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ruby--ruby/rational.c
tadf ed0bdbc575 * rational.c; edited rdoc. 
git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@23747 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
2009-06-19 13:59:08 +00:00

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/*
rational.c: Coded by Tadayoshi Funaba 2008,2009
This implementation is based on Keiju Ishitsuka's Rational library
which is written in ruby.
*/
#include "ruby.h"
#include <math.h>
#include <float.h>
#ifdef HAVE_IEEEFP_H
#include <ieeefp.h>
#endif
#define NDEBUG
#include <assert.h>
#define ZERO INT2FIX(0)
#define ONE INT2FIX(1)
#define TWO INT2FIX(2)
VALUE rb_cRational;
static ID id_abs, id_cmp, id_convert, id_equal_p, id_expt, id_fdiv,
id_floor, id_idiv, id_inspect, id_integer_p, id_negate, id_to_f,
id_to_i, id_to_s, id_truncate;
#define f_boolcast(x) ((x) ? Qtrue : Qfalse)
#define binop(n,op) \
inline static VALUE \
f_##n(VALUE x, VALUE y)\
{\
return rb_funcall(x, op, 1, y);\
}
#define fun1(n) \
inline static VALUE \
f_##n(VALUE x)\
{\
return rb_funcall(x, id_##n, 0);\
}
#define fun2(n) \
inline static VALUE \
f_##n(VALUE x, VALUE y)\
{\
return rb_funcall(x, id_##n, 1, y);\
}
inline static VALUE
f_add(VALUE x, VALUE y)
{
if (FIXNUM_P(y) && FIX2LONG(y) == 0)
return x;
else if (FIXNUM_P(x) && FIX2LONG(x) == 0)
return y;
return rb_funcall(x, '+', 1, y);
}
inline static VALUE
f_cmp(VALUE x, VALUE y)
{
if (FIXNUM_P(x) && FIXNUM_P(y)) {
long c = FIX2LONG(x) - FIX2LONG(y);
if (c > 0)
c = 1;
else if (c < 0)
c = -1;
return INT2FIX(c);
}
return rb_funcall(x, id_cmp, 1, y);
}
inline static VALUE
f_div(VALUE x, VALUE y)
{
if (FIXNUM_P(y) && FIX2LONG(y) == 1)
return x;
return rb_funcall(x, '/', 1, y);
}
inline static VALUE
f_gt_p(VALUE x, VALUE y)
{
if (FIXNUM_P(x) && FIXNUM_P(y))
return f_boolcast(FIX2LONG(x) > FIX2LONG(y));
return rb_funcall(x, '>', 1, y);
}
inline static VALUE
f_lt_p(VALUE x, VALUE y)
{
if (FIXNUM_P(x) && FIXNUM_P(y))
return f_boolcast(FIX2LONG(x) < FIX2LONG(y));
return rb_funcall(x, '<', 1, y);
}
binop(mod, '%')
inline static VALUE
f_mul(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
long iy = FIX2LONG(y);
if (iy == 0) {
if (FIXNUM_P(x) || TYPE(x) == T_BIGNUM)
return ZERO;
}
else if (iy == 1)
return x;
}
else if (FIXNUM_P(x)) {
long ix = FIX2LONG(x);
if (ix == 0) {
if (FIXNUM_P(y) || TYPE(y) == T_BIGNUM)
return ZERO;
}
else if (ix == 1)
return y;
}
return rb_funcall(x, '*', 1, y);
}
inline static VALUE
f_sub(VALUE x, VALUE y)
{
if (FIXNUM_P(y) && FIX2LONG(y) == 0)
return x;
return rb_funcall(x, '-', 1, y);
}
fun1(abs)
fun1(floor)
fun1(inspect)
fun1(integer_p)
fun1(negate)
fun1(to_f)
fun1(to_i)
fun1(to_s)
fun1(truncate)
inline static VALUE
f_equal_p(VALUE x, VALUE y)
{
if (FIXNUM_P(x) && FIXNUM_P(y))
return f_boolcast(FIX2LONG(x) == FIX2LONG(y));
return rb_funcall(x, id_equal_p, 1, y);
}
fun2(expt)
fun2(fdiv)
fun2(idiv)
inline static VALUE
f_negative_p(VALUE x)
{
if (FIXNUM_P(x))
return f_boolcast(FIX2LONG(x) < 0);
return rb_funcall(x, '<', 1, ZERO);
}
#define f_positive_p(x) (!f_negative_p(x))
inline static VALUE
f_zero_p(VALUE x)
{
if (FIXNUM_P(x))
return f_boolcast(FIX2LONG(x) == 0);
return rb_funcall(x, id_equal_p, 1, ZERO);
}
#define f_nonzero_p(x) (!f_zero_p(x))
inline static VALUE
f_one_p(VALUE x)
{
if (FIXNUM_P(x))
return f_boolcast(FIX2LONG(x) == 1);
return rb_funcall(x, id_equal_p, 1, ONE);
}
inline static VALUE
f_kind_of_p(VALUE x, VALUE c)
{
return rb_obj_is_kind_of(x, c);
}
inline static VALUE
k_numeric_p(VALUE x)
{
return f_kind_of_p(x, rb_cNumeric);
}
inline static VALUE
k_integer_p(VALUE x)
{
return f_kind_of_p(x, rb_cInteger);
}
inline static VALUE
k_float_p(VALUE x)
{
return f_kind_of_p(x, rb_cFloat);
}
inline static VALUE
k_rational_p(VALUE x)
{
return f_kind_of_p(x, rb_cRational);
}
#define k_exact_p(x) (!k_float_p(x))
#define k_inexact_p(x) k_float_p(x)
#ifndef NDEBUG
#define f_gcd f_gcd_orig
#endif
inline static long
i_gcd(long x, long y)
{
if (x < 0)
x = -x;
if (y < 0)
y = -y;
if (x == 0)
return y;
if (y == 0)
return x;
while (x > 0) {
long t = x;
x = y % x;
y = t;
}
return y;
}
inline static VALUE
f_gcd(VALUE x, VALUE y)
{
VALUE z;
if (FIXNUM_P(x) && FIXNUM_P(y))
return LONG2NUM(i_gcd(FIX2LONG(x), FIX2LONG(y)));
if (f_negative_p(x))
x = f_negate(x);
if (f_negative_p(y))
y = f_negate(y);
if (f_zero_p(x))
return y;
if (f_zero_p(y))
return x;
for (;;) {
if (FIXNUM_P(x)) {
if (FIX2LONG(x) == 0)
return y;
if (FIXNUM_P(y))
return LONG2NUM(i_gcd(FIX2LONG(x), FIX2LONG(y)));
}
z = x;
x = f_mod(y, x);
y = z;
}
/* NOTREACHED */
}
#ifndef NDEBUG
#undef f_gcd
inline static VALUE
f_gcd(VALUE x, VALUE y)
{
VALUE r = f_gcd_orig(x, y);
if (f_nonzero_p(r)) {
assert(f_zero_p(f_mod(x, r)));
assert(f_zero_p(f_mod(y, r)));
}
return r;
}
#endif
inline static VALUE
f_lcm(VALUE x, VALUE y)
{
if (f_zero_p(x) || f_zero_p(y))
return ZERO;
return f_abs(f_mul(f_div(x, f_gcd(x, y)), y));
}
#define get_dat1(x) \
struct RRational *dat;\
dat = ((struct RRational *)(x))
#define get_dat2(x,y) \
struct RRational *adat, *bdat;\
adat = ((struct RRational *)(x));\
bdat = ((struct RRational *)(y))
inline static VALUE
nurat_s_new_internal(VALUE klass, VALUE num, VALUE den)
{
NEWOBJ(obj, struct RRational);
OBJSETUP(obj, klass, T_RATIONAL);
obj->num = num;
obj->den = den;
return (VALUE)obj;
}
static VALUE
nurat_s_alloc(VALUE klass)
{
return nurat_s_new_internal(klass, ZERO, ONE);
}
#define rb_raise_zerodiv() rb_raise(rb_eZeroDivError, "divided by zero")
#if 0
static VALUE
nurat_s_new_bang(int argc, VALUE *argv, VALUE klass)
{
VALUE num, den;
switch (rb_scan_args(argc, argv, "11", &num, &den)) {
case 1:
if (!k_integer_p(num))
num = f_to_i(num);
den = ONE;
break;
default:
if (!k_integer_p(num))
num = f_to_i(num);
if (!k_integer_p(den))
den = f_to_i(den);
switch (FIX2INT(f_cmp(den, ZERO))) {
case -1:
num = f_negate(num);
den = f_negate(den);
break;
case 0:
rb_raise_zerodiv();
break;
}
break;
}
return nurat_s_new_internal(klass, num, den);
}
#endif
inline static VALUE
f_rational_new_bang1(VALUE klass, VALUE x)
{
return nurat_s_new_internal(klass, x, ONE);
}
inline static VALUE
f_rational_new_bang2(VALUE klass, VALUE x, VALUE y)
{
assert(f_positive_p(y));
assert(f_nonzero_p(y));
return nurat_s_new_internal(klass, x, y);
}
#ifdef CANONICALIZATION_FOR_MATHN
#define CANON
#endif
#ifdef CANON
static int canonicalization = 0;
void
nurat_canonicalization(int f)
{
canonicalization = f;
}
#endif
inline static void
nurat_int_check(VALUE num)
{
switch (TYPE(num)) {
case T_FIXNUM:
case T_BIGNUM:
break;
default:
if (!k_numeric_p(num) || !f_integer_p(num))
rb_raise(rb_eArgError, "not an integer");
}
}
inline static VALUE
nurat_int_value(VALUE num)
{
nurat_int_check(num);
if (!k_integer_p(num))
num = f_to_i(num);
return num;
}
inline static VALUE
nurat_s_canonicalize_internal(VALUE klass, VALUE num, VALUE den)
{
VALUE gcd;
switch (FIX2INT(f_cmp(den, ZERO))) {
case -1:
num = f_negate(num);
den = f_negate(den);
break;
case 0:
rb_raise_zerodiv();
break;
}
gcd = f_gcd(num, den);
num = f_idiv(num, gcd);
den = f_idiv(den, gcd);
#ifdef CANON
if (f_one_p(den) && canonicalization)
return num;
#endif
return nurat_s_new_internal(klass, num, den);
}
inline static VALUE
nurat_s_canonicalize_internal_no_reduce(VALUE klass, VALUE num, VALUE den)
{
switch (FIX2INT(f_cmp(den, ZERO))) {
case -1:
num = f_negate(num);
den = f_negate(den);
break;
case 0:
rb_raise_zerodiv();
break;
}
#ifdef CANON
if (f_one_p(den) && canonicalization)
return num;
#endif
return nurat_s_new_internal(klass, num, den);
}
static VALUE
nurat_s_new(int argc, VALUE *argv, VALUE klass)
{
VALUE num, den;
switch (rb_scan_args(argc, argv, "11", &num, &den)) {
case 1:
num = nurat_int_value(num);
den = ONE;
break;
default:
num = nurat_int_value(num);
den = nurat_int_value(den);
break;
}
return nurat_s_canonicalize_internal(klass, num, den);
}
inline static VALUE
f_rational_new1(VALUE klass, VALUE x)
{
assert(!k_rational_p(x));
return nurat_s_canonicalize_internal(klass, x, ONE);
}
inline static VALUE
f_rational_new2(VALUE klass, VALUE x, VALUE y)
{
assert(!k_rational_p(x));
assert(!k_rational_p(y));
return nurat_s_canonicalize_internal(klass, x, y);
}
inline static VALUE
f_rational_new_no_reduce1(VALUE klass, VALUE x)
{
assert(!k_rational_p(x));
return nurat_s_canonicalize_internal_no_reduce(klass, x, ONE);
}
inline static VALUE
f_rational_new_no_reduce2(VALUE klass, VALUE x, VALUE y)
{
assert(!k_rational_p(x));
assert(!k_rational_p(y));
return nurat_s_canonicalize_internal_no_reduce(klass, x, y);
}
static VALUE
nurat_f_rational(int argc, VALUE *argv, VALUE klass)
{
return rb_funcall2(rb_cRational, id_convert, argc, argv);
}
/*
* call-seq:
* rat.numerator => integer
*
* Returns the numerator of _rat_ as an +Integer+ object.
*
* For example:
*
* Rational(7).numerator #=> 7
* Rational(7, 1).numerator #=> 7
* Rational(4.3, 40.3).numerator #=> 4841369599423283
* Rational(9, -4).numerator #=> -9
* Rational(-2, -10).numerator #=> 1
*/
static VALUE
nurat_numerator(VALUE self)
{
get_dat1(self);
return dat->num;
}
/*
* call-seq:
* rat.denominator => integer
*
* Returns the denominator of _rat_ as an +Integer+ object. If _rat_ was
* created without an explicit denominator, +1+ is returned.
*
* For example:
*
* Rational(7).denominator #=> 1
* Rational(7, 1).denominator #=> 1
* Rational(4.3, 40.3).denominator #=> 45373766245757744
* Rational(9, -4).denominator #=> 4
* Rational(-2, -10).denominator #=> 5
*/
static VALUE
nurat_denominator(VALUE self)
{
get_dat1(self);
return dat->den;
}
#ifndef NDEBUG
#define f_imul f_imul_orig
#endif
inline static VALUE
f_imul(long a, long b)
{
VALUE r;
long c;
if (a == 0 || b == 0)
return ZERO;
else if (a == 1)
return LONG2NUM(b);
else if (b == 1)
return LONG2NUM(a);
c = a * b;
r = LONG2NUM(c);
if (NUM2LONG(r) != c || (c / a) != b)
r = rb_big_mul(rb_int2big(a), rb_int2big(b));
return r;
}
#ifndef NDEBUG
#undef f_imul
inline static VALUE
f_imul(long x, long y)
{
VALUE r = f_imul_orig(x, y);
assert(f_equal_p(r, f_mul(LONG2NUM(x), LONG2NUM(y))));
return r;
}
#endif
inline static VALUE
f_addsub(VALUE self, VALUE anum, VALUE aden, VALUE bnum, VALUE bden, int k)
{
VALUE num, den;
if (FIXNUM_P(anum) && FIXNUM_P(aden) &&
FIXNUM_P(bnum) && FIXNUM_P(bden)) {
long an = FIX2LONG(anum);
long ad = FIX2LONG(aden);
long bn = FIX2LONG(bnum);
long bd = FIX2LONG(bden);
long ig = i_gcd(ad, bd);
VALUE g = LONG2NUM(ig);
VALUE a = f_imul(an, bd / ig);
VALUE b = f_imul(bn, ad / ig);
VALUE c;
if (k == '+')
c = f_add(a, b);
else
c = f_sub(a, b);
b = f_idiv(aden, g);
g = f_gcd(c, g);
num = f_idiv(c, g);
a = f_idiv(bden, g);
den = f_mul(a, b);
}
else {
VALUE g = f_gcd(aden, bden);
VALUE a = f_mul(anum, f_idiv(bden, g));
VALUE b = f_mul(bnum, f_idiv(aden, g));
VALUE c;
if (k == '+')
c = f_add(a, b);
else
c = f_sub(a, b);
b = f_idiv(aden, g);
g = f_gcd(c, g);
num = f_idiv(c, g);
a = f_idiv(bden, g);
den = f_mul(a, b);
}
return f_rational_new_no_reduce2(CLASS_OF(self), num, den);
}
/*
* call-seq:
* rat + numeric => numeric_result
*
* Performs addition. The class of the resulting object depends on
* the class of _numeric_ and on the magnitude of the
* result.
*
* A +TypeError+ is raised unless _numeric_ is a +Numeric+ object.
*
* For example:
*
* Rational(2, 3) + Rational(2, 3) #=> (4/3)
* Rational(900) + Rational(1) #=> (900/1)
* Rational(-2, 9) + Rational(-9, 2) #=> (-85/18)
* Rational(9, 8) + 4 #=> (41/8)
* Rational(20, 9) + 9.8 #=> 12.022222222222222
* Rational(8, 7) + 2**20 #=> (7340040/7)
*/
static VALUE
nurat_add(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
{
get_dat1(self);
return f_addsub(self,
dat->num, dat->den,
other, ONE, '+');
}
case T_FLOAT:
return f_add(f_to_f(self), other);
case T_RATIONAL:
{
get_dat2(self, other);
return f_addsub(self,
adat->num, adat->den,
bdat->num, bdat->den, '+');
}
default:
return rb_num_coerce_bin(self, other, '+');
}
}
/*
* call-seq:
* rat - numeric => numeric_result
*
* Performs subtraction. The class of the resulting object depends on the
* class of _numeric_ and on the magnitude of the result.
*
* A +TypeError+ is raised unless _numeric_ is a +Numeric+ object.
*
* For example:
*
* Rational(2, 3) - Rational(2, 3) #=> (0/1)
* Rational(900) - Rational(1) #=> (899/1)
* Rational(-2, 9) - Rational(-9, 2) #=> (77/18)
* Rational(9, 8) - 4 #=> (23/8)
* Rational(20, 9) - 9.8 #=> -7.577777777777778
* Rational(8, 7) - 2**20 #=> (-7340024/7)
*/
static VALUE
nurat_sub(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
{
get_dat1(self);
return f_addsub(self,
dat->num, dat->den,
other, ONE, '-');
}
case T_FLOAT:
return f_sub(f_to_f(self), other);
case T_RATIONAL:
{
get_dat2(self, other);
return f_addsub(self,
adat->num, adat->den,
bdat->num, bdat->den, '-');
}
default:
return rb_num_coerce_bin(self, other, '-');
}
}
inline static VALUE
f_muldiv(VALUE self, VALUE anum, VALUE aden, VALUE bnum, VALUE bden, int k)
{
VALUE num, den;
if (k == '/') {
VALUE t;
if (f_negative_p(bnum)) {
anum = f_negate(anum);
bnum = f_negate(bnum);
}
t = bnum;
bnum = bden;
bden = t;
}
if (FIXNUM_P(anum) && FIXNUM_P(aden) &&
FIXNUM_P(bnum) && FIXNUM_P(bden)) {
long an = FIX2LONG(anum);
long ad = FIX2LONG(aden);
long bn = FIX2LONG(bnum);
long bd = FIX2LONG(bden);
long g1 = i_gcd(an, bd);
long g2 = i_gcd(ad, bn);
num = f_imul(an / g1, bn / g2);
den = f_imul(ad / g2, bd / g1);
}
else {
VALUE g1 = f_gcd(anum, bden);
VALUE g2 = f_gcd(aden, bnum);
num = f_mul(f_idiv(anum, g1), f_idiv(bnum, g2));
den = f_mul(f_idiv(aden, g2), f_idiv(bden, g1));
}
return f_rational_new_no_reduce2(CLASS_OF(self), num, den);
}
/*
* call-seq:
* rat * numeric => numeric_result
*
* Performs multiplication. The class of the resulting object depends on
* the class of _numeric_ and on the magnitude of the result.
*
* A +TypeError+ is raised unless _numeric_ is a +Numeric+ object.
*
* For example:
*
* Rational(2, 3) * Rational(2, 3) #=> (4/9)
* Rational(900) * Rational(1) #=> (900/1)
* Rational(-2, 9) * Rational(-9, 2) #=> (1/1)
* Rational(9, 8) * 4 #=> (9/2)
* Rational(20, 9) * 9.8 #=> 21.77777777777778
* Rational(8, 7) * 2**20 #=> (8388608/7)
*/
static VALUE
nurat_mul(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
{
get_dat1(self);
return f_muldiv(self,
dat->num, dat->den,
other, ONE, '*');
}
case T_FLOAT:
return f_mul(f_to_f(self), other);
case T_RATIONAL:
{
get_dat2(self, other);
return f_muldiv(self,
adat->num, adat->den,
bdat->num, bdat->den, '*');
}
default:
return rb_num_coerce_bin(self, other, '*');
}
}
/*
* call-seq:
* rat / numeric => numeric_result
* rat.quo(numeric) => numeric_result
*
* Performs division. The class of the resulting object depends on the class
* of _numeric_ and on the magnitude of the result.
*
* A +TypeError+ is raised unless _numeric_ is a +Numeric+ object. A
* +ZeroDivisionError+ is raised if _numeric_ is 0.
*
* For example:
*
* Rational(2, 3) / Rational(2, 3) #=> (1/1)
* Rational(900) / Rational(1) #=> (900/1)
* Rational(-2, 9) / Rational(-9, 2) #=> (4/81)
* Rational(9, 8) / 4 #=> (9/32)
* Rational(20, 9) / 9.8 #=> 0.22675736961451246
* Rational(8, 7) / 2**20 #=> (1/917504)
* Rational(2, 13) / 0 #=> ZeroDivisionError: divided by zero
* Rational(2, 13) / 0.0 #=> Infinity
*/
static VALUE
nurat_div(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
if (f_zero_p(other))
rb_raise_zerodiv();
{
get_dat1(self);
return f_muldiv(self,
dat->num, dat->den,
other, ONE, '/');
}
case T_FLOAT:
return rb_funcall(f_to_f(self), '/', 1, other);
case T_RATIONAL:
if (f_zero_p(other))
rb_raise_zerodiv();
{
get_dat2(self, other);
return f_muldiv(self,
adat->num, adat->den,
bdat->num, bdat->den, '/');
}
default:
return rb_num_coerce_bin(self, other, '/');
}
}
/*
* call-seq:
* rat.fdiv(numeric) => float
*
* Performs float division: dividing _rat_ by _numeric_. The return value is a
* +Float+ object.
*
* A +TypeError+ is raised unless _numeric_ is a +Numeric+ object.
*
* For example:
*
* Rational(2, 3).fdiv(1) #=> 0.6666666666666666
* Rational(2, 3).fdiv(0.5) #=> 1.3333333333333333
* Rational(2).fdiv(3) #=> 0.6666666666666666
* Rational(-9, 6.6).fdiv(6.6) #=> -0.20661157024793392
* Rational(-20).fdiv(0.0) #=> -Infinity
*/
static VALUE
nurat_fdiv(VALUE self, VALUE other)
{
return f_to_f(f_div(self, other));
}
/*
* call-seq:
* rat ** numeric => numeric_result
*
* Performs exponentiation, i.e. it raises _rat_ to the exponent _numeric_.
* The class of the resulting object depends on the class of _numeric_ and on
* the magnitude of the result. A +TypeError+ is raised unless _numeric_ is a
* +Numeric+ object.
*
* For example:
*
* Rational(2, 3) ** Rational(2, 3) #=> 0.7631428283688879
* Rational(900) ** Rational(1) #=> (900/1)
* Rational(-2, 9) ** Rational(-9, 2) #=> (4.793639101185069e-13-869.8739233809262i)
* Rational(9, 8) ** 4 #=> (6561/4096)
* Rational(20, 9) ** 9.8 #=> 2503.325740344559
* Rational(3, 2) ** 2**3 #=> (6561/256)
* Rational(2, 13) ** 0 #=> (1/1)
* Rational(2, 13) ** 0.0 #=> 1.0
*/
static VALUE
nurat_expt(VALUE self, VALUE other)
{
if (k_exact_p(other) && f_zero_p(other))
return f_rational_new_bang1(CLASS_OF(self), ONE);
if (k_rational_p(other)) {
get_dat1(other);
if (f_one_p(dat->den))
other = dat->num; /* good? */
}
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
{
VALUE num, den;
get_dat1(self);
switch (FIX2INT(f_cmp(other, ZERO))) {
case 1:
num = f_expt(dat->num, other);
den = f_expt(dat->den, other);
break;
case -1:
num = f_expt(dat->den, f_negate(other));
den = f_expt(dat->num, f_negate(other));
break;
default:
num = ONE;
den = ONE;
break;
}
return f_rational_new2(CLASS_OF(self), num, den);
}
case T_FLOAT:
case T_RATIONAL:
if (f_negative_p(self))
return f_expt(rb_complex_new1(self), other); /* explicitly */
return f_expt(f_to_f(self), other);
default:
return rb_num_coerce_bin(self, other, id_expt);
}
}
/*
* call-seq:
* rat <=> numeric => -1, 0, +1
*
* Performs comparison. Returns -1, 0, or +1 depending on whether _rat_ is
* less than, equal to, or greater than _numeric_. This is the basis for the
* tests in +Comparable+.
*
* A +TypeError+ is raised unless _numeric_ is a +Numeric+ object.
*
* For example:
*
* Rational(2, 3) <=> Rational(2, 3) #=> 0
* Rational(5) <=> 5 #=> 0
* Rational(900) <=> Rational(1) #=> 1
* Rational(-2, 9) <=> Rational(-9, 2) #=> 1
* Rational(9, 8) <=> 4 #=> -1
* Rational(20, 9) <=> 9.8 #=> -1
* Rational(5, 3) <=> 'string' #=> TypeError: String can't
* # be coerced into Rational
*/
static VALUE
nurat_cmp(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
{
get_dat1(self);
if (FIXNUM_P(dat->den) && FIX2LONG(dat->den) == 1)
return f_cmp(dat->num, other);
return f_cmp(self, f_rational_new_bang1(CLASS_OF(self), other));
}
case T_FLOAT:
return f_cmp(f_to_f(self), other);
case T_RATIONAL:
{
VALUE num1, num2;
get_dat2(self, other);
if (FIXNUM_P(adat->num) && FIXNUM_P(adat->den) &&
FIXNUM_P(bdat->num) && FIXNUM_P(bdat->den)) {
num1 = f_imul(FIX2LONG(adat->num), FIX2LONG(bdat->den));
num2 = f_imul(FIX2LONG(bdat->num), FIX2LONG(adat->den));
}
else {
num1 = f_mul(adat->num, bdat->den);
num2 = f_mul(bdat->num, adat->den);
}
return f_cmp(f_sub(num1, num2), ZERO);
}
default:
return rb_num_coerce_bin(self, other, id_cmp);
}
}
/*
* call-seq:
* rat == numeric => +true+ or +false+
*
* Tests for equality. Returns +true+ if _rat_ is equal to _numeric_; +false+
* otherwise.
*
* For example:
*
* Rational(2, 3) == Rational(2, 3) #=> +true+
* Rational(5) == 5 #=> +true+
* Rational(7, 1) == Rational(7) #=> +true+
* Rational(-2, 9) == Rational(-9, 2) #=> +false+
* Rational(9, 8) == 4 #=> +false+
* Rational(5, 3) == 'string' #=> +false+
*/
static VALUE
nurat_equal_p(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
{
get_dat1(self);
if (f_zero_p(dat->num) && f_zero_p(other))
return Qtrue;
if (!FIXNUM_P(dat->den))
return Qfalse;
if (FIX2LONG(dat->den) != 1)
return Qfalse;
if (f_equal_p(dat->num, other))
return Qtrue;
return Qfalse;
}
case T_FLOAT:
return f_equal_p(f_to_f(self), other);
case T_RATIONAL:
{
get_dat2(self, other);
if (f_zero_p(adat->num) && f_zero_p(bdat->num))
return Qtrue;
return f_boolcast(f_equal_p(adat->num, bdat->num) &&
f_equal_p(adat->den, bdat->den));
}
default:
return f_equal_p(other, self);
}
}
/*
* call-seq:
* rat.coerce(numeric) => array
*
* If _numeric_ is a +Rational+ object, returns an +Array+ containing _rat_
* and _numeric_. Otherwise, returns an +Array+ with both _rat_ and _numeric_
* represented in the most accurate common format. 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.
*
* For example:
*
* Rational(2).coerce(Rational(3)) #=> [(2), (3)]
* Rational(5).coerce(7) #=> [(7, 1), (5, 1)]
* Rational(9, 8).coerce(4) #=> [(4, 1), (9, 8)]
* Rational(7, 12).coerce(9.9876) #=> [9.9876, 0.5833333333333334]
* Rational(4).coerce(9/0.0) #=> [Infinity, 4.0]
* Rational(5, 3).coerce('string') #=> TypeError: String can't be
* # coerced into Rational
*/
static VALUE
nurat_coerce(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
return rb_assoc_new(f_rational_new_bang1(CLASS_OF(self), other), self);
case T_FLOAT:
return rb_assoc_new(other, f_to_f(self));
case T_RATIONAL:
return rb_assoc_new(other, self);
case T_COMPLEX:
if (k_exact_p(RCOMPLEX(other)->imag) && f_zero_p(RCOMPLEX(other)->imag))
return rb_assoc_new(f_rational_new_bang1
(CLASS_OF(self), RCOMPLEX(other)->real), self);
}
rb_raise(rb_eTypeError, "%s can't be coerced into %s",
rb_obj_classname(other), rb_obj_classname(self));
return Qnil;
}
/*
* call-seq:
* rat.div(numeric) => integer
*
* Uses +/+ to divide _rat_ by _numeric_, then returns the floor of the result
* as an +Integer+ object.
*
* A +TypeError+ is raised unless _numeric_ is a +Numeric+ object. A
* +ZeroDivisionError+ is raised if _numeric_ is 0. A +FloatDomainError+ is
* raised if _numeric_ is 0.0.
*
* For example:
*
* Rational(2, 3).div(Rational(2, 3)) #=> 1
* Rational(-2, 9).div(Rational(-9, 2)) #=> 0
* Rational(3, 4).div(0.1) #=> 7
* Rational(-9).div(9.9) #=> -1
* Rational(3.12).div(0.5) #=> 6
* Rational(200, 51).div(0) #=> ZeroDivisionError:
* # divided by zero
*/
static VALUE
nurat_idiv(VALUE self, VALUE other)
{
return f_floor(f_div(self, other));
}
/*
* call-seq:
* rat.modulo(numeric) => numeric
* rat % numeric => numeric
*
* Returns the modulo of _rat_ and _numeric_ as a +Numeric+ object.
*
* x.modulo(y) means x-y*(x/y).floor
*
* A +TypeError+ is raised unless _numeric_ is a +Numeric+ object. A
* +ZeroDivisionError+ is raised if _numeric_ is 0. A +FloatDomainError+ is
* raised if _numeric_ is 0.0.
*
* For example:
*
* Rational(2, 3) % Rational(2, 3) #=> (0/1)
* Rational(2) % Rational(300) #=> (2/1)
* Rational(-2, 9) % Rational(9, -2) #=> (-2/9)
* Rational(8.2) % 3.2 #=> 1.799999999999999
* Rational(198.1) % 2.3e3 #=> 198.1
* Rational(2, 5) % 0.0 #=> FloatDomainError: Infinity
*/
static VALUE
nurat_mod(VALUE self, VALUE other)
{
VALUE val = f_floor(f_div(self, other));
return f_sub(self, f_mul(other, val));
}
/*
* call-seq:
* rat.divmod(numeric) => array
*
* Returns a two-element +Array+ containing the quotient and modulus obtained
* by dividing _rat_ by _numeric_. Both elements are +Numeric+.
*
* A +ZeroDivisionError+ is raised if _numeric_ is 0. A +FloatDomainError+ is
* raised if _numeric_ is 0.0. A +TypeError+ is raised unless _numeric_ is a
* +Numeric+ object.
*
* For example:
*
* Rational(3).divmod(3) #=> [1, (0/1)]
* Rational(4).divmod(3) #=> [1, (1/1)]
* Rational(5).divmod(3) #=> [1, (2/1)]
* Rational(6).divmod(3) #=> [2, (0/1)]
* Rational(2, 3).divmod(Rational(2, 3)) #=> [1, (0/1)]
* Rational(-2, 9).divmod(Rational(9, -2)) #=> [0, (-2/9)]
* Rational(11.5).divmod(Rational(3.5)) #=> [3, (1/1)]
*/
static VALUE
nurat_divmod(VALUE self, VALUE other)
{
VALUE val = f_floor(f_div(self, other));
return rb_assoc_new(val, f_sub(self, f_mul(other, val)));
}
#if 0
/* :nodoc: */
static VALUE
nurat_quot(VALUE self, VALUE other)
{
return f_truncate(f_div(self, other));
}
#endif
/*
* call-seq:
* rat.remainder(numeric) => numeric_result
*
* Returns the remainder of dividing _rat_ by _numeric_ as a +Numeric+ object.
*
* x.remainder(y) means x-y*(x/y).truncate
*
* A +ZeroDivisionError+ is raised if _numeric_ is 0. A +FloatDomainError+ is
* raised if the result is Infinity or NaN, or _numeric_ is 0.0. A +TypeError+
* is raised unless _numeric_ is a +Numeric+ object.
*
* For example:
*
* Rational(3, 4).remainder(Rational(3)) #=> (3/4)
* Rational(12,13).remainder(-8) #=> (12/13)
* Rational(2,3).remainder(-Rational(3,2)) #=> (2/3)
* Rational(-5,7).remainder(7.1) #=> -0.7142857142857143
* Rational(1).remainder(0) # ZeroDivisionError:
* # divided by zero
*/
static VALUE
nurat_rem(VALUE self, VALUE other)
{
VALUE val = f_truncate(f_div(self, other));
return f_sub(self, f_mul(other, val));
}
#if 0
/* :nodoc: */
static VALUE
nurat_quotrem(VALUE self, VALUE other)
{
VALUE val = f_truncate(f_div(self, other));
return rb_assoc_new(val, f_sub(self, f_mul(other, val)));
}
#endif
/*
* call-seq:
* rat.abs => rational
*
* Returns the absolute value of _rat_. If _rat_ is positive, it is
* returned; if _rat_ is negative its negation is returned. The return value
* is a +Rational+ object.
*
* For example:
*
* Rational(2).abs #=> (2/1)
* Rational(-2).abs #=> (2/1)
* Rational(-8, -1).abs #=> (8/1)
* Rational(-20, 7).abs #=> (20/7)
*/
static VALUE
nurat_abs(VALUE self)
{
if (f_positive_p(self))
return self;
return f_negate(self);
}
#if 0
/* :nodoc: */
static VALUE
nurat_true(VALUE self)
{
return Qtrue;
}
#endif
static VALUE
nurat_floor(VALUE self)
{
get_dat1(self);
return f_idiv(dat->num, dat->den);
}
static VALUE
nurat_ceil(VALUE self)
{
get_dat1(self);
return f_negate(f_idiv(f_negate(dat->num), dat->den));
}
/*
* call-seq:
* rat.to_i => integer
*
* Returns _rat_ truncated to an integer as an +Integer+ object.
*
* Equivalent to
* <i>rat</i>.<code>truncate(</code>.
*
* For example:
*
* Rational(2, 3).to_i #=> 0
* Rational(3).to_i #=> 3
* Rational(300.6).to_i #=> 300
* Rational(98,71).to_i #=> 1
* Rational(-30,2).to_i #=> -15
*/
static VALUE
nurat_truncate(VALUE self)
{
get_dat1(self);
if (f_negative_p(dat->num))
return f_negate(f_idiv(f_negate(dat->num), dat->den));
return f_idiv(dat->num, dat->den);
}
static VALUE
nurat_round(VALUE self)
{
VALUE num, den, neg;
get_dat1(self);
num = dat->num;
den = dat->den;
neg = f_negative_p(num);
if (neg)
num = f_negate(num);
num = f_add(f_mul(num, TWO), den);
den = f_mul(den, TWO);
num = f_idiv(num, den);
if (neg)
num = f_negate(num);
return num;
}
static VALUE
nurat_round_common(int argc, VALUE *argv, VALUE self,
VALUE (*func)(VALUE))
{
VALUE n, b, s;
if (argc == 0)
return (*func)(self);
rb_scan_args(argc, argv, "01", &n);
if (!k_integer_p(n))
rb_raise(rb_eTypeError, "not an integer");
b = f_expt(INT2FIX(10), n);
s = f_mul(self, b);
s = (*func)(s);
s = f_div(f_rational_new_bang1(CLASS_OF(self), s), b);
if (f_lt_p(n, ONE))
s = f_to_i(s);
return s;
}
/*
* call-seq:
* rat.floor => integer
* rat.floor(precision=0) => numeric
*
* Returns the largest integer less than or equal to _rat_ as an +Integer+
* object. Contrast with +Rational#ceil+.
*
* An optional _precision_ argument can be supplied as an +Integer+. If
* _precision_ is positive the result is rounded downwards to that number of
* decimal places. If _precision_ is negative, the result is rounded downwards
* to the nearest 10**_precision_. By default _precision_ is equal to 0,
* causing the result to be a whole number.
*
* For example:
*
* Rational(2, 3).floor #=> 0
* Rational(3).floor #=> 3
* Rational(300.6).floor #=> 300
* Rational(98,71).floor #=> 1
* Rational(-30,2).floor #=> -15
*
* Rational(-1.125).floor.to_f #=> -2.0
* Rational(-1.125).floor(1).to_f #=> -1.2
* Rational(-1.125).floor(2).to_f #=> -1.13
* Rational(-1.125).floor(-2).to_f #=> -100.0
* Rational(-1.125).floor(-1).to_f #=> -10.0
*/
static VALUE
nurat_floor_n(int argc, VALUE *argv, VALUE self)
{
return nurat_round_common(argc, argv, self, nurat_floor);
}
/*
* call-seq:
* rat.ceil => integer
* rat.ceil(precision=0) => numeric
*
* Returns the smallest integer greater than or equal to _rat_ as an +Integer+
* object. Contrast with +Rational#floor+.
*
* An optional _precision_ argument can be supplied as an +Integer+. If
* _precision_ is positive the result is rounded upwards to that number of
* decimal places. If _precision_ is negative, the result is rounded upwards
* to the nearest 10**_precision_. By default _precision_ is equal to 0,
* causing the result to be a whole number.
*
* For example:
*
* Rational(2, 3).ceil #=> 1
* Rational(3).ceil #=> 3
* Rational(300.6).ceil #=> 301
* Rational(98, 71).ceil #=> 2
* Rational(-30, 2).ceil #=> -15
*
* Rational(-1.125).ceil.to_f #=> -1.0
* Rational(-1.125).ceil(1).to_f #=> -1.1
* Rational(-1.125).ceil(2).to_f #=> -1.12
* Rational(-1.125).ceil(-2).to_f #=> 0.0
*/
static VALUE
nurat_ceil_n(int argc, VALUE *argv, VALUE self)
{
return nurat_round_common(argc, argv, self, nurat_ceil);
}
/*
* call-seq:
* rat.truncate => integer
* rat.truncate(precision=0) => numeric
*
* Truncates self to an integer and returns the result as an +Integer+ object.
*
* An optional _precision_ argument can be supplied as an +Integer+. If
* _precision_ is positive the result is rounded downwards to that number of
* decimal places. If _precision_ is negative, the result is rounded downwards
* to the nearest 10**_precision_. By default _precision_ is equal to 0,
* causing the result to be a whole number.
*
* For example:
*
* Rational(2, 3).truncate #=> 0
* Rational(3).truncate #=> 3
* Rational(300.6).truncate #=> 300
* Rational(98,71).truncate #=> 1
* Rational(-30,2).truncate #=> -15
* Rational(-30, -11).truncate #=> 2
*
* Rational(-123.456).truncate(2).to_f #=> -123.45
* Rational(-123.456).truncate(1).to_f #=> -123.4
* Rational(-123.456).truncate.to_f #=> -123.0
* Rational(-123.456).truncate(-1).to_f #=> -120.0
* Rational(-123.456).truncate(-2).to_f #=> -100.0
*/
static VALUE
nurat_truncate_n(int argc, VALUE *argv, VALUE self)
{
return nurat_round_common(argc, argv, self, nurat_truncate);
}
/*
* call-seq:
* rat.round => integer
* rat.round(precision=0) => numeric
*
* Rounds _rat_ to an integer, and returns the result as an +Integer+ object.
*
* An optional _precision_ argument can be supplied as an +Integer+. If
* _precision_ is positive the result is rounded to that number of decimal
* places. If _precision_ is negative, the result is rounded to the nearest
* 10**_precision_. By default _precision_ is equal to 0, causing the result
* to be a whole number.
*
* A +TypeError+ is raised if _integer_ is given and not an +Integer+ object.
*
* For example:
*
* Rational(9, 3.3).round #=> 3
* Rational(9, 3.3).round(1) #=> (27/10)
* Rational(9,3.3).round(2) #=> (273/100)
* Rational(8, 7).round(5) #=> (57143/50000)
* Rational(-20, -3).round #=> 7
*
* Rational(-123.456).round(2).to_f #=> -123.46
* Rational(-123.456).round(1).to_f #=> -123.5
* Rational(-123.456).round.to_f #=> -123.0
* Rational(-123.456).round(-1).to_f #=> -120.0
* Rational(-123.456).round(-2).to_f #=> -100.0
*
*/
static VALUE
nurat_round_n(int argc, VALUE *argv, VALUE self)
{
return nurat_round_common(argc, argv, self, nurat_round);
}
/*
* call-seq:
* rat.to_f => float
*
* Converts _rat_ to a floating point number and returns the result as a
* +Float+ object.
*
* For example:
*
* Rational(2).to_f #=> 2.0
* Rational(9, 4).to_f #=> 2.25
* Rational(-3, 4).to_f #=> -0.75
* Rational(20, 3).to_f #=> 6.666666666666667
*/
static VALUE
nurat_to_f(VALUE self)
{
get_dat1(self);
return f_fdiv(dat->num, dat->den);
}
/*
* call-seq:
* rat.to_r => self
*
* Returns self, i.e. a +Rational+ object representing _rat_.
*
* For example:
*
* Rational(2).to_r #=> (2/1)
* Rational(-8, 6).to_r #=> (-4/3)
* Rational(39.2).to_r #=> (2758454771764429/70368744177664)
*/
static VALUE
nurat_to_r(VALUE self)
{
return self;
}
static VALUE
nurat_hash(VALUE self)
{
long v, h[3];
VALUE n;
get_dat1(self);
h[0] = rb_hash(rb_obj_class(self));
n = rb_hash(dat->num);
h[1] = NUM2LONG(n);
n = rb_hash(dat->den);
h[2] = NUM2LONG(n);
v = rb_memhash(h, sizeof(h));
return LONG2FIX(v);
}
static VALUE
nurat_format(VALUE self, VALUE (*func)(VALUE))
{
VALUE s;
get_dat1(self);
s = (*func)(dat->num);
rb_str_cat2(s, "/");
rb_str_concat(s, (*func)(dat->den));
return s;
}
/*
* call-seq:
* rat.to_s => string
*
* Returns a +String+ representation of _rat_ in the form
* "_numerator_/_denominator_".
*
* For example:
*
* Rational(2).to_s #=> "2/1"
* Rational(-8, 6).to_s #=> "-4/3"
* Rational(0.5).to_s #=> "1/2"
*/
static VALUE
nurat_to_s(VALUE self)
{
return nurat_format(self, f_to_s);
}
/*
* call-seq:
* rat.inspect => string
*
* Returns a +String+ containing a human-readable representation of _rat_ in
* the form "(_numerator_/_denominator_)".
*
* For example:
*
* Rational(2).to_s #=> "(2/1)"
* Rational(-8, 6).to_s #=> "(-4/3)"
* Rational(0.5).to_s #=> "(1/2)"
*/
static VALUE
nurat_inspect(VALUE self)
{
VALUE s;
s = rb_usascii_str_new2("(");
rb_str_concat(s, nurat_format(self, f_inspect));
rb_str_cat2(s, ")");
return s;
}
/* :nodoc: */
static VALUE
nurat_marshal_dump(VALUE self)
{
VALUE a;
get_dat1(self);
a = rb_assoc_new(dat->num, dat->den);
rb_copy_generic_ivar(a, self);
return a;
}
/* :nodoc: */
static VALUE
nurat_marshal_load(VALUE self, VALUE a)
{
get_dat1(self);
dat->num = RARRAY_PTR(a)[0];
dat->den = RARRAY_PTR(a)[1];
rb_copy_generic_ivar(self, a);
if (f_zero_p(dat->den))
rb_raise_zerodiv();
return self;
}
/* --- */
/*
* call-seq:
* int.gcd(_int2_) => integer
*
* Returns the greatest common divisor of _int_ and _int2_: the largest
* positive integer that divides the two without a remainder. The result is an
* +Integer+ object.
*
* An +ArgumentError+ is raised unless _int2_ is an +Integer+ object.
*
* For example:
*
* 2.gcd(2) #=> 2
* -2.gcd(2) #=> 2
* 8.gcd(6) #=> 2
* 25.gcd(5) #=> 5
*/
VALUE
rb_gcd(VALUE self, VALUE other)
{
other = nurat_int_value(other);
return f_gcd(self, other);
}
/*
* call-seq:
* int.lcm(_int2_) => integer
*
* Returns the least common multiple (or "lowest common multiple") of _int_
* and _int2_: the smallest positive integer that is a multiple of both
* integers. The result is an +Integer+ object.
*
* An +ArgumentError+ is raised unless _int2_ is an +Integer+ object.
*
* For example:
*
* 2.lcm(2) #=> 2
* -2.gcd(2) #=> 2
* 8.gcd(6) #=> 24
* 8.lcm(9) #=> 72
*/
VALUE
rb_lcm(VALUE self, VALUE other)
{
other = nurat_int_value(other);
return f_lcm(self, other);
}
/*
* call-seq:
* int.gcdlcm(_int2_) => array
*
* Returns a two-element +Array+ containing _int_.gcd(_int2_) and
* _int_.lcm(_int2_) respectively. That is, the greatest common divisor of
* _int_ and _int2_, then the least common multiple of _int_ and _int2_. Both
* elements are +Integer+ objects.
*
* An +ArgumentError+ is raised unless _int2_ is an +Integer+ object.
*
* For example:
*
* 2.gcdlcm(2) #=> [2, 2]
* -2.gcdlcm(2) #=> [2, 2]
* 8.gcdlcm(6) #=> [2, 24]
* 8.gcdlcm(9) #=> [1, 72]
* 9.gcdlcm(9**9) #=> [9, 387420489]
*/
VALUE
rb_gcdlcm(VALUE self, VALUE other)
{
other = nurat_int_value(other);
return rb_assoc_new(f_gcd(self, other), f_lcm(self, other));
}
VALUE
rb_rational_raw(VALUE x, VALUE y)
{
return nurat_s_new_internal(rb_cRational, x, y);
}
VALUE
rb_rational_new(VALUE x, VALUE y)
{
return nurat_s_canonicalize_internal(rb_cRational, x, y);
}
static VALUE nurat_s_convert(int argc, VALUE *argv, VALUE klass);
VALUE
rb_Rational(VALUE x, VALUE y)
{
VALUE a[2];
a[0] = x;
a[1] = y;
return nurat_s_convert(2, a, rb_cRational);
}
#define id_numerator rb_intern("numerator")
#define f_numerator(x) rb_funcall(x, id_numerator, 0)
#define id_denominator rb_intern("denominator")
#define f_denominator(x) rb_funcall(x, id_denominator, 0)
#define id_to_r rb_intern("to_r")
#define f_to_r(x) rb_funcall(x, id_to_r, 0)
/*
* call-seq:
* num.numerator => integer
*
* Returns the numerator of _num_ as an +Integer+ object.
*/
static VALUE
numeric_numerator(VALUE self)
{
return f_numerator(f_to_r(self));
}
static VALUE
numeric_denominator(VALUE self)
{
return f_denominator(f_to_r(self));
}
/*
* call-seq:
* int.numerator => self
*
* Returns self.
*/
static VALUE
integer_numerator(VALUE self)
{
return self;
}
/*
* call-seq:
* int.numerator => 1
*
* Returns 1.
*/
static VALUE
integer_denominator(VALUE self)
{
return INT2FIX(1);
}
/*
* call-seq:
* flo.numerator => integer
*
* Returns the numerator of _flo_ as an +Integer+ object.
*
* For example:
*
* 0.3.numerator #=> 5404319552844595 # machine dependent
* lambda{|x| x.numerator.fdiv(x.denominator)}.call(0.3) #=> 0.3
*/
static VALUE
float_numerator(VALUE self)
{
double d = RFLOAT_VALUE(self);
if (isinf(d) || isnan(d))
return self;
return rb_call_super(0, 0);
}
/*
* call-seq:
* flo.denominator => integer
*
* Returns the denominator of _flo_ as an +Integer+ object.
*
* For example:
*
* 0.3.denominator #=> 18014398509481984 # machine dependent
* lambda{|x| x.numerator.fdiv(x.denominator)}.call(0.3) #=> 0.3
*/
static VALUE
float_denominator(VALUE self)
{
double d = RFLOAT_VALUE(self);
if (isinf(d) || isnan(d))
return INT2FIX(1);
return rb_call_super(0, 0);
}
/*
* call-seq:
* nil.to_r => Rational(0, 1)
*
* Returns a +Rational+ object representing _nil_ as a rational number.
*
* For example:
*
* nil.to_r #=> (0/1)
*/
static VALUE
nilclass_to_r(VALUE self)
{
return rb_rational_new1(INT2FIX(0));
}
/*
* call-seq:
* int.to_r => rational
*
* Returns a +Rational+ object representing _int_ as a rational number.
*
* For example:
*
* 1.to_r #=> (1/1)
* 12.to_r #=> (12/1)
*/
static VALUE
integer_to_r(VALUE self)
{
return rb_rational_new1(self);
}
static void
float_decode_internal(VALUE self, VALUE *rf, VALUE *rn)
{
double f;
int n;
f = frexp(RFLOAT_VALUE(self), &n);
f = ldexp(f, DBL_MANT_DIG);
n -= DBL_MANT_DIG;
*rf = rb_dbl2big(f);
*rn = INT2FIX(n);
}
#if 0
static VALUE
float_decode(VALUE self)
{
VALUE f, n;
float_decode_internal(self, &f, &n);
return rb_assoc_new(f, n);
}
#endif
/*
* call-seq:
* flt.to_r => rational
*
* Returns _flt_ as an +Rational+ object. Raises a +FloatDomainError+ if _flt_
* is +Infinity+ or +NaN+.
*
* For example:
*
* 2.0.to_r #=> (2/1)
* 2.5.to_r #=> (5/2)
* -0.75.to_r #=> (-3/4)
* 0.0.to_r #=> (0/1)
* (1/0.0).to_r #=> FloatDomainError: Infinity
*/
static VALUE
float_to_r(VALUE self)
{
VALUE f, n;
float_decode_internal(self, &f, &n);
return f_mul(f, f_expt(INT2FIX(FLT_RADIX), n));
}
static VALUE rat_pat, an_e_pat, a_dot_pat, underscores_pat, an_underscore;
#define WS "\\s*"
#define DIGITS "(?:\\d(?:_\\d|\\d)*)"
#define NUMERATOR "(?:" DIGITS "?\\.)?" DIGITS "(?:[eE][-+]?" DIGITS ")?"
#define DENOMINATOR DIGITS
#define PATTERN "\\A" WS "([-+])?(" NUMERATOR ")(?:\\/(" DENOMINATOR "))?" WS
static void
make_patterns(void)
{
static const char rat_pat_source[] = PATTERN;
static const char an_e_pat_source[] = "[eE]";
static const char a_dot_pat_source[] = "\\.";
static const char underscores_pat_source[] = "_+";
if (rat_pat) return;
rat_pat = rb_reg_new(rat_pat_source, sizeof rat_pat_source - 1, 0);
rb_gc_register_mark_object(rat_pat);
an_e_pat = rb_reg_new(an_e_pat_source, sizeof an_e_pat_source - 1, 0);
rb_gc_register_mark_object(an_e_pat);
a_dot_pat = rb_reg_new(a_dot_pat_source, sizeof a_dot_pat_source - 1, 0);
rb_gc_register_mark_object(a_dot_pat);
underscores_pat = rb_reg_new(underscores_pat_source,
sizeof underscores_pat_source - 1, 0);
rb_gc_register_mark_object(underscores_pat);
an_underscore = rb_usascii_str_new2("_");
rb_gc_register_mark_object(an_underscore);
}
#define id_match rb_intern("match")
#define f_match(x,y) rb_funcall(x, id_match, 1, y)
#define id_aref rb_intern("[]")
#define f_aref(x,y) rb_funcall(x, id_aref, 1, y)
#define id_post_match rb_intern("post_match")
#define f_post_match(x) rb_funcall(x, id_post_match, 0)
#define id_split rb_intern("split")
#define f_split(x,y) rb_funcall(x, id_split, 1, y)
#include <ctype.h>
static VALUE
string_to_r_internal(VALUE self)
{
VALUE s, m;
s = self;
if (RSTRING_LEN(s) == 0)
return rb_assoc_new(Qnil, self);
m = f_match(rat_pat, s);
if (!NIL_P(m)) {
VALUE v, ifp, exp, ip, fp;
VALUE si = f_aref(m, INT2FIX(1));
VALUE nu = f_aref(m, INT2FIX(2));
VALUE de = f_aref(m, INT2FIX(3));
VALUE re = f_post_match(m);
{
VALUE a;
a = f_split(nu, an_e_pat);
ifp = RARRAY_PTR(a)[0];
if (RARRAY_LEN(a) != 2)
exp = Qnil;
else
exp = RARRAY_PTR(a)[1];
a = f_split(ifp, a_dot_pat);
ip = RARRAY_PTR(a)[0];
if (RARRAY_LEN(a) != 2)
fp = Qnil;
else
fp = RARRAY_PTR(a)[1];
}
v = rb_rational_new1(f_to_i(ip));
if (!NIL_P(fp)) {
char *p = StringValuePtr(fp);
long count = 0;
VALUE l;
while (*p) {
if (rb_isdigit(*p))
count++;
p++;
}
l = f_expt(INT2FIX(10), LONG2NUM(count));
v = f_mul(v, l);
v = f_add(v, f_to_i(fp));
v = f_div(v, l);
}
if (!NIL_P(si) && *StringValuePtr(si) == '-')
v = f_negate(v);
if (!NIL_P(exp))
v = f_mul(v, f_expt(INT2FIX(10), f_to_i(exp)));
#if 0
if (!NIL_P(de) && (!NIL_P(fp) || !NIL_P(exp)))
return rb_assoc_new(v, rb_usascii_str_new2("dummy"));
#endif
if (!NIL_P(de))
v = f_div(v, f_to_i(de));
return rb_assoc_new(v, re);
}
return rb_assoc_new(Qnil, self);
}
static VALUE
string_to_r_strict(VALUE self)
{
VALUE a = string_to_r_internal(self);
if (NIL_P(RARRAY_PTR(a)[0]) || RSTRING_LEN(RARRAY_PTR(a)[1]) > 0) {
VALUE s = f_inspect(self);
rb_raise(rb_eArgError, "invalid value for convert(): %s",
StringValuePtr(s));
}
return RARRAY_PTR(a)[0];
}
#define id_gsub rb_intern("gsub")
#define f_gsub(x,y,z) rb_funcall(x, id_gsub, 2, y, z)
/*
* call-seq:
* string.to_r => rational
*
* Returns a +Rational+ object representing _string_ as a rational number.
* Leading and trailing whitespace is ignored. Underscores may be used to
* separate numbers. If _string_ is not recognised as a rational, (0/1) is
* returned.
*
* For example:
*
* "2".to_r #=> (2/1)
* "300/2".to_r #=> (150/1)
* "-9.2/3".to_r #=> (-46/15)
* " 2/9 ".to_r #=> (2/9)
* "2_9".to_r #=> (29/1)
* "?".to_r #=> (0/1)
*/
static VALUE
string_to_r(VALUE self)
{
VALUE s, a, backref;
backref = rb_backref_get();
rb_match_busy(backref);
s = f_gsub(self, underscores_pat, an_underscore);
a = string_to_r_internal(s);
rb_backref_set(backref);
if (!NIL_P(RARRAY_PTR(a)[0]))
return RARRAY_PTR(a)[0];
return rb_rational_new1(INT2FIX(0));
}
#define id_to_r rb_intern("to_r")
#define f_to_r(x) rb_funcall(x, id_to_r, 0)
static VALUE
nurat_s_convert(int argc, VALUE *argv, VALUE klass)
{
VALUE a1, a2, backref;
rb_scan_args(argc, argv, "11", &a1, &a2);
if (NIL_P(a1) || (argc == 2 && NIL_P(a2)))
rb_raise(rb_eTypeError, "can't convert nil into Rational");
switch (TYPE(a1)) {
case T_COMPLEX:
if (k_exact_p(RCOMPLEX(a1)->imag) && f_zero_p(RCOMPLEX(a1)->imag))
a1 = RCOMPLEX(a1)->real;
}
switch (TYPE(a2)) {
case T_COMPLEX:
if (k_exact_p(RCOMPLEX(a2)->imag) && f_zero_p(RCOMPLEX(a2)->imag))
a2 = RCOMPLEX(a2)->real;
}
backref = rb_backref_get();
rb_match_busy(backref);
switch (TYPE(a1)) {
case T_FIXNUM:
case T_BIGNUM:
break;
case T_FLOAT:
a1 = f_to_r(a1);
break;
case T_STRING:
a1 = string_to_r_strict(a1);
break;
}
switch (TYPE(a2)) {
case T_FIXNUM:
case T_BIGNUM:
break;
case T_FLOAT:
a2 = f_to_r(a2);
break;
case T_STRING:
a2 = string_to_r_strict(a2);
break;
}
rb_backref_set(backref);
switch (TYPE(a1)) {
case T_RATIONAL:
if (argc == 1 || (k_exact_p(a2) && f_one_p(a2)))
return a1;
}
if (argc == 1) {
if (!(k_numeric_p(a1) && k_integer_p(a1)))
return rb_convert_type(a1, T_RATIONAL, "Rational", "to_r");
}
else {
if ((k_numeric_p(a1) && k_numeric_p(a2)) &&
(!f_integer_p(a1) || !f_integer_p(a2)))
return f_div(a1, a2);
}
{
VALUE argv2[2];
argv2[0] = a1;
argv2[1] = a2;
return nurat_s_new(argc, argv2, klass);
}
}
/*
* A +Rational+ object represents a rational number, which is any number that
* can be expressed as the quotient a/b of two integers (where the denominator
* is nonzero). Given that b may be equal to 1, every integer is rational.
*
* A +Rational+ object can be created with the +Rational()+ constructor:
*
* Rational(1) #=> (1/1)
* Rational(2, 3) #=> (2/3)
* Rational(0.5) #=> (1/2)
* Rational("2/7") #=> (2/7)
* Rational("0.25") #=> (1/4)
* Rational(10e3) #=> (10000/1)
*
* The first argument is the numerator, the second the denominator. If the
* denominator is not supplied it defaults to 1. The arguments can be
* +Numeric+ or +String+ objects.
*
* Rational(12) == Rational(12, 1) #=> true
*
* A +ZeroDivisionError+ will be raised if 0 is specified as the denominator:
*
* Rational(3, 0) #=> ZeroDivisionError: divided by zero
*
* The numerator and denominator of a +Rational+ object can be retrieved with
* the +Rational#numerator+ and +Rational#denominator+ accessors,
* respectively.
*
* rational = Rational(4, 7) #=> (4/7)
* rational.numerator #=> 4
* rational.denominator #=> 7
*
* A +Rational+ is automatically reduced into its simplest form:
*
* Rational(10, 2) #=> (5/1)
*
* +Numeric+ and +String+ objects can be converted into a +Rational+ with
* their +#to_r+ methods.
*
* 30.to_r #=> (30/1)
* 3.33.to_r #=> (1874623344892969/562949953421312)
* '33/3'.to_r #=> (11/1)
*
* The reverse operations work as you would expect:
*
* Rational(30, 1).to_i #=> 30
* Rational(1874623344892969, 562949953421312).to_f #=> 3.33
* Rational(11, 1).to_s #=> "11/1"
*
* +Rational+ objects can be compared with other +Numeric+ objects using the
* normal semantics:
*
* Rational(20, 10) == Rational(2, 1) #=> true
* Rational(10) > Rational(1) #=> true
* Rational(9, 2) <=> Rational(8, 3) #=> 1
*
* Similarly, standard mathematical operations support +Rational+ objects, too:
*
* Rational(9, 2) * 2 #=> (9/1)
* Rational(12, 29) / Rational(2,3) #=> (18/29)
* Rational(7,5) + Rational(60) #=> (307/5)
* Rational(22, 5) - Rational(5, 22) #=> (459/110)
* Rational(2,3) ** 3 #=> (8/27)
*/
void
Init_Rational(void)
{
#undef rb_intern
#define rb_intern(str) rb_intern_const(str)
assert(fprintf(stderr, "assert() is now active\n"));
id_abs = rb_intern("abs");
id_cmp = rb_intern("<=>");
id_convert = rb_intern("convert");
id_equal_p = rb_intern("==");
id_expt = rb_intern("**");
id_fdiv = rb_intern("fdiv");
id_floor = rb_intern("floor");
id_idiv = rb_intern("div");
id_inspect = rb_intern("inspect");
id_integer_p = rb_intern("integer?");
id_negate = rb_intern("-@");
id_to_f = rb_intern("to_f");
id_to_i = rb_intern("to_i");
id_to_s = rb_intern("to_s");
id_truncate = rb_intern("truncate");
rb_cRational = rb_define_class("Rational", rb_cNumeric);
rb_define_alloc_func(rb_cRational, nurat_s_alloc);
rb_undef_method(CLASS_OF(rb_cRational), "allocate");
#if 0
rb_define_private_method(CLASS_OF(rb_cRational), "new!", nurat_s_new_bang, -1);
rb_define_private_method(CLASS_OF(rb_cRational), "new", nurat_s_new, -1);
#else
rb_undef_method(CLASS_OF(rb_cRational), "new");
#endif
rb_define_global_function("Rational", nurat_f_rational, -1);
rb_define_method(rb_cRational, "numerator", nurat_numerator, 0);
rb_define_method(rb_cRational, "denominator", nurat_denominator, 0);
rb_define_method(rb_cRational, "+", nurat_add, 1);
rb_define_method(rb_cRational, "-", nurat_sub, 1);
rb_define_method(rb_cRational, "*", nurat_mul, 1);
rb_define_method(rb_cRational, "/", nurat_div, 1);
rb_define_method(rb_cRational, "quo", nurat_div, 1);
rb_define_method(rb_cRational, "fdiv", nurat_fdiv, 1);
rb_define_method(rb_cRational, "**", nurat_expt, 1);
rb_define_method(rb_cRational, "<=>", nurat_cmp, 1);
rb_define_method(rb_cRational, "==", nurat_equal_p, 1);
rb_define_method(rb_cRational, "coerce", nurat_coerce, 1);
rb_define_method(rb_cRational, "div", nurat_idiv, 1);
#if 0 /* NUBY */
rb_define_method(rb_cRational, "//", nurat_idiv, 1);
#endif
rb_define_method(rb_cRational, "modulo", nurat_mod, 1);
rb_define_method(rb_cRational, "%", nurat_mod, 1);
rb_define_method(rb_cRational, "divmod", nurat_divmod, 1);
#if 0
rb_define_method(rb_cRational, "quot", nurat_quot, 1);
#endif
rb_define_method(rb_cRational, "remainder", nurat_rem, 1);
#if 0
rb_define_method(rb_cRational, "quotrem", nurat_quotrem, 1);
#endif
rb_define_method(rb_cRational, "abs", nurat_abs, 0);
#if 0
rb_define_method(rb_cRational, "rational?", nurat_true, 0);
rb_define_method(rb_cRational, "exact?", nurat_true, 0);
#endif
rb_define_method(rb_cRational, "floor", nurat_floor_n, -1);
rb_define_method(rb_cRational, "ceil", nurat_ceil_n, -1);
rb_define_method(rb_cRational, "truncate", nurat_truncate_n, -1);
rb_define_method(rb_cRational, "round", nurat_round_n, -1);
rb_define_method(rb_cRational, "to_i", nurat_truncate, 0);
rb_define_method(rb_cRational, "to_f", nurat_to_f, 0);
rb_define_method(rb_cRational, "to_r", nurat_to_r, 0);
rb_define_method(rb_cRational, "hash", nurat_hash, 0);
rb_define_method(rb_cRational, "to_s", nurat_to_s, 0);
rb_define_method(rb_cRational, "inspect", nurat_inspect, 0);
rb_define_method(rb_cRational, "marshal_dump", nurat_marshal_dump, 0);
rb_define_method(rb_cRational, "marshal_load", nurat_marshal_load, 1);
/* --- */
rb_define_method(rb_cInteger, "gcd", rb_gcd, 1);
rb_define_method(rb_cInteger, "lcm", rb_lcm, 1);
rb_define_method(rb_cInteger, "gcdlcm", rb_gcdlcm, 1);
rb_define_method(rb_cNumeric, "numerator", numeric_numerator, 0);
rb_define_method(rb_cNumeric, "denominator", numeric_denominator, 0);
rb_define_method(rb_cInteger, "numerator", integer_numerator, 0);
rb_define_method(rb_cInteger, "denominator", integer_denominator, 0);
rb_define_method(rb_cFloat, "numerator", float_numerator, 0);
rb_define_method(rb_cFloat, "denominator", float_denominator, 0);
rb_define_method(rb_cNilClass, "to_r", nilclass_to_r, 0);
rb_define_method(rb_cInteger, "to_r", integer_to_r, 0);
rb_define_method(rb_cFloat, "to_r", float_to_r, 0);
make_patterns();
rb_define_method(rb_cString, "to_r", string_to_r, 0);
rb_define_private_method(CLASS_OF(rb_cRational), "convert", nurat_s_convert, -1);
}
/*
Local variables:
c-file-style: "ruby"
End:
*/
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