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ruby--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 "internal.h"
#include "ruby/util.h"
#include "id.h"
#include <ctype.h>
#include <math.h>
#include <stdio.h>
#if defined(__FreeBSD__) && __FreeBSD__ < 4
#include <floatingpoint.h>
#endif
#ifdef HAVE_FLOAT_H
#include <float.h>
#endif
#ifdef HAVE_IEEEFP_H
#include <ieeefp.h>
#endif
/* use IEEE 64bit values if not defined */
#ifndef FLT_RADIX
#define FLT_RADIX 2
#endif
#ifndef FLT_ROUNDS
#define FLT_ROUNDS 1
#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
#ifdef HAVE_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
#ifdef HAVE_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 VALUE fix_uminus(VALUE num);
static VALUE fix_mul(VALUE x, VALUE y);
static VALUE int_pow(long x, unsigned long y);
static ID id_coerce, id_div, id_divmod;
#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_cFixnum;
VALUE rb_eZeroDivError;
VALUE rb_eFloatDomainError;
static ID id_to, id_by;
void
rb_num_zerodiv(void)
{
rb_raise(rb_eZeroDivError, "divided by 0");
}
/* 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_TYPE_P(val, T_BIGNUM)) {
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 VALUE
compare_with_zero(VALUE num, ID mid)
{
VALUE zero = INT2FIX(0);
VALUE r = rb_check_funcall(num, mid, 1, &zero);
if (r == Qundef) {
rb_cmperr(mid, zero);
}
return r;
}
static inline int
positive_int_p(VALUE num)
{
const ID mid = '>';
if (FIXNUM_P(num)) {
if (method_basic_p(rb_cFixnum))
return (SIGNED_VALUE)num > 0;
}
else if (RB_TYPE_P(num, T_BIGNUM)) {
if (method_basic_p(rb_cBignum))
return BIGNUM_POSITIVE_P(num);
}
return RTEST(compare_with_zero(num, mid));
}
static inline int
negative_int_p(VALUE num)
{
const ID mid = '<';
if (FIXNUM_P(num)) {
if (method_basic_p(rb_cFixnum))
return (SIGNED_VALUE)num < 0;
}
else if (RB_TYPE_P(num, T_BIGNUM)) {
if (method_basic_p(rb_cBignum))
return BIGNUM_NEGATIVE_P(num);
}
return RTEST(compare_with_zero(num, mid));
}
int
rb_num_negative_p(VALUE num)
{
return negative_int_p(num);
}
/*
* call-seq:
* num.coerce(numeric) -> array
*
* If a +numeric+ is the same type as +num+, returns an array containing
* +numeric+ and +num+. Otherwise, returns an array with both a +numeric+ and
* +num+ represented as Float objects.
*
* This coercion mechanism is used by Ruby to handle mixed-type numeric
* operations: it is intended to find a compatible common type between the two
* operands of the operator.
*
* 1.coerce(2.5) #=> [2.5, 1.0]
* 1.2.coerce(3) #=> [3.0, 1.2]
* 1.coerce(2) #=> [2, 1]
*/
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);
}
static VALUE
coerce_body(VALUE *x)
{
return rb_funcall(x[1], id_coerce, 1, x[0]);
}
NORETURN(static void coerce_failed(VALUE x, VALUE y));
static void
coerce_failed(VALUE x, VALUE y)
{
if (SPECIAL_CONST_P(y) || BUILTIN_TYPE(y) == T_FLOAT) {
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 VALUE
coerce_rescue(VALUE *x)
{
coerce_failed(x[0], x[1]);
return Qnil; /* dummy */
}
static VALUE
coerce_rescue_quiet(VALUE *x)
{
return Qundef;
}
static int
do_coerce(VALUE *x, VALUE *y, int err)
{
VALUE ary;
VALUE a[2];
a[0] = *x; a[1] = *y;
if (!rb_respond_to(*y, id_coerce)) {
if (err) {
coerce_rescue(a);
}
return FALSE;
}
ary = rb_rescue(coerce_body, (VALUE)a, err ? coerce_rescue : coerce_rescue_quiet, (VALUE)a);
if (ary == Qundef) {
rb_warn("Numerical comparison operators will no more rescue exceptions of #coerce");
rb_warn("in the next release. Return nil in #coerce if the coercion is impossible.");
return FALSE;
}
if (!RB_TYPE_P(ary, T_ARRAY) || RARRAY_LEN(ary) != 2) {
if (err) {
rb_raise(rb_eTypeError, "coerce must return [x, y]");
}
else if (!NIL_P(ary)) {
rb_warn("Bad return value for #coerce, called by numerical comparison operators.");
rb_warn("#coerce must return [x, y]. The next release will raise an error for this.");
}
return FALSE;
}
*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;
}
VALUE
rb_num_coerce_relop(VALUE x, VALUE y, ID func)
{
VALUE c, x0 = x, y0 = y;
if (!do_coerce(&x, &y, FALSE) ||
NIL_P(c = rb_funcall(x, func, 1, y))) {
rb_cmperr(x0, y0);
return Qnil; /* not reached */
}
return c;
}
/*
* 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;
}
/*
* Numerics are immutable values, which should not be copied.
*
* Any attempt to use this method on a Numeric will raise a TypeError.
*/
static VALUE
num_init_copy(VALUE x, VALUE y)
{
rb_raise(rb_eTypeError, "can't copy %"PRIsVALUE, rb_obj_class(x));
UNREACHABLE;
}
/*
* call-seq:
* +num -> num
*
* Unary Plus---Returns the receiver's value.
*/
static VALUE
num_uplus(VALUE num)
{
return num;
}
/*
* call-seq:
* num.i -> Complex(0,num)
*
* Returns the corresponding imaginary number.
* Not available for complex numbers.
*/
static VALUE
num_imaginary(VALUE num)
{
return rb_complex_new(INT2FIX(0), num);
}
/*
* call-seq:
* -num -> numeric
*
* Unary Minus---Returns the receiver's value, negated.
*/
static VALUE
num_uminus(VALUE num)
{
VALUE zero;
zero = INT2FIX(0);
do_coerce(&zero, &num, TRUE);
return rb_funcall(zero, '-', 1, num);
}
/*
* call-seq:
* num.fdiv(numeric) -> float
*
* Returns float division.
*/
static VALUE
num_fdiv(VALUE x, VALUE y)
{
return rb_funcall(rb_Float(x), '/', 1, y);
}
/*
* call-seq:
* num.div(numeric) -> integer
*
* Uses +/+ to perform division, then converts the result to an integer.
* +numeric+ does not define the +/+ operator; this is left to subclasses.
*
* Equivalent to <code>num.divmod(numeric)[0]</code>.
*
* See Numeric#divmod.
*/
static VALUE
num_div(VALUE x, VALUE y)
{
if (rb_equal(INT2FIX(0), y)) rb_num_zerodiv();
return rb_funcall(rb_funcall(x, '/', 1, y), rb_intern("floor"), 0);
}
/*
* call-seq:
* num.modulo(numeric) -> real
*
* x.modulo(y) means x-y*(x/y).floor
*
* Equivalent to <code>num.divmod(numeric)[1]</code>.
*
* See Numeric#divmod.
*/
static VALUE
num_modulo(VALUE x, VALUE y)
{
return rb_funcall(x, '-', 1,
rb_funcall(y, '*', 1,
rb_funcall(x, id_div, 1, y)));
}
/*
* call-seq:
* num.remainder(numeric) -> real
*
* x.remainder(y) means x-y*(x/y).truncate
*
* See Numeric#divmod.
*/
static VALUE
num_remainder(VALUE x, VALUE y)
{
VALUE z = rb_funcall(x, '%', 1, y);
if ((!rb_equal(z, INT2FIX(0))) &&
((negative_int_p(x) &&
positive_int_p(y)) ||
(positive_int_p(x) &&
negative_int_p(y)))) {
return rb_funcall(z, '-', 1, y);
}
return z;
}
/*
* call-seq:
* num.divmod(numeric) -> array
*
* Returns an array containing the quotient and modulus obtained by dividing
* +num+ by +numeric+.
*
* If <code>q, r = * x.divmod(y)</code>, then
*
* q = floor(x/y)
* x = q*y+r
*
* The quotient is rounded toward -infinity, as shown in the following table:
*
* a | b | a.divmod(b) | a/b | a.modulo(b) | a.remainder(b)
* ------+-----+---------------+---------+-------------+---------------
* 13 | 4 | 3, 1 | 3 | 1 | 1
* ------+-----+---------------+---------+-------------+---------------
* 13 | -4 | -4, -3 | -4 | -3 | 1
* ------+-----+---------------+---------+-------------+---------------
* -13 | 4 | -4, 3 | -4 | 3 | -1
* ------+-----+---------------+---------+-------------+---------------
* -13 | -4 | 3, -1 | 3 | -1 | -1
* ------+-----+---------------+---------+-------------+---------------
* 11.5 | 4 | 2, 3.5 | 2.875 | 3.5 | 3.5
* ------+-----+---------------+---------+-------------+---------------
* 11.5 | -4 | -3, -0.5 | -2.875 | -0.5 | 3.5
* ------+-----+---------------+---------+-------------+---------------
* -11.5 | 4 | -3, 0.5 | -2.875 | 0.5 | -3.5
* ------+-----+---------------+---------+-------------+---------------
* -11.5 | -4 | 2, -3.5 | 2.875 | -3.5 | -3.5
*
*
* Examples
*
* 11.divmod(3) #=> [3, 2]
* 11.divmod(-3) #=> [-4, -1]
* 11.divmod(3.5) #=> [3, 0.5]
* (-11).divmod(3.5) #=> [-4, 3.0]
* (11.5).divmod(3.5) #=> [3, 1.0]
*/
static VALUE
num_divmod(VALUE x, VALUE y)
{
return rb_assoc_new(num_div(x, y), num_modulo(x, y));
}
/*
* call-seq:
* num.real? -> true or false
*
* Returns +true+ if +num+ is a Real number. (i.e. not Complex).
*/
static VALUE
num_real_p(VALUE num)
{
return Qtrue;
}
/*
* call-seq:
* num.integer? -> true or false
*
* Returns +true+ if +num+ is an Integer (including Fixnum and Bignum).
*
* (1.0).integer? #=> false
* (1).integer? #=> true
*/
static VALUE
num_int_p(VALUE num)
{
return Qfalse;
}
/*
* call-seq:
* num.abs -> numeric
* num.magnitude -> numeric
*
* Returns the absolute value of +num+.
*
* 12.abs #=> 12
* (-34.56).abs #=> 34.56
* -34.56.abs #=> 34.56
*
* Numeric#magnitude is an alias of Numeric#abs.
*/
static VALUE
num_abs(VALUE num)
{
if (negative_int_p(num)) {
return rb_funcall(num, idUMinus, 0);
}
return num;
}
/*
* call-seq:
* num.zero? -> true or false
*
* Returns +true+ if +num+ has a zero value.
*/
static VALUE
num_zero_p(VALUE num)
{
if (rb_equal(num, INT2FIX(0))) {
return Qtrue;
}
return Qfalse;
}
/*
* call-seq:
* num.nonzero? -> self or nil
*
* Returns +self+ if +num+ is not zero, +nil+ otherwise.
*
* This behavior is useful when chaining comparisons:
*
* a = %w( z Bb bB bb BB a aA Aa AA A )
* b = a.sort {|a,b| (a.downcase <=> b.downcase).nonzero? || a <=> b }
* b #=> ["A", "a", "AA", "Aa", "aA", "BB", "Bb", "bB", "bb", "z"]
*/
static VALUE
num_nonzero_p(VALUE num)
{
if (RTEST(rb_funcallv(num, rb_intern("zero?"), 0, 0))) {
return Qnil;
}
return num;
}
/*
* call-seq:
* num.to_int -> integer
*
* Invokes the child class's +to_i+ method to convert +num+ to an integer.
*
* 1.0.class => Float
* 1.0.to_int.class => Fixnum
* 1.0.to_i.class => Fixnum
*/
static VALUE
num_to_int(VALUE num)
{
return rb_funcallv(num, id_to_i, 0, 0);
}
/*
* call-seq:
* num.positive? -> true or false
*
* Returns +true+ if +num+ is greater than 0.
*/
static VALUE
num_positive_p(VALUE num)
{
const ID mid = '>';
if (FIXNUM_P(num)) {
if (method_basic_p(rb_cFixnum))
return (SIGNED_VALUE)num > (SIGNED_VALUE)INT2FIX(0) ? Qtrue : Qfalse;
}
else if (RB_TYPE_P(num, T_BIGNUM)) {
if (method_basic_p(rb_cBignum))
return BIGNUM_POSITIVE_P(num) && !rb_bigzero_p(num) ? Qtrue : Qfalse;
}
return compare_with_zero(num, mid);
}
/*
* call-seq:
* num.negative? -> true or false
*
* Returns +true+ if +num+ is less than 0.
*/
static VALUE
num_negative_p(VALUE num)
{
return negative_int_p(num) ? Qtrue : Qfalse;
}
/********************************************************************
*
* 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:
*
* - http://docs.sun.com/source/806-3568/ncg_goldberg.html
* - http://wiki.github.com/rdp/ruby_tutorials_core/ruby-talk-faq#wiki-floats_imprecise
* - http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems
*/
VALUE
rb_float_new_in_heap(double d)
{
NEWOBJ_OF(flt, struct RFloat, rb_cFloat, T_FLOAT | (RGENGC_WB_PROTECTED_FLOAT ? FL_WB_PROTECTED : 0));
flt->float_value = d;
OBJ_FREEZE(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))
return rb_usascii_str_new2(value < 0 ? "-Infinity" : "Infinity");
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 {
exp:
if (digs > 1) {
memmove(buf + 2, buf + 1, digs - 1);
}
else {
buf[2] = '0';
digs++;
}
buf[1] = '.';
rb_str_cat(s, buf, digs + 1);
rb_str_catf(s, "e%+03d", decpt - 1);
}
return s;
}
/*
* call-seq:
* float.coerce(numeric) -> array
*
* Returns an array with both a +numeric+ and a +float+ represented as Float
* objects.
*
* This is achieved by converting a +numeric+ to a Float.
*
* 1.2.coerce(3) #=> [3.0, 1.2]
* 2.5.coerce(1.1) #=> [1.1, 2.5]
*/
static VALUE
flo_coerce(VALUE x, VALUE y)
{
return rb_assoc_new(rb_Float(y), x);
}
/*
* call-seq:
* -float -> float
*
* Returns float, negated.
*/
static VALUE
flo_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+.
*/
static VALUE
flo_plus(VALUE x, VALUE y)
{
if (RB_TYPE_P(y, T_FIXNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y));
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y));
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '+');
}
}
/*
* call-seq:
* float - other -> float
*
* Returns a new float which is the difference of +float+ and +other+.
*/
static VALUE
flo_minus(VALUE x, VALUE y)
{
if (RB_TYPE_P(y, T_FIXNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y));
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y));
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '-');
}
}
/*
* call-seq:
* float * other -> float
*
* Returns a new float which is the product of +float+ and +other+.
*/
static VALUE
flo_mul(VALUE x, VALUE y)
{
if (RB_TYPE_P(y, T_FIXNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y));
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y));
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '*');
}
}
/*
* call-seq:
* float / other -> float
*
* Returns a new float which is the result of dividing +float+ by +other+.
*/
static VALUE
flo_div(VALUE x, VALUE y)
{
long f_y;
double d;
if (RB_TYPE_P(y, T_FIXNUM)) {
f_y = FIX2LONG(y);
return DBL2NUM(RFLOAT_VALUE(x) / (double)f_y);
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
d = rb_big2dbl(y);
return DBL2NUM(RFLOAT_VALUE(x) / d);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM(RFLOAT_VALUE(x) / RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '/');
}
}
/*
* call-seq:
* float.fdiv(numeric) -> float
* float.quo(numeric) -> float
*
* Returns <code>float / numeric</code>, same as Float#/.
*/
static VALUE
flo_quo(VALUE x, VALUE y)
{
return rb_funcall(x, '/', 1, 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 (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.
*/
double
ruby_float_mod(double x, double y)
{
double mod;
flodivmod(x, y, 0, &mod);
return mod;
}
/*
* call-seq:
* float % other -> float
* float.modulo(other) -> float
*
* Return the modulo after division of +float+ by +other+.
*
* 6543.21.modulo(137) #=> 104.21
* 6543.21.modulo(137.24) #=> 92.9299999999996
*/
static VALUE
flo_mod(VALUE x, VALUE y)
{
double fy;
if (RB_TYPE_P(y, T_FIXNUM)) {
fy = (double)FIX2LONG(y);
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
fy = rb_big2dbl(y);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
fy = RFLOAT_VALUE(y);
}
else {
return rb_num_coerce_bin(x, y, '%');
}
return DBL2NUM(ruby_float_mod(RFLOAT_VALUE(x), fy));
}
static VALUE
dbl2ival(double d)
{
d = round(d);
if (FIXABLE(d)) {
return LONG2FIX((long)d);
}
return rb_dbl2big(d);
}
/*
* call-seq:
* float.divmod(numeric) -> array
*
* See Numeric#divmod.
*
* 42.0.divmod 6 #=> [7, 0.0]
* 42.0.divmod 5 #=> [8, 2.0]
*/
static VALUE
flo_divmod(VALUE x, VALUE y)
{
double fy, div, mod;
volatile VALUE a, b;
if (RB_TYPE_P(y, T_FIXNUM)) {
fy = (double)FIX2LONG(y);
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
fy = rb_big2dbl(y);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
fy = RFLOAT_VALUE(y);
}
else {
return rb_num_coerce_bin(x, y, id_divmod);
}
flodivmod(RFLOAT_VALUE(x), fy, &div, &mod);
a = dbl2ival(div);
b = DBL2NUM(mod);
return rb_assoc_new(a, b);
}
/*
* call-seq:
*
* float ** other -> float
*
* Raises +float+ to the power of +other+.
*
* 2.0**3 #=> 8.0
*/
static VALUE
flo_pow(VALUE x, VALUE y)
{
double dx, dy;
if (RB_TYPE_P(y, T_FIXNUM)) {
dx = RFLOAT_VALUE(x);
dy = (double)FIX2LONG(y);
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
dx = RFLOAT_VALUE(x);
dy = rb_big2dbl(y);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
dx = RFLOAT_VALUE(x);
dy = RFLOAT_VALUE(y);
if (dx < 0 && dy != round(dy))
return rb_funcall(rb_complex_raw1(x), idPow, 1, y);
}
else {
return rb_num_coerce_bin(x, y, idPow);
}
return DBL2NUM(pow(dx, dy));
}
/*
* call-seq:
* num.eql?(numeric) -> true or false
*
* Returns +true+ if +num+ and +numeric+ are the same type and have equal
* values.
*
* 1 == 1.0 #=> true
* 1.eql?(1.0) #=> false
* (1.0).eql?(1.0) #=> true
*/
static VALUE
num_eql(VALUE x, VALUE y)
{
if (TYPE(x) != TYPE(y)) return Qfalse;
return rb_equal(x, y);
}
/*
* call-seq:
* number <=> other -> 0 or nil
*
* Returns zero if +number+ equals +other+, otherwise +nil+ is returned if the
* two values are incomparable.
*/
static VALUE
num_cmp(VALUE x, VALUE y)
{
if (x == y) return INT2FIX(0);
return Qnil;
}
static VALUE
num_equal(VALUE x, VALUE y)
{
if (x == y) return Qtrue;
return rb_funcall(y, id_eq, 1, x);
}
/*
* 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.
*
* The result of <code>NaN == NaN</code> is undefined, so the
* implementation-dependent value is returned.
*
* 1.0 == 1 #=> true
*
*/
static VALUE
flo_eq(VALUE x, VALUE y)
{
volatile double a, b;
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
return rb_integer_float_eq(y, x);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(b)) return Qfalse;
#endif
}
else {
return num_equal(x, y);
}
a = RFLOAT_VALUE(x);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(a)) return Qfalse;
#endif
return (a == b)?Qtrue:Qfalse;
}
/*
* 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));
}
VALUE
rb_dbl_hash(double d)
{
st_index_t hash;
/* normalize -0.0 to 0.0 */
if (d == 0.0) d = 0.0;
hash = rb_memhash(&d, sizeof(d));
return LONG2FIX(hash);
}
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, +1 or nil depending on whether +float+ is less than, equal
* to, or greater than +real+. This is the basis for the tests in Comparable.
*
* The result of <code>NaN <=> NaN</code> is undefined, so the
* implementation-dependent value is returned.
*
* +nil+ is returned if the two values are incomparable.
*/
static VALUE
flo_cmp(VALUE x, VALUE y)
{
double a, b;
VALUE i;
a = RFLOAT_VALUE(x);
if (isnan(a)) return Qnil;
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
VALUE rel = rb_integer_float_cmp(y, x);
if (FIXNUM_P(rel))
return INT2FIX(-FIX2INT(rel));
return rel;
}
else if (RB_TYPE_P(y, T_FLOAT)) {
b = RFLOAT_VALUE(y);
}
else {
if (isinf(a) && (i = rb_check_funcall(y, rb_intern("infinite?"), 0, 0)) != Qundef) {
if (RTEST(i)) {
int j = rb_cmpint(i, x, y);
j = (a > 0.0) ? (j > 0 ? 0 : +1) : (j < 0 ? 0 : -1);
return INT2FIX(j);
}
if (a > 0.0) return INT2FIX(1);
return INT2FIX(-1);
}
return rb_num_coerce_cmp(x, y, id_cmp);
}
return rb_dbl_cmp(a, b);
}
/*
* 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 the
* implementation-dependent value is returned.
*/
static VALUE
flo_gt(VALUE x, VALUE y)
{
double a, b;
a = RFLOAT_VALUE(x);
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
VALUE rel = rb_integer_float_cmp(y, x);
if (FIXNUM_P(rel))
return -FIX2INT(rel) > 0 ? Qtrue : Qfalse;
return Qfalse;
}
else if (RB_TYPE_P(y, T_FLOAT)) {
b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(b)) return Qfalse;
#endif
}
else {
return rb_num_coerce_relop(x, y, '>');
}
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(a)) return Qfalse;
#endif
return (a > b)?Qtrue:Qfalse;
}
/*
* call-seq:
* float >= real -> true or false
*
* Returns +true+ if +float+ is greater than or equal to +real+.
*
* The result of <code>NaN >= NaN</code> is undefined, so the
* implementation-dependent value is returned.
*/
static VALUE
flo_ge(VALUE x, VALUE y)
{
double a, b;
a = RFLOAT_VALUE(x);
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
VALUE rel = rb_integer_float_cmp(y, x);
if (FIXNUM_P(rel))
return -FIX2INT(rel) >= 0 ? Qtrue : Qfalse;
return Qfalse;
}
else if (RB_TYPE_P(y, T_FLOAT)) {
b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(b)) return Qfalse;
#endif
}
else {
return rb_num_coerce_relop(x, y, idGE);
}
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(a)) return Qfalse;
#endif
return (a >= b)?Qtrue:Qfalse;
}
/*
* call-seq:
* float < real -> true or false
*
* Returns +true+ if +float+ is less than +real+.
*
* The result of <code>NaN < NaN</code> is undefined, so the
* implementation-dependent value is returned.
*/
static VALUE
flo_lt(VALUE x, VALUE y)
{
double a, b;
a = RFLOAT_VALUE(x);
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
VALUE rel = rb_integer_float_cmp(y, x);
if (FIXNUM_P(rel))
return -FIX2INT(rel) < 0 ? Qtrue : Qfalse;
return Qfalse;
}
else if (RB_TYPE_P(y, T_FLOAT)) {
b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(b)) return Qfalse;
#endif
}
else {
return rb_num_coerce_relop(x, y, '<');
}
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(a)) return Qfalse;
#endif
return (a < b)?Qtrue:Qfalse;
}
/*
* call-seq:
* float <= real -> true or false
*
* Returns +true+ if +float+ is less than or equal to +real+.
*
* The result of <code>NaN <= NaN</code> is undefined, so the
* implementation-dependent value is returned.
*/
static VALUE
flo_le(VALUE x, VALUE y)
{
double a, b;
a = RFLOAT_VALUE(x);
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
VALUE rel = rb_integer_float_cmp(y, x);
if (FIXNUM_P(rel))
return -FIX2INT(rel) <= 0 ? Qtrue : Qfalse;
return Qfalse;
}
else if (RB_TYPE_P(y, T_FLOAT)) {
b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(b)) return Qfalse;
#endif
}
else {
return rb_num_coerce_relop(x, y, idLE);
}
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(a)) return Qfalse;
#endif
return (a <= b)?Qtrue:Qfalse;
}
/*
* call-seq:
* float.eql?(obj) -> true or false
*
* Returns +true+ only if +obj+ is a Float with the same value as +float+.
* Contrast this with Float#==, which performs type conversions.
*
* The result of <code>NaN.eql?(NaN)</code> is undefined, so the
* implementation-dependent value is returned.
*
* 1.0.eql?(1) #=> false
*/
static VALUE
flo_eql(VALUE x, VALUE y)
{
if (RB_TYPE_P(y, T_FLOAT)) {
double a = RFLOAT_VALUE(x);
double b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(a) || isnan(b)) return Qfalse;
#endif
if (a == b)
return Qtrue;
}
return Qfalse;
}
/*
* call-seq:
* float.to_f -> self
*
* Since +float+ is already a float, returns +self+.
*/
static VALUE
flo_to_f(VALUE num)
{
return num;
}
/*
* call-seq:
* float.abs -> float
* float.magnitude -> float
*
* Returns the absolute value of +float+.
*
* (-34.56).abs #=> 34.56
* -34.56.abs #=> 34.56
*
*/
static VALUE
flo_abs(VALUE flt)
{
double val = fabs(RFLOAT_VALUE(flt));
return DBL2NUM(val);
}
/*
* call-seq:
* float.zero? -> true or false
*
* Returns +true+ if +float+ is 0.0.
*
*/
static VALUE
flo_zero_p(VALUE num)
{
if (RFLOAT_VALUE(num) == 0.0) {
return Qtrue;
}
return Qfalse;
}
/*
* 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 isnan(value) ? Qtrue : Qfalse;
}
/*
* call-seq:
* float.infinite? -> nil, -1, +1
*
* Return values corresponding to the value of +float+:
*
* +finite+:: +nil+
* +-Infinity+:: +-1+
* ++Infinity+:: +1+
*
* For example:
*
* (0.0).infinite? #=> nil
* (-1.0/0.0).infinite? #=> -1
* (+1.0/0.0).infinite? #=> 1
*/
static VALUE
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 (it is not
* infinite, and Float#nan? is +false+).
*
*/
static VALUE
flo_is_finite_p(VALUE num)
{
double value = RFLOAT_VALUE(num);
#ifdef HAVE_ISFINITE
if (!isfinite(value))
return Qfalse;
#else
if (isinf(value) || isnan(value))
return Qfalse;
#endif
return Qtrue;
}
/*
* 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:
*
* p 0.01.next_float #=> 0.010000000000000002
* p 1.0.next_float #=> 1.0000000000000002
* p 100.0.next_float #=> 100.00000000000001
*
* p 0.01.next_float - 0.01 #=> 1.734723475976807e-18
* p 1.0.next_float - 1.0 #=> 2.220446049250313e-16
* p 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 }
* p f #=> 9.99999999999998 # should be 10.0 in the ideal world.
* p 10-f #=> 1.9539925233402755e-14 # the floating-point error.
* p(10.0.next_float-10) #=> 1.7763568394002505e-15 # 1 ulp (units in the last place).
* p((10-f)/(10.0.next_float-10)) #=> 11.0 # the error is 11 ulp.
* p((10-f)/(10*Float::EPSILON)) #=> 8.8 # approximation of the above.
* p "%a" % f #=> "0x1.3fffffffffff5p+3" # the last hex digit is 5. 16 - 5 = 11 ulp.
*
*/
static VALUE
flo_next_float(VALUE vx)
{
double x, y;
x = NUM2DBL(vx);
y = nextafter(x, INFINITY);
return DBL2NUM(y);
}
/*
* 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:
*
* p 0.01.prev_float #=> 0.009999999999999998
* p 1.0.prev_float #=> 0.9999999999999999
* p 100.0.prev_float #=> 99.99999999999999
*
* p 0.01 - 0.01.prev_float #=> 1.734723475976807e-18
* p 1.0 - 1.0.prev_float #=> 1.1102230246251565e-16
* p 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)
{
double x, y;
x = NUM2DBL(vx);
y = nextafter(x, -INFINITY);
return DBL2NUM(y);
}
/*
* call-seq:
* float.floor -> integer
*
* Returns the largest integer less than or equal to +float+.
*
* 1.2.floor #=> 1
* 2.0.floor #=> 2
* (-1.2).floor #=> -2
* (-2.0).floor #=> -2
*/
static VALUE
flo_floor(VALUE num)
{
double f = floor(RFLOAT_VALUE(num));
long val;
if (!FIXABLE(f)) {
return rb_dbl2big(f);
}
val = (long)f;
return LONG2FIX(val);
}
/*
* call-seq:
* float.ceil -> integer
*
* Returns the smallest Integer greater than or equal to +float+.
*
* 1.2.ceil #=> 2
* 2.0.ceil #=> 2
* (-1.2).ceil #=> -1
* (-2.0).ceil #=> -2
*/
static VALUE
flo_ceil(VALUE num)
{
double f = ceil(RFLOAT_VALUE(num));
long val;
if (!FIXABLE(f)) {
return rb_dbl2big(f);
}
val = (long)f;
return LONG2FIX(val);
}
/*
* Assumes num is an Integer, ndigits <= 0
*/
static VALUE
int_round_0(VALUE num, int ndigits)
{
VALUE n, f, h, r;
long bytes;
ID op;
/* If 10**N / 2 > num, then return 0 */
/* We have log_256(10) > 0.415241 and log_256(1/2) = -0.125, so */
bytes = FIXNUM_P(num) ? sizeof(long) : rb_funcall(num, idSize, 0);
if (-0.415241 * ndigits - 0.125 > bytes ) {
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 / 2) / y * y;
if (neg) x = -x;
return LONG2NUM(x);
}
if (RB_TYPE_P(f, T_FLOAT)) {
/* then int_pow overflow */
return INT2FIX(0);
}
h = rb_funcall(f, '/', 1, INT2FIX(2));
r = rb_funcall(num, '%', 1, f);
n = rb_funcall(num, '-', 1, r);
op = negative_int_p(num) ? idLE : '<';
if (!RTEST(rb_funcall(r, op, 1, h))) {
n = rb_funcall(n, '+', 1, f);
}
return n;
}
static VALUE
flo_truncate(VALUE num);
/*
* call-seq:
* float.round([ndigits]) -> integer or float
*
* Rounds +float+ to a given precision in decimal digits (default 0 digits).
*
* Precision may be negative. Returns a floating point number when +ndigits+
* is more than zero.
*
* 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
*
*/
static VALUE
flo_round(int argc, VALUE *argv, VALUE num)
{
VALUE nd;
double number, f, x;
int ndigits = 0;
int binexp;
enum {float_dig = DBL_DIG+2};
if (argc > 0 && rb_scan_args(argc, argv, "01", &nd) == 1) {
ndigits = NUM2INT(nd);
}
if (ndigits < 0) {
return int_round_0(flo_truncate(num), ndigits);
}
number = RFLOAT_VALUE(num);
if (ndigits == 0) {
return dbl2ival(number);
}
frexp(number, &binexp);
/* 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 (isinf(number) || isnan(number) ||
(ndigits >= float_dig - (binexp > 0 ? binexp / 4 : binexp / 3 - 1))) {
return num;
}
if (ndigits < - (binexp > 0 ? binexp / 3 + 1 : binexp / 4)) {
return DBL2NUM(0);
}
f = pow(10, ndigits);
x = round(number * f);
if (x > 0) {
if ((double)((x + 0.5) / f) <= number) x += 1;
}
else {
if ((double)((x - 0.5) / f) >= number) x -= 1;
}
return DBL2NUM(x / f);}
/*
* call-seq:
* float.to_i -> integer
* float.to_int -> integer
* float.truncate -> integer
*
* Returns the +float+ truncated to an Integer.
*
* Synonyms are #to_i, #to_int, and #truncate.
*/
static VALUE
flo_truncate(VALUE num)
{
double f = RFLOAT_VALUE(num);
long val;
if (f > 0.0) f = floor(f);
if (f < 0.0) f = ceil(f);
if (!FIXABLE(f)) {
return rb_dbl2big(f);
}
val = (long)f;
return LONG2FIX(val);
}
/*
* call-seq:
* float.positive? -> true or false
*
* Returns +true+ if +float+ is greater than 0.
*/
static VALUE
flo_positive_p(VALUE num)
{
double f = RFLOAT_VALUE(num);
return f > 0.0 ? Qtrue : Qfalse;
}
/*
* call-seq:
* float.negative? -> true or false
*
* Returns +true+ if +float+ is less than 0.
*/
static VALUE
flo_negative_p(VALUE num)
{
double f = RFLOAT_VALUE(num);
return f < 0.0 ? Qtrue : Qfalse;
}
/*
* call-seq:
* num.floor -> integer
*
* Returns the largest integer less than or equal to +num+.
*
* Numeric implements this by converting an Integer to a Float and invoking
* Float#floor.
*
* 1.floor #=> 1
* (-1).floor #=> -1
*/
static VALUE
num_floor(VALUE num)
{
return flo_floor(rb_Float(num));
}
/*
* call-seq:
* num.ceil -> integer
*
* Returns the smallest possible Integer that is greater than or equal to
* +num+.
*
* Numeric achieves this by converting itself to a Float then invoking
* Float#ceil.
*
* 1.ceil #=> 1
* 1.2.ceil #=> 2
* (-1.2).ceil #=> -1
* (-1.0).ceil #=> -1
*/
static VALUE
num_ceil(VALUE num)
{
return flo_ceil(rb_Float(num));
}
/*
* call-seq:
* num.round([ndigits]) -> integer or float
*
* Rounds +num+ to a given precision in decimal digits (default 0 digits).
*
* Precision may be negative. Returns a floating point number when +ndigits+
* is more than zero.
*
* Numeric implements this by converting itself to a Float and invoking
* Float#round.
*/
static VALUE
num_round(int argc, VALUE* argv, VALUE num)
{
return flo_round(argc, argv, rb_Float(num));
}
/*
* call-seq:
* num.truncate -> integer
*
* Returns +num+ truncated to an Integer.
*
* Numeric implements this by converting its value to a Float and invoking
* Float#truncate.
*/
static VALUE
num_truncate(VALUE num)
{
return flo_truncate(rb_Float(num));
}
static double
ruby_float_step_size(double beg, double end, double unit, int excl)
{
const double epsilon = DBL_EPSILON;
double n = (end - beg)/unit;
double err = (fabs(beg) + fabs(end) + fabs(end-beg)) / fabs(unit) * epsilon;
if (isinf(unit)) {
return unit > 0 ? beg <= end : beg >= end;
}
if (unit == 0) {
return INFINITY;
}
if (err>0.5) err=0.5;
if (excl) {
if (n<=0) return 0;
if (n<1)
n = 0;
else
n = floor(n - err);
}
else {
if (n<0) return 0;
n = floor(n + err);
}
return n+1;
}
int
ruby_float_step(VALUE from, VALUE to, VALUE step, int excl)
{
if (RB_TYPE_P(from, T_FLOAT) || RB_TYPE_P(to, T_FLOAT) || RB_TYPE_P(step, T_FLOAT)) {
double beg = NUM2DBL(from);
double end = NUM2DBL(to);
double unit = NUM2DBL(step);
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(INFINITY);
}
delta = FIX2LONG(to) - FIX2LONG(from);
if (diff < 0) {
diff = -diff;
delta = -delta;
}
if (excl) {
delta--;
}
if (delta < 0) {
return INT2FIX(0);
}
return ULONG2NUM(delta / diff + 1UL);
}
else if (RB_TYPE_P(from, T_FLOAT) || RB_TYPE_P(to, T_FLOAT) || RB_TYPE_P(step, T_FLOAT)) {
double n = ruby_float_step_size(NUM2DBL(from), NUM2DBL(to), NUM2DBL(step), excl);
if (isinf(n)) return DBL2NUM(n);
if (POSFIXABLE(n)) return LONG2FIX(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(INFINITY);
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_scan_args(int argc, const VALUE *argv, VALUE *to, VALUE *step)
{
VALUE hash;
int desc;
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");
*step = values[1];
}
}
else {
/* compatibility */
if (argc > 1 && NIL_P(*step)) {
rb_raise(rb_eTypeError, "step must be numeric");
}
if (rb_equal(*step, INT2FIX(0))) {
rb_raise(rb_eArgError, "step can't be 0");
}
}
if (NIL_P(*step)) {
*step = INT2FIX(1);
}
desc = !positive_int_p(*step);
if (NIL_P(*to)) {
*to = desc ? DBL2NUM(-INFINITY) : DBL2NUM(INFINITY);
}
return desc;
}
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);
return ruby_num_interval_step_size(from, to, step, FALSE);
}
/*
* call-seq:
* num.step(by: step, to: limit) {|i| block } -> self
* num.step(by: step, to: limit) -> an_enumerator
* num.step(limit=nil, step=1) {|i| block } -> self
* num.step(limit=nil, step=1) -> an_enumerator
*
* Invokes the given block with the sequence of numbers starting at +num+,
* incremented by +step+ (defaulted to +1+) on each call.
*
* The loop finishes when the value to be passed to the block is greater than
* +limit+ (if +step+ is positive) or less than +limit+ (if +step+ is
* negative), where <i>limit</i> is defaulted to infinity.
*
* In the recommended keyword argument style, either or both of
* +step+ and +limit+ (default infinity) can be omitted. In the
* fixed position argument style, zero as a step
* (i.e. num.step(limit, 0)) is not allowed for historical
* compatibility reasons.
*
* If all the arguments are integers, the loop operates using an integer
* counter.
*
* If any of the arguments are floating point numbers, all are converted to floats, and the loop is executed the following expression:
*
* floor(n + n*epsilon)+ 1
*
* Where the +n+ is the following:
*
* n = (limit - num)/step
*
* Otherwise, the loop starts at +num+, uses either the less-than (<) or
* greater-than (>) operator to compare the counter against +limit+, and
* increments itself using the <code>+</code> operator.
*
* If no block is given, an Enumerator is returned instead.
*
* For example:
*
* p 1.step.take(4)
* p 10.step(by: -1).take(4)
* 3.step(to: 5) { |i| print i, " " }
* 1.step(10, 2) { |i| print i, " " }
* Math::E.step(to: Math::PI, by: 0.2) { |f| print f, " " }
*
* Will produce:
*
* [1, 2, 3, 4]
* [10, 9, 8, 7]
* 3 4 5
* 1 3 5 7 9
* 2.71828182845905 2.91828182845905 3.11828182845905
*/
static VALUE
num_step(int argc, VALUE *argv, VALUE from)
{
VALUE to, step;
int desc, inf;
RETURN_SIZED_ENUMERATOR(from, argc, argv, num_step_size);
desc = num_step_scan_args(argc, argv, &to, &step);
if (RTEST(rb_num_coerce_cmp(step, INT2FIX(0), id_eq))) {
inf = 1;
}
else if (RB_TYPE_P(to, T_FLOAT)) {
double f = RFLOAT_VALUE(to);
inf = isinf(f) && (signbit(f) ? desc : !desc);
}
else inf = 0;
if (FIXNUM_P(from) && (inf || FIXNUM_P(to)) && FIXNUM_P(step)) {
long i = FIX2LONG(from);
long diff = FIX2LONG(step);
if (inf) {
for (;; i += diff)
rb_yield(LONG2FIX(i));
}
else {
long end = FIX2LONG(to);
if (desc) {
for (; i >= end; i += diff)
rb_yield(LONG2FIX(i));
}
else {
for (; i <= end; i += diff)
rb_yield(LONG2FIX(i));
}
}
}
else if (!ruby_float_step(from, to, step, FALSE)) {
VALUE i = from;
if (inf) {
for (;; i = rb_funcall(i, '+', 1, step))
rb_yield(i);
}
else {
ID cmp = desc ? '<' : '>';
for (; !RTEST(rb_funcall(i, cmp, 1, to)); i = rb_funcall(i, '+', 1, step))
rb_yield(i);
}
}
return from;
}
static char *
out_of_range_float(char (*pbuf)[24], VALUE val)
{
char *const buf = *pbuf;
char *s;
snprintf(buf, sizeof(*pbuf), "%-.10g", RFLOAT_VALUE(val));
if ((s = strchr(buf, ' ')) != 0) *s = '\0';
return buf;
}
#define FLOAT_OUT_OF_RANGE(val, type) do { \
char buf[24]; \
rb_raise(rb_eRangeError, "float %s out of range of "type, \
out_of_range_float(&buf, (val))); \
} while (0)
#define LONG_MIN_MINUS_ONE ((double)LONG_MIN-1)
#define LONG_MAX_PLUS_ONE (2*(double)(LONG_MAX/2+1))
#define ULONG_MAX_PLUS_ONE (2*(double)(ULONG_MAX/2+1))
#define LONG_MIN_MINUS_ONE_IS_LESS_THAN(n) \
(LONG_MIN_MINUS_ONE == (double)LONG_MIN ? \
LONG_MIN <= (n): \
LONG_MIN_MINUS_ONE < (n))
long
rb_num2long(VALUE val)
{
again:
if (NIL_P(val)) {
rb_raise(rb_eTypeError, "no implicit conversion from nil to integer");
}
if (FIXNUM_P(val)) return FIX2LONG(val);
else if (RB_TYPE_P(val, T_FLOAT)) {
if (RFLOAT_VALUE(val) < LONG_MAX_PLUS_ONE
&& LONG_MIN_MINUS_ONE_IS_LESS_THAN(RFLOAT_VALUE(val))) {
return (long)RFLOAT_VALUE(val);
}
else {
FLOAT_OUT_OF_RANGE(val, "integer");
}
}
else if (RB_TYPE_P(val, T_BIGNUM)) {
return rb_big2long(val);
}
else {
val = rb_to_int(val);
goto again;
}
}
static unsigned long
rb_num2ulong_internal(VALUE val, int *wrap_p)
{
again:
if (NIL_P(val)) {
rb_raise(rb_eTypeError, "no implicit conversion from nil to integer");
}
if (FIXNUM_P(val)) {
long l = FIX2LONG(val); /* this is FIX2LONG, inteneded */
if (wrap_p)
*wrap_p = l < 0;
return (unsigned long)l;
}
else if (RB_TYPE_P(val, T_FLOAT)) {
if (RFLOAT_VALUE(val) < ULONG_MAX_PLUS_ONE
&& LONG_MIN_MINUS_ONE_IS_LESS_THAN(RFLOAT_VALUE(val))) {
double d = RFLOAT_VALUE(val);
if (wrap_p)
*wrap_p = d <= -1.0; /* NUM2ULONG(v) uses v.to_int conceptually. */
if (0 <= d)
return (unsigned long)d;
return (unsigned long)(long)d;
}
else {
FLOAT_OUT_OF_RANGE(val, "integer");
}
}
else if (RB_TYPE_P(val, T_BIGNUM)) {
{
unsigned long ul = rb_big2ulong(val);
if (wrap_p)
*wrap_p = BIGNUM_NEGATIVE_P(val);
return ul;
}
}
else {
val = rb_to_int(val);
goto again;
}
}
unsigned long
rb_num2ulong(VALUE val)
{
return rb_num2ulong_internal(val, NULL);
}
#if SIZEOF_INT < SIZEOF_LONG
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");
}
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, negative_int_p(val));
return num;
}
#else
long
rb_num2int(VALUE val)
{
return rb_num2long(val);
}
long
rb_fix2int(VALUE val)
{
return FIX2INT(val);
}
#endif
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, negative_int_p(val));
return num;
}
VALUE
rb_num2fix(VALUE val)
{
long v;
if (FIXNUM_P(val)) return val;
v = rb_num2long(val);
if (!FIXABLE(v))
rb_raise(rb_eRangeError, "integer %ld out of range of fixnum", v);
return LONG2FIX(v);
}
#if HAVE_LONG_LONG
#define LLONG_MIN_MINUS_ONE ((double)LLONG_MIN-1)
#define LLONG_MAX_PLUS_ONE (2*(double)(LLONG_MAX/2+1))
#define ULLONG_MAX_PLUS_ONE (2*(double)(ULLONG_MAX/2+1))
#ifndef ULLONG_MAX
#define ULLONG_MAX ((unsigned LONG_LONG)LLONG_MAX*2+1)
#endif
#define LLONG_MIN_MINUS_ONE_IS_LESS_THAN(n) \
(LLONG_MIN_MINUS_ONE == (double)LLONG_MIN ? \
LLONG_MIN <= (n): \
LLONG_MIN_MINUS_ONE < (n))
LONG_LONG
rb_num2ll(VALUE val)
{
if (NIL_P(val)) {
rb_raise(rb_eTypeError, "no implicit conversion from nil");
}
if (FIXNUM_P(val)) return (LONG_LONG)FIX2LONG(val);
else if (RB_TYPE_P(val, T_FLOAT)) {
if (RFLOAT_VALUE(val) < LLONG_MAX_PLUS_ONE
&& (LLONG_MIN_MINUS_ONE_IS_LESS_THAN(RFLOAT_VALUE(val)))) {
return (LONG_LONG)(RFLOAT_VALUE(val));
}
else {
FLOAT_OUT_OF_RANGE(val, "long long");
}
}
else if (RB_TYPE_P(val, T_BIGNUM)) {
return rb_big2ll(val);
}
else if (RB_TYPE_P(val, T_STRING)) {
rb_raise(rb_eTypeError, "no implicit conversion from string");
}
else if (RB_TYPE_P(val, T_TRUE) || RB_TYPE_P(val, T_FALSE)) {
rb_raise(rb_eTypeError, "no implicit conversion from boolean");
}
val = rb_to_int(val);
return NUM2LL(val);
}
unsigned LONG_LONG
rb_num2ull(VALUE val)
{
if (RB_TYPE_P(val, T_NIL)) {
rb_raise(rb_eTypeError, "no implicit conversion from nil");
}
else if (RB_TYPE_P(val, T_FIXNUM)) {
return (LONG_LONG)FIX2LONG(val); /* this is FIX2LONG, inteneded */
}
else if (RB_TYPE_P(val, T_FLOAT)) {
if (RFLOAT_VALUE(val) < ULLONG_MAX_PLUS_ONE
&& LLONG_MIN_MINUS_ONE_IS_LESS_THAN(RFLOAT_VALUE(val))) {
if (0 <= RFLOAT_VALUE(val))
return (unsigned LONG_LONG)(RFLOAT_VALUE(val));
return (unsigned LONG_LONG)(LONG_LONG)(RFLOAT_VALUE(val));
}
else {
FLOAT_OUT_OF_RANGE(val, "unsigned long long");
}
}
else if (RB_TYPE_P(val, T_BIGNUM)) {
return rb_big2ull(val);
}
else if (RB_TYPE_P(val, T_STRING)) {
rb_raise(rb_eTypeError, "no implicit conversion from string");
}
else if (RB_TYPE_P(val, T_TRUE) || RB_TYPE_P(val, T_FALSE)) {
rb_raise(rb_eTypeError, "no implicit conversion from boolean");
}
val = rb_to_int(val);
return NUM2ULL(val);
}
#endif /* HAVE_LONG_LONG */
/*
* Document-class: Integer
*
* This class is the basis for the two concrete classes that hold whole
* numbers, Bignum and Fixnum.
*
*/
/*
* call-seq:
* int.to_i -> integer
*
* As +int+ is already an Integer, all these methods simply return the receiver.
*
* Synonyms are #to_int, #floor, #ceil, #truncate.
*/
static VALUE
int_to_i(VALUE num)
{
return num;
}
/*
* call-seq:
* int.integer? -> true
*
* Since +int+ is already an Integer, this always returns +true+.
*/
static VALUE
int_int_p(VALUE num)
{
return Qtrue;
}
/*
* call-seq:
* int.odd? -> true or false
*
* Returns +true+ if +int+ is an odd number.
*/
static VALUE
int_odd_p(VALUE num)
{
if (rb_funcall(num, '%', 1, INT2FIX(2)) != INT2FIX(0)) {
return Qtrue;
}
return Qfalse;
}
/*
* call-seq:
* int.even? -> true or false
*
* Returns +true+ if +int+ is an even number.
*/
static VALUE
int_even_p(VALUE num)
{
if (rb_funcall(num, '%', 1, INT2FIX(2)) == INT2FIX(0)) {
return Qtrue;
}
return Qfalse;
}
/*
* call-seq:
* int.next -> integer
* int.succ -> integer
*
* Returns the Integer equal to +int+ + 1.
*
* 1.next #=> 2
* (-1).next #=> 0
*/
static VALUE
fix_succ(VALUE num)
{
long i = FIX2LONG(num) + 1;
return LONG2NUM(i);
}
/*
* call-seq:
* int.next -> integer
* int.succ -> integer
*
* Returns the Integer equal to +int+ + 1, same as Fixnum#next.
*
* 1.next #=> 2
* (-1).next #=> 0
*/
VALUE
rb_int_succ(VALUE num)
{
if (FIXNUM_P(num)) {
long i = FIX2LONG(num) + 1;
return LONG2NUM(i);
}
if (RB_TYPE_P(num, T_BIGNUM)) {
return rb_big_plus(num, INT2FIX(1));
}
return rb_funcall(num, '+', 1, INT2FIX(1));
}
#define int_succ rb_int_succ
/*
* call-seq:
* int.pred -> integer
*
* Returns the Integer equal to +int+ - 1.
*
* 1.pred #=> 0
* (-1).pred #=> -2
*/
VALUE
rb_int_pred(VALUE num)
{
if (FIXNUM_P(num)) {
long i = FIX2LONG(num) - 1;
return LONG2NUM(i);
}
if (RB_TYPE_P(num, T_BIGNUM)) {
return rb_big_minus(num, INT2FIX(1));
}
return rb_funcall(num, '-', 1, INT2FIX(1));
}
#define int_pred rb_int_pred
VALUE
rb_enc_uint_chr(unsigned int code, rb_encoding *enc)
{
int n;
VALUE str;
switch (n = rb_enc_codelen(code, enc)) {
case ONIGERR_INVALID_CODE_POINT_VALUE:
rb_raise(rb_eRangeError, "invalid codepoint 0x%X in %s", code, rb_enc_name(enc));
break;
case ONIGERR_TOO_BIG_WIDE_CHAR_VALUE:
case 0:
rb_raise(rb_eRangeError, "%u out of char range", code);
break;
}
str = rb_enc_str_new(0, n, enc);
rb_enc_mbcput(code, RSTRING_PTR(str), enc);
if (rb_enc_precise_mbclen(RSTRING_PTR(str), RSTRING_END(str), enc) != n) {
rb_raise(rb_eRangeError, "invalid codepoint 0x%X in %s", code, rb_enc_name(enc));
}
return str;
}
/*
* call-seq:
* int.chr([encoding]) -> string
*
* Returns a string containing the character represented by the +int+'s value
* according to +encoding+.
*
* 65.chr #=> "A"
* 230.chr #=> "\346"
* 255.chr(Encoding::UTF_8) #=> "\303\277"
*/
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, "%d 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_check_arity(argc, 0, 1);
break;
}
enc = rb_to_encoding(argv[0]);
if (!enc) enc = rb_ascii8bit_encoding();
decode:
return rb_enc_uint_chr(i, enc);
}
/*
* call-seq:
* int.ord -> self
*
* Returns the +int+ itself.
*
* ?a.ord #=> 97
*
* This method is intended for compatibility to character constant in Ruby
* 1.9.
*
* For example, ?a.ord returns 97 both in 1.8 and 1.9.
*/
static VALUE
int_ord(VALUE num)
{
return num;
}
/********************************************************************
*
* Document-class: Fixnum
*
* Holds Integer values that can be represented in a native machine word
* (minus 1 bit). If any operation on a Fixnum exceeds this range, the value
* is automatically converted to a Bignum.
*
* Fixnum objects have immediate value. This means that when they are assigned
* or passed as parameters, the actual object is passed, rather than a
* reference to that object.
*
* Assignment does not alias Fixnum objects. There is effectively only one
* Fixnum object instance for any given integer value, so, for example, you
* cannot add a singleton method to a Fixnum. Any attempt to add a singleton
* method to a Fixnum object will raise a TypeError.
*/
/*
* call-seq:
* -fix -> integer
*
* Negates +fix+, which may return a Bignum.
*/
static VALUE
fix_uminus(VALUE num)
{
return LONG2NUM(-FIX2LONG(num));
}
VALUE
rb_fix2str(VALUE x, int base)
{
char buf[SIZEOF_VALUE*CHAR_BIT + 2], *b = buf + sizeof buf;
long val = FIX2LONG(x);
int neg = 0;
if (base < 2 || 36 < base) {
rb_raise(rb_eArgError, "invalid radix %d", base);
}
if (val == 0) {
return rb_usascii_str_new2("0");
}
if (val < 0) {
val = -val;
neg = 1;
}
*--b = '\0';
do {
*--b = ruby_digitmap[(int)(val % base)];
} while (val /= base);
if (neg) {
*--b = '-';
}
return rb_usascii_str_new2(b);
}
/*
* call-seq:
* fix.to_s(base=10) -> string
*
* Returns a string containing the representation of +fix+ 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"
*
*/
static VALUE
fix_to_s(int argc, VALUE *argv, VALUE x)
{
int base;
if (argc == 0) base = 10;
else {
VALUE b;
rb_scan_args(argc, argv, "01", &b);
base = NUM2INT(b);
}
return rb_fix2str(x, base);
}
/*
* call-seq:
* fix + numeric -> numeric_result
*
* Performs addition: the class of the resulting object depends on the class of
* +numeric+ and on the magnitude of the result. It may return a Bignum.
*/
static VALUE
fix_plus(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
long a, b, c;
VALUE r;
a = FIX2LONG(x);
b = FIX2LONG(y);
c = a + b;
r = LONG2NUM(c);
return r;
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return rb_big_plus(y, x);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM((double)FIX2LONG(x) + RFLOAT_VALUE(y));
}
else if (RB_TYPE_P(y, T_COMPLEX)) {
VALUE rb_nucomp_add(VALUE, VALUE);
return rb_nucomp_add(y, x);
}
else {
return rb_num_coerce_bin(x, y, '+');
}
}
/*
* call-seq:
* fix - numeric -> numeric_result
*
* Performs subtraction: the class of the resulting object depends on the class
* of +numeric+ and on the magnitude of the result. It may return a Bignum.
*/
static VALUE
fix_minus(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
long a, b, c;
VALUE r;
a = FIX2LONG(x);
b = FIX2LONG(y);
c = a - b;
r = LONG2NUM(c);
return r;
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
x = rb_int2big(FIX2LONG(x));
return rb_big_minus(x, y);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM((double)FIX2LONG(x) - RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '-');
}
}
#define SQRT_LONG_MAX ((SIGNED_VALUE)1<<((SIZEOF_LONG*CHAR_BIT-1)/2))
/*tests if N*N would overflow*/
#define FIT_SQRT_LONG(n) (((n)<SQRT_LONG_MAX)&&((n)>=-SQRT_LONG_MAX))
/*
* call-seq:
* fix * numeric -> numeric_result
*
* Performs multiplication: the class of the resulting object depends on the
* class of +numeric+ and on the magnitude of the result. It may return a
* Bignum.
*/
static VALUE
fix_mul(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
#ifdef __HP_cc
/* avoids an optimization bug of HP aC++/ANSI C B3910B A.06.05 [Jul 25 2005] */
volatile
#endif
long a, b;
#if SIZEOF_LONG * 2 <= SIZEOF_LONG_LONG
LONG_LONG d;
#else
VALUE r;
#endif
a = FIX2LONG(x);
b = FIX2LONG(y);
#if SIZEOF_LONG * 2 <= SIZEOF_LONG_LONG
d = (LONG_LONG)a * b;
if (FIXABLE(d)) return LONG2FIX(d);
return rb_ll2inum(d);
#else
if (a == 0) return x;
if (MUL_OVERFLOW_FIXNUM_P(a, b))
r = rb_big_mul(rb_int2big(a), rb_int2big(b));
else
r = LONG2FIX(a * b);
return r;
#endif
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return rb_big_mul(y, x);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM((double)FIX2LONG(x) * RFLOAT_VALUE(y));
}
else if (RB_TYPE_P(y, T_COMPLEX)) {
VALUE rb_nucomp_mul(VALUE, VALUE);
return rb_nucomp_mul(y, x);
}
else {
return rb_num_coerce_bin(x, y, '*');
}
}
static void
fixdivmod(long x, long y, long *divp, long *modp)
{
long div, mod;
if (y == 0) rb_num_zerodiv();
if (y < 0) {
if (x < 0)
div = -x / -y;
else
div = - (x / -y);
}
else {
if (x < 0)
div = - (-x / y);
else
div = x / y;
}
mod = x - div*y;
if ((mod < 0 && y > 0) || (mod > 0 && y < 0)) {
mod += y;
div -= 1;
}
if (divp) *divp = div;
if (modp) *modp = mod;
}
/*
* call-seq:
* fix.fdiv(numeric) -> float
*
* Returns the floating point result of dividing +fix+ by +numeric+.
*
* 654321.fdiv(13731) #=> 47.6528293642124
* 654321.fdiv(13731.24) #=> 47.6519964693647
*
*/
static VALUE
fix_fdiv(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
return DBL2NUM((double)FIX2LONG(x) / (double)FIX2LONG(y));
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return rb_big_fdiv(rb_int2big(FIX2LONG(x)), y);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM((double)FIX2LONG(x) / RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, rb_intern("fdiv"));
}
}
static VALUE
fix_divide(VALUE x, VALUE y, ID op)
{
if (FIXNUM_P(y)) {
long div;
fixdivmod(FIX2LONG(x), FIX2LONG(y), &div, 0);
return LONG2NUM(div);
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
x = rb_int2big(FIX2LONG(x));
return rb_big_div(x, y);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
{
double div;
if (op == '/') {
div = (double)FIX2LONG(x) / RFLOAT_VALUE(y);
return DBL2NUM(div);
}
else {
if (RFLOAT_VALUE(y) == 0) rb_num_zerodiv();
div = (double)FIX2LONG(x) / RFLOAT_VALUE(y);
return rb_dbl2big(floor(div));
}
}
}
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);
}
}
/*
* call-seq:
* fix / numeric -> numeric_result
*
* Performs division: the class of the resulting object depends on the class of
* +numeric+ and on the magnitude of the result. It may return a Bignum.
*/
static VALUE
fix_div(VALUE x, VALUE y)
{
return fix_divide(x, y, '/');
}
/*
* call-seq:
* fix.div(numeric) -> integer
*
* Performs integer division: returns integer result of dividing +fix+ by
* +numeric+.
*/
static VALUE
fix_idiv(VALUE x, VALUE y)
{
return fix_divide(x, y, id_div);
}
/*
* call-seq:
* fix % other -> real
* fix.modulo(other) -> real
*
* Returns +fix+ modulo +other+.
*
* See Numeric#divmod for more information.
*/
static VALUE
fix_mod(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
long mod;
fixdivmod(FIX2LONG(x), FIX2LONG(y), 0, &mod);
return LONG2NUM(mod);
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
x = rb_int2big(FIX2LONG(x));
return rb_big_modulo(x, y);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM(ruby_float_mod((double)FIX2LONG(x), RFLOAT_VALUE(y)));
}
else {
return rb_num_coerce_bin(x, y, '%');
}
}
/*
* call-seq:
* fix.divmod(numeric) -> array
*
* See Numeric#divmod.
*/
static VALUE
fix_divmod(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
long div, mod;
fixdivmod(FIX2LONG(x), FIX2LONG(y), &div, &mod);
return rb_assoc_new(LONG2NUM(div), LONG2NUM(mod));
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
x = rb_int2big(FIX2LONG(x));
return rb_big_divmod(x, y);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
{
double div, mod;
volatile VALUE a, b;
flodivmod((double)FIX2LONG(x), RFLOAT_VALUE(y), &div, &mod);
a = dbl2ival(div);
b = DBL2NUM(mod);
return rb_assoc_new(a, b);
}
}
else {
return rb_num_coerce_bin(x, y, id_divmod);
}
}
static VALUE
int_pow(long x, unsigned long y)
{
int neg = x < 0;
long z = 1;
if (neg) x = -x;
if (y & 1)
z = x;
else
neg = 0;
y &= ~1;
do {
while (y % 2 == 0) {
if (!FIT_SQRT_LONG(x)) {
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;
}
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
rb_int_positive_pow(long x, unsigned long y)
{
return int_pow(x, y);
}
/*
* call-seq:
* fix ** numeric -> numeric_result
*
* Raises +fix+ to the power of +numeric+, which may be negative or
* fractional.
*
* 2 ** 3 #=> 8
* 2 ** -1 #=> (1/2)
* 2 ** 0.5 #=> 1.4142135623731
*/
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) {
if (b % 2 == 0)
return INT2FIX(1);
else
return INT2FIX(-1);
}
if (b < 0)
return rb_funcall(rb_rational_raw1(x), idPow, 1, y);
if (b == 0) return INT2FIX(1);
if (b == 1) return x;
if (a == 0) {
if (b > 0) return INT2FIX(0);
return DBL2NUM(INFINITY);
}
return int_pow(a, b);
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
if (a == 1) return INT2FIX(1);
if (a == -1) {
if (int_even_p(y)) return INT2FIX(1);
else return INT2FIX(-1);
}
if (negative_int_p(y))
return rb_funcall(rb_rational_raw1(x), idPow, 1, y);
if (a == 0) return INT2FIX(0);
x = rb_int2big(FIX2LONG(x));
return rb_big_pow(x, y);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
if (RFLOAT_VALUE(y) == 0.0) return DBL2NUM(1.0);
if (a == 0) {
return DBL2NUM(RFLOAT_VALUE(y) < 0 ? INFINITY : 0.0);
}
if (a == 1) return DBL2NUM(1.0);
{
double dy = RFLOAT_VALUE(y);
if (a < 0 && dy != round(dy))
return rb_funcall(rb_complex_raw1(x), idPow, 1, y);
return DBL2NUM(pow((double)a, dy));
}
}
else {
return rb_num_coerce_bin(x, y, idPow);
}
}
/*
* call-seq:
* fix == other -> true or false
*
* Return +true+ if +fix+ equals +other+ numerically.
*
* 1 == 2 #=> false
* 1 == 1.0 #=> true
*/
static VALUE
fix_equal(VALUE x, VALUE y)
{
if (x == y) return Qtrue;
if (FIXNUM_P(y)) return Qfalse;
else if (RB_TYPE_P(y, T_BIGNUM)) {
return rb_big_eq(y, x);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return rb_integer_float_eq(x, y);
}
else {
return num_equal(x, y);
}
}
/*
* call-seq:
* fix <=> numeric -> -1, 0, +1 or nil
*
* Comparison---Returns +-1+, +0+, ++1+ or +nil+ depending on whether +fix+ is
* less than, equal to, or greater than +numeric+.
*
* This is the basis for the tests in the Comparable module.
*
* +nil+ is returned if the two values are incomparable.
*/
static VALUE
fix_cmp(VALUE x, VALUE y)
{
if (x == y) return INT2FIX(0);
if (FIXNUM_P(y)) {
if (FIX2LONG(x) > FIX2LONG(y)) return INT2FIX(1);
return INT2FIX(-1);
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return rb_big_cmp(rb_int2big(FIX2LONG(x)), y);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return rb_integer_float_cmp(x, y);
}
else {
return rb_num_coerce_cmp(x, y, id_cmp);
}
}
/*
* call-seq:
* fix > real -> true or false
*
* Returns +true+ if the value of +fix+ is greater than that of +real+.
*/
static VALUE
fix_gt(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
if (FIX2LONG(x) > FIX2LONG(y)) return Qtrue;
return Qfalse;
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return FIX2INT(rb_big_cmp(rb_int2big(FIX2LONG(x)), y)) > 0 ? Qtrue : Qfalse;
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return rb_integer_float_cmp(x, y) == INT2FIX(1) ? Qtrue : Qfalse;
}
else {
return rb_num_coerce_relop(x, y, '>');
}
}
/*
* call-seq:
* fix >= real -> true or false
*
* Returns +true+ if the value of +fix+ is greater than or equal to that of
* +real+.
*/
static VALUE
fix_ge(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
if (FIX2LONG(x) >= FIX2LONG(y)) return Qtrue;
return Qfalse;
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return FIX2INT(rb_big_cmp(rb_int2big(FIX2LONG(x)), y)) >= 0 ? Qtrue : Qfalse;
}
else if (RB_TYPE_P(y, T_FLOAT)) {
VALUE rel = rb_integer_float_cmp(x, y);
return rel == INT2FIX(1) || rel == INT2FIX(0) ? Qtrue : Qfalse;
}
else {
return rb_num_coerce_relop(x, y, idGE);
}
}
/*
* call-seq:
* fix < real -> true or false
*
* Returns +true+ if the value of +fix+ is less than that of +real+.
*/
static VALUE
fix_lt(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
if (FIX2LONG(x) < FIX2LONG(y)) return Qtrue;
return Qfalse;
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return FIX2INT(rb_big_cmp(rb_int2big(FIX2LONG(x)), y)) < 0 ? Qtrue : Qfalse;
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return rb_integer_float_cmp(x, y) == INT2FIX(-1) ? Qtrue : Qfalse;
}
else {
return rb_num_coerce_relop(x, y, '<');
}
}
/*
* call-seq:
* fix <= real -> true or false
*
* Returns +true+ if the value of +fix+ is less than or equal to that of
* +real+.
*/
static VALUE
fix_le(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
if (FIX2LONG(x) <= FIX2LONG(y)) return Qtrue;
return Qfalse;
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return FIX2INT(rb_big_cmp(rb_int2big(FIX2LONG(x)), y)) <= 0 ? Qtrue : Qfalse;
}
else if (RB_TYPE_P(y, T_FLOAT)) {
VALUE rel = rb_integer_float_cmp(x, y);
return rel == INT2FIX(-1) || rel == INT2FIX(0) ? Qtrue : Qfalse;
}
else {
return rb_num_coerce_relop(x, y, idLE);
}
}
/*
* call-seq:
* ~fix -> integer
*
* One's complement: returns a number where each bit is flipped.
*/
static VALUE
fix_rev(VALUE num)
{
return ~num | FIXNUM_FLAG;
}
static int
bit_coerce(VALUE *x, VALUE *y)
{
if (!FIXNUM_P(*y) && !RB_TYPE_P(*y, T_BIGNUM)) {
VALUE orig = *x;
do_coerce(x, y, TRUE);
if (!FIXNUM_P(*x) && !RB_TYPE_P(*x, T_BIGNUM)
&& !FIXNUM_P(*y) && !RB_TYPE_P(*y, T_BIGNUM)) {
coerce_failed(orig, *y);
}
}
return TRUE;
}
VALUE
rb_num_coerce_bit(VALUE x, VALUE y, ID func)
{
bit_coerce(&x, &y);
return rb_funcall(x, func, 1, y);
}
/*
* call-seq:
* fix & integer -> integer_result
*
* Bitwise AND.
*/
static VALUE
fix_and(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
long val = FIX2LONG(x) & FIX2LONG(y);
return LONG2NUM(val);
}
if (RB_TYPE_P(y, T_BIGNUM)) {
return rb_big_and(y, x);
}
bit_coerce(&x, &y);
return rb_funcall(x, '&', 1, y);
}
/*
* call-seq:
* fix | integer -> integer_result
*
* Bitwise OR.
*/
static VALUE
fix_or(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
long val = FIX2LONG(x) | FIX2LONG(y);
return LONG2NUM(val);
}
if (RB_TYPE_P(y, T_BIGNUM)) {
return rb_big_or(y, x);
}
bit_coerce(&x, &y);
return rb_funcall(x, '|', 1, y);
}
/*
* call-seq:
* fix ^ integer -> integer_result
*
* Bitwise EXCLUSIVE OR.
*/
static VALUE
fix_xor(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
long val = FIX2LONG(x) ^ FIX2LONG(y);
return LONG2NUM(val);
}
if (RB_TYPE_P(y, T_BIGNUM)) {
return rb_big_xor(y, x);
}
bit_coerce(&x, &y);
return rb_funcall(x, '^', 1, y);
}
static VALUE fix_lshift(long, unsigned long);
static VALUE fix_rshift(long, unsigned long);
/*
* call-seq:
* fix << count -> integer
*
* Shifts +fix+ 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);
}
/*
* call-seq:
* fix >> count -> integer
*
* Shifts +fix+ 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);
}
/*
* call-seq:
* fix[n] -> 0, 1
*
* Bit Reference---Returns the +n+th bit in the binary representation of
* +fix+, where <code>fix[0]</code> is the least significant bit.
*
* For example:
*
* a = 0b11001100101010
* 30.downto(0) do |n| print a[n] end
* #=> 0000000000000000011001100101010
*/
static VALUE
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);
}
/*
* call-seq:
* fix.to_f -> float
*
* Converts +fix+ to a Float.
*
*/
static VALUE
fix_to_f(VALUE num)
{
double val;
val = (double)FIX2LONG(num);
return DBL2NUM(val);
}
/*
* call-seq:
* fix.abs -> integer
* fix.magnitude -> integer
*
* Returns the absolute value of +fix+.
*
* -12345.abs #=> 12345
* 12345.abs #=> 12345
*
*/
static VALUE
fix_abs(VALUE fix)
{
long i = FIX2LONG(fix);
if (i < 0) i = -i;
return LONG2NUM(i);
}
/*
* call-seq:
* fix.size -> fixnum
*
* Returns the number of bytes in the machine representation of +fix+.
*
* 1.size #=> 4
* -1.size #=> 4
* 2147483647.size #=> 4
*/
static VALUE
fix_size(VALUE fix)
{
return INT2FIX(sizeof(long));
}
/*
* call-seq:
* int.bit_length -> integer
*
* Returns the number of bits of the value of <i>int</i>.
*
* "the number of bits" means that
* the bit position of the highest bit which is different to the sign bit.
* (The bit position of the bit 2**n is n+1.)
* If there is no such bit (zero or minus one), zero is returned.
*
* I.e. This method returns ceil(log2(int < 0 ? -int : int+1)).
*
* (-2**12-1).bit_length #=> 13
* (-2**12).bit_length #=> 12
* (-2**12+1).bit_length #=> 12
* -0x101.bit_length #=> 9
* -0x100.bit_length #=> 8
* -0xff.bit_length #=> 8
* -2.bit_length #=> 1
* -1.bit_length #=> 0
* 0.bit_length #=> 0
* 1.bit_length #=> 1
* 0xff.bit_length #=> 8
* 0x100.bit_length #=> 9
* (2**12-1).bit_length #=> 12
* (2**12).bit_length #=> 13
* (2**12+1).bit_length #=> 13
*
* This method can be used to detect overflow in Array#pack as follows.
*
* if n.bit_length < 32
* [n].pack("l") # no overflow
* else
* raise "overflow"
* end
*/
static VALUE
rb_fix_bit_length(VALUE fix)
{
long v = FIX2LONG(fix);
if (v < 0)
v = ~v;
return LONG2FIX(bit_length(v));
}
static VALUE
int_upto_size(VALUE from, VALUE args, VALUE eobj)
{
return ruby_num_interval_step_size(from, RARRAY_AREF(args, 0), INT2FIX(1), FALSE);
}
/*
* call-seq:
* 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.
*
* For example:
*
* 5.upto(10) { |i| print i, " " }
* #=> 5 6 7 8 9 10
*/
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));
}
if (NIL_P(c)) rb_cmperr(i, to);
}
return from;
}
static VALUE
int_downto_size(VALUE from, VALUE args, VALUE eobj)
{
return ruby_num_interval_step_size(from, RARRAY_AREF(args, 0), INT2FIX(-1), FALSE);
}
/*
* call-seq:
* int.downto(limit) {|i| block } -> self
* int.downto(limit) -> an_enumerator
*
* Iterates the given block, passing 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, ".. " }
* print " Liftoff!\n"
* #=> "5.. 4.. 3.. 2.. 1.. Liftoff!"
*/
static VALUE
int_downto(VALUE from, VALUE to)
{
RETURN_SIZED_ENUMERATOR(from, 1, &to, int_downto_size);
if (FIXNUM_P(from) && FIXNUM_P(to)) {
long i, end;
end = FIX2LONG(to);
for (i=FIX2LONG(from); i >= end; i--) {
rb_yield(LONG2FIX(i));
}
}
else {
VALUE i = from, c;
while (!(c = rb_funcall(i, '<', 1, to))) {
rb_yield(i);
i = rb_funcall(i, '-', 1, INT2FIX(1));
}
if (NIL_P(c)) rb_cmperr(i, to);
}
return from;
}
static VALUE
int_dotimes_size(VALUE num, VALUE args, VALUE eobj)
{
if (FIXNUM_P(num)) {
if (NUM2LONG(num) <= 0) return INT2FIX(0);
}
else {
if (RTEST(rb_funcall(num, '<', 1, INT2FIX(0)))) return INT2FIX(0);
}
return num;
}
/*
* call-seq:
* 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 do |i|
* print i, " "
* end
* #=> 0 1 2 3 4
*/
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;
}
/*
* call-seq:
* int.round([ndigits]) -> integer or float
*
* Rounds +int+ to a given precision in decimal digits (default 0 digits).
*
* Precision may be negative. Returns a floating point number when +ndigits+
* is positive, +self+ for zero, and round down for negative.
*
* 1.round #=> 1
* 1.round(2) #=> 1.0
* 15.round(-1) #=> 20
*/
static VALUE
int_round(int argc, VALUE* argv, VALUE num)
{
VALUE n;
int ndigits;
if (argc == 0) return num;
rb_scan_args(argc, argv, "1", &n);
ndigits = NUM2INT(n);
if (ndigits > 0) {
return rb_Float(num);
}
if (ndigits == 0) {
return num;
}
return int_round_0(num, ndigits);
}
/*
* call-seq:
* fix.zero? -> true or false
*
* Returns +true+ if +fix+ is zero.
*
*/
static VALUE
fix_zero_p(VALUE num)
{
if (FIX2LONG(num) == 0) {
return Qtrue;
}
return Qfalse;
}
/*
* call-seq:
* fix.odd? -> true or false
*
* Returns +true+ if +fix+ is an odd number.
*/
static VALUE
fix_odd_p(VALUE num)
{
if (num & 2) {
return Qtrue;
}
return Qfalse;
}
/*
* call-seq:
* fix.even? -> true or false
*
* Returns +true+ if +fix+ is an even number.
*/
static VALUE
fix_even_p(VALUE num)
{
if (num & 2) {
return Qfalse;
}
return Qtrue;
}
/*
* 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
* +infinite+ 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
* puts 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 and duplication.
*
* Integer.new(1) #=> NoMethodError: undefined method `new' for Integer:Class
* 1.dup #=> TypeError: can't dup Fixnum
*
* 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
*/
void
Init_Numeric(void)
{
#undef rb_intern
#define rb_intern(str) rb_intern_const(str)
#if defined(__FreeBSD__) && __FreeBSD__ < 4
/* allow divide by zero -- Inf */
fpsetmask(fpgetmask() & ~(FP_X_DZ|FP_X_INV|FP_X_OFL));
#elif defined(_UNICOSMP)
/* Turn off floating point exceptions for divide by zero, etc. */
_set_Creg(0, 0);
#endif
id_coerce = rb_intern("coerce");
id_div = rb_intern("div");
id_divmod = rb_intern("divmod");
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, "initialize_copy", num_init_copy, 1);
rb_define_method(rb_cNumeric, "coerce", num_coerce, 1);
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, "real?", num_real_p, 0);
rb_define_method(rb_cNumeric, "integer?", num_int_p, 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, 0);
rb_define_method(rb_cNumeric, "ceil", num_ceil, 0);
rb_define_method(rb_cNumeric, "round", num_round, -1);
rb_define_method(rb_cNumeric, "truncate", num_truncate, 0);
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_method(rb_cInteger, "integer?", int_int_p, 0);
rb_define_method(rb_cInteger, "odd?", int_odd_p, 0);
rb_define_method(rb_cInteger, "even?", int_even_p, 0);
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, "ord", int_ord, 0);
rb_define_method(rb_cInteger, "to_i", int_to_i, 0);
rb_define_method(rb_cInteger, "to_int", int_to_i, 0);
rb_define_method(rb_cInteger, "floor", int_to_i, 0);
rb_define_method(rb_cInteger, "ceil", int_to_i, 0);
rb_define_method(rb_cInteger, "truncate", int_to_i, 0);
rb_define_method(rb_cInteger, "round", int_round, -1);
rb_cFixnum = rb_define_class("Fixnum", rb_cInteger);
rb_define_method(rb_cFixnum, "to_s", fix_to_s, -1);
rb_define_alias(rb_cFixnum, "inspect", "to_s");
rb_define_method(rb_cFixnum, "-@", fix_uminus, 0);
rb_define_method(rb_cFixnum, "+", fix_plus, 1);
rb_define_method(rb_cFixnum, "-", fix_minus, 1);
rb_define_method(rb_cFixnum, "*", fix_mul, 1);
rb_define_method(rb_cFixnum, "/", fix_div, 1);
rb_define_method(rb_cFixnum, "div", fix_idiv, 1);
rb_define_method(rb_cFixnum, "%", fix_mod, 1);
rb_define_method(rb_cFixnum, "modulo", fix_mod, 1);
rb_define_method(rb_cFixnum, "divmod", fix_divmod, 1);
rb_define_method(rb_cFixnum, "fdiv", fix_fdiv, 1);
rb_define_method(rb_cFixnum, "**", fix_pow, 1);
rb_define_method(rb_cFixnum, "abs", fix_abs, 0);
rb_define_method(rb_cFixnum, "magnitude", fix_abs, 0);
rb_define_method(rb_cFixnum, "==", fix_equal, 1);
rb_define_method(rb_cFixnum, "===", fix_equal, 1);
rb_define_method(rb_cFixnum, "<=>", fix_cmp, 1);
rb_define_method(rb_cFixnum, ">", fix_gt, 1);
rb_define_method(rb_cFixnum, ">=", fix_ge, 1);
rb_define_method(rb_cFixnum, "<", fix_lt, 1);
rb_define_method(rb_cFixnum, "<=", fix_le, 1);
rb_define_method(rb_cFixnum, "~", fix_rev, 0);
rb_define_method(rb_cFixnum, "&", fix_and, 1);
rb_define_method(rb_cFixnum, "|", fix_or, 1);
rb_define_method(rb_cFixnum, "^", fix_xor, 1);
rb_define_method(rb_cFixnum, "[]", fix_aref, 1);
rb_define_method(rb_cFixnum, "<<", rb_fix_lshift, 1);
rb_define_method(rb_cFixnum, ">>", rb_fix_rshift, 1);
rb_define_method(rb_cFixnum, "to_f", fix_to_f, 0);
rb_define_method(rb_cFixnum, "size", fix_size, 0);
rb_define_method(rb_cFixnum, "bit_length", rb_fix_bit_length, 0);
rb_define_method(rb_cFixnum, "zero?", fix_zero_p, 0);
rb_define_method(rb_cFixnum, "odd?", fix_odd_p, 0);
rb_define_method(rb_cFixnum, "even?", fix_even_p, 0);
rb_define_method(rb_cFixnum, "succ", fix_succ, 0);
rb_cFloat = rb_define_class("Float", rb_cNumeric);
rb_undef_alloc_func(rb_cFloat);
rb_undef_method(CLASS_OF(rb_cFloat), "new");
/*
* Represents the rounding mode for floating point addition.
*
* Usually defaults to 1, rounding to the nearest number.
*
* Other modes include:
*
* -1:: Indeterminable
* 0:: Rounding towards zero
* 1:: Rounding to the nearest number
* 2:: Rounding towards positive infinity
* 3:: Rounding towards negative infinity
*/
rb_define_const(rb_cFloat, "ROUNDS", INT2FIX(FLT_ROUNDS));
/*
* 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 posable 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(INFINITY));
/*
* 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, "-@", flo_uminus, 0);
rb_define_method(rb_cFloat, "+", flo_plus, 1);
rb_define_method(rb_cFloat, "-", flo_minus, 1);
rb_define_method(rb_cFloat, "*", flo_mul, 1);
rb_define_method(rb_cFloat, "/", flo_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, "**", flo_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, ">", flo_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_f", flo_to_f, 0);
rb_define_method(rb_cFloat, "abs", flo_abs, 0);
rb_define_method(rb_cFloat, "magnitude", flo_abs, 0);
rb_define_method(rb_cFloat, "zero?", flo_zero_p, 0);
rb_define_method(rb_cFloat, "to_i", flo_truncate, 0);
rb_define_method(rb_cFloat, "to_int", flo_truncate, 0);
rb_define_method(rb_cFloat, "floor", flo_floor, 0);
rb_define_method(rb_cFloat, "ceil", flo_ceil, 0);
rb_define_method(rb_cFloat, "round", flo_round, -1);
rb_define_method(rb_cFloat, "truncate", flo_truncate, 0);
rb_define_method(rb_cFloat, "nan?", flo_is_nan_p, 0);
rb_define_method(rb_cFloat, "infinite?", flo_is_infinite_p, 0);
rb_define_method(rb_cFloat, "finite?", 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);
rb_define_method(rb_cFloat, "positive?", flo_positive_p, 0);
rb_define_method(rb_cFloat, "negative?", flo_negative_p, 0);
id_to = rb_intern("to");
id_by = rb_intern("by");
}
#undef rb_float_value
double
rb_float_value(VALUE v)
{
return rb_float_value_inline(v);
}
#undef rb_float_new
VALUE
rb_float_new(double d)
{
return rb_float_new_inline(d);
}
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