#include "ruby.h"
#include "internal.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_eqeq_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, id_i_num, id_i_den;
#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) || RB_TYPE_P(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) || RB_TYPE_P(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)
inline static VALUE
f_to_i(VALUE x)
{
if (RB_TYPE_P(x, T_STRING))
return rb_str_to_inum(x, 10, 0);
return rb_funcall(x, id_to_i, 0);
}
inline static VALUE
f_to_f(VALUE x)
{
if (RB_TYPE_P(x, T_STRING))
return DBL2NUM(rb_str_to_dbl(x, 0));
return rb_funcall(x, id_to_f, 0);
}
fun1(to_s)
fun1(truncate)
inline static VALUE
f_eqeq_p(VALUE x, VALUE y)
{
if (FIXNUM_P(x) && FIXNUM_P(y))
return f_boolcast(FIX2LONG(x) == FIX2LONG(y));
return rb_funcall(x, id_eqeq_p, 1, y);
}
fun2(expt)
fun2(fdiv)
fun2(idiv)
#define f_expt10(x) f_expt(INT2FIX(10), x)
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)
{
switch (TYPE(x)) {
case T_FIXNUM:
return f_boolcast(FIX2LONG(x) == 0);
case T_BIGNUM:
return Qfalse;
case T_RATIONAL:
{
VALUE num = RRATIONAL(x)->num;
return f_boolcast(FIXNUM_P(num) && FIX2LONG(num) == 0);
}
}
return rb_funcall(x, id_eqeq_p, 1, ZERO);
}
#define f_nonzero_p(x) (!f_zero_p(x))
inline static VALUE
f_one_p(VALUE x)
{
switch (TYPE(x)) {
case T_FIXNUM:
return f_boolcast(FIX2LONG(x) == 1);
case T_BIGNUM:
return Qfalse;
case T_RATIONAL:
{
VALUE num = RRATIONAL(x)->num;
VALUE den = RRATIONAL(x)->den;
return f_boolcast(FIXNUM_P(num) && FIX2LONG(num) == 1 &&
FIXNUM_P(den) && FIX2LONG(den) == 1);
}
}
return rb_funcall(x, id_eqeq_p, 1, ONE);
}
inline static VALUE
f_minus_one_p(VALUE x)
{
switch (TYPE(x)) {
case T_FIXNUM:
return f_boolcast(FIX2LONG(x) == -1);
case T_BIGNUM:
return Qfalse;
case T_RATIONAL:
{
VALUE num = RRATIONAL(x)->num;
VALUE den = RRATIONAL(x)->den;
return f_boolcast(FIXNUM_P(num) && FIX2LONG(num) == -1 &&
FIXNUM_P(den) && FIX2LONG(den) == 1);
}
}
return rb_funcall(x, id_eqeq_p, 1, INT2FIX(-1));
}
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)
#define k_exact_zero_p(x) (k_exact_p(x) && f_zero_p(x))
#define k_exact_one_p(x) (k_exact_p(x) && f_one_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;
}
}
#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_OF(obj, struct RRational, 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 0")
#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;
RUBY_FUNC_EXPORTED 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_eTypeError, "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);
}
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;
if (a == 0 || b == 0)
return ZERO;
else if (a == 1)
return LONG2NUM(b);
else if (b == 1)
return LONG2NUM(a);
if (MUL_OVERFLOW_LONG_P(a, b))
r = rb_big_mul(rb_int2big(a), rb_int2big(b));
else
r = LONG2NUM(a * 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_eqeq_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, '*');
}
}
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:
{
double x = RFLOAT_VALUE(other), den;
get_dat1(self);
if (isnan(x)) return DBL2NUM(NAN);
if (isinf(x)) return INT2FIX(0);
if (x != 0.0 && modf(x, &den) == 0.0) {
return rb_rational_raw2(dat->num, f_mul(rb_dbl2big(den), dat->den));
}
}
return rb_funcall(f_to_f(self), '/', 1, other);
case T_RATIONAL:
if (f_zero_p(other))
rb_raise_zerodiv();
{
get_dat2(self, other);
if (f_one_p(self))
return f_rational_new_no_reduce2(CLASS_OF(self),
bdat->den, bdat->num);
return f_muldiv(self,
adat->num, adat->den,
bdat->num, bdat->den, '/');
}
default:
return rb_num_coerce_bin(self, other, '/');
}
}
static VALUE
nurat_fdiv(VALUE self, VALUE other)
{
if (f_zero_p(other))
return f_div(self, f_to_f(other));
return f_to_f(f_div(self, other));
}
inline static VALUE
f_odd_p(VALUE integer)
{
if (rb_funcall(integer, '%', 1, INT2FIX(2)) != INT2FIX(0)) {
return Qtrue;
}
return Qfalse;
}
static VALUE
nurat_expt(VALUE self, VALUE other)
{
if (k_numeric_p(other) && k_exact_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;
}
if (k_numeric_p(other) && k_exact_p(other)) {
get_dat1(self);
if (f_one_p(dat->den))
if (f_one_p(dat->num))
return f_rational_new_bang1(CLASS_OF(self), ONE);
else if (f_minus_one_p(dat->num) && k_integer_p(other))
return f_rational_new_bang1(CLASS_OF(self), INT2FIX(f_odd_p(other) ? -1 : 1));
else if (f_zero_p(dat->num))
if (FIX2INT(f_cmp(other, ZERO)) == -1)
rb_raise_zerodiv();
else
return f_rational_new_bang1(CLASS_OF(self), ZERO);
}
switch (TYPE(other)) {
case T_FIXNUM:
{
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_BIGNUM:
rb_warn("in a**b, b may be too big");
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);
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_cmp(self, other, id_cmp);
}
}
static VALUE
nurat_eqeq_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_eqeq_p(dat->num, other))
return Qtrue;
return Qfalse;
}
case T_FLOAT:
return f_eqeq_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_eqeq_p(adat->num, bdat->num) &&
f_eqeq_p(adat->den, bdat->den));
}
default:
return f_eqeq_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));
case T_RATIONAL:
return rb_assoc_new(other, self);
case T_COMPLEX:
if (k_exact_zero_p(RCOMPLEX(other)->imag))
return rb_assoc_new(f_rational_new_bang1
(CLASS_OF(self), RCOMPLEX(other)->real), self);
else
return rb_assoc_new(other, rb_Complex(self, INT2FIX(0)));
}
rb_raise(rb_eTypeError, "%s can't be coerced into %s",
rb_obj_classname(other), rb_obj_classname(self));
return Qnil;
}
#if 0
static VALUE
nurat_idiv(VALUE self, VALUE other)
{
return f_idiv(self, other);
}
static VALUE
nurat_quot(VALUE self, VALUE other)
{
return f_truncate(f_div(self, other));
}
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
#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)
{
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
f_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_expt10(n);
s = f_mul(self, b);
if (k_float_p(s)) {
if (f_lt_p(n, ZERO))
return ZERO;
return self;
}
if (!k_rational_p(s)) {
s = f_rational_new_bang1(CLASS_OF(self), s);
}
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;
}
static VALUE
nurat_floor_n(int argc, VALUE *argv, VALUE self)
{
return f_round_common(argc, argv, self, nurat_floor);
}
static VALUE
nurat_ceil_n(int argc, VALUE *argv, VALUE self)
{
return f_round_common(argc, argv, self, nurat_ceil);
}
static VALUE
nurat_truncate_n(int argc, VALUE *argv, VALUE self)
{
return f_round_common(argc, argv, self, nurat_truncate);
}
static VALUE
nurat_round_n(int argc, VALUE *argv, VALUE self)
{
return f_round_common(argc, argv, self, nurat_round);
}
static VALUE
nurat_to_f(VALUE self)
{
get_dat1(self);
return f_fdiv(dat->num, dat->den);
}
static VALUE
nurat_to_r(VALUE self)
{
return self;
}
#define id_ceil rb_intern("ceil")
#define f_ceil(x) rb_funcall((x), id_ceil, 0)
#define id_quo rb_intern("quo")
#define f_quo(x,y) rb_funcall((x), id_quo, 1, (y))
#define f_reciprocal(x) f_quo(ONE, (x))
static void
nurat_rationalize_internal(VALUE a, VALUE b, VALUE *p, VALUE *q)
{
VALUE c, k, t, p0, p1, p2, q0, q1, q2;
p0 = ZERO;
p1 = ONE;
q0 = ONE;
q1 = ZERO;
while (1) {
c = f_ceil(a);
if (f_lt_p(c, b))
break;
k = f_sub(c, ONE);
p2 = f_add(f_mul(k, p1), p0);
q2 = f_add(f_mul(k, q1), q0);
t = f_reciprocal(f_sub(b, k));
b = f_reciprocal(f_sub(a, k));
a = t;
p0 = p1;
q0 = q1;
p1 = p2;
q1 = q2;
}
*p = f_add(f_mul(c, p1), p0);
*q = f_add(f_mul(c, q1), q0);
}
static VALUE
nurat_rationalize(int argc, VALUE *argv, VALUE self)
{
VALUE e, a, b, p, q;
if (argc == 0)
return self;
if (f_negative_p(self))
return f_negate(nurat_rationalize(argc, argv, f_abs(self)));
rb_scan_args(argc, argv, "01", &e);
e = f_abs(e);
a = f_sub(self, e);
b = f_add(self, e);
if (f_eqeq_p(a, b))
return self;
nurat_rationalize_internal(a, b, &p, &q);
return f_rational_new2(CLASS_OF(self), p, q);
}
static VALUE
nurat_hash(VALUE self)
{
st_index_t v, h[2];
VALUE n;
get_dat1(self);
n = rb_hash(dat->num);
h[0] = NUM2LONG(n);
n = rb_hash(dat->den);
h[1] = NUM2LONG(n);
v = rb_memhash(h, sizeof(h));
return LONG2FIX(v);
}
static VALUE
f_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;
}
static VALUE
nurat_to_s(VALUE self)
{
return f_format(self, f_to_s);
}
static VALUE
nurat_inspect(VALUE self)
{
VALUE s;
s = rb_usascii_str_new2("(");
rb_str_concat(s, f_format(self, f_inspect));
rb_str_cat2(s, ")");
return s;
}
static VALUE
nurat_dumper(VALUE self)
{
return self;
}
static VALUE
nurat_loader(VALUE self, VALUE a)
{
get_dat1(self);
dat->num = rb_ivar_get(a, id_i_num);
dat->den = rb_ivar_get(a, id_i_den);
return self;
}
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;
}
static VALUE
nurat_marshal_load(VALUE self, VALUE a)
{
rb_check_frozen(self);
rb_check_trusted(self);
Check_Type(a, T_ARRAY);
if (RARRAY_LEN(a) != 2)
rb_raise(rb_eArgError, "marshaled rational must have an array whose length is 2 but %ld", RARRAY_LEN(a));
if (f_zero_p(RARRAY_PTR(a)[1]))
rb_raise_zerodiv();
rb_ivar_set(self, id_i_num, RARRAY_PTR(a)[0]);
rb_ivar_set(self, id_i_den, RARRAY_PTR(a)[1]);
return self;
}
VALUE
rb_rational_reciprocal(VALUE x)
{
get_dat1(x);
return f_rational_new_no_reduce2(CLASS_OF(x), dat->den, dat->num);
}
VALUE
rb_gcd(VALUE self, VALUE other)
{
other = nurat_int_value(other);
return f_gcd(self, other);
}
VALUE
rb_lcm(VALUE self, VALUE other)
{
other = nurat_int_value(other);
return f_lcm(self, other);
}
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)
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));
}
static VALUE
integer_numerator(VALUE self)
{
return self;
}
static VALUE
integer_denominator(VALUE self)
{
return INT2FIX(1);
}
static VALUE
float_numerator(VALUE self)
{
double d = RFLOAT_VALUE(self);
if (isinf(d) || isnan(d))
return self;
return rb_call_super(0, 0);
}
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);
}
static VALUE
nilclass_to_r(VALUE self)
{
return rb_rational_new1(INT2FIX(0));
}
static VALUE
nilclass_rationalize(int argc, VALUE *argv, VALUE self)
{
rb_scan_args(argc, argv, "01", NULL);
return nilclass_to_r(self);
}
static VALUE
integer_to_r(VALUE self)
{
return rb_rational_new1(self);
}
static VALUE
integer_rationalize(int argc, VALUE *argv, VALUE self)
{
rb_scan_args(argc, argv, "01", NULL);
return integer_to_r(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
#define id_lshift rb_intern("<<")
#define f_lshift(x,n) rb_funcall((x), id_lshift, 1, (n))
static VALUE
float_to_r(VALUE self)
{
VALUE f, n;
float_decode_internal(self, &f, &n);
#if FLT_RADIX == 2
{
long ln = FIX2LONG(n);
if (ln == 0)
return f_to_r(f);
if (ln > 0)
return f_to_r(f_lshift(f, n));
ln = -ln;
return rb_rational_new2(f, f_lshift(ONE, INT2FIX(ln)));
}
#else
return f_to_r(f_mul(f, f_expt(INT2FIX(FLT_RADIX), n)));
#endif
}
static VALUE
float_rationalize(int argc, VALUE *argv, VALUE self)
{
VALUE e, a, b, p, q;
if (f_negative_p(self))
return f_negate(float_rationalize(argc, argv, f_abs(self)));
rb_scan_args(argc, argv, "01", &e);
if (argc != 0) {
e = f_abs(e);
a = f_sub(self, e);
b = f_add(self, e);
}
else {
VALUE f, n;
float_decode_internal(self, &f, &n);
if (f_zero_p(f) || f_positive_p(n))
return rb_rational_new1(f_lshift(f, n));
#if FLT_RADIX == 2
{
VALUE two_times_f, den;
two_times_f = f_mul(TWO, f);
den = f_lshift(ONE, f_sub(ONE, n));
a = rb_rational_new2(f_sub(two_times_f, ONE), den);
b = rb_rational_new2(f_add(two_times_f, ONE), den);
}
#else
{
VALUE radix_times_f, den;
radix_times_f = f_mul(INT2FIX(FLT_RADIX), f);
den = f_expt(INT2FIX(FLT_RADIX), f_sub(ONE, n));
a = rb_rational_new2(f_sub(radix_times_f, INT2FIX(FLT_RADIX - 1)), den);
b = rb_rational_new2(f_add(radix_times_f, INT2FIX(FLT_RADIX - 1)), den);
}
#endif
}
if (f_eqeq_p(a, b))
return f_to_r(self);
nurat_rationalize_internal(a, b, &p, &q);
return rb_rational_new2(p, q);
}
#include <ctype.h>
inline static int
issign(int c)
{
return (c == '-' || c == '+');
}
static int
read_sign(const char **s)
{
int sign = '?';
if (issign(**s)) {
sign = **s;
(*s)++;
}
return sign;
}
inline static int
isdecimal(int c)
{
return isdigit((unsigned char)c);
}
static int
read_digits(const char **s, int strict,
VALUE *num, int *count)
{
char *b, *bb;
int us = 1, ret = 1;
VALUE tmp;
if (!isdecimal(**s)) {
*num = ZERO;
return 0;
}
bb = b = ALLOCV_N(char, tmp, strlen(*s) + 1);
while (isdecimal(**s) || **s == '_') {
if (**s == '_') {
if (strict) {
if (us) {
ret = 0;
goto conv;
}
}
us = 1;
}
else {
if (count)
(*count)++;
*b++ = **s;
us = 0;
}
(*s)++;
}
if (us)
do {
(*s)--;
} while (**s == '_');
conv:
*b = '\0';
*num = rb_cstr_to_inum(bb, 10, 0);
ALLOCV_END(tmp);
return ret;
}
inline static int
islettere(int c)
{
return (c == 'e' || c == 'E');
}
static int
read_num(const char **s, int numsign, int strict,
VALUE *num)
{
VALUE ip, fp, exp;
*num = rb_rational_new2(ZERO, ONE);
exp = Qnil;
if (**s != '.') {
if (!read_digits(s, strict, &ip, NULL))
return 0;
*num = rb_rational_new2(ip, ONE);
}
if (**s == '.') {
int count = 0;
(*s)++;
if (!read_digits(s, strict, &fp, &count))
return 0;
{
VALUE l = f_expt10(INT2NUM(count));
*num = f_mul(*num, l);
*num = f_add(*num, fp);
*num = f_div(*num, l);
}
}
if (islettere(**s)) {
int expsign;
(*s)++;
expsign = read_sign(s);
if (!read_digits(s, strict, &exp, NULL))
return 0;
if (expsign == '-')
exp = f_negate(exp);
}
if (numsign == '-')
*num = f_negate(*num);
if (!NIL_P(exp)) {
VALUE l = f_expt10(exp);
*num = f_mul(*num, l);
}
return 1;
}
inline static int
read_den(const char **s, int strict,
VALUE *num)
{
if (!read_digits(s, strict, num, NULL))
return 0;
return 1;
}
static int
read_rat_nos(const char **s, int sign, int strict,
VALUE *num)
{
VALUE den;
if (!read_num(s, sign, strict, num))
return 0;
if (**s == '/') {
(*s)++;
if (!read_den(s, strict, &den))
return 0;
if (!(FIXNUM_P(den) && FIX2LONG(den) == 1))
*num = f_div(*num, den);
}
return 1;
}
static int
read_rat(const char **s, int strict,
VALUE *num)
{
int sign;
sign = read_sign(s);
if (!read_rat_nos(s, sign, strict, num))
return 0;
return 1;
}
inline static void
skip_ws(const char **s)
{
while (isspace((unsigned char)**s))
(*s)++;
}
static int
parse_rat(const char *s, int strict,
VALUE *num)
{
skip_ws(&s);
if (!read_rat(&s, strict, num))
return 0;
skip_ws(&s);
if (strict)
if (*s != '\0')
return 0;
return 1;
}
static VALUE
string_to_r_strict(VALUE self)
{
char *s;
VALUE num;
rb_must_asciicompat(self);
s = RSTRING_PTR(self);
if (!s || memchr(s, '\0', RSTRING_LEN(self)))
rb_raise(rb_eArgError, "string contains null byte");
if (s && s[RSTRING_LEN(self)]) {
rb_str_modify(self);
s = RSTRING_PTR(self);
s[RSTRING_LEN(self)] = '\0';
}
if (!s)
s = (char *)"";
if (!parse_rat(s, 1, &num)) {
VALUE ins = f_inspect(self);
rb_raise(rb_eArgError, "invalid value for convert(): %s",
StringValuePtr(ins));
}
if (RB_TYPE_P(num, T_FLOAT))
rb_raise(rb_eFloatDomainError, "Infinity");
return num;
}
static VALUE
string_to_r(VALUE self)
{
char *s;
VALUE num;
rb_must_asciicompat(self);
s = RSTRING_PTR(self);
if (s && s[RSTRING_LEN(self)]) {
rb_str_modify(self);
s = RSTRING_PTR(self);
s[RSTRING_LEN(self)] = '\0';
}
if (!s)
s = (char *)"";
(void)parse_rat(s, 0, &num);
if (RB_TYPE_P(num, T_FLOAT))
rb_raise(rb_eFloatDomainError, "Infinity");
return num;
}
VALUE
rb_cstr_to_rat(const char *s, int strict)
{
VALUE num;
(void)parse_rat(s, strict, &num);
if (RB_TYPE_P(num, T_FLOAT))
rb_raise(rb_eFloatDomainError, "Infinity");
return num;
}
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_zero_p(RCOMPLEX(a1)->imag))
a1 = RCOMPLEX(a1)->real;
}
switch (TYPE(a2)) {
case T_COMPLEX:
if (k_exact_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_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);
}
}
void
Init_Rational(void)
{
VALUE compat;
#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_eqeq_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");
id_i_num = rb_intern("@numerator");
id_i_den = rb_intern("@denominator");
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_eqeq_p, 1);
rb_define_method(rb_cRational, "coerce", nurat_coerce, 1);
#if 0
rb_define_method(rb_cRational, "//", nurat_idiv, 1);
#endif
#if 0
rb_define_method(rb_cRational, "quot", nurat_quot, 1);
rb_define_method(rb_cRational, "quotrem", nurat_quotrem, 1);
#endif
#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, "rationalize", nurat_rationalize, -1);
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_private_method(rb_cRational, "marshal_dump", nurat_marshal_dump, 0);
compat = rb_define_class_under(rb_cRational, "compatible", rb_cObject);
rb_define_private_method(compat, "marshal_load", nurat_marshal_load, 1);
rb_marshal_define_compat(rb_cRational, compat, nurat_dumper, nurat_loader);
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_cNilClass, "rationalize", nilclass_rationalize, -1);
rb_define_method(rb_cInteger, "to_r", integer_to_r, 0);
rb_define_method(rb_cInteger, "rationalize", integer_rationalize, -1);
rb_define_method(rb_cFloat, "to_r", float_to_r, 0);
rb_define_method(rb_cFloat, "rationalize", float_rationalize, -1);
rb_define_method(rb_cString, "to_r", string_to_r, 0);
rb_define_private_method(CLASS_OF(rb_cRational), "convert", nurat_s_convert, -1);
}