mirror of
https://github.com/ruby/ruby.git
synced 2022-11-09 12:17:21 -05:00
d16b68cb22
ndigits higher than 14 can result in values that are slightly too large due to floating point limitations. Converting to rational for the calculation and then back to float fixes these issues. Fixes [Bug #14635] Fixes [Bug #17183] Co-authored by: Yusuke Endoh <mame@ruby-lang.org>
5697 lines
132 KiB
C
5697 lines
132 KiB
C
/**********************************************************************
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numeric.c -
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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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#ifdef HAVE_FLOAT_H
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#include <float.h>
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#endif
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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/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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/* 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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#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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#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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if (x > 0.0) {
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f = floor(x);
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x = f + (x - f >= 0.5);
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}
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else if (x < 0.0) {
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f = ceil(x);
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x = f - (f - x >= 0.5);
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}
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return x;
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}
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#endif
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static double
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round_half_up(double x, double s)
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{
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double f, xs = x * s;
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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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}
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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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static double
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round_half_down(double x, double s)
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{
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double f, xs = x * s;
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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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}
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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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static double
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round_half_even(double x, double s)
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{
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double f, d, xs = x * s;
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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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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_TYPE_P(val, T_BIGNUM)) {
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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_TYPE_P(num, T_BIGNUM)) {
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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_TYPE_P(num, T_BIGNUM)) {
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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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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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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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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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|
|
/*
|
|
* call-seq:
|
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* num.coerce(numeric) -> array
|
|
*
|
|
* If +numeric+ is the same type as +num+, returns an array
|
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* <code>[numeric, num]</code>. Otherwise, returns an array with both
|
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* +numeric+ and +num+ represented as Float objects.
|
|
*
|
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* This coercion mechanism is used by Ruby to handle mixed-type numeric
|
|
* operations: it is intended to find a compatible common type between the two
|
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* operands of the operator.
|
|
*
|
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* 1.coerce(2.5) #=> [2.5, 1.0]
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* 1.2.coerce(3) #=> [3.0, 1.2]
|
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* 1.coerce(2) #=> [2, 1]
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|
*/
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|
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static VALUE
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num_coerce(VALUE x, VALUE y)
|
|
{
|
|
if (CLASS_OF(x) == CLASS_OF(y))
|
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return rb_assoc_new(y, x);
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x = rb_Float(x);
|
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y = rb_Float(y);
|
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return rb_assoc_new(y, x);
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|
}
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|
|
NORETURN(static void coerce_failed(VALUE x, VALUE y));
|
|
static void
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|
coerce_failed(VALUE x, VALUE y)
|
|
{
|
|
if (SPECIAL_CONST_P(y) || SYMBOL_P(y) || RB_FLOAT_TYPE_P(y)) {
|
|
y = rb_inspect(y);
|
|
}
|
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else {
|
|
y = rb_obj_class(y);
|
|
}
|
|
rb_raise(rb_eTypeError, "%"PRIsVALUE" can't be coerced into %"PRIsVALUE,
|
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y, rb_obj_class(x));
|
|
}
|
|
|
|
static int
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|
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:
|
|
* num.clone(freeze: true) -> num
|
|
*
|
|
* Returns the receiver. +freeze+ cannot be +false+.
|
|
*/
|
|
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:
|
|
* num.dup -> num
|
|
*
|
|
* Returns the receiver.
|
|
*/
|
|
static VALUE
|
|
num_dup(VALUE x)
|
|
{
|
|
return x;
|
|
}
|
|
#else
|
|
# define num_dup num_uplus
|
|
#endif
|
|
|
|
/*
|
|
* call-seq:
|
|
* +num -> num
|
|
*
|
|
* Unary Plus---Returns the receiver.
|
|
*/
|
|
|
|
static VALUE
|
|
num_uplus(VALUE num)
|
|
{
|
|
return num;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* num.i -> Complex(0, num)
|
|
*
|
|
* Returns the corresponding imaginary number.
|
|
* Not available for complex numbers.
|
|
*
|
|
* -42.i #=> (0-42i)
|
|
* 2.0.i #=> (0+2.0i)
|
|
*/
|
|
|
|
static VALUE
|
|
num_imaginary(VALUE num)
|
|
{
|
|
return rb_complex_new(INT2FIX(0), num);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* -num -> 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:
|
|
* num.fdiv(numeric) -> float
|
|
*
|
|
* Returns float division.
|
|
*/
|
|
|
|
static VALUE
|
|
num_fdiv(VALUE x, VALUE y)
|
|
{
|
|
return rb_funcall(rb_Float(x), '/', 1, y);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* num.div(numeric) -> integer
|
|
*
|
|
* Uses +/+ to perform division, then converts the result to an integer.
|
|
* Numeric does not define the +/+ operator; this is left to subclasses.
|
|
*
|
|
* Equivalent to <code>num.divmod(numeric)[0]</code>.
|
|
*
|
|
* See Numeric#divmod.
|
|
*/
|
|
|
|
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:
|
|
* num.modulo(numeric) -> real
|
|
*
|
|
* <code>x.modulo(y)</code> means <code>x-y*(x/y).floor</code>.
|
|
*
|
|
* Equivalent to <code>num.divmod(numeric)[1]</code>.
|
|
*
|
|
* See Numeric#divmod.
|
|
*/
|
|
|
|
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:
|
|
* num.remainder(numeric) -> real
|
|
*
|
|
* <code>x.remainder(y)</code> means <code>x-y*(x/y).truncate</code>.
|
|
*
|
|
* See Numeric#divmod.
|
|
*/
|
|
|
|
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_TYPE_P(y, T_FLOAT)) {
|
|
if (isinf(RFLOAT_VALUE(y))) {
|
|
return x;
|
|
}
|
|
}
|
|
return rb_funcall(z, '-', 1, y);
|
|
}
|
|
return z;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* num.divmod(numeric) -> array
|
|
*
|
|
* Returns an array containing the quotient and modulus obtained by dividing
|
|
* +num+ by +numeric+.
|
|
*
|
|
* If <code>q, r = x.divmod(y)</code>, then
|
|
*
|
|
* q = floor(x/y)
|
|
* x = q*y + r
|
|
*
|
|
* The quotient is rounded toward negative infinity, as shown in the
|
|
* following table:
|
|
*
|
|
* a | b | a.divmod(b) | a/b | a.modulo(b) | a.remainder(b)
|
|
* ------+-----+---------------+---------+-------------+---------------
|
|
* 13 | 4 | 3, 1 | 3 | 1 | 1
|
|
* ------+-----+---------------+---------+-------------+---------------
|
|
* 13 | -4 | -4, -3 | -4 | -3 | 1
|
|
* ------+-----+---------------+---------+-------------+---------------
|
|
* -13 | 4 | -4, 3 | -4 | 3 | -1
|
|
* ------+-----+---------------+---------+-------------+---------------
|
|
* -13 | -4 | 3, -1 | 3 | -1 | -1
|
|
* ------+-----+---------------+---------+-------------+---------------
|
|
* 11.5 | 4 | 2, 3.5 | 2.875 | 3.5 | 3.5
|
|
* ------+-----+---------------+---------+-------------+---------------
|
|
* 11.5 | -4 | -3, -0.5 | -2.875 | -0.5 | 3.5
|
|
* ------+-----+---------------+---------+-------------+---------------
|
|
* -11.5 | 4 | -3, 0.5 | -2.875 | 0.5 | -3.5
|
|
* ------+-----+---------------+---------+-------------+---------------
|
|
* -11.5 | -4 | 2, -3.5 | 2.875 | -3.5 | -3.5
|
|
*
|
|
*
|
|
* Examples
|
|
*
|
|
* 11.divmod(3) #=> [3, 2]
|
|
* 11.divmod(-3) #=> [-4, -1]
|
|
* 11.divmod(3.5) #=> [3, 0.5]
|
|
* (-11).divmod(3.5) #=> [-4, 3.0]
|
|
* 11.5.divmod(3.5) #=> [3, 1.0]
|
|
*/
|
|
|
|
static VALUE
|
|
num_divmod(VALUE x, VALUE y)
|
|
{
|
|
return rb_assoc_new(num_div(x, y), num_modulo(x, y));
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* num.abs -> numeric
|
|
* num.magnitude -> numeric
|
|
*
|
|
* Returns the absolute value of +num+.
|
|
*
|
|
* 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:
|
|
* num.zero? -> true or false
|
|
*
|
|
* Returns +true+ if +num+ has a zero value.
|
|
*/
|
|
|
|
static VALUE
|
|
num_zero_p(VALUE num)
|
|
{
|
|
return rb_equal(num, INT2FIX(0));
|
|
}
|
|
|
|
static VALUE
|
|
int_zero_p(VALUE num)
|
|
{
|
|
if (FIXNUM_P(num)) {
|
|
if (FIXNUM_ZERO_P(num)) {
|
|
return Qtrue;
|
|
}
|
|
}
|
|
else {
|
|
assert(RB_TYPE_P(num, T_BIGNUM));
|
|
if (rb_bigzero_p(num)) {
|
|
/* this should not happen usually */
|
|
return Qtrue;
|
|
}
|
|
}
|
|
return Qfalse;
|
|
}
|
|
|
|
VALUE
|
|
rb_int_zero_p(VALUE num)
|
|
{
|
|
return int_zero_p(num);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* num.nonzero? -> self or nil
|
|
*
|
|
* Returns +self+ if +num+ is not zero, +nil+ otherwise.
|
|
*
|
|
* This behavior is useful when chaining comparisons:
|
|
*
|
|
* a = %w( z Bb bB bb BB a aA Aa AA A )
|
|
* b = a.sort {|a,b| (a.downcase <=> b.downcase).nonzero? || a <=> b }
|
|
* b #=> ["A", "a", "AA", "Aa", "aA", "BB", "Bb", "bB", "bb", "z"]
|
|
*/
|
|
|
|
static VALUE
|
|
num_nonzero_p(VALUE num)
|
|
{
|
|
if (RTEST(num_funcall0(num, rb_intern("zero?")))) {
|
|
return Qnil;
|
|
}
|
|
return num;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* num.to_int -> integer
|
|
*
|
|
* Invokes the child class's +to_i+ method to convert +num+ to an integer.
|
|
*
|
|
* 1.0.class #=> Float
|
|
* 1.0.to_int.class #=> Integer
|
|
* 1.0.to_i.class #=> Integer
|
|
*/
|
|
|
|
static VALUE
|
|
num_to_int(VALUE num)
|
|
{
|
|
return num_funcall0(num, id_to_i);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* num.positive? -> true or false
|
|
*
|
|
* Returns +true+ if +num+ is greater than 0.
|
|
*/
|
|
|
|
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_TYPE_P(num, T_BIGNUM)) {
|
|
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:
|
|
* num.negative? -> true or false
|
|
*
|
|
* Returns +true+ if +num+ is less than 0.
|
|
*/
|
|
|
|
static VALUE
|
|
num_negative_p(VALUE num)
|
|
{
|
|
return RBOOL(rb_num_negative_int_p(num));
|
|
}
|
|
|
|
|
|
/********************************************************************
|
|
*
|
|
* Document-class: Float
|
|
*
|
|
* Float objects represent inexact real numbers 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
|
|
*/
|
|
|
|
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));
|
|
|
|
flt->float_value = d;
|
|
OBJ_FREEZE((VALUE)flt);
|
|
return (VALUE)flt;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* float.to_s -> string
|
|
*
|
|
* Returns a string containing a representation of +self+.
|
|
* As well as a fixed or exponential form of the +float+,
|
|
* the call may return +NaN+, +Infinity+, and +-Infinity+.
|
|
*/
|
|
|
|
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:
|
|
* float.coerce(numeric) -> array
|
|
*
|
|
* Returns an array with both +numeric+ and +float+ represented as Float
|
|
* objects.
|
|
*
|
|
* This is achieved by converting +numeric+ to a Float.
|
|
*
|
|
* 1.2.coerce(3) #=> [3.0, 1.2]
|
|
* 2.5.coerce(1.1) #=> [1.1, 2.5]
|
|
*/
|
|
|
|
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:
|
|
* float + other -> float
|
|
*
|
|
* Returns a new Float which is the sum of +float+ and +other+.
|
|
*/
|
|
|
|
VALUE
|
|
rb_float_plus(VALUE x, VALUE y)
|
|
{
|
|
if (RB_TYPE_P(y, T_FIXNUM)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y));
|
|
}
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y));
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y));
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, '+');
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* float - other -> float
|
|
*
|
|
* Returns a new Float which is the difference of +float+ and +other+.
|
|
*/
|
|
|
|
VALUE
|
|
rb_float_minus(VALUE x, VALUE y)
|
|
{
|
|
if (RB_TYPE_P(y, T_FIXNUM)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y));
|
|
}
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y));
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y));
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, '-');
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* float * other -> float
|
|
*
|
|
* Returns a new Float which is the product of +float+ and +other+.
|
|
*/
|
|
|
|
VALUE
|
|
rb_float_mul(VALUE x, VALUE y)
|
|
{
|
|
if (RB_TYPE_P(y, T_FIXNUM)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y));
|
|
}
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y));
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
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:
|
|
* float / other -> float
|
|
*
|
|
* Returns a new Float which is the result of dividing +float+ by +other+.
|
|
*/
|
|
|
|
VALUE
|
|
rb_float_div(VALUE x, VALUE y)
|
|
{
|
|
double num = RFLOAT_VALUE(x);
|
|
double den;
|
|
double ret;
|
|
|
|
if (RB_TYPE_P(y, T_FIXNUM)) {
|
|
den = FIX2LONG(y);
|
|
}
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
den = rb_big2dbl(y);
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
den = RFLOAT_VALUE(y);
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, '/');
|
|
}
|
|
|
|
ret = double_div_double(num, den);
|
|
return DBL2NUM(ret);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* float.fdiv(numeric) -> float
|
|
* float.quo(numeric) -> float
|
|
*
|
|
* Returns <code>float / numeric</code>, same as Float#/.
|
|
*/
|
|
|
|
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:
|
|
* float % other -> float
|
|
* float.modulo(other) -> float
|
|
*
|
|
* Returns the modulo after division of +float+ by +other+.
|
|
*
|
|
* 6543.21.modulo(137) #=> 104.21000000000004
|
|
* 6543.21.modulo(137.24) #=> 92.92999999999961
|
|
*/
|
|
|
|
static VALUE
|
|
flo_mod(VALUE x, VALUE y)
|
|
{
|
|
double fy;
|
|
|
|
if (RB_TYPE_P(y, T_FIXNUM)) {
|
|
fy = (double)FIX2LONG(y);
|
|
}
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
fy = rb_big2dbl(y);
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
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:
|
|
* float.divmod(numeric) -> array
|
|
*
|
|
* See Numeric#divmod.
|
|
*
|
|
* 42.0.divmod(6) #=> [7, 0.0]
|
|
* 42.0.divmod(5) #=> [8, 2.0]
|
|
*/
|
|
|
|
static VALUE
|
|
flo_divmod(VALUE x, VALUE y)
|
|
{
|
|
double fy, div, mod;
|
|
volatile VALUE a, b;
|
|
|
|
if (RB_TYPE_P(y, T_FIXNUM)) {
|
|
fy = (double)FIX2LONG(y);
|
|
}
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
fy = rb_big2dbl(y);
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
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:
|
|
* float ** other -> float
|
|
*
|
|
* Raises +float+ to the power of +other+.
|
|
*
|
|
* 2.0**3 #=> 8.0
|
|
*/
|
|
|
|
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 (RB_TYPE_P(y, T_FIXNUM)) {
|
|
dx = RFLOAT_VALUE(x);
|
|
dy = (double)FIX2LONG(y);
|
|
}
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
dx = RFLOAT_VALUE(x);
|
|
dy = rb_big2dbl(y);
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
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:
|
|
* num.eql?(numeric) -> true or false
|
|
*
|
|
* Returns +true+ if +num+ and +numeric+ are the same type and have equal
|
|
* values. Contrast this with Numeric#==, which performs type conversions.
|
|
*
|
|
* 1 == 1.0 #=> true
|
|
* 1.eql?(1.0) #=> false
|
|
* 1.0.eql?(1.0) #=> true
|
|
*/
|
|
|
|
static VALUE
|
|
num_eql(VALUE x, VALUE y)
|
|
{
|
|
if (TYPE(x) != TYPE(y)) return Qfalse;
|
|
|
|
if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_eql(x, y);
|
|
}
|
|
|
|
return rb_equal(x, y);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* number <=> other -> 0 or nil
|
|
*
|
|
* Returns zero if +number+ equals +other+, otherwise returns +nil+.
|
|
*/
|
|
|
|
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:
|
|
* float == obj -> true or false
|
|
*
|
|
* Returns +true+ only if +obj+ has the same value as +float+.
|
|
* Contrast this with Float#eql?, which requires +obj+ to be a Float.
|
|
*
|
|
* 1.0 == 1 #=> true
|
|
*
|
|
* The result of <code>NaN == NaN</code> is undefined,
|
|
* so an implementation-dependent value is returned.
|
|
*/
|
|
|
|
MJIT_FUNC_EXPORTED VALUE
|
|
rb_float_equal(VALUE x, VALUE y)
|
|
{
|
|
volatile double a, b;
|
|
|
|
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
|
|
return rb_integer_float_eq(y, x);
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
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 (a == b)?Qtrue:Qfalse;
|
|
}
|
|
|
|
#define flo_eq rb_float_equal
|
|
static VALUE rb_dbl_hash(double d);
|
|
|
|
/*
|
|
* call-seq:
|
|
* float.hash -> integer
|
|
*
|
|
* Returns a hash code for this float.
|
|
*
|
|
* 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:
|
|
* float <=> real -> -1, 0, +1, or nil
|
|
*
|
|
* Returns -1, 0, or +1 depending on whether +float+ is
|
|
* less than, equal to, or greater than +real+.
|
|
* This is the basis for the tests in the Comparable module.
|
|
*
|
|
* The result of <code>NaN <=> NaN</code> is undefined,
|
|
* so an implementation-dependent value is returned.
|
|
*
|
|
* +nil+ is returned if the two values are incomparable.
|
|
*/
|
|
|
|
static VALUE
|
|
flo_cmp(VALUE x, VALUE y)
|
|
{
|
|
double a, b;
|
|
VALUE i;
|
|
|
|
a = RFLOAT_VALUE(x);
|
|
if (isnan(a)) return Qnil;
|
|
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
|
|
VALUE rel = rb_integer_float_cmp(y, x);
|
|
if (FIXNUM_P(rel))
|
|
return LONG2FIX(-FIX2LONG(rel));
|
|
return rel;
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
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:
|
|
* float > real -> true or false
|
|
*
|
|
* Returns +true+ if +float+ is greater than +real+.
|
|
*
|
|
* The result of <code>NaN > NaN</code> is undefined,
|
|
* so an implementation-dependent value is returned.
|
|
*/
|
|
|
|
VALUE
|
|
rb_float_gt(VALUE x, VALUE y)
|
|
{
|
|
double a, b;
|
|
|
|
a = RFLOAT_VALUE(x);
|
|
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
|
|
VALUE rel = rb_integer_float_cmp(y, x);
|
|
if (FIXNUM_P(rel))
|
|
return RBOOL(-FIX2LONG(rel) > 0);
|
|
return Qfalse;
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
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 (a > b)?Qtrue:Qfalse;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* float >= real -> true or false
|
|
*
|
|
* Returns +true+ if +float+ is greater than or equal to +real+.
|
|
*
|
|
* The result of <code>NaN >= NaN</code> is undefined,
|
|
* so an implementation-dependent value is returned.
|
|
*/
|
|
|
|
static VALUE
|
|
flo_ge(VALUE x, VALUE y)
|
|
{
|
|
double a, b;
|
|
|
|
a = RFLOAT_VALUE(x);
|
|
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
|
|
VALUE rel = rb_integer_float_cmp(y, x);
|
|
if (FIXNUM_P(rel))
|
|
return RBOOL(-FIX2LONG(rel) >= 0);
|
|
return Qfalse;
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
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 (a >= b)?Qtrue:Qfalse;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* float < real -> true or false
|
|
*
|
|
* Returns +true+ if +float+ is less than +real+.
|
|
*
|
|
* The result of <code>NaN < NaN</code> is undefined,
|
|
* so an implementation-dependent value is returned.
|
|
*/
|
|
|
|
static VALUE
|
|
flo_lt(VALUE x, VALUE y)
|
|
{
|
|
double a, b;
|
|
|
|
a = RFLOAT_VALUE(x);
|
|
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
|
|
VALUE rel = rb_integer_float_cmp(y, x);
|
|
if (FIXNUM_P(rel))
|
|
return RBOOL(-FIX2LONG(rel) < 0);
|
|
return Qfalse;
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
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 (a < b)?Qtrue:Qfalse;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* float <= real -> true or false
|
|
*
|
|
* Returns +true+ if +float+ is less than or equal to +real+.
|
|
*
|
|
* The result of <code>NaN <= NaN</code> is undefined,
|
|
* so an implementation-dependent value is returned.
|
|
*/
|
|
|
|
static VALUE
|
|
flo_le(VALUE x, VALUE y)
|
|
{
|
|
double a, b;
|
|
|
|
a = RFLOAT_VALUE(x);
|
|
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
|
|
VALUE rel = rb_integer_float_cmp(y, x);
|
|
if (FIXNUM_P(rel))
|
|
return RBOOL(-FIX2LONG(rel) <= 0);
|
|
return Qfalse;
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
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 (a <= b)?Qtrue:Qfalse;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* float.eql?(obj) -> true or false
|
|
*
|
|
* Returns +true+ only if +obj+ is a Float with the same value as +float+.
|
|
* Contrast this with Float#==, which performs type conversions.
|
|
*
|
|
* 1.0.eql?(1) #=> false
|
|
*
|
|
* The result of <code>NaN.eql?(NaN)</code> is undefined,
|
|
* so an implementation-dependent value is returned.
|
|
*/
|
|
|
|
MJIT_FUNC_EXPORTED VALUE
|
|
rb_float_eql(VALUE x, VALUE y)
|
|
{
|
|
if (RB_TYPE_P(y, T_FLOAT)) {
|
|
double a = RFLOAT_VALUE(x);
|
|
double b = RFLOAT_VALUE(y);
|
|
#if MSC_VERSION_BEFORE(1300)
|
|
if (isnan(a) || isnan(b)) return Qfalse;
|
|
#endif
|
|
if (a == b)
|
|
return Qtrue;
|
|
}
|
|
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:
|
|
* float.nan? -> true or false
|
|
*
|
|
* Returns +true+ if +float+ is an invalid IEEE floating point number.
|
|
*
|
|
* a = -1.0 #=> -1.0
|
|
* a.nan? #=> false
|
|
* a = 0.0/0.0 #=> NaN
|
|
* a.nan? #=> true
|
|
*/
|
|
|
|
static VALUE
|
|
flo_is_nan_p(VALUE num)
|
|
{
|
|
double value = RFLOAT_VALUE(num);
|
|
|
|
return RBOOL(isnan(value));
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* float.infinite? -> -1, 1, or nil
|
|
*
|
|
* Returns +nil+, -1, or 1 depending on whether the value is
|
|
* finite, <code>-Infinity</code>, or <code>+Infinity</code>.
|
|
*
|
|
* (0.0).infinite? #=> nil
|
|
* (-1.0/0.0).infinite? #=> -1
|
|
* (+1.0/0.0).infinite? #=> 1
|
|
*/
|
|
|
|
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:
|
|
* float.finite? -> true or false
|
|
*
|
|
* Returns +true+ if +float+ is a valid IEEE floating point number,
|
|
* i.e. it is not infinite and Float#nan? is +false+.
|
|
*/
|
|
|
|
VALUE
|
|
rb_flo_is_finite_p(VALUE num)
|
|
{
|
|
double value = RFLOAT_VALUE(num);
|
|
|
|
#ifdef HAVE_ISFINITE
|
|
if (!isfinite(value))
|
|
return Qfalse;
|
|
#else
|
|
if (isinf(value) || isnan(value))
|
|
return Qfalse;
|
|
#endif
|
|
|
|
return Qtrue;
|
|
}
|
|
|
|
static VALUE
|
|
flo_nextafter(VALUE flo, double value)
|
|
{
|
|
double x, y;
|
|
x = NUM2DBL(flo);
|
|
y = nextafter(x, value);
|
|
return DBL2NUM(y);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* float.next_float -> float
|
|
*
|
|
* Returns the next representable floating point number.
|
|
*
|
|
* Float::MAX.next_float and Float::INFINITY.next_float is Float::INFINITY.
|
|
*
|
|
* Float::NAN.next_float is Float::NAN.
|
|
*
|
|
* For example:
|
|
*
|
|
* 0.01.next_float #=> 0.010000000000000002
|
|
* 1.0.next_float #=> 1.0000000000000002
|
|
* 100.0.next_float #=> 100.00000000000001
|
|
*
|
|
* 0.01.next_float - 0.01 #=> 1.734723475976807e-18
|
|
* 1.0.next_float - 1.0 #=> 2.220446049250313e-16
|
|
* 100.0.next_float - 100.0 #=> 1.4210854715202004e-14
|
|
*
|
|
* f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.next_float }
|
|
* #=> 0x1.47ae147ae147bp-7 0.01
|
|
* # 0x1.47ae147ae147cp-7 0.010000000000000002
|
|
* # 0x1.47ae147ae147dp-7 0.010000000000000004
|
|
* # 0x1.47ae147ae147ep-7 0.010000000000000005
|
|
* # 0x1.47ae147ae147fp-7 0.010000000000000007
|
|
* # 0x1.47ae147ae148p-7 0.010000000000000009
|
|
* # 0x1.47ae147ae1481p-7 0.01000000000000001
|
|
* # 0x1.47ae147ae1482p-7 0.010000000000000012
|
|
* # 0x1.47ae147ae1483p-7 0.010000000000000014
|
|
* # 0x1.47ae147ae1484p-7 0.010000000000000016
|
|
* # 0x1.47ae147ae1485p-7 0.010000000000000018
|
|
* # 0x1.47ae147ae1486p-7 0.01000000000000002
|
|
* # 0x1.47ae147ae1487p-7 0.010000000000000021
|
|
* # 0x1.47ae147ae1488p-7 0.010000000000000023
|
|
* # 0x1.47ae147ae1489p-7 0.010000000000000024
|
|
* # 0x1.47ae147ae148ap-7 0.010000000000000026
|
|
* # 0x1.47ae147ae148bp-7 0.010000000000000028
|
|
* # 0x1.47ae147ae148cp-7 0.01000000000000003
|
|
* # 0x1.47ae147ae148dp-7 0.010000000000000031
|
|
* # 0x1.47ae147ae148ep-7 0.010000000000000033
|
|
*
|
|
* 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.
|
|
*/
|
|
static VALUE
|
|
flo_next_float(VALUE vx)
|
|
{
|
|
return flo_nextafter(vx, HUGE_VAL);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* float.prev_float -> float
|
|
*
|
|
* Returns the previous representable floating point number.
|
|
*
|
|
* (-Float::MAX).prev_float and (-Float::INFINITY).prev_float is -Float::INFINITY.
|
|
*
|
|
* Float::NAN.prev_float is Float::NAN.
|
|
*
|
|
* For example:
|
|
*
|
|
* 0.01.prev_float #=> 0.009999999999999998
|
|
* 1.0.prev_float #=> 0.9999999999999999
|
|
* 100.0.prev_float #=> 99.99999999999999
|
|
*
|
|
* 0.01 - 0.01.prev_float #=> 1.734723475976807e-18
|
|
* 1.0 - 1.0.prev_float #=> 1.1102230246251565e-16
|
|
* 100.0 - 100.0.prev_float #=> 1.4210854715202004e-14
|
|
*
|
|
* f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.prev_float }
|
|
* #=> 0x1.47ae147ae147bp-7 0.01
|
|
* # 0x1.47ae147ae147ap-7 0.009999999999999998
|
|
* # 0x1.47ae147ae1479p-7 0.009999999999999997
|
|
* # 0x1.47ae147ae1478p-7 0.009999999999999995
|
|
* # 0x1.47ae147ae1477p-7 0.009999999999999993
|
|
* # 0x1.47ae147ae1476p-7 0.009999999999999992
|
|
* # 0x1.47ae147ae1475p-7 0.00999999999999999
|
|
* # 0x1.47ae147ae1474p-7 0.009999999999999988
|
|
* # 0x1.47ae147ae1473p-7 0.009999999999999986
|
|
* # 0x1.47ae147ae1472p-7 0.009999999999999985
|
|
* # 0x1.47ae147ae1471p-7 0.009999999999999983
|
|
* # 0x1.47ae147ae147p-7 0.009999999999999981
|
|
* # 0x1.47ae147ae146fp-7 0.00999999999999998
|
|
* # 0x1.47ae147ae146ep-7 0.009999999999999978
|
|
* # 0x1.47ae147ae146dp-7 0.009999999999999976
|
|
* # 0x1.47ae147ae146cp-7 0.009999999999999974
|
|
* # 0x1.47ae147ae146bp-7 0.009999999999999972
|
|
* # 0x1.47ae147ae146ap-7 0.00999999999999997
|
|
* # 0x1.47ae147ae1469p-7 0.009999999999999969
|
|
* # 0x1.47ae147ae1468p-7 0.009999999999999967
|
|
*/
|
|
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;
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* float.floor([ndigits]) -> integer or float
|
|
*
|
|
* Returns the largest number less than or equal to +float+ with
|
|
* a precision of +ndigits+ decimal digits (default: 0).
|
|
*
|
|
* When the precision is negative, the returned value is an integer
|
|
* with at least <code>ndigits.abs</code> trailing zeros.
|
|
*
|
|
* Returns a floating point number when +ndigits+ is positive,
|
|
* otherwise returns an integer.
|
|
*
|
|
* 1.2.floor #=> 1
|
|
* 2.0.floor #=> 2
|
|
* (-1.2).floor #=> -2
|
|
* (-2.0).floor #=> -2
|
|
*
|
|
* 1.234567.floor(2) #=> 1.23
|
|
* 1.234567.floor(3) #=> 1.234
|
|
* 1.234567.floor(4) #=> 1.2345
|
|
* 1.234567.floor(5) #=> 1.23456
|
|
*
|
|
* 34567.89.floor(-5) #=> 0
|
|
* 34567.89.floor(-4) #=> 30000
|
|
* 34567.89.floor(-3) #=> 34000
|
|
* 34567.89.floor(-2) #=> 34500
|
|
* 34567.89.floor(-1) #=> 34560
|
|
* 34567.89.floor(0) #=> 34567
|
|
* 34567.89.floor(1) #=> 34567.8
|
|
* 34567.89.floor(2) #=> 34567.89
|
|
* 34567.89.floor(3) #=> 34567.89
|
|
*
|
|
* Note that the limited precision of floating point arithmetic
|
|
* might lead to surprising results:
|
|
*
|
|
* (0.3 / 0.1).floor #=> 2 (!)
|
|
*/
|
|
|
|
static VALUE
|
|
flo_floor(int argc, VALUE *argv, VALUE num)
|
|
{
|
|
int ndigits = 0;
|
|
if (rb_check_arity(argc, 0, 1)) {
|
|
ndigits = NUM2INT(argv[0]);
|
|
}
|
|
return rb_float_floor(num, ndigits);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* float.ceil([ndigits]) -> integer or float
|
|
*
|
|
* Returns the smallest number greater than or equal to +float+ with
|
|
* a precision of +ndigits+ decimal digits (default: 0).
|
|
*
|
|
* When the precision is negative, the returned value is an integer
|
|
* with at least <code>ndigits.abs</code> trailing zeros.
|
|
*
|
|
* Returns a floating point number when +ndigits+ is positive,
|
|
* otherwise returns an integer.
|
|
*
|
|
* 1.2.ceil #=> 2
|
|
* 2.0.ceil #=> 2
|
|
* (-1.2).ceil #=> -1
|
|
* (-2.0).ceil #=> -2
|
|
*
|
|
* 1.234567.ceil(2) #=> 1.24
|
|
* 1.234567.ceil(3) #=> 1.235
|
|
* 1.234567.ceil(4) #=> 1.2346
|
|
* 1.234567.ceil(5) #=> 1.23457
|
|
*
|
|
* 34567.89.ceil(-5) #=> 100000
|
|
* 34567.89.ceil(-4) #=> 40000
|
|
* 34567.89.ceil(-3) #=> 35000
|
|
* 34567.89.ceil(-2) #=> 34600
|
|
* 34567.89.ceil(-1) #=> 34570
|
|
* 34567.89.ceil(0) #=> 34568
|
|
* 34567.89.ceil(1) #=> 34567.9
|
|
* 34567.89.ceil(2) #=> 34567.89
|
|
* 34567.89.ceil(3) #=> 34567.89
|
|
*
|
|
* Note that the limited precision of floating point arithmetic
|
|
* might lead to surprising results:
|
|
*
|
|
* (2.1 / 0.7).ceil #=> 4 (!)
|
|
*/
|
|
|
|
static VALUE
|
|
flo_ceil(int argc, VALUE *argv, VALUE num)
|
|
{
|
|
int ndigits = 0;
|
|
|
|
if (rb_check_arity(argc, 0, 1)) {
|
|
ndigits = NUM2INT(argv[0]);
|
|
}
|
|
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_TYPE_P(num, T_BIGNUM)) {
|
|
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_TYPE_P(f, T_FLOAT)) {
|
|
/* 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_TYPE_P(f, T_FLOAT)) {
|
|
/* 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_TYPE_P(f, T_FLOAT)) {
|
|
/* 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_TYPE_P(f, T_FLOAT)) {
|
|
/* 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:
|
|
* float.round([ndigits] [, half: mode]) -> integer or float
|
|
*
|
|
* Returns +float+ rounded to the nearest value with
|
|
* a precision of +ndigits+ decimal digits (default: 0).
|
|
*
|
|
* When the precision is negative, the returned value is an integer
|
|
* with at least <code>ndigits.abs</code> trailing zeros.
|
|
*
|
|
* Returns a floating point number when +ndigits+ is positive,
|
|
* otherwise returns an integer.
|
|
*
|
|
* 1.4.round #=> 1
|
|
* 1.5.round #=> 2
|
|
* 1.6.round #=> 2
|
|
* (-1.5).round #=> -2
|
|
*
|
|
* 1.234567.round(2) #=> 1.23
|
|
* 1.234567.round(3) #=> 1.235
|
|
* 1.234567.round(4) #=> 1.2346
|
|
* 1.234567.round(5) #=> 1.23457
|
|
*
|
|
* 34567.89.round(-5) #=> 0
|
|
* 34567.89.round(-4) #=> 30000
|
|
* 34567.89.round(-3) #=> 35000
|
|
* 34567.89.round(-2) #=> 34600
|
|
* 34567.89.round(-1) #=> 34570
|
|
* 34567.89.round(0) #=> 34568
|
|
* 34567.89.round(1) #=> 34567.9
|
|
* 34567.89.round(2) #=> 34567.89
|
|
* 34567.89.round(3) #=> 34567.89
|
|
*
|
|
* If the optional +half+ keyword argument is given,
|
|
* numbers that are half-way between two possible rounded values
|
|
* will be rounded according to the specified tie-breaking +mode+:
|
|
*
|
|
* * <code>:up</code> or +nil+: round half away from zero (default)
|
|
* * <code>:down</code>: round half toward zero
|
|
* * <code>:even</code>: round half toward the nearest even number
|
|
*
|
|
* 2.5.round(half: :up) #=> 3
|
|
* 2.5.round(half: :down) #=> 2
|
|
* 2.5.round(half: :even) #=> 2
|
|
* 3.5.round(half: :up) #=> 4
|
|
* 3.5.round(half: :down) #=> 3
|
|
* 3.5.round(half: :even) #=> 4
|
|
* (-2.5).round(half: :up) #=> -3
|
|
* (-2.5).round(half: :down) #=> -2
|
|
* (-2.5).round(half: :even) #=> -2
|
|
*/
|
|
|
|
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:
|
|
* float.to_i -> integer
|
|
* float.to_int -> integer
|
|
*
|
|
* Returns the +float+ truncated to an Integer.
|
|
*
|
|
* 1.2.to_i #=> 1
|
|
* (-1.2).to_i #=> -1
|
|
*
|
|
* Note that the limited precision of floating point arithmetic
|
|
* might lead to surprising results:
|
|
*
|
|
* (0.3 / 0.1).to_i #=> 2 (!)
|
|
*
|
|
* #to_int is an alias for #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:
|
|
* float.truncate([ndigits]) -> integer or float
|
|
*
|
|
* Returns +float+ truncated (toward zero) to
|
|
* a precision of +ndigits+ decimal digits (default: 0).
|
|
*
|
|
* When the precision is negative, the returned value is an integer
|
|
* with at least <code>ndigits.abs</code> trailing zeros.
|
|
*
|
|
* Returns a floating point number when +ndigits+ is positive,
|
|
* otherwise returns an integer.
|
|
*
|
|
* 2.8.truncate #=> 2
|
|
* (-2.8).truncate #=> -2
|
|
* 1.234567.truncate(2) #=> 1.23
|
|
* 34567.89.truncate(-2) #=> 34500
|
|
*
|
|
* Note that the limited precision of floating point arithmetic
|
|
* might lead to surprising results:
|
|
*
|
|
* (0.3 / 0.1).truncate #=> 2 (!)
|
|
*/
|
|
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:
|
|
* num.floor([ndigits]) -> integer or float
|
|
*
|
|
* Returns the largest number less than or equal to +num+ with
|
|
* a precision of +ndigits+ decimal digits (default: 0).
|
|
*
|
|
* Numeric implements this by converting its value 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:
|
|
* num.ceil([ndigits]) -> integer or float
|
|
*
|
|
* Returns the smallest number greater than or equal to +num+ with
|
|
* a precision of +ndigits+ decimal digits (default: 0).
|
|
*
|
|
* Numeric implements this by converting its value 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:
|
|
* num.round([ndigits]) -> integer or float
|
|
*
|
|
* Returns +num+ rounded to the nearest value with
|
|
* a precision of +ndigits+ decimal digits (default: 0).
|
|
*
|
|
* Numeric implements this by converting its value 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:
|
|
* num.truncate([ndigits]) -> integer or float
|
|
*
|
|
* Returns +num+ truncated (toward zero) to
|
|
* a precision of +ndigits+ decimal digits (default: 0).
|
|
*
|
|
* Numeric implements this by converting its value 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 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);
|
|
if (beg < end) {
|
|
if ((n+1)*unit+beg < end)
|
|
n++;
|
|
}
|
|
else if (beg > end) {
|
|
if ((n+1)*unit+beg > end)
|
|
n++;
|
|
}
|
|
}
|
|
else {
|
|
if (n<0) return 0;
|
|
n = floor(n + err);
|
|
if (beg < end) {
|
|
if ((n+1)*unit+beg <= end)
|
|
n++;
|
|
}
|
|
else if (beg > end) {
|
|
if ((n+1)*unit+beg >= end)
|
|
n++;
|
|
}
|
|
}
|
|
return n+1;
|
|
}
|
|
|
|
int
|
|
ruby_float_step(VALUE from, VALUE to, VALUE step, int excl, int allow_endless)
|
|
{
|
|
if (RB_TYPE_P(from, T_FLOAT) || RB_TYPE_P(to, T_FLOAT) || RB_TYPE_P(step, T_FLOAT)) {
|
|
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_TYPE_P(from, T_FLOAT) || RB_TYPE_P(to, T_FLOAT) || RB_TYPE_P(step, T_FLOAT)) {
|
|
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_TYPE_P(num, T_BIGNUM)) {
|
|
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:
|
|
* num.step(by: step, to: limit) {|i| block } -> self
|
|
* num.step(by: step, to: limit) -> an_enumerator
|
|
* num.step(by: step, to: limit) -> an_arithmetic_sequence
|
|
* num.step(limit=nil, step=1) {|i| block } -> self
|
|
* num.step(limit=nil, step=1) -> an_enumerator
|
|
* num.step(limit=nil, step=1) -> an_arithmetic_sequence
|
|
*
|
|
* Invokes the given block with the sequence of numbers starting at +num+,
|
|
* incremented by +step+ (defaulted to +1+) on each call.
|
|
*
|
|
* The loop finishes when the value to be passed to the block is greater than
|
|
* +limit+ (if +step+ is positive) or less than +limit+ (if +step+ is
|
|
* negative), where +limit+ is defaulted to infinity.
|
|
*
|
|
* In the recommended keyword argument style, either or both of
|
|
* +step+ and +limit+ (default infinity) can be omitted. In the
|
|
* fixed position argument style, zero as a step
|
|
* (i.e. <code>num.step(limit, 0)</code>) is not allowed for historical
|
|
* compatibility reasons.
|
|
*
|
|
* 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 - num)/step</i>.
|
|
*
|
|
* Otherwise, the loop starts at +num+, uses either the
|
|
* less-than (<code><</code>) or greater-than (<code>></code>) operator
|
|
* to compare the counter against +limit+,
|
|
* and increments itself using the <code>+</code> operator.
|
|
*
|
|
* If no block is given, an Enumerator is returned instead.
|
|
* Especially, the enumerator is an Enumerator::ArithmeticSequence
|
|
* if both +limit+ and +step+ are kind of Numeric or <code>nil</code>.
|
|
*
|
|
* For example:
|
|
*
|
|
* p 1.step.take(4)
|
|
* p 10.step(by: -1).take(4)
|
|
* 3.step(to: 5) {|i| print i, " " }
|
|
* 1.step(10, 2) {|i| print i, " " }
|
|
* Math::E.step(to: Math::PI, by: 0.2) {|f| print f, " " }
|
|
*
|
|
* Will produce:
|
|
*
|
|
* [1, 2, 3, 4]
|
|
* [10, 9, 8, 7]
|
|
* 3 4 5
|
|
* 1 3 5 7 9
|
|
* 2.718281828459045 2.9182818284590453 3.118281828459045
|
|
*/
|
|
|
|
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_TYPE_P(to, T_FLOAT)) {
|
|
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_TYPE_P(val, T_FLOAT)) {
|
|
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_TYPE_P(val, T_BIGNUM)) {
|
|
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_TYPE_P(val, T_FLOAT)) {
|
|
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_TYPE_P(val, T_BIGNUM)) {
|
|
{
|
|
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, rb_num_negative_int_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, rb_num_negative_int_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_TYPE_P(val, T_FLOAT)) {
|
|
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_TYPE_P(val, T_BIGNUM)) {
|
|
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 (RB_TYPE_P(val, T_NIL)) {
|
|
rb_raise(rb_eTypeError, "no implicit conversion from nil");
|
|
}
|
|
else if (RB_TYPE_P(val, T_FIXNUM)) {
|
|
return (LONG_LONG)FIX2LONG(val); /* this is FIX2LONG, intended */
|
|
}
|
|
else if (RB_TYPE_P(val, T_FLOAT)) {
|
|
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_TYPE_P(val, T_BIGNUM)) {
|
|
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
|
|
*
|
|
* Holds Integer values. You cannot add a singleton method to an
|
|
* Integer object, any attempt to do so will raise a TypeError.
|
|
*
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_odd_p(VALUE num)
|
|
{
|
|
if (FIXNUM_P(num)) {
|
|
return RBOOL(num & 2);
|
|
}
|
|
else {
|
|
assert(RB_TYPE_P(num, T_BIGNUM));
|
|
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_TYPE_P(num, T_BIGNUM));
|
|
return rb_big_even_p(num);
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_int_even_p(VALUE num)
|
|
{
|
|
return int_even_p(num);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* int.allbits?(mask) -> true or false
|
|
*
|
|
* Returns +true+ if all bits of <code>+int+ & +mask+</code> are 1.
|
|
*/
|
|
|
|
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:
|
|
* int.anybits?(mask) -> true or false
|
|
*
|
|
* Returns +true+ if any bits of <code>+int+ & +mask+</code> are 1.
|
|
*/
|
|
|
|
static VALUE
|
|
int_anybits_p(VALUE num, VALUE mask)
|
|
{
|
|
mask = rb_to_int(mask);
|
|
return int_zero_p(rb_int_and(num, mask)) ? Qfalse : Qtrue;
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* int.nobits?(mask) -> true or false
|
|
*
|
|
* Returns +true+ if no bits of <code>+int+ & +mask+</code> are 1.
|
|
*/
|
|
|
|
static VALUE
|
|
int_nobits_p(VALUE num, VALUE mask)
|
|
{
|
|
mask = rb_to_int(mask);
|
|
return int_zero_p(rb_int_and(num, mask));
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#succ
|
|
* Document-method: Integer#next
|
|
* call-seq:
|
|
* int.next -> integer
|
|
* int.succ -> integer
|
|
*
|
|
* Returns the successor of +int+,
|
|
* i.e. the Integer equal to <code>int+1</code>.
|
|
*
|
|
* 1.next #=> 2
|
|
* (-1).next #=> 0
|
|
* 1.succ #=> 2
|
|
* (-1).succ #=> 0
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_succ(VALUE num)
|
|
{
|
|
if (FIXNUM_P(num)) {
|
|
long i = FIX2LONG(num) + 1;
|
|
return LONG2NUM(i);
|
|
}
|
|
if (RB_TYPE_P(num, T_BIGNUM)) {
|
|
return rb_big_plus(num, INT2FIX(1));
|
|
}
|
|
return num_funcall1(num, '+', INT2FIX(1));
|
|
}
|
|
|
|
#define int_succ rb_int_succ
|
|
|
|
/*
|
|
* call-seq:
|
|
* int.pred -> integer
|
|
*
|
|
* Returns the predecessor of +int+,
|
|
* i.e. the Integer equal to <code>int-1</code>.
|
|
*
|
|
* 1.pred #=> 0
|
|
* (-1).pred #=> -2
|
|
*/
|
|
|
|
static VALUE
|
|
rb_int_pred(VALUE num)
|
|
{
|
|
if (FIXNUM_P(num)) {
|
|
long i = FIX2LONG(num) - 1;
|
|
return LONG2NUM(i);
|
|
}
|
|
if (RB_TYPE_P(num, T_BIGNUM)) {
|
|
return rb_big_minus(num, INT2FIX(1));
|
|
}
|
|
return num_funcall1(num, '-', INT2FIX(1));
|
|
}
|
|
|
|
#define int_pred rb_int_pred
|
|
|
|
/*
|
|
* Document-method: Integer#chr
|
|
* call-seq:
|
|
* int.chr([encoding]) -> string
|
|
*
|
|
* Returns a string containing the character represented by the +int+'s value
|
|
* according to +encoding+.
|
|
*
|
|
* 65.chr #=> "A"
|
|
* 230.chr #=> "\xE6"
|
|
* 255.chr(Encoding::UTF_8) #=> "\u00FF"
|
|
*/
|
|
|
|
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;
|
|
}
|
|
|
|
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_TYPE_P(num, T_BIGNUM));
|
|
return rb_big_uminus(num);
|
|
}
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#to_s
|
|
* call-seq:
|
|
* int.to_s(base=10) -> string
|
|
*
|
|
* Returns a string containing the place-value representation of +int+
|
|
* with radix +base+ (between 2 and 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"
|
|
*/
|
|
|
|
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
|
|
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_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big2str(x, base);
|
|
}
|
|
|
|
return rb_any_to_s(x);
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#+
|
|
* call-seq:
|
|
* int + numeric -> numeric_result
|
|
*
|
|
* Performs addition: the class of the resulting object depends on
|
|
* the class of +numeric+.
|
|
*/
|
|
|
|
static VALUE
|
|
fix_plus(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
return rb_fix_plus_fix(x, y);
|
|
}
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
return rb_big_plus(y, x);
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
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);
|
|
}
|
|
|
|
VALUE
|
|
rb_int_plus(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_plus(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_plus(x, y);
|
|
}
|
|
return rb_num_coerce_bin(x, y, '+');
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#-
|
|
* call-seq:
|
|
* int - numeric -> numeric_result
|
|
*
|
|
* Performs subtraction: the class of the resulting object depends on
|
|
* the class of +numeric+.
|
|
*/
|
|
|
|
static VALUE
|
|
fix_minus(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
return rb_fix_minus_fix(x, y);
|
|
}
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
x = rb_int2big(FIX2LONG(x));
|
|
return rb_big_minus(x, y);
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
return DBL2NUM((double)FIX2LONG(x) - RFLOAT_VALUE(y));
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, '-');
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_int_minus(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_minus(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
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))
|
|
|
|
/*
|
|
* Document-method: Integer#*
|
|
* call-seq:
|
|
* int * numeric -> numeric_result
|
|
*
|
|
* Performs multiplication: the class of the resulting object depends on
|
|
* the class of +numeric+.
|
|
*/
|
|
|
|
static VALUE
|
|
fix_mul(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
return rb_fix_mul_fix(x, y);
|
|
}
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
switch (x) {
|
|
case INT2FIX(0): return x;
|
|
case INT2FIX(1): return y;
|
|
}
|
|
return rb_big_mul(y, x);
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
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, '*');
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_int_mul(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_mul(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
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_TYPE_P(y, T_BIGNUM)) {
|
|
return rb_big_fdiv_double(rb_int2big(FIX2LONG(x)), y);
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
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_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_fdiv_double(x, y);
|
|
}
|
|
else {
|
|
return nan("");
|
|
}
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#fdiv
|
|
* call-seq:
|
|
* int.fdiv(numeric) -> float
|
|
*
|
|
* Returns the floating point result of dividing +int+ by +numeric+.
|
|
*
|
|
* 654321.fdiv(13731) #=> 47.652829364212366
|
|
* 654321.fdiv(13731.24) #=> 47.65199646936475
|
|
* -654321.fdiv(13731) #=> -47.652829364212366
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_fdiv(VALUE x, VALUE y)
|
|
{
|
|
if (RB_INTEGER_TYPE_P(x)) {
|
|
return DBL2NUM(rb_int_fdiv_double(x, y));
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#/
|
|
* call-seq:
|
|
* int / numeric -> numeric_result
|
|
*
|
|
* Performs division: the class of the resulting object depends on
|
|
* the class of +numeric+.
|
|
*/
|
|
|
|
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_TYPE_P(y, T_BIGNUM)) {
|
|
x = rb_int2big(FIX2LONG(x));
|
|
return rb_big_div(x, y);
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
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, '/');
|
|
}
|
|
|
|
VALUE
|
|
rb_int_div(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_div(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_div(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#div
|
|
* call-seq:
|
|
* int.div(numeric) -> integer
|
|
*
|
|
* Performs integer division: returns the integer result of dividing +int+
|
|
* by +numeric+.
|
|
*/
|
|
|
|
static VALUE
|
|
fix_idiv(VALUE x, VALUE y)
|
|
{
|
|
return fix_divide(x, y, id_div);
|
|
}
|
|
|
|
VALUE
|
|
rb_int_idiv(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_idiv(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_idiv(x, y);
|
|
}
|
|
return num_div(x, y);
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#%
|
|
* Document-method: Integer#modulo
|
|
* call-seq:
|
|
* int % other -> real
|
|
* int.modulo(other) -> real
|
|
*
|
|
* Returns +int+ modulo +other+.
|
|
*
|
|
* See Numeric#divmod for more information.
|
|
*/
|
|
|
|
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_TYPE_P(y, T_BIGNUM)) {
|
|
x = rb_int2big(FIX2LONG(x));
|
|
return rb_big_modulo(x, y);
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
return DBL2NUM(ruby_float_mod((double)FIX2LONG(x), RFLOAT_VALUE(y)));
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, '%');
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_int_modulo(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_mod(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_modulo(x, y);
|
|
}
|
|
return num_modulo(x, y);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* int.remainder(numeric) -> real
|
|
*
|
|
* Returns the remainder after dividing +int+ by +numeric+.
|
|
*
|
|
* <code>x.remainder(y)</code> means <code>x-y*(x/y).truncate</code>.
|
|
*
|
|
* 5.remainder(3) #=> 2
|
|
* -5.remainder(3) #=> -2
|
|
* 5.remainder(-3) #=> 2
|
|
* -5.remainder(-3) #=> -2
|
|
* 5.remainder(1.5) #=> 0.5
|
|
*
|
|
* See Numeric#divmod.
|
|
*/
|
|
|
|
static VALUE
|
|
int_remainder(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return num_remainder(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_remainder(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#divmod
|
|
* call-seq:
|
|
* int.divmod(numeric) -> array
|
|
*
|
|
* See Numeric#divmod.
|
|
*/
|
|
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_TYPE_P(y, T_BIGNUM)) {
|
|
x = rb_int2big(FIX2LONG(x));
|
|
return rb_big_divmod(x, y);
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
{
|
|
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);
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_int_divmod(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_divmod(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_divmod(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#**
|
|
* call-seq:
|
|
* int ** numeric -> numeric_result
|
|
*
|
|
* Raises +int+ to the power of +numeric+, which may be negative or
|
|
* fractional.
|
|
* The result may be an Integer, a Float, a Rational, or a complex number.
|
|
*
|
|
* 2 ** 3 #=> 8
|
|
* 2 ** -1 #=> (1/2)
|
|
* 2 ** 0.5 #=> 1.4142135623730951
|
|
* (-1) ** 0.5 #=> (0.0+1.0i)
|
|
*
|
|
* 123456789 ** 2 #=> 15241578750190521
|
|
* 123456789 ** 1.2 #=> 5126464716.0993185
|
|
* 123456789 ** -2 #=> (1/15241578750190521)
|
|
*/
|
|
|
|
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_TYPE_P(y, T_BIGNUM)) {
|
|
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_TYPE_P(y, T_FLOAT)) {
|
|
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);
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_int_pow(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_pow(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
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;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#==
|
|
* Document-method: Integer#===
|
|
* call-seq:
|
|
* int == other -> true or false
|
|
*
|
|
* Returns +true+ if +int+ equals +other+ numerically.
|
|
* Contrast this with Integer#eql?, which requires +other+ to be an Integer.
|
|
*
|
|
* 1 == 2 #=> false
|
|
* 1 == 1.0 #=> true
|
|
*/
|
|
|
|
static VALUE
|
|
fix_equal(VALUE x, VALUE y)
|
|
{
|
|
if (x == y) return Qtrue;
|
|
if (FIXNUM_P(y)) return Qfalse;
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
return rb_big_eq(y, x);
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
return rb_integer_float_eq(x, y);
|
|
}
|
|
else {
|
|
return num_equal(x, y);
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_int_equal(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_equal(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_eq(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#<=>
|
|
* call-seq:
|
|
* int <=> numeric -> -1, 0, +1, or nil
|
|
*
|
|
* Comparison---Returns -1, 0, or +1 depending on whether +int+ is
|
|
* less than, equal to, or greater than +numeric+.
|
|
*
|
|
* This is the basis for the tests in the Comparable module.
|
|
*
|
|
* +nil+ is returned if the two values are incomparable.
|
|
*/
|
|
|
|
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_TYPE_P(y, T_BIGNUM)) {
|
|
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_TYPE_P(y, T_FLOAT)) {
|
|
return rb_integer_float_cmp(x, y);
|
|
}
|
|
else {
|
|
return rb_num_coerce_cmp(x, y, id_cmp);
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_int_cmp(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_cmp(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_cmp(x, y);
|
|
}
|
|
else {
|
|
rb_raise(rb_eNotImpError, "need to define `<=>' in %s", rb_obj_classname(x));
|
|
}
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#>
|
|
* call-seq:
|
|
* int > real -> true or false
|
|
*
|
|
* Returns +true+ if the value of +int+ is greater than that of +real+.
|
|
*/
|
|
|
|
static VALUE
|
|
fix_gt(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
if (FIX2LONG(x) > FIX2LONG(y)) return Qtrue;
|
|
return Qfalse;
|
|
}
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
return RBOOL(rb_big_cmp(y, x) == INT2FIX(-1));
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
return RBOOL(rb_integer_float_cmp(x, y) == INT2FIX(1));
|
|
}
|
|
else {
|
|
return rb_num_coerce_relop(x, y, '>');
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_int_gt(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_gt(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_gt(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#>=
|
|
* call-seq:
|
|
* int >= real -> true or false
|
|
*
|
|
* Returns +true+ if the value of +int+ is greater than or equal to that of
|
|
* +real+.
|
|
*/
|
|
|
|
static VALUE
|
|
fix_ge(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
if (FIX2LONG(x) >= FIX2LONG(y)) return Qtrue;
|
|
return Qfalse;
|
|
}
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
return RBOOL(rb_big_cmp(y, x) != INT2FIX(+1));
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
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);
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_int_ge(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_ge(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_ge(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#<
|
|
* call-seq:
|
|
* int < real -> true or false
|
|
*
|
|
* Returns +true+ if the value of +int+ is less than that of +real+.
|
|
*/
|
|
|
|
static VALUE
|
|
fix_lt(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
if (FIX2LONG(x) < FIX2LONG(y)) return Qtrue;
|
|
return Qfalse;
|
|
}
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
return RBOOL(rb_big_cmp(y, x) == INT2FIX(+1));
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
return RBOOL(rb_integer_float_cmp(x, y) == INT2FIX(-1));
|
|
}
|
|
else {
|
|
return rb_num_coerce_relop(x, y, '<');
|
|
}
|
|
}
|
|
|
|
static VALUE
|
|
int_lt(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_lt(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_lt(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#<=
|
|
* call-seq:
|
|
* int <= real -> true or false
|
|
*
|
|
* Returns +true+ if the value of +int+ is less than or equal to that of
|
|
* +real+.
|
|
*/
|
|
|
|
static VALUE
|
|
fix_le(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
if (FIX2LONG(x) <= FIX2LONG(y)) return Qtrue;
|
|
return Qfalse;
|
|
}
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
return RBOOL(rb_big_cmp(y, x) != INT2FIX(-1));
|
|
}
|
|
else if (RB_TYPE_P(y, T_FLOAT)) {
|
|
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);
|
|
}
|
|
}
|
|
|
|
static VALUE
|
|
int_le(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_le(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
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_TYPE_P(num, T_BIGNUM)) {
|
|
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;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#&
|
|
* call-seq:
|
|
* int & other_int -> integer
|
|
*
|
|
* Bitwise AND.
|
|
*/
|
|
|
|
static VALUE
|
|
fix_and(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
long val = FIX2LONG(x) & FIX2LONG(y);
|
|
return LONG2NUM(val);
|
|
}
|
|
|
|
if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
return rb_big_and(y, x);
|
|
}
|
|
|
|
return rb_num_coerce_bit(x, y, '&');
|
|
}
|
|
|
|
VALUE
|
|
rb_int_and(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_and(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_and(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#|
|
|
* call-seq:
|
|
* int | other_int -> integer
|
|
*
|
|
* Bitwise OR.
|
|
*/
|
|
|
|
static VALUE
|
|
fix_or(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
long val = FIX2LONG(x) | FIX2LONG(y);
|
|
return LONG2NUM(val);
|
|
}
|
|
|
|
if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
return rb_big_or(y, x);
|
|
}
|
|
|
|
return rb_num_coerce_bit(x, y, '|');
|
|
}
|
|
|
|
static VALUE
|
|
int_or(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_or(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_or(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#^
|
|
* call-seq:
|
|
* int ^ other_int -> integer
|
|
*
|
|
* Bitwise EXCLUSIVE OR.
|
|
*/
|
|
|
|
static VALUE
|
|
fix_xor(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
long val = FIX2LONG(x) ^ FIX2LONG(y);
|
|
return LONG2NUM(val);
|
|
}
|
|
|
|
if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
return rb_big_xor(y, x);
|
|
}
|
|
|
|
return rb_num_coerce_bit(x, y, '^');
|
|
}
|
|
|
|
static VALUE
|
|
int_xor(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return fix_xor(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_xor(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#<<
|
|
* call-seq:
|
|
* int << count -> integer
|
|
*
|
|
* Returns +int+ shifted left +count+ positions, or right if +count+
|
|
* is negative.
|
|
*/
|
|
|
|
static VALUE
|
|
rb_fix_lshift(VALUE x, VALUE y)
|
|
{
|
|
long val, width;
|
|
|
|
val = NUM2LONG(x);
|
|
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);
|
|
}
|
|
|
|
VALUE
|
|
rb_int_lshift(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return rb_fix_lshift(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return rb_big_lshift(x, y);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#>>
|
|
* call-seq:
|
|
* int >> count -> integer
|
|
*
|
|
* Returns +int+ shifted right +count+ positions, or left if +count+
|
|
* is negative.
|
|
*/
|
|
|
|
static VALUE
|
|
rb_fix_rshift(VALUE x, VALUE y)
|
|
{
|
|
long i, val;
|
|
|
|
val = FIX2LONG(x);
|
|
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);
|
|
}
|
|
|
|
static VALUE
|
|
rb_int_rshift(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return rb_fix_rshift(x, y);
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
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 (RTEST(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_TYPE_P(num, T_BIGNUM)) {
|
|
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;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#[]
|
|
* call-seq:
|
|
* int[n] -> 0, 1
|
|
* int[n, m] -> num
|
|
* int[range] -> num
|
|
*
|
|
* Bit Reference---Returns the <code>n</code>th bit in the
|
|
* binary representation of +int+, where <code>int[0]</code>
|
|
* is the least significant bit.
|
|
*
|
|
* a = 0b11001100101010
|
|
* 30.downto(0) {|n| print a[n] }
|
|
* #=> 0000000000000000011001100101010
|
|
*
|
|
* a = 9**15
|
|
* 50.downto(0) {|n| print a[n] }
|
|
* #=> 000101110110100000111000011110010100111100010111001
|
|
*
|
|
* In principle, <code>n[i]</code> is equivalent to <code>(n >> i) & 1</code>.
|
|
* Thus, any negative index always returns zero:
|
|
*
|
|
* p 255[-1] #=> 0
|
|
*
|
|
* Range operations <code>n[i, len]</code> and <code>n[i..j]</code>
|
|
* are naturally extended.
|
|
*
|
|
* * <code>n[i, len]</code> equals to <code>(n >> i) & ((1 << len) - 1)</code>.
|
|
* * <code>n[i..j]</code> equals to <code>(n >> i) & ((1 << (j - i + 1)) - 1)</code>.
|
|
* * <code>n[i...j]</code> equals to <code>(n >> i) & ((1 << (j - i)) - 1)</code>.
|
|
* * <code>n[i..]</code> equals to <code>(n >> i)</code>.
|
|
* * <code>n[..j]</code> is zero if <code>n & ((1 << (j + 1)) - 1)</code> is zero. Otherwise, raises an ArgumentError.
|
|
* * <code>n[...j]</code> is zero if <code>n & ((1 << j) - 1)</code> is zero. Otherwise, raises an ArgumentError.
|
|
*
|
|
* Note that range operation may exhaust memory.
|
|
* For example, <code>-1[0, 1000000000000]</code> will raise NoMemoryError.
|
|
*/
|
|
|
|
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;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#to_f
|
|
* call-seq:
|
|
* int.to_f -> float
|
|
*
|
|
* Converts +int+ to a Float. If +int+ doesn't fit in a Float,
|
|
* the result is infinity.
|
|
*/
|
|
|
|
static VALUE
|
|
int_to_f(VALUE num)
|
|
{
|
|
double val;
|
|
|
|
if (FIXNUM_P(num)) {
|
|
val = (double)FIX2LONG(num);
|
|
}
|
|
else if (RB_TYPE_P(num, T_BIGNUM)) {
|
|
val = rb_big2dbl(num);
|
|
}
|
|
else {
|
|
rb_raise(rb_eNotImpError, "Unknown subclass for to_f: %s", rb_obj_classname(num));
|
|
}
|
|
|
|
return DBL2NUM(val);
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#abs
|
|
* Document-method: Integer#magnitude
|
|
* call-seq:
|
|
* int.abs -> integer
|
|
* int.magnitude -> integer
|
|
*
|
|
* Returns the absolute value of +int+.
|
|
*
|
|
* (-12345).abs #=> 12345
|
|
* -12345.abs #=> 12345
|
|
* 12345.abs #=> 12345
|
|
*
|
|
* Integer#magnitude is an alias for Integer#abs.
|
|
*/
|
|
|
|
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_TYPE_P(num, T_BIGNUM)) {
|
|
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_TYPE_P(num, T_BIGNUM)) {
|
|
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_TYPE_P(num, T_BIGNUM)) {
|
|
return rb_big_bit_length(num);
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#digits
|
|
* call-seq:
|
|
* int.digits -> array
|
|
* int.digits(base) -> array
|
|
*
|
|
* Returns the digits of +int+'s place-value representation
|
|
* with radix +base+ (default: 10).
|
|
* The digits are returned as an array with the least significant digit
|
|
* as the first array element.
|
|
*
|
|
* +base+ must be greater than or equal to 2.
|
|
*
|
|
* 12345.digits #=> [5, 4, 3, 2, 1]
|
|
* 12345.digits(7) #=> [4, 6, 6, 0, 5]
|
|
* 12345.digits(100) #=> [45, 23, 1]
|
|
*
|
|
* -12345.digits(7) #=> Math::DomainError
|
|
*/
|
|
|
|
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_TYPE_P(base, T_BIGNUM))
|
|
base = rb_big_norm(base);
|
|
|
|
if (FIXNUM_P(base) && FIX2LONG(base) < 2)
|
|
rb_raise(rb_eArgError, "invalid radix %ld", FIX2LONG(base));
|
|
else if (RB_TYPE_P(base, T_BIGNUM) && 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;
|
|
}
|
|
|
|
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_TYPE_P(base_value, T_BIGNUM))
|
|
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_TYPE_P(num, T_BIGNUM))
|
|
return rb_int_digits_bigbase(num, LONG2FIX(base));
|
|
|
|
return Qnil;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#upto
|
|
* call-seq:
|
|
* int.upto(limit) {|i| block } -> self
|
|
* int.upto(limit) -> an_enumerator
|
|
*
|
|
* Iterates the given block, passing in integer values from +int+ up to and
|
|
* including +limit+.
|
|
*
|
|
* If no block is given, an Enumerator is returned instead.
|
|
*
|
|
* 5.upto(10) {|i| print i, " " } #=> 5 6 7 8 9 10
|
|
*/
|
|
|
|
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);
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#downto
|
|
* call-seq:
|
|
* int.downto(limit) {|i| block } -> self
|
|
* int.downto(limit) -> an_enumerator
|
|
*
|
|
* Iterates the given block, passing in decreasing values from +int+ down to
|
|
* and including +limit+.
|
|
*
|
|
* If no block is given, an Enumerator is returned instead.
|
|
*
|
|
* 5.downto(1) { |n| print n, ".. " }
|
|
* puts "Liftoff!"
|
|
* #=> "5.. 4.. 3.. 2.. 1.. Liftoff!"
|
|
*/
|
|
|
|
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);
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#times
|
|
* call-seq:
|
|
* int.times {|i| block } -> self
|
|
* int.times -> an_enumerator
|
|
*
|
|
* Iterates the given block +int+ times, passing in values from zero to
|
|
* <code>int - 1</code>.
|
|
*
|
|
* If no block is given, an Enumerator is returned instead.
|
|
*
|
|
* 5.times {|i| print i, " " } #=> 0 1 2 3 4
|
|
*/
|
|
|
|
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;
|
|
}
|
|
|
|
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(rb_funcall(i, '<', 1, num))) break;
|
|
rb_yield(i);
|
|
i = rb_funcall(i, '+', 1, INT2FIX(1));
|
|
}
|
|
}
|
|
return num;
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#round
|
|
* call-seq:
|
|
* int.round([ndigits] [, half: mode]) -> integer or float
|
|
*
|
|
* Returns +int+ rounded to the nearest value with
|
|
* a precision of +ndigits+ decimal digits (default: 0).
|
|
*
|
|
* When the precision is negative, the returned value is an integer
|
|
* with at least <code>ndigits.abs</code> trailing zeros.
|
|
*
|
|
* Returns +self+ when +ndigits+ is zero or positive.
|
|
*
|
|
* 1.round #=> 1
|
|
* 1.round(2) #=> 1
|
|
* 15.round(-1) #=> 20
|
|
* (-15).round(-1) #=> -20
|
|
*
|
|
* The optional +half+ keyword argument is available
|
|
* similar to Float#round.
|
|
*
|
|
* 25.round(-1, half: :up) #=> 30
|
|
* 25.round(-1, half: :down) #=> 20
|
|
* 25.round(-1, half: :even) #=> 20
|
|
* 35.round(-1, half: :up) #=> 40
|
|
* 35.round(-1, half: :down) #=> 30
|
|
* 35.round(-1, half: :even) #=> 40
|
|
* (-25).round(-1, half: :up) #=> -30
|
|
* (-25).round(-1, half: :down) #=> -20
|
|
* (-25).round(-1, half: :even) #=> -20
|
|
*/
|
|
|
|
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);
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#floor
|
|
* call-seq:
|
|
* int.floor([ndigits]) -> integer or float
|
|
*
|
|
* Returns the largest number less than or equal to +int+ with
|
|
* a precision of +ndigits+ decimal digits (default: 0).
|
|
*
|
|
* When the precision is negative, the returned value is an integer
|
|
* with at least <code>ndigits.abs</code> trailing zeros.
|
|
*
|
|
* Returns +self+ when +ndigits+ is zero or positive.
|
|
*
|
|
* 1.floor #=> 1
|
|
* 1.floor(2) #=> 1
|
|
* 18.floor(-1) #=> 10
|
|
* (-18).floor(-1) #=> -20
|
|
*/
|
|
|
|
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);
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#ceil
|
|
* call-seq:
|
|
* int.ceil([ndigits]) -> integer or float
|
|
*
|
|
* Returns the smallest number greater than or equal to +int+ with
|
|
* a precision of +ndigits+ decimal digits (default: 0).
|
|
*
|
|
* When the precision is negative, the returned value is an integer
|
|
* with at least <code>ndigits.abs</code> trailing zeros.
|
|
*
|
|
* Returns +self+ when +ndigits+ is zero or positive.
|
|
*
|
|
* 1.ceil #=> 1
|
|
* 1.ceil(2) #=> 1
|
|
* 18.ceil(-1) #=> 20
|
|
* (-18).ceil(-1) #=> -10
|
|
*/
|
|
|
|
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);
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#truncate
|
|
* call-seq:
|
|
* int.truncate([ndigits]) -> integer or float
|
|
*
|
|
* Returns +int+ truncated (toward zero) to
|
|
* a precision of +ndigits+ decimal digits (default: 0).
|
|
*
|
|
* When the precision is negative, the returned value is an integer
|
|
* with at least <code>ndigits.abs</code> trailing zeros.
|
|
*
|
|
* Returns +self+ when +ndigits+ is zero or positive.
|
|
*
|
|
* 1.truncate #=> 1
|
|
* 1.truncate(2) #=> 1
|
|
* 18.truncate(-1) #=> 10
|
|
* (-18).truncate(-1) #=> -10
|
|
*/
|
|
|
|
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)
|
|
|
|
/*
|
|
* Document-method: Integer::sqrt
|
|
* call-seq:
|
|
* Integer.sqrt(n) -> integer
|
|
*
|
|
* Returns the integer square root of the non-negative integer +n+,
|
|
* i.e. the largest non-negative integer less than or equal to the
|
|
* square root of +n+.
|
|
*
|
|
* Integer.sqrt(0) #=> 0
|
|
* Integer.sqrt(1) #=> 1
|
|
* Integer.sqrt(24) #=> 4
|
|
* Integer.sqrt(25) #=> 5
|
|
* Integer.sqrt(10**400) #=> 10**200
|
|
*
|
|
* Equivalent to <code>Math.sqrt(n).floor</code>, 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 (!)
|
|
*
|
|
* If +n+ is not an Integer, it is converted to an Integer first.
|
|
* If +n+ is negative, a Math::DomainError is raised.
|
|
*/
|
|
|
|
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);
|
|
}
|
|
}
|
|
|
|
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}[Object.html#class-Object-label-What-27s+Here].
|
|
* - Includes {module Comparable}[Comparable.html#module-Comparable-label-What-27s+Here].
|
|
*
|
|
* Here, class \Numeric provides methods for:
|
|
*
|
|
* - {Querying}[#class-Numeric-label-Querying]
|
|
* - {Comparing}[#class-Numeric-label-Comparing]
|
|
* - {Converting}[#class-Numeric-label-Converting]
|
|
* - {Other}[#class-Numeric-label-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
|
|
*
|
|
* - {<=>}[#method-i-3C-3D-3E]:: 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", 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);
|
|
|
|
/* An obsolete class, use Integer */
|
|
rb_define_const(rb_cObject, "Fixnum", rb_cInteger);
|
|
rb_deprecate_constant(rb_cObject, "Fixnum");
|
|
|
|
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);
|
|
}
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#include "numeric.rbinc"
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