mirror of
https://github.com/ruby/ruby.git
synced 2022-11-09 12:17:21 -05:00
803a072630
This patch is suggested by nobu.
Benchmark result:
```
require 'benchmark'
n = 10 ** 7
Benchmark.bm do |x|
x.report("Fixnum/Fixnum") { a, b = 5, 2; n.times { a.ceildiv(b) } }
x.report("Bignum/Bignum") { a, b = 10**100, 10**99 - 1; n.times { a.ceildiv(b) } }
x.report("Bignum/Fixnum") { a, b = 10**100, 3; n.times { a.ceildiv(b) } }
end
```
Original:
```
user system total real
Fixnum/Fixnum 3.340009 0.043029 3.383038 ( 3.384022)
Bignum/Bignum 8.229500 0.118543 8.348043 ( 8.349574)
Bignum/Fixnum 8.328971 0.097842 8.426813 ( 8.426952)
```
Improved:
```
user system total real
Fixnum/Fixnum 0.699140 0.000961 0.700101 ( 0.700199)
Bignum/Bignum 5.076165 0.083160 5.159325 ( 5.159360)
Bignum/Fixnum 5.548684 0.115372 5.664056 ( 5.666735)
```
6430 lines
156 KiB
C
6430 lines
156 KiB
C
/**********************************************************************
|
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numeric.c -
|
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|
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$Author$
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created at: Fri Aug 13 18:33:09 JST 1993
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Copyright (C) 1993-2007 Yukihiro Matsumoto
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**********************************************************************/
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#include "ruby/internal/config.h"
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#include <assert.h>
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#include <ctype.h>
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#include <math.h>
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#include <stdio.h>
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|
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#ifdef HAVE_FLOAT_H
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#include <float.h>
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#endif
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|
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#ifdef HAVE_IEEEFP_H
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#include <ieeefp.h>
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#endif
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#include "id.h"
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#include "internal.h"
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#include "internal/array.h"
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#include "internal/compilers.h"
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#include "internal/complex.h"
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#include "internal/enumerator.h"
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#include "internal/gc.h"
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#include "internal/hash.h"
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#include "internal/numeric.h"
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#include "internal/object.h"
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#include "internal/rational.h"
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#include "internal/string.h"
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#include "internal/util.h"
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#include "internal/variable.h"
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#include "ruby/encoding.h"
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#include "ruby/util.h"
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#include "builtin.h"
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|
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/* use IEEE 64bit values if not defined */
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#ifndef FLT_RADIX
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#define FLT_RADIX 2
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#endif
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#ifndef DBL_MIN
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#define DBL_MIN 2.2250738585072014e-308
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#endif
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#ifndef DBL_MAX
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#define DBL_MAX 1.7976931348623157e+308
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#endif
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#ifndef DBL_MIN_EXP
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#define DBL_MIN_EXP (-1021)
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#endif
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#ifndef DBL_MAX_EXP
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#define DBL_MAX_EXP 1024
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#endif
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#ifndef DBL_MIN_10_EXP
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#define DBL_MIN_10_EXP (-307)
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#endif
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#ifndef DBL_MAX_10_EXP
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#define DBL_MAX_10_EXP 308
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#endif
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#ifndef DBL_DIG
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#define DBL_DIG 15
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#endif
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#ifndef DBL_MANT_DIG
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#define DBL_MANT_DIG 53
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#endif
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#ifndef DBL_EPSILON
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#define DBL_EPSILON 2.2204460492503131e-16
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#endif
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#ifndef USE_RB_INFINITY
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#elif !defined(WORDS_BIGENDIAN) /* BYTE_ORDER == LITTLE_ENDIAN */
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const union bytesequence4_or_float rb_infinity = {{0x00, 0x00, 0x80, 0x7f}};
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#else
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const union bytesequence4_or_float rb_infinity = {{0x7f, 0x80, 0x00, 0x00}};
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#endif
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|
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#ifndef USE_RB_NAN
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#elif !defined(WORDS_BIGENDIAN) /* BYTE_ORDER == LITTLE_ENDIAN */
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const union bytesequence4_or_float rb_nan = {{0x00, 0x00, 0xc0, 0x7f}};
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#else
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const union bytesequence4_or_float rb_nan = {{0x7f, 0xc0, 0x00, 0x00}};
|
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#endif
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|
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#ifndef HAVE_ROUND
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double
|
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round(double x)
|
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{
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double f;
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|
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if (x > 0.0) {
|
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f = floor(x);
|
|
x = f + (x - f >= 0.5);
|
|
}
|
|
else if (x < 0.0) {
|
|
f = ceil(x);
|
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x = f - (f - x >= 0.5);
|
|
}
|
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return x;
|
|
}
|
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#endif
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|
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static double
|
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round_half_up(double x, double s)
|
|
{
|
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double f, xs = x * s;
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|
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f = round(xs);
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if (s == 1.0) return f;
|
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if (x > 0) {
|
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if ((double)((f + 0.5) / s) <= x) f += 1;
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x = f;
|
|
}
|
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else {
|
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if ((double)((f - 0.5) / s) >= x) f -= 1;
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x = f;
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}
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return x;
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}
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|
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static double
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round_half_down(double x, double s)
|
|
{
|
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double f, xs = x * s;
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|
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f = round(xs);
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if (x > 0) {
|
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if ((double)((f - 0.5) / s) >= x) f -= 1;
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x = f;
|
|
}
|
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else {
|
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if ((double)((f + 0.5) / s) <= x) f += 1;
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x = f;
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}
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return x;
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|
}
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|
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static double
|
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round_half_even(double x, double s)
|
|
{
|
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double f, d, xs = x * s;
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|
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if (x > 0.0) {
|
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f = floor(xs);
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d = xs - f;
|
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if (d > 0.5)
|
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d = 1.0;
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else if (d == 0.5 || ((double)((f + 0.5) / s) <= x))
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d = fmod(f, 2.0);
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else
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d = 0.0;
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x = f + d;
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}
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else if (x < 0.0) {
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f = ceil(xs);
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d = f - xs;
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if (d > 0.5)
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d = 1.0;
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else if (d == 0.5 || ((double)((f - 0.5) / s) >= x))
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d = fmod(-f, 2.0);
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else
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d = 0.0;
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x = f - d;
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}
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return x;
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}
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|
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static VALUE fix_lshift(long, unsigned long);
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static VALUE fix_rshift(long, unsigned long);
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static VALUE int_pow(long x, unsigned long y);
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static VALUE rb_int_floor(VALUE num, int ndigits);
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static VALUE rb_int_ceil(VALUE num, int ndigits);
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static VALUE flo_to_i(VALUE num);
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static int float_round_overflow(int ndigits, int binexp);
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static int float_round_underflow(int ndigits, int binexp);
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static ID id_coerce;
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#define id_div idDiv
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#define id_divmod idDivmod
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#define id_to_i idTo_i
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#define id_eq idEq
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#define id_cmp idCmp
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VALUE rb_cNumeric;
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VALUE rb_cFloat;
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VALUE rb_cInteger;
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VALUE rb_eZeroDivError;
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VALUE rb_eFloatDomainError;
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static ID id_to, id_by;
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void
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rb_num_zerodiv(void)
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{
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rb_raise(rb_eZeroDivError, "divided by 0");
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}
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enum ruby_num_rounding_mode
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rb_num_get_rounding_option(VALUE opts)
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{
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static ID round_kwds[1];
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VALUE rounding;
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VALUE str;
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const char *s;
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if (!NIL_P(opts)) {
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if (!round_kwds[0]) {
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round_kwds[0] = rb_intern_const("half");
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}
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if (!rb_get_kwargs(opts, round_kwds, 0, 1, &rounding)) goto noopt;
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if (SYMBOL_P(rounding)) {
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str = rb_sym2str(rounding);
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}
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else if (NIL_P(rounding)) {
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goto noopt;
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}
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else if (!RB_TYPE_P(str = rounding, T_STRING)) {
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str = rb_check_string_type(rounding);
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if (NIL_P(str)) goto invalid;
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}
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rb_must_asciicompat(str);
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s = RSTRING_PTR(str);
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switch (RSTRING_LEN(str)) {
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case 2:
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if (rb_memcicmp(s, "up", 2) == 0)
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return RUBY_NUM_ROUND_HALF_UP;
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break;
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case 4:
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if (rb_memcicmp(s, "even", 4) == 0)
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return RUBY_NUM_ROUND_HALF_EVEN;
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if (strncasecmp(s, "down", 4) == 0)
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return RUBY_NUM_ROUND_HALF_DOWN;
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break;
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}
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invalid:
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rb_raise(rb_eArgError, "invalid rounding mode: % "PRIsVALUE, rounding);
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}
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noopt:
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return RUBY_NUM_ROUND_DEFAULT;
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}
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/* experimental API */
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int
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rb_num_to_uint(VALUE val, unsigned int *ret)
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{
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#define NUMERR_TYPE 1
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#define NUMERR_NEGATIVE 2
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#define NUMERR_TOOLARGE 3
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if (FIXNUM_P(val)) {
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long v = FIX2LONG(val);
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#if SIZEOF_INT < SIZEOF_LONG
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if (v > (long)UINT_MAX) return NUMERR_TOOLARGE;
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#endif
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if (v < 0) return NUMERR_NEGATIVE;
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*ret = (unsigned int)v;
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return 0;
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}
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if (RB_BIGNUM_TYPE_P(val)) {
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if (BIGNUM_NEGATIVE_P(val)) return NUMERR_NEGATIVE;
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#if SIZEOF_INT < SIZEOF_LONG
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/* long is 64bit */
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return NUMERR_TOOLARGE;
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#else
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/* long is 32bit */
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if (rb_absint_size(val, NULL) > sizeof(int)) return NUMERR_TOOLARGE;
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*ret = (unsigned int)rb_big2ulong((VALUE)val);
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return 0;
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#endif
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}
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return NUMERR_TYPE;
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}
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#define method_basic_p(klass) rb_method_basic_definition_p(klass, mid)
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static inline int
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int_pos_p(VALUE num)
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{
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if (FIXNUM_P(num)) {
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return FIXNUM_POSITIVE_P(num);
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}
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else if (RB_BIGNUM_TYPE_P(num)) {
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return BIGNUM_POSITIVE_P(num);
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}
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rb_raise(rb_eTypeError, "not an Integer");
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}
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static inline int
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int_neg_p(VALUE num)
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{
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if (FIXNUM_P(num)) {
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return FIXNUM_NEGATIVE_P(num);
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}
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else if (RB_BIGNUM_TYPE_P(num)) {
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return BIGNUM_NEGATIVE_P(num);
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}
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rb_raise(rb_eTypeError, "not an Integer");
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}
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int
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rb_int_positive_p(VALUE num)
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{
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return int_pos_p(num);
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}
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int
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rb_int_negative_p(VALUE num)
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{
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return int_neg_p(num);
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}
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int
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rb_num_negative_p(VALUE num)
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{
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return rb_num_negative_int_p(num);
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}
|
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static VALUE
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num_funcall_op_0(VALUE x, VALUE arg, int recursive)
|
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{
|
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ID func = (ID)arg;
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if (recursive) {
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const char *name = rb_id2name(func);
|
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if (ISALNUM(name[0])) {
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rb_name_error(func, "%"PRIsVALUE".%"PRIsVALUE,
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x, ID2SYM(func));
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}
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else if (name[0] && name[1] == '@' && !name[2]) {
|
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rb_name_error(func, "%c%"PRIsVALUE,
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name[0], x);
|
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}
|
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else {
|
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rb_name_error(func, "%"PRIsVALUE"%"PRIsVALUE,
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ID2SYM(func), x);
|
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}
|
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}
|
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return rb_funcallv(x, func, 0, 0);
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}
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static VALUE
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num_funcall0(VALUE x, ID func)
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{
|
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return rb_exec_recursive(num_funcall_op_0, x, (VALUE)func);
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}
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NORETURN(static void num_funcall_op_1_recursion(VALUE x, ID func, VALUE y));
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|
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static void
|
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num_funcall_op_1_recursion(VALUE x, ID func, VALUE y)
|
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{
|
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const char *name = rb_id2name(func);
|
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if (ISALNUM(name[0])) {
|
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rb_name_error(func, "%"PRIsVALUE".%"PRIsVALUE"(%"PRIsVALUE")",
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x, ID2SYM(func), y);
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}
|
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else {
|
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rb_name_error(func, "%"PRIsVALUE"%"PRIsVALUE"%"PRIsVALUE,
|
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x, ID2SYM(func), y);
|
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}
|
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}
|
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|
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static VALUE
|
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num_funcall_op_1(VALUE y, VALUE arg, int recursive)
|
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{
|
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ID func = (ID)((VALUE *)arg)[0];
|
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VALUE x = ((VALUE *)arg)[1];
|
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if (recursive) {
|
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num_funcall_op_1_recursion(x, func, y);
|
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}
|
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return rb_funcall(x, func, 1, y);
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}
|
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|
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static VALUE
|
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num_funcall1(VALUE x, ID func, VALUE y)
|
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{
|
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VALUE args[2];
|
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args[0] = (VALUE)func;
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args[1] = x;
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return rb_exec_recursive_paired(num_funcall_op_1, y, x, (VALUE)args);
|
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}
|
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|
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/*
|
|
* call-seq:
|
|
* coerce(other) -> array
|
|
*
|
|
* Returns a 2-element array containing two numeric elements,
|
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* formed from the two operands +self+ and +other+,
|
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* of a common compatible type.
|
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*
|
|
* Of the Core and Standard Library classes,
|
|
* Integer, Rational, and Complex use this implementation.
|
|
*
|
|
* Examples:
|
|
*
|
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* i = 2 # => 2
|
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* i.coerce(3) # => [3, 2]
|
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* i.coerce(3.0) # => [3.0, 2.0]
|
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* i.coerce(Rational(1, 2)) # => [0.5, 2.0]
|
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* i.coerce(Complex(3, 4)) # Raises RangeError.
|
|
*
|
|
* r = Rational(5, 2) # => (5/2)
|
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* r.coerce(2) # => [(2/1), (5/2)]
|
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* r.coerce(2.0) # => [2.0, 2.5]
|
|
* r.coerce(Rational(2, 3)) # => [(2/3), (5/2)]
|
|
* r.coerce(Complex(3, 4)) # => [(3+4i), ((5/2)+0i)]
|
|
*
|
|
* c = Complex(2, 3) # => (2+3i)
|
|
* c.coerce(2) # => [(2+0i), (2+3i)]
|
|
* c.coerce(2.0) # => [(2.0+0i), (2+3i)]
|
|
* c.coerce(Rational(1, 2)) # => [((1/2)+0i), (2+3i)]
|
|
* c.coerce(Complex(3, 4)) # => [(3+4i), (2+3i)]
|
|
*
|
|
* Raises an exception if any type conversion fails.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
num_coerce(VALUE x, VALUE y)
|
|
{
|
|
if (CLASS_OF(x) == CLASS_OF(y))
|
|
return rb_assoc_new(y, x);
|
|
x = rb_Float(x);
|
|
y = rb_Float(y);
|
|
return rb_assoc_new(y, x);
|
|
}
|
|
|
|
NORETURN(static void coerce_failed(VALUE x, VALUE y));
|
|
static void
|
|
coerce_failed(VALUE x, VALUE y)
|
|
{
|
|
if (SPECIAL_CONST_P(y) || SYMBOL_P(y) || RB_FLOAT_TYPE_P(y)) {
|
|
y = rb_inspect(y);
|
|
}
|
|
else {
|
|
y = rb_obj_class(y);
|
|
}
|
|
rb_raise(rb_eTypeError, "%"PRIsVALUE" can't be coerced into %"PRIsVALUE,
|
|
y, rb_obj_class(x));
|
|
}
|
|
|
|
static int
|
|
do_coerce(VALUE *x, VALUE *y, int err)
|
|
{
|
|
VALUE ary = rb_check_funcall(*y, id_coerce, 1, x);
|
|
if (ary == Qundef) {
|
|
if (err) {
|
|
coerce_failed(*x, *y);
|
|
}
|
|
return FALSE;
|
|
}
|
|
if (!err && NIL_P(ary)) {
|
|
return FALSE;
|
|
}
|
|
if (!RB_TYPE_P(ary, T_ARRAY) || RARRAY_LEN(ary) != 2) {
|
|
rb_raise(rb_eTypeError, "coerce must return [x, y]");
|
|
}
|
|
|
|
*x = RARRAY_AREF(ary, 0);
|
|
*y = RARRAY_AREF(ary, 1);
|
|
return TRUE;
|
|
}
|
|
|
|
VALUE
|
|
rb_num_coerce_bin(VALUE x, VALUE y, ID func)
|
|
{
|
|
do_coerce(&x, &y, TRUE);
|
|
return rb_funcall(x, func, 1, y);
|
|
}
|
|
|
|
VALUE
|
|
rb_num_coerce_cmp(VALUE x, VALUE y, ID func)
|
|
{
|
|
if (do_coerce(&x, &y, FALSE))
|
|
return rb_funcall(x, func, 1, y);
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
ensure_cmp(VALUE c, VALUE x, VALUE y)
|
|
{
|
|
if (NIL_P(c)) rb_cmperr(x, y);
|
|
return c;
|
|
}
|
|
|
|
VALUE
|
|
rb_num_coerce_relop(VALUE x, VALUE y, ID func)
|
|
{
|
|
VALUE x0 = x, y0 = y;
|
|
|
|
if (!do_coerce(&x, &y, FALSE)) {
|
|
rb_cmperr(x0, y0);
|
|
UNREACHABLE_RETURN(Qnil);
|
|
}
|
|
return ensure_cmp(rb_funcall(x, func, 1, y), x0, y0);
|
|
}
|
|
|
|
NORETURN(static VALUE num_sadded(VALUE x, VALUE name));
|
|
|
|
/*
|
|
* :nodoc:
|
|
*
|
|
* Trap attempts to add methods to Numeric objects. Always raises a TypeError.
|
|
*
|
|
* Numerics should be values; singleton_methods should not be added to them.
|
|
*/
|
|
|
|
static VALUE
|
|
num_sadded(VALUE x, VALUE name)
|
|
{
|
|
ID mid = rb_to_id(name);
|
|
/* ruby_frame = ruby_frame->prev; */ /* pop frame for "singleton_method_added" */
|
|
rb_remove_method_id(rb_singleton_class(x), mid);
|
|
rb_raise(rb_eTypeError,
|
|
"can't define singleton method \"%"PRIsVALUE"\" for %"PRIsVALUE,
|
|
rb_id2str(mid),
|
|
rb_obj_class(x));
|
|
|
|
UNREACHABLE_RETURN(Qnil);
|
|
}
|
|
|
|
#if 0
|
|
/*
|
|
* call-seq:
|
|
* clone(freeze: true) -> self
|
|
*
|
|
* Returns +self+.
|
|
*
|
|
* Raises an exception if the value for +freeze+ is neither +true+ nor +nil+.
|
|
*
|
|
* Related: Numeric#dup.
|
|
*
|
|
*/
|
|
static VALUE
|
|
num_clone(int argc, VALUE *argv, VALUE x)
|
|
{
|
|
return rb_immutable_obj_clone(argc, argv, x);
|
|
}
|
|
#else
|
|
# define num_clone rb_immutable_obj_clone
|
|
#endif
|
|
|
|
#if 0
|
|
/*
|
|
* call-seq:
|
|
* dup -> self
|
|
*
|
|
* Returns +self+.
|
|
*
|
|
* Related: Numeric#clone.
|
|
*
|
|
*/
|
|
static VALUE
|
|
num_dup(VALUE x)
|
|
{
|
|
return x;
|
|
}
|
|
#else
|
|
# define num_dup num_uplus
|
|
#endif
|
|
|
|
/*
|
|
* call-seq:
|
|
* +self -> self
|
|
*
|
|
* Returns +self+.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
num_uplus(VALUE num)
|
|
{
|
|
return num;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* i -> complex
|
|
*
|
|
* Returns <tt>Complex(0, self)</tt>:
|
|
*
|
|
* 2.i # => (0+2i)
|
|
* -2.i # => (0-2i)
|
|
* 2.0.i # => (0+2.0i)
|
|
* Rational(1, 2).i # => (0+(1/2)*i)
|
|
* Complex(3, 4).i # Raises NoMethodError.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
num_imaginary(VALUE num)
|
|
{
|
|
return rb_complex_new(INT2FIX(0), num);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* -self -> numeric
|
|
*
|
|
* Unary Minus---Returns the receiver, negated.
|
|
*/
|
|
|
|
static VALUE
|
|
num_uminus(VALUE num)
|
|
{
|
|
VALUE zero;
|
|
|
|
zero = INT2FIX(0);
|
|
do_coerce(&zero, &num, TRUE);
|
|
|
|
return num_funcall1(zero, '-', num);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* fdiv(other) -> float
|
|
*
|
|
* Returns the quotient <tt>self/other</tt> as a float,
|
|
* using method +/+ in the derived class of +self+.
|
|
* (\Numeric itself does not define method +/+.)
|
|
*
|
|
* Of the Core and Standard Library classes,
|
|
* only BigDecimal uses this implementation.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
num_fdiv(VALUE x, VALUE y)
|
|
{
|
|
return rb_funcall(rb_Float(x), '/', 1, y);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* div(other) -> integer
|
|
*
|
|
* Returns the quotient <tt>self/other</tt> as an integer (via +floor+),
|
|
* using method +/+ in the derived class of +self+.
|
|
* (\Numeric itself does not define method +/+.)
|
|
*
|
|
* Of the Core and Standard Library classes,
|
|
* Only Float and Rational use this implementation.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
num_div(VALUE x, VALUE y)
|
|
{
|
|
if (rb_equal(INT2FIX(0), y)) rb_num_zerodiv();
|
|
return rb_funcall(num_funcall1(x, '/', y), rb_intern("floor"), 0);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self % other -> real_numeric
|
|
*
|
|
* Returns +self+ modulo +other+ as a real number.
|
|
*
|
|
* Of the Core and Standard Library classes,
|
|
* only Rational uses this implementation.
|
|
*
|
|
* For \Rational +r+ and real number +n+, these expressions are equivalent:
|
|
*
|
|
* r % n
|
|
* r-n*(r/n).floor
|
|
* r.divmod(n)[1]
|
|
*
|
|
* See Numeric#divmod.
|
|
*
|
|
* Examples:
|
|
*
|
|
* r = Rational(1, 2) # => (1/2)
|
|
* r2 = Rational(2, 3) # => (2/3)
|
|
* r % r2 # => (1/2)
|
|
* r % 2 # => (1/2)
|
|
* r % 2.0 # => 0.5
|
|
*
|
|
* r = Rational(301,100) # => (301/100)
|
|
* r2 = Rational(7,5) # => (7/5)
|
|
* r % r2 # => (21/100)
|
|
* r % -r2 # => (-119/100)
|
|
* (-r) % r2 # => (119/100)
|
|
* (-r) %-r2 # => (-21/100)
|
|
*
|
|
* Numeric#modulo is an alias for Numeric#%.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
num_modulo(VALUE x, VALUE y)
|
|
{
|
|
VALUE q = num_funcall1(x, id_div, y);
|
|
return rb_funcall(x, '-', 1,
|
|
rb_funcall(y, '*', 1, q));
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* remainder(other) -> real_number
|
|
*
|
|
* Returns the remainder after dividing +self+ by +other+.
|
|
*
|
|
* Of the Core and Standard Library classes,
|
|
* only Float and Rational use this implementation.
|
|
*
|
|
* Examples:
|
|
*
|
|
* 11.0.remainder(4) # => 3.0
|
|
* 11.0.remainder(-4) # => 3.0
|
|
* -11.0.remainder(4) # => -3.0
|
|
* -11.0.remainder(-4) # => -3.0
|
|
*
|
|
* 12.0.remainder(4) # => 0.0
|
|
* 12.0.remainder(-4) # => 0.0
|
|
* -12.0.remainder(4) # => -0.0
|
|
* -12.0.remainder(-4) # => -0.0
|
|
*
|
|
* 13.0.remainder(4.0) # => 1.0
|
|
* 13.0.remainder(Rational(4, 1)) # => 1.0
|
|
*
|
|
* Rational(13, 1).remainder(4) # => (1/1)
|
|
* Rational(13, 1).remainder(-4) # => (1/1)
|
|
* Rational(-13, 1).remainder(4) # => (-1/1)
|
|
* Rational(-13, 1).remainder(-4) # => (-1/1)
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
num_remainder(VALUE x, VALUE y)
|
|
{
|
|
VALUE z = num_funcall1(x, '%', y);
|
|
|
|
if ((!rb_equal(z, INT2FIX(0))) &&
|
|
((rb_num_negative_int_p(x) &&
|
|
rb_num_positive_int_p(y)) ||
|
|
(rb_num_positive_int_p(x) &&
|
|
rb_num_negative_int_p(y)))) {
|
|
if (RB_FLOAT_TYPE_P(y)) {
|
|
if (isinf(RFLOAT_VALUE(y))) {
|
|
return x;
|
|
}
|
|
}
|
|
return rb_funcall(z, '-', 1, y);
|
|
}
|
|
return z;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* divmod(other) -> array
|
|
*
|
|
* Returns a 2-element array <tt>[q, r]</tt>, where
|
|
*
|
|
* q = (self/other).floor # Quotient
|
|
* r = self % other # Remainder
|
|
*
|
|
* Of the Core and Standard Library classes,
|
|
* only Rational uses this implementation.
|
|
*
|
|
* Examples:
|
|
*
|
|
* Rational(11, 1).divmod(4) # => [2, (3/1)]
|
|
* Rational(11, 1).divmod(-4) # => [-3, (-1/1)]
|
|
* Rational(-11, 1).divmod(4) # => [-3, (1/1)]
|
|
* Rational(-11, 1).divmod(-4) # => [2, (-3/1)]
|
|
*
|
|
* Rational(12, 1).divmod(4) # => [3, (0/1)]
|
|
* Rational(12, 1).divmod(-4) # => [-3, (0/1)]
|
|
* Rational(-12, 1).divmod(4) # => [-3, (0/1)]
|
|
* Rational(-12, 1).divmod(-4) # => [3, (0/1)]
|
|
*
|
|
* Rational(13, 1).divmod(4.0) # => [3, 1.0]
|
|
* Rational(13, 1).divmod(Rational(4, 11)) # => [35, (3/11)]
|
|
*/
|
|
|
|
static VALUE
|
|
num_divmod(VALUE x, VALUE y)
|
|
{
|
|
return rb_assoc_new(num_div(x, y), num_modulo(x, y));
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* abs -> numeric
|
|
*
|
|
* Returns the absolute value of +self+.
|
|
*
|
|
* 12.abs #=> 12
|
|
* (-34.56).abs #=> 34.56
|
|
* -34.56.abs #=> 34.56
|
|
*
|
|
* Numeric#magnitude is an alias for Numeric#abs.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
num_abs(VALUE num)
|
|
{
|
|
if (rb_num_negative_int_p(num)) {
|
|
return num_funcall0(num, idUMinus);
|
|
}
|
|
return num;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* zero? -> true or false
|
|
*
|
|
* Returns +true+ if +zero+ has a zero value, +false+ otherwise.
|
|
*
|
|
* Of the Core and Standard Library classes,
|
|
* only Rational and Complex use this implementation.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
num_zero_p(VALUE num)
|
|
{
|
|
return rb_equal(num, INT2FIX(0));
|
|
}
|
|
|
|
static bool
|
|
int_zero_p(VALUE num)
|
|
{
|
|
if (FIXNUM_P(num)) {
|
|
return FIXNUM_ZERO_P(num);
|
|
}
|
|
assert(RB_BIGNUM_TYPE_P(num));
|
|
return rb_bigzero_p(num);
|
|
}
|
|
|
|
VALUE
|
|
rb_int_zero_p(VALUE num)
|
|
{
|
|
return RBOOL(int_zero_p(num));
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* nonzero? -> self or nil
|
|
*
|
|
* Returns +self+ if +self+ is not a zero value, +nil+ otherwise;
|
|
* uses method <tt>zero?</tt> for the evaluation.
|
|
*
|
|
* The returned +self+ allows the method to be chained:
|
|
*
|
|
* a = %w[z Bb bB bb BB a aA Aa AA A]
|
|
* a.sort {|a, b| (a.downcase <=> b.downcase).nonzero? || a <=> b }
|
|
* # => ["A", "a", "AA", "Aa", "aA", "BB", "Bb", "bB", "bb", "z"]
|
|
*
|
|
* Of the Core and Standard Library classes,
|
|
* Integer, Float, Rational, and Complex use this implementation.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
num_nonzero_p(VALUE num)
|
|
{
|
|
if (RTEST(num_funcall0(num, rb_intern("zero?")))) {
|
|
return Qnil;
|
|
}
|
|
return num;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* to_int -> integer
|
|
*
|
|
* Returns +self+ as an integer;
|
|
* converts using method +to_i+ in the derived class.
|
|
*
|
|
* Of the Core and Standard Library classes,
|
|
* only Rational and Complex use this implementation.
|
|
*
|
|
* Examples:
|
|
*
|
|
* Rational(1, 2).to_int # => 0
|
|
* Rational(2, 1).to_int # => 2
|
|
* Complex(2, 0).to_int # => 2
|
|
* Complex(2, 1) # Raises RangeError (non-zero imaginary part)
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
num_to_int(VALUE num)
|
|
{
|
|
return num_funcall0(num, id_to_i);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* positive? -> true or false
|
|
*
|
|
* Returns +true+ if +self+ is greater than 0, +false+ otherwise.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
num_positive_p(VALUE num)
|
|
{
|
|
const ID mid = '>';
|
|
|
|
if (FIXNUM_P(num)) {
|
|
if (method_basic_p(rb_cInteger))
|
|
return RBOOL((SIGNED_VALUE)num > (SIGNED_VALUE)INT2FIX(0));
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(num)) {
|
|
if (method_basic_p(rb_cInteger))
|
|
return RBOOL(BIGNUM_POSITIVE_P(num) && !rb_bigzero_p(num));
|
|
}
|
|
return rb_num_compare_with_zero(num, mid);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* negative? -> true or false
|
|
*
|
|
* Returns +true+ if +self+ is less than 0, +false+ otherwise.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
num_negative_p(VALUE num)
|
|
{
|
|
return RBOOL(rb_num_negative_int_p(num));
|
|
}
|
|
|
|
|
|
/********************************************************************
|
|
*
|
|
* Document-class: Float
|
|
*
|
|
* A \Float object represents a sometimes-inexact real number using the native
|
|
* architecture's double-precision floating point representation.
|
|
*
|
|
* Floating point has a different arithmetic and is an inexact number.
|
|
* So you should know its esoteric system. See following:
|
|
*
|
|
* - https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html
|
|
* - https://github.com/rdp/ruby_tutorials_core/wiki/Ruby-Talk-FAQ#floats_imprecise
|
|
* - https://en.wikipedia.org/wiki/Floating_point#Accuracy_problems
|
|
*
|
|
* You can create a \Float object explicitly with:
|
|
*
|
|
* - A {floating-point literal}[rdoc-ref:syntax/literals.rdoc@Float+Literals].
|
|
*
|
|
* You can convert certain objects to Floats with:
|
|
*
|
|
* - \Method #Float.
|
|
*
|
|
* == What's Here
|
|
*
|
|
* First, what's elsewhere. \Class \Float:
|
|
*
|
|
* - Inherits from {class Numeric}[rdoc-ref:Numeric@What-27s+Here].
|
|
*
|
|
* Here, class \Float provides methods for:
|
|
*
|
|
* - {Querying}[rdoc-ref:Float@Querying]
|
|
* - {Comparing}[rdoc-ref:Float@Comparing]
|
|
* - {Converting}[rdoc-ref:Float@Converting]
|
|
*
|
|
* === Querying
|
|
*
|
|
* - #finite?: Returns whether +self+ is finite.
|
|
* - #hash: Returns the integer hash code for +self+.
|
|
* - #infinite?: Returns whether +self+ is infinite.
|
|
* - #nan?: Returns whether +self+ is a NaN (not-a-number).
|
|
*
|
|
* === Comparing
|
|
*
|
|
* - #<: Returns whether +self+ is less than the given value.
|
|
* - #<=: Returns whether +self+ is less than or equal to the given value.
|
|
* - #<=>: Returns a number indicating whether +self+ is less than, equal
|
|
* to, or greater than the given value.
|
|
* - #== (aliased as #=== and #eql?): Returns whether +self+ is equal to
|
|
* the given value.
|
|
* - #>: Returns whether +self+ is greater than the given value.
|
|
* - #>=: Returns whether +self+ is greater than or equal to the given value.
|
|
*
|
|
* === Converting
|
|
*
|
|
* - #% (aliased as #modulo): Returns +self+ modulo the given value.
|
|
* - #*: Returns the product of +self+ and the given value.
|
|
* - #**: Returns the value of +self+ raised to the power of the given value.
|
|
* - #+: Returns the sum of +self+ and the given value.
|
|
* - #-: Returns the difference of +self+ and the given value.
|
|
* - #/: Returns the quotient of +self+ and the given value.
|
|
* - #ceil: Returns the smallest number greater than or equal to +self+.
|
|
* - #coerce: Returns a 2-element array containing the given value converted to a \Float
|
|
and +self+
|
|
* - #divmod: Returns a 2-element array containing the quotient and remainder
|
|
* results of dividing +self+ by the given value.
|
|
* - #fdiv: Returns the Float result of dividing +self+ by the given value.
|
|
* - #floor: Returns the greatest number smaller than or equal to +self+.
|
|
* - #next_float: Returns the next-larger representable \Float.
|
|
* - #prev_float: Returns the next-smaller representable \Float.
|
|
* - #quo: Returns the quotient from dividing +self+ by the given value.
|
|
* - #round: Returns +self+ rounded to the nearest value, to a given precision.
|
|
* - #to_i (aliased as #to_int): Returns +self+ truncated to an Integer.
|
|
* - #to_s (aliased as #inspect): Returns a string containing the place-value
|
|
* representation of +self+ in the given radix.
|
|
* - #truncate: Returns +self+ truncated to a given precision.
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_float_new_in_heap(double d)
|
|
{
|
|
NEWOBJ_OF(flt, struct RFloat, rb_cFloat, T_FLOAT | (RGENGC_WB_PROTECTED_FLOAT ? FL_WB_PROTECTED : 0));
|
|
|
|
#if SIZEOF_DOUBLE <= SIZEOF_VALUE
|
|
flt->float_value = d;
|
|
#else
|
|
union {
|
|
double d;
|
|
rb_float_value_type v;
|
|
} u = {d};
|
|
flt->float_value = u.v;
|
|
#endif
|
|
OBJ_FREEZE((VALUE)flt);
|
|
return (VALUE)flt;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* to_s -> string
|
|
*
|
|
* Returns a string containing a representation of +self+;
|
|
* depending of the value of +self+, the string representation
|
|
* may contain:
|
|
*
|
|
* - A fixed-point number.
|
|
* - A number in "scientific notation" (containing an exponent).
|
|
* - 'Infinity'.
|
|
* - '-Infinity'.
|
|
* - 'NaN' (indicating not-a-number).
|
|
*
|
|
* 3.14.to_s # => "3.14"
|
|
* (10.1**50).to_s # => "1.644631821843879e+50"
|
|
* (10.1**500).to_s # => "Infinity"
|
|
* (-10.1**500).to_s # => "-Infinity"
|
|
* (0.0/0.0).to_s # => "NaN"
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
flo_to_s(VALUE flt)
|
|
{
|
|
enum {decimal_mant = DBL_MANT_DIG-DBL_DIG};
|
|
enum {float_dig = DBL_DIG+1};
|
|
char buf[float_dig + (decimal_mant + CHAR_BIT - 1) / CHAR_BIT + 10];
|
|
double value = RFLOAT_VALUE(flt);
|
|
VALUE s;
|
|
char *p, *e;
|
|
int sign, decpt, digs;
|
|
|
|
if (isinf(value)) {
|
|
static const char minf[] = "-Infinity";
|
|
const int pos = (value > 0); /* skip "-" */
|
|
return rb_usascii_str_new(minf+pos, strlen(minf)-pos);
|
|
}
|
|
else if (isnan(value))
|
|
return rb_usascii_str_new2("NaN");
|
|
|
|
p = ruby_dtoa(value, 0, 0, &decpt, &sign, &e);
|
|
s = sign ? rb_usascii_str_new_cstr("-") : rb_usascii_str_new(0, 0);
|
|
if ((digs = (int)(e - p)) >= (int)sizeof(buf)) digs = (int)sizeof(buf) - 1;
|
|
memcpy(buf, p, digs);
|
|
xfree(p);
|
|
if (decpt > 0) {
|
|
if (decpt < digs) {
|
|
memmove(buf + decpt + 1, buf + decpt, digs - decpt);
|
|
buf[decpt] = '.';
|
|
rb_str_cat(s, buf, digs + 1);
|
|
}
|
|
else if (decpt <= DBL_DIG) {
|
|
long len;
|
|
char *ptr;
|
|
rb_str_cat(s, buf, digs);
|
|
rb_str_resize(s, (len = RSTRING_LEN(s)) + decpt - digs + 2);
|
|
ptr = RSTRING_PTR(s) + len;
|
|
if (decpt > digs) {
|
|
memset(ptr, '0', decpt - digs);
|
|
ptr += decpt - digs;
|
|
}
|
|
memcpy(ptr, ".0", 2);
|
|
}
|
|
else {
|
|
goto exp;
|
|
}
|
|
}
|
|
else if (decpt > -4) {
|
|
long len;
|
|
char *ptr;
|
|
rb_str_cat(s, "0.", 2);
|
|
rb_str_resize(s, (len = RSTRING_LEN(s)) - decpt + digs);
|
|
ptr = RSTRING_PTR(s);
|
|
memset(ptr += len, '0', -decpt);
|
|
memcpy(ptr -= decpt, buf, digs);
|
|
}
|
|
else {
|
|
goto exp;
|
|
}
|
|
return s;
|
|
|
|
exp:
|
|
if (digs > 1) {
|
|
memmove(buf + 2, buf + 1, digs - 1);
|
|
}
|
|
else {
|
|
buf[2] = '0';
|
|
digs++;
|
|
}
|
|
buf[1] = '.';
|
|
rb_str_cat(s, buf, digs + 1);
|
|
rb_str_catf(s, "e%+03d", decpt - 1);
|
|
return s;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* coerce(other) -> array
|
|
*
|
|
* Returns a 2-element array containing +other+ converted to a \Float
|
|
* and +self+:
|
|
*
|
|
* f = 3.14 # => 3.14
|
|
* f.coerce(2) # => [2.0, 3.14]
|
|
* f.coerce(2.0) # => [2.0, 3.14]
|
|
* f.coerce(Rational(1, 2)) # => [0.5, 3.14]
|
|
* f.coerce(Complex(1, 0)) # => [1.0, 3.14]
|
|
*
|
|
* Raises an exception if a type conversion fails.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
flo_coerce(VALUE x, VALUE y)
|
|
{
|
|
return rb_assoc_new(rb_Float(y), x);
|
|
}
|
|
|
|
MJIT_FUNC_EXPORTED VALUE
|
|
rb_float_uminus(VALUE flt)
|
|
{
|
|
return DBL2NUM(-RFLOAT_VALUE(flt));
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self + other -> numeric
|
|
*
|
|
* Returns a new \Float which is the sum of +self+ and +other+:
|
|
*
|
|
* f = 3.14
|
|
* f + 1 # => 4.140000000000001
|
|
* f + 1.0 # => 4.140000000000001
|
|
* f + Rational(1, 1) # => 4.140000000000001
|
|
* f + Complex(1, 0) # => (4.140000000000001+0i)
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_float_plus(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y));
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y));
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y));
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, '+');
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self - other -> numeric
|
|
*
|
|
* Returns a new \Float which is the difference of +self+ and +other+:
|
|
*
|
|
* f = 3.14
|
|
* f - 1 # => 2.14
|
|
* f - 1.0 # => 2.14
|
|
* f - Rational(1, 1) # => 2.14
|
|
* f - Complex(1, 0) # => (2.14+0i)
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_float_minus(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y));
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y));
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y));
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, '-');
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self * other -> numeric
|
|
*
|
|
* Returns a new \Float which is the product of +self+ and +other+:
|
|
*
|
|
* f = 3.14
|
|
* f * 2 # => 6.28
|
|
* f * 2.0 # => 6.28
|
|
* f * Rational(1, 2) # => 1.57
|
|
* f * Complex(2, 0) # => (6.28+0.0i)
|
|
*/
|
|
|
|
VALUE
|
|
rb_float_mul(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y));
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y));
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y));
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, '*');
|
|
}
|
|
}
|
|
|
|
static double
|
|
double_div_double(double x, double y)
|
|
{
|
|
if (LIKELY(y != 0.0)) {
|
|
return x / y;
|
|
}
|
|
else if (x == 0.0) {
|
|
return nan("");
|
|
}
|
|
else {
|
|
double z = signbit(y) ? -1.0 : 1.0;
|
|
return x * z * HUGE_VAL;
|
|
}
|
|
}
|
|
|
|
MJIT_FUNC_EXPORTED VALUE
|
|
rb_flo_div_flo(VALUE x, VALUE y)
|
|
{
|
|
double num = RFLOAT_VALUE(x);
|
|
double den = RFLOAT_VALUE(y);
|
|
double ret = double_div_double(num, den);
|
|
return DBL2NUM(ret);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self / other -> numeric
|
|
*
|
|
* Returns a new \Float which is the result of dividing +self+ by +other+:
|
|
*
|
|
* f = 3.14
|
|
* f / 2 # => 1.57
|
|
* f / 2.0 # => 1.57
|
|
* f / Rational(2, 1) # => 1.57
|
|
* f / Complex(2, 0) # => (1.57+0.0i)
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_float_div(VALUE x, VALUE y)
|
|
{
|
|
double num = RFLOAT_VALUE(x);
|
|
double den;
|
|
double ret;
|
|
|
|
if (FIXNUM_P(y)) {
|
|
den = FIX2LONG(y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
den = rb_big2dbl(y);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
den = RFLOAT_VALUE(y);
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, '/');
|
|
}
|
|
|
|
ret = double_div_double(num, den);
|
|
return DBL2NUM(ret);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* quo(other) -> numeric
|
|
*
|
|
* Returns the quotient from dividing +self+ by +other+:
|
|
*
|
|
* f = 3.14
|
|
* f.quo(2) # => 1.57
|
|
* f.quo(-2) # => -1.57
|
|
* f.quo(Rational(2, 1)) # => 1.57
|
|
* f.quo(Complex(2, 0)) # => (1.57+0.0i)
|
|
*
|
|
* Float#fdiv is an alias for Float#quo.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
flo_quo(VALUE x, VALUE y)
|
|
{
|
|
return num_funcall1(x, '/', y);
|
|
}
|
|
|
|
static void
|
|
flodivmod(double x, double y, double *divp, double *modp)
|
|
{
|
|
double div, mod;
|
|
|
|
if (isnan(y)) {
|
|
/* y is NaN so all results are NaN */
|
|
if (modp) *modp = y;
|
|
if (divp) *divp = y;
|
|
return;
|
|
}
|
|
if (y == 0.0) rb_num_zerodiv();
|
|
if ((x == 0.0) || (isinf(y) && !isinf(x)))
|
|
mod = x;
|
|
else {
|
|
#ifdef HAVE_FMOD
|
|
mod = fmod(x, y);
|
|
#else
|
|
double z;
|
|
|
|
modf(x/y, &z);
|
|
mod = x - z * y;
|
|
#endif
|
|
}
|
|
if (isinf(x) && !isinf(y))
|
|
div = x;
|
|
else {
|
|
div = (x - mod) / y;
|
|
if (modp && divp) div = round(div);
|
|
}
|
|
if (y*mod < 0) {
|
|
mod += y;
|
|
div -= 1.0;
|
|
}
|
|
if (modp) *modp = mod;
|
|
if (divp) *divp = div;
|
|
}
|
|
|
|
/*
|
|
* Returns the modulo of division of x by y.
|
|
* An error will be raised if y == 0.
|
|
*/
|
|
|
|
MJIT_FUNC_EXPORTED double
|
|
ruby_float_mod(double x, double y)
|
|
{
|
|
double mod;
|
|
flodivmod(x, y, 0, &mod);
|
|
return mod;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self % other -> float
|
|
*
|
|
* Returns +self+ modulo +other+ as a float.
|
|
*
|
|
* For float +f+ and real number +r+, these expressions are equivalent:
|
|
*
|
|
* f % r
|
|
* f-r*(f/r).floor
|
|
* f.divmod(r)[1]
|
|
*
|
|
* See Numeric#divmod.
|
|
*
|
|
* Examples:
|
|
*
|
|
* 10.0 % 2 # => 0.0
|
|
* 10.0 % 3 # => 1.0
|
|
* 10.0 % 4 # => 2.0
|
|
*
|
|
* 10.0 % -2 # => 0.0
|
|
* 10.0 % -3 # => -2.0
|
|
* 10.0 % -4 # => -2.0
|
|
*
|
|
* 10.0 % 4.0 # => 2.0
|
|
* 10.0 % Rational(4, 1) # => 2.0
|
|
*
|
|
* Float#modulo is an alias for Float#%.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
flo_mod(VALUE x, VALUE y)
|
|
{
|
|
double fy;
|
|
|
|
if (FIXNUM_P(y)) {
|
|
fy = (double)FIX2LONG(y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
fy = rb_big2dbl(y);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
fy = RFLOAT_VALUE(y);
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, '%');
|
|
}
|
|
return DBL2NUM(ruby_float_mod(RFLOAT_VALUE(x), fy));
|
|
}
|
|
|
|
static VALUE
|
|
dbl2ival(double d)
|
|
{
|
|
if (FIXABLE(d)) {
|
|
return LONG2FIX((long)d);
|
|
}
|
|
return rb_dbl2big(d);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* divmod(other) -> array
|
|
*
|
|
* Returns a 2-element array <tt>[q, r]</tt>, where
|
|
*
|
|
* q = (self/other).floor # Quotient
|
|
* r = self % other # Remainder
|
|
*
|
|
* Examples:
|
|
*
|
|
* 11.0.divmod(4) # => [2, 3.0]
|
|
* 11.0.divmod(-4) # => [-3, -1.0]
|
|
* -11.0.divmod(4) # => [-3, 1.0]
|
|
* -11.0.divmod(-4) # => [2, -3.0]
|
|
*
|
|
* 12.0.divmod(4) # => [3, 0.0]
|
|
* 12.0.divmod(-4) # => [-3, 0.0]
|
|
* -12.0.divmod(4) # => [-3, -0.0]
|
|
* -12.0.divmod(-4) # => [3, -0.0]
|
|
*
|
|
* 13.0.divmod(4.0) # => [3, 1.0]
|
|
* 13.0.divmod(Rational(4, 1)) # => [3, 1.0]
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
flo_divmod(VALUE x, VALUE y)
|
|
{
|
|
double fy, div, mod;
|
|
volatile VALUE a, b;
|
|
|
|
if (FIXNUM_P(y)) {
|
|
fy = (double)FIX2LONG(y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
fy = rb_big2dbl(y);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
fy = RFLOAT_VALUE(y);
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, id_divmod);
|
|
}
|
|
flodivmod(RFLOAT_VALUE(x), fy, &div, &mod);
|
|
a = dbl2ival(div);
|
|
b = DBL2NUM(mod);
|
|
return rb_assoc_new(a, b);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self ** other -> numeric
|
|
*
|
|
* Raises +self+ to the power of +other+:
|
|
*
|
|
* f = 3.14
|
|
* f ** 2 # => 9.8596
|
|
* f ** -2 # => 0.1014239928597509
|
|
* f ** 2.1 # => 11.054834900588839
|
|
* f ** Rational(2, 1) # => 9.8596
|
|
* f ** Complex(2, 0) # => (9.8596+0i)
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_float_pow(VALUE x, VALUE y)
|
|
{
|
|
double dx, dy;
|
|
if (y == INT2FIX(2)) {
|
|
dx = RFLOAT_VALUE(x);
|
|
return DBL2NUM(dx * dx);
|
|
}
|
|
else if (FIXNUM_P(y)) {
|
|
dx = RFLOAT_VALUE(x);
|
|
dy = (double)FIX2LONG(y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
dx = RFLOAT_VALUE(x);
|
|
dy = rb_big2dbl(y);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
dx = RFLOAT_VALUE(x);
|
|
dy = RFLOAT_VALUE(y);
|
|
if (dx < 0 && dy != round(dy))
|
|
return rb_dbl_complex_new_polar_pi(pow(-dx, dy), dy);
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, idPow);
|
|
}
|
|
return DBL2NUM(pow(dx, dy));
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* eql?(other) -> true or false
|
|
*
|
|
* Returns +true+ if +self+ and +other+ are the same type and have equal values.
|
|
*
|
|
* Of the Core and Standard Library classes,
|
|
* only Integer, Rational, and Complex use this implementation.
|
|
*
|
|
* Examples:
|
|
*
|
|
* 1.eql?(1) # => true
|
|
* 1.eql?(1.0) # => false
|
|
* 1.eql?(Rational(1, 1)) # => false
|
|
* 1.eql?(Complex(1, 0)) # => false
|
|
*
|
|
* \Method +eql?+ is different from +==+ in that +eql?+ requires matching types,
|
|
* while +==+ does not.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
num_eql(VALUE x, VALUE y)
|
|
{
|
|
if (TYPE(x) != TYPE(y)) return Qfalse;
|
|
|
|
if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_eql(x, y);
|
|
}
|
|
|
|
return rb_equal(x, y);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self <=> other -> zero or nil
|
|
*
|
|
* Returns zero if +self+ is the same as +other+, +nil+ otherwise.
|
|
*
|
|
* No subclass in the Ruby Core or Standard Library uses this implementation.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
num_cmp(VALUE x, VALUE y)
|
|
{
|
|
if (x == y) return INT2FIX(0);
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
num_equal(VALUE x, VALUE y)
|
|
{
|
|
VALUE result;
|
|
if (x == y) return Qtrue;
|
|
result = num_funcall1(y, id_eq, x);
|
|
return RBOOL(RTEST(result));
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self == other -> true or false
|
|
*
|
|
* Returns +true+ if +other+ has the same value as +self+, +false+ otherwise:
|
|
*
|
|
* 2.0 == 2 # => true
|
|
* 2.0 == 2.0 # => true
|
|
* 2.0 == Rational(2, 1) # => true
|
|
* 2.0 == Complex(2, 0) # => true
|
|
*
|
|
* <tt>Float::NAN == Float::NAN</tt> returns an implementation-dependent value.
|
|
*
|
|
* Related: Float#eql? (requires +other+ to be a \Float).
|
|
*
|
|
*/
|
|
|
|
MJIT_FUNC_EXPORTED VALUE
|
|
rb_float_equal(VALUE x, VALUE y)
|
|
{
|
|
volatile double a, b;
|
|
|
|
if (RB_INTEGER_TYPE_P(y)) {
|
|
return rb_integer_float_eq(y, x);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
b = RFLOAT_VALUE(y);
|
|
#if MSC_VERSION_BEFORE(1300)
|
|
if (isnan(b)) return Qfalse;
|
|
#endif
|
|
}
|
|
else {
|
|
return num_equal(x, y);
|
|
}
|
|
a = RFLOAT_VALUE(x);
|
|
#if MSC_VERSION_BEFORE(1300)
|
|
if (isnan(a)) return Qfalse;
|
|
#endif
|
|
return RBOOL(a == b);
|
|
}
|
|
|
|
#define flo_eq rb_float_equal
|
|
static VALUE rb_dbl_hash(double d);
|
|
|
|
/*
|
|
* call-seq:
|
|
* hash -> integer
|
|
*
|
|
* Returns the integer hash value for +self+.
|
|
*
|
|
* See also Object#hash.
|
|
*/
|
|
|
|
static VALUE
|
|
flo_hash(VALUE num)
|
|
{
|
|
return rb_dbl_hash(RFLOAT_VALUE(num));
|
|
}
|
|
|
|
static VALUE
|
|
rb_dbl_hash(double d)
|
|
{
|
|
return ST2FIX(rb_dbl_long_hash(d));
|
|
}
|
|
|
|
VALUE
|
|
rb_dbl_cmp(double a, double b)
|
|
{
|
|
if (isnan(a) || isnan(b)) return Qnil;
|
|
if (a == b) return INT2FIX(0);
|
|
if (a > b) return INT2FIX(1);
|
|
if (a < b) return INT2FIX(-1);
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self <=> other -> -1, 0, +1, or nil
|
|
*
|
|
* Returns a value that depends on the numeric relation
|
|
* between +self+ and +other+:
|
|
*
|
|
* - -1, if +self+ is less than +other+.
|
|
* - 0, if +self+ is equal to +other+.
|
|
* - 1, if +self+ is greater than +other+.
|
|
* - +nil+, if the two values are incommensurate.
|
|
*
|
|
* Examples:
|
|
*
|
|
* 2.0 <=> 2 # => 0
|
|
2.0 <=> 2.0 # => 0
|
|
2.0 <=> Rational(2, 1) # => 0
|
|
2.0 <=> Complex(2, 0) # => 0
|
|
2.0 <=> 1.9 # => 1
|
|
2.0 <=> 2.1 # => -1
|
|
2.0 <=> 'foo' # => nil
|
|
*
|
|
* This is the basis for the tests in the Comparable module.
|
|
*
|
|
* <tt>Float::NAN <=> Float::NAN</tt> returns an implementation-dependent value.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
flo_cmp(VALUE x, VALUE y)
|
|
{
|
|
double a, b;
|
|
VALUE i;
|
|
|
|
a = RFLOAT_VALUE(x);
|
|
if (isnan(a)) return Qnil;
|
|
if (RB_INTEGER_TYPE_P(y)) {
|
|
VALUE rel = rb_integer_float_cmp(y, x);
|
|
if (FIXNUM_P(rel))
|
|
return LONG2FIX(-FIX2LONG(rel));
|
|
return rel;
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
b = RFLOAT_VALUE(y);
|
|
}
|
|
else {
|
|
if (isinf(a) && (i = rb_check_funcall(y, rb_intern("infinite?"), 0, 0)) != Qundef) {
|
|
if (RTEST(i)) {
|
|
int j = rb_cmpint(i, x, y);
|
|
j = (a > 0.0) ? (j > 0 ? 0 : +1) : (j < 0 ? 0 : -1);
|
|
return INT2FIX(j);
|
|
}
|
|
if (a > 0.0) return INT2FIX(1);
|
|
return INT2FIX(-1);
|
|
}
|
|
return rb_num_coerce_cmp(x, y, id_cmp);
|
|
}
|
|
return rb_dbl_cmp(a, b);
|
|
}
|
|
|
|
MJIT_FUNC_EXPORTED int
|
|
rb_float_cmp(VALUE x, VALUE y)
|
|
{
|
|
return NUM2INT(ensure_cmp(flo_cmp(x, y), x, y));
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self > other -> true or false
|
|
*
|
|
* Returns +true+ if +self+ is numerically greater than +other+:
|
|
*
|
|
* 2.0 > 1 # => true
|
|
* 2.0 > 1.0 # => true
|
|
* 2.0 > Rational(1, 2) # => true
|
|
* 2.0 > 2.0 # => false
|
|
*
|
|
* <tt>Float::NAN > Float::NAN</tt> returns an implementation-dependent value.
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_float_gt(VALUE x, VALUE y)
|
|
{
|
|
double a, b;
|
|
|
|
a = RFLOAT_VALUE(x);
|
|
if (RB_INTEGER_TYPE_P(y)) {
|
|
VALUE rel = rb_integer_float_cmp(y, x);
|
|
if (FIXNUM_P(rel))
|
|
return RBOOL(-FIX2LONG(rel) > 0);
|
|
return Qfalse;
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
b = RFLOAT_VALUE(y);
|
|
#if MSC_VERSION_BEFORE(1300)
|
|
if (isnan(b)) return Qfalse;
|
|
#endif
|
|
}
|
|
else {
|
|
return rb_num_coerce_relop(x, y, '>');
|
|
}
|
|
#if MSC_VERSION_BEFORE(1300)
|
|
if (isnan(a)) return Qfalse;
|
|
#endif
|
|
return RBOOL(a > b);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self >= other -> true or false
|
|
*
|
|
* Returns +true+ if +self+ is numerically greater than or equal to +other+:
|
|
*
|
|
* 2.0 >= 1 # => true
|
|
* 2.0 >= 1.0 # => true
|
|
* 2.0 >= Rational(1, 2) # => true
|
|
* 2.0 >= 2.0 # => true
|
|
* 2.0 >= 2.1 # => false
|
|
*
|
|
* <tt>Float::NAN >= Float::NAN</tt> returns an implementation-dependent value.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
flo_ge(VALUE x, VALUE y)
|
|
{
|
|
double a, b;
|
|
|
|
a = RFLOAT_VALUE(x);
|
|
if (RB_TYPE_P(y, T_FIXNUM) || RB_BIGNUM_TYPE_P(y)) {
|
|
VALUE rel = rb_integer_float_cmp(y, x);
|
|
if (FIXNUM_P(rel))
|
|
return RBOOL(-FIX2LONG(rel) >= 0);
|
|
return Qfalse;
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
b = RFLOAT_VALUE(y);
|
|
#if MSC_VERSION_BEFORE(1300)
|
|
if (isnan(b)) return Qfalse;
|
|
#endif
|
|
}
|
|
else {
|
|
return rb_num_coerce_relop(x, y, idGE);
|
|
}
|
|
#if MSC_VERSION_BEFORE(1300)
|
|
if (isnan(a)) return Qfalse;
|
|
#endif
|
|
return RBOOL(a >= b);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self < other -> true or false
|
|
*
|
|
* Returns +true+ if +self+ is numerically less than +other+:
|
|
*
|
|
* 2.0 < 3 # => true
|
|
* 2.0 < 3.0 # => true
|
|
* 2.0 < Rational(3, 1) # => true
|
|
* 2.0 < 2.0 # => false
|
|
*
|
|
* <tt>Float::NAN < Float::NAN</tt> returns an implementation-dependent value.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
flo_lt(VALUE x, VALUE y)
|
|
{
|
|
double a, b;
|
|
|
|
a = RFLOAT_VALUE(x);
|
|
if (RB_INTEGER_TYPE_P(y)) {
|
|
VALUE rel = rb_integer_float_cmp(y, x);
|
|
if (FIXNUM_P(rel))
|
|
return RBOOL(-FIX2LONG(rel) < 0);
|
|
return Qfalse;
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
b = RFLOAT_VALUE(y);
|
|
#if MSC_VERSION_BEFORE(1300)
|
|
if (isnan(b)) return Qfalse;
|
|
#endif
|
|
}
|
|
else {
|
|
return rb_num_coerce_relop(x, y, '<');
|
|
}
|
|
#if MSC_VERSION_BEFORE(1300)
|
|
if (isnan(a)) return Qfalse;
|
|
#endif
|
|
return RBOOL(a < b);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self <= other -> true or false
|
|
*
|
|
* Returns +true+ if +self+ is numerically less than or equal to +other+:
|
|
*
|
|
* 2.0 <= 3 # => true
|
|
* 2.0 <= 3.0 # => true
|
|
* 2.0 <= Rational(3, 1) # => true
|
|
* 2.0 <= 2.0 # => true
|
|
* 2.0 <= 1.0 # => false
|
|
*
|
|
* <tt>Float::NAN <= Float::NAN</tt> returns an implementation-dependent value.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
flo_le(VALUE x, VALUE y)
|
|
{
|
|
double a, b;
|
|
|
|
a = RFLOAT_VALUE(x);
|
|
if (RB_INTEGER_TYPE_P(y)) {
|
|
VALUE rel = rb_integer_float_cmp(y, x);
|
|
if (FIXNUM_P(rel))
|
|
return RBOOL(-FIX2LONG(rel) <= 0);
|
|
return Qfalse;
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
b = RFLOAT_VALUE(y);
|
|
#if MSC_VERSION_BEFORE(1300)
|
|
if (isnan(b)) return Qfalse;
|
|
#endif
|
|
}
|
|
else {
|
|
return rb_num_coerce_relop(x, y, idLE);
|
|
}
|
|
#if MSC_VERSION_BEFORE(1300)
|
|
if (isnan(a)) return Qfalse;
|
|
#endif
|
|
return RBOOL(a <= b);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* eql?(other) -> true or false
|
|
*
|
|
* Returns +true+ if +other+ is a \Float with the same value as +self+,
|
|
* +false+ otherwise:
|
|
*
|
|
* 2.0.eql?(2.0) # => true
|
|
* 2.0.eql?(1.0) # => false
|
|
* 2.0.eql?(1) # => false
|
|
* 2.0.eql?(Rational(2, 1)) # => false
|
|
* 2.0.eql?(Complex(2, 0)) # => false
|
|
*
|
|
* <tt>Float::NAN.eql?(Float::NAN)</tt> returns an implementation-dependent value.
|
|
*
|
|
* Related: Float#== (performs type conversions).
|
|
*/
|
|
|
|
MJIT_FUNC_EXPORTED VALUE
|
|
rb_float_eql(VALUE x, VALUE y)
|
|
{
|
|
if (RB_FLOAT_TYPE_P(y)) {
|
|
double a = RFLOAT_VALUE(x);
|
|
double b = RFLOAT_VALUE(y);
|
|
#if MSC_VERSION_BEFORE(1300)
|
|
if (isnan(a) || isnan(b)) return Qfalse;
|
|
#endif
|
|
return RBOOL(a == b);
|
|
}
|
|
return Qfalse;
|
|
}
|
|
|
|
#define flo_eql rb_float_eql
|
|
|
|
MJIT_FUNC_EXPORTED VALUE
|
|
rb_float_abs(VALUE flt)
|
|
{
|
|
double val = fabs(RFLOAT_VALUE(flt));
|
|
return DBL2NUM(val);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* nan? -> true or false
|
|
*
|
|
* Returns +true+ if +self+ is a NaN, +false+ otherwise.
|
|
*
|
|
* f = -1.0 #=> -1.0
|
|
* f.nan? #=> false
|
|
* f = 0.0/0.0 #=> NaN
|
|
* f.nan? #=> true
|
|
*/
|
|
|
|
static VALUE
|
|
flo_is_nan_p(VALUE num)
|
|
{
|
|
double value = RFLOAT_VALUE(num);
|
|
|
|
return RBOOL(isnan(value));
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* infinite? -> -1, 1, or nil
|
|
*
|
|
* Returns:
|
|
*
|
|
* - 1, if +self+ is <tt>Infinity</tt>.
|
|
* - -1 if +self+ is <tt>-Infinity</tt>.
|
|
* - +nil+, otherwise.
|
|
*
|
|
* Examples:
|
|
*
|
|
* f = 1.0/0.0 # => Infinity
|
|
* f.infinite? # => 1
|
|
* f = -1.0/0.0 # => -Infinity
|
|
* f.infinite? # => -1
|
|
* f = 1.0 # => 1.0
|
|
* f.infinite? # => nil
|
|
* f = 0.0/0.0 # => NaN
|
|
* f.infinite? # => nil
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_flo_is_infinite_p(VALUE num)
|
|
{
|
|
double value = RFLOAT_VALUE(num);
|
|
|
|
if (isinf(value)) {
|
|
return INT2FIX( value < 0 ? -1 : 1 );
|
|
}
|
|
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* finite? -> true or false
|
|
*
|
|
* Returns +true+ if +self+ is not +Infinity+, +-Infinity+, or +NaN+,
|
|
* +false+ otherwise:
|
|
*
|
|
* f = 2.0 # => 2.0
|
|
* f.finite? # => true
|
|
* f = 1.0/0.0 # => Infinity
|
|
* f.finite? # => false
|
|
* f = -1.0/0.0 # => -Infinity
|
|
* f.finite? # => false
|
|
* f = 0.0/0.0 # => NaN
|
|
* f.finite? # => false
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_flo_is_finite_p(VALUE num)
|
|
{
|
|
double value = RFLOAT_VALUE(num);
|
|
|
|
return RBOOL(isfinite(value));
|
|
}
|
|
|
|
static VALUE
|
|
flo_nextafter(VALUE flo, double value)
|
|
{
|
|
double x, y;
|
|
x = NUM2DBL(flo);
|
|
y = nextafter(x, value);
|
|
return DBL2NUM(y);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* next_float -> float
|
|
*
|
|
* Returns the next-larger representable \Float.
|
|
*
|
|
* These examples show the internally stored values (64-bit hexadecimal)
|
|
* for each \Float +f+ and for the corresponding <tt>f.next_float</tt>:
|
|
*
|
|
* f = 0.0 # 0x0000000000000000
|
|
* f.next_float # 0x0000000000000001
|
|
*
|
|
* f = 0.01 # 0x3f847ae147ae147b
|
|
* f.next_float # 0x3f847ae147ae147c
|
|
*
|
|
* In the remaining examples here, the output is shown in the usual way
|
|
* (result +to_s+):
|
|
*
|
|
* 0.01.next_float # => 0.010000000000000002
|
|
* 1.0.next_float # => 1.0000000000000002
|
|
* 100.0.next_float # => 100.00000000000001
|
|
*
|
|
* f = 0.01
|
|
* (0..3).each_with_index {|i| printf "%2d %-20a %s\n", i, f, f.to_s; f = f.next_float }
|
|
*
|
|
* Output:
|
|
*
|
|
* 0 0x1.47ae147ae147bp-7 0.01
|
|
* 1 0x1.47ae147ae147cp-7 0.010000000000000002
|
|
* 2 0x1.47ae147ae147dp-7 0.010000000000000004
|
|
* 3 0x1.47ae147ae147ep-7 0.010000000000000005
|
|
*
|
|
* f = 0.0; 100.times { f += 0.1 }
|
|
* f # => 9.99999999999998 # should be 10.0 in the ideal world.
|
|
* 10-f # => 1.9539925233402755e-14 # the floating point error.
|
|
* 10.0.next_float-10 # => 1.7763568394002505e-15 # 1 ulp (unit in the last place).
|
|
* (10-f)/(10.0.next_float-10) # => 11.0 # the error is 11 ulp.
|
|
* (10-f)/(10*Float::EPSILON) # => 8.8 # approximation of the above.
|
|
* "%a" % 10 # => "0x1.4p+3"
|
|
* "%a" % f # => "0x1.3fffffffffff5p+3" # the last hex digit is 5. 16 - 5 = 11 ulp.
|
|
*
|
|
* Related: Float#prev_float
|
|
*
|
|
*/
|
|
static VALUE
|
|
flo_next_float(VALUE vx)
|
|
{
|
|
return flo_nextafter(vx, HUGE_VAL);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* float.prev_float -> float
|
|
*
|
|
* Returns the next-smaller representable \Float.
|
|
*
|
|
* These examples show the internally stored values (64-bit hexadecimal)
|
|
* for each \Float +f+ and for the corresponding <tt>f.pev_float</tt>:
|
|
*
|
|
* f = 5e-324 # 0x0000000000000001
|
|
* f.prev_float # 0x0000000000000000
|
|
*
|
|
* f = 0.01 # 0x3f847ae147ae147b
|
|
* f.prev_float # 0x3f847ae147ae147a
|
|
*
|
|
* In the remaining examples here, the output is shown in the usual way
|
|
* (result +to_s+):
|
|
*
|
|
* 0.01.prev_float # => 0.009999999999999998
|
|
* 1.0.prev_float # => 0.9999999999999999
|
|
* 100.0.prev_float # => 99.99999999999999
|
|
*
|
|
* f = 0.01
|
|
* (0..3).each_with_index {|i| printf "%2d %-20a %s\n", i, f, f.to_s; f = f.prev_float }
|
|
*
|
|
* Output:
|
|
*
|
|
* 0 0x1.47ae147ae147bp-7 0.01
|
|
* 1 0x1.47ae147ae147ap-7 0.009999999999999998
|
|
* 2 0x1.47ae147ae1479p-7 0.009999999999999997
|
|
* 3 0x1.47ae147ae1478p-7 0.009999999999999995
|
|
*
|
|
* Related: Float#next_float.
|
|
*
|
|
*/
|
|
static VALUE
|
|
flo_prev_float(VALUE vx)
|
|
{
|
|
return flo_nextafter(vx, -HUGE_VAL);
|
|
}
|
|
|
|
VALUE
|
|
rb_float_floor(VALUE num, int ndigits)
|
|
{
|
|
double number;
|
|
number = RFLOAT_VALUE(num);
|
|
if (number == 0.0) {
|
|
return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0);
|
|
}
|
|
if (ndigits > 0) {
|
|
int binexp;
|
|
double f, mul, res;
|
|
frexp(number, &binexp);
|
|
if (float_round_overflow(ndigits, binexp)) return num;
|
|
if (number > 0.0 && float_round_underflow(ndigits, binexp))
|
|
return DBL2NUM(0.0);
|
|
f = pow(10, ndigits);
|
|
mul = floor(number * f);
|
|
res = (mul + 1) / f;
|
|
if (res > number)
|
|
res = mul / f;
|
|
return DBL2NUM(res);
|
|
}
|
|
else {
|
|
num = dbl2ival(floor(number));
|
|
if (ndigits < 0) num = rb_int_floor(num, ndigits);
|
|
return num;
|
|
}
|
|
}
|
|
|
|
static int
|
|
flo_ndigits(int argc, VALUE *argv)
|
|
{
|
|
if (rb_check_arity(argc, 0, 1)) {
|
|
return NUM2INT(argv[0]);
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* floor(ndigits = 0) -> float or integer
|
|
*
|
|
* Returns the largest number less than or equal to +self+ with
|
|
* a precision of +ndigits+ decimal digits.
|
|
*
|
|
* When +ndigits+ is positive, returns a float with +ndigits+
|
|
* digits after the decimal point (as available):
|
|
*
|
|
* f = 12345.6789
|
|
* f.floor(1) # => 12345.6
|
|
* f.floor(3) # => 12345.678
|
|
* f = -12345.6789
|
|
* f.floor(1) # => -12345.7
|
|
* f.floor(3) # => -12345.679
|
|
*
|
|
* When +ndigits+ is non-positive, returns an integer with at least
|
|
* <code>ndigits.abs</code> trailing zeros:
|
|
*
|
|
* f = 12345.6789
|
|
* f.floor(0) # => 12345
|
|
* f.floor(-3) # => 12000
|
|
* f = -12345.6789
|
|
* f.floor(0) # => -12346
|
|
* f.floor(-3) # => -13000
|
|
*
|
|
* Note that the limited precision of floating-point arithmetic
|
|
* may lead to surprising results:
|
|
*
|
|
* (0.3 / 0.1).floor #=> 2 (!)
|
|
*
|
|
* Related: Float#ceil.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
flo_floor(int argc, VALUE *argv, VALUE num)
|
|
{
|
|
int ndigits = flo_ndigits(argc, argv);
|
|
return rb_float_floor(num, ndigits);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* ceil(ndigits = 0) -> float or integer
|
|
*
|
|
* Returns the smallest number greater than or equal to +self+ with
|
|
* a precision of +ndigits+ decimal digits.
|
|
*
|
|
* When +ndigits+ is positive, returns a float with +ndigits+
|
|
* digits after the decimal point (as available):
|
|
*
|
|
* f = 12345.6789
|
|
* f.ceil(1) # => 12345.7
|
|
* f.ceil(3) # => 12345.679
|
|
* f = -12345.6789
|
|
* f.ceil(1) # => -12345.6
|
|
* f.ceil(3) # => -12345.678
|
|
*
|
|
* When +ndigits+ is non-positive, returns an integer with at least
|
|
* <code>ndigits.abs</code> trailing zeros:
|
|
*
|
|
* f = 12345.6789
|
|
* f.ceil(0) # => 12346
|
|
* f.ceil(-3) # => 13000
|
|
* f = -12345.6789
|
|
* f.ceil(0) # => -12345
|
|
* f.ceil(-3) # => -12000
|
|
*
|
|
* Note that the limited precision of floating-point arithmetic
|
|
* may lead to surprising results:
|
|
*
|
|
* (2.1 / 0.7).ceil #=> 4 (!)
|
|
*
|
|
* Related: Float#floor.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
flo_ceil(int argc, VALUE *argv, VALUE num)
|
|
{
|
|
int ndigits = flo_ndigits(argc, argv);
|
|
return rb_float_ceil(num, ndigits);
|
|
}
|
|
|
|
VALUE
|
|
rb_float_ceil(VALUE num, int ndigits)
|
|
{
|
|
double number, f;
|
|
|
|
number = RFLOAT_VALUE(num);
|
|
if (number == 0.0) {
|
|
return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0);
|
|
}
|
|
if (ndigits > 0) {
|
|
int binexp;
|
|
frexp(number, &binexp);
|
|
if (float_round_overflow(ndigits, binexp)) return num;
|
|
if (number < 0.0 && float_round_underflow(ndigits, binexp))
|
|
return DBL2NUM(0.0);
|
|
f = pow(10, ndigits);
|
|
f = ceil(number * f) / f;
|
|
return DBL2NUM(f);
|
|
}
|
|
else {
|
|
num = dbl2ival(ceil(number));
|
|
if (ndigits < 0) num = rb_int_ceil(num, ndigits);
|
|
return num;
|
|
}
|
|
}
|
|
|
|
static int
|
|
int_round_zero_p(VALUE num, int ndigits)
|
|
{
|
|
long bytes;
|
|
/* If 10**N / 2 > num, then return 0 */
|
|
/* We have log_256(10) > 0.415241 and log_256(1/2) = -0.125, so */
|
|
if (FIXNUM_P(num)) {
|
|
bytes = sizeof(long);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(num)) {
|
|
bytes = rb_big_size(num);
|
|
}
|
|
else {
|
|
bytes = NUM2LONG(rb_funcall(num, idSize, 0));
|
|
}
|
|
return (-0.415241 * ndigits - 0.125 > bytes);
|
|
}
|
|
|
|
static SIGNED_VALUE
|
|
int_round_half_even(SIGNED_VALUE x, SIGNED_VALUE y)
|
|
{
|
|
SIGNED_VALUE z = +(x + y / 2) / y;
|
|
if ((z * y - x) * 2 == y) {
|
|
z &= ~1;
|
|
}
|
|
return z * y;
|
|
}
|
|
|
|
static SIGNED_VALUE
|
|
int_round_half_up(SIGNED_VALUE x, SIGNED_VALUE y)
|
|
{
|
|
return (x + y / 2) / y * y;
|
|
}
|
|
|
|
static SIGNED_VALUE
|
|
int_round_half_down(SIGNED_VALUE x, SIGNED_VALUE y)
|
|
{
|
|
return (x + y / 2 - 1) / y * y;
|
|
}
|
|
|
|
static int
|
|
int_half_p_half_even(VALUE num, VALUE n, VALUE f)
|
|
{
|
|
return (int)rb_int_odd_p(rb_int_idiv(n, f));
|
|
}
|
|
|
|
static int
|
|
int_half_p_half_up(VALUE num, VALUE n, VALUE f)
|
|
{
|
|
return int_pos_p(num);
|
|
}
|
|
|
|
static int
|
|
int_half_p_half_down(VALUE num, VALUE n, VALUE f)
|
|
{
|
|
return int_neg_p(num);
|
|
}
|
|
|
|
/*
|
|
* Assumes num is an Integer, ndigits <= 0
|
|
*/
|
|
static VALUE
|
|
rb_int_round(VALUE num, int ndigits, enum ruby_num_rounding_mode mode)
|
|
{
|
|
VALUE n, f, h, r;
|
|
|
|
if (int_round_zero_p(num, ndigits)) {
|
|
return INT2FIX(0);
|
|
}
|
|
|
|
f = int_pow(10, -ndigits);
|
|
if (FIXNUM_P(num) && FIXNUM_P(f)) {
|
|
SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f);
|
|
int neg = x < 0;
|
|
if (neg) x = -x;
|
|
x = ROUND_CALL(mode, int_round, (x, y));
|
|
if (neg) x = -x;
|
|
return LONG2NUM(x);
|
|
}
|
|
if (RB_FLOAT_TYPE_P(f)) {
|
|
/* then int_pow overflow */
|
|
return INT2FIX(0);
|
|
}
|
|
h = rb_int_idiv(f, INT2FIX(2));
|
|
r = rb_int_modulo(num, f);
|
|
n = rb_int_minus(num, r);
|
|
r = rb_int_cmp(r, h);
|
|
if (FIXNUM_POSITIVE_P(r) ||
|
|
(FIXNUM_ZERO_P(r) && ROUND_CALL(mode, int_half_p, (num, n, f)))) {
|
|
n = rb_int_plus(n, f);
|
|
}
|
|
return n;
|
|
}
|
|
|
|
static VALUE
|
|
rb_int_floor(VALUE num, int ndigits)
|
|
{
|
|
VALUE f;
|
|
|
|
if (int_round_zero_p(num, ndigits))
|
|
return INT2FIX(0);
|
|
f = int_pow(10, -ndigits);
|
|
if (FIXNUM_P(num) && FIXNUM_P(f)) {
|
|
SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f);
|
|
int neg = x < 0;
|
|
if (neg) x = -x + y - 1;
|
|
x = x / y * y;
|
|
if (neg) x = -x;
|
|
return LONG2NUM(x);
|
|
}
|
|
if (RB_FLOAT_TYPE_P(f)) {
|
|
/* then int_pow overflow */
|
|
return INT2FIX(0);
|
|
}
|
|
return rb_int_minus(num, rb_int_modulo(num, f));
|
|
}
|
|
|
|
static VALUE
|
|
rb_int_ceil(VALUE num, int ndigits)
|
|
{
|
|
VALUE f;
|
|
|
|
if (int_round_zero_p(num, ndigits))
|
|
return INT2FIX(0);
|
|
f = int_pow(10, -ndigits);
|
|
if (FIXNUM_P(num) && FIXNUM_P(f)) {
|
|
SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f);
|
|
int neg = x < 0;
|
|
if (neg) x = -x;
|
|
else x += y - 1;
|
|
x = (x / y) * y;
|
|
if (neg) x = -x;
|
|
return LONG2NUM(x);
|
|
}
|
|
if (RB_FLOAT_TYPE_P(f)) {
|
|
/* then int_pow overflow */
|
|
return INT2FIX(0);
|
|
}
|
|
return rb_int_plus(num, rb_int_minus(f, rb_int_modulo(num, f)));
|
|
}
|
|
|
|
VALUE
|
|
rb_int_truncate(VALUE num, int ndigits)
|
|
{
|
|
VALUE f;
|
|
VALUE m;
|
|
|
|
if (int_round_zero_p(num, ndigits))
|
|
return INT2FIX(0);
|
|
f = int_pow(10, -ndigits);
|
|
if (FIXNUM_P(num) && FIXNUM_P(f)) {
|
|
SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f);
|
|
int neg = x < 0;
|
|
if (neg) x = -x;
|
|
x = x / y * y;
|
|
if (neg) x = -x;
|
|
return LONG2NUM(x);
|
|
}
|
|
if (RB_FLOAT_TYPE_P(f)) {
|
|
/* then int_pow overflow */
|
|
return INT2FIX(0);
|
|
}
|
|
m = rb_int_modulo(num, f);
|
|
if (int_neg_p(num)) {
|
|
return rb_int_plus(num, rb_int_minus(f, m));
|
|
}
|
|
else {
|
|
return rb_int_minus(num, m);
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* round(ndigits = 0, half: :up]) -> integer or float
|
|
*
|
|
* Returns +self+ rounded to the nearest value with
|
|
* a precision of +ndigits+ decimal digits.
|
|
*
|
|
* When +ndigits+ is non-negative, returns a float with +ndigits+
|
|
* after the decimal point (as available):
|
|
*
|
|
* f = 12345.6789
|
|
* f.round(1) # => 12345.7
|
|
* f.round(3) # => 12345.679
|
|
* f = -12345.6789
|
|
* f.round(1) # => -12345.7
|
|
* f.round(3) # => -12345.679
|
|
*
|
|
* When +ndigits+ is negative, returns an integer
|
|
* with at least <tt>ndigits.abs</tt> trailing zeros:
|
|
*
|
|
* f = 12345.6789
|
|
* f.round(0) # => 12346
|
|
* f.round(-3) # => 12000
|
|
* f = -12345.6789
|
|
* f.round(0) # => -12346
|
|
* f.round(-3) # => -12000
|
|
*
|
|
* If keyword argument +half+ is given,
|
|
* and +self+ is equidistant from the two candidate values,
|
|
* the rounding is according to the given +half+ value:
|
|
*
|
|
* - +:up+ or +nil+: round away from zero:
|
|
*
|
|
* 2.5.round(half: :up) # => 3
|
|
* 3.5.round(half: :up) # => 4
|
|
* (-2.5).round(half: :up) # => -3
|
|
*
|
|
* - +:down+: round toward zero:
|
|
*
|
|
* 2.5.round(half: :down) # => 2
|
|
* 3.5.round(half: :down) # => 3
|
|
* (-2.5).round(half: :down) # => -2
|
|
*
|
|
* - +:even+: round toward the candidate whose last nonzero digit is even:
|
|
*
|
|
* 2.5.round(half: :even) # => 2
|
|
* 3.5.round(half: :even) # => 4
|
|
* (-2.5).round(half: :even) # => -2
|
|
*
|
|
* Raises and exception if the value for +half+ is invalid.
|
|
*
|
|
* Related: Float#truncate.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
flo_round(int argc, VALUE *argv, VALUE num)
|
|
{
|
|
double number, f, x;
|
|
VALUE nd, opt;
|
|
int ndigits = 0;
|
|
enum ruby_num_rounding_mode mode;
|
|
|
|
if (rb_scan_args(argc, argv, "01:", &nd, &opt)) {
|
|
ndigits = NUM2INT(nd);
|
|
}
|
|
mode = rb_num_get_rounding_option(opt);
|
|
number = RFLOAT_VALUE(num);
|
|
if (number == 0.0) {
|
|
return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0);
|
|
}
|
|
if (ndigits < 0) {
|
|
return rb_int_round(flo_to_i(num), ndigits, mode);
|
|
}
|
|
if (ndigits == 0) {
|
|
x = ROUND_CALL(mode, round, (number, 1.0));
|
|
return dbl2ival(x);
|
|
}
|
|
if (isfinite(number)) {
|
|
int binexp;
|
|
frexp(number, &binexp);
|
|
if (float_round_overflow(ndigits, binexp)) return num;
|
|
if (float_round_underflow(ndigits, binexp)) return DBL2NUM(0);
|
|
if (ndigits > 14) {
|
|
/* In this case, pow(10, ndigits) may not be accurate. */
|
|
return rb_flo_round_by_rational(argc, argv, num);
|
|
}
|
|
f = pow(10, ndigits);
|
|
x = ROUND_CALL(mode, round, (number, f));
|
|
return DBL2NUM(x / f);
|
|
}
|
|
return num;
|
|
}
|
|
|
|
static int
|
|
float_round_overflow(int ndigits, int binexp)
|
|
{
|
|
enum {float_dig = DBL_DIG+2};
|
|
|
|
/* Let `exp` be such that `number` is written as:"0.#{digits}e#{exp}",
|
|
i.e. such that 10 ** (exp - 1) <= |number| < 10 ** exp
|
|
Recall that up to float_dig digits can be needed to represent a double,
|
|
so if ndigits + exp >= float_dig, the intermediate value (number * 10 ** ndigits)
|
|
will be an integer and thus the result is the original number.
|
|
If ndigits + exp <= 0, the result is 0 or "1e#{exp}", so
|
|
if ndigits + exp < 0, the result is 0.
|
|
We have:
|
|
2 ** (binexp-1) <= |number| < 2 ** binexp
|
|
10 ** ((binexp-1)/log_2(10)) <= |number| < 10 ** (binexp/log_2(10))
|
|
If binexp >= 0, and since log_2(10) = 3.322259:
|
|
10 ** (binexp/4 - 1) < |number| < 10 ** (binexp/3)
|
|
floor(binexp/4) <= exp <= ceil(binexp/3)
|
|
If binexp <= 0, swap the /4 and the /3
|
|
So if ndigits + floor(binexp/(4 or 3)) >= float_dig, the result is number
|
|
If ndigits + ceil(binexp/(3 or 4)) < 0 the result is 0
|
|
*/
|
|
if (ndigits >= float_dig - (binexp > 0 ? binexp / 4 : binexp / 3 - 1)) {
|
|
return TRUE;
|
|
}
|
|
return FALSE;
|
|
}
|
|
|
|
static int
|
|
float_round_underflow(int ndigits, int binexp)
|
|
{
|
|
if (ndigits < - (binexp > 0 ? binexp / 3 + 1 : binexp / 4)) {
|
|
return TRUE;
|
|
}
|
|
return FALSE;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* to_i -> integer
|
|
*
|
|
* Returns +self+ truncated to an Integer.
|
|
*
|
|
* 1.2.to_i # => 1
|
|
* (-1.2).to_i # => -1
|
|
*
|
|
* Note that the limited precision of floating-point arithmetic
|
|
* may lead to surprising results:
|
|
*
|
|
* (0.3 / 0.1).to_i # => 2 (!)
|
|
*
|
|
* Float#to_int is an alias for Float#to_i.
|
|
*/
|
|
|
|
static VALUE
|
|
flo_to_i(VALUE num)
|
|
{
|
|
double f = RFLOAT_VALUE(num);
|
|
|
|
if (f > 0.0) f = floor(f);
|
|
if (f < 0.0) f = ceil(f);
|
|
|
|
return dbl2ival(f);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* truncate(ndigits = 0) -> float or integer
|
|
*
|
|
* Returns +self+ truncated (toward zero) to
|
|
* a precision of +ndigits+ decimal digits.
|
|
*
|
|
* When +ndigits+ is positive, returns a float with +ndigits+ digits
|
|
* after the decimal point (as available):
|
|
*
|
|
* f = 12345.6789
|
|
* f.truncate(1) # => 12345.6
|
|
* f.truncate(3) # => 12345.678
|
|
* f = -12345.6789
|
|
* f.truncate(1) # => -12345.6
|
|
* f.truncate(3) # => -12345.678
|
|
*
|
|
* When +ndigits+ is negative, returns an integer
|
|
* with at least <tt>ndigits.abs</tt> trailing zeros:
|
|
*
|
|
* f = 12345.6789
|
|
* f.truncate(0) # => 12345
|
|
* f.truncate(-3) # => 12000
|
|
* f = -12345.6789
|
|
* f.truncate(0) # => -12345
|
|
* f.truncate(-3) # => -12000
|
|
*
|
|
* Note that the limited precision of floating-point arithmetic
|
|
* may lead to surprising results:
|
|
*
|
|
* (0.3 / 0.1).truncate #=> 2 (!)
|
|
*
|
|
* Related: Float#round.
|
|
*
|
|
*/
|
|
static VALUE
|
|
flo_truncate(int argc, VALUE *argv, VALUE num)
|
|
{
|
|
if (signbit(RFLOAT_VALUE(num)))
|
|
return flo_ceil(argc, argv, num);
|
|
else
|
|
return flo_floor(argc, argv, num);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* floor(digits = 0) -> integer or float
|
|
*
|
|
* Returns the largest number that is less than or equal to +self+ with
|
|
* a precision of +digits+ decimal digits.
|
|
*
|
|
* \Numeric implements this by converting +self+ to a Float and
|
|
* invoking Float#floor.
|
|
*/
|
|
|
|
static VALUE
|
|
num_floor(int argc, VALUE *argv, VALUE num)
|
|
{
|
|
return flo_floor(argc, argv, rb_Float(num));
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* ceil(digits = 0) -> integer or float
|
|
*
|
|
* Returns the smallest number that is greater than or equal to +self+ with
|
|
* a precision of +digits+ decimal digits.
|
|
*
|
|
* \Numeric implements this by converting +self+ to a Float and
|
|
* invoking Float#ceil.
|
|
*/
|
|
|
|
static VALUE
|
|
num_ceil(int argc, VALUE *argv, VALUE num)
|
|
{
|
|
return flo_ceil(argc, argv, rb_Float(num));
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* round(digits = 0) -> integer or float
|
|
*
|
|
* Returns +self+ rounded to the nearest value with
|
|
* a precision of +digits+ decimal digits.
|
|
*
|
|
* \Numeric implements this by converting +self+ to a Float and
|
|
* invoking Float#round.
|
|
*/
|
|
|
|
static VALUE
|
|
num_round(int argc, VALUE* argv, VALUE num)
|
|
{
|
|
return flo_round(argc, argv, rb_Float(num));
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* truncate(digits = 0) -> integer or float
|
|
*
|
|
* Returns +self+ truncated (toward zero) to
|
|
* a precision of +digits+ decimal digits.
|
|
*
|
|
* \Numeric implements this by converting +self+ to a Float and
|
|
* invoking Float#truncate.
|
|
*/
|
|
|
|
static VALUE
|
|
num_truncate(int argc, VALUE *argv, VALUE num)
|
|
{
|
|
return flo_truncate(argc, argv, rb_Float(num));
|
|
}
|
|
|
|
double
|
|
ruby_float_step_size(double beg, double end, double unit, int excl)
|
|
{
|
|
const double epsilon = DBL_EPSILON;
|
|
double d, n, err;
|
|
|
|
if (unit == 0) {
|
|
return HUGE_VAL;
|
|
}
|
|
if (isinf(unit)) {
|
|
return unit > 0 ? beg <= end : beg >= end;
|
|
}
|
|
n= (end - beg)/unit;
|
|
err = (fabs(beg) + fabs(end) + fabs(end-beg)) / fabs(unit) * epsilon;
|
|
if (err>0.5) err=0.5;
|
|
if (excl) {
|
|
if (n<=0) return 0;
|
|
if (n<1)
|
|
n = 0;
|
|
else
|
|
n = floor(n - err);
|
|
d = +((n + 1) * unit) + beg;
|
|
if (beg < end) {
|
|
if (d < end)
|
|
n++;
|
|
}
|
|
else if (beg > end) {
|
|
if (d > end)
|
|
n++;
|
|
}
|
|
}
|
|
else {
|
|
if (n<0) return 0;
|
|
n = floor(n + err);
|
|
d = +((n + 1) * unit) + beg;
|
|
if (beg < end) {
|
|
if (d <= end)
|
|
n++;
|
|
}
|
|
else if (beg > end) {
|
|
if (d >= end)
|
|
n++;
|
|
}
|
|
}
|
|
return n+1;
|
|
}
|
|
|
|
int
|
|
ruby_float_step(VALUE from, VALUE to, VALUE step, int excl, int allow_endless)
|
|
{
|
|
if (RB_FLOAT_TYPE_P(from) || RB_FLOAT_TYPE_P(to) || RB_FLOAT_TYPE_P(step)) {
|
|
double unit = NUM2DBL(step);
|
|
double beg = NUM2DBL(from);
|
|
double end = (allow_endless && NIL_P(to)) ? (unit < 0 ? -1 : 1)*HUGE_VAL : NUM2DBL(to);
|
|
double n = ruby_float_step_size(beg, end, unit, excl);
|
|
long i;
|
|
|
|
if (isinf(unit)) {
|
|
/* if unit is infinity, i*unit+beg is NaN */
|
|
if (n) rb_yield(DBL2NUM(beg));
|
|
}
|
|
else if (unit == 0) {
|
|
VALUE val = DBL2NUM(beg);
|
|
for (;;)
|
|
rb_yield(val);
|
|
}
|
|
else {
|
|
for (i=0; i<n; i++) {
|
|
double d = i*unit+beg;
|
|
if (unit >= 0 ? end < d : d < end) d = end;
|
|
rb_yield(DBL2NUM(d));
|
|
}
|
|
}
|
|
return TRUE;
|
|
}
|
|
return FALSE;
|
|
}
|
|
|
|
VALUE
|
|
ruby_num_interval_step_size(VALUE from, VALUE to, VALUE step, int excl)
|
|
{
|
|
if (FIXNUM_P(from) && FIXNUM_P(to) && FIXNUM_P(step)) {
|
|
long delta, diff;
|
|
|
|
diff = FIX2LONG(step);
|
|
if (diff == 0) {
|
|
return DBL2NUM(HUGE_VAL);
|
|
}
|
|
delta = FIX2LONG(to) - FIX2LONG(from);
|
|
if (diff < 0) {
|
|
diff = -diff;
|
|
delta = -delta;
|
|
}
|
|
if (excl) {
|
|
delta--;
|
|
}
|
|
if (delta < 0) {
|
|
return INT2FIX(0);
|
|
}
|
|
return ULONG2NUM(delta / diff + 1UL);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(from) || RB_FLOAT_TYPE_P(to) || RB_FLOAT_TYPE_P(step)) {
|
|
double n = ruby_float_step_size(NUM2DBL(from), NUM2DBL(to), NUM2DBL(step), excl);
|
|
|
|
if (isinf(n)) return DBL2NUM(n);
|
|
if (POSFIXABLE(n)) return LONG2FIX((long)n);
|
|
return rb_dbl2big(n);
|
|
}
|
|
else {
|
|
VALUE result;
|
|
ID cmp = '>';
|
|
switch (rb_cmpint(rb_num_coerce_cmp(step, INT2FIX(0), id_cmp), step, INT2FIX(0))) {
|
|
case 0: return DBL2NUM(HUGE_VAL);
|
|
case -1: cmp = '<'; break;
|
|
}
|
|
if (RTEST(rb_funcall(from, cmp, 1, to))) return INT2FIX(0);
|
|
result = rb_funcall(rb_funcall(to, '-', 1, from), id_div, 1, step);
|
|
if (!excl || RTEST(rb_funcall(rb_funcall(from, '+', 1, rb_funcall(result, '*', 1, step)), cmp, 1, to))) {
|
|
result = rb_funcall(result, '+', 1, INT2FIX(1));
|
|
}
|
|
return result;
|
|
}
|
|
}
|
|
|
|
static int
|
|
num_step_negative_p(VALUE num)
|
|
{
|
|
const ID mid = '<';
|
|
VALUE zero = INT2FIX(0);
|
|
VALUE r;
|
|
|
|
if (FIXNUM_P(num)) {
|
|
if (method_basic_p(rb_cInteger))
|
|
return (SIGNED_VALUE)num < 0;
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(num)) {
|
|
if (method_basic_p(rb_cInteger))
|
|
return BIGNUM_NEGATIVE_P(num);
|
|
}
|
|
|
|
r = rb_check_funcall(num, '>', 1, &zero);
|
|
if (r == Qundef) {
|
|
coerce_failed(num, INT2FIX(0));
|
|
}
|
|
return !RTEST(r);
|
|
}
|
|
|
|
static int
|
|
num_step_extract_args(int argc, const VALUE *argv, VALUE *to, VALUE *step, VALUE *by)
|
|
{
|
|
VALUE hash;
|
|
|
|
argc = rb_scan_args(argc, argv, "02:", to, step, &hash);
|
|
if (!NIL_P(hash)) {
|
|
ID keys[2];
|
|
VALUE values[2];
|
|
keys[0] = id_to;
|
|
keys[1] = id_by;
|
|
rb_get_kwargs(hash, keys, 0, 2, values);
|
|
if (values[0] != Qundef) {
|
|
if (argc > 0) rb_raise(rb_eArgError, "to is given twice");
|
|
*to = values[0];
|
|
}
|
|
if (values[1] != Qundef) {
|
|
if (argc > 1) rb_raise(rb_eArgError, "step is given twice");
|
|
*by = values[1];
|
|
}
|
|
}
|
|
|
|
return argc;
|
|
}
|
|
|
|
static int
|
|
num_step_check_fix_args(int argc, VALUE *to, VALUE *step, VALUE by, int fix_nil, int allow_zero_step)
|
|
{
|
|
int desc;
|
|
if (by != Qundef) {
|
|
*step = by;
|
|
}
|
|
else {
|
|
/* compatibility */
|
|
if (argc > 1 && NIL_P(*step)) {
|
|
rb_raise(rb_eTypeError, "step must be numeric");
|
|
}
|
|
}
|
|
if (!allow_zero_step && rb_equal(*step, INT2FIX(0))) {
|
|
rb_raise(rb_eArgError, "step can't be 0");
|
|
}
|
|
if (NIL_P(*step)) {
|
|
*step = INT2FIX(1);
|
|
}
|
|
desc = num_step_negative_p(*step);
|
|
if (fix_nil && NIL_P(*to)) {
|
|
*to = desc ? DBL2NUM(-HUGE_VAL) : DBL2NUM(HUGE_VAL);
|
|
}
|
|
return desc;
|
|
}
|
|
|
|
static int
|
|
num_step_scan_args(int argc, const VALUE *argv, VALUE *to, VALUE *step, int fix_nil, int allow_zero_step)
|
|
{
|
|
VALUE by = Qundef;
|
|
argc = num_step_extract_args(argc, argv, to, step, &by);
|
|
return num_step_check_fix_args(argc, to, step, by, fix_nil, allow_zero_step);
|
|
}
|
|
|
|
static VALUE
|
|
num_step_size(VALUE from, VALUE args, VALUE eobj)
|
|
{
|
|
VALUE to, step;
|
|
int argc = args ? RARRAY_LENINT(args) : 0;
|
|
const VALUE *argv = args ? RARRAY_CONST_PTR(args) : 0;
|
|
|
|
num_step_scan_args(argc, argv, &to, &step, TRUE, FALSE);
|
|
|
|
return ruby_num_interval_step_size(from, to, step, FALSE);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* step(to = nil, by = 1) {|n| ... } -> self
|
|
* step(to = nil, by = 1) -> enumerator
|
|
* step(to = nil, by: 1) {|n| ... } -> self
|
|
* step(to = nil, by: 1) -> enumerator
|
|
* step(by: 1, to: ) {|n| ... } -> self
|
|
* step(by: 1, to: ) -> enumerator
|
|
* step(by: , to: nil) {|n| ... } -> self
|
|
* step(by: , to: nil) -> enumerator
|
|
*
|
|
* Generates a sequence of numbers; with a block given, traverses the sequence.
|
|
*
|
|
* Of the Core and Standard Library classes,
|
|
* Integer, Float, and Rational use this implementation.
|
|
*
|
|
* A quick example:
|
|
*
|
|
* squares = []
|
|
* 1.step(by: 2, to: 10) {|i| squares.push(i*i) }
|
|
* squares # => [1, 9, 25, 49, 81]
|
|
*
|
|
* The generated sequence:
|
|
*
|
|
* - Begins with +self+.
|
|
* - Continues at intervals of +step+ (which may not be zero).
|
|
* - Ends with the last number that is within or equal to +limit+;
|
|
* that is, less than or equal to +limit+ if +step+ is positive,
|
|
* greater than or equal to +limit+ if +step+ is negative.
|
|
* If +limit+ is not given, the sequence is of infinite length.
|
|
*
|
|
* If a block is given, calls the block with each number in the sequence;
|
|
* returns +self+. If no block is given, returns an Enumerator::ArithmeticSequence.
|
|
*
|
|
* <b>Keyword Arguments</b>
|
|
*
|
|
* With keyword arguments +by+ and +to+,
|
|
* their values (or defaults) determine the step and limit:
|
|
*
|
|
* # Both keywords given.
|
|
* squares = []
|
|
* 4.step(by: 2, to: 10) {|i| squares.push(i*i) } # => 4
|
|
* squares # => [16, 36, 64, 100]
|
|
* cubes = []
|
|
* 3.step(by: -1.5, to: -3) {|i| cubes.push(i*i*i) } # => 3
|
|
* cubes # => [27.0, 3.375, 0.0, -3.375, -27.0]
|
|
* squares = []
|
|
* 1.2.step(by: 0.2, to: 2.0) {|f| squares.push(f*f) }
|
|
* squares # => [1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4.0]
|
|
*
|
|
* squares = []
|
|
* Rational(6/5).step(by: 0.2, to: 2.0) {|r| squares.push(r*r) }
|
|
* squares # => [1.0, 1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4.0]
|
|
*
|
|
* # Only keyword to given.
|
|
* squares = []
|
|
* 4.step(to: 10) {|i| squares.push(i*i) } # => 4
|
|
* squares # => [16, 25, 36, 49, 64, 81, 100]
|
|
* # Only by given.
|
|
*
|
|
* # Only keyword by given
|
|
* squares = []
|
|
* 4.step(by:2) {|i| squares.push(i*i); break if i > 10 }
|
|
* squares # => [16, 36, 64, 100, 144]
|
|
*
|
|
* # No block given.
|
|
* e = 3.step(by: -1.5, to: -3) # => (3.step(by: -1.5, to: -3))
|
|
* e.class # => Enumerator::ArithmeticSequence
|
|
*
|
|
* <b>Positional Arguments</b>
|
|
*
|
|
* With optional positional arguments +limit+ and +step+,
|
|
* their values (or defaults) determine the step and limit:
|
|
*
|
|
* squares = []
|
|
* 4.step(10, 2) {|i| squares.push(i*i) } # => 4
|
|
* squares # => [16, 36, 64, 100]
|
|
* squares = []
|
|
* 4.step(10) {|i| squares.push(i*i) }
|
|
* squares # => [16, 25, 36, 49, 64, 81, 100]
|
|
* squares = []
|
|
* 4.step {|i| squares.push(i*i); break if i > 10 } # => nil
|
|
* squares # => [16, 25, 36, 49, 64, 81, 100, 121]
|
|
*
|
|
* <b>Implementation Notes</b>
|
|
*
|
|
* If all the arguments are integers, the loop operates using an integer
|
|
* counter.
|
|
*
|
|
* If any of the arguments are floating point numbers, all are converted
|
|
* to floats, and the loop is executed
|
|
* <i>floor(n + n*Float::EPSILON) + 1</i> times,
|
|
* where <i>n = (limit - self)/step</i>.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
num_step(int argc, VALUE *argv, VALUE from)
|
|
{
|
|
VALUE to, step;
|
|
int desc, inf;
|
|
|
|
if (!rb_block_given_p()) {
|
|
VALUE by = Qundef;
|
|
|
|
num_step_extract_args(argc, argv, &to, &step, &by);
|
|
if (by != Qundef) {
|
|
step = by;
|
|
}
|
|
if (NIL_P(step)) {
|
|
step = INT2FIX(1);
|
|
}
|
|
else if (rb_equal(step, INT2FIX(0))) {
|
|
rb_raise(rb_eArgError, "step can't be 0");
|
|
}
|
|
if ((NIL_P(to) || rb_obj_is_kind_of(to, rb_cNumeric)) &&
|
|
rb_obj_is_kind_of(step, rb_cNumeric)) {
|
|
return rb_arith_seq_new(from, ID2SYM(rb_frame_this_func()), argc, argv,
|
|
num_step_size, from, to, step, FALSE);
|
|
}
|
|
|
|
return SIZED_ENUMERATOR(from, 2, ((VALUE [2]){to, step}), num_step_size);
|
|
}
|
|
|
|
desc = num_step_scan_args(argc, argv, &to, &step, TRUE, FALSE);
|
|
if (rb_equal(step, INT2FIX(0))) {
|
|
inf = 1;
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(to)) {
|
|
double f = RFLOAT_VALUE(to);
|
|
inf = isinf(f) && (signbit(f) ? desc : !desc);
|
|
}
|
|
else inf = 0;
|
|
|
|
if (FIXNUM_P(from) && (inf || FIXNUM_P(to)) && FIXNUM_P(step)) {
|
|
long i = FIX2LONG(from);
|
|
long diff = FIX2LONG(step);
|
|
|
|
if (inf) {
|
|
for (;; i += diff)
|
|
rb_yield(LONG2FIX(i));
|
|
}
|
|
else {
|
|
long end = FIX2LONG(to);
|
|
|
|
if (desc) {
|
|
for (; i >= end; i += diff)
|
|
rb_yield(LONG2FIX(i));
|
|
}
|
|
else {
|
|
for (; i <= end; i += diff)
|
|
rb_yield(LONG2FIX(i));
|
|
}
|
|
}
|
|
}
|
|
else if (!ruby_float_step(from, to, step, FALSE, FALSE)) {
|
|
VALUE i = from;
|
|
|
|
if (inf) {
|
|
for (;; i = rb_funcall(i, '+', 1, step))
|
|
rb_yield(i);
|
|
}
|
|
else {
|
|
ID cmp = desc ? '<' : '>';
|
|
|
|
for (; !RTEST(rb_funcall(i, cmp, 1, to)); i = rb_funcall(i, '+', 1, step))
|
|
rb_yield(i);
|
|
}
|
|
}
|
|
return from;
|
|
}
|
|
|
|
static char *
|
|
out_of_range_float(char (*pbuf)[24], VALUE val)
|
|
{
|
|
char *const buf = *pbuf;
|
|
char *s;
|
|
|
|
snprintf(buf, sizeof(*pbuf), "%-.10g", RFLOAT_VALUE(val));
|
|
if ((s = strchr(buf, ' ')) != 0) *s = '\0';
|
|
return buf;
|
|
}
|
|
|
|
#define FLOAT_OUT_OF_RANGE(val, type) do { \
|
|
char buf[24]; \
|
|
rb_raise(rb_eRangeError, "float %s out of range of "type, \
|
|
out_of_range_float(&buf, (val))); \
|
|
} while (0)
|
|
|
|
#define LONG_MIN_MINUS_ONE ((double)LONG_MIN-1)
|
|
#define LONG_MAX_PLUS_ONE (2*(double)(LONG_MAX/2+1))
|
|
#define ULONG_MAX_PLUS_ONE (2*(double)(ULONG_MAX/2+1))
|
|
#define LONG_MIN_MINUS_ONE_IS_LESS_THAN(n) \
|
|
(LONG_MIN_MINUS_ONE == (double)LONG_MIN ? \
|
|
LONG_MIN <= (n): \
|
|
LONG_MIN_MINUS_ONE < (n))
|
|
|
|
long
|
|
rb_num2long(VALUE val)
|
|
{
|
|
again:
|
|
if (NIL_P(val)) {
|
|
rb_raise(rb_eTypeError, "no implicit conversion from nil to integer");
|
|
}
|
|
|
|
if (FIXNUM_P(val)) return FIX2LONG(val);
|
|
|
|
else if (RB_FLOAT_TYPE_P(val)) {
|
|
if (RFLOAT_VALUE(val) < LONG_MAX_PLUS_ONE
|
|
&& LONG_MIN_MINUS_ONE_IS_LESS_THAN(RFLOAT_VALUE(val))) {
|
|
return (long)RFLOAT_VALUE(val);
|
|
}
|
|
else {
|
|
FLOAT_OUT_OF_RANGE(val, "integer");
|
|
}
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(val)) {
|
|
return rb_big2long(val);
|
|
}
|
|
else {
|
|
val = rb_to_int(val);
|
|
goto again;
|
|
}
|
|
}
|
|
|
|
static unsigned long
|
|
rb_num2ulong_internal(VALUE val, int *wrap_p)
|
|
{
|
|
again:
|
|
if (NIL_P(val)) {
|
|
rb_raise(rb_eTypeError, "no implicit conversion from nil to integer");
|
|
}
|
|
|
|
if (FIXNUM_P(val)) {
|
|
long l = FIX2LONG(val); /* this is FIX2LONG, intended */
|
|
if (wrap_p)
|
|
*wrap_p = l < 0;
|
|
return (unsigned long)l;
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(val)) {
|
|
double d = RFLOAT_VALUE(val);
|
|
if (d < ULONG_MAX_PLUS_ONE && LONG_MIN_MINUS_ONE_IS_LESS_THAN(d)) {
|
|
if (wrap_p)
|
|
*wrap_p = d <= -1.0; /* NUM2ULONG(v) uses v.to_int conceptually. */
|
|
if (0 <= d)
|
|
return (unsigned long)d;
|
|
return (unsigned long)(long)d;
|
|
}
|
|
else {
|
|
FLOAT_OUT_OF_RANGE(val, "integer");
|
|
}
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(val)) {
|
|
{
|
|
unsigned long ul = rb_big2ulong(val);
|
|
if (wrap_p)
|
|
*wrap_p = BIGNUM_NEGATIVE_P(val);
|
|
return ul;
|
|
}
|
|
}
|
|
else {
|
|
val = rb_to_int(val);
|
|
goto again;
|
|
}
|
|
}
|
|
|
|
unsigned long
|
|
rb_num2ulong(VALUE val)
|
|
{
|
|
return rb_num2ulong_internal(val, NULL);
|
|
}
|
|
|
|
void
|
|
rb_out_of_int(SIGNED_VALUE num)
|
|
{
|
|
rb_raise(rb_eRangeError, "integer %"PRIdVALUE " too %s to convert to `int'",
|
|
num, num < 0 ? "small" : "big");
|
|
}
|
|
|
|
#if SIZEOF_INT < SIZEOF_LONG
|
|
static void
|
|
check_int(long num)
|
|
{
|
|
if ((long)(int)num != num) {
|
|
rb_out_of_int(num);
|
|
}
|
|
}
|
|
|
|
static void
|
|
check_uint(unsigned long num, int sign)
|
|
{
|
|
if (sign) {
|
|
/* minus */
|
|
if (num < (unsigned long)INT_MIN)
|
|
rb_raise(rb_eRangeError, "integer %ld too small to convert to `unsigned int'", (long)num);
|
|
}
|
|
else {
|
|
/* plus */
|
|
if (UINT_MAX < num)
|
|
rb_raise(rb_eRangeError, "integer %lu too big to convert to `unsigned int'", num);
|
|
}
|
|
}
|
|
|
|
long
|
|
rb_num2int(VALUE val)
|
|
{
|
|
long num = rb_num2long(val);
|
|
|
|
check_int(num);
|
|
return num;
|
|
}
|
|
|
|
long
|
|
rb_fix2int(VALUE val)
|
|
{
|
|
long num = FIXNUM_P(val)?FIX2LONG(val):rb_num2long(val);
|
|
|
|
check_int(num);
|
|
return num;
|
|
}
|
|
|
|
unsigned long
|
|
rb_num2uint(VALUE val)
|
|
{
|
|
int wrap;
|
|
unsigned long num = rb_num2ulong_internal(val, &wrap);
|
|
|
|
check_uint(num, wrap);
|
|
return num;
|
|
}
|
|
|
|
unsigned long
|
|
rb_fix2uint(VALUE val)
|
|
{
|
|
unsigned long num;
|
|
|
|
if (!FIXNUM_P(val)) {
|
|
return rb_num2uint(val);
|
|
}
|
|
num = FIX2ULONG(val);
|
|
|
|
check_uint(num, FIXNUM_NEGATIVE_P(val));
|
|
return num;
|
|
}
|
|
#else
|
|
long
|
|
rb_num2int(VALUE val)
|
|
{
|
|
return rb_num2long(val);
|
|
}
|
|
|
|
long
|
|
rb_fix2int(VALUE val)
|
|
{
|
|
return FIX2INT(val);
|
|
}
|
|
|
|
unsigned long
|
|
rb_num2uint(VALUE val)
|
|
{
|
|
return rb_num2ulong(val);
|
|
}
|
|
|
|
unsigned long
|
|
rb_fix2uint(VALUE val)
|
|
{
|
|
return RB_FIX2ULONG(val);
|
|
}
|
|
#endif
|
|
|
|
NORETURN(static void rb_out_of_short(SIGNED_VALUE num));
|
|
static void
|
|
rb_out_of_short(SIGNED_VALUE num)
|
|
{
|
|
rb_raise(rb_eRangeError, "integer %"PRIdVALUE " too %s to convert to `short'",
|
|
num, num < 0 ? "small" : "big");
|
|
}
|
|
|
|
static void
|
|
check_short(long num)
|
|
{
|
|
if ((long)(short)num != num) {
|
|
rb_out_of_short(num);
|
|
}
|
|
}
|
|
|
|
static void
|
|
check_ushort(unsigned long num, int sign)
|
|
{
|
|
if (sign) {
|
|
/* minus */
|
|
if (num < (unsigned long)SHRT_MIN)
|
|
rb_raise(rb_eRangeError, "integer %ld too small to convert to `unsigned short'", (long)num);
|
|
}
|
|
else {
|
|
/* plus */
|
|
if (USHRT_MAX < num)
|
|
rb_raise(rb_eRangeError, "integer %lu too big to convert to `unsigned short'", num);
|
|
}
|
|
}
|
|
|
|
short
|
|
rb_num2short(VALUE val)
|
|
{
|
|
long num = rb_num2long(val);
|
|
|
|
check_short(num);
|
|
return num;
|
|
}
|
|
|
|
short
|
|
rb_fix2short(VALUE val)
|
|
{
|
|
long num = FIXNUM_P(val)?FIX2LONG(val):rb_num2long(val);
|
|
|
|
check_short(num);
|
|
return num;
|
|
}
|
|
|
|
unsigned short
|
|
rb_num2ushort(VALUE val)
|
|
{
|
|
int wrap;
|
|
unsigned long num = rb_num2ulong_internal(val, &wrap);
|
|
|
|
check_ushort(num, wrap);
|
|
return num;
|
|
}
|
|
|
|
unsigned short
|
|
rb_fix2ushort(VALUE val)
|
|
{
|
|
unsigned long num;
|
|
|
|
if (!FIXNUM_P(val)) {
|
|
return rb_num2ushort(val);
|
|
}
|
|
num = FIX2ULONG(val);
|
|
|
|
check_ushort(num, FIXNUM_NEGATIVE_P(val));
|
|
return num;
|
|
}
|
|
|
|
VALUE
|
|
rb_num2fix(VALUE val)
|
|
{
|
|
long v;
|
|
|
|
if (FIXNUM_P(val)) return val;
|
|
|
|
v = rb_num2long(val);
|
|
if (!FIXABLE(v))
|
|
rb_raise(rb_eRangeError, "integer %ld out of range of fixnum", v);
|
|
return LONG2FIX(v);
|
|
}
|
|
|
|
#if HAVE_LONG_LONG
|
|
|
|
#define LLONG_MIN_MINUS_ONE ((double)LLONG_MIN-1)
|
|
#define LLONG_MAX_PLUS_ONE (2*(double)(LLONG_MAX/2+1))
|
|
#define ULLONG_MAX_PLUS_ONE (2*(double)(ULLONG_MAX/2+1))
|
|
#ifndef ULLONG_MAX
|
|
#define ULLONG_MAX ((unsigned LONG_LONG)LLONG_MAX*2+1)
|
|
#endif
|
|
#define LLONG_MIN_MINUS_ONE_IS_LESS_THAN(n) \
|
|
(LLONG_MIN_MINUS_ONE == (double)LLONG_MIN ? \
|
|
LLONG_MIN <= (n): \
|
|
LLONG_MIN_MINUS_ONE < (n))
|
|
|
|
LONG_LONG
|
|
rb_num2ll(VALUE val)
|
|
{
|
|
if (NIL_P(val)) {
|
|
rb_raise(rb_eTypeError, "no implicit conversion from nil");
|
|
}
|
|
|
|
if (FIXNUM_P(val)) return (LONG_LONG)FIX2LONG(val);
|
|
|
|
else if (RB_FLOAT_TYPE_P(val)) {
|
|
double d = RFLOAT_VALUE(val);
|
|
if (d < LLONG_MAX_PLUS_ONE && (LLONG_MIN_MINUS_ONE_IS_LESS_THAN(d))) {
|
|
return (LONG_LONG)d;
|
|
}
|
|
else {
|
|
FLOAT_OUT_OF_RANGE(val, "long long");
|
|
}
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(val)) {
|
|
return rb_big2ll(val);
|
|
}
|
|
else if (RB_TYPE_P(val, T_STRING)) {
|
|
rb_raise(rb_eTypeError, "no implicit conversion from string");
|
|
}
|
|
else if (RB_TYPE_P(val, T_TRUE) || RB_TYPE_P(val, T_FALSE)) {
|
|
rb_raise(rb_eTypeError, "no implicit conversion from boolean");
|
|
}
|
|
|
|
val = rb_to_int(val);
|
|
return NUM2LL(val);
|
|
}
|
|
|
|
unsigned LONG_LONG
|
|
rb_num2ull(VALUE val)
|
|
{
|
|
if (NIL_P(val)) {
|
|
rb_raise(rb_eTypeError, "no implicit conversion from nil");
|
|
}
|
|
else if (FIXNUM_P(val)) {
|
|
return (LONG_LONG)FIX2LONG(val); /* this is FIX2LONG, intended */
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(val)) {
|
|
double d = RFLOAT_VALUE(val);
|
|
if (d < ULLONG_MAX_PLUS_ONE && LLONG_MIN_MINUS_ONE_IS_LESS_THAN(d)) {
|
|
if (0 <= d)
|
|
return (unsigned LONG_LONG)d;
|
|
return (unsigned LONG_LONG)(LONG_LONG)d;
|
|
}
|
|
else {
|
|
FLOAT_OUT_OF_RANGE(val, "unsigned long long");
|
|
}
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(val)) {
|
|
return rb_big2ull(val);
|
|
}
|
|
else if (RB_TYPE_P(val, T_STRING)) {
|
|
rb_raise(rb_eTypeError, "no implicit conversion from string");
|
|
}
|
|
else if (RB_TYPE_P(val, T_TRUE) || RB_TYPE_P(val, T_FALSE)) {
|
|
rb_raise(rb_eTypeError, "no implicit conversion from boolean");
|
|
}
|
|
|
|
val = rb_to_int(val);
|
|
return NUM2ULL(val);
|
|
}
|
|
|
|
#endif /* HAVE_LONG_LONG */
|
|
|
|
/********************************************************************
|
|
*
|
|
* Document-class: Integer
|
|
*
|
|
* An \Integer object represents an integer value.
|
|
*
|
|
* You can create an \Integer object explicitly with:
|
|
*
|
|
* - An {integer literal}[rdoc-ref:syntax/literals.rdoc@Integer+Literals].
|
|
*
|
|
* You can convert certain objects to Integers with:
|
|
*
|
|
* - \Method #Integer.
|
|
*
|
|
* An attempt to add a singleton method to an instance of this class
|
|
* causes an exception to be raised.
|
|
*
|
|
* == What's Here
|
|
*
|
|
* First, what's elsewhere. \Class \Integer:
|
|
*
|
|
* - Inherits from {class Numeric}[rdoc-ref:Numeric@What-27s+Here].
|
|
*
|
|
* Here, class \Integer provides methods for:
|
|
*
|
|
* - {Querying}[rdoc-ref:Integer@Querying]
|
|
* - {Comparing}[rdoc-ref:Integer@Comparing]
|
|
* - {Converting}[rdoc-ref:Integer@Converting]
|
|
* - {Other}[rdoc-ref:Integer@Other]
|
|
*
|
|
* === Querying
|
|
*
|
|
* - #allbits?: Returns whether all bits in +self+ are set.
|
|
* - #anybits?: Returns whether any bits in +self+ are set.
|
|
* - #nobits?: Returns whether no bits in +self+ are set.
|
|
*
|
|
* === Comparing
|
|
*
|
|
* - #<: Returns whether +self+ is less than the given value.
|
|
* - #<=: Returns whether +self+ is less than or equal to the given value.
|
|
* - #<=>: Returns a number indicating whether +self+ is less than, equal
|
|
* to, or greater than the given value.
|
|
* - #== (aliased as #===): Returns whether +self+ is equal to the given
|
|
* value.
|
|
* - #>: Returns whether +self+ is greater than the given value.
|
|
* - #>=: Returns whether +self+ is greater than or equal to the given value.
|
|
*
|
|
* === Converting
|
|
*
|
|
* - ::sqrt: Returns the integer square root of the given value.
|
|
* - ::try_convert: Returns the given value converted to an \Integer.
|
|
* - #% (aliased as #modulo): Returns +self+ modulo the given value.
|
|
* - #&: Returns the bitwise AND of +self+ and the given value.
|
|
* - #*: Returns the product of +self+ and the given value.
|
|
* - #**: Returns the value of +self+ raised to the power of the given value.
|
|
* - #+: Returns the sum of +self+ and the given value.
|
|
* - #-: Returns the difference of +self+ and the given value.
|
|
* - #/: Returns the quotient of +self+ and the given value.
|
|
* - #<<: Returns the value of +self+ after a leftward bit-shift.
|
|
* - #>>: Returns the value of +self+ after a rightward bit-shift.
|
|
* - #[]: Returns a slice of bits from +self+.
|
|
* - #^: Returns the bitwise EXCLUSIVE OR of +self+ and the given value.
|
|
* - #ceil: Returns the smallest number greater than or equal to +self+.
|
|
* - #chr: Returns a 1-character string containing the character
|
|
* represented by the value of +self+.
|
|
* - #digits: Returns an array of integers representing the base-radix digits
|
|
* of +self+.
|
|
* - #div: Returns the integer result of dividing +self+ by the given value.
|
|
* - #divmod: Returns a 2-element array containing the quotient and remainder
|
|
* results of dividing +self+ by the given value.
|
|
* - #fdiv: Returns the Float result of dividing +self+ by the given value.
|
|
* - #floor: Returns the greatest number smaller than or equal to +self+.
|
|
* - #pow: Returns the modular exponentiation of +self+.
|
|
* - #pred: Returns the integer predecessor of +self+.
|
|
* - #remainder: Returns the remainder after dividing +self+ by the given value.
|
|
* - #round: Returns +self+ rounded to the nearest value with the given precision.
|
|
* - #succ (aliased as #next): Returns the integer successor of +self+.
|
|
* - #to_f: Returns +self+ converted to a Float.
|
|
* - #to_s (aliased as #inspect): Returns a string containing the place-value
|
|
* representation of +self+ in the given radix.
|
|
* - #truncate: Returns +self+ truncated to the given precision.
|
|
* - #|: Returns the bitwise OR of +self+ and the given value.
|
|
*
|
|
* === Other
|
|
*
|
|
* - #downto: Calls the given block with each integer value from +self+
|
|
* down to the given value.
|
|
* - #times: Calls the given block +self+ times with each integer
|
|
* in <tt>(0..self-1)</tt>.
|
|
* - #upto: Calls the given block with each integer value from +self+
|
|
* up to the given value.
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_odd_p(VALUE num)
|
|
{
|
|
if (FIXNUM_P(num)) {
|
|
return RBOOL(num & 2);
|
|
}
|
|
else {
|
|
assert(RB_BIGNUM_TYPE_P(num));
|
|
return rb_big_odd_p(num);
|
|
}
|
|
}
|
|
|
|
static VALUE
|
|
int_even_p(VALUE num)
|
|
{
|
|
if (FIXNUM_P(num)) {
|
|
return RBOOL((num & 2) == 0);
|
|
}
|
|
else {
|
|
assert(RB_BIGNUM_TYPE_P(num));
|
|
return rb_big_even_p(num);
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_int_even_p(VALUE num)
|
|
{
|
|
return int_even_p(num);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* allbits?(mask) -> true or false
|
|
*
|
|
* Returns +true+ if all bits that are set (=1) in +mask+
|
|
* are also set in +self+; returns +false+ otherwise.
|
|
*
|
|
* Example values:
|
|
*
|
|
* 0b1010101 self
|
|
* 0b1010100 mask
|
|
* 0b1010100 self & mask
|
|
* true self.allbits?(mask)
|
|
*
|
|
* 0b1010100 self
|
|
* 0b1010101 mask
|
|
* 0b1010100 self & mask
|
|
* false self.allbits?(mask)
|
|
*
|
|
* Related: Integer#anybits?, Integer#nobits?.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_allbits_p(VALUE num, VALUE mask)
|
|
{
|
|
mask = rb_to_int(mask);
|
|
return rb_int_equal(rb_int_and(num, mask), mask);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* anybits?(mask) -> true or false
|
|
*
|
|
* Returns +true+ if any bit that is set (=1) in +mask+
|
|
* is also set in +self+; returns +false+ otherwise.
|
|
*
|
|
* Example values:
|
|
*
|
|
* 0b10000010 self
|
|
* 0b11111111 mask
|
|
* 0b10000010 self & mask
|
|
* true self.anybits?(mask)
|
|
*
|
|
* 0b00000000 self
|
|
* 0b11111111 mask
|
|
* 0b00000000 self & mask
|
|
* false self.anybits?(mask)
|
|
*
|
|
* Related: Integer#allbits?, Integer#nobits?.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_anybits_p(VALUE num, VALUE mask)
|
|
{
|
|
mask = rb_to_int(mask);
|
|
return RBOOL(!int_zero_p(rb_int_and(num, mask)));
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* nobits?(mask) -> true or false
|
|
*
|
|
* Returns +true+ if no bit that is set (=1) in +mask+
|
|
* is also set in +self+; returns +false+ otherwise.
|
|
*
|
|
* Example values:
|
|
*
|
|
* 0b11110000 self
|
|
* 0b00001111 mask
|
|
* 0b00000000 self & mask
|
|
* true self.nobits?(mask)
|
|
*
|
|
* 0b00000001 self
|
|
* 0b11111111 mask
|
|
* 0b00000001 self & mask
|
|
* false self.nobits?(mask)
|
|
*
|
|
* Related: Integer#allbits?, Integer#anybits?.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_nobits_p(VALUE num, VALUE mask)
|
|
{
|
|
mask = rb_to_int(mask);
|
|
return RBOOL(int_zero_p(rb_int_and(num, mask)));
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* succ -> next_integer
|
|
*
|
|
* Returns the successor integer of +self+ (equivalent to <tt>self + 1</tt>):
|
|
*
|
|
* 1.succ #=> 2
|
|
* -1.succ #=> 0
|
|
*
|
|
* Integer#next is an alias for Integer#succ.
|
|
*
|
|
* Related: Integer#pred (predecessor value).
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_succ(VALUE num)
|
|
{
|
|
if (FIXNUM_P(num)) {
|
|
long i = FIX2LONG(num) + 1;
|
|
return LONG2NUM(i);
|
|
}
|
|
if (RB_BIGNUM_TYPE_P(num)) {
|
|
return rb_big_plus(num, INT2FIX(1));
|
|
}
|
|
return num_funcall1(num, '+', INT2FIX(1));
|
|
}
|
|
|
|
#define int_succ rb_int_succ
|
|
|
|
/*
|
|
* call-seq:
|
|
* pred -> next_integer
|
|
*
|
|
* Returns the predecessor of +self+ (equivalent to <tt>self - 1</tt>):
|
|
*
|
|
* 1.pred #=> 0
|
|
* -1.pred #=> -2
|
|
*
|
|
* Related: Integer#succ (successor value).
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
rb_int_pred(VALUE num)
|
|
{
|
|
if (FIXNUM_P(num)) {
|
|
long i = FIX2LONG(num) - 1;
|
|
return LONG2NUM(i);
|
|
}
|
|
if (RB_BIGNUM_TYPE_P(num)) {
|
|
return rb_big_minus(num, INT2FIX(1));
|
|
}
|
|
return num_funcall1(num, '-', INT2FIX(1));
|
|
}
|
|
|
|
#define int_pred rb_int_pred
|
|
|
|
VALUE
|
|
rb_enc_uint_chr(unsigned int code, rb_encoding *enc)
|
|
{
|
|
int n;
|
|
VALUE str;
|
|
switch (n = rb_enc_codelen(code, enc)) {
|
|
case ONIGERR_INVALID_CODE_POINT_VALUE:
|
|
rb_raise(rb_eRangeError, "invalid codepoint 0x%X in %s", code, rb_enc_name(enc));
|
|
break;
|
|
case ONIGERR_TOO_BIG_WIDE_CHAR_VALUE:
|
|
case 0:
|
|
rb_raise(rb_eRangeError, "%u out of char range", code);
|
|
break;
|
|
}
|
|
str = rb_enc_str_new(0, n, enc);
|
|
rb_enc_mbcput(code, RSTRING_PTR(str), enc);
|
|
if (rb_enc_precise_mbclen(RSTRING_PTR(str), RSTRING_END(str), enc) != n) {
|
|
rb_raise(rb_eRangeError, "invalid codepoint 0x%X in %s", code, rb_enc_name(enc));
|
|
}
|
|
return str;
|
|
}
|
|
|
|
/* call-seq:
|
|
* chr -> string
|
|
* chr(encoding) -> string
|
|
*
|
|
* Returns a 1-character string containing the character
|
|
* represented by the value of +self+, according to the given +encoding+.
|
|
*
|
|
* 65.chr # => "A"
|
|
* 0.chr # => "\x00"
|
|
* 255.chr # => "\xFF"
|
|
* string = 255.chr(Encoding::UTF_8)
|
|
* string.encoding # => Encoding::UTF_8
|
|
*
|
|
* Raises an exception if +self+ is negative.
|
|
*
|
|
* Related: Integer#ord.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_chr(int argc, VALUE *argv, VALUE num)
|
|
{
|
|
char c;
|
|
unsigned int i;
|
|
rb_encoding *enc;
|
|
|
|
if (rb_num_to_uint(num, &i) == 0) {
|
|
}
|
|
else if (FIXNUM_P(num)) {
|
|
rb_raise(rb_eRangeError, "%ld out of char range", FIX2LONG(num));
|
|
}
|
|
else {
|
|
rb_raise(rb_eRangeError, "bignum out of char range");
|
|
}
|
|
|
|
switch (argc) {
|
|
case 0:
|
|
if (0xff < i) {
|
|
enc = rb_default_internal_encoding();
|
|
if (!enc) {
|
|
rb_raise(rb_eRangeError, "%u out of char range", i);
|
|
}
|
|
goto decode;
|
|
}
|
|
c = (char)i;
|
|
if (i < 0x80) {
|
|
return rb_usascii_str_new(&c, 1);
|
|
}
|
|
else {
|
|
return rb_str_new(&c, 1);
|
|
}
|
|
case 1:
|
|
break;
|
|
default:
|
|
rb_error_arity(argc, 0, 1);
|
|
}
|
|
enc = rb_to_encoding(argv[0]);
|
|
if (!enc) enc = rb_ascii8bit_encoding();
|
|
decode:
|
|
return rb_enc_uint_chr(i, enc);
|
|
}
|
|
|
|
/*
|
|
* Fixnum
|
|
*/
|
|
|
|
static VALUE
|
|
fix_uminus(VALUE num)
|
|
{
|
|
return LONG2NUM(-FIX2LONG(num));
|
|
}
|
|
|
|
VALUE
|
|
rb_int_uminus(VALUE num)
|
|
{
|
|
if (FIXNUM_P(num)) {
|
|
return fix_uminus(num);
|
|
}
|
|
else {
|
|
assert(RB_BIGNUM_TYPE_P(num));
|
|
return rb_big_uminus(num);
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_fix2str(VALUE x, int base)
|
|
{
|
|
char buf[SIZEOF_VALUE*CHAR_BIT + 1], *const e = buf + sizeof buf, *b = e;
|
|
long val = FIX2LONG(x);
|
|
unsigned long u;
|
|
int neg = 0;
|
|
|
|
if (base < 2 || 36 < base) {
|
|
rb_raise(rb_eArgError, "invalid radix %d", base);
|
|
}
|
|
#if SIZEOF_LONG < SIZEOF_VOIDP
|
|
# if SIZEOF_VOIDP == SIZEOF_LONG_LONG
|
|
if ((val >= 0 && (x & 0xFFFFFFFF00000000ull)) ||
|
|
(val < 0 && (x & 0xFFFFFFFF00000000ull) != 0xFFFFFFFF00000000ull)) {
|
|
rb_bug("Unnormalized Fixnum value %p", (void *)x);
|
|
}
|
|
# else
|
|
/* should do something like above code, but currently ruby does not know */
|
|
/* such platforms */
|
|
# endif
|
|
#endif
|
|
if (val == 0) {
|
|
return rb_usascii_str_new2("0");
|
|
}
|
|
if (val < 0) {
|
|
u = 1 + (unsigned long)(-(val + 1)); /* u = -val avoiding overflow */
|
|
neg = 1;
|
|
}
|
|
else {
|
|
u = val;
|
|
}
|
|
do {
|
|
*--b = ruby_digitmap[(int)(u % base)];
|
|
} while (u /= base);
|
|
if (neg) {
|
|
*--b = '-';
|
|
}
|
|
|
|
return rb_usascii_str_new(b, e - b);
|
|
}
|
|
|
|
static VALUE rb_fix_to_s_static[10];
|
|
|
|
MJIT_FUNC_EXPORTED VALUE
|
|
rb_fix_to_s(VALUE x)
|
|
{
|
|
long i = FIX2LONG(x);
|
|
if (i >= 0 && i < 10) {
|
|
return rb_fix_to_s_static[i];
|
|
}
|
|
return rb_fix2str(x, 10);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* to_s(base = 10) -> string
|
|
*
|
|
* Returns a string containing the place-value representation of +self+
|
|
* in radix +base+ (in 2..36).
|
|
*
|
|
* 12345.to_s # => "12345"
|
|
* 12345.to_s(2) # => "11000000111001"
|
|
* 12345.to_s(8) # => "30071"
|
|
* 12345.to_s(10) # => "12345"
|
|
* 12345.to_s(16) # => "3039"
|
|
* 12345.to_s(36) # => "9ix"
|
|
* 78546939656932.to_s(36) # => "rubyrules"
|
|
*
|
|
* Raises an exception if +base+ is out of range.
|
|
*
|
|
* Integer#inspect is an alias for Integer#to_s.
|
|
*
|
|
*/
|
|
|
|
MJIT_FUNC_EXPORTED VALUE
|
|
rb_int_to_s(int argc, VALUE *argv, VALUE x)
|
|
{
|
|
int base;
|
|
|
|
if (rb_check_arity(argc, 0, 1))
|
|
base = NUM2INT(argv[0]);
|
|
else
|
|
base = 10;
|
|
return rb_int2str(x, base);
|
|
}
|
|
|
|
VALUE
|
|
rb_int2str(VALUE x, int base)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return rb_fix2str(x, base);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big2str(x, base);
|
|
}
|
|
|
|
return rb_any_to_s(x);
|
|
}
|
|
|
|
static VALUE
|
|
fix_plus(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
return rb_fix_plus_fix(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
return rb_big_plus(y, x);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return DBL2NUM((double)FIX2LONG(x) + RFLOAT_VALUE(y));
|
|
}
|
|
else if (RB_TYPE_P(y, T_COMPLEX)) {
|
|
return rb_complex_plus(y, x);
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, '+');
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_fix_plus(VALUE x, VALUE y)
|
|
{
|
|
return fix_plus(x, y);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self + numeric -> numeric_result
|
|
*
|
|
* Performs addition:
|
|
*
|
|
* 2 + 2 # => 4
|
|
* -2 + 2 # => 0
|
|
* -2 + -2 # => -4
|
|
* 2 + 2.0 # => 4.0
|
|
* 2 + Rational(2, 1) # => (4/1)
|
|
* 2 + Complex(2, 0) # => (4+0i)
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_plus(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_plus(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_plus(x, y);
|
|
}
|
|
return rb_num_coerce_bin(x, y, '+');
|
|
}
|
|
|
|
static VALUE
|
|
fix_minus(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
return rb_fix_minus_fix(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
x = rb_int2big(FIX2LONG(x));
|
|
return rb_big_minus(x, y);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return DBL2NUM((double)FIX2LONG(x) - RFLOAT_VALUE(y));
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, '-');
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self - numeric -> numeric_result
|
|
*
|
|
* Performs subtraction:
|
|
*
|
|
* 4 - 2 # => 2
|
|
* -4 - 2 # => -6
|
|
* -4 - -2 # => -2
|
|
* 4 - 2.0 # => 2.0
|
|
* 4 - Rational(2, 1) # => (2/1)
|
|
* 4 - Complex(2, 0) # => (2+0i)
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_minus(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_minus(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_minus(x, y);
|
|
}
|
|
return rb_num_coerce_bin(x, y, '-');
|
|
}
|
|
|
|
|
|
#define SQRT_LONG_MAX HALF_LONG_MSB
|
|
/*tests if N*N would overflow*/
|
|
#define FIT_SQRT_LONG(n) (((n)<SQRT_LONG_MAX)&&((n)>=-SQRT_LONG_MAX))
|
|
|
|
static VALUE
|
|
fix_mul(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
return rb_fix_mul_fix(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
switch (x) {
|
|
case INT2FIX(0): return x;
|
|
case INT2FIX(1): return y;
|
|
}
|
|
return rb_big_mul(y, x);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return DBL2NUM((double)FIX2LONG(x) * RFLOAT_VALUE(y));
|
|
}
|
|
else if (RB_TYPE_P(y, T_COMPLEX)) {
|
|
return rb_complex_mul(y, x);
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, '*');
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self * numeric -> numeric_result
|
|
*
|
|
* Performs multiplication:
|
|
*
|
|
* 4 * 2 # => 8
|
|
* 4 * -2 # => -8
|
|
* -4 * 2 # => -8
|
|
* 4 * 2.0 # => 8.0
|
|
* 4 * Rational(1, 3) # => (4/3)
|
|
* 4 * Complex(2, 0) # => (8+0i)
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_mul(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_mul(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_mul(x, y);
|
|
}
|
|
return rb_num_coerce_bin(x, y, '*');
|
|
}
|
|
|
|
static double
|
|
fix_fdiv_double(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
return double_div_double(FIX2LONG(x), FIX2LONG(y));
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
return rb_big_fdiv_double(rb_int2big(FIX2LONG(x)), y);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return double_div_double(FIX2LONG(x), RFLOAT_VALUE(y));
|
|
}
|
|
else {
|
|
return NUM2DBL(rb_num_coerce_bin(x, y, idFdiv));
|
|
}
|
|
}
|
|
|
|
double
|
|
rb_int_fdiv_double(VALUE x, VALUE y)
|
|
{
|
|
if (RB_INTEGER_TYPE_P(y) && !FIXNUM_ZERO_P(y)) {
|
|
VALUE gcd = rb_gcd(x, y);
|
|
if (!FIXNUM_ZERO_P(gcd)) {
|
|
x = rb_int_idiv(x, gcd);
|
|
y = rb_int_idiv(y, gcd);
|
|
}
|
|
}
|
|
if (FIXNUM_P(x)) {
|
|
return fix_fdiv_double(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_fdiv_double(x, y);
|
|
}
|
|
else {
|
|
return nan("");
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* fdiv(numeric) -> float
|
|
*
|
|
* Returns the Float result of dividing +self+ by +numeric+:
|
|
*
|
|
* 4.fdiv(2) # => 2.0
|
|
* 4.fdiv(-2) # => -2.0
|
|
* -4.fdiv(2) # => -2.0
|
|
* 4.fdiv(2.0) # => 2.0
|
|
* 4.fdiv(Rational(3, 4)) # => 5.333333333333333
|
|
*
|
|
* Raises an exception if +numeric+ cannot be converted to a Float.
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_fdiv(VALUE x, VALUE y)
|
|
{
|
|
if (RB_INTEGER_TYPE_P(x)) {
|
|
return DBL2NUM(rb_int_fdiv_double(x, y));
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
fix_divide(VALUE x, VALUE y, ID op)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
if (FIXNUM_ZERO_P(y)) rb_num_zerodiv();
|
|
return rb_fix_div_fix(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
x = rb_int2big(FIX2LONG(x));
|
|
return rb_big_div(x, y);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
if (op == '/') {
|
|
double d = FIX2LONG(x);
|
|
return rb_flo_div_flo(DBL2NUM(d), y);
|
|
}
|
|
else {
|
|
VALUE v;
|
|
if (RFLOAT_VALUE(y) == 0) rb_num_zerodiv();
|
|
v = fix_divide(x, y, '/');
|
|
return flo_floor(0, 0, v);
|
|
}
|
|
}
|
|
else {
|
|
if (RB_TYPE_P(y, T_RATIONAL) &&
|
|
op == '/' && FIX2LONG(x) == 1)
|
|
return rb_rational_reciprocal(y);
|
|
return rb_num_coerce_bin(x, y, op);
|
|
}
|
|
}
|
|
|
|
static VALUE
|
|
fix_div(VALUE x, VALUE y)
|
|
{
|
|
return fix_divide(x, y, '/');
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self / numeric -> numeric_result
|
|
*
|
|
* Performs division; for integer +numeric+, truncates the result to an integer:
|
|
*
|
|
* 4 / 3 # => 1
|
|
* 4 / -3 # => -2
|
|
* -4 / 3 # => -2
|
|
* -4 / -3 # => 1
|
|
*
|
|
* For other +numeric+, returns non-integer result:
|
|
*
|
|
* 4 / 3.0 # => 1.3333333333333333
|
|
* 4 / Rational(3, 1) # => (4/3)
|
|
* 4 / Complex(3, 0) # => ((4/3)+0i)
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_div(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_div(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_div(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
fix_idiv(VALUE x, VALUE y)
|
|
{
|
|
return fix_divide(x, y, id_div);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* div(numeric) -> integer
|
|
*
|
|
* Performs integer division; returns the integer result of dividing +self+
|
|
* by +numeric+:
|
|
*
|
|
* 4.div(3) # => 1
|
|
* 4.div(-3) # => -2
|
|
* -4.div(3) # => -2
|
|
* -4.div(-3) # => 1
|
|
* 4.div(3.0) # => 1
|
|
* 4.div(Rational(3, 1)) # => 1
|
|
*
|
|
* Raises an exception if +numeric+ does not have method +div+.
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_idiv(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_idiv(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_idiv(x, y);
|
|
}
|
|
return num_div(x, y);
|
|
}
|
|
|
|
static VALUE
|
|
fix_mod(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
if (FIXNUM_ZERO_P(y)) rb_num_zerodiv();
|
|
return rb_fix_mod_fix(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
x = rb_int2big(FIX2LONG(x));
|
|
return rb_big_modulo(x, y);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return DBL2NUM(ruby_float_mod((double)FIX2LONG(x), RFLOAT_VALUE(y)));
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, '%');
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self % other -> real_number
|
|
*
|
|
* Returns +self+ modulo +other+ as a real number.
|
|
*
|
|
* For integer +n+ and real number +r+, these expressions are equivalent:
|
|
*
|
|
* n % r
|
|
* n-r*(n/r).floor
|
|
* n.divmod(r)[1]
|
|
*
|
|
* See Numeric#divmod.
|
|
*
|
|
* Examples:
|
|
*
|
|
* 10 % 2 # => 0
|
|
* 10 % 3 # => 1
|
|
* 10 % 4 # => 2
|
|
*
|
|
* 10 % -2 # => 0
|
|
* 10 % -3 # => -2
|
|
* 10 % -4 # => -2
|
|
*
|
|
* 10 % 3.0 # => 1.0
|
|
* 10 % Rational(3, 1) # => (1/1)
|
|
*
|
|
* Integer#modulo is an alias for Integer#%.
|
|
*
|
|
*/
|
|
VALUE
|
|
rb_int_modulo(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_mod(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_modulo(x, y);
|
|
}
|
|
return num_modulo(x, y);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* remainder(other) -> real_number
|
|
*
|
|
* Returns the remainder after dividing +self+ by +other+.
|
|
*
|
|
* Examples:
|
|
*
|
|
* 11.remainder(4) # => 3
|
|
* 11.remainder(-4) # => 3
|
|
* -11.remainder(4) # => -3
|
|
* -11.remainder(-4) # => -3
|
|
*
|
|
* 12.remainder(4) # => 0
|
|
* 12.remainder(-4) # => 0
|
|
* -12.remainder(4) # => 0
|
|
* -12.remainder(-4) # => 0
|
|
*
|
|
* 13.remainder(4.0) # => 1.0
|
|
* 13.remainder(Rational(4, 1)) # => (1/1)
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_remainder(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return num_remainder(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_remainder(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
fix_divmod(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
VALUE div, mod;
|
|
if (FIXNUM_ZERO_P(y)) rb_num_zerodiv();
|
|
rb_fix_divmod_fix(x, y, &div, &mod);
|
|
return rb_assoc_new(div, mod);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
x = rb_int2big(FIX2LONG(x));
|
|
return rb_big_divmod(x, y);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
{
|
|
double div, mod;
|
|
volatile VALUE a, b;
|
|
|
|
flodivmod((double)FIX2LONG(x), RFLOAT_VALUE(y), &div, &mod);
|
|
a = dbl2ival(div);
|
|
b = DBL2NUM(mod);
|
|
return rb_assoc_new(a, b);
|
|
}
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, id_divmod);
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* divmod(other) -> array
|
|
*
|
|
* Returns a 2-element array <tt>[q, r]</tt>, where
|
|
*
|
|
* q = (self/other).floor # Quotient
|
|
* r = self % other # Remainder
|
|
*
|
|
* Examples:
|
|
*
|
|
* 11.divmod(4) # => [2, 3]
|
|
* 11.divmod(-4) # => [-3, -1]
|
|
* -11.divmod(4) # => [-3, 1]
|
|
* -11.divmod(-4) # => [2, -3]
|
|
*
|
|
* 12.divmod(4) # => [3, 0]
|
|
* 12.divmod(-4) # => [-3, 0]
|
|
* -12.divmod(4) # => [-3, 0]
|
|
* -12.divmod(-4) # => [3, 0]
|
|
*
|
|
* 13.divmod(4.0) # => [3, 1.0]
|
|
* 13.divmod(Rational(4, 1)) # => [3, (1/1)]
|
|
*
|
|
*/
|
|
VALUE
|
|
rb_int_divmod(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_divmod(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_divmod(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self ** numeric -> numeric_result
|
|
*
|
|
* Raises +self+ to the power of +numeric+:
|
|
*
|
|
* 2 ** 3 # => 8
|
|
* 2 ** -3 # => (1/8)
|
|
* -2 ** 3 # => -8
|
|
* -2 ** -3 # => (-1/8)
|
|
* 2 ** 3.3 # => 9.849155306759329
|
|
* 2 ** Rational(3, 1) # => (8/1)
|
|
* 2 ** Complex(3, 0) # => (8+0i)
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_pow(long x, unsigned long y)
|
|
{
|
|
int neg = x < 0;
|
|
long z = 1;
|
|
|
|
if (y == 0) return INT2FIX(1);
|
|
if (y == 1) return LONG2NUM(x);
|
|
if (neg) x = -x;
|
|
if (y & 1)
|
|
z = x;
|
|
else
|
|
neg = 0;
|
|
y &= ~1;
|
|
do {
|
|
while (y % 2 == 0) {
|
|
if (!FIT_SQRT_LONG(x)) {
|
|
goto bignum;
|
|
}
|
|
x = x * x;
|
|
y >>= 1;
|
|
}
|
|
{
|
|
if (MUL_OVERFLOW_FIXNUM_P(x, z)) {
|
|
goto bignum;
|
|
}
|
|
z = x * z;
|
|
}
|
|
} while (--y);
|
|
if (neg) z = -z;
|
|
return LONG2NUM(z);
|
|
|
|
VALUE v;
|
|
bignum:
|
|
v = rb_big_pow(rb_int2big(x), LONG2NUM(y));
|
|
if (RB_FLOAT_TYPE_P(v)) /* infinity due to overflow */
|
|
return v;
|
|
if (z != 1) v = rb_big_mul(rb_int2big(neg ? -z : z), v);
|
|
return v;
|
|
}
|
|
|
|
VALUE
|
|
rb_int_positive_pow(long x, unsigned long y)
|
|
{
|
|
return int_pow(x, y);
|
|
}
|
|
|
|
static VALUE
|
|
fix_pow_inverted(VALUE x, VALUE minusb)
|
|
{
|
|
if (x == INT2FIX(0)) {
|
|
rb_num_zerodiv();
|
|
UNREACHABLE_RETURN(Qundef);
|
|
}
|
|
else {
|
|
VALUE y = rb_int_pow(x, minusb);
|
|
|
|
if (RB_FLOAT_TYPE_P(y)) {
|
|
double d = pow((double)FIX2LONG(x), RFLOAT_VALUE(y));
|
|
return DBL2NUM(1.0 / d);
|
|
}
|
|
else {
|
|
return rb_rational_raw(INT2FIX(1), y);
|
|
}
|
|
}
|
|
}
|
|
|
|
static VALUE
|
|
fix_pow(VALUE x, VALUE y)
|
|
{
|
|
long a = FIX2LONG(x);
|
|
|
|
if (FIXNUM_P(y)) {
|
|
long b = FIX2LONG(y);
|
|
|
|
if (a == 1) return INT2FIX(1);
|
|
if (a == -1) return INT2FIX(b % 2 ? -1 : 1);
|
|
if (b < 0) return fix_pow_inverted(x, fix_uminus(y));
|
|
if (b == 0) return INT2FIX(1);
|
|
if (b == 1) return x;
|
|
if (a == 0) return INT2FIX(0);
|
|
return int_pow(a, b);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
if (a == 1) return INT2FIX(1);
|
|
if (a == -1) return INT2FIX(int_even_p(y) ? 1 : -1);
|
|
if (BIGNUM_NEGATIVE_P(y)) return fix_pow_inverted(x, rb_big_uminus(y));
|
|
if (a == 0) return INT2FIX(0);
|
|
x = rb_int2big(FIX2LONG(x));
|
|
return rb_big_pow(x, y);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
double dy = RFLOAT_VALUE(y);
|
|
if (dy == 0.0) return DBL2NUM(1.0);
|
|
if (a == 0) {
|
|
return DBL2NUM(dy < 0 ? HUGE_VAL : 0.0);
|
|
}
|
|
if (a == 1) return DBL2NUM(1.0);
|
|
if (a < 0 && dy != round(dy))
|
|
return rb_dbl_complex_new_polar_pi(pow(-(double)a, dy), dy);
|
|
return DBL2NUM(pow((double)a, dy));
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, idPow);
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self ** numeric -> numeric_result
|
|
*
|
|
* Raises +self+ to the power of +numeric+:
|
|
*
|
|
* 2 ** 3 # => 8
|
|
* 2 ** -3 # => (1/8)
|
|
* -2 ** 3 # => -8
|
|
* -2 ** -3 # => (-1/8)
|
|
* 2 ** 3.3 # => 9.849155306759329
|
|
* 2 ** Rational(3, 1) # => (8/1)
|
|
* 2 ** Complex(3, 0) # => (8+0i)
|
|
*
|
|
*/
|
|
VALUE
|
|
rb_int_pow(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_pow(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_pow(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
VALUE
|
|
rb_num_pow(VALUE x, VALUE y)
|
|
{
|
|
VALUE z = rb_int_pow(x, y);
|
|
if (!NIL_P(z)) return z;
|
|
if (RB_FLOAT_TYPE_P(x)) return rb_float_pow(x, y);
|
|
if (SPECIAL_CONST_P(x)) return Qnil;
|
|
switch (BUILTIN_TYPE(x)) {
|
|
case T_COMPLEX:
|
|
return rb_complex_pow(x, y);
|
|
case T_RATIONAL:
|
|
return rb_rational_pow(x, y);
|
|
default:
|
|
break;
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
fix_equal(VALUE x, VALUE y)
|
|
{
|
|
if (x == y) return Qtrue;
|
|
if (FIXNUM_P(y)) return Qfalse;
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
return rb_big_eq(y, x);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return rb_integer_float_eq(x, y);
|
|
}
|
|
else {
|
|
return num_equal(x, y);
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self == other -> true or false
|
|
*
|
|
* Returns +true+ if +self+ is numerically equal to +other+; +false+ otherwise.
|
|
*
|
|
* 1 == 2 #=> false
|
|
* 1 == 1.0 #=> true
|
|
*
|
|
* Related: Integer#eql? (requires +other+ to be an \Integer).
|
|
*
|
|
* Integer#=== is an alias for Integer#==.
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_equal(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_equal(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_eq(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
fix_cmp(VALUE x, VALUE y)
|
|
{
|
|
if (x == y) return INT2FIX(0);
|
|
if (FIXNUM_P(y)) {
|
|
if (FIX2LONG(x) > FIX2LONG(y)) return INT2FIX(1);
|
|
return INT2FIX(-1);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
VALUE cmp = rb_big_cmp(y, x);
|
|
switch (cmp) {
|
|
case INT2FIX(+1): return INT2FIX(-1);
|
|
case INT2FIX(-1): return INT2FIX(+1);
|
|
}
|
|
return cmp;
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return rb_integer_float_cmp(x, y);
|
|
}
|
|
else {
|
|
return rb_num_coerce_cmp(x, y, id_cmp);
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self <=> other -> -1, 0, +1, or nil
|
|
*
|
|
* Returns:
|
|
*
|
|
* - -1, if +self+ is less than +other+.
|
|
* - 0, if +self+ is equal to +other+.
|
|
* - 1, if +self+ is greater then +other+.
|
|
* - +nil+, if +self+ and +other+ are incomparable.
|
|
*
|
|
* Examples:
|
|
*
|
|
* 1 <=> 2 # => -1
|
|
* 1 <=> 1 # => 0
|
|
* 1 <=> 0 # => 1
|
|
* 1 <=> 'foo' # => nil
|
|
*
|
|
* 1 <=> 1.0 # => 0
|
|
* 1 <=> Rational(1, 1) # => 0
|
|
* 1 <=> Complex(1, 0) # => 0
|
|
*
|
|
* This method is the basis for comparisons in module Comparable.
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_cmp(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_cmp(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_cmp(x, y);
|
|
}
|
|
else {
|
|
rb_raise(rb_eNotImpError, "need to define `<=>' in %s", rb_obj_classname(x));
|
|
}
|
|
}
|
|
|
|
static VALUE
|
|
fix_gt(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
return RBOOL(FIX2LONG(x) > FIX2LONG(y));
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
return RBOOL(rb_big_cmp(y, x) == INT2FIX(-1));
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return RBOOL(rb_integer_float_cmp(x, y) == INT2FIX(1));
|
|
}
|
|
else {
|
|
return rb_num_coerce_relop(x, y, '>');
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self > other -> true or false
|
|
*
|
|
* Returns +true+ if the value of +self+ is greater than that of +other+:
|
|
*
|
|
* 1 > 0 # => true
|
|
* 1 > 1 # => false
|
|
* 1 > 2 # => false
|
|
* 1 > 0.5 # => true
|
|
* 1 > Rational(1, 2) # => true
|
|
*
|
|
* Raises an exception if the comparison cannot be made.
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_gt(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_gt(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_gt(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
fix_ge(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
return RBOOL(FIX2LONG(x) >= FIX2LONG(y));
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
return RBOOL(rb_big_cmp(y, x) != INT2FIX(+1));
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
VALUE rel = rb_integer_float_cmp(x, y);
|
|
return RBOOL(rel == INT2FIX(1) || rel == INT2FIX(0));
|
|
}
|
|
else {
|
|
return rb_num_coerce_relop(x, y, idGE);
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self >= real -> true or false
|
|
*
|
|
* Returns +true+ if the value of +self+ is greater than or equal to
|
|
* that of +other+:
|
|
*
|
|
* 1 >= 0 # => true
|
|
* 1 >= 1 # => true
|
|
* 1 >= 2 # => false
|
|
* 1 >= 0.5 # => true
|
|
* 1 >= Rational(1, 2) # => true
|
|
*
|
|
* Raises an exception if the comparison cannot be made.
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_ge(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_ge(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_ge(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
fix_lt(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
return RBOOL(FIX2LONG(x) < FIX2LONG(y));
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
return RBOOL(rb_big_cmp(y, x) == INT2FIX(+1));
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return RBOOL(rb_integer_float_cmp(x, y) == INT2FIX(-1));
|
|
}
|
|
else {
|
|
return rb_num_coerce_relop(x, y, '<');
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self < other -> true or false
|
|
*
|
|
* Returns +true+ if the value of +self+ is less than that of +other+:
|
|
*
|
|
* 1 < 0 # => false
|
|
* 1 < 1 # => false
|
|
* 1 < 2 # => true
|
|
* 1 < 0.5 # => false
|
|
* 1 < Rational(1, 2) # => false
|
|
*
|
|
* Raises an exception if the comparison cannot be made.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_lt(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_lt(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_lt(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
fix_le(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
return RBOOL(FIX2LONG(x) <= FIX2LONG(y));
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
return RBOOL(rb_big_cmp(y, x) != INT2FIX(-1));
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
VALUE rel = rb_integer_float_cmp(x, y);
|
|
return RBOOL(rel == INT2FIX(-1) || rel == INT2FIX(0));
|
|
}
|
|
else {
|
|
return rb_num_coerce_relop(x, y, idLE);
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self <= real -> true or false
|
|
*
|
|
* Returns +true+ if the value of +self+ is less than or equal to
|
|
* that of +other+:
|
|
*
|
|
* 1 <= 0 # => false
|
|
* 1 <= 1 # => true
|
|
* 1 <= 2 # => true
|
|
* 1 <= 0.5 # => false
|
|
* 1 <= Rational(1, 2) # => false
|
|
*
|
|
* Raises an exception if the comparison cannot be made.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_le(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_le(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_le(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
fix_comp(VALUE num)
|
|
{
|
|
return ~num | FIXNUM_FLAG;
|
|
}
|
|
|
|
VALUE
|
|
rb_int_comp(VALUE num)
|
|
{
|
|
if (FIXNUM_P(num)) {
|
|
return fix_comp(num);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(num)) {
|
|
return rb_big_comp(num);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
num_funcall_bit_1(VALUE y, VALUE arg, int recursive)
|
|
{
|
|
ID func = (ID)((VALUE *)arg)[0];
|
|
VALUE x = ((VALUE *)arg)[1];
|
|
if (recursive) {
|
|
num_funcall_op_1_recursion(x, func, y);
|
|
}
|
|
return rb_check_funcall(x, func, 1, &y);
|
|
}
|
|
|
|
VALUE
|
|
rb_num_coerce_bit(VALUE x, VALUE y, ID func)
|
|
{
|
|
VALUE ret, args[3];
|
|
|
|
args[0] = (VALUE)func;
|
|
args[1] = x;
|
|
args[2] = y;
|
|
do_coerce(&args[1], &args[2], TRUE);
|
|
ret = rb_exec_recursive_paired(num_funcall_bit_1,
|
|
args[2], args[1], (VALUE)args);
|
|
if (ret == Qundef) {
|
|
/* show the original object, not coerced object */
|
|
coerce_failed(x, y);
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
static VALUE
|
|
fix_and(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
long val = FIX2LONG(x) & FIX2LONG(y);
|
|
return LONG2NUM(val);
|
|
}
|
|
|
|
if (RB_BIGNUM_TYPE_P(y)) {
|
|
return rb_big_and(y, x);
|
|
}
|
|
|
|
return rb_num_coerce_bit(x, y, '&');
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self & other -> integer
|
|
*
|
|
* Bitwise AND; each bit in the result is 1 if both corresponding bits
|
|
* in +self+ and +other+ are 1, 0 otherwise:
|
|
*
|
|
* "%04b" % (0b0101 & 0b0110) # => "0100"
|
|
*
|
|
* Raises an exception if +other+ is not an \Integer.
|
|
*
|
|
* Related: Integer#| (bitwise OR), Integer#^ (bitwise EXCLUSIVE OR).
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_and(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_and(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_and(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
fix_or(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
long val = FIX2LONG(x) | FIX2LONG(y);
|
|
return LONG2NUM(val);
|
|
}
|
|
|
|
if (RB_BIGNUM_TYPE_P(y)) {
|
|
return rb_big_or(y, x);
|
|
}
|
|
|
|
return rb_num_coerce_bit(x, y, '|');
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self | other -> integer
|
|
*
|
|
* Bitwise OR; each bit in the result is 1 if either corresponding bit
|
|
* in +self+ or +other+ is 1, 0 otherwise:
|
|
*
|
|
* "%04b" % (0b0101 | 0b0110) # => "0111"
|
|
*
|
|
* Raises an exception if +other+ is not an \Integer.
|
|
*
|
|
* Related: Integer#& (bitwise AND), Integer#^ (bitwise EXCLUSIVE OR).
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_or(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_or(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_or(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
fix_xor(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
long val = FIX2LONG(x) ^ FIX2LONG(y);
|
|
return LONG2NUM(val);
|
|
}
|
|
|
|
if (RB_BIGNUM_TYPE_P(y)) {
|
|
return rb_big_xor(y, x);
|
|
}
|
|
|
|
return rb_num_coerce_bit(x, y, '^');
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self ^ other -> integer
|
|
*
|
|
* Bitwise EXCLUSIVE OR; each bit in the result is 1 if the corresponding bits
|
|
* in +self+ and +other+ are different, 0 otherwise:
|
|
*
|
|
* "%04b" % (0b0101 ^ 0b0110) # => "0011"
|
|
*
|
|
* Raises an exception if +other+ is not an \Integer.
|
|
*
|
|
* Related: Integer#& (bitwise AND), Integer#| (bitwise OR).
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_xor(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_xor(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_xor(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
rb_fix_lshift(VALUE x, VALUE y)
|
|
{
|
|
long val, width;
|
|
|
|
val = NUM2LONG(x);
|
|
if (!val) return (rb_to_int(y), INT2FIX(0));
|
|
if (!FIXNUM_P(y))
|
|
return rb_big_lshift(rb_int2big(val), y);
|
|
width = FIX2LONG(y);
|
|
if (width < 0)
|
|
return fix_rshift(val, (unsigned long)-width);
|
|
return fix_lshift(val, width);
|
|
}
|
|
|
|
static VALUE
|
|
fix_lshift(long val, unsigned long width)
|
|
{
|
|
if (width > (SIZEOF_LONG*CHAR_BIT-1)
|
|
|| ((unsigned long)val)>>(SIZEOF_LONG*CHAR_BIT-1-width) > 0) {
|
|
return rb_big_lshift(rb_int2big(val), ULONG2NUM(width));
|
|
}
|
|
val = val << width;
|
|
return LONG2NUM(val);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self << count -> integer
|
|
*
|
|
* Returns +self+ with bits shifted +count+ positions to the left,
|
|
* or to the right if +count+ is negative:
|
|
*
|
|
* n = 0b11110000
|
|
* "%08b" % (n << 1) # => "111100000"
|
|
* "%08b" % (n << 3) # => "11110000000"
|
|
* "%08b" % (n << -1) # => "01111000"
|
|
* "%08b" % (n << -3) # => "00011110"
|
|
*
|
|
* Related: Integer#>>.
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_lshift(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return rb_fix_lshift(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_lshift(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
rb_fix_rshift(VALUE x, VALUE y)
|
|
{
|
|
long i, val;
|
|
|
|
val = FIX2LONG(x);
|
|
if (!val) return (rb_to_int(y), INT2FIX(0));
|
|
if (!FIXNUM_P(y))
|
|
return rb_big_rshift(rb_int2big(val), y);
|
|
i = FIX2LONG(y);
|
|
if (i == 0) return x;
|
|
if (i < 0)
|
|
return fix_lshift(val, (unsigned long)-i);
|
|
return fix_rshift(val, i);
|
|
}
|
|
|
|
static VALUE
|
|
fix_rshift(long val, unsigned long i)
|
|
{
|
|
if (i >= sizeof(long)*CHAR_BIT-1) {
|
|
if (val < 0) return INT2FIX(-1);
|
|
return INT2FIX(0);
|
|
}
|
|
val = RSHIFT(val, i);
|
|
return LONG2FIX(val);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self >> count -> integer
|
|
*
|
|
* Returns +self+ with bits shifted +count+ positions to the right,
|
|
* or to the left if +count+ is negative:
|
|
*
|
|
* n = 0b11110000
|
|
* "%08b" % (n >> 1) # => "01111000"
|
|
* "%08b" % (n >> 3) # => "00011110"
|
|
* "%08b" % (n >> -1) # => "111100000"
|
|
* "%08b" % (n >> -3) # => "11110000000"
|
|
*
|
|
* Related: Integer#<<.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
rb_int_rshift(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return rb_fix_rshift(x, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(x)) {
|
|
return rb_big_rshift(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
MJIT_FUNC_EXPORTED VALUE
|
|
rb_fix_aref(VALUE fix, VALUE idx)
|
|
{
|
|
long val = FIX2LONG(fix);
|
|
long i;
|
|
|
|
idx = rb_to_int(idx);
|
|
if (!FIXNUM_P(idx)) {
|
|
idx = rb_big_norm(idx);
|
|
if (!FIXNUM_P(idx)) {
|
|
if (!BIGNUM_SIGN(idx) || val >= 0)
|
|
return INT2FIX(0);
|
|
return INT2FIX(1);
|
|
}
|
|
}
|
|
i = FIX2LONG(idx);
|
|
|
|
if (i < 0) return INT2FIX(0);
|
|
if (SIZEOF_LONG*CHAR_BIT-1 <= i) {
|
|
if (val < 0) return INT2FIX(1);
|
|
return INT2FIX(0);
|
|
}
|
|
if (val & (1L<<i))
|
|
return INT2FIX(1);
|
|
return INT2FIX(0);
|
|
}
|
|
|
|
|
|
/* copied from "r_less" in range.c */
|
|
/* compares _a_ and _b_ and returns:
|
|
* < 0: a < b
|
|
* = 0: a = b
|
|
* > 0: a > b or non-comparable
|
|
*/
|
|
static int
|
|
compare_indexes(VALUE a, VALUE b)
|
|
{
|
|
VALUE r = rb_funcall(a, id_cmp, 1, b);
|
|
|
|
if (NIL_P(r))
|
|
return INT_MAX;
|
|
return rb_cmpint(r, a, b);
|
|
}
|
|
|
|
static VALUE
|
|
generate_mask(VALUE len)
|
|
{
|
|
return rb_int_minus(rb_int_lshift(INT2FIX(1), len), INT2FIX(1));
|
|
}
|
|
|
|
static VALUE
|
|
int_aref1(VALUE num, VALUE arg)
|
|
{
|
|
VALUE orig_num = num, beg, end;
|
|
int excl;
|
|
|
|
if (rb_range_values(arg, &beg, &end, &excl)) {
|
|
if (NIL_P(beg)) {
|
|
/* beginless range */
|
|
if (!RTEST(num_negative_p(end))) {
|
|
if (!excl) end = rb_int_plus(end, INT2FIX(1));
|
|
VALUE mask = generate_mask(end);
|
|
if (int_zero_p(rb_int_and(num, mask))) {
|
|
return INT2FIX(0);
|
|
}
|
|
else {
|
|
rb_raise(rb_eArgError, "The beginless range for Integer#[] results in infinity");
|
|
}
|
|
}
|
|
else {
|
|
return INT2FIX(0);
|
|
}
|
|
}
|
|
num = rb_int_rshift(num, beg);
|
|
|
|
int cmp = compare_indexes(beg, end);
|
|
if (!NIL_P(end) && cmp < 0) {
|
|
VALUE len = rb_int_minus(end, beg);
|
|
if (!excl) len = rb_int_plus(len, INT2FIX(1));
|
|
VALUE mask = generate_mask(len);
|
|
num = rb_int_and(num, mask);
|
|
}
|
|
else if (cmp == 0) {
|
|
if (excl) return INT2FIX(0);
|
|
num = orig_num;
|
|
arg = beg;
|
|
goto one_bit;
|
|
}
|
|
return num;
|
|
}
|
|
|
|
one_bit:
|
|
if (FIXNUM_P(num)) {
|
|
return rb_fix_aref(num, arg);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(num)) {
|
|
return rb_big_aref(num, arg);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
int_aref2(VALUE num, VALUE beg, VALUE len)
|
|
{
|
|
num = rb_int_rshift(num, beg);
|
|
VALUE mask = generate_mask(len);
|
|
num = rb_int_and(num, mask);
|
|
return num;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* self[offset] -> 0 or 1
|
|
* self[offset, size] -> integer
|
|
* self[range] -> integer
|
|
*
|
|
* Returns a slice of bits from +self+.
|
|
*
|
|
* With argument +offset+, returns the bit at the given offset,
|
|
* where offset 0 refers to the least significant bit:
|
|
*
|
|
* n = 0b10 # => 2
|
|
* n[0] # => 0
|
|
* n[1] # => 1
|
|
* n[2] # => 0
|
|
* n[3] # => 0
|
|
*
|
|
* In principle, <code>n[i]</code> is equivalent to <code>(n >> i) & 1</code>.
|
|
* Thus, negative index always returns zero:
|
|
*
|
|
* 255[-1] # => 0
|
|
*
|
|
* With arguments +offset+ and +size+, returns +size+ bits from +self+,
|
|
* beginning at +offset+ and including bits of greater significance:
|
|
*
|
|
* n = 0b111000 # => 56
|
|
* "%010b" % n[0, 10] # => "0000111000"
|
|
* "%010b" % n[4, 10] # => "0000000011"
|
|
*
|
|
* With argument +range+, returns <tt>range.size</tt> bits from +self+,
|
|
* beginning at <tt>range.begin</tt> and including bits of greater significance:
|
|
*
|
|
* n = 0b111000 # => 56
|
|
* "%010b" % n[0..9] # => "0000111000"
|
|
* "%010b" % n[4..9] # => "0000000011"
|
|
*
|
|
* Raises an exception if the slice cannot be constructed.
|
|
*/
|
|
|
|
static VALUE
|
|
int_aref(int const argc, VALUE * const argv, VALUE const num)
|
|
{
|
|
rb_check_arity(argc, 1, 2);
|
|
if (argc == 2) {
|
|
return int_aref2(num, argv[0], argv[1]);
|
|
}
|
|
return int_aref1(num, argv[0]);
|
|
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* to_f -> float
|
|
*
|
|
* Converts +self+ to a Float:
|
|
*
|
|
* 1.to_f # => 1.0
|
|
* -1.to_f # => -1.0
|
|
*
|
|
* If the value of +self+ does not fit in a \Float,
|
|
* the result is infinity:
|
|
*
|
|
* (10**400).to_f # => Infinity
|
|
* (-10**400).to_f # => -Infinity
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_to_f(VALUE num)
|
|
{
|
|
double val;
|
|
|
|
if (FIXNUM_P(num)) {
|
|
val = (double)FIX2LONG(num);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(num)) {
|
|
val = rb_big2dbl(num);
|
|
}
|
|
else {
|
|
rb_raise(rb_eNotImpError, "Unknown subclass for to_f: %s", rb_obj_classname(num));
|
|
}
|
|
|
|
return DBL2NUM(val);
|
|
}
|
|
|
|
static VALUE
|
|
fix_abs(VALUE fix)
|
|
{
|
|
long i = FIX2LONG(fix);
|
|
|
|
if (i < 0) i = -i;
|
|
|
|
return LONG2NUM(i);
|
|
}
|
|
|
|
VALUE
|
|
rb_int_abs(VALUE num)
|
|
{
|
|
if (FIXNUM_P(num)) {
|
|
return fix_abs(num);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(num)) {
|
|
return rb_big_abs(num);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
fix_size(VALUE fix)
|
|
{
|
|
return INT2FIX(sizeof(long));
|
|
}
|
|
|
|
MJIT_FUNC_EXPORTED VALUE
|
|
rb_int_size(VALUE num)
|
|
{
|
|
if (FIXNUM_P(num)) {
|
|
return fix_size(num);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(num)) {
|
|
return rb_big_size_m(num);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
rb_fix_bit_length(VALUE fix)
|
|
{
|
|
long v = FIX2LONG(fix);
|
|
if (v < 0)
|
|
v = ~v;
|
|
return LONG2FIX(bit_length(v));
|
|
}
|
|
|
|
VALUE
|
|
rb_int_bit_length(VALUE num)
|
|
{
|
|
if (FIXNUM_P(num)) {
|
|
return rb_fix_bit_length(num);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(num)) {
|
|
return rb_big_bit_length(num);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
rb_fix_digits(VALUE fix, long base)
|
|
{
|
|
VALUE digits;
|
|
long x = FIX2LONG(fix);
|
|
|
|
assert(x >= 0);
|
|
|
|
if (base < 2)
|
|
rb_raise(rb_eArgError, "invalid radix %ld", base);
|
|
|
|
if (x == 0)
|
|
return rb_ary_new_from_args(1, INT2FIX(0));
|
|
|
|
digits = rb_ary_new();
|
|
while (x > 0) {
|
|
long q = x % base;
|
|
rb_ary_push(digits, LONG2NUM(q));
|
|
x /= base;
|
|
}
|
|
|
|
return digits;
|
|
}
|
|
|
|
static VALUE
|
|
rb_int_digits_bigbase(VALUE num, VALUE base)
|
|
{
|
|
VALUE digits, bases;
|
|
|
|
assert(!rb_num_negative_p(num));
|
|
|
|
if (RB_BIGNUM_TYPE_P(base))
|
|
base = rb_big_norm(base);
|
|
|
|
if (FIXNUM_P(base) && FIX2LONG(base) < 2)
|
|
rb_raise(rb_eArgError, "invalid radix %ld", FIX2LONG(base));
|
|
else if (RB_BIGNUM_TYPE_P(base) && BIGNUM_NEGATIVE_P(base))
|
|
rb_raise(rb_eArgError, "negative radix");
|
|
|
|
if (FIXNUM_P(base) && FIXNUM_P(num))
|
|
return rb_fix_digits(num, FIX2LONG(base));
|
|
|
|
if (FIXNUM_P(num))
|
|
return rb_ary_new_from_args(1, num);
|
|
|
|
if (int_lt(rb_int_div(rb_int_bit_length(num), rb_int_bit_length(base)), INT2FIX(50))) {
|
|
digits = rb_ary_new();
|
|
while (!FIXNUM_P(num) || FIX2LONG(num) > 0) {
|
|
VALUE qr = rb_int_divmod(num, base);
|
|
rb_ary_push(digits, RARRAY_AREF(qr, 1));
|
|
num = RARRAY_AREF(qr, 0);
|
|
}
|
|
return digits;
|
|
}
|
|
|
|
bases = rb_ary_new();
|
|
for (VALUE b = base; int_lt(b, num) == Qtrue; b = rb_int_mul(b, b)) {
|
|
rb_ary_push(bases, b);
|
|
}
|
|
digits = rb_ary_new_from_args(1, num);
|
|
while (RARRAY_LEN(bases)) {
|
|
VALUE b = rb_ary_pop(bases);
|
|
long i, last_idx = RARRAY_LEN(digits) - 1;
|
|
for(i = last_idx; i >= 0; i--) {
|
|
VALUE n = RARRAY_AREF(digits, i);
|
|
VALUE divmod = rb_int_divmod(n, b);
|
|
VALUE div = RARRAY_AREF(divmod, 0);
|
|
VALUE mod = RARRAY_AREF(divmod, 1);
|
|
if (i != last_idx || div != INT2FIX(0)) rb_ary_store(digits, 2 * i + 1, div);
|
|
rb_ary_store(digits, 2 * i, mod);
|
|
}
|
|
}
|
|
|
|
return digits;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* digits(base = 10) -> array_of_integers
|
|
*
|
|
* Returns an array of integers representing the +base+-radix
|
|
* digits of +self+;
|
|
* the first element of the array represents the least significant digit:
|
|
*
|
|
* 12345.digits # => [5, 4, 3, 2, 1]
|
|
* 12345.digits(7) # => [4, 6, 6, 0, 5]
|
|
* 12345.digits(100) # => [45, 23, 1]
|
|
*
|
|
* Raises an exception if +self+ is negative or +base+ is less than 2.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
rb_int_digits(int argc, VALUE *argv, VALUE num)
|
|
{
|
|
VALUE base_value;
|
|
long base;
|
|
|
|
if (rb_num_negative_p(num))
|
|
rb_raise(rb_eMathDomainError, "out of domain");
|
|
|
|
if (rb_check_arity(argc, 0, 1)) {
|
|
base_value = rb_to_int(argv[0]);
|
|
if (!RB_INTEGER_TYPE_P(base_value))
|
|
rb_raise(rb_eTypeError, "wrong argument type %s (expected Integer)",
|
|
rb_obj_classname(argv[0]));
|
|
if (RB_BIGNUM_TYPE_P(base_value))
|
|
return rb_int_digits_bigbase(num, base_value);
|
|
|
|
base = FIX2LONG(base_value);
|
|
if (base < 0)
|
|
rb_raise(rb_eArgError, "negative radix");
|
|
else if (base < 2)
|
|
rb_raise(rb_eArgError, "invalid radix %ld", base);
|
|
}
|
|
else
|
|
base = 10;
|
|
|
|
if (FIXNUM_P(num))
|
|
return rb_fix_digits(num, base);
|
|
else if (RB_BIGNUM_TYPE_P(num))
|
|
return rb_int_digits_bigbase(num, LONG2FIX(base));
|
|
|
|
return Qnil;
|
|
}
|
|
|
|
static VALUE
|
|
int_upto_size(VALUE from, VALUE args, VALUE eobj)
|
|
{
|
|
return ruby_num_interval_step_size(from, RARRAY_AREF(args, 0), INT2FIX(1), FALSE);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* upto(limit) {|i| ... } -> self
|
|
* upto(limit) -> enumerator
|
|
*
|
|
* Calls the given block with each integer value from +self+ up to +limit+;
|
|
* returns +self+:
|
|
*
|
|
* a = []
|
|
* 5.upto(10) {|i| a << i } # => 5
|
|
* a # => [5, 6, 7, 8, 9, 10]
|
|
* a = []
|
|
* -5.upto(0) {|i| a << i } # => -5
|
|
* a # => [-5, -4, -3, -2, -1, 0]
|
|
* 5.upto(4) {|i| fail 'Cannot happen' } # => 5
|
|
*
|
|
* With no block given, returns an Enumerator.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_upto(VALUE from, VALUE to)
|
|
{
|
|
RETURN_SIZED_ENUMERATOR(from, 1, &to, int_upto_size);
|
|
if (FIXNUM_P(from) && FIXNUM_P(to)) {
|
|
long i, end;
|
|
|
|
end = FIX2LONG(to);
|
|
for (i = FIX2LONG(from); i <= end; i++) {
|
|
rb_yield(LONG2FIX(i));
|
|
}
|
|
}
|
|
else {
|
|
VALUE i = from, c;
|
|
|
|
while (!(c = rb_funcall(i, '>', 1, to))) {
|
|
rb_yield(i);
|
|
i = rb_funcall(i, '+', 1, INT2FIX(1));
|
|
}
|
|
ensure_cmp(c, i, to);
|
|
}
|
|
return from;
|
|
}
|
|
|
|
static VALUE
|
|
int_downto_size(VALUE from, VALUE args, VALUE eobj)
|
|
{
|
|
return ruby_num_interval_step_size(from, RARRAY_AREF(args, 0), INT2FIX(-1), FALSE);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* downto(limit) {|i| ... } -> self
|
|
* downto(limit) -> enumerator
|
|
*
|
|
* Calls the given block with each integer value from +self+ down to +limit+;
|
|
* returns +self+:
|
|
*
|
|
* a = []
|
|
* 10.downto(5) {|i| a << i } # => 10
|
|
* a # => [10, 9, 8, 7, 6, 5]
|
|
* a = []
|
|
* 0.downto(-5) {|i| a << i } # => 0
|
|
* a # => [0, -1, -2, -3, -4, -5]
|
|
* 4.downto(5) {|i| fail 'Cannot happen' } # => 4
|
|
*
|
|
* With no block given, returns an Enumerator.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_downto(VALUE from, VALUE to)
|
|
{
|
|
RETURN_SIZED_ENUMERATOR(from, 1, &to, int_downto_size);
|
|
if (FIXNUM_P(from) && FIXNUM_P(to)) {
|
|
long i, end;
|
|
|
|
end = FIX2LONG(to);
|
|
for (i=FIX2LONG(from); i >= end; i--) {
|
|
rb_yield(LONG2FIX(i));
|
|
}
|
|
}
|
|
else {
|
|
VALUE i = from, c;
|
|
|
|
while (!(c = rb_funcall(i, '<', 1, to))) {
|
|
rb_yield(i);
|
|
i = rb_funcall(i, '-', 1, INT2FIX(1));
|
|
}
|
|
if (NIL_P(c)) rb_cmperr(i, to);
|
|
}
|
|
return from;
|
|
}
|
|
|
|
static VALUE
|
|
int_dotimes_size(VALUE num, VALUE args, VALUE eobj)
|
|
{
|
|
if (FIXNUM_P(num)) {
|
|
if (NUM2LONG(num) <= 0) return INT2FIX(0);
|
|
}
|
|
else {
|
|
if (RTEST(rb_funcall(num, '<', 1, INT2FIX(0)))) return INT2FIX(0);
|
|
}
|
|
return num;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* times {|i| ... } -> self
|
|
* times -> enumerator
|
|
*
|
|
* Calls the given block +self+ times with each integer in <tt>(0..self-1)</tt>:
|
|
*
|
|
* a = []
|
|
* 5.times {|i| a.push(i) } # => 5
|
|
* a # => [0, 1, 2, 3, 4]
|
|
*
|
|
* With no block given, returns an Enumerator.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_dotimes(VALUE num)
|
|
{
|
|
RETURN_SIZED_ENUMERATOR(num, 0, 0, int_dotimes_size);
|
|
|
|
if (FIXNUM_P(num)) {
|
|
long i, end;
|
|
|
|
end = FIX2LONG(num);
|
|
for (i=0; i<end; i++) {
|
|
rb_yield_1(LONG2FIX(i));
|
|
}
|
|
}
|
|
else {
|
|
VALUE i = INT2FIX(0);
|
|
|
|
for (;;) {
|
|
if (!RTEST(int_le(i, num))) break;
|
|
rb_yield(i);
|
|
i = rb_int_plus(i, INT2FIX(1));
|
|
}
|
|
}
|
|
return num;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* round(ndigits= 0, half: :up) -> integer
|
|
*
|
|
* Returns +self+ rounded to the nearest value with
|
|
* a precision of +ndigits+ decimal digits.
|
|
*
|
|
* When +ndigits+ is negative, the returned value
|
|
* has at least <tt>ndigits.abs</tt> trailing zeros:
|
|
*
|
|
* 555.round(-1) # => 560
|
|
* 555.round(-2) # => 600
|
|
* 555.round(-3) # => 1000
|
|
* -555.round(-2) # => -600
|
|
* 555.round(-4) # => 0
|
|
*
|
|
* Returns +self+ when +ndigits+ is zero or positive.
|
|
*
|
|
* 555.round # => 555
|
|
* 555.round(1) # => 555
|
|
* 555.round(50) # => 555
|
|
*
|
|
* If keyword argument +half+ is given,
|
|
* and +self+ is equidistant from the two candidate values,
|
|
* the rounding is according to the given +half+ value:
|
|
*
|
|
* - +:up+ or +nil+: round away from zero:
|
|
*
|
|
* 25.round(-1, half: :up) # => 30
|
|
* (-25).round(-1, half: :up) # => -30
|
|
*
|
|
* - +:down+: round toward zero:
|
|
*
|
|
* 25.round(-1, half: :down) # => 20
|
|
* (-25).round(-1, half: :down) # => -20
|
|
*
|
|
*
|
|
* - +:even+: round toward the candidate whose last nonzero digit is even:
|
|
*
|
|
* 25.round(-1, half: :even) # => 20
|
|
* 15.round(-1, half: :even) # => 20
|
|
* (-25).round(-1, half: :even) # => -20
|
|
*
|
|
* Raises and exception if the value for +half+ is invalid.
|
|
*
|
|
* Related: Integer#truncate.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_round(int argc, VALUE* argv, VALUE num)
|
|
{
|
|
int ndigits;
|
|
int mode;
|
|
VALUE nd, opt;
|
|
|
|
if (!rb_scan_args(argc, argv, "01:", &nd, &opt)) return num;
|
|
ndigits = NUM2INT(nd);
|
|
mode = rb_num_get_rounding_option(opt);
|
|
if (ndigits >= 0) {
|
|
return num;
|
|
}
|
|
return rb_int_round(num, ndigits, mode);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* floor(ndigits = 0) -> integer
|
|
*
|
|
* Returns the largest number less than or equal to +self+ with
|
|
* a precision of +ndigits+ decimal digits.
|
|
*
|
|
* When +ndigits+ is negative, the returned value
|
|
* has at least <tt>ndigits.abs</tt> trailing zeros:
|
|
*
|
|
* 555.floor(-1) # => 550
|
|
* 555.floor(-2) # => 500
|
|
* -555.floor(-2) # => -600
|
|
* 555.floor(-3) # => 0
|
|
*
|
|
* Returns +self+ when +ndigits+ is zero or positive.
|
|
*
|
|
* 555.floor # => 555
|
|
* 555.floor(50) # => 555
|
|
*
|
|
* Related: Integer#ceil.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_floor(int argc, VALUE* argv, VALUE num)
|
|
{
|
|
int ndigits;
|
|
|
|
if (!rb_check_arity(argc, 0, 1)) return num;
|
|
ndigits = NUM2INT(argv[0]);
|
|
if (ndigits >= 0) {
|
|
return num;
|
|
}
|
|
return rb_int_floor(num, ndigits);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* ceil(ndigits = 0) -> integer
|
|
*
|
|
* Returns the smallest number greater than or equal to +self+ with
|
|
* a precision of +ndigits+ decimal digits.
|
|
*
|
|
* When the precision is negative, the returned value is an integer
|
|
* with at least <code>ndigits.abs</code> trailing zeros:
|
|
*
|
|
* 555.ceil(-1) # => 560
|
|
* 555.ceil(-2) # => 600
|
|
* -555.ceil(-2) # => -500
|
|
* 555.ceil(-3) # => 1000
|
|
*
|
|
* Returns +self+ when +ndigits+ is zero or positive.
|
|
*
|
|
* 555.ceil # => 555
|
|
* 555.ceil(50) # => 555
|
|
*
|
|
* Related: Integer#floor.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_ceil(int argc, VALUE* argv, VALUE num)
|
|
{
|
|
int ndigits;
|
|
|
|
if (!rb_check_arity(argc, 0, 1)) return num;
|
|
ndigits = NUM2INT(argv[0]);
|
|
if (ndigits >= 0) {
|
|
return num;
|
|
}
|
|
return rb_int_ceil(num, ndigits);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* truncate(ndigits = 0) -> integer
|
|
*
|
|
* Returns +self+ truncated (toward zero) to
|
|
* a precision of +ndigits+ decimal digits.
|
|
*
|
|
* When +ndigits+ is negative, the returned value
|
|
* has at least <tt>ndigits.abs</tt> trailing zeros:
|
|
*
|
|
* 555.truncate(-1) # => 550
|
|
* 555.truncate(-2) # => 500
|
|
* -555.truncate(-2) # => -500
|
|
*
|
|
* Returns +self+ when +ndigits+ is zero or positive.
|
|
*
|
|
* 555.truncate # => 555
|
|
* 555.truncate(50) # => 555
|
|
*
|
|
* Related: Integer#round.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
int_truncate(int argc, VALUE* argv, VALUE num)
|
|
{
|
|
int ndigits;
|
|
|
|
if (!rb_check_arity(argc, 0, 1)) return num;
|
|
ndigits = NUM2INT(argv[0]);
|
|
if (ndigits >= 0) {
|
|
return num;
|
|
}
|
|
return rb_int_truncate(num, ndigits);
|
|
}
|
|
|
|
#define DEFINE_INT_SQRT(rettype, prefix, argtype) \
|
|
rettype \
|
|
prefix##_isqrt(argtype n) \
|
|
{ \
|
|
if (!argtype##_IN_DOUBLE_P(n)) { \
|
|
unsigned int b = bit_length(n); \
|
|
argtype t; \
|
|
rettype x = (rettype)(n >> (b/2+1)); \
|
|
x |= ((rettype)1LU << (b-1)/2); \
|
|
while ((t = n/x) < (argtype)x) x = (rettype)((x + t) >> 1); \
|
|
return x; \
|
|
} \
|
|
return (rettype)sqrt(argtype##_TO_DOUBLE(n)); \
|
|
}
|
|
|
|
#if SIZEOF_LONG*CHAR_BIT > DBL_MANT_DIG
|
|
# define RB_ULONG_IN_DOUBLE_P(n) ((n) < (1UL << DBL_MANT_DIG))
|
|
#else
|
|
# define RB_ULONG_IN_DOUBLE_P(n) 1
|
|
#endif
|
|
#define RB_ULONG_TO_DOUBLE(n) (double)(n)
|
|
#define RB_ULONG unsigned long
|
|
DEFINE_INT_SQRT(unsigned long, rb_ulong, RB_ULONG)
|
|
|
|
#if 2*SIZEOF_BDIGIT > SIZEOF_LONG
|
|
# if 2*SIZEOF_BDIGIT*CHAR_BIT > DBL_MANT_DIG
|
|
# define BDIGIT_DBL_IN_DOUBLE_P(n) ((n) < ((BDIGIT_DBL)1UL << DBL_MANT_DIG))
|
|
# else
|
|
# define BDIGIT_DBL_IN_DOUBLE_P(n) 1
|
|
# endif
|
|
# ifdef ULL_TO_DOUBLE
|
|
# define BDIGIT_DBL_TO_DOUBLE(n) ULL_TO_DOUBLE(n)
|
|
# else
|
|
# define BDIGIT_DBL_TO_DOUBLE(n) (double)(n)
|
|
# endif
|
|
DEFINE_INT_SQRT(BDIGIT, rb_bdigit_dbl, BDIGIT_DBL)
|
|
#endif
|
|
|
|
#define domain_error(msg) \
|
|
rb_raise(rb_eMathDomainError, "Numerical argument is out of domain - " #msg)
|
|
|
|
/*
|
|
* call-seq:
|
|
* Integer.sqrt(numeric) -> integer
|
|
*
|
|
* Returns the integer square root of the non-negative integer +n+,
|
|
* which is the largest non-negative integer less than or equal to the
|
|
* square root of +numeric+.
|
|
*
|
|
* Integer.sqrt(0) # => 0
|
|
* Integer.sqrt(1) # => 1
|
|
* Integer.sqrt(24) # => 4
|
|
* Integer.sqrt(25) # => 5
|
|
* Integer.sqrt(10**400) # => 10**200
|
|
*
|
|
* If +numeric+ is not an \Integer, it is converted to an \Integer:
|
|
*
|
|
* Integer.sqrt(Complex(4, 0)) # => 2
|
|
* Integer.sqrt(Rational(4, 1)) # => 2
|
|
* Integer.sqrt(4.0) # => 2
|
|
* Integer.sqrt(3.14159) # => 1
|
|
*
|
|
* This method is equivalent to <tt>Math.sqrt(numeric).floor</tt>,
|
|
* except that the result of the latter code may differ from the true value
|
|
* due to the limited precision of floating point arithmetic.
|
|
*
|
|
* Integer.sqrt(10**46) # => 100000000000000000000000
|
|
* Math.sqrt(10**46).floor # => 99999999999999991611392
|
|
*
|
|
* Raises an exception if +numeric+ is negative.
|
|
*
|
|
*/
|
|
|
|
static VALUE
|
|
rb_int_s_isqrt(VALUE self, VALUE num)
|
|
{
|
|
unsigned long n, sq;
|
|
num = rb_to_int(num);
|
|
if (FIXNUM_P(num)) {
|
|
if (FIXNUM_NEGATIVE_P(num)) {
|
|
domain_error("isqrt");
|
|
}
|
|
n = FIX2ULONG(num);
|
|
sq = rb_ulong_isqrt(n);
|
|
return LONG2FIX(sq);
|
|
}
|
|
else {
|
|
size_t biglen;
|
|
if (RBIGNUM_NEGATIVE_P(num)) {
|
|
domain_error("isqrt");
|
|
}
|
|
biglen = BIGNUM_LEN(num);
|
|
if (biglen == 0) return INT2FIX(0);
|
|
#if SIZEOF_BDIGIT <= SIZEOF_LONG
|
|
/* short-circuit */
|
|
if (biglen == 1) {
|
|
n = BIGNUM_DIGITS(num)[0];
|
|
sq = rb_ulong_isqrt(n);
|
|
return ULONG2NUM(sq);
|
|
}
|
|
#endif
|
|
return rb_big_isqrt(num);
|
|
}
|
|
}
|
|
|
|
/* :nodoc: */
|
|
static VALUE
|
|
int_s_try_convert(VALUE self, VALUE num)
|
|
{
|
|
return rb_check_integer_type(num);
|
|
}
|
|
|
|
/*
|
|
* Document-class: ZeroDivisionError
|
|
*
|
|
* Raised when attempting to divide an integer by 0.
|
|
*
|
|
* 42 / 0 #=> ZeroDivisionError: divided by 0
|
|
*
|
|
* Note that only division by an exact 0 will raise the exception:
|
|
*
|
|
* 42 / 0.0 #=> Float::INFINITY
|
|
* 42 / -0.0 #=> -Float::INFINITY
|
|
* 0 / 0.0 #=> NaN
|
|
*/
|
|
|
|
/*
|
|
* Document-class: FloatDomainError
|
|
*
|
|
* Raised when attempting to convert special float values (in particular
|
|
* +Infinity+ or +NaN+) to numerical classes which don't support them.
|
|
*
|
|
* Float::INFINITY.to_r #=> FloatDomainError: Infinity
|
|
*/
|
|
|
|
/*
|
|
* Document-class: Numeric
|
|
*
|
|
* Numeric is the class from which all higher-level numeric classes should inherit.
|
|
*
|
|
* Numeric allows instantiation of heap-allocated objects. Other core numeric classes such as
|
|
* Integer are implemented as immediates, which means that each Integer is a single immutable
|
|
* object which is always passed by value.
|
|
*
|
|
* a = 1
|
|
* 1.object_id == a.object_id #=> true
|
|
*
|
|
* There can only ever be one instance of the integer +1+, for example. Ruby ensures this
|
|
* by preventing instantiation. If duplication is attempted, the same instance is returned.
|
|
*
|
|
* Integer.new(1) #=> NoMethodError: undefined method `new' for Integer:Class
|
|
* 1.dup #=> 1
|
|
* 1.object_id == 1.dup.object_id #=> true
|
|
*
|
|
* For this reason, Numeric should be used when defining other numeric classes.
|
|
*
|
|
* Classes which inherit from Numeric must implement +coerce+, which returns a two-member
|
|
* Array containing an object that has been coerced into an instance of the new class
|
|
* and +self+ (see #coerce).
|
|
*
|
|
* Inheriting classes should also implement arithmetic operator methods (<code>+</code>,
|
|
* <code>-</code>, <code>*</code> and <code>/</code>) and the <code><=></code> operator (see
|
|
* Comparable). These methods may rely on +coerce+ to ensure interoperability with
|
|
* instances of other numeric classes.
|
|
*
|
|
* class Tally < Numeric
|
|
* def initialize(string)
|
|
* @string = string
|
|
* end
|
|
*
|
|
* def to_s
|
|
* @string
|
|
* end
|
|
*
|
|
* def to_i
|
|
* @string.size
|
|
* end
|
|
*
|
|
* def coerce(other)
|
|
* [self.class.new('|' * other.to_i), self]
|
|
* end
|
|
*
|
|
* def <=>(other)
|
|
* to_i <=> other.to_i
|
|
* end
|
|
*
|
|
* def +(other)
|
|
* self.class.new('|' * (to_i + other.to_i))
|
|
* end
|
|
*
|
|
* def -(other)
|
|
* self.class.new('|' * (to_i - other.to_i))
|
|
* end
|
|
*
|
|
* def *(other)
|
|
* self.class.new('|' * (to_i * other.to_i))
|
|
* end
|
|
*
|
|
* def /(other)
|
|
* self.class.new('|' * (to_i / other.to_i))
|
|
* end
|
|
* end
|
|
*
|
|
* tally = Tally.new('||')
|
|
* puts tally * 2 #=> "||||"
|
|
* puts tally > 1 #=> true
|
|
*
|
|
* == What's Here
|
|
*
|
|
* First, what's elsewhere. \Class \Numeric:
|
|
*
|
|
* - Inherits from {class Object}[rdoc-ref:Object@What-27s+Here].
|
|
* - Includes {module Comparable}[rdoc-ref:Comparable@What-27s+Here].
|
|
*
|
|
* Here, class \Numeric provides methods for:
|
|
*
|
|
* - {Querying}[rdoc-ref:Numeric@Querying]
|
|
* - {Comparing}[rdoc-ref:Numeric@Comparing]
|
|
* - {Converting}[rdoc-ref:Numeric@Converting]
|
|
* - {Other}[rdoc-ref:Numeric@Other]
|
|
*
|
|
* === Querying
|
|
*
|
|
* - #finite?: Returns true unless +self+ is infinite or not a number.
|
|
* - #infinite?: Returns -1, +nil+ or +1, depending on whether +self+
|
|
* is <tt>-Infinity<tt>, finite, or <tt>+Infinity</tt>.
|
|
* - #integer?: Returns whether +self+ is an integer.
|
|
* - #negative?: Returns whether +self+ is negative.
|
|
* - #nonzero?: Returns whether +self+ is not zero.
|
|
* - #positive?: Returns whether +self+ is positive.
|
|
* - #real?: Returns whether +self+ is a real value.
|
|
* - #zero?: Returns whether +self+ is zero.
|
|
*
|
|
* === Comparing
|
|
*
|
|
* - #<=>: Returns:
|
|
*
|
|
* - -1 if +self+ is less than the given value.
|
|
* - 0 if +self+ is equal to the given value.
|
|
* - 1 if +self+ is greater than the given value.
|
|
* - +nil+ if +self+ and the given value are not comparable.
|
|
*
|
|
* - #eql?: Returns whether +self+ and the given value have the same value and type.
|
|
*
|
|
* === Converting
|
|
*
|
|
* - #% (aliased as #modulo): Returns the remainder of +self+ divided by the given value.
|
|
* - #-@: Returns the value of +self+, negated.
|
|
* - #abs (aliased as #magnitude): Returns the absolute value of +self+.
|
|
* - #abs2: Returns the square of +self+.
|
|
* - #angle (aliased as #arg and #phase): Returns 0 if +self+ is positive,
|
|
* Math::PI otherwise.
|
|
* - #ceil: Returns the smallest number greater than or equal to +self+,
|
|
* to a given precision.
|
|
* - #coerce: Returns array <tt>[coerced_self, coerced_other]</tt>
|
|
* for the given other value.
|
|
* - #conj (aliased as #conjugate): Returns the complex conjugate of +self+.
|
|
* - #denominator: Returns the denominator (always positive)
|
|
* of the Rational representation of +self+.
|
|
* - #div: Returns the value of +self+ divided by the given value
|
|
* and converted to an integer.
|
|
* - #divmod: Returns array <tt>[quotient, modulus]</tt> resulting
|
|
* from dividing +self+ the given divisor.
|
|
* - #fdiv: Returns the Float result of dividing +self+ by the given divisor.
|
|
* - #floor: Returns the largest number less than or equal to +self+,
|
|
* to a given precision.
|
|
* - #i: Returns the Complex object <tt>Complex(0, self)</tt>.
|
|
* the given value.
|
|
* - #imaginary (aliased as #imag): Returns the imaginary part of the +self+.
|
|
* - #numerator: Returns the numerator of the Rational representation of +self+;
|
|
* has the same sign as +self+.
|
|
* - #polar: Returns the array <tt>[self.abs, self.arg]</tt>.
|
|
* - #quo: Returns the value of +self+ divided by the given value.
|
|
* - #real: Returns the real part of +self+.
|
|
* - #rect (aliased as #rectangular): Returns the array <tt>[self, 0]</tt>.
|
|
* - #remainder: Returns <tt>self-arg*(self/arg).truncate</tt> for the given +arg+.
|
|
* - #round: Returns the value of +self+ rounded to the nearest value
|
|
* for the given a precision.
|
|
* - #to_c: Returns the Complex representation of +self+.
|
|
* - #to_int: Returns the Integer representation of +self+, truncating if necessary.
|
|
* - #truncate: Returns +self+ truncated (toward zero) to a given precision.
|
|
*
|
|
* === Other
|
|
*
|
|
* - #clone: Returns +self+; does not allow freezing.
|
|
* - #dup (aliased as #+@): Returns +self+.
|
|
* - #step: Invokes the given block with the sequence of specified numbers.
|
|
*
|
|
*/
|
|
void
|
|
Init_Numeric(void)
|
|
{
|
|
#ifdef _UNICOSMP
|
|
/* Turn off floating point exceptions for divide by zero, etc. */
|
|
_set_Creg(0, 0);
|
|
#endif
|
|
id_coerce = rb_intern_const("coerce");
|
|
id_to = rb_intern_const("to");
|
|
id_by = rb_intern_const("by");
|
|
|
|
rb_eZeroDivError = rb_define_class("ZeroDivisionError", rb_eStandardError);
|
|
rb_eFloatDomainError = rb_define_class("FloatDomainError", rb_eRangeError);
|
|
rb_cNumeric = rb_define_class("Numeric", rb_cObject);
|
|
|
|
rb_define_method(rb_cNumeric, "singleton_method_added", num_sadded, 1);
|
|
rb_include_module(rb_cNumeric, rb_mComparable);
|
|
rb_define_method(rb_cNumeric, "coerce", num_coerce, 1);
|
|
rb_define_method(rb_cNumeric, "clone", num_clone, -1);
|
|
rb_define_method(rb_cNumeric, "dup", num_dup, 0);
|
|
|
|
rb_define_method(rb_cNumeric, "i", num_imaginary, 0);
|
|
rb_define_method(rb_cNumeric, "+@", num_uplus, 0);
|
|
rb_define_method(rb_cNumeric, "-@", num_uminus, 0);
|
|
rb_define_method(rb_cNumeric, "<=>", num_cmp, 1);
|
|
rb_define_method(rb_cNumeric, "eql?", num_eql, 1);
|
|
rb_define_method(rb_cNumeric, "fdiv", num_fdiv, 1);
|
|
rb_define_method(rb_cNumeric, "div", num_div, 1);
|
|
rb_define_method(rb_cNumeric, "divmod", num_divmod, 1);
|
|
rb_define_method(rb_cNumeric, "%", num_modulo, 1);
|
|
rb_define_method(rb_cNumeric, "modulo", num_modulo, 1);
|
|
rb_define_method(rb_cNumeric, "remainder", num_remainder, 1);
|
|
rb_define_method(rb_cNumeric, "abs", num_abs, 0);
|
|
rb_define_method(rb_cNumeric, "magnitude", num_abs, 0);
|
|
rb_define_method(rb_cNumeric, "to_int", num_to_int, 0);
|
|
|
|
rb_define_method(rb_cNumeric, "zero?", num_zero_p, 0);
|
|
rb_define_method(rb_cNumeric, "nonzero?", num_nonzero_p, 0);
|
|
|
|
rb_define_method(rb_cNumeric, "floor", num_floor, -1);
|
|
rb_define_method(rb_cNumeric, "ceil", num_ceil, -1);
|
|
rb_define_method(rb_cNumeric, "round", num_round, -1);
|
|
rb_define_method(rb_cNumeric, "truncate", num_truncate, -1);
|
|
rb_define_method(rb_cNumeric, "step", num_step, -1);
|
|
rb_define_method(rb_cNumeric, "positive?", num_positive_p, 0);
|
|
rb_define_method(rb_cNumeric, "negative?", num_negative_p, 0);
|
|
|
|
rb_cInteger = rb_define_class("Integer", rb_cNumeric);
|
|
rb_undef_alloc_func(rb_cInteger);
|
|
rb_undef_method(CLASS_OF(rb_cInteger), "new");
|
|
rb_define_singleton_method(rb_cInteger, "sqrt", rb_int_s_isqrt, 1);
|
|
rb_define_singleton_method(rb_cInteger, "try_convert", int_s_try_convert, 1);
|
|
|
|
rb_define_method(rb_cInteger, "to_s", rb_int_to_s, -1);
|
|
rb_define_alias(rb_cInteger, "inspect", "to_s");
|
|
rb_define_method(rb_cInteger, "allbits?", int_allbits_p, 1);
|
|
rb_define_method(rb_cInteger, "anybits?", int_anybits_p, 1);
|
|
rb_define_method(rb_cInteger, "nobits?", int_nobits_p, 1);
|
|
rb_define_method(rb_cInteger, "upto", int_upto, 1);
|
|
rb_define_method(rb_cInteger, "downto", int_downto, 1);
|
|
rb_define_method(rb_cInteger, "times", int_dotimes, 0);
|
|
rb_define_method(rb_cInteger, "succ", int_succ, 0);
|
|
rb_define_method(rb_cInteger, "next", int_succ, 0);
|
|
rb_define_method(rb_cInteger, "pred", int_pred, 0);
|
|
rb_define_method(rb_cInteger, "chr", int_chr, -1);
|
|
rb_define_method(rb_cInteger, "to_f", int_to_f, 0);
|
|
rb_define_method(rb_cInteger, "floor", int_floor, -1);
|
|
rb_define_method(rb_cInteger, "ceil", int_ceil, -1);
|
|
rb_define_method(rb_cInteger, "truncate", int_truncate, -1);
|
|
rb_define_method(rb_cInteger, "round", int_round, -1);
|
|
rb_define_method(rb_cInteger, "<=>", rb_int_cmp, 1);
|
|
|
|
rb_define_method(rb_cInteger, "+", rb_int_plus, 1);
|
|
rb_define_method(rb_cInteger, "-", rb_int_minus, 1);
|
|
rb_define_method(rb_cInteger, "*", rb_int_mul, 1);
|
|
rb_define_method(rb_cInteger, "/", rb_int_div, 1);
|
|
rb_define_method(rb_cInteger, "div", rb_int_idiv, 1);
|
|
rb_define_method(rb_cInteger, "%", rb_int_modulo, 1);
|
|
rb_define_method(rb_cInteger, "modulo", rb_int_modulo, 1);
|
|
rb_define_method(rb_cInteger, "remainder", int_remainder, 1);
|
|
rb_define_method(rb_cInteger, "divmod", rb_int_divmod, 1);
|
|
rb_define_method(rb_cInteger, "fdiv", rb_int_fdiv, 1);
|
|
rb_define_method(rb_cInteger, "**", rb_int_pow, 1);
|
|
|
|
rb_define_method(rb_cInteger, "pow", rb_int_powm, -1); /* in bignum.c */
|
|
|
|
rb_define_method(rb_cInteger, "===", rb_int_equal, 1);
|
|
rb_define_method(rb_cInteger, "==", rb_int_equal, 1);
|
|
rb_define_method(rb_cInteger, ">", rb_int_gt, 1);
|
|
rb_define_method(rb_cInteger, ">=", rb_int_ge, 1);
|
|
rb_define_method(rb_cInteger, "<", int_lt, 1);
|
|
rb_define_method(rb_cInteger, "<=", int_le, 1);
|
|
|
|
rb_define_method(rb_cInteger, "&", rb_int_and, 1);
|
|
rb_define_method(rb_cInteger, "|", int_or, 1);
|
|
rb_define_method(rb_cInteger, "^", int_xor, 1);
|
|
rb_define_method(rb_cInteger, "[]", int_aref, -1);
|
|
|
|
rb_define_method(rb_cInteger, "<<", rb_int_lshift, 1);
|
|
rb_define_method(rb_cInteger, ">>", rb_int_rshift, 1);
|
|
|
|
rb_define_method(rb_cInteger, "digits", rb_int_digits, -1);
|
|
|
|
rb_fix_to_s_static[0] = rb_fstring_literal("0");
|
|
rb_fix_to_s_static[1] = rb_fstring_literal("1");
|
|
rb_fix_to_s_static[2] = rb_fstring_literal("2");
|
|
rb_fix_to_s_static[3] = rb_fstring_literal("3");
|
|
rb_fix_to_s_static[4] = rb_fstring_literal("4");
|
|
rb_fix_to_s_static[5] = rb_fstring_literal("5");
|
|
rb_fix_to_s_static[6] = rb_fstring_literal("6");
|
|
rb_fix_to_s_static[7] = rb_fstring_literal("7");
|
|
rb_fix_to_s_static[8] = rb_fstring_literal("8");
|
|
rb_fix_to_s_static[9] = rb_fstring_literal("9");
|
|
for(int i = 0; i < 10; i++) {
|
|
rb_gc_register_mark_object(rb_fix_to_s_static[i]);
|
|
}
|
|
|
|
rb_cFloat = rb_define_class("Float", rb_cNumeric);
|
|
|
|
rb_undef_alloc_func(rb_cFloat);
|
|
rb_undef_method(CLASS_OF(rb_cFloat), "new");
|
|
|
|
/*
|
|
* The base of the floating point, or number of unique digits used to
|
|
* represent the number.
|
|
*
|
|
* Usually defaults to 2 on most systems, which would represent a base-10 decimal.
|
|
*/
|
|
rb_define_const(rb_cFloat, "RADIX", INT2FIX(FLT_RADIX));
|
|
/*
|
|
* The number of base digits for the +double+ data type.
|
|
*
|
|
* Usually defaults to 53.
|
|
*/
|
|
rb_define_const(rb_cFloat, "MANT_DIG", INT2FIX(DBL_MANT_DIG));
|
|
/*
|
|
* The minimum number of significant decimal digits in a double-precision
|
|
* floating point.
|
|
*
|
|
* Usually defaults to 15.
|
|
*/
|
|
rb_define_const(rb_cFloat, "DIG", INT2FIX(DBL_DIG));
|
|
/*
|
|
* The smallest possible exponent value in a double-precision floating
|
|
* point.
|
|
*
|
|
* Usually defaults to -1021.
|
|
*/
|
|
rb_define_const(rb_cFloat, "MIN_EXP", INT2FIX(DBL_MIN_EXP));
|
|
/*
|
|
* The largest possible exponent value in a double-precision floating
|
|
* point.
|
|
*
|
|
* Usually defaults to 1024.
|
|
*/
|
|
rb_define_const(rb_cFloat, "MAX_EXP", INT2FIX(DBL_MAX_EXP));
|
|
/*
|
|
* The smallest negative exponent in a double-precision floating point
|
|
* where 10 raised to this power minus 1.
|
|
*
|
|
* Usually defaults to -307.
|
|
*/
|
|
rb_define_const(rb_cFloat, "MIN_10_EXP", INT2FIX(DBL_MIN_10_EXP));
|
|
/*
|
|
* The largest positive exponent in a double-precision floating point where
|
|
* 10 raised to this power minus 1.
|
|
*
|
|
* Usually defaults to 308.
|
|
*/
|
|
rb_define_const(rb_cFloat, "MAX_10_EXP", INT2FIX(DBL_MAX_10_EXP));
|
|
/*
|
|
* The smallest positive normalized number in a double-precision floating point.
|
|
*
|
|
* Usually defaults to 2.2250738585072014e-308.
|
|
*
|
|
* If the platform supports denormalized numbers,
|
|
* there are numbers between zero and Float::MIN.
|
|
* 0.0.next_float returns the smallest positive floating point number
|
|
* including denormalized numbers.
|
|
*/
|
|
rb_define_const(rb_cFloat, "MIN", DBL2NUM(DBL_MIN));
|
|
/*
|
|
* The largest possible integer in a double-precision floating point number.
|
|
*
|
|
* Usually defaults to 1.7976931348623157e+308.
|
|
*/
|
|
rb_define_const(rb_cFloat, "MAX", DBL2NUM(DBL_MAX));
|
|
/*
|
|
* The difference between 1 and the smallest double-precision floating
|
|
* point number greater than 1.
|
|
*
|
|
* Usually defaults to 2.2204460492503131e-16.
|
|
*/
|
|
rb_define_const(rb_cFloat, "EPSILON", DBL2NUM(DBL_EPSILON));
|
|
/*
|
|
* An expression representing positive infinity.
|
|
*/
|
|
rb_define_const(rb_cFloat, "INFINITY", DBL2NUM(HUGE_VAL));
|
|
/*
|
|
* An expression representing a value which is "not a number".
|
|
*/
|
|
rb_define_const(rb_cFloat, "NAN", DBL2NUM(nan("")));
|
|
|
|
rb_define_method(rb_cFloat, "to_s", flo_to_s, 0);
|
|
rb_define_alias(rb_cFloat, "inspect", "to_s");
|
|
rb_define_method(rb_cFloat, "coerce", flo_coerce, 1);
|
|
rb_define_method(rb_cFloat, "+", rb_float_plus, 1);
|
|
rb_define_method(rb_cFloat, "-", rb_float_minus, 1);
|
|
rb_define_method(rb_cFloat, "*", rb_float_mul, 1);
|
|
rb_define_method(rb_cFloat, "/", rb_float_div, 1);
|
|
rb_define_method(rb_cFloat, "quo", flo_quo, 1);
|
|
rb_define_method(rb_cFloat, "fdiv", flo_quo, 1);
|
|
rb_define_method(rb_cFloat, "%", flo_mod, 1);
|
|
rb_define_method(rb_cFloat, "modulo", flo_mod, 1);
|
|
rb_define_method(rb_cFloat, "divmod", flo_divmod, 1);
|
|
rb_define_method(rb_cFloat, "**", rb_float_pow, 1);
|
|
rb_define_method(rb_cFloat, "==", flo_eq, 1);
|
|
rb_define_method(rb_cFloat, "===", flo_eq, 1);
|
|
rb_define_method(rb_cFloat, "<=>", flo_cmp, 1);
|
|
rb_define_method(rb_cFloat, ">", rb_float_gt, 1);
|
|
rb_define_method(rb_cFloat, ">=", flo_ge, 1);
|
|
rb_define_method(rb_cFloat, "<", flo_lt, 1);
|
|
rb_define_method(rb_cFloat, "<=", flo_le, 1);
|
|
rb_define_method(rb_cFloat, "eql?", flo_eql, 1);
|
|
rb_define_method(rb_cFloat, "hash", flo_hash, 0);
|
|
|
|
rb_define_method(rb_cFloat, "to_i", flo_to_i, 0);
|
|
rb_define_method(rb_cFloat, "to_int", flo_to_i, 0);
|
|
rb_define_method(rb_cFloat, "floor", flo_floor, -1);
|
|
rb_define_method(rb_cFloat, "ceil", flo_ceil, -1);
|
|
rb_define_method(rb_cFloat, "round", flo_round, -1);
|
|
rb_define_method(rb_cFloat, "truncate", flo_truncate, -1);
|
|
|
|
rb_define_method(rb_cFloat, "nan?", flo_is_nan_p, 0);
|
|
rb_define_method(rb_cFloat, "infinite?", rb_flo_is_infinite_p, 0);
|
|
rb_define_method(rb_cFloat, "finite?", rb_flo_is_finite_p, 0);
|
|
rb_define_method(rb_cFloat, "next_float", flo_next_float, 0);
|
|
rb_define_method(rb_cFloat, "prev_float", flo_prev_float, 0);
|
|
}
|
|
|
|
#undef rb_float_value
|
|
double
|
|
rb_float_value(VALUE v)
|
|
{
|
|
return rb_float_value_inline(v);
|
|
}
|
|
|
|
#undef rb_float_new
|
|
VALUE
|
|
rb_float_new(double d)
|
|
{
|
|
return rb_float_new_inline(d);
|
|
}
|
|
|
|
#include "numeric.rbinc"
|