[2], args[1], (VALUE)args);
4997  if (UNDEF_P(ret)) {
4998  /* show the original object, not coerced object */
4999  coerce_failed(x, y);
5000  }
5001  return ret;
5002 }
5003 
5004 static VALUE
5005 fix_and(VALUE x, VALUE y)
5006 {
5007  if (FIXNUM_P(y)) {
5008  long val = FIX2LONG(x) & FIX2LONG(y);
5009  return LONG2NUM(val);
5010  }
5011 
5012  if (RB_BIGNUM_TYPE_P(y)) {
5013  return rb_big_and(y, x);
5014  }
5015 
5016  return rb_num_coerce_bit(x, y, '&');
5017 }
5018 
5019 /*
5020  * call-seq:
5021  * self & other -> integer
5022  *
5023  * Bitwise AND; each bit in the result is 1 if both corresponding bits
5024  * in +self+ and +other+ are 1, 0 otherwise:
5025  *
5026  * "%04b" % (0b0101 & 0b0110) # => "0100"
5027  *
5028  * Raises an exception if +other+ is not an \Integer.
5029  *
5030  * Related: Integer#| (bitwise OR), Integer#^ (bitwise EXCLUSIVE OR).
5031  *
5032  */
5033 
5034 VALUE
5035 rb_int_and(VALUE x, VALUE y)
5036 {
5037  if (FIXNUM_P(x)) {
5038  return fix_and(x, y);
5039  }
5040  else if (RB_BIGNUM_TYPE_P(x)) {
5041  return rb_big_and(x, y);
5042  }
5043  return Qnil;
5044 }
5045 
5046 static VALUE
5047 fix_or(VALUE x, VALUE y)
5048 {
5049  if (FIXNUM_P(y)) {
5050  long val = FIX2LONG(x) | FIX2LONG(y);
5051  return LONG2NUM(val);
5052  }
5053 
5054  if (RB_BIGNUM_TYPE_P(y)) {
5055  return rb_big_or(y, x);
5056  }
5057 
5058  return rb_num_coerce_bit(x, y, '|');
5059 }
5060 
5061 /*
5062  * call-seq:
5063  * self | other -> integer
5064  *
5065  * Bitwise OR; each bit in the result is 1 if either corresponding bit
5066  * in +self+ or +other+ is 1, 0 otherwise:
5067  *
5068  * "%04b" % (0b0101 | 0b0110) # => "0111"
5069  *
5070  * Raises an exception if +other+ is not an \Integer.
5071  *
5072  * Related: Integer#& (bitwise AND), Integer#^ (bitwise EXCLUSIVE OR).
5073  *
5074  */
5075 
5076 static VALUE
5077 int_or(VALUE x, VALUE y)
5078 {
5079  if (FIXNUM_P(x)) {
5080  return fix_or(x, y);
5081  }
5082  else if (RB_BIGNUM_TYPE_P(x)) {
5083  return rb_big_or(x, y);
5084  }
5085  return Qnil;
5086 }
5087 
5088 static VALUE
5089 fix_xor(VALUE x, VALUE y)
5090 {
5091  if (FIXNUM_P(y)) {
5092  long val = FIX2LONG(x) ^ FIX2LONG(y);
5093  return LONG2NUM(val);
5094  }
5095 
5096  if (RB_BIGNUM_TYPE_P(y)) {
5097  return rb_big_xor(y, x);
5098  }
5099 
5100  return rb_num_coerce_bit(x, y, '^');
5101 }
5102 
5103 /*
5104  * call-seq:
5105  * self ^ other -> integer
5106  *
5107  * Bitwise EXCLUSIVE OR; each bit in the result is 1 if the corresponding bits
5108  * in +self+ and +other+ are different, 0 otherwise:
5109  *
5110  * "%04b" % (0b0101 ^ 0b0110) # => "0011"
5111  *
5112  * Raises an exception if +other+ is not an \Integer.
5113  *
5114  * Related: Integer#& (bitwise AND), Integer#| (bitwise OR).
5115  *
5116  */
5117 
5118 static VALUE
5119 int_xor(VALUE x, VALUE y)
5120 {
5121  if (FIXNUM_P(x)) {
5122  return fix_xor(x, y);
5123  }
5124  else if (RB_BIGNUM_TYPE_P(x)) {
5125  return rb_big_xor(x, y);
5126  }
5127  return Qnil;
5128 }
5129 
5130 static VALUE
5131 rb_fix_lshift(VALUE x, VALUE y)
5132 {
5133  long val, width;
5134 
5135  val = NUM2LONG(x);
5136  if (!val) return (rb_to_int(y), INT2FIX(0));
5137  if (!FIXNUM_P(y))
5138  return rb_big_lshift(rb_int2big(val), y);
5139  width = FIX2LONG(y);
5140  if (width < 0)
5141  return fix_rshift(val, (unsigned long)-width);
5142  return fix_lshift(val, width);
5143 }
5144 
5145 static VALUE
5146 fix_lshift(long val, unsigned long width)
5147 {
5148  if (width > (SIZEOF_LONG*CHAR_BIT-1)
5149  || ((unsigned long)val)>>(SIZEOF_LONG*CHAR_BIT-1-width) > 0) {
5150  return rb_big_lshift(rb_int2big(val), ULONG2NUM(width));
5151  }
5152  val = val << width;
5153  return LONG2NUM(val);
5154 }
5155 
5156 /*
5157  * call-seq:
5158  * self << count -> integer
5159  *
5160  * Returns +self+ with bits shifted +count+ positions to the left,
5161  * or to the right if +count+ is negative:
5162  *
5163  * n = 0b11110000
5164  * "%08b" % (n << 1) # => "111100000"
5165  * "%08b" % (n << 3) # => "11110000000"
5166  * "%08b" % (n << -1) # => "01111000"
5167  * "%08b" % (n << -3) # => "00011110"
5168  *
5169  * Related: Integer#>>.
5170  *
5171  */
5172 
5173 VALUE
5174 rb_int_lshift(VALUE x, VALUE y)
5175 {
5176  if (FIXNUM_P(x)) {
5177  return rb_fix_lshift(x, y);
5178  }
5179  else if (RB_BIGNUM_TYPE_P(x)) {
5180  return rb_big_lshift(x, y);
5181  }
5182  return Qnil;
5183 }
5184 
5185 static VALUE
5186 rb_fix_rshift(VALUE x, VALUE y)
5187 {
5188  long i, val;
5189 
5190  val = FIX2LONG(x);
5191  if (!val) return (rb_to_int(y), INT2FIX(0));
5192  if (!FIXNUM_P(y))
5193  return rb_big_rshift(rb_int2big(val), y);
5194  i = FIX2LONG(y);
5195  if (i == 0) return x;
5196  if (i < 0)
5197  return fix_lshift(val, (unsigned long)-i);
5198  return fix_rshift(val, i);
5199 }
5200 
5201 static VALUE
5202 fix_rshift(long val, unsigned long i)
5203 {
5204  if (i >= sizeof(long)*CHAR_BIT-1) {
5205  if (val < 0) return INT2FIX(-1);
5206  return INT2FIX(0);
5207  }
5208  val = RSHIFT(val, i);
5209  return LONG2FIX(val);
5210 }
5211 
5212 /*
5213  * call-seq:
5214  * self >> count -> integer
5215  *
5216  * Returns +self+ with bits shifted +count+ positions to the right,
5217  * or to the left if +count+ is negative:
5218  *
5219  * n = 0b11110000
5220  * "%08b" % (n >> 1) # => "01111000"
5221  * "%08b" % (n >> 3) # => "00011110"
5222  * "%08b" % (n >> -1) # => "111100000"
5223  * "%08b" % (n >> -3) # => "11110000000"
5224  *
5225  * Related: Integer#<<.
5226  *
5227  */
5228 
5229 VALUE
5230 rb_int_rshift(VALUE x, VALUE y)
5231 {
5232  if (FIXNUM_P(x)) {
5233  return rb_fix_rshift(x, y);
5234  }
5235  else if (RB_BIGNUM_TYPE_P(x)) {
5236  return rb_big_rshift(x, y);
5237  }
5238  return Qnil;
5239 }
5240 
5241 VALUE
5242 rb_fix_aref(VALUE fix, VALUE idx)
5243 {
5244  long val = FIX2LONG(fix);
5245  long i;
5246 
5247  idx = rb_to_int(idx);
5248  if (!FIXNUM_P(idx)) {
5249  idx = rb_big_norm(idx);
5250  if (!FIXNUM_P(idx)) {
5251  if (!BIGNUM_SIGN(idx) || val >= 0)
5252  return INT2FIX(0);
5253  return INT2FIX(1);
5254  }
5255  }
5256  i = FIX2LONG(idx);
5257 
5258  if (i < 0) return INT2FIX(0);
5259  if (SIZEOF_LONG*CHAR_BIT-1 <= i) {
5260  if (val < 0) return INT2FIX(1);
5261  return INT2FIX(0);
5262  }
5263  if (val & (1L<<i))
5264  return INT2FIX(1);
5265  return INT2FIX(0);
5266 }
5267 
5268 
5269 /* copied from "r_less" in range.c */
5270 /* compares _a_ and _b_ and returns:
5271  * < 0: a < b
5272  * = 0: a = b
5273  * > 0: a > b or non-comparable
5274  */
5275 static int
5276 compare_indexes(VALUE a, VALUE b)
5277 {
5278  VALUE r = rb_funcall(a, id_cmp, 1, b);
5279 
5280  if (NIL_P(r))
5281  return INT_MAX;
5282  return rb_cmpint(r, a, b);
5283 }
5284 
5285 static VALUE
5286 generate_mask(VALUE len)
5287 {
5288  return rb_int_minus(rb_int_lshift(INT2FIX(1), len), INT2FIX(1));
5289 }
5290 
5291 static VALUE
5292 int_aref1(VALUE num, VALUE arg)
5293 {
5294  VALUE orig_num = num, beg, end;
5295  int excl;
5296 
5297  if (rb_range_values(arg, &beg, &end, &excl)) {
5298  if (NIL_P(beg)) {
5299  /* beginless range */
5300  if (!RTEST(num_negative_p(end))) {
5301  if (!excl) end = rb_int_plus(end, INT2FIX(1));
5302  VALUE mask = generate_mask(end);
5303  if (int_zero_p(rb_int_and(num, mask))) {
5304  return INT2FIX(0);
5305  }
5306  else {
5307  rb_raise(rb_eArgError, "The beginless range for Integer#[] results in infinity");
5308  }
5309  }
5310  else {
5311  return INT2FIX(0);
5312  }
5313  }
5314  num = rb_int_rshift(num, beg);
5315 
5316  int cmp = compare_indexes(beg, end);
5317  if (!NIL_P(end) && cmp < 0) {
5318  VALUE len = rb_int_minus(end, beg);
5319  if (!excl) len = rb_int_plus(len, INT2FIX(1));
5320  VALUE mask = generate_mask(len);
5321  num = rb_int_and(num, mask);
5322  }
5323  else if (cmp == 0) {
5324  if (excl) return INT2FIX(0);
5325  num = orig_num;
5326  arg = beg;
5327  goto one_bit;
5328  }
5329  return num;
5330  }
5331 
5332 one_bit:
5333  if (FIXNUM_P(num)) {
5334  return rb_fix_aref(num, arg);
5335  }
5336  else if (RB_BIGNUM_TYPE_P(num)) {
5337  return rb_big_aref(num, arg);
5338  }
5339  return Qnil;
5340 }
5341 
5342 static VALUE
5343 int_aref2(VALUE num, VALUE beg, VALUE len)
5344 {
5345  num = rb_int_rshift(num, beg);
5346  VALUE mask = generate_mask(len);
5347  num = rb_int_and(num, mask);
5348  return num;
5349 }
5350 
5351 /*
5352  * call-seq:
5353  * self[offset] -> 0 or 1
5354  * self[offset, size] -> integer
5355  * self[range] -> integer
5356  *
5357  * Returns a slice of bits from +self+.
5358  *
5359  * With argument +offset+, returns the bit at the given offset,
5360  * where offset 0 refers to the least significant bit:
5361  *
5362  * n = 0b10 # => 2
5363  * n[0] # => 0
5364  * n[1] # => 1
5365  * n[2] # => 0
5366  * n[3] # => 0
5367  *
5368  * In principle, <code>n[i]</code> is equivalent to <code>(n >> i) & 1</code>.
5369  * Thus, negative index always returns zero:
5370  *
5371  * 255[-1] # => 0
5372  *
5373  * With arguments +offset+ and +size+, returns +size+ bits from +self+,
5374  * beginning at +offset+ and including bits of greater significance:
5375  *
5376  * n = 0b111000 # => 56
5377  * "%010b" % n[0, 10] # => "0000111000"
5378  * "%010b" % n[4, 10] # => "0000000011"
5379  *
5380  * With argument +range+, returns <tt>range.size</tt> bits from +self+,
5381  * beginning at <tt>range.begin</tt> and including bits of greater significance:
5382  *
5383  * n = 0b111000 # => 56
5384  * "%010b" % n[0..9] # => "0000111000"
5385  * "%010b" % n[4..9] # => "0000000011"
5386  *
5387  * Raises an exception if the slice cannot be constructed.
5388  */
5389 
5390 static VALUE
5391 int_aref(int const argc, VALUE * const argv, VALUE const num)
5392 {
5393  rb_check_arity(argc, 1, 2);
5394  if (argc == 2) {
5395  return int_aref2(num, argv[0], argv[1]);
5396  }
5397  return int_aref1(num, argv[0]);
5398 
5399  return Qnil;
5400 }
5401 
5402 /*
5403  * call-seq:
5404  * to_f -> float
5405  *
5406  * Converts +self+ to a Float:
5407  *
5408  * 1.to_f # => 1.0
5409  * -1.to_f # => -1.0
5410  *
5411  * If the value of +self+ does not fit in a Float,
5412  * the result is infinity:
5413  *
5414  * (10**400).to_f # => Infinity
5415  * (-10**400).to_f # => -Infinity
5416  *
5417  */
5418 
5419 static VALUE
5420 int_to_f(VALUE num)
5421 {
5422  double val;
5423 
5424  if (FIXNUM_P(num)) {
5425  val = (double)FIX2LONG(num);
5426  }
5427  else if (RB_BIGNUM_TYPE_P(num)) {
5428  val = rb_big2dbl(num);
5429  }
5430  else {
5431  rb_raise(rb_eNotImpError, "Unknown subclass for to_f: %s", rb_obj_classname(num));
5432  }
5433 
5434  return DBL2NUM(val);
5435 }
5436 
5437 static VALUE
5438 fix_abs(VALUE fix)
5439 {
5440  long i = FIX2LONG(fix);
5441 
5442  if (i < 0) i = -i;
5443 
5444  return LONG2NUM(i);
5445 }
5446 
5447 VALUE
5448 rb_int_abs(VALUE num)
5449 {
5450  if (FIXNUM_P(num)) {
5451  return fix_abs(num);
5452  }
5453  else if (RB_BIGNUM_TYPE_P(num)) {
5454  return rb_big_abs(num);
5455  }
5456  return Qnil;
5457 }
5458 
5459 static VALUE
5460 fix_size(VALUE fix)
5461 {
5462  return INT2FIX(sizeof(long));
5463 }
5464 
5465 VALUE
5466 rb_int_size(VALUE num)
5467 {
5468  if (FIXNUM_P(num)) {
5469  return fix_size(num);
5470  }
5471  else if (RB_BIGNUM_TYPE_P(num)) {
5472  return rb_big_size_m(num);
5473  }
5474  return Qnil;
5475 }
5476 
5477 static VALUE
5478 rb_fix_bit_length(VALUE fix)
5479 {
5480  long v = FIX2LONG(fix);
5481  if (v < 0)
5482  v = ~v;
5483  return LONG2FIX(bit_length(v));
5484 }
5485 
5486 VALUE
5487 rb_int_bit_length(VALUE num)
5488 {
5489  if (FIXNUM_P(num)) {
5490  return rb_fix_bit_length(num);
5491  }
5492  else if (RB_BIGNUM_TYPE_P(num)) {
5493  return rb_big_bit_length(num);
5494  }
5495  return Qnil;
5496 }
5497 
5498 static VALUE
5499 rb_fix_digits(VALUE fix, long base)
5500 {
5501  VALUE digits;
5502  long x = FIX2LONG(fix);
5503 
5504  RUBY_ASSERT(x >= 0);
5505 
5506  if (base < 2)
5507  rb_raise(rb_eArgError, "invalid radix %ld", base);
5508 
5509  if (x == 0)
5510  return rb_ary_new_from_args(1, INT2FIX(0));
5511 
5512  digits = rb_ary_new();
5513  while (x >= base) {
5514  long q = x % base;
5515  rb_ary_push(digits, LONG2NUM(q));
5516  x /= base;
5517  }
5518  rb_ary_push(digits, LONG2NUM(x));
5519 
5520  return digits;
5521 }
5522 
5523 static VALUE
5524 rb_int_digits_bigbase(VALUE num, VALUE base)
5525 {
5526  VALUE digits, bases;
5527 
5528  RUBY_ASSERT(!rb_num_negative_p(num));
5529 
5530  if (RB_BIGNUM_TYPE_P(base))
5531  base = rb_big_norm(base);
5532 
5533  if (FIXNUM_P(base) && FIX2LONG(base) < 2)
5534  rb_raise(rb_eArgError, "invalid radix %ld", FIX2LONG(base));
5535  else if (RB_BIGNUM_TYPE_P(base) && BIGNUM_NEGATIVE_P(base))
5536  rb_raise(rb_eArgError, "negative radix");
5537 
5538  if (FIXNUM_P(base) && FIXNUM_P(num))
5539  return rb_fix_digits(num, FIX2LONG(base));
5540 
5541  if (FIXNUM_P(num))
5542  return rb_ary_new_from_args(1, num);
5543 
5544  if (int_lt(rb_int_div(rb_int_bit_length(num), rb_int_bit_length(base)), INT2FIX(50))) {
5545  digits = rb_ary_new();
5546  while (!FIXNUM_P(num) || FIX2LONG(num) > 0) {
5547  VALUE qr = rb_int_divmod(num, base);
5548  rb_ary_push(digits, RARRAY_AREF(qr, 1));
5549  num = RARRAY_AREF(qr, 0);
5550  }
5551  return digits;
5552  }
5553 
5554  bases = rb_ary_new();
5555  for (VALUE b = base; int_lt(b, num) == Qtrue; b = rb_int_mul(b, b)) {
5556  rb_ary_push(bases, b);
5557  }
5558  digits = rb_ary_new_from_args(1, num);
5559  while (RARRAY_LEN(bases)) {
5560  VALUE b = rb_ary_pop(bases);
5561  long i, last_idx = RARRAY_LEN(digits) - 1;
5562  for(i = last_idx; i >= 0; i--) {
5563  VALUE n = RARRAY_AREF(digits, i);
5564  VALUE divmod = rb_int_divmod(n, b);
5565  VALUE div = RARRAY_AREF(divmod, 0);
5566  VALUE mod = RARRAY_AREF(divmod, 1);
5567  if (i != last_idx || div != INT2FIX(0)) rb_ary_store(digits, 2 * i + 1, div);
5568  rb_ary_store(digits, 2 * i, mod);
5569  }
5570  }
5571 
5572  return digits;
5573 }
5574 
5575 /*
5576  * call-seq:
5577  * digits(base = 10) -> array_of_integers
5578  *
5579  * Returns an array of integers representing the +base+-radix
5580  * digits of +self+;
5581  * the first element of the array represents the least significant digit:
5582  *
5583  * 12345.digits # => [5, 4, 3, 2, 1]
5584  * 12345.digits(7) # => [4, 6, 6, 0, 5]
5585  * 12345.digits(100) # => [45, 23, 1]
5586  *
5587  * Raises an exception if +self+ is negative or +base+ is less than 2.
5588  *
5589  */
5590 
5591 static VALUE
5592 rb_int_digits(int argc, VALUE *argv, VALUE num)
5593 {
5594  VALUE base_value;
5595  long base;
5596 
5597  if (rb_num_negative_p(num))
5598  rb_raise(rb_eMathDomainError, "out of domain");
5599 
5600  if (rb_check_arity(argc, 0, 1)) {
5601  base_value = rb_to_int(argv[0]);
5602  if (!RB_INTEGER_TYPE_P(base_value))
5603  rb_raise(rb_eTypeError, "wrong argument type %s (expected Integer)",
5604  rb_obj_classname(argv[0]));
5605  if (RB_BIGNUM_TYPE_P(base_value))
5606  return rb_int_digits_bigbase(num, base_value);
5607 
5608  base = FIX2LONG(base_value);
5609  if (base < 0)
5610  rb_raise(rb_eArgError, "negative radix");
5611  else if (base < 2)
5612  rb_raise(rb_eArgError, "invalid radix %ld", base);
5613  }
5614  else
5615  base = 10;
5616 
5617  if (FIXNUM_P(num))
5618  return rb_fix_digits(num, base);
5619  else if (RB_BIGNUM_TYPE_P(num))
5620  return rb_int_digits_bigbase(num, LONG2FIX(base));
5621 
5622  return Qnil;
5623 }
5624 
5625 static VALUE
5626 int_upto_size(VALUE from, VALUE args, VALUE eobj)
5627 {
5628  return ruby_num_interval_step_size(from, RARRAY_AREF(args, 0), INT2FIX(1), FALSE);
5629 }
5630 
5631 /*
5632  * call-seq:
5633  * upto(limit) {|i| ... } -> self
5634  * upto(limit) -> enumerator
5635  *
5636  * Calls the given block with each integer value from +self+ up to +limit+;
5637  * returns +self+:
5638  *
5639  * a = []
5640  * 5.upto(10) {|i| a << i } # => 5
5641  * a # => [5, 6, 7, 8, 9, 10]
5642  * a = []
5643  * -5.upto(0) {|i| a << i } # => -5
5644  * a # => [-5, -4, -3, -2, -1, 0]
5645  * 5.upto(4) {|i| fail 'Cannot happen' } # => 5
5646  *
5647  * With no block given, returns an Enumerator.
5648  *
5649  */
5650 
5651 static VALUE
5652 int_upto(VALUE from, VALUE to)
5653 {
5654  RETURN_SIZED_ENUMERATOR(from, 1, &to, int_upto_size);
5655  if (FIXNUM_P(from) && FIXNUM_P(to)) {
5656  long i, end;
5657 
5658  end = FIX2LONG(to);
5659  for (i = FIX2LONG(from); i <= end; i++) {
5660  rb_yield(LONG2FIX(i));
5661  }
5662  }
5663  else {
5664  VALUE i = from, c;
5665 
5666  while (!(c = rb_funcall(i, '>', 1, to))) {
5667  rb_yield(i);
5668  i = rb_funcall(i, '+', 1, INT2FIX(1));
5669  }
5670  ensure_cmp(c, i, to);
5671  }
5672  return from;
5673 }
5674 
5675 static VALUE
5676 int_downto_size(VALUE from, VALUE args, VALUE eobj)
5677 {
5678  return ruby_num_interval_step_size(from, RARRAY_AREF(args, 0), INT2FIX(-1), FALSE);
5679 }
5680 
5681 /*
5682  * call-seq:
5683  * downto(limit) {|i| ... } -> self
5684  * downto(limit) -> enumerator
5685  *
5686  * Calls the given block with each integer value from +self+ down to +limit+;
5687  * returns +self+:
5688  *
5689  * a = []
5690  * 10.downto(5) {|i| a << i } # => 10
5691  * a # => [10, 9, 8, 7, 6, 5]
5692  * a = []
5693  * 0.downto(-5) {|i| a << i } # => 0
5694  * a # => [0, -1, -2, -3, -4, -5]
5695  * 4.downto(5) {|i| fail 'Cannot happen' } # => 4
5696  *
5697  * With no block given, returns an Enumerator.
5698  *
5699  */
5700 
5701 static VALUE
5702 int_downto(VALUE from, VALUE to)
5703 {
5704  RETURN_SIZED_ENUMERATOR(from, 1, &to, int_downto_size);
5705  if (FIXNUM_P(from) && FIXNUM_P(to)) {
5706  long i, end;
5707 
5708  end = FIX2LONG(to);
5709  for (i=FIX2LONG(from); i >= end; i--) {
5710  rb_yield(LONG2FIX(i));
5711  }
5712  }
5713  else {
5714  VALUE i = from, c;
5715 
5716  while (!(c = rb_funcall(i, '<', 1, to))) {
5717  rb_yield(i);
5718  i = rb_funcall(i, '-', 1, INT2FIX(1));
5719  }
5720  if (NIL_P(c)) rb_cmperr(i, to);
5721  }
5722  return from;
5723 }
5724 
5725 static VALUE
5726 int_dotimes_size(VALUE num, VALUE args, VALUE eobj)
5727 {
5728  return int_neg_p(num) ? INT2FIX(0) : num;
5729 }
5730 
5731 /*
5732  * call-seq:
5733  * round(ndigits= 0, half: :up) -> integer
5734  *
5735  * Returns +self+ rounded to the nearest value with
5736  * a precision of +ndigits+ decimal digits.
5737  *
5738  * When +ndigits+ is negative, the returned value
5739  * has at least <tt>ndigits.abs</tt> trailing zeros:
5740  *
5741  * 555.round(-1) # => 560
5742  * 555.round(-2) # => 600
5743  * 555.round(-3) # => 1000
5744  * -555.round(-2) # => -600
5745  * 555.round(-4) # => 0
5746  *
5747  * Returns +self+ when +ndigits+ is zero or positive.
5748  *
5749  * 555.round # => 555
5750  * 555.round(1) # => 555
5751  * 555.round(50) # => 555
5752  *
5753  * If keyword argument +half+ is given,
5754  * and +self+ is equidistant from the two candidate values,
5755  * the rounding is according to the given +half+ value:
5756  *
5757  * - +:up+ or +nil+: round away from zero:
5758  *
5759  * 25.round(-1, half: :up) # => 30
5760  * (-25).round(-1, half: :up) # => -30
5761  *
5762  * - +:down+: round toward zero:
5763  *
5764  * 25.round(-1, half: :down) # => 20
5765  * (-25).round(-1, half: :down) # => -20
5766  *
5767  *
5768  * - +:even+: round toward the candidate whose last nonzero digit is even:
5769  *
5770  * 25.round(-1, half: :even) # => 20
5771  * 15.round(-1, half: :even) # => 20
5772  * (-25).round(-1, half: :even) # => -20
5773  *
5774  * Raises and exception if the value for +half+ is invalid.
5775  *
5776  * Related: Integer#truncate.
5777  *
5778  */
5779 
5780 static VALUE
5781 int_round(int argc, VALUE* argv, VALUE num)
5782 {
5783  int ndigits;
5784  int mode;
5785  VALUE nd, opt;
5786 
5787  if (!rb_scan_args(argc, argv, "01:", &nd, &opt)) return num;
5788  ndigits = NUM2INT(nd);
5789  mode = rb_num_get_rounding_option(opt);
5790  if (ndigits >= 0) {
5791  return num;
5792  }
5793  return rb_int_round(num, ndigits, mode);
5794 }
5795 
5796 /*
5797  * :markup: markdown
5798  *
5799  * call-seq:
5800  * floor(ndigits = 0) -> integer
5801  *
5802  * Returns an integer that is a "floor" value for `self`,
5803  * as specified by the given `ndigits`,
5804  * which must be an
5805  * [integer-convertible object](rdoc-ref:implicit_conversion.rdoc@Integer-Convertible+Objects).
5806  *
5807  * - When `self` is zero, returns zero (regardless of the value of `ndigits`):
5808  *
5809  * ```
5810  * 0.floor(2) # => 0
5811  * 0.floor(-2) # => 0
5812  * ```
5813  *
5814  * - When `self` is non-zero and `ndigits` is non-negative, returns `self`:
5815  *
5816  * ```
5817  * 555.floor # => 555
5818  * 555.floor(50) # => 555
5819  * ```
5820  *
5821  * - When `self` is non-zero and `ndigits` is negative,
5822  * returns a value based on a computed granularity:
5823  *
5824  * - The granularity is `10 ** ndigits.abs`.
5825  * - The returned value is the largest multiple of the granularity
5826  * that is less than or equal to `self`.
5827  *
5828  * Examples with positive `self`:
5829  *
5830  * | ndigits | Granularity | 1234.floor(ndigits) |
5831  * |--------:|------------:|--------------------:|
5832  * | -1 | 10 | 1230 |
5833  * | -2 | 100 | 1200 |
5834  * | -3 | 1000 | 1000 |
5835  * | -4 | 10000 | 0 |
5836  * | -5 | 100000 | 0 |
5837  *
5838  * Examples with negative `self`:
5839  *
5840  * | ndigits | Granularity | -1234.floor(ndigits) |
5841  * |--------:|------------:|---------------------:|
5842  * | -1 | 10 | -1240 |
5843  * | -2 | 100 | -1300 |
5844  * | -3 | 1000 | -2000 |
5845  * | -4 | 10000 | -10000 |
5846  * | -5 | 100000 | -100000 |
5847  *
5848  * Related: Integer#ceil.
5849  *
5850  */
5851 
5852 static VALUE
5853 int_floor(int argc, VALUE* argv, VALUE num)
5854 {
5855  int ndigits;
5856 
5857  if (!rb_check_arity(argc, 0, 1)) return num;
5858  ndigits = NUM2INT(argv[0]);
5859  if (ndigits >= 0) {
5860  return num;
5861  }
5862  return rb_int_floor(num, ndigits);
5863 }
5864 
5865 /*
5866  * :markup: markdown
5867  *
5868  * call-seq:
5869  * ceil(ndigits = 0) -> integer
5870  *
5871  * Returns an integer that is a "ceiling" value for `self`,
5872  * as specified by the given `ndigits`,
5873  * which must be an
5874  * [integer-convertible object](rdoc-ref:implicit_conversion.rdoc@Integer-Convertible+Objects).
5875  *
5876  * - When `self` is zero, returns zero (regardless of the value of `ndigits`):
5877  *
5878  * ```
5879  * 0.ceil(2) # => 0
5880  * 0.ceil(-2) # => 0
5881  * ```
5882  *
5883  * - When `self` is non-zero and `ndigits` is non-negative, returns `self`:
5884  *
5885  * ```
5886  * 555.ceil # => 555
5887  * 555.ceil(50) # => 555
5888  * ```
5889  *
5890  * - When `self` is non-zero and `ndigits` is negative,
5891  * returns a value based on a computed granularity:
5892  *
5893  * - The granularity is `10 ** ndigits.abs`.
5894  * - The returned value is the smallest multiple of the granularity
5895  * that is greater than or equal to `self`.
5896  *
5897  * Examples with positive `self`:
5898  *
5899  * | ndigits | Granularity | 1234.ceil(ndigits) |
5900  * |--------:|------------:|-------------------:|
5901  * | -1 | 10 | 1240 |
5902  * | -2 | 100 | 1300 |
5903  * | -3 | 1000 | 2000 |
5904  * | -4 | 10000 | 10000 |
5905  * | -5 | 100000 | 100000 |
5906  *
5907  * Examples with negative `self`:
5908  *
5909  * | ndigits | Granularity | -1234.ceil(ndigits) |
5910  * |--------:|------------:|--------------------:|
5911  * | -1 | 10 | -1230 |
5912  * | -2 | 100 | -1200 |
5913  * | -3 | 1000 | -1000 |
5914  * | -4 | 10000 | 0 |
5915  * | -5 | 100000 | 0 |
5916  *
5917  * Related: Integer#floor.
5918  */
5919 
5920 static VALUE
5921 int_ceil(int argc, VALUE* argv, VALUE num)
5922 {
5923  int ndigits;
5924 
5925  if (!rb_check_arity(argc, 0, 1)) return num;
5926  ndigits = NUM2INT(argv[0]);
5927  if (ndigits >= 0) {
5928  return num;
5929  }
5930  return rb_int_ceil(num, ndigits);
5931 }
5932 
5933 /*
5934  * call-seq:
5935  * truncate(ndigits = 0) -> integer
5936  *
5937  * Returns +self+ truncated (toward zero) to
5938  * a precision of +ndigits+ decimal digits.
5939  *
5940  * When +ndigits+ is negative, the returned value
5941  * has at least <tt>ndigits.abs</tt> trailing zeros:
5942  *
5943  * 555.truncate(-1) # => 550
5944  * 555.truncate(-2) # => 500
5945  * -555.truncate(-2) # => -500
5946  *
5947  * Returns +self+ when +ndigits+ is zero or positive.
5948  *
5949  * 555.truncate # => 555
5950  * 555.truncate(50) # => 555
5951  *
5952  * Related: Integer#round.
5953  *
5954  */
5955 
5956 static VALUE
5957 int_truncate(int argc, VALUE* argv, VALUE num)
5958 {
5959  int ndigits;
5960 
5961  if (!rb_check_arity(argc, 0, 1)) return num;
5962  ndigits = NUM2INT(argv[0]);
5963  if (ndigits >= 0) {
5964  return num;
5965  }
5966  return rb_int_truncate(num, ndigits);
5967 }
5968 
5969 #define DEFINE_INT_SQRT(rettype, prefix, argtype) \
5970 rettype \
5971 prefix##_isqrt(argtype n) \
5972 { \
5973  if (!argtype##_IN_DOUBLE_P(n)) { \
5974  unsigned int b = bit_length(n); \
5975  argtype t; \
5976  rettype x = (rettype)(n >> (b/2+1)); \
5977  x |= ((rettype)1LU << (b-1)/2); \
5978  while ((t = n/x) < (argtype)x) x = (rettype)((x + t) >> 1); \
5979  return x; \
5980  } \
5981  return (rettype)sqrt(argtype##_TO_DOUBLE(n)); \
5982 }
5983 
5984 #if SIZEOF_LONG*CHAR_BIT > DBL_MANT_DIG
5985 # define RB_ULONG_IN_DOUBLE_P(n) ((n) < (1UL << DBL_MANT_DIG))
5986 #else
5987 # define RB_ULONG_IN_DOUBLE_P(n) 1
5988 #endif
5989 #define RB_ULONG_TO_DOUBLE(n) (double)(n)
5990 #define RB_ULONG unsigned long
5991 DEFINE_INT_SQRT(unsigned long, rb_ulong, RB_ULONG)
5992 
5993 #if 2*SIZEOF_BDIGIT > SIZEOF_LONG
5994 # if 2*SIZEOF_BDIGIT*CHAR_BIT > DBL_MANT_DIG
5995 # define BDIGIT_DBL_IN_DOUBLE_P(n) ((n) < ((BDIGIT_DBL)1UL << DBL_MANT_DIG))
5996 # else
5997 # define BDIGIT_DBL_IN_DOUBLE_P(n) 1
5998 # endif
5999 # ifdef ULL_TO_DOUBLE
6000 # define BDIGIT_DBL_TO_DOUBLE(n) ULL_TO_DOUBLE(n)
6001 # else
6002 # define BDIGIT_DBL_TO_DOUBLE(n) (double)(n)
6003 # endif
6004 DEFINE_INT_SQRT(BDIGIT, rb_bdigit_dbl, BDIGIT_DBL)
6005 #endif
6006 
6007 #define domain_error(msg) \
6008  rb_raise(rb_eMathDomainError, "Numerical argument is out of domain - " #msg)
6009 
6010 /*
6011  * call-seq:
6012  * Integer.sqrt(numeric) -> integer
6013  *
6014  * Returns the integer square root of the non-negative integer +n+,
6015  * which is the largest non-negative integer less than or equal to the
6016  * square root of +numeric+.
6017  *
6018  * Integer.sqrt(0) # => 0
6019  * Integer.sqrt(1) # => 1
6020  * Integer.sqrt(24) # => 4
6021  * Integer.sqrt(25) # => 5
6022  * Integer.sqrt(10**400) # => 10**200
6023  *
6024  * If +numeric+ is not an \Integer, it is converted to an \Integer:
6025  *
6026  * Integer.sqrt(Complex(4, 0)) # => 2
6027  * Integer.sqrt(Rational(4, 1)) # => 2
6028  * Integer.sqrt(4.0) # => 2
6029  * Integer.sqrt(3.14159) # => 1
6030  *
6031  * This method is equivalent to <tt>Math.sqrt(numeric).floor</tt>,
6032  * except that the result of the latter code may differ from the true value
6033  * due to the limited precision of floating point arithmetic.
6034  *
6035  * Integer.sqrt(10**46) # => 100000000000000000000000
6036  * Math.sqrt(10**46).floor # => 99999999999999991611392
6037  *
6038  * Raises an exception if +numeric+ is negative.
6039  *
6040  */
6041 
6042 static VALUE
6043 rb_int_s_isqrt(VALUE self, VALUE num)
6044 {
6045  unsigned long n, sq;
6046  num = rb_to_int(num);
6047  if (FIXNUM_P(num)) {
6048  if (FIXNUM_NEGATIVE_P(num)) {
6049  domain_error("isqrt");
6050  }
6051  n = FIX2ULONG(num);
6052  sq = rb_ulong_isqrt(n);
6053  return LONG2FIX(sq);
6054  }
6055  else {
6056  size_t biglen;
6057  if (RBIGNUM_NEGATIVE_P(num)) {
6058  domain_error("isqrt");
6059  }
6060  biglen = BIGNUM_LEN(num);
6061  if (biglen == 0) return INT2FIX(0);
6062 #if SIZEOF_BDIGIT <= SIZEOF_LONG
6063  /* short-circuit */
6064  if (biglen == 1) {
6065  n = BIGNUM_DIGITS(num)[0];
6066  sq = rb_ulong_isqrt(n);
6067  return ULONG2NUM(sq);
6068  }
6069 #endif
6070  return rb_big_isqrt(num);
6071  }
6072 }
6073 
6074 /*
6075  * call-seq:
6076  * Integer.try_convert(object) -> object, integer, or nil
6077  *
6078  * If +object+ is an \Integer object, returns +object+.
6079  * Integer.try_convert(1) # => 1
6080  *
6081  * Otherwise if +object+ responds to <tt>:to_int</tt>,
6082  * calls <tt>object.to_int</tt> and returns the result.
6083  * Integer.try_convert(1.25) # => 1
6084  *
6085  * Returns +nil+ if +object+ does not respond to <tt>:to_int</tt>
6086  * Integer.try_convert([]) # => nil
6087  *
6088  * Raises an exception unless <tt>object.to_int</tt> returns an \Integer object.
6089  */
6090 static VALUE
6091 int_s_try_convert(VALUE self, VALUE num)
6092 {
6093  return rb_check_integer_type(num);
6094 }
6095 
6096 /*
6097  * Document-class: ZeroDivisionError
6098  *
6099  * Raised when attempting to divide an integer by 0.
6100  *
6101  * 42 / 0 #=> ZeroDivisionError: divided by 0
6102  *
6103  * Note that only division by an exact 0 will raise the exception:
6104  *
6105  * 42 / 0.0 #=> Float::INFINITY
6106  * 42 / -0.0 #=> -Float::INFINITY
6107  * 0 / 0.0 #=> NaN
6108  */
6109 
6110 /*
6111  * Document-class: FloatDomainError
6112  *
6113  * Raised when attempting to convert special float values (in particular
6114  * +Infinity+ or +NaN+) to numerical classes which don't support them.
6115  *
6116  * Float::INFINITY.to_r #=> FloatDomainError: Infinity
6117  */
6118 
6119 /*
6120  * Document-class: Numeric
6121  *
6122  * \Numeric is the class from which all higher-level numeric classes should inherit.
6123  *
6124  * \Numeric allows instantiation of heap-allocated objects. Other core numeric classes such as
6125  * Integer are implemented as immediates, which means that each Integer is a single immutable
6126  * object which is always passed by value.
6127  *
6128  * a = 1
6129  * 1.object_id == a.object_id #=> true
6130  *
6131  * There can only ever be one instance of the integer +1+, for example. Ruby ensures this
6132  * by preventing instantiation. If duplication is attempted, the same instance is returned.
6133  *
6134  * Integer.new(1) #=> NoMethodError: undefined method `new' for Integer:Class
6135  * 1.dup #=> 1
6136  * 1.object_id == 1.dup.object_id #=> true
6137  *
6138  * For this reason, \Numeric should be used when defining other numeric classes.
6139  *
6140  * Classes which inherit from \Numeric must implement +coerce+, which returns a two-member
6141  * Array containing an object that has been coerced into an instance of the new class
6142  * and +self+ (see #coerce).
6143  *
6144  * Inheriting classes should also implement arithmetic operator methods (<code>+</code>,
6145  * <code>-</code>, <code>*</code> and <code>/</code>) and the <code><=></code> operator (see
6146  * Comparable). These methods may rely on +coerce+ to ensure interoperability with
6147  * instances of other numeric classes.
6148  *
6149  * class Tally < Numeric
6150  * def initialize(string)
6151  * @string = string
6152  * end
6153  *
6154  * def to_s
6155  * @string
6156  * end
6157  *
6158  * def to_i
6159  * @string.size
6160  * end
6161  *
6162  * def coerce(other)
6163  * [self.class.new('|' * other.to_i), self]
6164  * end
6165  *
6166  * def <=>(other)
6167  * to_i <=> other.to_i
6168  * end
6169  *
6170  * def +(other)
6171  * self.class.new('|' * (to_i + other.to_i))
6172  * end
6173  *
6174  * def -(other)
6175  * self.class.new('|' * (to_i - other.to_i))
6176  * end
6177  *
6178  * def *(other)
6179  * self.class.new('|' * (to_i * other.to_i))
6180  * end
6181  *
6182  * def /(other)
6183  * self.class.new('|' * (to_i / other.to_i))
6184  * end
6185  * end
6186  *
6187  * tally = Tally.new('||')
6188  * puts tally * 2 #=> "||||"
6189  * puts tally > 1 #=> true
6190  *
6191  * == What's Here
6192  *
6193  * First, what's elsewhere. \Class \Numeric:
6194  *
6195  * - Inherits from {class Object}[rdoc-ref:Object@What-27s+Here].
6196  * - Includes {module Comparable}[rdoc-ref:Comparable@What-27s+Here].
6197  *
6198  * Here, class \Numeric provides methods for:
6199  *
6200  * - {Querying}[rdoc-ref:Numeric@Querying]
6201  * - {Comparing}[rdoc-ref:Numeric@Comparing]
6202  * - {Converting}[rdoc-ref:Numeric@Converting]
6203  * - {Other}[rdoc-ref:Numeric@Other]
6204  *
6205  * === Querying
6206  *
6207  * - #finite?: Returns true unless +self+ is infinite or not a number.
6208  * - #infinite?: Returns -1, +nil+ or +1, depending on whether +self+
6209  * is <tt>-Infinity<tt>, finite, or <tt>+Infinity</tt>.
6210  * - #integer?: Returns whether +self+ is an integer.
6211  * - #negative?: Returns whether +self+ is negative.
6212  * - #nonzero?: Returns whether +self+ is not zero.
6213  * - #positive?: Returns whether +self+ is positive.
6214  * - #real?: Returns whether +self+ is a real value.
6215  * - #zero?: Returns whether +self+ is zero.
6216  *
6217  * === Comparing
6218  *
6219  * - #<=>: Returns:
6220  *
6221  * - -1 if +self+ is less than the given value.
6222  * - 0 if +self+ is equal to the given value.
6223  * - 1 if +self+ is greater than the given value.
6224  * - +nil+ if +self+ and the given value are not comparable.
6225  *
6226  * - #eql?: Returns whether +self+ and the given value have the same value and type.
6227  *
6228  * === Converting
6229  *
6230  * - #% (aliased as #modulo): Returns the remainder of +self+ divided by the given value.
6231  * - #-@: Returns the value of +self+, negated.
6232  * - #abs (aliased as #magnitude): Returns the absolute value of +self+.
6233  * - #abs2: Returns the square of +self+.
6234  * - #angle (aliased as #arg and #phase): Returns 0 if +self+ is positive,
6235  * Math::PI otherwise.
6236  * - #ceil: Returns the smallest number greater than or equal to +self+,
6237  * to a given precision.
6238  * - #coerce: Returns array <tt>[coerced_self, coerced_other]</tt>
6239  * for the given other value.
6240  * - #conj (aliased as #conjugate): Returns the complex conjugate of +self+.
6241  * - #denominator: Returns the denominator (always positive)
6242  * of the Rational representation of +self+.
6243  * - #div: Returns the value of +self+ divided by the given value
6244  * and converted to an integer.
6245  * - #divmod: Returns array <tt>[quotient, modulus]</tt> resulting
6246  * from dividing +self+ the given divisor.
6247  * - #fdiv: Returns the Float result of dividing +self+ by the given divisor.
6248  * - #floor: Returns the largest number less than or equal to +self+,
6249  * to a given precision.
6250  * - #i: Returns the Complex object <tt>Complex(0, self)</tt>.
6251  * the given value.
6252  * - #imaginary (aliased as #imag): Returns the imaginary part of the +self+.
6253  * - #numerator: Returns the numerator of the Rational representation of +self+;
6254  * has the same sign as +self+.
6255  * - #polar: Returns the array <tt>[self.abs, self.arg]</tt>.
6256  * - #quo: Returns the value of +self+ divided by the given value.
6257  * - #real: Returns the real part of +self+.
6258  * - #rect (aliased as #rectangular): Returns the array <tt>[self, 0]</tt>.
6259  * - #remainder: Returns <tt>self-arg*(self/arg).truncate</tt> for the given +arg+.
6260  * - #round: Returns the value of +self+ rounded to the nearest value
6261  * for the given a precision.
6262  * - #to_c: Returns the Complex representation of +self+.
6263  * - #to_int: Returns the Integer representation of +self+, truncating if necessary.
6264  * - #truncate: Returns +self+ truncated (toward zero) to a given precision.
6265  *
6266  * === Other
6267  *
6268  * - #clone: Returns +self+; does not allow freezing.
6269  * - #dup (aliased as #+@): Returns +self+.
6270  * - #step: Invokes the given block with the sequence of specified numbers.
6271  *
6272  */
6273 void
6274 Init_Numeric(void)
6275 {
6276 #ifdef _UNICOSMP
6277  /* Turn off floating point exceptions for divide by zero, etc. */
6278  _set_Creg(0, 0);
6279 #endif
6280  id_coerce = rb_intern_const("coerce");
6281  id_to = rb_intern_const("to");
6282  id_by = rb_intern_const("by");
6283 
6284  rb_eZeroDivError = rb_define_class("ZeroDivisionError", rb_eStandardError);
6285  rb_eFloatDomainError = rb_define_class("FloatDomainError", rb_eRangeError);
6286  rb_cNumeric = rb_define_class("Numeric", rb_cObject);
6287 
6288  rb_define_method(rb_cNumeric, "singleton_method_added", num_sadded, 1);
6290  rb_define_method(rb_cNumeric, "coerce", num_coerce, 1);
6291  rb_define_method(rb_cNumeric, "clone", num_clone, -1);
6292 
6293  rb_define_method(rb_cNumeric, "i", num_imaginary, 0);
6294  rb_define_method(rb_cNumeric, "-@", num_uminus, 0);
6295  rb_define_method(rb_cNumeric, "<=>", num_cmp, 1);
6296  rb_define_method(rb_cNumeric, "eql?", num_eql, 1);
6297  rb_define_method(rb_cNumeric, "fdiv", num_fdiv, 1);
6298  rb_define_method(rb_cNumeric, "div", num_div, 1);
6299  rb_define_method(rb_cNumeric, "divmod", num_divmod, 1);
6300  rb_define_method(rb_cNumeric, "%", num_modulo, 1);
6301  rb_define_method(rb_cNumeric, "modulo", num_modulo, 1);
6302  rb_define_method(rb_cNumeric, "remainder", num_remainder, 1);
6303  rb_define_method(rb_cNumeric, "abs", num_abs, 0);
6304  rb_define_method(rb_cNumeric, "magnitude", num_abs, 0);
6305  rb_define_method(rb_cNumeric, "to_int", num_to_int, 0);
6306 
6307  rb_define_method(rb_cNumeric, "zero?", num_zero_p, 0);
6308  rb_define_method(rb_cNumeric, "nonzero?", num_nonzero_p, 0);
6309 
6310  rb_define_method(rb_cNumeric, "floor", num_floor, -1);
6311  rb_define_method(rb_cNumeric, "ceil", num_ceil, -1);
6312  rb_define_method(rb_cNumeric, "round", num_round, -1);
6313  rb_define_method(rb_cNumeric, "truncate", num_truncate, -1);
6314  rb_define_method(rb_cNumeric, "step", num_step, -1);
6315  rb_define_method(rb_cNumeric, "positive?", num_positive_p, 0);
6316  rb_define_method(rb_cNumeric, "negative?", num_negative_p, 0);
6317 
6318  rb_cInteger = rb_define_class("Integer", rb_cNumeric);
6321  rb_define_singleton_method(rb_cInteger, "sqrt", rb_int_s_isqrt, 1);
6322  rb_define_singleton_method(rb_cInteger, "try_convert", int_s_try_convert, 1);
6323 
6324  rb_define_method(rb_cInteger, "to_s", rb_int_to_s, -1);
6325  rb_define_alias(rb_cInteger, "inspect", "to_s");
6326  rb_define_method(rb_cInteger, "allbits?", int_allbits_p, 1);
6327  rb_define_method(rb_cInteger, "anybits?", int_anybits_p, 1);
6328  rb_define_method(rb_cInteger, "nobits?", int_nobits_p, 1);
6329  rb_define_method(rb_cInteger, "upto", int_upto, 1);
6330  rb_define_method(rb_cInteger, "downto", int_downto, 1);
6331  rb_define_method(rb_cInteger, "succ", int_succ, 0);
6332  rb_define_method(rb_cInteger, "next", int_succ, 0);
6333  rb_define_method(rb_cInteger, "pred", int_pred, 0);
6334  rb_define_method(rb_cInteger, "chr", int_chr, -1);
6335  rb_define_method(rb_cInteger, "to_f", int_to_f, 0);
6336  rb_define_method(rb_cInteger, "floor", int_floor, -1);
6337  rb_define_method(rb_cInteger, "ceil", int_ceil, -1);
6338  rb_define_method(rb_cInteger, "truncate", int_truncate, -1);
6339  rb_define_method(rb_cInteger, "round", int_round, -1);
6340  rb_define_method(rb_cInteger, "<=>", rb_int_cmp, 1);
6341 
6342  rb_define_method(rb_cInteger, "+", rb_int_plus, 1);
6343  rb_define_method(rb_cInteger, "-", rb_int_minus, 1);
6344  rb_define_method(rb_cInteger, "*", rb_int_mul, 1);
6345  rb_define_method(rb_cInteger, "/", rb_int_div, 1);
6346  rb_define_method(rb_cInteger, "div", rb_int_idiv, 1);
6347  rb_define_method(rb_cInteger, "%", rb_int_modulo, 1);
6348  rb_define_method(rb_cInteger, "modulo", rb_int_modulo, 1);
6349  rb_define_method(rb_cInteger, "remainder", int_remainder, 1);
6350  rb_define_method(rb_cInteger, "divmod", rb_int_divmod, 1);
6351  rb_define_method(rb_cInteger, "fdiv", rb_int_fdiv, 1);
6352  rb_define_method(rb_cInteger, "**", rb_int_pow, 1);
6353 
6354  rb_define_method(rb_cInteger, "pow", rb_int_powm, -1); /* in bignum.c */
6355 
6356  rb_define_method(rb_cInteger, "===", rb_int_equal, 1);
6357  rb_define_method(rb_cInteger, "==", rb_int_equal, 1);
6358  rb_define_method(rb_cInteger, ">", rb_int_gt, 1);
6359  rb_define_method(rb_cInteger, ">=", rb_int_ge, 1);
6360  rb_define_method(rb_cInteger, "<", int_lt, 1);
6361  rb_define_method(rb_cInteger, "<=", int_le, 1);
6362 
6363  rb_define_method(rb_cInteger, "&", rb_int_and, 1);
6364  rb_define_method(rb_cInteger, "|", int_or, 1);
6365  rb_define_method(rb_cInteger, "^", int_xor, 1);
6366  rb_define_method(rb_cInteger, "[]", int_aref, -1);
6367 
6368  rb_define_method(rb_cInteger, "<<", rb_int_lshift, 1);
6369  rb_define_method(rb_cInteger, ">>", rb_int_rshift, 1);
6370 
6371  rb_define_method(rb_cInteger, "digits", rb_int_digits, -1);
6372 
6373 #define fix_to_s_static(n) do { \
6374  VALUE lit = rb_fstring_literal(#n); \
6375  rb_fix_to_s_static[n] = lit; \
6376  rb_vm_register_global_object(lit); \
6377  RB_GC_GUARD(lit); \
6378  } while (0)
6379 
6380  fix_to_s_static(0);
6381  fix_to_s_static(1);
6382  fix_to_s_static(2);
6383  fix_to_s_static(3);
6384  fix_to_s_static(4);
6385  fix_to_s_static(5);
6386  fix_to_s_static(6);
6387  fix_to_s_static(7);
6388  fix_to_s_static(8);
6389  fix_to_s_static(9);
6390 
6391 #undef fix_to_s_static
6392 
6394 
6397 
6398  /*
6399  * The base of the floating point, or number of unique digits used to
6400  * represent the number.
6401  *
6402  * Usually defaults to 2 on most systems, which would represent a base-10 decimal.
6403  */
6404  rb_define_const(rb_cFloat, "RADIX", INT2FIX(FLT_RADIX));
6405  /*
6406  * The number of base digits for the +double+ data type.
6407  *
6408  * Usually defaults to 53.
6409  */
6410  rb_define_const(rb_cFloat, "MANT_DIG", INT2FIX(DBL_MANT_DIG));
6411  /*
6412  * The minimum number of significant decimal digits in a double-precision
6413  * floating point.
6414  *
6415  * Usually defaults to 15.
6416  */
6417  rb_define_const(rb_cFloat, "DIG", INT2FIX(DBL_DIG));
6418  /*
6419  * The smallest possible exponent value in a double-precision floating
6420  * point.
6421  *
6422  * Usually defaults to -1021.
6423  */
6424  rb_define_const(rb_cFloat, "MIN_EXP", INT2FIX(DBL_MIN_EXP));
6425  /*
6426  * The largest possible exponent value in a double-precision floating
6427  * point.
6428  *
6429  * Usually defaults to 1024.
6430  */
6431  rb_define_const(rb_cFloat, "MAX_EXP", INT2FIX(DBL_MAX_EXP));
6432  /*
6433  * The smallest negative exponent in a double-precision floating point
6434  * where 10 raised to this power minus 1.
6435  *
6436  * Usually defaults to -307.
6437  */
6438  rb_define_const(rb_cFloat, "MIN_10_EXP", INT2FIX(DBL_MIN_10_EXP));
6439  /*
6440  * The largest positive exponent in a double-precision floating point where
6441  * 10 raised to this power minus 1.
6442  *
6443  * Usually defaults to 308.
6444  */
6445  rb_define_const(rb_cFloat, "MAX_10_EXP", INT2FIX(DBL_MAX_10_EXP));
6446  /*
6447  * The smallest positive normalized number in a double-precision floating point.
6448  *
6449  * Usually defaults to 2.2250738585072014e-308.
6450  *
6451  * If the platform supports denormalized numbers,
6452  * there are numbers between zero and Float::MIN.
6453  * 0.0.next_float returns the smallest positive floating point number
6454  * including denormalized numbers.
6455  */
6456  rb_define_const(rb_cFloat, "MIN", DBL2NUM(DBL_MIN));
6457  /*
6458  * The largest possible integer in a double-precision floating point number.
6459  *
6460  * Usually defaults to 1.7976931348623157e+308.
6461  */
6462  rb_define_const(rb_cFloat, "MAX", DBL2NUM(DBL_MAX));
6463  /*
6464  * The difference between 1 and the smallest double-precision floating
6465  * point number greater than 1.
6466  *
6467  * Usually defaults to 2.2204460492503131e-16.
6468  */
6469  rb_define_const(rb_cFloat, "EPSILON", DBL2NUM(DBL_EPSILON));
6470  /*
6471  * An expression representing positive infinity.
6472  */
6473  rb_define_const(rb_cFloat, "INFINITY", DBL2NUM(HUGE_VAL));
6474  /*
6475  * An expression representing a value which is "not a number".
6476  */
6477  rb_define_const(rb_cFloat, "NAN", DBL2NUM(nan("")));
6478 
6479  rb_define_method(rb_cFloat, "to_s", flo_to_s, 0);
6480  rb_define_alias(rb_cFloat, "inspect", "to_s");
6481  rb_define_method(rb_cFloat, "coerce", flo_coerce, 1);
6482  rb_define_method(rb_cFloat, "+", rb_float_plus, 1);
6483  rb_define_method(rb_cFloat, "-", rb_float_minus, 1);
6484  rb_define_method(rb_cFloat, "*", rb_float_mul, 1);
6485  rb_define_method(rb_cFloat, "/", rb_float_div, 1);
6486  rb_define_method(rb_cFloat, "quo", flo_quo, 1);
6487  rb_define_method(rb_cFloat, "fdiv", flo_quo, 1);
6488  rb_define_method(rb_cFloat, "%", flo_mod, 1);
6489  rb_define_method(rb_cFloat, "modulo", flo_mod, 1);
6490  rb_define_method(rb_cFloat, "divmod", flo_divmod, 1);
6491  rb_define_method(rb_cFloat, "**", rb_float_pow, 1);
6492  rb_define_method(rb_cFloat, "==", flo_eq, 1);
6493  rb_define_method(rb_cFloat, "===", flo_eq, 1);
6494  rb_define_method(rb_cFloat, "<=>", flo_cmp, 1);
6495  rb_define_method(rb_cFloat, ">", rb_float_gt, 1);
6496  rb_define_method(rb_cFloat, ">=", flo_ge, 1);
6497  rb_define_method(rb_cFloat, "<", flo_lt, 1);
6498  rb_define_method(rb_cFloat, "<=", flo_le, 1);
6499  rb_define_method(rb_cFloat, "eql?", flo_eql, 1);
6500  rb_define_method(rb_cFloat, "hash", flo_hash, 0);
6501 
6502  rb_define_method(rb_cFloat, "to_i", flo_to_i, 0);
6503  rb_define_method(rb_cFloat, "to_int", flo_to_i, 0);
6504  rb_define_method(rb_cFloat, "floor", flo_floor, -1);
6505  rb_define_method(rb_cFloat, "ceil", flo_ceil, -1);
6506  rb_define_method(rb_cFloat, "round", flo_round, -1);
6507  rb_define_method(rb_cFloat, "truncate", flo_truncate, -1);
6508 
6509  rb_define_method(rb_cFloat, "nan?", flo_is_nan_p, 0);
6510  rb_define_method(rb_cFloat, "infinite?", rb_flo_is_infinite_p, 0);
6511  rb_define_method(rb_cFloat, "finite?", rb_flo_is_finite_p, 0);
6512  rb_define_method(rb_cFloat, "next_float", flo_next_float, 0);
6513  rb_define_method(rb_cFloat, "prev_float", flo_prev_float, 0);
6514 }
6515 
6516 #undef rb_float_value
6517 double
6519 {
6520  return rb_float_value_inline(v);
6521 }
6522 
6523 #undef rb_float_new
6524 VALUE
6525 rb_float_new(double d)
6526 {
6527  return rb_float_new_inline(d);
6528 }
6529 
6530 #include "numeric.rbinc"
#define RUBY_ASSERT(...)
Asserts that the given expression is truthy if and only if RUBY_DEBUG is truthy.
Definition: assert.h:219
#define LONG_LONG
Definition: long_long.h:38
#define rb_define_singleton_method(klass, mid, func, arity)
Defines klass.mid.
Definition: cxxanyargs.hpp:685
double rb_float_value(VALUE num)
Extracts its double value from an instance of rb_cFloat.
Definition: numeric.c:6518
VALUE rb_float_new_in_heap(double d)
Identical to rb_float_new(), except it does not generate Flonums.
Definition: numeric.c:991
VALUE rb_float_new(double d)
Converts a C's double into an instance of rb_cFloat.
Definition: numeric.c:6525
void rb_include_module(VALUE klass, VALUE module)
Includes a module to a class.
Definition: class.c:1187
VALUE rb_define_class(const char *name, VALUE super)
Defines a top-level class.
Definition: class.c:980
VALUE rb_singleton_class(VALUE obj)
Finds or creates the singleton class of the passed object.
Definition: class.c:2297
void rb_define_alias(VALUE klass, const char *name1, const char *name2)
Defines an alias of a method.
Definition: class.c:2345
void rb_undef_method(VALUE klass, const char *name)
Defines an undef of a method.
Definition: class.c:2166
int rb_scan_args(int argc, const VALUE *argv, const char *fmt,...)
Retrieves argument from argc and argv to given VALUE references according to the format string.
Definition: class.c:2635
void rb_define_method(VALUE klass, const char *name, VALUE(*func)(ANYARGS), int argc)
Defines a method.
Definition: class.c:2142
int rb_block_given_p(void)
Determines if the current method is given a block.
Definition: eval.c:916
int rb_get_kwargs(VALUE keyword_hash, const ID *table, int required, int optional, VALUE *values)
Keyword argument deconstructor.
Definition: class.c:2424
#define T_COMPLEX
Old name of RUBY_T_COMPLEX.
Definition: value_type.h:59
#define TYPE(_)
Old name of rb_type.
Definition: value_type.h:108
#define RB_INTEGER_TYPE_P
Old name of rb_integer_type_p.
Definition: value_type.h:87
#define NUM2LL
Old name of RB_NUM2LL.
Definition: long_long.h:34
#define RFLOAT_VALUE
Old name of rb_float_value.
Definition: double.h:28
#define T_STRING
Old name of RUBY_T_STRING.
Definition: value_type.h:78
#define Qundef
Old name of RUBY_Qundef.
#define INT2FIX
Old name of RB_INT2FIX.
Definition: long.h:48
#define T_FLOAT
Old name of RUBY_T_FLOAT.
Definition: value_type.h:64
#define ID2SYM
Old name of RB_ID2SYM.
Definition: symbol.h:44
#define SPECIAL_CONST_P
Old name of RB_SPECIAL_CONST_P.
#define OBJ_FREEZE
Old name of RB_OBJ_FREEZE.
Definition: fl_type.h:135
#define ULONG2NUM
Old name of RB_ULONG2NUM.
Definition: long.h:60
#define T_FIXNUM
Old name of RUBY_T_FIXNUM.
Definition: value_type.h:63
#define UNREACHABLE_RETURN
Old name of RBIMPL_UNREACHABLE_RETURN.
Definition: assume.h:29
#define FIXNUM_FLAG
Old name of RUBY_FIXNUM_FLAG.
#define CLASS_OF
Old name of rb_class_of.
Definition: globals.h:203
#define FIXABLE
Old name of RB_FIXABLE.
Definition: fixnum.h:25
#define LONG2FIX
Old name of RB_INT2FIX.
Definition: long.h:49
#define FIX2INT
Old name of RB_FIX2INT.
Definition: int.h:41
#define FIX2ULONG
Old name of RB_FIX2ULONG.
Definition: long.h:47
#define T_TRUE
Old name of RUBY_T_TRUE.
Definition: value_type.h:81
#define T_RATIONAL
Old name of RUBY_T_RATIONAL.
Definition: value_type.h:76
#define NUM2DBL
Old name of rb_num2dbl.
Definition: double.h:27
#define LONG2NUM
Old name of RB_LONG2NUM.
Definition: long.h:50
#define rb_usascii_str_new2
Old name of rb_usascii_str_new_cstr.
Definition: string.h:1680
#define T_FALSE
Old name of RUBY_T_FALSE.
Definition: value_type.h:61
#define Qtrue
Old name of RUBY_Qtrue.
#define ST2FIX
Old name of RB_ST2FIX.
Definition: st_data_t.h:33
#define NUM2INT
Old name of RB_NUM2INT.
Definition: int.h:44
#define Qnil
Old name of RUBY_Qnil.
#define Qfalse
Old name of RUBY_Qfalse.
#define FIX2LONG
Old name of RB_FIX2LONG.
Definition: long.h:46
#define T_ARRAY
Old name of RUBY_T_ARRAY.
Definition: value_type.h:56
#define NIL_P
Old name of RB_NIL_P.
#define NUM2ULL
Old name of RB_NUM2ULL.
Definition: long_long.h:35
#define FL_WB_PROTECTED
Old name of RUBY_FL_WB_PROTECTED.
Definition: fl_type.h:59
#define POSFIXABLE
Old name of RB_POSFIXABLE.
Definition: fixnum.h:29
#define DBL2NUM
Old name of rb_float_new.
Definition: double.h:29
#define BUILTIN_TYPE
Old name of RB_BUILTIN_TYPE.
Definition: value_type.h:85
#define NUM2LONG
Old name of RB_NUM2LONG.
Definition: long.h:51
#define FIXNUM_P
Old name of RB_FIXNUM_P.
#define ISALNUM
Old name of rb_isalnum.
Definition: ctype.h:91
#define SYMBOL_P
Old name of RB_SYMBOL_P.
Definition: value_type.h:88
void rb_raise(VALUE exc_class, const char *fmt,...)
Exception entry point.
Definition: error.c:3635
VALUE rb_eNotImpError
NotImplementedError exception.
Definition: error.c:1418
void rb_bug(const char *fmt,...)
Interpreter panic switch.
Definition: error.c:1089
void rb_name_error(ID id, const char *fmt,...)
Raises an instance of rb_eNameError.
Definition: error.c:2215
VALUE rb_eZeroDivError
ZeroDivisionError exception.
Definition: numeric.c:200
VALUE rb_eStandardError
StandardError exception.
Definition: error.c:1405
VALUE rb_eRangeError
RangeError exception.
Definition: error.c:1412
VALUE rb_eTypeError
TypeError exception.
Definition: error.c:1408
VALUE rb_eFloatDomainError
FloatDomainError exception.
Definition: numeric.c:201
VALUE rb_eArgError
ArgumentError exception.
Definition: error.c:1409
VALUE rb_eMathDomainError
Math::DomainError exception.
Definition: math.c:30
VALUE rb_Float(VALUE val)
This is the logic behind Kernel#Float.
Definition: object.c:3595
VALUE rb_any_to_s(VALUE obj)
Generates a textual representation of the given object.
Definition: object.c:669
VALUE rb_cInteger
Module class.
Definition: numeric.c:198
VALUE rb_cNumeric
Numeric class.
Definition: numeric.c:196
VALUE rb_obj_class(VALUE obj)
Queries the class of an object.
Definition: object.c:247
VALUE rb_inspect(VALUE obj)
Generates a human-readable textual representation of the given object.
Definition: object.c:680
VALUE rb_equal(VALUE lhs, VALUE rhs)
This function is an optimised version of calling #==.
Definition: object.c:179
VALUE rb_obj_is_kind_of(VALUE obj, VALUE klass)
Queries if the given object is an instance (of possibly descendants) of the given class.
Definition: object.c:865
VALUE rb_mComparable
Comparable module.
Definition: compar.c:19
VALUE rb_cFloat
Float class.
Definition: numeric.c:197
VALUE rb_to_int(VALUE val)
Identical to rb_check_to_int(), except it raises in case of conversion mismatch.
Definition: object.c:3188
Encoding relates APIs.
int rb_enc_precise_mbclen(const char *p, const char *e, rb_encoding *enc)
Queries the number of bytes of the character at the passed pointer.
Definition: encoding.c:1191
int rb_enc_codelen(int code, rb_encoding *enc)
Queries the number of bytes requested to represent the passed code point using the passed encoding.
Definition: encoding.c:1241
rb_encoding * rb_default_internal_encoding(void)
Queries the "default internal" encoding.
Definition: encoding.c:1676
rb_encoding * rb_to_encoding(VALUE obj)
Identical to rb_find_encoding(), except it raises an exception instead of returning NULL.
Definition: encoding.c:323
rb_encoding * rb_ascii8bit_encoding(void)
Queries the encoding that represents ASCII-8BIT a.k.a.
Definition: encoding.c:1463
static int rb_enc_mbcput(unsigned int c, void *buf, rb_encoding *enc)
Identical to rb_enc_uint_chr(), except it writes back to the passed buffer instead of allocating one.
Definition: encoding.h:643
static const char * rb_enc_name(rb_encoding *enc)
Queries the (canonical) name of the passed encoding.
Definition: encoding.h:417
VALUE rb_enc_uint_chr(unsigned int code, rb_encoding *enc)
Encodes the passed code point into a series of bytes.
Definition: numeric.c:3803
VALUE rb_enc_str_new(const char *ptr, long len, rb_encoding *enc)
Identical to rb_str_new(), except it additionally takes an encoding.
Definition: string.c:1068
VALUE rb_funcall(VALUE recv, ID mid, int n,...)
Calls a method.
Definition: vm_eval.c:1099
VALUE rb_funcallv(VALUE recv, ID mid, int argc, const VALUE *argv)
Identical to rb_funcall(), except it takes the method arguments as a C array.
Definition: vm_eval.c:1058
#define RGENGC_WB_PROTECTED_FLOAT
This is a compile-time flag to enable/disable write barrier for struct RFloat.
Definition: gc.h:534
Defines RBIMPL_HAS_BUILTIN.
VALUE rb_ary_new(void)
Allocates a new, empty array.
Definition: array.c:741
VALUE rb_ary_pop(VALUE ary)
Destructively deletes an element from the end of the passed array and returns what was deleted.
Definition: array.c:1425
VALUE rb_ary_push(VALUE ary, VALUE elem)
Special case of rb_ary_cat() that it adds only one element.
Definition: array.c:1378
VALUE rb_ary_new_from_args(long n,...)
Constructs an array from the passed objects.
Definition: array.c:747
VALUE rb_assoc_new(VALUE car, VALUE cdr)
Identical to rb_ary_new_from_values(), except it expects exactly two parameters.
Definition: array.c:995
void rb_ary_store(VALUE ary, long key, VALUE val)
Destructively stores the passed value to the passed array's passed index.
Definition: array.c:1201
VALUE rb_big_lshift(VALUE x, VALUE y)
Performs shift left.
Definition: bignum.c:6656
VALUE rb_big_and(VALUE x, VALUE y)
Performs bitwise and of the passed two objects.
Definition: bignum.c:6395
VALUE rb_big_or(VALUE x, VALUE y)
Performs bitwise or of the passed two objects.
Definition: bignum.c:6514
VALUE rb_big_minus(VALUE x, VALUE y)
Performs subtraction of the passed two objects.
Definition: bignum.c:5881
VALUE rb_big_modulo(VALUE x, VALUE y)
Performs modulo of the passed two objects.
Definition: bignum.c:6135
VALUE rb_big_pow(VALUE x, VALUE y)
Raises x to the powerof y.
Definition: bignum.c:6276
int rb_bigzero_p(VALUE x)
Queries if the passed bignum instance is a "bigzero".
Definition: bignum.c:2959
VALUE rb_big_plus(VALUE x, VALUE y)
Performs addition of the passed two objects.
Definition: bignum.c:5852
size_t rb_absint_size(VALUE val, int *nlz_bits_ret)
Calculates the number of bytes needed to represent the absolute value of the passed integer.
Definition: bignum.c:3289
unsigned long rb_big2ulong(VALUE x)
Converts a bignum into C's unsigned long.
Definition: bignum.c:5161
VALUE rb_big_idiv(VALUE x, VALUE y)
Performs "integer division".
Definition: bignum.c:6129
VALUE rb_big2str(VALUE x, int base)
Generates a place-value representation of the passed integer.
Definition: bignum.c:5127
VALUE rb_big_cmp(VALUE lhs, VALUE rhs)
Compares the passed two bignums.
Definition: bignum.c:5449
VALUE rb_dbl2big(double d)
Converts a C's double into a bignum.
Definition: bignum.c:5285
VALUE rb_big_mul(VALUE x, VALUE y)
Performs multiplication of the passed two objects.
Definition: bignum.c:5965
VALUE rb_big_eql(VALUE lhs, VALUE rhs)
Equality, in terms of eql?.
Definition: bignum.c:5573
VALUE rb_big_divmod(VALUE x, VALUE y)
Performs "divmod" operation.
Definition: bignum.c:6167
VALUE rb_big_xor(VALUE x, VALUE y)
Performs exclusive or of the passed two objects.
Definition: bignum.c:6608
VALUE rb_big_div(VALUE x, VALUE y)
Performs division of the passed two objects.
Definition: bignum.c:6123
VALUE rb_big_norm(VALUE x)
Normalises the passed bignum.
Definition: bignum.c:3194
VALUE rb_big_rshift(VALUE x, VALUE y)
Performs shift right.
Definition: bignum.c:6686
double rb_big2dbl(VALUE x)
Converts a bignum into C's double.
Definition: bignum.c:5346
long rb_big2long(VALUE x)
Converts a bignum into C's long.
Definition: bignum.c:5176
VALUE rb_big_eq(VALUE lhs, VALUE rhs)
Equality, in terms of ==.
Definition: bignum.c:5554
int rb_cmpint(VALUE val, VALUE a, VALUE b)
Canonicalises the passed val, which is the return value of a <=> b, into C's {-1, 0,...
Definition: bignum.c:2965
void rb_cmperr(VALUE a, VALUE b)
Raises "comparison failed" error.
Definition: compar.c:28
VALUE rb_complex_new(VALUE real, VALUE imag)
Constructs a Complex, by first multiplying the imaginary part with 1i then adds it to the real part.
Definition: complex.c:1755
VALUE rb_complex_plus(VALUE x, VALUE y)
Performs addition of the passed two objects.
Definition: complex.c:832
VALUE rb_complex_mul(VALUE x, VALUE y)
Performs multiplication of the passed two objects.
Definition: complex.c:928
VALUE rb_complex_pow(VALUE base, VALUE exp)
Performs exponentiation of the passed two objects.
Definition: complex.c:1123
#define RETURN_SIZED_ENUMERATOR(obj, argc, argv, size_fn)
This roughly resembles return enum_for(__callee__) unless block_given?.
Definition: enumerator.h:206
#define SIZED_ENUMERATOR_KW(obj, argc, argv, size_fn, kw_splat)
This is an implementation detail of RETURN_SIZED_ENUMERATOR_KW().
Definition: enumerator.h:193
static int rb_check_arity(int argc, int min, int max)
Ensures that the passed integer is in the passed range.
Definition: error.h:284
ID rb_frame_this_func(void)
Queries the name of the Ruby level method that is calling this function.
Definition: eval.c:1094
void rb_num_zerodiv(void)
Just always raises an exception.
Definition: numeric.c:206
VALUE rb_num2fix(VALUE val)
Converts a numeric value into a Fixnum.
Definition: numeric.c:3442
VALUE rb_fix2str(VALUE val, int base)
Generates a place-value representation of the given Fixnum, with given radix.
Definition: numeric.c:3909
VALUE rb_int_positive_pow(long x, unsigned long y)
Raises the passed x to the power of y.
Definition: numeric.c:4559
VALUE rb_dbl_cmp(double lhs, double rhs)
Compares two doubles.
Definition: numeric.c:1633
VALUE rb_num_coerce_bit(VALUE lhs, VALUE rhs, ID op)
This one is optimised for bitwise operations, but the API is identical to rb_num_coerce_bin().
Definition: numeric.c:4987
VALUE rb_num_coerce_relop(VALUE lhs, VALUE rhs, ID op)
Identical to rb_num_coerce_cmp(), except for return values.
Definition: numeric.c:499
VALUE rb_num_coerce_cmp(VALUE lhs, VALUE rhs, ID op)
Identical to rb_num_coerce_bin(), except for return values.
Definition: numeric.c:484
VALUE rb_num_coerce_bin(VALUE lhs, VALUE rhs, ID op)
Coerced binary operation.
Definition: numeric.c:477
int rb_range_values(VALUE range, VALUE *begp, VALUE *endp, int *exclp)
Deconstructs a range into its components.
Definition: range.c:1754
VALUE rb_rational_raw(VALUE num, VALUE den)
Identical to rb_rational_new(), except it skips argument validations.
Definition: rational.c:1960
int rb_memcicmp(const void *s1, const void *s2, long n)
Identical to st_locale_insensitive_strcasecmp(), except it is timing safe and returns something diffe...
Definition: re.c:95
VALUE rb_str_cat(VALUE dst, const char *src, long srclen)
Destructively appends the passed contents to the string.
Definition: string.c:3443
VALUE rb_usascii_str_new(const char *ptr, long len)
Identical to rb_str_new(), except it generates a string of "US ASCII" encoding.
Definition: string.c:1056
VALUE rb_usascii_str_new_cstr(const char *ptr)
Identical to rb_str_new_cstr(), except it generates a string of "US ASCII" encoding.
Definition: string.c:1086
void rb_must_asciicompat(VALUE obj)
Asserts that the given string's encoding is (Ruby's definition of) ASCII compatible.
Definition: string.c:2692
VALUE rb_str_new(const char *ptr, long len)
Allocates an instance of rb_cString.
Definition: string.c:1050
VALUE rb_check_string_type(VALUE obj)
Try converting an object to its stringised representation using its to_str method,...
Definition: string.c:2850
VALUE rb_str_resize(VALUE str, long len)
Overwrites the length of the string.
Definition: string.c:3315
VALUE rb_exec_recursive(VALUE(*f)(VALUE g, VALUE h, int r), VALUE g, VALUE h)
"Recursion" API entry point.
VALUE rb_exec_recursive_paired(VALUE(*f)(VALUE g, VALUE h, int r), VALUE g, VALUE p, VALUE h)
Identical to rb_exec_recursive(), except it checks for the recursion on the ordered pair of { g,...
void rb_undef_alloc_func(VALUE klass)
Deletes the allocator function of a class.
Definition: vm_method.c:1291
VALUE rb_check_funcall(VALUE recv, ID mid, int argc, const VALUE *argv)
Identical to rb_funcallv(), except it returns RUBY_Qundef instead of raising rb_eNoMethodError.
Definition: vm_eval.c:668
void rb_remove_method_id(VALUE klass, ID mid)
Identical to rb_remove_method(), except it accepts the method name as ID.
Definition: vm_method.c:1712
static ID rb_intern_const(const char *str)
This is a "tiny optimisation" over rb_intern().
Definition: symbol.h:277
const char * rb_id2name(ID id)
Retrieves the name mapped to the given id.
Definition: symbol.c:992
ID rb_intern(const char *name)
Finds or creates a symbol of the given name.
Definition: symbol.c:823
VALUE rb_sym2str(VALUE symbol)
Obtain a frozen string representation of a symbol (not including the leading colon).
Definition: symbol.c:970
ID rb_to_id(VALUE str)
Identical to rb_intern(), except it takes an instance of rb_cString.
Definition: string.c:12463
VALUE rb_id2str(ID id)
Identical to rb_id2name(), except it returns a frozen Ruby String instead of a C String.
Definition: symbol.c:986
void rb_define_const(VALUE klass, const char *name, VALUE val)
Defines a Ruby level constant under a namespace.
Definition: variable.c:3726
char * ptr
Pointer to the underlying memory region, of at least capa bytes.
Definition: io.h:2
int len
Length of the buffer.
Definition: io.h:8
unsigned long rb_num2uint(VALUE num)
Converts an instance of rb_cNumeric into C's unsigned long.
Definition: numeric.c:3356
long rb_fix2int(VALUE num)
Identical to rb_num2int().
Definition: numeric.c:3350
long rb_num2int(VALUE num)
Converts an instance of rb_cNumeric into C's long.
Definition: numeric.c:3344
unsigned long rb_fix2uint(VALUE num)
Identical to rb_num2uint().
Definition: numeric.c:3362
VALUE rb_str_catf(VALUE dst, const char *fmt,...)
Identical to rb_sprintf(), except it renders the output to the specified object rather than creating ...
Definition: sprintf.c:1240
LONG_LONG rb_num2ll(VALUE num)
Converts an instance of rb_cNumeric into C's long long.
unsigned LONG_LONG rb_num2ull(VALUE num)
Converts an instance of rb_cNumeric into C's unsigned long long.
VALUE rb_int2big(intptr_t i)
Converts a C's intptr_t into an instance of rb_cInteger.
Definition: bignum.c:3222
VALUE rb_yield(VALUE val)
Yields the block.
Definition: vm_eval.c:1354
#define RB_FIX2ULONG
Just another name of rb_fix2ulong.
Definition: long.h:54
void rb_out_of_int(SIGNED_VALUE num)
This is an utility function to raise an rb_eRangeError.
Definition: numeric.c:3271
long rb_num2long(VALUE num)
Converts an instance of rb_cNumeric into C's long.
Definition: numeric.c:3196
unsigned long rb_num2ulong(VALUE num)
Converts an instance of rb_cNumeric into C's unsigned long.
Definition: numeric.c:3265
#define RARRAY_LEN
Just another name of rb_array_len.
Definition: rarray.h:51
static int RARRAY_LENINT(VALUE ary)
Identical to rb_array_len(), except it differs for the return type.
Definition: rarray.h:281
#define RARRAY_AREF(a, i)
Definition: rarray.h:403
#define RARRAY_CONST_PTR
Just another name of rb_array_const_ptr.
Definition: rarray.h:52
static bool RBIGNUM_NEGATIVE_P(VALUE b)
Checks if the bignum is negative.
Definition: rbignum.h:74
static char * RSTRING_END(VALUE str)
Queries the end of the contents pointer of the string.
Definition: rstring.h:442
static char * RSTRING_PTR(VALUE str)
Queries the contents pointer of the string.
Definition: rstring.h:416
static long RSTRING_LEN(VALUE str)
Queries the length of the string.
Definition: rstring.h:367
const char * rb_obj_classname(VALUE obj)
Queries the name of the class of the passed object.
Definition: variable.c:427
short rb_num2short(VALUE num)
Converts an instance of rb_cNumeric into C's short.
Definition: numeric.c:3400
unsigned short rb_num2ushort(VALUE num)
Converts an instance of rb_cNumeric into C's unsigned short.
Definition: numeric.c:3418
short rb_fix2short(VALUE num)
Identical to rb_num2short().
Definition: numeric.c:3409
unsigned short rb_fix2ushort(VALUE num)
Identical to rb_num2ushort().
Definition: numeric.c:3428
#define RTEST
This is an old name of RB_TEST.
Definition: numeric.h:51
intptr_t SIGNED_VALUE
A signed integer type that has the same width with VALUE.
Definition: value.h:63
uintptr_t ID
Type that represents a Ruby identifier such as a variable name.
Definition: value.h:52
#define SIZEOF_VALUE
Identical to sizeof(VALUE), except it is a macro that can also be used inside of preprocessor directi...
Definition: value.h:69
uintptr_t VALUE
Type that represents a Ruby object.
Definition: value.h:40
static bool RB_FLOAT_TYPE_P(VALUE obj)
Queries if the object is an instance of rb_cFloat.
Definition: value_type.h:264
static bool RB_TYPE_P(VALUE obj, enum ruby_value_type t)
Queries if the given object is of given type.
Definition: value_type.h:376