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ruby--ruby/rational.c
tadf 5d6602c44e * complex.c (nucomp_int_check): function for DRY real check. 
* complex.c (nucomp_{add,sub,mul,div,expt}): use rb_num_coerce_bin().



git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@15896 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
2008-04-03 12:55:27 +00:00

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/*
rational.c: Coded by Tadayoshi Funaba 2008
This implementation is based on Keiju Ishitsuka's Rational library
which is written in ruby.
*/
#include "ruby.h"
#include <math.h>
#include <float.h>
#define NDEBUG
#include <assert.h>
#ifndef RATIONAL_NAME
#define RATIONAL_NAME "Rational"
#endif
#define ZERO INT2FIX(0)
#define ONE INT2FIX(1)
#define TWO INT2FIX(2)
VALUE rb_cRational;
static ID id_Unify, id_abs, id_cmp, id_convert, id_equal_p,
id_expt, id_floor, id_format,id_idiv, id_inspect, id_negate, id_new,
id_new_bang, 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)
{
VALUE r;
if (FIXNUM_P(y)) {
if (FIX2LONG(y) == 0)
r = x;
else
r = rb_funcall(x, '+', 1, y);
} else if (FIXNUM_P(x)) {
if (FIX2LONG(x) == 0)
r = y;
else
r = rb_funcall(x, '+', 1, y);
} else
r = rb_funcall(x, '+', 1, y);
return r;
}
inline static VALUE
f_cmp(VALUE x, VALUE y)
{
VALUE r;
if (FIXNUM_P(x) && FIXNUM_P(y)) {
long c = FIX2LONG(x) - FIX2LONG(y);
if (c > 0)
c = 1;
else if (c < 0)
c = -1;
r = INT2FIX(c);
} else
r = rb_funcall(x, id_cmp, 1, y);
return r;
}
inline static VALUE
f_div(VALUE x, VALUE y)
{
VALUE r;
if (FIXNUM_P(y) && FIX2LONG(y) == 1)
r = x;
else
r = rb_funcall(x, '/', 1, y);
return r;
}
inline static VALUE
f_gt_p(VALUE x, VALUE y)
{
VALUE r;
if (FIXNUM_P(x) && FIXNUM_P(y))
r = f_boolcast(FIX2LONG(x) > FIX2LONG(y));
else
r = rb_funcall(x, '>', 1, y);
return r;
}
inline static VALUE
f_lt_p(VALUE x, VALUE y)
{
VALUE r;
if (FIXNUM_P(x) && FIXNUM_P(y))
r = f_boolcast(FIX2LONG(x) < FIX2LONG(y));
else
r = rb_funcall(x, '<', 1, y);
return r;
}
binop(mod, '%')
inline static VALUE
f_mul(VALUE x, VALUE y)
{
VALUE r;
if (FIXNUM_P(y)) {
long _iy = FIX2LONG(y);
if (_iy == 0) {
if (TYPE(x) == T_FLOAT)
r = rb_float_new(0.0);
else
r = ZERO;
} else if (_iy == 1)
r = x;
else
r = rb_funcall(x, '*', 1, y);
} else if (FIXNUM_P(x)) {
long _ix = FIX2LONG(x);
if (_ix == 0) {
if (TYPE(y) == T_FLOAT)
r = rb_float_new(0.0);
else
r = ZERO;
} else if (_ix == 1)
r = y;
else
r = rb_funcall(x, '*', 1, y);
} else
r = rb_funcall(x, '*', 1, y);
return r;
}
inline static VALUE
f_sub(VALUE x, VALUE y)
{
VALUE r;
if (FIXNUM_P(y)) {
if (FIX2LONG(y) == 0)
r = x;
else
r = rb_funcall(x, '-', 1, y);
} else
r = rb_funcall(x, '-', 1, y);
return r;
}
binop(xor, '^')
fun1(abs)
fun1(floor)
fun1(inspect)
fun1(negate)
fun1(to_f)
fun1(to_i)
fun1(to_s)
fun1(truncate)
inline static VALUE
f_equal_p(VALUE x, VALUE y)
{
VALUE r;
if (FIXNUM_P(x) && FIXNUM_P(y))
r = f_boolcast(FIX2LONG(x) == FIX2LONG(y));
else
r = rb_funcall(x, id_equal_p, 1, y);
return r;
}
fun2(expt)
fun2(idiv)
inline static VALUE
f_negative_p(VALUE x)
{
VALUE r;
if (FIXNUM_P(x))
r = f_boolcast(FIX2LONG(x) < 0);
else
r = rb_funcall(x, '<', 1, ZERO);
return r;
}
inline static VALUE
f_zero_p(VALUE x)
{
VALUE r;
if (FIXNUM_P(x))
r = f_boolcast(FIX2LONG(x) == 0);
else
r = rb_funcall(x, id_equal_p, 1, ZERO);
return r;
}
inline static VALUE
f_one_p(VALUE x)
{
VALUE r;
if (FIXNUM_P(x))
r = f_boolcast(FIX2LONG(x) == 1);
else
r = rb_funcall(x, id_equal_p, 1, ONE);
return r;
}
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);
}
#ifndef NDEBUG
#define f_gcd f_gcd_orig
#endif
inline static long
i_gcd(long x, long y)
{
long b;
if (x < 0)
x = -x;
if (y < 0)
y = -y;
if (x == 0)
return y;
if (y == 0)
return x;
b = 0;
while ((x & 1) == 0 && (y & 1) == 0) {
b += 1;
x >>= 1;
y >>= 1;
}
while ((x & 1) == 0)
x >>= 1;
while ((y & 1) == 0)
y >>= 1;
while (x != y) {
if (y > x) {
long t;
t = x;
x = y;
y = t;
}
x -= y;
while ((x & 1) == 0)
x >>= 1;
}
return x << b;
}
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_zero_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;
else
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);
}
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);
if (f_negative_p(den)) {
num = f_negate(num);
den = f_negate(den);
}
break;
}
return nurat_s_new_internal(klass, num, den);
}
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_negative_p(y));
assert(!f_zero_p(y));
return nurat_s_new_internal(klass, x, y);
}
#define f_unify_p(klass) rb_const_defined(klass, id_Unify)
inline static void
nurat_int_check(VALUE num)
{
switch (TYPE(num)) {
case T_FIXNUM:
case T_BIGNUM:
break;
default:
rb_raise(rb_eArgError, "not an integer");
}
}
inline static VALUE
nurat_s_canonicalize_internal(VALUE klass, VALUE num, VALUE den)
{
VALUE gcd;
switch (FIX2INT(f_cmp(den, ZERO))) {
case -1:
if (f_negative_p(den)) {
num = f_negate(num);
den = f_negate(den);
}
break;
case 0:
rb_raise(rb_eZeroDivError, "devided by zero");
break;
}
gcd = f_gcd(num, den);
num = f_idiv(num, gcd);
den = f_idiv(den, gcd);
if (f_one_p(den) && f_unify_p(klass))
return num;
else
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:
if (f_negative_p(den)) {
num = f_negate(num);
den = f_negate(den);
}
break;
case 0:
rb_raise(rb_eZeroDivError, "devided by zero");
break;
}
if (f_equal_p(den, ONE) && f_unify_p(klass))
return num;
else
return nurat_s_new_internal(klass, num, den);
}
#if 0
static VALUE
nurat_s_canonicalize(int argc, VALUE *argv, VALUE klass)
{
VALUE num, den;
switch (rb_scan_args(argc, argv, "11", &num, &den)) {
case 1:
den = ONE;
break;
}
nurat_int_check(num);
nurat_int_check(den);
return nurat_s_canonicalize_internal(klass, num, den);
}
#endif
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:
den = ONE;
break;
}
nurat_int_check(num);
nurat_int_check(den);
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);
}
static VALUE
nurat_numerator(VALUE self)
{
get_dat1(self);
return dat->num;
}
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);
}
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, '+');
}
}
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);
}
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, '*');
}
}
#define id_to_r rb_intern("to_r")
#define f_to_r(x) rb_funcall(x, id_to_r, 0)
static VALUE
nurat_division(VALUE self, VALUE other, int rdiv)
{
again:
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
if (f_zero_p(other))
rb_raise(rb_eZeroDivError, "devided by zero");
{
get_dat1(self);
return f_muldiv(self,
dat->num, dat->den,
other, ONE, '/');
}
case T_FLOAT:
if (rdiv) {
other = f_to_r(other);
goto again;
}
return rb_funcall(f_to_f(self), '/', 1, other);
case T_RATIONAL:
if (f_zero_p(other))
rb_raise(rb_eZeroDivError, "devided by zero");
{
get_dat2(self, other);
return f_muldiv(self,
adat->num, adat->den,
bdat->num, bdat->den, '/');
}
default:
return rb_num_coerce_bin(self, other, '/');
}
}
static VALUE
nurat_div(VALUE self, VALUE other)
{
return nurat_division(self, other, Qfalse);
}
static VALUE
nurat_rdiv(VALUE self, VALUE other)
{
return nurat_division(self, other, Qtrue);
}
static VALUE
nurat_fdiv(VALUE self, VALUE other)
{
return f_div(f_to_f(self), other);
}
static VALUE
nurat_expt(VALUE self, VALUE other)
{
if (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;
}
if (f_negative_p(den)) { /* or use normal new */
num = f_negate(num);
den = f_negate(den);
}
return f_rational_new_bang2(CLASS_OF(self), num, den);
}
case T_FLOAT:
case T_RATIONAL:
return f_expt(f_to_f(self), other);
default:
return rb_num_coerce_bin(self, other, id_expt);
}
}
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);
else
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);
}
}
static VALUE
nurat_equal_p(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
{
get_dat1(self);
if (!FIXNUM_P(dat->den))
return Qfalse;
if (FIX2LONG(dat->den) != 1)
return Qfalse;
if (f_equal_p(dat->num, other))
return Qtrue;
else
return Qfalse;
}
case T_FLOAT:
return f_equal_p(f_to_f(self), other);
case T_RATIONAL:
{
get_dat2(self, other);
return f_boolcast(f_equal_p(adat->num, bdat->num) &&
f_equal_p(adat->den, bdat->den));
}
default:
return f_equal_p(other, self);
}
}
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));
}
rb_raise(rb_eTypeError, "%s can't be coerced into %s",
rb_obj_classname(other), rb_obj_classname(self));
return Qnil;
}
static VALUE
nurat_idiv(VALUE self, VALUE other)
{
return f_floor(f_div(self, other));
}
static VALUE
nurat_mod(VALUE self, VALUE other)
{
VALUE val = f_floor(f_div(self, other));
return f_sub(self, f_mul(other, val));
}
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
static VALUE
nurat_quot(VALUE self, VALUE other)
{
return f_truncate(f_div(self, other));
}
#endif
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
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
static VALUE
nurat_abs(VALUE self)
{
if (!f_negative_p(self))
return self;
else
return f_negate(self);
}
#if 0
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));
}
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)
{
get_dat1(self);
if (f_negative_p(dat->num)) {
VALUE num, den;
num = f_negate(dat->num);
num = f_add(f_mul(num, TWO), dat->den);
den = f_mul(dat->den, TWO);
return f_negate(f_idiv(num, den));
} else {
VALUE num = f_add(f_mul(dat->num, TWO), dat->den);
VALUE den = f_mul(dat->den, TWO);
return f_idiv(num, den);
}
}
#define f_size(x) rb_funcall(x, rb_intern("size"), 0)
#define f_rshift(x,y) rb_funcall(x, rb_intern(">>"), 1, y)
inline static long
i_ilog2(VALUE x)
{
long q, r, fx;
assert(!f_lt_p(x, ONE));
q = (NUM2LONG(f_size(x)) - sizeof(long)) * 8 + 1;
if (q > 0)
x = f_rshift(x, LONG2NUM(q));
fx = NUM2LONG(x);
r = -1;
while (fx) {
fx >>= 1;
r += 1;
}
return q + r;
}
static VALUE
nurat_to_f(VALUE self)
{
VALUE num, den;
int minus = 0;
long nl, dl, ml, ne, de;
int e;
double f;
{
get_dat1(self);
if (f_zero_p(dat->num))
return rb_float_new(0.0);
num = dat->num;
den = dat->den;
}
if (f_negative_p(num)) {
num = f_negate(num);
minus = 1;
}
nl = i_ilog2(num);
dl = i_ilog2(den);
ml = (long)(log(DBL_MAX) / log(2.0) - 1); /* should be a static */
ne = 0;
if (nl > ml) {
ne = nl - ml;
num = f_rshift(num, LONG2NUM(ne));
}
de = 0;
if (dl > ml) {
de = dl - ml;
den = f_rshift(den, LONG2NUM(de));
}
e = (int)(ne - de);
if ((e > DBL_MAX_EXP) || (e < DBL_MIN_EXP)) {
rb_warn("%s out of Float range", rb_obj_classname(self));
return rb_float_new(e > 0 ? HUGE_VAL : 0.0);
}
f = NUM2DBL(num) / NUM2DBL(den);
if (minus)
f = -f;
f = ldexp(f, e);
if (isinf(f) || isnan(f))
rb_warn("%s out of Float range", rb_obj_classname(self));
return rb_float_new(f);
}
static VALUE
nurat_to_r(VALUE self)
{
return self;
}
static VALUE
nurat_hash(VALUE self)
{
get_dat1(self);
return f_xor(dat->num, dat->den);
}
static VALUE
nurat_to_s(VALUE self)
{
get_dat1(self);
if (f_one_p(dat->den))
return f_to_s(dat->num);
else
return rb_funcall(rb_mKernel, id_format, 3,
rb_str_new2("%d/%d"), dat->num, dat->den);
}
static VALUE
nurat_inspect(VALUE self)
{
get_dat1(self);
return rb_funcall(rb_mKernel, id_format, 3,
rb_str_new2("Rational(%d, %d)"), dat->num, dat->den);
}
static VALUE
nurat_marshal_dump(VALUE self)
{
get_dat1(self);
return rb_assoc_new(dat->num, dat->den);
}
static VALUE
nurat_marshal_load(VALUE self, VALUE a)
{
get_dat1(self);
dat->num = RARRAY_PTR(a)[0];
dat->den = RARRAY_PTR(a)[1];
return self;
}
/* --- */
VALUE
rb_gcd(VALUE self, VALUE other)
{
nurat_int_check(other);
return f_gcd(self, other);
}
VALUE
rb_lcm(VALUE self, VALUE other)
{
nurat_int_check(other);
return f_lcm(self, other);
}
VALUE
rb_gcdlcm(VALUE self, VALUE other)
{
nurat_int_check(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);
}
static VALUE
nilclass_to_r(VALUE self)
{
return rb_rational_new1(INT2FIX(0));
}
static VALUE
integer_to_r(VALUE self)
{
return rb_rational_new1(self);
}
static VALUE
float_decode(VALUE self)
{
double f;
int n;
f = frexp(RFLOAT_VALUE(self), &n);
f = ldexp(f, DBL_MANT_DIG);
n -= DBL_MANT_DIG;
return rb_assoc_new(f_to_i(rb_float_new(f)), INT2FIX(n));
}
static VALUE
float_to_r(VALUE self)
{
VALUE a = float_decode(self);
return f_mul(RARRAY_PTR(a)[0],
f_expt(INT2FIX(FLT_RADIX), RARRAY_PTR(a)[1]));
}
static VALUE rat_pat, an_e_pat, a_dot_pat, underscores_pat, an_underscore;
#define DIGITS "(?:\\d(?:_\\d|\\d)*)"
#define NUMERATOR "(?:" DIGITS "?\\.)?" DIGITS "(?:[eE][-+]?" DIGITS ")?"
#define DENOMINATOR "[-+]?" DIGITS
#define PATTERN "\\A([-+])?(" NUMERATOR ")(?:\\/(" DENOMINATOR "))?"
static void
make_patterns(void)
{
static char rat_pat_source[] = PATTERN;
static char an_e_pat_source[] = "[eE]";
static char a_dot_pat_source[] = "\\.";
static char underscores_pat_source[] = "_+";
rat_pat = rb_reg_new(rat_pat_source, sizeof rat_pat_source - 1, 0);
rb_global_variable(&rat_pat);
an_e_pat = rb_reg_new(an_e_pat_source, sizeof an_e_pat_source - 1, 0);
rb_global_variable(&an_e_pat);
a_dot_pat = rb_reg_new(a_dot_pat_source, sizeof a_dot_pat_source - 1, 0);
rb_global_variable(&a_dot_pat);
underscores_pat = rb_reg_new(underscores_pat_source,
sizeof underscores_pat_source - 1, 0);
rb_global_variable(&underscores_pat);
an_underscore = rb_str_new2("_");
rb_global_variable(&an_underscore);
}
#define id_strip rb_intern("strip")
#define f_strip(x) rb_funcall(x, id_strip, 0)
#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 = f_strip(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 (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(exp))
v = f_mul(v, f_expt(INT2FIX(10), f_to_i(exp)));
if (!NIL_P(si) && *StringValuePtr(si) == '-')
v = f_negate(v);
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 Rational: %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)
static VALUE
string_to_r(VALUE self)
{
VALUE s = f_gsub(self, underscores_pat, an_underscore);
VALUE a = string_to_r_internal(s);
if (!NIL_P(RARRAY_PTR(a)[0]))
return RARRAY_PTR(a)[0];
return rb_rational_new1(INT2FIX(0));
}
static VALUE
nurat_s_convert(int argc, VALUE *argv, VALUE klass)
{
VALUE a1, a2;
a1 = Qnil;
a2 = Qnil;
rb_scan_args(argc, argv, "02", &a1, &a2);
switch (TYPE(a1)) {
case T_COMPLEX:
if (k_float_p(RCOMPLEX(a1)->image) || !f_zero_p(RCOMPLEX(a1)->image)) {
VALUE s = f_to_s(a1);
rb_raise(rb_eRangeError, "can't accept %s",
StringValuePtr(s));
}
a1 = RCOMPLEX(a1)->real;
}
switch (TYPE(a2)) {
case T_COMPLEX:
if (k_float_p(RCOMPLEX(a2)->image) || !f_zero_p(RCOMPLEX(a2)->image)) {
VALUE s = f_to_s(a2);
rb_raise(rb_eRangeError, "can't accept %s",
StringValuePtr(s));
}
a2 = RCOMPLEX(a2)->real;
}
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;
}
switch (TYPE(a1)) {
case T_RATIONAL:
if (NIL_P(a2) || f_zero_p(a2))
return a1;
else
return f_div(a1, a2);
}
switch (TYPE(a2)) {
case T_RATIONAL:
return f_div(a1, a2);
}
{
VALUE argv2[2];
argv2[0] = a1;
argv2[1] = a2;
return nurat_s_new(argc, argv2, klass);
}
}
static VALUE
nurat_s_induced_from(VALUE klass, VALUE n)
{
return f_to_r(n);
}
void
Init_Rational(void)
{
assert(fprintf(stderr, "assert() is now active\n"));
id_Unify = rb_intern("Unify");
id_abs = rb_intern("abs");
id_cmp = rb_intern("<=>");
id_convert = rb_intern("convert");
id_equal_p = rb_intern("==");
id_expt = rb_intern("**");
id_floor = rb_intern("floor");
id_format = rb_intern("format");
id_idiv = rb_intern("div");
id_inspect = rb_intern("inspect");
id_negate = rb_intern("-@");
id_new = rb_intern("new");
id_new_bang = rb_intern("new!");
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_NAME, rb_cNumeric);
rb_define_alloc_func(rb_cRational, nurat_s_alloc);
rb_funcall(rb_cRational, rb_intern("private_class_method"), 1,
ID2SYM(rb_intern("allocate")));
rb_define_singleton_method(rb_cRational, "new!", nurat_s_new_bang, -1);
rb_funcall(rb_cRational, rb_intern("private_class_method"), 1,
ID2SYM(rb_intern("new!")));
rb_define_singleton_method(rb_cRational, "new", nurat_s_new, -1);
rb_funcall(rb_cRational, rb_intern("private_class_method"), 1,
ID2SYM(rb_intern("new")));
rb_define_global_function(RATIONAL_NAME, 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_rdiv, 1);
rb_define_method(rb_cRational, "rdiv", nurat_rdiv, 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 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, 0);
rb_define_method(rb_cRational, "ceil", nurat_ceil, 0);
rb_define_method(rb_cRational, "truncate", nurat_truncate, 0);
rb_define_method(rb_cRational, "round", nurat_round, 0);
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_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_singleton_method(rb_cRational, "convert", nurat_s_convert, -1);
rb_funcall(rb_cRational, rb_intern("private_class_method"), 1,
ID2SYM(rb_intern("convert")));
rb_include_module(rb_cRational, rb_mPrecision);
rb_define_singleton_method(rb_cRational, "induced_from",
nurat_s_induced_from, 1);
}
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