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ruby/numeric.c

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/**********************************************************************
numeric.c -
$Author$
created at: Fri Aug 13 18:33:09 JST 1993
Copyright (C) 1993-2007 Yukihiro Matsumoto
**********************************************************************/
#include "ruby/internal/config.h"
#include <assert.h>
#include <ctype.h>
#include <math.h>
#include <stdio.h>
#ifdef HAVE_FLOAT_H
#include <float.h>
#endif
#ifdef HAVE_IEEEFP_H
#include <ieeefp.h>
#endif
#include "id.h"
#include "internal.h"
#include "internal/array.h"
#include "internal/compilers.h"
#include "internal/complex.h"
#include "internal/enumerator.h"
#include "internal/gc.h"
#include "internal/hash.h"
#include "internal/numeric.h"
#include "internal/object.h"
#include "internal/rational.h"
#include "internal/util.h"
#include "internal/variable.h"
#include "ruby/encoding.h"
#include "ruby/util.h"
#include "builtin.h"
/* use IEEE 64bit values if not defined */
#ifndef FLT_RADIX
#define FLT_RADIX 2
#endif
#ifndef DBL_MIN
#define DBL_MIN 2.2250738585072014e-308
#endif
#ifndef DBL_MAX
#define DBL_MAX 1.7976931348623157e+308
#endif
#ifndef DBL_MIN_EXP
#define DBL_MIN_EXP (-1021)
#endif
#ifndef DBL_MAX_EXP
#define DBL_MAX_EXP 1024
#endif
#ifndef DBL_MIN_10_EXP
#define DBL_MIN_10_EXP (-307)
#endif
#ifndef DBL_MAX_10_EXP
#define DBL_MAX_10_EXP 308
#endif
#ifndef DBL_DIG
#define DBL_DIG 15
#endif
#ifndef DBL_MANT_DIG
#define DBL_MANT_DIG 53
#endif
#ifndef DBL_EPSILON
#define DBL_EPSILON 2.2204460492503131e-16
#endif
#ifndef USE_RB_INFINITY
#elif !defined(WORDS_BIGENDIAN) /* BYTE_ORDER == LITTLE_ENDIAN */
const union bytesequence4_or_float rb_infinity = {{0x00, 0x00, 0x80, 0x7f}};
#else
const union bytesequence4_or_float rb_infinity = {{0x7f, 0x80, 0x00, 0x00}};
#endif
#ifndef USE_RB_NAN
#elif !defined(WORDS_BIGENDIAN) /* BYTE_ORDER == LITTLE_ENDIAN */
const union bytesequence4_or_float rb_nan = {{0x00, 0x00, 0xc0, 0x7f}};
#else
const union bytesequence4_or_float rb_nan = {{0x7f, 0xc0, 0x00, 0x00}};
#endif
#ifndef HAVE_ROUND
double
round(double x)
{
double f;
if (x > 0.0) {
f = floor(x);
x = f + (x - f >= 0.5);
}
else if (x < 0.0) {
f = ceil(x);
x = f - (f - x >= 0.5);
}
return x;
}
#endif
static double
round_half_up(double x, double s)
{
double f, xs = x * s;
f = round(xs);
if (s == 1.0) return f;
if (x > 0) {
if ((double)((f + 0.5) / s) <= x) f += 1;
x = f;
}
else {
if ((double)((f - 0.5) / s) >= x) f -= 1;
x = f;
}
return x;
}
static double
round_half_down(double x, double s)
{
double f, xs = x * s;
f = round(xs);
if (x > 0) {
if ((double)((f - 0.5) / s) >= x) f -= 1;
x = f;
}
else {
if ((double)((f + 0.5) / s) <= x) f += 1;
x = f;
}
return x;
}
static double
round_half_even(double x, double s)
{
double f, d, xs = x * s;
if (x > 0.0) {
f = floor(xs);
d = xs - f;
if (d > 0.5)
d = 1.0;
else if (d == 0.5 || ((double)((f + 0.5) / s) <= x))
d = fmod(f, 2.0);
else
d = 0.0;
x = f + d;
}
else if (x < 0.0) {
f = ceil(xs);
d = f - xs;
if (d > 0.5)
d = 1.0;
else if (d == 0.5 || ((double)((f - 0.5) / s) >= x))
d = fmod(-f, 2.0);
else
d = 0.0;
x = f - d;
}
return x;
}
static VALUE fix_lshift(long, unsigned long);
static VALUE fix_rshift(long, unsigned long);
static VALUE int_pow(long x, unsigned long y);
static VALUE rb_int_floor(VALUE num, int ndigits);
static VALUE rb_int_ceil(VALUE num, int ndigits);
static VALUE flo_to_i(VALUE num);
static int float_round_overflow(int ndigits, int binexp);
static int float_round_underflow(int ndigits, int binexp);
static ID id_coerce;
#define id_div idDiv
#define id_divmod idDivmod
#define id_to_i idTo_i
#define id_eq idEq
#define id_cmp idCmp
VALUE rb_cNumeric;
VALUE rb_cFloat;
VALUE rb_cInteger;
VALUE rb_eZeroDivError;
VALUE rb_eFloatDomainError;
static ID id_to, id_by;
void
rb_num_zerodiv(void)
{
rb_raise(rb_eZeroDivError, "divided by 0");
}
enum ruby_num_rounding_mode
rb_num_get_rounding_option(VALUE opts)
{
static ID round_kwds[1];
VALUE rounding;
VALUE str;
const char *s;
if (!NIL_P(opts)) {
if (!round_kwds[0]) {
round_kwds[0] = rb_intern_const("half");
}
if (!rb_get_kwargs(opts, round_kwds, 0, 1, &rounding)) goto noopt;
if (SYMBOL_P(rounding)) {
str = rb_sym2str(rounding);
}
else if (NIL_P(rounding)) {
goto noopt;
}
else if (!RB_TYPE_P(str = rounding, T_STRING)) {
str = rb_check_string_type(rounding);
if (NIL_P(str)) goto invalid;
}
rb_must_asciicompat(str);
s = RSTRING_PTR(str);
switch (RSTRING_LEN(str)) {
case 2:
if (rb_memcicmp(s, "up", 2) == 0)
return RUBY_NUM_ROUND_HALF_UP;
break;
case 4:
if (rb_memcicmp(s, "even", 4) == 0)
return RUBY_NUM_ROUND_HALF_EVEN;
if (strncasecmp(s, "down", 4) == 0)
return RUBY_NUM_ROUND_HALF_DOWN;
break;
}
invalid:
rb_raise(rb_eArgError, "invalid rounding mode: % "PRIsVALUE, rounding);
}
noopt:
return RUBY_NUM_ROUND_DEFAULT;
}
/* experimental API */
int
rb_num_to_uint(VALUE val, unsigned int *ret)
{
#define NUMERR_TYPE 1
#define NUMERR_NEGATIVE 2
#define NUMERR_TOOLARGE 3
if (FIXNUM_P(val)) {
long v = FIX2LONG(val);
#if SIZEOF_INT < SIZEOF_LONG
if (v > (long)UINT_MAX) return NUMERR_TOOLARGE;
#endif
if (v < 0) return NUMERR_NEGATIVE;
*ret = (unsigned int)v;
return 0;
}
if (RB_BIGNUM_TYPE_P(val)) {
if (BIGNUM_NEGATIVE_P(val)) return NUMERR_NEGATIVE;
#if SIZEOF_INT < SIZEOF_LONG
/* long is 64bit */
return NUMERR_TOOLARGE;
#else
/* long is 32bit */
if (rb_absint_size(val, NULL) > sizeof(int)) return NUMERR_TOOLARGE;
*ret = (unsigned int)rb_big2ulong((VALUE)val);
return 0;
#endif
}
return NUMERR_TYPE;
}
#define method_basic_p(klass) rb_method_basic_definition_p(klass, mid)
static inline int
int_pos_p(VALUE num)
{
if (FIXNUM_P(num)) {
return FIXNUM_POSITIVE_P(num);
}
else if (RB_BIGNUM_TYPE_P(num)) {
return BIGNUM_POSITIVE_P(num);
}
rb_raise(rb_eTypeError, "not an Integer");
}
static inline int
int_neg_p(VALUE num)
{
if (FIXNUM_P(num)) {
return FIXNUM_NEGATIVE_P(num);
}
else if (RB_BIGNUM_TYPE_P(num)) {
return BIGNUM_NEGATIVE_P(num);
}
rb_raise(rb_eTypeError, "not an Integer");
}
int
rb_int_positive_p(VALUE num)
{
return int_pos_p(num);
}
int
rb_int_negative_p(VALUE num)
{
return int_neg_p(num);
}
int
rb_num_negative_p(VALUE num)
{
return rb_num_negative_int_p(num);
}
static VALUE
num_funcall_op_0(VALUE x, VALUE arg, int recursive)
{
ID func = (ID)arg;
if (recursive) {
const char *name = rb_id2name(func);
if (ISALNUM(name[0])) {
rb_name_error(func, "%"PRIsVALUE".%"PRIsVALUE,
x, ID2SYM(func));
}
else if (name[0] && name[1] == '@' && !name[2]) {
rb_name_error(func, "%c%"PRIsVALUE,
name[0], x);
}
else {
rb_name_error(func, "%"PRIsVALUE"%"PRIsVALUE,
ID2SYM(func), x);
}
}
return rb_funcallv(x, func, 0, 0);
}
static VALUE
num_funcall0(VALUE x, ID func)
{
return rb_exec_recursive(num_funcall_op_0, x, (VALUE)func);
}
NORETURN(static void num_funcall_op_1_recursion(VALUE x, ID func, VALUE y));
static void
num_funcall_op_1_recursion(VALUE x, ID func, VALUE y)
{
const char *name = rb_id2name(func);
if (ISALNUM(name[0])) {
rb_name_error(func, "%"PRIsVALUE".%"PRIsVALUE"(%"PRIsVALUE")",
x, ID2SYM(func), y);
}
else {
rb_name_error(func, "%"PRIsVALUE"%"PRIsVALUE"%"PRIsVALUE,
x, ID2SYM(func), y);
}
}
static VALUE
num_funcall_op_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_funcall(x, func, 1, y);
}
static VALUE
num_funcall1(VALUE x, ID func, VALUE y)
{
VALUE args[2];
args[0] = (VALUE)func;
args[1] = x;
return rb_exec_recursive_paired(num_funcall_op_1, y, x, (VALUE)args);
}
/*
* call-seq:
* coerce(other) -> array
*
* Returns a 2-element array containing two numeric elements,
* formed from the two operands +self+ and +other+,
* of a common compatible type.
*
* Of the Core and Standard Library classes,
* Integer, Rational, and Complex use this implementation.
*
* Examples:
*
* i = 2 # => 2
* i.coerce(3) # => [3, 2]
* i.coerce(3.0) # => [3.0, 2.0]
* i.coerce(Rational(1, 2)) # => [0.5, 2.0]
* i.coerce(Complex(3, 4)) # Raises RangeError.
*
* r = Rational(5, 2) # => (5/2)
* r.coerce(2) # => [(2/1), (5/2)]
* r.coerce(2.0) # => [2.0, 2.5]
* r.coerce(Rational(2, 3)) # => [(2/3), (5/2)]
* r.coerce(Complex(3, 4)) # => [(3+4i), ((5/2)+0i)]
*
* c = Complex(2, 3) # => (2+3i)
* c.coerce(2) # => [(2+0i), (2+3i)]
* c.coerce(2.0) # => [(2.0+0i), (2+3i)]
* c.coerce(Rational(1, 2)) # => [((1/2)+0i), (2+3i)]
* c.coerce(Complex(3, 4)) # => [(3+4i), (2+3i)]
*
* Raises an exception if any type conversion fails.
*
*/
static VALUE
num_coerce(VALUE x, VALUE y)
{
if (CLASS_OF(x) == CLASS_OF(y))
return rb_assoc_new(y, x);
x = rb_Float(x);
y = rb_Float(y);
return rb_assoc_new(y, x);
}
NORETURN(static void coerce_failed(VALUE x, VALUE y));
static void
coerce_failed(VALUE x, VALUE y)
{
if (SPECIAL_CONST_P(y) || SYMBOL_P(y) || RB_FLOAT_TYPE_P(y)) {
y = rb_inspect(y);
}
else {
y = rb_obj_class(y);
}
rb_raise(rb_eTypeError, "%"PRIsVALUE" can't be coerced into %"PRIsVALUE,
y, rb_obj_class(x));
}
static int
do_coerce(VALUE *x, VALUE *y, int err)
{
VALUE ary = rb_check_funcall(*y, id_coerce, 1, x);
if (ary == Qundef) {
if (err) {
coerce_failed(*x, *y);
}
return FALSE;
}
if (!err && NIL_P(ary)) {
return FALSE;
}
if (!RB_TYPE_P(ary, T_ARRAY) || RARRAY_LEN(ary) != 2) {
rb_raise(rb_eTypeError, "coerce must return [x, y]");
}
*x = RARRAY_AREF(ary, 0);
*y = RARRAY_AREF(ary, 1);
return TRUE;
}
VALUE
rb_num_coerce_bin(VALUE x, VALUE y, ID func)
{
do_coerce(&x, &y, TRUE);
return rb_funcall(x, func, 1, y);
}
VALUE
rb_num_coerce_cmp(VALUE x, VALUE y, ID func)
{
if (do_coerce(&x, &y, FALSE))
return rb_funcall(x, func, 1, y);
return Qnil;
}
static VALUE
ensure_cmp(VALUE c, VALUE x, VALUE y)
{
if (NIL_P(c)) rb_cmperr(x, y);
return c;
}
VALUE
rb_num_coerce_relop(VALUE x, VALUE y, ID func)
{
VALUE x0 = x, y0 = y;
if (!do_coerce(&x, &y, FALSE)) {
rb_cmperr(x0, y0);
UNREACHABLE_RETURN(Qnil);
}
return ensure_cmp(rb_funcall(x, func, 1, y), x0, y0);
}
NORETURN(static VALUE num_sadded(VALUE x, VALUE name));
/*
* :nodoc:
*
* Trap attempts to add methods to Numeric objects. Always raises a TypeError.
*
* Numerics should be values; singleton_methods should not be added to them.
*/
static VALUE
num_sadded(VALUE x, VALUE name)
{
ID mid = rb_to_id(name);
/* ruby_frame = ruby_frame->prev; */ /* pop frame for "singleton_method_added" */
rb_remove_method_id(rb_singleton_class(x), mid);
rb_raise(rb_eTypeError,
"can't define singleton method \"%"PRIsVALUE"\" for %"PRIsVALUE,
rb_id2str(mid),
rb_obj_class(x));
UNREACHABLE_RETURN(Qnil);
}
#if 0
/*
* call-seq:
* clone(freeze: true) -> self
*
* Returns +self+.
*
* Raises an exception if the value for +freeze+ is neither +true+ nor +nil+.
*
* Related: Numeric#dup.
*
*/
static VALUE
num_clone(int argc, VALUE *argv, VALUE x)
{
return rb_immutable_obj_clone(argc, argv, x);
}
#else
# define num_clone rb_immutable_obj_clone
#endif
#if 0
/*
* call-seq:
* dup -> self
*
* Returns +self+.
*
* Related: Numeric#clone.
*
*/
static VALUE
num_dup(VALUE x)
{
return x;
}
#else
# define num_dup num_uplus
#endif
/*
* call-seq:
* +self -> self
*
* Returns +self+.
*
*/
static VALUE
num_uplus(VALUE num)
{
return num;
}
/*
* call-seq:
* i -> complex
*
* Returns <tt>Complex(0, self)</tt>:
*
* 2.i # => (0+2i)
* -2.i # => (0-2i)
* 2.0.i # => (0+2.0i)
* Rational(1, 2).i # => (0+(1/2)*i)
* Complex(3, 4).i # Raises NoMethodError.
*
*/
static VALUE
num_imaginary(VALUE num)
{
return rb_complex_new(INT2FIX(0), num);
}
/*
* call-seq:
* -self -> numeric
*
* Unary Minus---Returns the receiver, negated.
*/
static VALUE
num_uminus(VALUE num)
{
VALUE zero;
zero = INT2FIX(0);
do_coerce(&zero, &num, TRUE);
return num_funcall1(zero, '-', num);
}
/*
* call-seq:
* fdiv(other) -> float
*
* Returns the quotient <tt>self/other</tt> as a float,
* using method +/+ in the derived class of +self+.
* (\Numeric itself does not define method +/+.)
*
* Of the Core and Standard Library classes,
* only BigDecimal uses this implementation.
*
*/
static VALUE
num_fdiv(VALUE x, VALUE y)
{
return rb_funcall(rb_Float(x), '/', 1, y);
}
/*
* call-seq:
* div(other) -> integer
*
* Returns the quotient <tt>self/other</tt> as an integer (via +floor+),
* using method +/+ in the derived class of +self+.
* (\Numeric itself does not define method +/+.)
*
* Of the Core and Standard Library classes,
* Float, Rational, and Complex use this implementation.
*
*/
static VALUE
num_div(VALUE x, VALUE y)
{
if (rb_equal(INT2FIX(0), y)) rb_num_zerodiv();
return rb_funcall(num_funcall1(x, '/', y), rb_intern("floor"), 0);
}
/*
* call-seq:
* self % other -> real_numeric
*
* Returns +self+ modulo +other+ as a real number.
*
* Of the Core and Standard Library classes,
* only Rational uses this implementation.
*
* For \Rational +r+ and real number +n+, these expressions are equivalent:
*
* c % n
* c-n*(c/n).floor
* c.divmod(n)[1]
*
* See Numeric#divmod.
*
* Examples:
*
* r = Rational(1, 2) # => (1/2)
* r2 = Rational(2, 3) # => (2/3)
* r % r2 # => (1/2)
* r % 2 # => (1/2)
* r % 2.0 # => 0.5
*
* r = Rational(301,100) # => (301/100)
* r2 = Rational(7,5) # => (7/5)
* r % r2 # => (21/100)
* r % -r2 # => (-119/100)
* (-r) % r2 # => (119/100)
* (-r) %-r2 # => (-21/100)
*
* Numeric#modulo is an alias for Numeric#%.
*
*/
static VALUE
num_modulo(VALUE x, VALUE y)
{
VALUE q = num_funcall1(x, id_div, y);
return rb_funcall(x, '-', 1,
rb_funcall(y, '*', 1, q));
}
/*
* call-seq:
* remainder(other) -> real_number
*
* Returns the remainder after dividing +self+ by +other+.
*
* Of the Core and Standard Library classes,
* only Float and Rational use this implementation.
*
* Examples:
*
* 11.0.remainder(4) # => 3.0
* 11.0.remainder(-4) # => 3.0
* -11.0.remainder(4) # => -3.0
* -11.0.remainder(-4) # => -3.0
*
* 12.0.remainder(4) # => 0.0
* 12.0.remainder(-4) # => 0.0
* -12.0.remainder(4) # => -0.0
* -12.0.remainder(-4) # => -0.0
*
* 13.0.remainder(4.0) # => 1.0
* 13.0.remainder(Rational(4, 1)) # => 1.0
*
* Rational(13, 1).remainder(4) # => (1/1)
* Rational(13, 1).remainder(-4) # => (1/1)
* Rational(-13, 1).remainder(4) # => (-1/1)
* Rational(-13, 1).remainder(-4) # => (-1/1)
*
*/
static VALUE
num_remainder(VALUE x, VALUE y)
{
VALUE z = num_funcall1(x, '%', y);
if ((!rb_equal(z, INT2FIX(0))) &&
((rb_num_negative_int_p(x) &&
rb_num_positive_int_p(y)) ||
(rb_num_positive_int_p(x) &&
rb_num_negative_int_p(y)))) {
if (RB_FLOAT_TYPE_P(y)) {
if (isinf(RFLOAT_VALUE(y))) {
return x;
}
}
return rb_funcall(z, '-', 1, y);
}
return z;
}
/*
* call-seq:
* divmod(other) -> array
*
* Returns a 2-element array <tt>[q, r]</tt>, where
*
* q = (self/other).floor # Quotient
* r = self % other # Remainder
*
* Of the Core and Standard Library classes,
* only Rational uses this implementation.
*
* Examples:
*
* Rational(11, 1).divmod(4) # => [2, (3/1)]
* Rational(11, 1).divmod(-4) # => [-3, (-1/1)]
* Rational(-11, 1).divmod(4) # => [-3, (1/1)]
* Rational(-11, 1).divmod(-4) # => [2, (-3/1)]
*
* Rational(12, 1).divmod(4) # => [3, (0/1)]
* Rational(12, 1).divmod(-4) # => [-3, (0/1)]
* Rational(-12, 1).divmod(4) # => [-3, (0/1)]
* Rational(-12, 1).divmod(-4) # => [3, (0/1)]
*
* Rational(13, 1).divmod(4.0) # => [3, 1.0]
* Rational(13, 1).divmod(Rational(4, 11)) # => [35, (3/11)]
*/
static VALUE
num_divmod(VALUE x, VALUE y)
{
return rb_assoc_new(num_div(x, y), num_modulo(x, y));
}
/*
* call-seq:
* abs -> numeric
*
* Returns the absolute value of +self+.
*
* 12.abs #=> 12
* (-34.56).abs #=> 34.56
* -34.56.abs #=> 34.56
*
* Numeric#magnitude is an alias for Numeric#abs.
*
*/
static VALUE
num_abs(VALUE num)
{
if (rb_num_negative_int_p(num)) {
return num_funcall0(num, idUMinus);
}
return num;
}
/*
* call-seq:
* zero? -> true or false
*
* Returns +true+ if +zero+ has a zero value, +false+ otherwise.
*
* Of the Core and Standard Library classes,
* only Rational and Complex use this implementation.
*
*/
static VALUE
num_zero_p(VALUE num)
{
return rb_equal(num, INT2FIX(0));
}
static VALUE
int_zero_p(VALUE num)
{
if (FIXNUM_P(num)) {
return RBOOL(FIXNUM_ZERO_P(num));
}
assert(RB_BIGNUM_TYPE_P(num));
return RBOOL(rb_bigzero_p(num));
}
VALUE
rb_int_zero_p(VALUE num)
{
return int_zero_p(num);
}
/*
* call-seq:
* nonzero? -> self or nil
*
* Returns +self+ if +self+ is not a zero value, +nil+ otherwise;
* uses method <tt>zero?</tt> for the evaluation.
*
* The returned +self+ allows the method to be chained:
*
* a = %w[z Bb bB bb BB a aA Aa AA A]
* a.sort {|a, b| (a.downcase <=> b.downcase).nonzero? || a <=> b }
* # => ["A", "a", "AA", "Aa", "aA", "BB", "Bb", "bB", "bb", "z"]
*
* Of the Core and Standard Library classes,
* Integer, Float, Rational, and Complex use this implementation.
*
*/
static VALUE
num_nonzero_p(VALUE num)
{
if (RTEST(num_funcall0(num, rb_intern("zero?")))) {
return Qnil;
}
return num;
}
/*
* call-seq:
* to_int -> integer
*
* Returns +self+ as an integer;
* converts using method +to_i+ in the derived class.
*
* Of the Core and Standard Library classes,
* only Rational and Complex use this implementation.
*
* Examples:
*
* Rational(1, 2).to_int # => 0
* Rational(2, 1).to_int # => 2
* Complex(2, 0).to_int # => 2
* Complex(2, 1) # Raises RangeError (non-zero imaginary part)
*
*/
static VALUE
num_to_int(VALUE num)
{
return num_funcall0(num, id_to_i);
}
/*
* call-seq:
* positive? -> true or false
*
* Returns +true+ if +self+ is greater than 0, +false+ otherwise.
*
*/
static VALUE
num_positive_p(VALUE num)
{
const ID mid = '>';
if (FIXNUM_P(num)) {
if (method_basic_p(rb_cInteger))
return RBOOL((SIGNED_VALUE)num > (SIGNED_VALUE)INT2FIX(0));
}
else if (RB_BIGNUM_TYPE_P(num)) {
if (method_basic_p(rb_cInteger))
return RBOOL(BIGNUM_POSITIVE_P(num) && !rb_bigzero_p(num));
}
return rb_num_compare_with_zero(num, mid);
}
/*
* call-seq:
* negative? -> true or false
*
* Returns +true+ if +self+ is less than 0, +false+ otherwise.
*
*/
static VALUE
num_negative_p(VALUE num)
{
return RBOOL(rb_num_negative_int_p(num));
}
/********************************************************************
*
* Document-class: Float
*
* 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));
#if SIZEOF_DOUBLE <= SIZEOF_VALUE
flt->float_value = d;
#else
union {
double d;
rb_float_value_type v;
} u = {d};
flt->float_value = u.v;
#endif
OBJ_FREEZE((VALUE)flt);
return (VALUE)flt;
}
/*
* call-seq:
* 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:
* coerce(other) -> array
*
* Returns a 2-element array containing +other+ converted to a \Float
* and +self+:
*
* f = 3.14 # => 3.14
* f.coerce(2) # => [2.0, 3.14]
* f.coerce(2.0) # => [2.0, 3.14]
* f.coerce(Rational(1, 2)) # => [0.5, 3.14]
* f.coerce(Complex(3, 4)) # Raises RangeError.
*
* Related: Numeric#coerce (for other numeric types).
*
* Raises an exception if a type conversion fails.
*
*/
static VALUE
flo_coerce(VALUE x, VALUE y)
{
return rb_assoc_new(rb_Float(y), x);
}
MJIT_FUNC_EXPORTED VALUE
rb_float_uminus(VALUE flt)
{
return DBL2NUM(-RFLOAT_VALUE(flt));
}
/*
* call-seq:
* float + other -> float
*
* Returns a new Float which is the sum of +float+ and +other+.
*/
VALUE
rb_float_plus(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y));
}
else if (RB_BIGNUM_TYPE_P(y)) {
return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y));
}
else if (RB_FLOAT_TYPE_P(y)) {
return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '+');
}
}
/*
* call-seq:
* float - other -> float
*
* Returns a new Float which is the difference of +float+ and +other+.
*/
VALUE
rb_float_minus(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y));
}
else if (RB_BIGNUM_TYPE_P(y)) {
return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y));
}
else if (RB_FLOAT_TYPE_P(y)) {
return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '-');
}
}
/*
* call-seq:
* float * other -> float
*
* Returns a new Float which is the product of +float+ and +other+.
*/
VALUE
rb_float_mul(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y));
}
else if (RB_BIGNUM_TYPE_P(y)) {
return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y));
}
else if (RB_FLOAT_TYPE_P(y)) {
return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '*');
}
}
static double
double_div_double(double x, double y)
{
if (LIKELY(y != 0.0)) {
return x / y;
}
else if (x == 0.0) {
return nan("");
}
else {
double z = signbit(y) ? -1.0 : 1.0;
return x * z * HUGE_VAL;
}
}
MJIT_FUNC_EXPORTED VALUE
rb_flo_div_flo(VALUE x, VALUE y)
{
double num = RFLOAT_VALUE(x);
double den = RFLOAT_VALUE(y);
double ret = double_div_double(num, den);
return DBL2NUM(ret);
}
/*
* call-seq:
* 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 (FIXNUM_P(y)) {
den = FIX2LONG(y);
}
else if (RB_BIGNUM_TYPE_P(y)) {
den = rb_big2dbl(y);
}
else if (RB_FLOAT_TYPE_P(y)) {
den = RFLOAT_VALUE(y);
}
else {
return rb_num_coerce_bin(x, y, '/');
}
ret = double_div_double(num, den);
return DBL2NUM(ret);
}
/*
* call-seq:
* 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:
* self % other -> float
*
* Returns +self+ modulo +other+ as a float.
*
* For float +f+ and real number +r+, these expressions are equivalent:
*
* f % r
* f-r*(f/r).floor
* f.divmod(r)[1]
*
* See Numeric#divmod.
*
* Examples:
*
* 10.0 % 2 # => 0.0
* 10.0 % 3 # => 1.0
* 10.0 % 4 # => 2.0
*
* 10.0 % -2 # => 0.0
* 10.0 % -3 # => -2.0
* 10.0 % -4 # => -2.0
*
* 10.0 % 4.0 # => 2.0
* 10.0 % Rational(4, 1) # => 2.0
*
* Float#modulo is an alias for Float#%.
*
*/
static VALUE
flo_mod(VALUE x, VALUE y)
{
double fy;
if (FIXNUM_P(y)) {
fy = (double)FIX2LONG(y);
}
else if (RB_BIGNUM_TYPE_P(y)) {
fy = rb_big2dbl(y);
}
else if (RB_FLOAT_TYPE_P(y)) {
fy = RFLOAT_VALUE(y);
}
else {
return rb_num_coerce_bin(x, y, '%');
}
return DBL2NUM(ruby_float_mod(RFLOAT_VALUE(x), fy));
}
static VALUE
dbl2ival(double d)
{
if (FIXABLE(d)) {
return LONG2FIX((long)d);
}
return rb_dbl2big(d);
}
/*
* call-seq:
* divmod(other) -> array
*
* Returns a 2-element array <tt>[q, r]</tt>, where
*
* q = (self/other).floor # Quotient
* r = self % other # Remainder
*
* Examples:
*
* 11.0.divmod(4) # => [2, 3.0]
* 11.0.divmod(-4) # => [-3, -1.0]
* -11.0.divmod(4) # => [-3, 1.0]
* -11.0.divmod(-4) # => [2, -3.0]
*
* 12.0.divmod(4) # => [3, 0.0]
* 12.0.divmod(-4) # => [-3, 0.0]
* -12.0.divmod(4) # => [-3, -0.0]
* -12.0.divmod(-4) # => [3, -0.0]
*
* 13.0.divmod(4.0) # => [3, 1.0]
* 13.0.divmod(Rational(4, 1)) # => [3, 1.0]
*
*/
static VALUE
flo_divmod(VALUE x, VALUE y)
{
double fy, div, mod;
volatile VALUE a, b;
if (FIXNUM_P(y)) {
fy = (double)FIX2LONG(y);
}
else if (RB_BIGNUM_TYPE_P(y)) {
fy = rb_big2dbl(y);
}
else if (RB_FLOAT_TYPE_P(y)) {
fy = RFLOAT_VALUE(y);
}
else {
return rb_num_coerce_bin(x, y, id_divmod);
}
flodivmod(RFLOAT_VALUE(x), fy, &div, &mod);
a = dbl2ival(div);
b = DBL2NUM(mod);
return rb_assoc_new(a, b);
}
/*
* call-seq:
* 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 (FIXNUM_P(y)) {
dx = RFLOAT_VALUE(x);
dy = (double)FIX2LONG(y);
}
else if (RB_BIGNUM_TYPE_P(y)) {
dx = RFLOAT_VALUE(x);
dy = rb_big2dbl(y);
}
else if (RB_FLOAT_TYPE_P(y)) {
dx = RFLOAT_VALUE(x);
dy = RFLOAT_VALUE(y);
if (dx < 0 && dy != round(dy))
return rb_dbl_complex_new_polar_pi(pow(-dx, dy), dy);
}
else {
return rb_num_coerce_bin(x, y, idPow);
}
return DBL2NUM(pow(dx, dy));
}
/*
* call-seq:
* eql?(other) -> true or false
*
* Returns +true+ if +self+ and +other+ are the same type and have equal values.
*
* Of the Core and Standard Library classes,
* only Integer, Rational, and Complex use this implementation.
*
* Examples:
*
* 1.eql?(1) # => true
* 1.eql?(1.0) # => false
* 1.eql?(Rational(1, 1)) # => false
* 1.eql?(Complex(1, 0)) # => false
*
* \Method +eql?+ is different from +==+ in that +eql?+ requires matching types,
* while +==+ does not.
*
*/
static VALUE
num_eql(VALUE x, VALUE y)
{
if (TYPE(x) != TYPE(y)) return Qfalse;
if (RB_BIGNUM_TYPE_P(x)) {
return rb_big_eql(x, y);
}
return rb_equal(x, y);
}
/*
* call-seq:
* self <=> other -> zero or nil
*
* Returns zero if +self+ is the same as +other+, +nil+ otherwise.
*
* No subclass in the Ruby Core or Standard Library uses this implementation.
*
*/
static VALUE
num_cmp(VALUE x, VALUE y)
{
if (x == y) return INT2FIX(0);
return Qnil;
}
static VALUE
num_equal(VALUE x, VALUE y)
{
VALUE result;
if (x == y) return Qtrue;
result = num_funcall1(y, id_eq, x);
return RBOOL(RTEST(result));
}
/*
* call-seq:
* 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_INTEGER_TYPE_P(y)) {
return rb_integer_float_eq(y, x);
}
else if (RB_FLOAT_TYPE_P(y)) {
b = RFLOAT_VALUE(y);
#if MSC_VERSION_BEFORE(1300)
if (isnan(b)) return Qfalse;
#endif
}
else {
return num_equal(x, y);
}
a = RFLOAT_VALUE(x);
#if MSC_VERSION_BEFORE(1300)
if (isnan(a)) return Qfalse;
#endif
return RBOOL(a == b);
}
#define flo_eq rb_float_equal
static VALUE rb_dbl_hash(double d);
/*
* call-seq:
* 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_INTEGER_TYPE_P(y)) {
VALUE rel = rb_integer_float_cmp(y, x);
if (FIXNUM_P(rel))
return LONG2FIX(-FIX2LONG(rel));
return rel;
}
else if (RB_FLOAT_TYPE_P(y)) {
b = RFLOAT_VALUE(y);
}
else {
if (isinf(a) && (i = rb_check_funcall(y, rb_intern("infinite?"), 0, 0)) != Qundef) {
if (RTEST(i)) {
int j = rb_cmpint(i, x, y);
j = (a > 0.0) ? (j > 0 ? 0 : +1) : (j < 0 ? 0 : -1);
return INT2FIX(j);
}
if (a > 0.0) return INT2FIX(1);
return INT2FIX(-1);
}
return rb_num_coerce_cmp(x, y, id_cmp);
}
return rb_dbl_cmp(a, b);
}
MJIT_FUNC_EXPORTED int
rb_float_cmp(VALUE x, VALUE y)
{
return NUM2INT(ensure_cmp(flo_cmp(x, y), x, y));
}
/*
* call-seq:
* 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_INTEGER_TYPE_P(y)) {
VALUE rel = rb_integer_float_cmp(y, x);
if (FIXNUM_P(rel))
return RBOOL(-FIX2LONG(rel) > 0);
return Qfalse;
}
else if (RB_FLOAT_TYPE_P(y)) {
b = RFLOAT_VALUE(y);
#if MSC_VERSION_BEFORE(1300)
if (isnan(b)) return Qfalse;
#endif
}
else {
return rb_num_coerce_relop(x, y, '>');
}
#if MSC_VERSION_BEFORE(1300)
if (isnan(a)) return Qfalse;
#endif
return RBOOL(a > b);
}
/*
* call-seq:
* 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_BIGNUM_TYPE_P(y)) {
VALUE rel = rb_integer_float_cmp(y, x);
if (FIXNUM_P(rel))
return RBOOL(-FIX2LONG(rel) >= 0);
return Qfalse;
}
else if (RB_FLOAT_TYPE_P(y)) {
b = RFLOAT_VALUE(y);
#if MSC_VERSION_BEFORE(1300)
if (isnan(b)) return Qfalse;
#endif
}
else {
return rb_num_coerce_relop(x, y, idGE);
}
#if MSC_VERSION_BEFORE(1300)
if (isnan(a)) return Qfalse;
#endif
return RBOOL(a >= b);
}
/*
* call-seq:
* 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_INTEGER_TYPE_P(y)) {
VALUE rel = rb_integer_float_cmp(y, x);
if (FIXNUM_P(rel))
return RBOOL(-FIX2LONG(rel) < 0);
return Qfalse;
}
else if (RB_FLOAT_TYPE_P(y)) {
b = RFLOAT_VALUE(y);
#if MSC_VERSION_BEFORE(1300)
if (isnan(b)) return Qfalse;
#endif
}
else {
return rb_num_coerce_relop(x, y, '<');
}
#if MSC_VERSION_BEFORE(1300)
if (isnan(a)) return Qfalse;
#endif
return RBOOL(a < b);
}
/*
* call-seq:
* 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_INTEGER_TYPE_P(y)) {
VALUE rel = rb_integer_float_cmp(y, x);
if (FIXNUM_P(rel))
return RBOOL(-FIX2LONG(rel) <= 0);
return Qfalse;
}
else if (RB_FLOAT_TYPE_P(y)) {
b = RFLOAT_VALUE(y);
#if MSC_VERSION_BEFORE(1300)
if (isnan(b)) return Qfalse;
#endif
}
else {
return rb_num_coerce_relop(x, y, idLE);
}
#if MSC_VERSION_BEFORE(1300)
if (isnan(a)) return Qfalse;
#endif
return RBOOL(a <= b);
}
/*
* call-seq:
* 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_FLOAT_TYPE_P(y)) {
double a = RFLOAT_VALUE(x);
double b = RFLOAT_VALUE(y);
#if MSC_VERSION_BEFORE(1300)
if (isnan(a) || isnan(b)) return Qfalse;
#endif
return RBOOL(a == b);
}
return Qfalse;
}
#define flo_eql rb_float_eql
MJIT_FUNC_EXPORTED VALUE
rb_float_abs(VALUE flt)
{
double val = fabs(RFLOAT_VALUE(flt));
return DBL2NUM(val);
}
/*
* call-seq:
* 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);
return RBOOL(isfinite(value));
}
static VALUE
flo_nextafter(VALUE flo, double value)
{
double x, y;
x = NUM2DBL(flo);
y = nextafter(x, value);
return DBL2NUM(y);
}
/*
* call-seq:
* 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 int
flo_ndigits(int argc, VALUE *argv)
{
if (rb_check_arity(argc, 0, 1)) {
return NUM2INT(argv[0]);
}
return 0;
}
static VALUE
flo_floor(int argc, VALUE *argv, VALUE num)
{
int ndigits = flo_ndigits(argc, argv);
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 = flo_ndigits(argc, argv);
return rb_float_ceil(num, ndigits);
}
VALUE
rb_float_ceil(VALUE num, int ndigits)
{
double number, f;
number = RFLOAT_VALUE(num);
if (number == 0.0) {
return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0);
}
if (ndigits > 0) {
int binexp;
frexp(number, &binexp);
if (float_round_overflow(ndigits, binexp)) return num;
if (number < 0.0 && float_round_underflow(ndigits, binexp))
return DBL2NUM(0.0);
f = pow(10, ndigits);
f = ceil(number * f) / f;
return DBL2NUM(f);
}
else {
num = dbl2ival(ceil(number));
if (ndigits < 0) num = rb_int_ceil(num, ndigits);
return num;
}
}
static int
int_round_zero_p(VALUE num, int ndigits)
{
long bytes;
/* If 10**N / 2 > num, then return 0 */
/* We have log_256(10) > 0.415241 and log_256(1/2) = -0.125, so */
if (FIXNUM_P(num)) {
bytes = sizeof(long);
}
else if (RB_BIGNUM_TYPE_P(num)) {
bytes = rb_big_size(num);
}
else {
bytes = NUM2LONG(rb_funcall(num, idSize, 0));
}
return (-0.415241 * ndigits - 0.125 > bytes);
}
static SIGNED_VALUE
int_round_half_even(SIGNED_VALUE x, SIGNED_VALUE y)
{
SIGNED_VALUE z = +(x + y / 2) / y;
if ((z * y - x) * 2 == y) {
z &= ~1;
}
return z * y;
}
static SIGNED_VALUE
int_round_half_up(SIGNED_VALUE x, SIGNED_VALUE y)
{
return (x + y / 2) / y * y;
}
static SIGNED_VALUE
int_round_half_down(SIGNED_VALUE x, SIGNED_VALUE y)
{
return (x + y / 2 - 1) / y * y;
}
static int
int_half_p_half_even(VALUE num, VALUE n, VALUE f)
{
return (int)rb_int_odd_p(rb_int_idiv(n, f));
}
static int
int_half_p_half_up(VALUE num, VALUE n, VALUE f)
{
return int_pos_p(num);
}
static int
int_half_p_half_down(VALUE num, VALUE n, VALUE f)
{
return int_neg_p(num);
}
/*
* Assumes num is an Integer, ndigits <= 0
*/
static VALUE
rb_int_round(VALUE num, int ndigits, enum ruby_num_rounding_mode mode)
{
VALUE n, f, h, r;
if (int_round_zero_p(num, ndigits)) {
return INT2FIX(0);
}
f = int_pow(10, -ndigits);
if (FIXNUM_P(num) && FIXNUM_P(f)) {
SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f);
int neg = x < 0;
if (neg) x = -x;
x = ROUND_CALL(mode, int_round, (x, y));
if (neg) x = -x;
return LONG2NUM(x);
}
if (RB_FLOAT_TYPE_P(f)) {
/* then int_pow overflow */
return INT2FIX(0);
}
h = rb_int_idiv(f, INT2FIX(2));
r = rb_int_modulo(num, f);
n = rb_int_minus(num, r);
r = rb_int_cmp(r, h);
if (FIXNUM_POSITIVE_P(r) ||
(FIXNUM_ZERO_P(r) && ROUND_CALL(mode, int_half_p, (num, n, f)))) {
n = rb_int_plus(n, f);
}
return n;
}
static VALUE
rb_int_floor(VALUE num, int ndigits)
{
VALUE f;
if (int_round_zero_p(num, ndigits))
return INT2FIX(0);
f = int_pow(10, -ndigits);
if (FIXNUM_P(num) && FIXNUM_P(f)) {
SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f);
int neg = x < 0;
if (neg) x = -x + y - 1;
x = x / y * y;
if (neg) x = -x;
return LONG2NUM(x);
}
if (RB_FLOAT_TYPE_P(f)) {
/* then int_pow overflow */
return INT2FIX(0);
}
return rb_int_minus(num, rb_int_modulo(num, f));
}
static VALUE
rb_int_ceil(VALUE num, int ndigits)
{
VALUE f;
if (int_round_zero_p(num, ndigits))
return INT2FIX(0);
f = int_pow(10, -ndigits);
if (FIXNUM_P(num) && FIXNUM_P(f)) {
SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f);
int neg = x < 0;
if (neg) x = -x;
else x += y - 1;
x = (x / y) * y;
if (neg) x = -x;
return LONG2NUM(x);
}
if (RB_FLOAT_TYPE_P(f)) {
/* then int_pow overflow */
return INT2FIX(0);
}
return rb_int_plus(num, rb_int_minus(f, rb_int_modulo(num, f)));
}
VALUE
rb_int_truncate(VALUE num, int ndigits)
{
VALUE f;
VALUE m;
if (int_round_zero_p(num, ndigits))
return INT2FIX(0);
f = int_pow(10, -ndigits);
if (FIXNUM_P(num) && FIXNUM_P(f)) {
SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f);
int neg = x < 0;
if (neg) x = -x;
x = x / y * y;
if (neg) x = -x;
return LONG2NUM(x);
}
if (RB_FLOAT_TYPE_P(f)) {
/* then int_pow overflow */
return INT2FIX(0);
}
m = rb_int_modulo(num, f);
if (int_neg_p(num)) {
return rb_int_plus(num, rb_int_minus(f, m));
}
else {
return rb_int_minus(num, m);
}
}
/*
* call-seq:
* 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:
* floor(digits = 0) -> integer or float
*
* Returns the largest number that is less than or equal to +self+ with
* a precision of +digits+ decimal digits.
*
* \Numeric implements this by converting +self+ to a Float and
* invoking Float#floor.
*/
static VALUE
num_floor(int argc, VALUE *argv, VALUE num)
{
return flo_floor(argc, argv, rb_Float(num));
}
/*
* call-seq:
* ceil(digits = 0) -> integer or float
*
* Returns the smallest number that is greater than or equal to +self+ with
* a precision of +digits+ decimal digits.
*
* \Numeric implements this by converting +self+ to a Float and
* invoking Float#ceil.
*/
static VALUE
num_ceil(int argc, VALUE *argv, VALUE num)
{
return flo_ceil(argc, argv, rb_Float(num));
}
/*
* call-seq:
* round(digits = 0) -> integer or float
*
* Returns +self+ rounded to the nearest value with
* a precision of +digits+ decimal digits.
*
* \Numeric implements this by converting +self+ to a Float and
* invoking Float#round.
*/
static VALUE
num_round(int argc, VALUE* argv, VALUE num)
{
return flo_round(argc, argv, rb_Float(num));
}
/*
* call-seq:
* truncate(digits = 0) -> integer or float
*
* Returns +self+ truncated (toward zero) to
* a precision of +digits+ decimal digits.
*
* \Numeric implements this by converting +self+ to a Float and
* invoking Float#truncate.
*/
static VALUE
num_truncate(int argc, VALUE *argv, VALUE num)
{
return flo_truncate(argc, argv, rb_Float(num));
}
double
ruby_float_step_size(double beg, double end, double unit, int excl)
{
const double epsilon = DBL_EPSILON;
double 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_FLOAT_TYPE_P(from) || RB_FLOAT_TYPE_P(to) || RB_FLOAT_TYPE_P(step)) {
double unit = NUM2DBL(step);
double beg = NUM2DBL(from);
double end = (allow_endless && NIL_P(to)) ? (unit < 0 ? -1 : 1)*HUGE_VAL : NUM2DBL(to);
double n = ruby_float_step_size(beg, end, unit, excl);
long i;
if (isinf(unit)) {
/* if unit is infinity, i*unit+beg is NaN */
if (n) rb_yield(DBL2NUM(beg));
}
else if (unit == 0) {
VALUE val = DBL2NUM(beg);
for (;;)
rb_yield(val);
}
else {
for (i=0; i<n; i++) {
double d = i*unit+beg;
if (unit >= 0 ? end < d : d < end) d = end;
rb_yield(DBL2NUM(d));
}
}
return TRUE;
}
return FALSE;
}
VALUE
ruby_num_interval_step_size(VALUE from, VALUE to, VALUE step, int excl)
{
if (FIXNUM_P(from) && FIXNUM_P(to) && FIXNUM_P(step)) {
long delta, diff;
diff = FIX2LONG(step);
if (diff == 0) {
return DBL2NUM(HUGE_VAL);
}
delta = FIX2LONG(to) - FIX2LONG(from);
if (diff < 0) {
diff = -diff;
delta = -delta;
}
if (excl) {
delta--;
}
if (delta < 0) {
return INT2FIX(0);
}
return ULONG2NUM(delta / diff + 1UL);
}
else if (RB_FLOAT_TYPE_P(from) || RB_FLOAT_TYPE_P(to) || RB_FLOAT_TYPE_P(step)) {
double n = ruby_float_step_size(NUM2DBL(from), NUM2DBL(to), NUM2DBL(step), excl);
if (isinf(n)) return DBL2NUM(n);
if (POSFIXABLE(n)) return LONG2FIX((long)n);
return rb_dbl2big(n);
}
else {
VALUE result;
ID cmp = '>';
switch (rb_cmpint(rb_num_coerce_cmp(step, INT2FIX(0), id_cmp), step, INT2FIX(0))) {
case 0: return DBL2NUM(HUGE_VAL);
case -1: cmp = '<'; break;
}
if (RTEST(rb_funcall(from, cmp, 1, to))) return INT2FIX(0);
result = rb_funcall(rb_funcall(to, '-', 1, from), id_div, 1, step);
if (!excl || RTEST(rb_funcall(rb_funcall(from, '+', 1, rb_funcall(result, '*', 1, step)), cmp, 1, to))) {
result = rb_funcall(result, '+', 1, INT2FIX(1));
}
return result;
}
}
static int
num_step_negative_p(VALUE num)
{
const ID mid = '<';
VALUE zero = INT2FIX(0);
VALUE r;
if (FIXNUM_P(num)) {
if (method_basic_p(rb_cInteger))
return (SIGNED_VALUE)num < 0;
}
else if (RB_BIGNUM_TYPE_P(num)) {
if (method_basic_p(rb_cInteger))
return BIGNUM_NEGATIVE_P(num);
}
r = rb_check_funcall(num, '>', 1, &zero);
if (r == Qundef) {
coerce_failed(num, INT2FIX(0));
}
return !RTEST(r);
}
static int
num_step_extract_args(int argc, const VALUE *argv, VALUE *to, VALUE *step, VALUE *by)
{
VALUE hash;
argc = rb_scan_args(argc, argv, "02:", to, step, &hash);
if (!NIL_P(hash)) {
ID keys[2];
VALUE values[2];
keys[0] = id_to;
keys[1] = id_by;
rb_get_kwargs(hash, keys, 0, 2, values);
if (values[0] != Qundef) {
if (argc > 0) rb_raise(rb_eArgError, "to is given twice");
*to = values[0];
}
if (values[1] != Qundef) {
if (argc > 1) rb_raise(rb_eArgError, "step is given twice");
*by = values[1];
}
}
return argc;
}
static int
num_step_check_fix_args(int argc, VALUE *to, VALUE *step, VALUE by, int fix_nil, int allow_zero_step)
{
int desc;
if (by != Qundef) {
*step = by;
}
else {
/* compatibility */
if (argc > 1 && NIL_P(*step)) {
rb_raise(rb_eTypeError, "step must be numeric");
}
}
if (!allow_zero_step && rb_equal(*step, INT2FIX(0))) {
rb_raise(rb_eArgError, "step can't be 0");
}
if (NIL_P(*step)) {
*step = INT2FIX(1);
}
desc = num_step_negative_p(*step);
if (fix_nil && NIL_P(*to)) {
*to = desc ? DBL2NUM(-HUGE_VAL) : DBL2NUM(HUGE_VAL);
}
return desc;
}
static int
num_step_scan_args(int argc, const VALUE *argv, VALUE *to, VALUE *step, int fix_nil, int allow_zero_step)
{
VALUE by = Qundef;
argc = num_step_extract_args(argc, argv, to, step, &by);
return num_step_check_fix_args(argc, to, step, by, fix_nil, allow_zero_step);
}
static VALUE
num_step_size(VALUE from, VALUE args, VALUE eobj)
{
VALUE to, step;
int argc = args ? RARRAY_LENINT(args) : 0;
const VALUE *argv = args ? RARRAY_CONST_PTR(args) : 0;
num_step_scan_args(argc, argv, &to, &step, TRUE, FALSE);
return ruby_num_interval_step_size(from, to, step, FALSE);
}
/*
* call-seq:
* step(to = nil, by = 1) {|n| ... } -> self
* step(to = nil, by = 1) -> enumerator
* step(to = nil, by: 1) {|n| ... } -> self
* step(to = nil, by: 1) -> enumerator
* step(by: 1, to: ) {|n| ... } -> self
* step(by: 1, to: ) -> enumerator
* step(by: , to: nil) {|n| ... } -> self
* step(by: , to: nil) -> enumerator
*
* Generates a sequence of numbers; with a block given, traverses the sequence.
*
* Of the Core and Standard Library classes,
* Integer, Float, and Rational use this implementation.
*
* A quick example:
*
* squares = []
* 1.step(by: 2, to: 10) {|i| squares.push(i*i) }
* squares # => [1, 9, 25, 49, 81]
*
* The generated sequence:
*
* - Begins with +self+.
* - Continues at intervals of +step+ (which may not be zero).
* - Ends with the last number that is within or equal to +limit+;
* that is, less than or equal to +limit+ if +step+ is positive,
* greater than or equal to +limit+ if +step+ is negative.
* If +limit+ is not given, the sequence is of infinite length.
*
* If a block is given, calls the block with each number in the sequence;
* returns +self+. If no block is given, returns an Enumerator::ArithmeticSequence.
*
* <b>Keyword Arguments</b>
*
* With keyword arguments +by+ and +to+,
* their values (or defaults) determine the step and limit:
*
* # Both keywords given.
* squares = []
* 4.step(by: 2, to: 10) {|i| squares.push(i*i) } # => 4
* squares # => [16, 36, 64, 100]
* cubes = []
* 3.step(by: -1.5, to: -3) {|i| cubes.push(i*i*i) } # => 3
* cubes # => [27.0, 3.375, 0.0, -3.375, -27.0]
* squares = []
* 1.2.step(by: 0.2, to: 2.0) {|f| squares.push(f*f) }
* squares # => [1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4.0]
*
* squares = []
* Rational(6/5).step(by: 0.2, to: 2.0) {|r| squares.push(r*r) }
* squares # => [1.0, 1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4.0]
*
* # Only keyword to given.
* squares = []
* 4.step(to: 10) {|i| squares.push(i*i) } # => 4
* squares # => [16, 25, 36, 49, 64, 81, 100]
* # Only by given.
*
* # Only keyword by given
* squares = []
* 4.step(by:2) {|i| squares.push(i*i); break if i > 10 }
* squares # => [16, 36, 64, 100, 144]
*
* # No block given.
* e = 3.step(by: -1.5, to: -3) # => (3.step(by: -1.5, to: -3))
* e.class # => Enumerator::ArithmeticSequence
*
* <b>Positional Arguments</b>
*
* With optional positional arguments +limit+ and +step+,
* their values (or defaults) determine the step and limit:
*
* squares = []
* 4.step(10, 2) {|i| squares.push(i*i) } # => 4
* squares # => [16, 36, 64, 100]
* squares = []
* 4.step(10) {|i| squares.push(i*i) }
* squares # => [16, 25, 36, 49, 64, 81, 100]
* squares = []
* 4.step {|i| squares.push(i*i); break if i > 10 } # => nil
* squares # => [16, 25, 36, 49, 64, 81, 100, 121]
*
* <b>Implementation Notes</b>
*
* If all the arguments are integers, the loop operates using an integer
* counter.
*
* If any of the arguments are floating point numbers, all are converted
* to floats, and the loop is executed
* <i>floor(n + n*Float::EPSILON) + 1</i> times,
* where <i>n = (limit - self)/step</i>.
*
*/
static VALUE
num_step(int argc, VALUE *argv, VALUE from)
{
VALUE to, step;
int desc, inf;
if (!rb_block_given_p()) {
VALUE by = Qundef;
num_step_extract_args(argc, argv, &to, &step, &by);
if (by != Qundef) {
step = by;
}
if (NIL_P(step)) {
step = INT2FIX(1);
}
else if (rb_equal(step, INT2FIX(0))) {
rb_raise(rb_eArgError, "step can't be 0");
}
if ((NIL_P(to) || rb_obj_is_kind_of(to, rb_cNumeric)) &&
rb_obj_is_kind_of(step, rb_cNumeric)) {
return rb_arith_seq_new(from, ID2SYM(rb_frame_this_func()), argc, argv,
num_step_size, from, to, step, FALSE);
}
return SIZED_ENUMERATOR(from, 2, ((VALUE [2]){to, step}), num_step_size);
}
desc = num_step_scan_args(argc, argv, &to, &step, TRUE, FALSE);
if (rb_equal(step, INT2FIX(0))) {
inf = 1;
}
else if (RB_FLOAT_TYPE_P(to)) {
double f = RFLOAT_VALUE(to);
inf = isinf(f) && (signbit(f) ? desc : !desc);
}
else inf = 0;
if (FIXNUM_P(from) && (inf || FIXNUM_P(to)) && FIXNUM_P(step)) {
long i = FIX2LONG(from);
long diff = FIX2LONG(step);
if (inf) {
for (;; i += diff)
rb_yield(LONG2FIX(i));
}
else {
long end = FIX2LONG(to);
if (desc) {
for (; i >= end; i += diff)
rb_yield(LONG2FIX(i));
}
else {
for (; i <= end; i += diff)
rb_yield(LONG2FIX(i));
}
}
}
else if (!ruby_float_step(from, to, step, FALSE, FALSE)) {
VALUE i = from;
if (inf) {
for (;; i = rb_funcall(i, '+', 1, step))
rb_yield(i);
}
else {
ID cmp = desc ? '<' : '>';
for (; !RTEST(rb_funcall(i, cmp, 1, to)); i = rb_funcall(i, '+', 1, step))
rb_yield(i);
}
}
return from;
}
static char *
out_of_range_float(char (*pbuf)[24], VALUE val)
{
char *const buf = *pbuf;
char *s;
snprintf(buf, sizeof(*pbuf), "%-.10g", RFLOAT_VALUE(val));
if ((s = strchr(buf, ' ')) != 0) *s = '\0';
return buf;
}
#define FLOAT_OUT_OF_RANGE(val, type) do { \
char buf[24]; \
rb_raise(rb_eRangeError, "float %s out of range of "type, \
out_of_range_float(&buf, (val))); \
} while (0)
#define LONG_MIN_MINUS_ONE ((double)LONG_MIN-1)
#define LONG_MAX_PLUS_ONE (2*(double)(LONG_MAX/2+1))
#define ULONG_MAX_PLUS_ONE (2*(double)(ULONG_MAX/2+1))
#define LONG_MIN_MINUS_ONE_IS_LESS_THAN(n) \
(LONG_MIN_MINUS_ONE == (double)LONG_MIN ? \
LONG_MIN <= (n): \
LONG_MIN_MINUS_ONE < (n))
long
rb_num2long(VALUE val)
{
again:
if (NIL_P(val)) {
rb_raise(rb_eTypeError, "no implicit conversion from nil to integer");
}
if (FIXNUM_P(val)) return FIX2LONG(val);
else if (RB_FLOAT_TYPE_P(val)) {
if (RFLOAT_VALUE(val) < LONG_MAX_PLUS_ONE
&& LONG_MIN_MINUS_ONE_IS_LESS_THAN(RFLOAT_VALUE(val))) {
return (long)RFLOAT_VALUE(val);
}
else {
FLOAT_OUT_OF_RANGE(val, "integer");
}
}
else if (RB_BIGNUM_TYPE_P(val)) {
return rb_big2long(val);
}
else {
val = rb_to_int(val);
goto again;
}
}
static unsigned long
rb_num2ulong_internal(VALUE val, int *wrap_p)
{
again:
if (NIL_P(val)) {
rb_raise(rb_eTypeError, "no implicit conversion from nil to integer");
}
if (FIXNUM_P(val)) {
long l = FIX2LONG(val); /* this is FIX2LONG, intended */
if (wrap_p)
*wrap_p = l < 0;
return (unsigned long)l;
}
else if (RB_FLOAT_TYPE_P(val)) {
double d = RFLOAT_VALUE(val);
if (d < ULONG_MAX_PLUS_ONE && LONG_MIN_MINUS_ONE_IS_LESS_THAN(d)) {
if (wrap_p)
*wrap_p = d <= -1.0; /* NUM2ULONG(v) uses v.to_int conceptually. */
if (0 <= d)
return (unsigned long)d;
return (unsigned long)(long)d;
}
else {
FLOAT_OUT_OF_RANGE(val, "integer");
}
}
else if (RB_BIGNUM_TYPE_P(val)) {
{
unsigned long ul = rb_big2ulong(val);
if (wrap_p)
*wrap_p = BIGNUM_NEGATIVE_P(val);
return ul;
}
}
else {
val = rb_to_int(val);
goto again;
}
}
unsigned long
rb_num2ulong(VALUE val)
{
return rb_num2ulong_internal(val, NULL);
}
void
rb_out_of_int(SIGNED_VALUE num)
{
rb_raise(rb_eRangeError, "integer %"PRIdVALUE " too %s to convert to `int'",
num, num < 0 ? "small" : "big");
}
#if SIZEOF_INT < SIZEOF_LONG
static void
check_int(long num)
{
if ((long)(int)num != num) {
rb_out_of_int(num);
}
}
static void
check_uint(unsigned long num, int sign)
{
if (sign) {
/* minus */
if (num < (unsigned long)INT_MIN)
rb_raise(rb_eRangeError, "integer %ld too small to convert to `unsigned int'", (long)num);
}
else {
/* plus */
if (UINT_MAX < num)
rb_raise(rb_eRangeError, "integer %lu too big to convert to `unsigned int'", num);
}
}
long
rb_num2int(VALUE val)
{
long num = rb_num2long(val);
check_int(num);
return num;
}
long
rb_fix2int(VALUE val)
{
long num = FIXNUM_P(val)?FIX2LONG(val):rb_num2long(val);
check_int(num);
return num;
}
unsigned long
rb_num2uint(VALUE val)
{
int wrap;
unsigned long num = rb_num2ulong_internal(val, &wrap);
check_uint(num, wrap);
return num;
}
unsigned long
rb_fix2uint(VALUE val)
{
unsigned long num;
if (!FIXNUM_P(val)) {
return rb_num2uint(val);
}
num = FIX2ULONG(val);
check_uint(num, FIXNUM_NEGATIVE_P(val));
return num;
}
#else
long
rb_num2int(VALUE val)
{
return rb_num2long(val);
}
long
rb_fix2int(VALUE val)
{
return FIX2INT(val);
}
unsigned long
rb_num2uint(VALUE val)
{
return rb_num2ulong(val);
}
unsigned long
rb_fix2uint(VALUE val)
{
return RB_FIX2ULONG(val);
}
#endif
NORETURN(static void rb_out_of_short(SIGNED_VALUE num));
static void
rb_out_of_short(SIGNED_VALUE num)
{
rb_raise(rb_eRangeError, "integer %"PRIdVALUE " too %s to convert to `short'",
num, num < 0 ? "small" : "big");
}
static void
check_short(long num)
{
if ((long)(short)num != num) {
rb_out_of_short(num);
}
}
static void
check_ushort(unsigned long num, int sign)
{
if (sign) {
/* minus */
if (num < (unsigned long)SHRT_MIN)
rb_raise(rb_eRangeError, "integer %ld too small to convert to `unsigned short'", (long)num);
}
else {
/* plus */
if (USHRT_MAX < num)
rb_raise(rb_eRangeError, "integer %lu too big to convert to `unsigned short'", num);
}
}
short
rb_num2short(VALUE val)
{
long num = rb_num2long(val);
check_short(num);
return num;
}
short
rb_fix2short(VALUE val)
{
long num = FIXNUM_P(val)?FIX2LONG(val):rb_num2long(val);
check_short(num);
return num;
}
unsigned short
rb_num2ushort(VALUE val)
{
int wrap;
unsigned long num = rb_num2ulong_internal(val, &wrap);
check_ushort(num, wrap);
return num;
}
unsigned short
rb_fix2ushort(VALUE val)
{
unsigned long num;
if (!FIXNUM_P(val)) {
return rb_num2ushort(val);
}
num = FIX2ULONG(val);
check_ushort(num, FIXNUM_NEGATIVE_P(val));
return num;
}
VALUE
rb_num2fix(VALUE val)
{
long v;
if (FIXNUM_P(val)) return val;
v = rb_num2long(val);
if (!FIXABLE(v))
rb_raise(rb_eRangeError, "integer %ld out of range of fixnum", v);
return LONG2FIX(v);
}
#if HAVE_LONG_LONG
#define LLONG_MIN_MINUS_ONE ((double)LLONG_MIN-1)
#define LLONG_MAX_PLUS_ONE (2*(double)(LLONG_MAX/2+1))
#define ULLONG_MAX_PLUS_ONE (2*(double)(ULLONG_MAX/2+1))
#ifndef ULLONG_MAX
#define ULLONG_MAX ((unsigned LONG_LONG)LLONG_MAX*2+1)
#endif
#define LLONG_MIN_MINUS_ONE_IS_LESS_THAN(n) \
(LLONG_MIN_MINUS_ONE == (double)LLONG_MIN ? \
LLONG_MIN <= (n): \
LLONG_MIN_MINUS_ONE < (n))
LONG_LONG
rb_num2ll(VALUE val)
{
if (NIL_P(val)) {
rb_raise(rb_eTypeError, "no implicit conversion from nil");
}
if (FIXNUM_P(val)) return (LONG_LONG)FIX2LONG(val);
else if (RB_FLOAT_TYPE_P(val)) {
double d = RFLOAT_VALUE(val);
if (d < LLONG_MAX_PLUS_ONE && (LLONG_MIN_MINUS_ONE_IS_LESS_THAN(d))) {
return (LONG_LONG)d;
}
else {
FLOAT_OUT_OF_RANGE(val, "long long");
}
}
else if (RB_BIGNUM_TYPE_P(val)) {
return rb_big2ll(val);
}
else if (RB_TYPE_P(val, T_STRING)) {
rb_raise(rb_eTypeError, "no implicit conversion from string");
}
else if (RB_TYPE_P(val, T_TRUE) || RB_TYPE_P(val, T_FALSE)) {
rb_raise(rb_eTypeError, "no implicit conversion from boolean");
}
val = rb_to_int(val);
return NUM2LL(val);
}
unsigned LONG_LONG
rb_num2ull(VALUE val)
{
if (NIL_P(val)) {
rb_raise(rb_eTypeError, "no implicit conversion from nil");
}
else if (FIXNUM_P(val)) {
return (LONG_LONG)FIX2LONG(val); /* this is FIX2LONG, intended */
}
else if (RB_FLOAT_TYPE_P(val)) {
double d = RFLOAT_VALUE(val);
if (d < ULLONG_MAX_PLUS_ONE && LLONG_MIN_MINUS_ONE_IS_LESS_THAN(d)) {
if (0 <= d)
return (unsigned LONG_LONG)d;
return (unsigned LONG_LONG)(LONG_LONG)d;
}
else {
FLOAT_OUT_OF_RANGE(val, "unsigned long long");
}
}
else if (RB_BIGNUM_TYPE_P(val)) {
return rb_big2ull(val);
}
else if (RB_TYPE_P(val, T_STRING)) {
rb_raise(rb_eTypeError, "no implicit conversion from string");
}
else if (RB_TYPE_P(val, T_TRUE) || RB_TYPE_P(val, T_FALSE)) {
rb_raise(rb_eTypeError, "no implicit conversion from boolean");
}
val = rb_to_int(val);
return NUM2ULL(val);
}
#endif /* HAVE_LONG_LONG */
/********************************************************************
*
* Document-class: Integer
*
* 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_BIGNUM_TYPE_P(num));
return rb_big_odd_p(num);
}
}
static VALUE
int_even_p(VALUE num)
{
if (FIXNUM_P(num)) {
return RBOOL((num & 2) == 0);
}
else {
assert(RB_BIGNUM_TYPE_P(num));
return rb_big_even_p(num);
}
}
VALUE
rb_int_even_p(VALUE num)
{
return int_even_p(num);
}
/*
* call-seq:
* 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_BIGNUM_TYPE_P(num)) {
return rb_big_plus(num, INT2FIX(1));
}
return num_funcall1(num, '+', INT2FIX(1));
}
#define int_succ rb_int_succ
/*
* call-seq:
* 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_BIGNUM_TYPE_P(num)) {
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_BIGNUM_TYPE_P(num));
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_BIGNUM_TYPE_P(x)) {
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_BIGNUM_TYPE_P(y)) {
return rb_big_plus(y, x);
}
else if (RB_FLOAT_TYPE_P(y)) {
return DBL2NUM((double)FIX2LONG(x) + RFLOAT_VALUE(y));
}
else if (RB_TYPE_P(y, T_COMPLEX)) {
return rb_complex_plus(y, x);
}
else {
return rb_num_coerce_bin(x, y, '+');
}
}
VALUE
rb_fix_plus(VALUE x, VALUE y)
{
return fix_plus(x, y);
}
VALUE
rb_int_plus(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_plus(x, y);
}
else if (RB_BIGNUM_TYPE_P(x)) {
return rb_big_plus(x, y);
}
return rb_num_coerce_bin(x, y, '+');
}
/*
* 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_BIGNUM_TYPE_P(y)) {
x = rb_int2big(FIX2LONG(x));
return rb_big_minus(x, y);
}
else if (RB_FLOAT_TYPE_P(y)) {
return DBL2NUM((double)FIX2LONG(x) - RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '-');
}
}
VALUE
rb_int_minus(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_minus(x, y);
}
else if (RB_BIGNUM_TYPE_P(x)) {
return rb_big_minus(x, y);
}
return rb_num_coerce_bin(x, y, '-');
}
#define SQRT_LONG_MAX HALF_LONG_MSB
/*tests if N*N would overflow*/
#define FIT_SQRT_LONG(n) (((n)<SQRT_LONG_MAX)&&((n)>=-SQRT_LONG_MAX))
/*
* 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_BIGNUM_TYPE_P(y)) {
switch (x) {
case INT2FIX(0): return x;
case INT2FIX(1): return y;
}
return rb_big_mul(y, x);
}
else if (RB_FLOAT_TYPE_P(y)) {
return DBL2NUM((double)FIX2LONG(x) * RFLOAT_VALUE(y));
}
else if (RB_TYPE_P(y, T_COMPLEX)) {
return rb_complex_mul(y, x);
}
else {
return rb_num_coerce_bin(x, y, '*');
}
}
VALUE
rb_int_mul(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_mul(x, y);
}
else if (RB_BIGNUM_TYPE_P(x)) {
return rb_big_mul(x, y);
}
return rb_num_coerce_bin(x, y, '*');
}
static double
fix_fdiv_double(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
return double_div_double(FIX2LONG(x), FIX2LONG(y));
}
else if (RB_BIGNUM_TYPE_P(y)) {
return rb_big_fdiv_double(rb_int2big(FIX2LONG(x)), y);
}
else if (RB_FLOAT_TYPE_P(y)) {
return double_div_double(FIX2LONG(x), RFLOAT_VALUE(y));
}
else {
return NUM2DBL(rb_num_coerce_bin(x, y, idFdiv));
}
}
double
rb_int_fdiv_double(VALUE x, VALUE y)
{
if (RB_INTEGER_TYPE_P(y) && !FIXNUM_ZERO_P(y)) {
VALUE gcd = rb_gcd(x, y);
if (!FIXNUM_ZERO_P(gcd)) {
x = rb_int_idiv(x, gcd);
y = rb_int_idiv(y, gcd);
}
}
if (FIXNUM_P(x)) {
return fix_fdiv_double(x, y);
}
else if (RB_BIGNUM_TYPE_P(x)) {
return rb_big_fdiv_double(x, y);
}
else {
return nan("");
}
}
/*
* 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_BIGNUM_TYPE_P(y)) {
x = rb_int2big(FIX2LONG(x));
return rb_big_div(x, y);
}
else if (RB_FLOAT_TYPE_P(y)) {
if (op == '/') {
double d = FIX2LONG(x);
return rb_flo_div_flo(DBL2NUM(d), y);
}
else {
VALUE v;
if (RFLOAT_VALUE(y) == 0) rb_num_zerodiv();
v = fix_divide(x, y, '/');
return flo_floor(0, 0, v);
}
}
else {
if (RB_TYPE_P(y, T_RATIONAL) &&
op == '/' && FIX2LONG(x) == 1)
return rb_rational_reciprocal(y);
return rb_num_coerce_bin(x, y, op);
}
}
static VALUE
fix_div(VALUE x, VALUE y)
{
return fix_divide(x, y, '/');
}
VALUE
rb_int_div(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_div(x, y);
}
else if (RB_BIGNUM_TYPE_P(x)) {
return rb_big_div(x, y);
}
return Qnil;
}
/*
* 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_BIGNUM_TYPE_P(x)) {
return rb_big_idiv(x, y);
}
return num_div(x, y);
}
static VALUE
fix_mod(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
if (FIXNUM_ZERO_P(y)) rb_num_zerodiv();
return rb_fix_mod_fix(x, y);
}
else if (RB_BIGNUM_TYPE_P(y)) {
x = rb_int2big(FIX2LONG(x));
return rb_big_modulo(x, y);
}
else if (RB_FLOAT_TYPE_P(y)) {
return DBL2NUM(ruby_float_mod((double)FIX2LONG(x), RFLOAT_VALUE(y)));
}
else {
return rb_num_coerce_bin(x, y, '%');
}
}
/*
* call-seq:
* self % other -> real_number
*
* Returns +self+ modulo +other+ as a real number.
*
* For integer +n+ and real number +r+, these expressions are equivalent:
*
* n % r
* n-r*(n/r).floor
* n.divmod(r)[1]
*
* See Numeric#divmod.
*
* Examples:
*
* 10 % 2 # => 0
* 10 % 3 # => 1
* 10 % 4 # => 2
*
* 10 % -2 # => 0
* 10 % -3 # => -2
* 10 % -4 # => -2
*
* 10 % 3.0 # => 1.0
* 10 % Rational(3, 1) # => (1/1)
*
* Integer#modulo is an alias for Integer#%.
*
*/
VALUE
rb_int_modulo(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_mod(x, y);
}
else if (RB_BIGNUM_TYPE_P(x)) {
return rb_big_modulo(x, y);
}
return num_modulo(x, y);
}
/*
* call-seq:
* remainder(other) -> real_number
*
* Returns the remainder after dividing +self+ by +other+.
*
* Examples:
*
* 11.remainder(4) # => 3
* 11.remainder(-4) # => 3
* -11.remainder(4) # => -3
* -11.remainder(-4) # => -3
*
* 12.remainder(4) # => 0
* 12.remainder(-4) # => 0
* -12.remainder(4) # => 0
* -12.remainder(-4) # => 0
*
* 13.remainder(4.0) # => 1.0
* 13.remainder(Rational(4, 1)) # => (1/1)
*
*/
static VALUE
int_remainder(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return num_remainder(x, y);
}
else if (RB_BIGNUM_TYPE_P(x)) {
return rb_big_remainder(x, y);
}
return Qnil;
}
static VALUE
fix_divmod(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
VALUE div, mod;
if (FIXNUM_ZERO_P(y)) rb_num_zerodiv();
rb_fix_divmod_fix(x, y, &div, &mod);
return rb_assoc_new(div, mod);
}
else if (RB_BIGNUM_TYPE_P(y)) {
x = rb_int2big(FIX2LONG(x));
return rb_big_divmod(x, y);
}
else if (RB_FLOAT_TYPE_P(y)) {
{
double div, mod;
volatile VALUE a, b;
flodivmod((double)FIX2LONG(x), RFLOAT_VALUE(y), &div, &mod);
a = dbl2ival(div);
b = DBL2NUM(mod);
return rb_assoc_new(a, b);
}
}
else {
return rb_num_coerce_bin(x, y, id_divmod);
}
}
/*
* call-seq:
* divmod(other) -> array
*
* Returns a 2-element array <tt>[q, r]</tt>, where
*
* q = (self/other).floor # Quotient
* r = self % other # Remainder
*
* Examples:
*
* 11.divmod(4) # => [2, 3]
* 11.divmod(-4) # => [-3, -1]
* -11.divmod(4) # => [-3, 1]
* -11.divmod(-4) # => [2, -3]
*
* 12.divmod(4) # => [3, 0]
* 12.divmod(-4) # => [-3, 0]
* -12.divmod(4) # => [-3, 0]
* -12.divmod(-4) # => [3, 0]
*
* 13.divmod(4.0) # => [3, 1.0]
* 13.divmod(Rational(4, 1)) # => [3, (1/1)]
*
*/
VALUE
rb_int_divmod(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_divmod(x, y);
}
else if (RB_BIGNUM_TYPE_P(x)) {
return rb_big_divmod(x, y);
}
return Qnil;
}
/*
* 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_BIGNUM_TYPE_P(y)) {
if (a == 1) return INT2FIX(1);
if (a == -1) return INT2FIX(int_even_p(y) ? 1 : -1);
if (BIGNUM_NEGATIVE_P(y)) return fix_pow_inverted(x, rb_big_uminus(y));
if (a == 0) return INT2FIX(0);
x = rb_int2big(FIX2LONG(x));
return rb_big_pow(x, y);
}
else if (RB_FLOAT_TYPE_P(y)) {
double dy = RFLOAT_VALUE(y);
if (dy == 0.0) return DBL2NUM(1.0);
if (a == 0) {
return DBL2NUM(dy < 0 ? HUGE_VAL : 0.0);
}
if (a == 1) return DBL2NUM(1.0);
if (a < 0 && dy != round(dy))
return rb_dbl_complex_new_polar_pi(pow(-(double)a, dy), dy);
return DBL2NUM(pow((double)a, dy));
}
else {
return rb_num_coerce_bin(x, y, idPow);
}
}
VALUE
rb_int_pow(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_pow(x, y);
}
else if (RB_BIGNUM_TYPE_P(x)) {
return rb_big_pow(x, y);
}
return Qnil;
}
VALUE
rb_num_pow(VALUE x, VALUE y)
{
VALUE z = rb_int_pow(x, y);
if (!NIL_P(z)) return z;
if (RB_FLOAT_TYPE_P(x)) return rb_float_pow(x, y);
if (SPECIAL_CONST_P(x)) return Qnil;
switch (BUILTIN_TYPE(x)) {
case T_COMPLEX:
return rb_complex_pow(x, y);
case T_RATIONAL:
return rb_rational_pow(x, y);
default:
break;
}
return Qnil;
}
/*
* 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_BIGNUM_TYPE_P(y)) {
return rb_big_eq(y, x);
}
else if (RB_FLOAT_TYPE_P(y)) {
return rb_integer_float_eq(x, y);
}
else {
return num_equal(x, y);
}
}
VALUE
rb_int_equal(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_equal(x, y);
}
else if (RB_BIGNUM_TYPE_P(x)) {
return rb_big_eq(x, y);
}
return Qnil;
}
/*
* 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_BIGNUM_TYPE_P(y)) {
VALUE cmp = rb_big_cmp(y, x);
switch (cmp) {
case INT2FIX(+1): return INT2FIX(-1);
case INT2FIX(-1): return INT2FIX(+1);
}
return cmp;
}
else if (RB_FLOAT_TYPE_P(y)) {
return rb_integer_float_cmp(x, y);
}
else {
return rb_num_coerce_cmp(x, y, id_cmp);
}
}
VALUE
rb_int_cmp(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_cmp(x, y);
}
else if (RB_BIGNUM_TYPE_P(x)) {
return rb_big_cmp(x, y);
}
else {
rb_raise(rb_eNotImpError, "need to define `<=>' in %s", rb_obj_classname(x));
}
}
/*
* 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)) {
return RBOOL(FIX2LONG(x) > FIX2LONG(y));
}
else if (RB_BIGNUM_TYPE_P(y)) {
return RBOOL(rb_big_cmp(y, x) == INT2FIX(-1));
}
else if (RB_FLOAT_TYPE_P(y)) {
return RBOOL(rb_integer_float_cmp(x, y) == INT2FIX(1));
}
else {
return rb_num_coerce_relop(x, y, '>');
}
}
VALUE
rb_int_gt(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_gt(x, y);
}
else if (RB_BIGNUM_TYPE_P(x)) {
return rb_big_gt(x, y);
}
return Qnil;
}
/*
* 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)) {
return RBOOL(FIX2LONG(x) >= FIX2LONG(y));
}
else if (RB_BIGNUM_TYPE_P(y)) {
return RBOOL(rb_big_cmp(y, x) != INT2FIX(+1));
}
else if (RB_FLOAT_TYPE_P(y)) {
VALUE rel = rb_integer_float_cmp(x, y);
return RBOOL(rel == INT2FIX(1) || rel == INT2FIX(0));
}
else {
return rb_num_coerce_relop(x, y, idGE);
}
}
VALUE
rb_int_ge(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_ge(x, y);
}
else if (RB_BIGNUM_TYPE_P(x)) {
return rb_big_ge(x, y);
}
return Qnil;
}
/*
* 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)) {
return RBOOL(FIX2LONG(x) < FIX2LONG(y));
}
else if (RB_BIGNUM_TYPE_P(y)) {
return RBOOL(rb_big_cmp(y, x) == INT2FIX(+1));
}
else if (RB_FLOAT_TYPE_P(y)) {
return RBOOL(rb_integer_float_cmp(x, y) == INT2FIX(-1));
}
else {
return rb_num_coerce_relop(x, y, '<');
}
}
static VALUE
int_lt(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_lt(x, y);
}
else if (RB_BIGNUM_TYPE_P(x)) {
return rb_big_lt(x, y);
}
return Qnil;
}
/*
* 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)) {
return RBOOL(FIX2LONG(x) <= FIX2LONG(y));
}
else if (RB_BIGNUM_TYPE_P(y)) {
return RBOOL(rb_big_cmp(y, x) != INT2FIX(-1));
}
else if (RB_FLOAT_TYPE_P(y)) {
VALUE rel = rb_integer_float_cmp(x, y);
return RBOOL(rel == INT2FIX(-1) || rel == INT2FIX(0));
}
else {
return rb_num_coerce_relop(x, y, idLE);
}
}
static VALUE
int_le(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_le(x, y);
}
else if (RB_BIGNUM_TYPE_P(x)) {
return rb_big_le(x, y);
}
return Qnil;
}
static VALUE
fix_comp(VALUE num)
{
return ~num | FIXNUM_FLAG;
}
VALUE
rb_int_comp(VALUE num)
{
if (FIXNUM_P(num)) {
return fix_comp(num);
}
else if (RB_BIGNUM_TYPE_P(num)) {
return rb_big_comp(num);
}
return Qnil;
}
static VALUE
num_funcall_bit_1(VALUE y, VALUE arg, int recursive)
{
ID func = (ID)((VALUE *)arg)[0];
VALUE x = ((VALUE *)arg)[1];
if (recursive) {
num_funcall_op_1_recursion(x, func, y);
}
return rb_check_funcall(x, func, 1, &y);
}
VALUE
rb_num_coerce_bit(VALUE x, VALUE y, ID func)
{
VALUE ret, args[3];
args[0] = (VALUE)func;
args[1] = x;
args[2] = y;
do_coerce(&args[1], &args[2], TRUE);
ret = rb_exec_recursive_paired(num_funcall_bit_1,
args[2], args[1], (VALUE)args);
if (ret == Qundef) {
/* show the original object, not coerced object */
coerce_failed(x, y);
}
return ret;
}
/*
* 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_BIGNUM_TYPE_P(y)) {
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_BIGNUM_TYPE_P(x)) {
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_BIGNUM_TYPE_P(y)) {
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_BIGNUM_TYPE_P(x)) {
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_BIGNUM_TYPE_P(y)) {
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_BIGNUM_TYPE_P(x)) {
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_BIGNUM_TYPE_P(x)) {
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_BIGNUM_TYPE_P(x)) {
return rb_big_rshift(x, y);
}
return Qnil;
}
MJIT_FUNC_EXPORTED VALUE
rb_fix_aref(VALUE fix, VALUE idx)
{
long val = FIX2LONG(fix);
long i;
idx = rb_to_int(idx);
if (!FIXNUM_P(idx)) {
idx = rb_big_norm(idx);
if (!FIXNUM_P(idx)) {
if (!BIGNUM_SIGN(idx) || val >= 0)
return INT2FIX(0);
return INT2FIX(1);
}
}
i = FIX2LONG(idx);
if (i < 0) return INT2FIX(0);
if (SIZEOF_LONG*CHAR_BIT-1 <= i) {
if (val < 0) return INT2FIX(1);
return INT2FIX(0);
}
if (val & (1L<<i))
return INT2FIX(1);
return INT2FIX(0);
}
/* copied from "r_less" in range.c */
/* compares _a_ and _b_ and returns:
* < 0: a < b
* = 0: a = b
* > 0: a > b or non-comparable
*/
static int
compare_indexes(VALUE a, VALUE b)
{
VALUE r = rb_funcall(a, id_cmp, 1, b);
if (NIL_P(r))
return INT_MAX;
return rb_cmpint(r, a, b);
}
static VALUE
generate_mask(VALUE len)
{
return rb_int_minus(rb_int_lshift(INT2FIX(1), len), INT2FIX(1));
}
static VALUE
int_aref1(VALUE num, VALUE arg)
{
VALUE orig_num = num, beg, end;
int excl;
if (rb_range_values(arg, &beg, &end, &excl)) {
if (NIL_P(beg)) {
/* beginless range */
if (!RTEST(num_negative_p(end))) {
if (!excl) end = rb_int_plus(end, INT2FIX(1));
VALUE mask = generate_mask(end);
if (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_BIGNUM_TYPE_P(num)) {
return rb_big_aref(num, arg);
}
return Qnil;
}
static VALUE
int_aref2(VALUE num, VALUE beg, VALUE len)
{
num = rb_int_rshift(num, beg);
VALUE mask = generate_mask(len);
num = rb_int_and(num, mask);
return num;
}
/*
* 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_BIGNUM_TYPE_P(num)) {
val = rb_big2dbl(num);
}
else {
rb_raise(rb_eNotImpError, "Unknown subclass for to_f: %s", rb_obj_classname(num));
}
return DBL2NUM(val);
}
static VALUE
fix_abs(VALUE fix)
{
long i = FIX2LONG(fix);
if (i < 0) i = -i;
return LONG2NUM(i);
}
VALUE
rb_int_abs(VALUE num)
{
if (FIXNUM_P(num)) {
return fix_abs(num);
}
else if (RB_BIGNUM_TYPE_P(num)) {
return rb_big_abs(num);
}
return Qnil;
}
static VALUE
fix_size(VALUE fix)
{
return INT2FIX(sizeof(long));
}
MJIT_FUNC_EXPORTED VALUE
rb_int_size(VALUE num)
{
if (FIXNUM_P(num)) {
return fix_size(num);
}
else if (RB_BIGNUM_TYPE_P(num)) {
return rb_big_size_m(num);
}
return Qnil;
}
static VALUE
rb_fix_bit_length(VALUE fix)
{
long v = FIX2LONG(fix);
if (v < 0)
v = ~v;
return LONG2FIX(bit_length(v));
}
VALUE
rb_int_bit_length(VALUE num)
{
if (FIXNUM_P(num)) {
return rb_fix_bit_length(num);
}
else if (RB_BIGNUM_TYPE_P(num)) {
return rb_big_bit_length(num);
}
return Qnil;
}
/*
* 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_BIGNUM_TYPE_P(base))
base = rb_big_norm(base);
if (FIXNUM_P(base) && FIX2LONG(base) < 2)
rb_raise(rb_eArgError, "invalid radix %ld", FIX2LONG(base));
else if (RB_BIGNUM_TYPE_P(base) && BIGNUM_NEGATIVE_P(base))
rb_raise(rb_eArgError, "negative radix");
if (FIXNUM_P(base) && FIXNUM_P(num))
return rb_fix_digits(num, FIX2LONG(base));
if (FIXNUM_P(num))
return rb_ary_new_from_args(1, num);
if (int_lt(rb_int_div(rb_int_bit_length(num), rb_int_bit_length(base)), INT2FIX(50))) {
digits = rb_ary_new();
while (!FIXNUM_P(num) || FIX2LONG(num) > 0) {
VALUE qr = rb_int_divmod(num, base);
rb_ary_push(digits, RARRAY_AREF(qr, 1));
num = RARRAY_AREF(qr, 0);
}
return digits;
}
bases = rb_ary_new();
for (VALUE b = base; int_lt(b, num) == Qtrue; b = rb_int_mul(b, b)) {
rb_ary_push(bases, b);
}
digits = rb_ary_new_from_args(1, num);
while (RARRAY_LEN(bases)) {
VALUE b = rb_ary_pop(bases);
long i, last_idx = RARRAY_LEN(digits) - 1;
for(i = last_idx; i >= 0; i--) {
VALUE n = RARRAY_AREF(digits, i);
VALUE divmod = rb_int_divmod(n, b);
VALUE div = RARRAY_AREF(divmod, 0);
VALUE mod = RARRAY_AREF(divmod, 1);
if (i != last_idx || div != INT2FIX(0)) rb_ary_store(digits, 2 * i + 1, div);
rb_ary_store(digits, 2 * i, mod);
}
}
return digits;
}
static VALUE
rb_int_digits(int argc, VALUE *argv, VALUE num)
{
VALUE base_value;
long base;
if (rb_num_negative_p(num))
rb_raise(rb_eMathDomainError, "out of domain");
if (rb_check_arity(argc, 0, 1)) {
base_value = rb_to_int(argv[0]);
if (!RB_INTEGER_TYPE_P(base_value))
rb_raise(rb_eTypeError, "wrong argument type %s (expected Integer)",
rb_obj_classname(argv[0]));
if (RB_BIGNUM_TYPE_P(base_value))
return rb_int_digits_bigbase(num, base_value);
base = FIX2LONG(base_value);
if (base < 0)
rb_raise(rb_eArgError, "negative radix");
else if (base < 2)
rb_raise(rb_eArgError, "invalid radix %ld", base);
}
else
base = 10;
if (FIXNUM_P(num))
return rb_fix_digits(num, base);
else if (RB_BIGNUM_TYPE_P(num))
return rb_int_digits_bigbase(num, LONG2FIX(base));
return Qnil;
}
/*
* 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);
}
#include "numeric.rbinc"
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