diff options
| -rw-r--r-- | ChangeLog | 9 | ||||
| -rw-r--r-- | complex.c | 307 | ||||
| -rw-r--r-- | rational.c | 617 | ||||
| -rw-r--r-- | test/ruby/test_rational2.rb | 1360 |
4 files changed, 2173 insertions, 120 deletions
@@ -1,3 +1,12 @@ +Thu Mar 20 21:20:19 2008 Tadayoshi Funaba <tadf@dotrb.org> + + * rational.c: some improvements (include Shin-ichiro HARA's + effort). + + * complex.c: some improvemtns. + + * test/ruby/test_rational2.rb: new. + Thu Mar 20 00:21:12 2008 Nobuyoshi Nakada <nobu@ruby-lang.org> * io.c (argf_initialize_copy): get rid of segfault. @@ -28,61 +28,264 @@ static ID id_Unify, id_abs, id_abs2, id_arg, id_atan2_bang, id_cmp, id_numerator, id_polar, id_quo, id_scalar_p, id_sin, id_sqrt, id_to_f, id_to_i, id_to_r, id_to_s, id_truncate; -#define f_add(x,y) rb_funcall(x, '+', 1, y) -#define f_div(x,y) rb_funcall(x, '/', 1, y) -#define f_gt_p(x,y) rb_funcall(x, '>', 1, y) -#define f_lt_p(x,y) rb_funcall(x, '<', 1, y) -#define f_mod(x,y) rb_funcall(x, '%', 1, y) -#define f_mul(x,y) rb_funcall(x, '*', 1, y) -#define f_sub(x,y) rb_funcall(x, '-', 1, y) -#define f_xor(x,y) rb_funcall(x, '^', 1, y) - -#define f_abs(x) rb_funcall(x, id_abs, 0) -#define f_abs2(x) rb_funcall(x, id_abs2, 0) -#define f_arg(x) rb_funcall(x, id_arg, 0) -#define f_conjugate(x) rb_funcall(x, id_conjugate, 0) -#define f_denominator(x) rb_funcall(x, id_denominator, 0) -#define f_exact_p(x) rb_funcall(x, id_exact_p, 0) -#define f_floor(x) rb_funcall(x, id_floor, 0) -#define f_negate(x) rb_funcall(x, id_negate, 0) -#define f_numerator(x) rb_funcall(x, id_numerator, 0) -#define f_polar(x) rb_funcall(x, id_polar, 0) -#define f_scalar_p(x) rb_funcall(x, id_scalar_p, 0) -#define f_to_f(x) rb_funcall(x, id_to_f, 0) -#define f_to_i(x) rb_funcall(x, id_to_i, 0) -#define f_to_r(x) rb_funcall(x, id_to_r, 0) -#define f_to_s(x) rb_funcall(x, id_to_s, 0) -#define f_truncate(x) rb_funcall(x, id_truncate, 0) -#define f_cmp(x,y) rb_funcall(x, id_cmp, 1, y) -#define f_coerce(x,y) rb_funcall(x, id_coerce, 1, y) -#define f_divmod(x,y) rb_funcall(x, id_divmod, 1, y) -#define f_equal_p(x,y) rb_funcall(x, id_equal_p, 1, y) -#define f_expt(x,y) rb_funcall(x, id_expt, 1, y) -#define f_idiv(x,y) rb_funcall(x, id_idiv, 1, y) -#define f_inspect(x) rb_funcall(x, id_inspect, 0) -#define f_quo(x,y) rb_funcall(x, id_quo, 1, y) +#define f_boolcast(x) ((x) ? Qtrue : Qfalse) -#if 0 -#define m_cos(x) rb_funcall(rb_mMath, id_cos, 1, x) -#define m_exp_bang(x) rb_funcall(rb_mMath, id_exp_bang, 1, x) -#define m_log_bang(x) rb_funcall(rb_mMath, id_log_bang, 1, x) -#define m_sin(x) rb_funcall(rb_mMath, id_sin, 1, x) -#define m_sqrt(x) rb_funcall(rb_mMath, id_sqrt, 1, x) -#define m_atan2_bang(x,y) rb_funcall(rb_mMath, id_atan2_bang, 2, x, y) -#define m_hypot(x,y) rb_funcall(rb_mMath, id_hypot, 2, x, y) -#endif +#define binop(n,op) \ +inline static VALUE \ +f_##n(VALUE x, VALUE y)\ +{\ + return rb_funcall(x, op, 1, y);\ +} -#define f_negative_p(x) f_lt_p(x, ZERO) -#define f_zero_p(x) f_equal_p(x, ZERO) -#define f_one_p(x) f_equal_p(x, ONE) -#define f_kind_of_p(x,c) rb_obj_is_kind_of(x, c) -#define k_numeric_p(x) f_kind_of_p(x, rb_cNumeric) -#define k_integer_p(x) f_kind_of_p(x, rb_cInteger) -#define k_float_p(x) f_kind_of_p(x, rb_cFloat) -#define k_rational_p(x) f_kind_of_p(x, rb_cRational) -#define k_complex_p(x) f_kind_of_p(x, rb_cComplex) +#define fun1(n) \ +inline static VALUE \ +f_##n(VALUE x)\ +{\ + return rb_funcall(x, id_##n, 0);\ +} -#define f_boolcast(x) ((x) ? Qtrue : Qfalse) +#define fun2(n) \ +inline static VALUE \ +f_##n(VALUE x, VALUE y)\ +{\ + return rb_funcall(x, id_##n, 1, y);\ +} + +#define math1(n) \ +inline static VALUE \ +m_##n(VALUE x)\ +{\ + return rb_funcall(rb_mMath, id_##n, 1, x);\ +} + +#define math2(n) \ +inline static VALUE \ +m_##n(VALUE x, VALUE y)\ +{\ + return rb_funcall(rb_mMath, id_##n, 2, x, y);\ +} + +inline static VALUE +f_add(VALUE x, VALUE y) +{ + VALUE _r; + if (FIXNUM_P(y)) { + if (FIX2INT(y) == 0) + _r = x; + else + _r = rb_funcall(x, '+', 1, y); + } else if (FIXNUM_P(x)) { + if (FIX2INT(x) == 0) + _r = y; + else + _r = rb_funcall(x, '+', 1, y); + } else + _r = rb_funcall(x, '+', 1, y); + return _r; +} + +inline static VALUE +f_div(x, y) +{ + VALUE _r; + if (FIXNUM_P(y) && FIX2INT(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(FIX2INT(x) > FIX2INT(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(FIX2INT(x) < FIX2INT(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)) { + int _iy = FIX2INT(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)) { + int _ix = FIX2INT(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 (FIX2INT(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(abs2) +fun1(arg) +fun1(conjugate) +fun1(denominator) +fun1(exact_p) +fun1(floor) +fun1(inspect) +fun1(negate) +fun1(numerator) +fun1(polar) +fun1(scalar_p) +fun1(to_f) +fun1(to_i) +fun1(to_r) +fun1(to_s) +fun1(truncate) + +inline static VALUE +f_cmp(VALUE x, VALUE y) +{ + VALUE _r; + if (FIXNUM_P(x) && FIXNUM_P(y)) { + int c = FIX2INT(x) - FIX2INT(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; +} + +fun2(coerce) +fun2(divmod) + +inline static VALUE +f_equal_p(VALUE x, VALUE y) +{ + VALUE _r; + if (FIXNUM_P(x) && FIXNUM_P(y)) + _r = f_boolcast(FIX2INT(x) == FIX2INT(y)); + else + _r = rb_funcall(x, id_equal_p, 1, y); + return _r; +} + +fun2(expt) +fun2(idiv) +fun2(quo) + +inline static VALUE +f_negative_p(VALUE x) +{ + VALUE _r; + if (FIXNUM_P(x)) + _r = f_boolcast(FIX2INT(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(FIX2INT(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(FIX2INT(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); +} + +inline static VALUE +k_complex_p(VALUE x) +{ + return f_kind_of_p(x, rb_cComplex); +} inline static VALUE f_generic_p(VALUE x) diff --git a/rational.c b/rational.c index de028ee041..066a73d4bf 100644 --- a/rational.c +++ b/rational.c @@ -25,39 +25,237 @@ static ID id_Unify, id_cmp, id_coerce, 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_add(x,y) rb_funcall(x, '+', 1, y) -#define f_div(x,y) rb_funcall(x, '/', 1, y) -#define f_gt_p(x,y) rb_funcall(x, '>', 1, y) -#define f_lt_p(x,y) rb_funcall(x, '<', 1, y) -#define f_mod(x,y) rb_funcall(x, '%', 1, y) -#define f_mul(x,y) rb_funcall(x, '*', 1, y) -#define f_sub(x,y) rb_funcall(x, '-', 1, y) -#define f_xor(x,y) rb_funcall(x, '^', 1, y) - -#define f_floor(x) rb_funcall(x, id_floor, 0) -#define f_inspect(x) rb_funcall(x, id_inspect, 0) -#define f_to_f(x) rb_funcall(x, id_to_f, 0) -#define f_to_i(x) rb_funcall(x, id_to_i, 0) -#define f_to_s(x) rb_funcall(x, id_to_s, 0) -#define f_truncate(x) rb_funcall(x, id_truncate, 0) -#define f_cmp(x,y) rb_funcall(x, id_cmp, 1, y) -#define f_coerce(x,y) rb_funcall(x, id_coerce, 1, y) -#define f_equal_p(x,y) rb_funcall(x, id_equal_p, 1, y) -#define f_expt(x,y) rb_funcall(x, id_expt, 1, y) -#define f_idiv(x,y) rb_funcall(x, id_idiv, 1, y) -#define f_negate(x) rb_funcall(x, id_negate, 0) - -#define f_negative_p(x) f_lt_p(x, ZERO) -#define f_zero_p(x) f_equal_p(x, ZERO) -#define f_one_p(x) f_equal_p(x, ONE) -#define f_kind_of_p(x,c) rb_obj_is_kind_of(x, c) -#define k_numeric_p(x) f_kind_of_p(x, rb_cNumeric) -#define k_integer_p(x) f_kind_of_p(x, rb_cInteger) -#define k_float_p(x) f_kind_of_p(x, rb_cFloat) -#define k_rational_p(x) f_kind_of_p(x, rb_cRational) - #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 (FIX2INT(y) == 0) + _r = x; + else + _r = rb_funcall(x, '+', 1, y); + } else if (FIXNUM_P(x)) { + if (FIX2INT(x) == 0) + _r = y; + else + _r = rb_funcall(x, '+', 1, y); + } else + _r = rb_funcall(x, '+', 1, y); + return _r; +} + +inline static VALUE +f_div(x, y) +{ + VALUE _r; + if (FIXNUM_P(y) && FIX2INT(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(FIX2INT(x) > FIX2INT(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(FIX2INT(x) < FIX2INT(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)) { + int _iy = FIX2INT(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)) { + int _ix = FIX2INT(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 (FIX2INT(y) == 0) + _r = x; + else + _r = rb_funcall(x, '-', 1, y); + } else + _r = rb_funcall(x, '-', 1, y); + return _r; +} + +binop(xor, '^') + +fun1(floor) +fun1(inspect) +fun1(negate) +fun1(to_f) +fun1(to_i) +fun1(to_s) +fun1(truncate) + +inline static VALUE +f_cmp(VALUE x, VALUE y) +{ + VALUE _r; + if (FIXNUM_P(x) && FIXNUM_P(y)) { + int c = FIX2INT(x) - FIX2INT(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; +} + +fun2(coerce) + +inline static VALUE +f_equal_p(VALUE x, VALUE y) +{ + VALUE _r; + if (FIXNUM_P(x) && FIXNUM_P(y)) + _r = f_boolcast(FIX2INT(x) == FIX2INT(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(FIX2INT(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(FIX2INT(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(FIX2INT(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) { @@ -133,6 +331,21 @@ f_gcd(VALUE x, VALUE y) /* 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 + VALUE rb_gcd(VALUE x, VALUE y) { @@ -236,6 +449,27 @@ nurat_s_canonicalize_internal(VALUE klass, VALUE num, VALUE den) 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); +} + static VALUE nurat_s_canonicalize(int argc, VALUE *argv, VALUE klass) { @@ -311,6 +545,21 @@ f_rational_new2(VALUE klass, VALUE x, VALUE 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) { @@ -331,27 +580,112 @@ nurat_denominator(VALUE 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: - return f_add(self, f_rational_new_bang1(CLASS_OF(self), other)); + { + 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: { - VALUE num1, num2; - get_dat2(self, other); - num1 = f_mul(adat->num, bdat->den); - num2 = f_mul(bdat->num, adat->den); - - return f_rational_new2(CLASS_OF(self), - f_add(num1, num2), - f_mul(adat->den, bdat->den)); + return f_addsub(self, + adat->num, adat->den, + bdat->num, bdat->den, '+'); } default: { @@ -367,21 +701,22 @@ nurat_sub(VALUE self, VALUE other) switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: - return f_sub(self, f_rational_new_bang1(CLASS_OF(self), other)); + { + 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: { - VALUE num1, num2; - get_dat2(self, other); - num1 = f_mul(adat->num, bdat->den); - num2 = f_mul(bdat->num, adat->den); - - return f_rational_new2(CLASS_OF(self), - f_sub(num1, num2), - f_mul(adat->den, bdat->den)); + return f_addsub(self, + adat->num, adat->den, + bdat->num, bdat->den, '-'); } default: { @@ -391,25 +726,66 @@ nurat_sub(VALUE self, VALUE 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: - return f_mul(self, f_rational_new_bang1(CLASS_OF(self), other)); + { + 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: { - VALUE num, den; - get_dat2(self, other); - num = f_mul(adat->num, bdat->num); - den = f_mul(adat->den, bdat->den); - - return f_rational_new2(CLASS_OF(self), num, den); + return f_muldiv(self, + adat->num, adat->den, + bdat->num, bdat->den, '*'); } default: { @@ -427,19 +803,24 @@ nurat_div(VALUE self, VALUE other) case T_BIGNUM: if (f_zero_p(other)) rb_raise(rb_eZeroDivError, "devided by zero"); - return f_div(self, f_rational_new_bang1(CLASS_OF(self), other)); + { + get_dat1(self); + + return f_muldiv(self, + dat->num, dat->den, + other, ONE, '/'); + } case T_FLOAT: return f_div(f_to_f(self), other); case T_RATIONAL: + if (f_zero_p(other)) + rb_raise(rb_eZeroDivError, "devided by zero"); { - VALUE num, den; - get_dat2(self, other); - num = f_mul(adat->num, bdat->den); - den = f_mul(adat->den, bdat->num); - - return f_rational_new2(CLASS_OF(self), num, den); + return f_muldiv(self, + adat->num, adat->den, + bdat->num, bdat->den, '/'); } default: { @@ -513,7 +894,14 @@ nurat_cmp(VALUE self, VALUE other) switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: - return f_cmp(self, f_rational_new_bang1(CLASS_OF(self), other)); + { + get_dat1(self); + + if (FIXNUM_P(dat->den) && FIX2INT(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: @@ -522,8 +910,14 @@ nurat_cmp(VALUE self, VALUE other) get_dat2(self, other); - num1 = f_mul(adat->num, bdat->den); - num2 = f_mul(bdat->num, adat->den); + if (FIXNUM_P(adat->num) && FIXNUM_P(adat->den) && + FIXNUM_P(bdat->num) && FIXNUM_P(bdat->den)) { + num1 = f_imul(FIX2INT(adat->num), FIX2INT(bdat->den)); + num2 = f_imul(FIX2INT(bdat->num), FIX2INT(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: @@ -540,7 +934,18 @@ nurat_equal_p(VALUE self, VALUE other) switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: - return f_equal_p(self, f_rational_new_bang1(CLASS_OF(self), other)); + { + get_dat1(self); + + if (!FIXNUM_P(dat->den)) + return Qfalse; + if (FIX2INT(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: @@ -666,11 +1071,87 @@ nurat_round(VALUE self) } } +#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; +} + +#include <float.h> + static VALUE nurat_to_f(VALUE self) { get_dat1(self); - return f_div(f_to_f(dat->num), dat->den); /* enough? */ + VALUE num, den; + int minus = 0; + long nl, dl, ml, ne, de; + int e; + double f; + + 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) - 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 diff --git a/test/ruby/test_rational2.rb b/test/ruby/test_rational2.rb new file mode 100644 index 0000000000..641bfea565 --- /dev/null +++ b/test/ruby/test_rational2.rb @@ -0,0 +1,1360 @@ +require 'test/unit' + +class Rational_Test2 < Test::Unit::TestCase + + def test_kumi + assert_equal(Rational(2, 1), + Rational(1, 1) + Rational(1, 1)) + assert_equal(Rational(0, 1), + Rational(1, 1) - Rational(1, 1)) + assert_equal(Rational(1, 1), + Rational(1, 1) * Rational(1, 1)) + assert_equal(Rational(1, 1), + Rational(1, 1) / Rational(1, 1)) + assert_equal(Rational(3, 1), + Rational(1, 1) + Rational(2, 1)) + assert_equal(Rational(-1, 1), + Rational(1, 1) - Rational(2, 1)) + assert_equal(Rational(2, 1), + Rational(1, 1) * Rational(2, 1)) + assert_equal(Rational(1, 2), + Rational(1, 1) / Rational(2, 1)) + assert_equal(Rational(4, 1), + Rational(1, 1) + Rational(3, 1)) + assert_equal(Rational(-2, 1), + Rational(1, 1) - Rational(3, 1)) + assert_equal(Rational(3, 1), + Rational(1, 1) * Rational(3, 1)) + assert_equal(Rational(1, 3), + Rational(1, 1) / Rational(3, 1)) + assert_equal(Rational(1073741790, 1), + Rational(1, 1) + Rational(1073741789, 1)) + assert_equal(Rational(-1073741788, 1), + Rational(1, 1) - Rational(1073741789, 1)) + assert_equal(Rational(1073741789, 1), + Rational(1, 1) * Rational(1073741789, 1)) + assert_equal(Rational(1, 1073741789), + Rational(1, 1) / Rational(1073741789, 1)) + assert_equal(Rational(1073741828, 1), + Rational(1, 1) + Rational(1073741827, 1)) + assert_equal(Rational(-1073741826, 1), + Rational(1, 1) - Rational(1073741827, 1)) + assert_equal(Rational(1073741827, 1), + Rational(1, 1) * Rational(1073741827, 1)) + assert_equal(Rational(1, 1073741827), + Rational(1, 1) / Rational(1073741827, 1)) + assert_equal(Rational(5, 3), + Rational(1, 1) + Rational(2, 3)) + assert_equal(Rational(1, 3), + Rational(1, 1) - Rational(2, 3)) + assert_equal(Rational(2, 3), + Rational(1, 1) * Rational(2, 3)) + assert_equal(Rational(3, 2), + Rational(1, 1) / Rational(2, 3)) + assert_equal(Rational(5, 2), + Rational(1, 1) + Rational(3, 2)) + assert_equal(Rational(-1, 2), + Rational(1, 1) - Rational(3, 2)) + assert_equal(Rational(3, 2), + Rational(1, 1) * Rational(3, 2)) + assert_equal(Rational(2, 3), + Rational(1, 1) / Rational(3, 2)) + assert_equal(Rational(1073741792, 1073741789), + Rational(1, 1) + Rational(3, 1073741789)) + assert_equal(Rational(1073741786, 1073741789), + Rational(1, 1) - Rational(3, 1073741789)) + assert_equal(Rational(3, 1073741789), + Rational(1, 1) * Rational(3, 1073741789)) + assert_equal(Rational(1073741789, 3), + Rational(1, 1) / Rational(3, 1073741789)) + assert_equal(Rational(1073741792, 3), + Rational(1, 1) + Rational(1073741789, 3)) + assert_equal(Rational(-1073741786, 3), + Rational(1, 1) - Rational(1073741789, 3)) + assert_equal(Rational(1073741789, 3), + Rational(1, 1) * Rational(1073741789, 3)) + assert_equal(Rational(3, 1073741789), + Rational(1, 1) / Rational(1073741789, 3)) + assert_equal(Rational(1073741830, 1073741827), + Rational(1, 1) + Rational(3, 1073741827)) + assert_equal(Rational(1073741824, 1073741827), + Rational(1, 1) - Rational(3, 1073741827)) + assert_equal(Rational(3, 1073741827), + Rational(1, 1) * Rational(3, 1073741827)) + assert_equal(Rational(1073741827, 3), + Rational(1, 1) / Rational(3, 1073741827)) + assert_equal(Rational(1073741830, 3), + Rational(1, 1) + Rational(1073741827, 3)) + assert_equal(Rational(-1073741824, 3), + Rational(1, 1) - Rational(1073741827, 3)) + assert_equal(Rational(1073741827, 3), + Rational(1, 1) * Rational(1073741827, 3)) + assert_equal(Rational(3, 1073741827), + Rational(1, 1) / Rational(1073741827, 3)) + assert_equal(Rational(2147483616, 1073741827), + Rational(1, 1) + Rational(1073741789, 1073741827)) + assert_equal(Rational(38, 1073741827), + Rational(1, 1) - Rational(1073741789, 1073741827)) + assert_equal(Rational(1073741789, 1073741827), + Rational(1, 1) * Rational(1073741789, 1073741827)) + assert_equal(Rational(1073741827, 1073741789), + Rational(1, 1) / Rational(1073741789, 1073741827)) + assert_equal(Rational(2147483616, 1073741789), + Rational(1, 1) + Rational(1073741827, 1073741789)) + assert_equal(Rational(-38, 1073741789), + Rational(1, 1) - Rational(1073741827, 1073741789)) + assert_equal(Rational(1073741827, 1073741789), + Rational(1, 1) * Rational(1073741827, 1073741789)) + assert_equal(Rational(1073741789, 1073741827), + Rational(1, 1) / Rational(1073741827, 1073741789)) + assert_equal(Rational(3, 1), + Rational(2, 1) + Rational(1, 1)) + assert_equal(Rational(1, 1), + Rational(2, 1) - Rational(1, 1)) + assert_equal(Rational(2, 1), + Rational(2, 1) * Rational(1, 1)) + assert_equal(Rational(2, 1), + Rational(2, 1) / Rational(1, 1)) + assert_equal(Rational(4, 1), + Rational(2, 1) + Rational(2, 1)) + assert_equal(Rational(0, 1), + Rational(2, 1) - Rational(2, 1)) + assert_equal(Rational(4, 1), + Rational(2, 1) * Rational(2, 1)) + assert_equal(Rational(1, 1), + Rational(2, 1) / Rational(2, 1)) + assert_equal(Rational(5, 1), + Rational(2, 1) + Rational(3, 1)) + assert_equal(Rational(-1, 1), + Rational(2, 1) - Rational(3, 1)) + assert_equal(Rational(6, 1), + Rational(2, 1) * Rational(3, 1)) + assert_equal(Rational(2, 3), + Rational(2, 1) / Rational(3, 1)) + assert_equal(Rational(1073741791, 1), + Rational(2, 1) + Rational(1073741789, 1)) + assert_equal(Rational(-1073741787, 1), + Rational(2, 1) - Rational(1073741789, 1)) + assert_equal(Rational(2147483578, 1), + Rational(2, 1) * Rational(1073741789, 1)) + assert_equal(Rational(2, 1073741789), + Rational(2, 1) / Rational(1073741789, 1)) + assert_equal(Rational(1073741829, 1), + Rational(2, 1) + Rational(1073741827, 1)) + assert_equal(Rational(-1073741825, 1), + Rational(2, 1) - Rational(1073741827, 1)) + assert_equal(Rational(2147483654, 1), + Rational(2, 1) * Rational(1073741827, 1)) + assert_equal(Rational(2, 1073741827), + Rational(2, 1) / Rational(1073741827, 1)) + assert_equal(Rational(8, 3), + Rational(2, 1) + Rational(2, 3)) + assert_equal(Rational(4, 3), + Rational(2, 1) - Rational(2, 3)) + assert_equal(Rational(4, 3), + Rational(2, 1) * Rational(2, 3)) + assert_equal(Rational(3, 1), + Rational(2, 1) / Rational(2, 3)) + assert_equal(Rational(7, 2), + Rational(2, 1) + Rational(3, 2)) + assert_equal(Rational(1, 2), + Rational(2, 1) - Rational(3, 2)) + assert_equal(Rational(3, 1), + Rational(2, 1) * Rational(3, 2)) + assert_equal(Rational(4, 3), + Rational(2, 1) / Rational(3, 2)) + assert_equal(Rational(2147483581, 1073741789), + Rational(2, 1) + Rational(3, 1073741789)) + assert_equal(Rational(2147483575, 1073741789), + Rational(2, 1) - Rational(3, 1073741789)) + assert_equal(Rational(6, 1073741789), + Rational(2, 1) * Rational(3, 1073741789)) + assert_equal(Rational(2147483578, 3), + Rational(2, 1) / Rational(3, 1073741789)) + assert_equal(Rational(1073741795, 3), + Rational(2, 1) + Rational(1073741789, 3)) + assert_equal(Rational(-1073741783, 3), + Rational(2, 1) - Rational(1073741789, 3)) + assert_equal(Rational(2147483578, 3), + Rational(2, 1) * Rational(1073741789, 3)) + assert_equal(Rational(6, 1073741789), + Rational(2, 1) / Rational(1073741789, 3)) + assert_equal(Rational(2147483657, 1073741827), + Rational(2, 1) + Rational(3, 1073741827)) + assert_equal(Rational(2147483651, 1073741827), + Rational(2, 1) - Rational(3, 1073741827)) + assert_equal(Rational(6, 1073741827), + Rational(2, 1) * Rational(3, 1073741827)) + assert_equal(Rational(2147483654, 3), + Rational(2, 1) / Rational(3, 1073741827)) + assert_equal(Rational(1073741833, 3), + Rational(2, 1) + Rational(1073741827, 3)) + assert_equal(Rational(-1073741821, 3), + Rational(2, 1) - Rational(1073741827, 3)) + assert_equal(Rational(2147483654, 3), + Rational(2, 1) * Rational(1073741827, 3)) + assert_equal(Rational(6, 1073741827), + Rational(2, 1) / Rational(1073741827, 3)) + assert_equal(Rational(3221225443, 1073741827), + Rational(2, 1) + Rational(1073741789, 1073741827)) + assert_equal(Rational(1073741865, 1073741827), + Rational(2, 1) - Rational(1073741789, 1073741827)) + assert_equal(Rational(2147483578, 1073741827), + Rational(2, 1) * Rational(1073741789, 1073741827)) + assert_equal(Rational(2147483654, 1073741789), + Rational(2, 1) / Rational(1073741789, 1073741827)) + assert_equal(Rational(3221225405, 1073741789), + Rational(2, 1) + Rational(1073741827, 1073741789)) + assert_equal(Rational(1073741751, 1073741789), + Rational(2, 1) - Rational(1073741827, 1073741789)) + assert_equal(Rational(2147483654, 1073741789), + Rational(2, 1) * Rational(1073741827, 1073741789)) + assert_equal(Rational(2147483578, 1073741827), + Rational(2, 1) / Rational(1073741827, 1073741789)) + assert_equal(Rational(4, 1), + Rational(3, 1) + Rational(1, 1)) + assert_equal(Rational(2, 1), + Rational(3, 1) - Rational(1, 1)) + assert_equal(Rational(3, 1), + Rational(3, 1) * Rational(1, 1)) + assert_equal(Rational(3, 1), + Rational(3, 1) / Rational(1, 1)) + assert_equal(Rational(5, 1), + Rational(3, 1) + Rational(2, 1)) + assert_equal(Rational(1, 1), + Rational(3, 1) - Rational(2, 1)) + assert_equal(Rational(6, 1), + Rational(3, 1) * Rational(2, 1)) + assert_equal(Rational(3, 2), + Rational(3, 1) / Rational(2, 1)) + assert_equal(Rational(6, 1), + Rational(3, 1) + Rational(3, 1)) + assert_equal(Rational(0, 1), + Rational(3, 1) - Rational(3, 1)) + assert_equal(Rational(9, 1), + Rational(3, 1) * Rational(3, 1)) + assert_equal(Rational(1, 1), + Rational(3, 1) / Rational(3, 1)) + assert_equal(Rational(1073741792, 1), + Rational(3, 1) + Rational(1073741789, 1)) + assert_equal(Rational(-1073741786, 1), + Rational(3, 1) - Rational(1073741789, 1)) + assert_equal(Rational(3221225367, 1), + Rational(3, 1) * Rational(1073741789, 1)) + assert_equal(Rational(3, 1073741789), + Rational(3, 1) / Rational(1073741789, 1)) + assert_equal(Rational(1073741830, 1), + Rational(3, 1) + Rational(1073741827, 1)) + assert_equal(Rational(-1073741824, 1), + Rational(3, 1) - Rational(1073741827, 1)) + assert_equal(Rational(3221225481, 1), + Rational(3, 1) * Rational(1073741827, 1)) + assert_equal(Rational(3, 1073741827), + Rational(3, 1) / Rational(1073741827, 1)) + assert_equal(Rational(11, 3), + Rational(3, 1) + Rational(2, 3)) + assert_equal(Rational(7, 3), + Rational(3, 1) - Rational(2, 3)) + assert_equal(Rational(2, 1), + Rational(3, 1) * Rational(2, 3)) + assert_equal(Rational(9, 2), + Rational(3, 1) / Rational(2, 3)) + assert_equal(Rational(9, 2), + Rational(3, 1) + Rational(3, 2)) + assert_equal(Rational(3, 2), + Rational(3, 1) - Rational(3, 2)) + assert_equal(Rational(9, 2), + Rational(3, 1) * Rational(3, 2)) + assert_equal(Rational(2, 1), + Rational(3, 1) / Rational(3, 2)) + assert_equal(Rational(3221225370, 1073741789), + Rational(3, 1) + Rational(3, 1073741789)) + assert_equal(Rational(3221225364, 1073741789), + Rational(3, 1) - Rational(3, 1073741789)) + assert_equal(Rational(9, 1073741789), + Rational(3, 1) * Rational(3, 1073741789)) + assert_equal(Rational(1073741789, 1), + Rational(3, 1) / Rational(3, 1073741789)) + assert_equal(Rational(1073741798, 3), + Rational(3, 1) + Rational(1073741789, 3)) + assert_equal(Rational(-1073741780, 3), + Rational(3, 1) - Rational(1073741789, 3)) + assert_equal(Rational(1073741789, 1), + Rational(3, 1) * Rational(1073741789, 3)) + assert_equal(Rational(9, 1073741789), + Rational(3, 1) / Rational(1073741789, 3)) + assert_equal(Rational(3221225484, 1073741827), + Rational(3, 1) + Rational(3, 1073741827)) + assert_equal(Rational(3221225478, 1073741827), + Rational(3, 1) - Rational(3, 1073741827)) + assert_equal(Rational(9, 1073741827), + Rational(3, 1) * Rational(3, 1073741827)) + assert_equal(Rational(1073741827, 1), + Rational(3, 1) / Rational(3, 1073741827)) + assert_equal(Rational(1073741836, 3), + Rational(3, 1) + Rational(1073741827, 3)) + assert_equal(Rational(-1073741818, 3), + Rational(3, 1) - Rational(1073741827, 3)) + assert_equal(Rational(1073741827, 1), + Rational(3, 1) * Rational(1073741827, 3)) + assert_equal(Rational(9, 1073741827), + Rational(3, 1) / Rational(1073741827, 3)) + assert_equal(Rational(4294967270, 1073741827), + Rational(3, 1) + Rational(1073741789, 1073741827)) + assert_equal(Rational(2147483692, 1073741827), + Rational(3, 1) - Rational(1073741789, 1073741827)) + assert_equal(Rational(3221225367, 1073741827), + Rational(3, 1) * Rational(1073741789, 1073741827)) + assert_equal(Rational(3221225481, 1073741789), + Rational(3, 1) / Rational(1073741789, 1073741827)) + assert_equal(Rational(4294967194, 1073741789), + Rational(3, 1) + Rational(1073741827, 1073741789)) + assert_equal(Rational(2147483540, 1073741789), + Rational(3, 1) - Rational(1073741827, 1073741789)) + assert_equal(Rational(3221225481, 1073741789), + Rational(3, 1) * Rational(1073741827, 1073741789)) + assert_equal(Rational(3221225367, 1073741827), + Rational(3, 1) / Rational(1073741827, 1073741789)) + assert_equal(Rational(1073741790, 1), + Rational(1073741789, 1) + Rational(1, 1)) + assert_equal(Rational(1073741788, 1), + Rational(1073741789, 1) - Rational(1, 1)) + assert_equal(Rational(1073741789, 1), + Rational(1073741789, 1) * Rational(1, 1)) + assert_equal(Rational(1073741789, 1), + Rational(1073741789, 1) / Rational(1, 1)) + assert_equal(Rational(1073741791, 1), + Rational(1073741789, 1) + Rational(2, 1)) + assert_equal(Rational(1073741787, 1), + Rational(1073741789, 1) - Rational(2, 1)) + assert_equal(Rational(2147483578, 1), + Rational(1073741789, 1) * Rational(2, 1)) + assert_equal(Rational(1073741789, 2), + Rational(1073741789, 1) / Rational(2, 1)) + assert_equal(Rational(1073741792, 1), + Rational(1073741789, 1) + Rational(3, 1)) + assert_equal(Rational(1073741786, 1), + Rational(1073741789, 1) - Rational(3, 1)) + assert_equal(Rational(3221225367, 1), + Rational(1073741789, 1) * Rational(3, 1)) + assert_equal(Rational(1073741789, 3), + Rational(1073741789, 1) / Rational(3, 1)) + assert_equal(Rational(2147483578, 1), + Rational(1073741789, 1) + Rational(1073741789, 1)) + assert_equal(Rational(0, 1), + Rational(1073741789, 1) - Rational(1073741789, 1)) + assert_equal(Rational(1152921429444920521, 1), + Rational(1073741789, 1) * Rational(1073741789, 1)) + assert_equal(Rational(1, 1), + Rational(1073741789, 1) / Rational(1073741789, 1)) + assert_equal(Rational(2147483616, 1), + Rational(1073741789, 1) + Rational(1073741827, 1)) + assert_equal(Rational(-38, 1), + Rational(1073741789, 1) - Rational(1073741827, 1)) + assert_equal(Rational(1152921470247108503, 1), + Rational(1073741789, 1) * Rational(1073741827, 1)) + assert_equal(Rational(1073741789, 1073741827), + Rational(1073741789, 1) / Rational(1073741827, 1)) + assert_equal(Rational(3221225369, 3), + Rational(1073741789, 1) + Rational(2, 3)) + assert_equal(Rational(3221225365, 3), + Rational(1073741789, 1) - Rational(2, 3)) + assert_equal(Rational(2147483578, 3), + Rational(1073741789, 1) * Rational(2, 3)) + assert_equal(Rational(3221225367, 2), + Rational(1073741789, 1) / Rational(2, 3)) + assert_equal(Rational(2147483581, 2), + Rational(1073741789, 1) + Rational(3, 2)) + assert_equal(Rational(2147483575, 2), + Rational(1073741789, 1) - Rational(3, 2)) + assert_equal(Rational(3221225367, 2), + Rational(1073741789, 1) * Rational(3, 2)) + assert_equal(Rational(2147483578, 3), + Rational(1073741789, 1) / Rational(3, 2)) + assert_equal(Rational(1152921429444920524, 1073741789), + Rational(1073741789, 1) + Rational(3, 1073741789)) + assert_equal(Rational(1152921429444920518, 1073741789), + Rational(1073741789, 1) - Rational(3, 1073741789)) + assert_equal(Rational(3, 1), + Rational(1073741789, 1) * Rational(3, 1073741789)) + assert_equal(Rational(1152921429444920521, 3), + Rational(1073741789, 1) / Rational(3, 1073741789)) + assert_equal(Rational(4294967156, 3), + Rational(1073741789, 1) + Rational(1073741789, 3)) + assert_equal(Rational(2147483578, 3), + Rational(1073741789, 1) - Rational(1073741789, 3)) + assert_equal(Rational(1152921429444920521, 3), + Rational(1073741789, 1) * Rational(1073741789, 3)) + assert_equal(Rational(3, 1), + Rational(1073741789, 1) / Rational(1073741789, 3)) + assert_equal(Rational(1152921470247108506, 1073741827), + Rational(1073741789, 1) + Rational(3, 1073741827)) + assert_equal(Rational(1152921470247108500, 1073741827), + Rational(1073741789, 1) - Rational(3, 1073741827)) + assert_equal(Rational(3221225367, 1073741827), + Rational(1073741789, 1) * Rational(3, 1073741827)) + assert_equal(Rational(1152921470247108503, 3), + Rational(1073741789, 1) / Rational(3, 1073741827)) + assert_equal(Rational(4294967194, 3), + Rational(1073741789, 1) + Rational(1073741827, 3)) + assert_equal(Rational(2147483540, 3), + Rational(1073741789, 1) - Rational(1073741827, 3)) + assert_equal(Rational(1152921470247108503, 3), + Rational(1073741789, 1) * Rational(1073741827, 3)) + assert_equal(Rational(3221225367, 1073741827), + Rational(1073741789, 1) / Rational(1073741827, 3)) + assert_equal(Rational(1152921471320850292, 1073741827), + Rational(1073741789, 1) + Rational(1073741789, 1073741827)) + assert_equal(Rational(1152921469173366714, 1073741827), + Rational(1073741789, 1) - Rational(1073741789, 1073741827)) + assert_equal(Rational(1152921429444920521, 1073741827), + Rational(1073741789, 1) * Rational(1073741789, 1073741827)) + assert_equal(Rational(1073741827, 1), + Rational(1073741789, 1) / Rational(1073741789, 1073741827)) + assert_equal(Rational(1152921430518662348, 1073741789), + Rational(1073741789, 1) + Rational(1073741827, 1073741789)) + assert_equal(Rational(1152921428371178694, 1073741789), + Rational(1073741789, 1) - Rational(1073741827, 1073741789)) + assert_equal(Rational(1073741827, 1), + Rational(1073741789, 1) * Rational(1073741827, 1073741789)) + assert_equal(Rational(1152921429444920521, 1073741827), + Rational(1073741789, 1) / Rational(1073741827, 1073741789)) + assert_equal(Rational(1073741828, 1), + Rational(1073741827, 1) + Rational(1, 1)) + assert_equal(Rational(1073741826, 1), + Rational(1073741827, 1) - Rational(1, 1)) + assert_equal(Rational(1073741827, 1), + Rational(1073741827, 1) * Rational(1, 1)) + assert_equal(Rational(1073741827, 1), + Rational(1073741827, 1) / Rational(1, 1)) + assert_equal(Rational(1073741829, 1), + Rational(1073741827, 1) + Rational(2, 1)) + assert_equal(Rational(1073741825, 1), + Rational(1073741827, 1) - Rational(2, 1)) + assert_equal(Rational(2147483654, 1), + Rational(1073741827, 1) * Rational(2, 1)) + assert_equal(Rational(1073741827, 2), + Rational(1073741827, 1) / Rational(2, 1)) + assert_equal(Rational(1073741830, 1), + Rational(1073741827, 1) + Rational(3, 1)) + assert_equal(Rational(1073741824, 1), + Rational(1073741827, 1) - Rational(3, 1)) + assert_equal(Rational(3221225481, 1), + Rational(1073741827, 1) * Rational(3, 1)) + assert_equal(Rational(1073741827, 3), + Rational(1073741827, 1) / Rational(3, 1)) + assert_equal(Rational(2147483616, 1), + Rational(1073741827, 1) + Rational(1073741789, 1)) + assert_equal(Rational(38, 1), + Rational(1073741827, 1) - Rational(1073741789, 1)) + assert_equal(Rational(1152921470247108503, 1), + Rational(1073741827, 1) * Rational(1073741789, 1)) + assert_equal(Rational(1073741827, 1073741789), + Rational(1073741827, 1) / Rational(1073741789, 1)) + assert_equal(Rational(2147483654, 1), + Rational(1073741827, 1) + Rational(1073741827, 1)) + assert_equal(Rational(0, 1), + Rational(1073741827, 1) - Rational(1073741827, 1)) + assert_equal(Rational(1152921511049297929, 1), + Rational(1073741827, 1) * Rational(1073741827, 1)) + assert_equal(Rational(1, 1), + Rational(1073741827, 1) / Rational(1073741827, 1)) + assert_equal(Rational(3221225483, 3), + Rational(1073741827, 1) + Rational(2, 3)) + assert_equal(Rational(3221225479, 3), + Rational(1073741827, 1) - Rational(2, 3)) + assert_equal(Rational(2147483654, 3), + Rational(1073741827, 1) * Rational(2, 3)) + assert_equal(Rational(3221225481, 2), + Rational(1073741827, 1) / Rational(2, 3)) + assert_equal(Rational(2147483657, 2), + Rational(1073741827, 1) + Rational(3, 2)) + assert_equal(Rational(2147483651, 2), + Rational(1073741827, 1) - Rational(3, 2)) + assert_equal(Rational(3221225481, 2), + Rational(1073741827, 1) * Rational(3, 2)) + assert_equal(Rational(2147483654, 3), + Rational(1073741827, 1) / Rational(3, 2)) + assert_equal(Rational(1152921470247108506, 1073741789), + Rational(1073741827, 1) + Rational(3, 1073741789)) + assert_equal(Rational(1152921470247108500, 1073741789), + Rational(1073741827, 1) - Rational(3, 1073741789)) + assert_equal(Rational(3221225481, 1073741789), + Rational(1073741827, 1) * Rational(3, 1073741789)) + assert_equal(Rational(1152921470247108503, 3), + Rational(1073741827, 1) / Rational(3, 1073741789)) + assert_equal(Rational(4294967270, 3), + Rational(1073741827, 1) + Rational(1073741789, 3)) + assert_equal(Rational(2147483692, 3), + Rational(1073741827, 1) - Rational(1073741789, 3)) + assert_equal(Rational(1152921470247108503, 3), + Rational(1073741827, 1) * Rational(1073741789, 3)) + assert_equal(Rational(3221225481, 1073741789), + Rational(1073741827, 1) / Rational(1073741789, 3)) + assert_equal(Rational(1152921511049297932, 1073741827), + Rational(1073741827, 1) + Rational(3, 1073741827)) + assert_equal(Rational(1152921511049297926, 1073741827), + Rational(1073741827, 1) - Rational(3, 1073741827)) + assert_equal(Rational(3, 1), + Rational(1073741827, 1) * Rational(3, 1073741827)) + assert_equal(Rational(1152921511049297929, 3), + Rational(1073741827, 1) / Rational(3, 1073741827)) + assert_equal(Rational(4294967308, 3), + Rational(1073741827, 1) + Rational(1073741827, 3)) + assert_equal(Rational(2147483654, 3), + Rational(1073741827, 1) - Rational(1073741827, 3)) + assert_equal(Rational(1152921511049297929, 3), + Rational(1073741827, 1) * Rational(1073741827, 3)) + assert_equal(Rational(3, 1), + Rational(1073741827, 1) / Rational(1073741827, 3)) + assert_equal(Rational(1152921512123039718, 1073741827), + Rational(1073741827, 1) + Rational(1073741789, 1073741827)) + assert_equal(Rational(1152921509975556140, 1073741827), + Rational(1073741827, 1) - Rational(1073741789, 1073741827)) + assert_equal(Rational(1073741789, 1), + Rational(1073741827, 1) * Rational(1073741789, 1073741827)) + assert_equal(Rational(1152921511049297929, 1073741789), + Rational(1073741827, 1) / Rational(1073741789, 1073741827)) + assert_equal(Rational(1152921471320850330, 1073741789), + Rational(1073741827, 1) + Rational(1073741827, 1073741789)) + assert_equal(Rational(1152921469173366676, 1073741789), + Rational(1073741827, 1) - Rational(1073741827, 1073741789)) + assert_equal(Rational(1152921511049297929, 1073741789), + Rational(1073741827, 1) * Rational(1073741827, 1073741789)) + assert_equal(Rational(1073741789, 1), + Rational(1073741827, 1) / Rational(1073741827, 1073741789)) + assert_equal(Rational(5, 3), + Rational(2, 3) + Rational(1, 1)) + assert_equal(Rational(-1, 3), + Rational(2, 3) - Rational(1, 1)) + assert_equal(Rational(2, 3), + Rational(2, 3) * Rational(1, 1)) + assert_equal(Rational(2, 3), + Rational(2, 3) / Rational(1, 1)) + assert_equal(Rational(8, 3), + Rational(2, 3) + Rational(2, 1)) + assert_equal(Rational(-4, 3), + Rational(2, 3) - Rational(2, 1)) + assert_equal(Rational(4, 3), + Rational(2, 3) * Rational(2, 1)) + assert_equal(Rational(1, 3), + Rational(2, 3) / Rational(2, 1)) + assert_equal(Rational(11, 3), + Rational(2, 3) + Rational(3, 1)) + assert_equal(Rational(-7, 3), + Rational(2, 3) - Rational(3, 1)) + assert_equal(Rational(2, 1), + Rational(2, 3) * Rational(3, 1)) + assert_equal(Rational(2, 9), + Rational(2, 3) / Rational(3, 1)) + assert_equal(Rational(3221225369, 3), + Rational(2, 3) + Rational(1073741789, 1)) + assert_equal(Rational(-3221225365, 3), + Rational(2, 3) - Rational(1073741789, 1)) + assert_equal(Rational(2147483578, 3), + Rational(2, 3) * Rational(1073741789, 1)) + assert_equal(Rational(2, 3221225367), + Rational(2, 3) / Rational(1073741789, 1)) + assert_equal(Rational(3221225483, 3), + Rational(2, 3) + Rational(1073741827, 1)) + assert_equal(Rational(-3221225479, 3), + Rational(2, 3) - Rational(1073741827, 1)) + assert_equal(Rational(2147483654, 3), + Rational(2, 3) * Rational(1073741827, 1)) + assert_equal(Rational(2, 3221225481), + Rational(2, 3) / Rational(1073741827, 1)) + assert_equal(Rational(4, 3), + Rational(2, 3) + Rational(2, 3)) + assert_equal(Rational(0, 1), + Rational(2, 3) - Rational(2, 3)) + assert_equal(Rational(4, 9), + Rational(2, 3) * Rational(2, 3)) + assert_equal(Rational(1, 1), + Rational(2, 3) / Rational(2, 3)) + assert_equal(Rational(13, 6), + Rational(2, 3) + Rational(3, 2)) + assert_equal(Rational(-5, 6), + Rational(2, 3) - Rational(3, 2)) + assert_equal(Rational(1, 1), + Rational(2, 3) * Rational(3, 2)) + assert_equal(Rational(4, 9), + Rational(2, 3) / Rational(3, 2)) + assert_equal(Rational(2147483587, 3221225367), + Rational(2, 3) + Rational(3, 1073741789)) + assert_equal(Rational(2147483569, 3221225367), + Rational(2, 3) - Rational(3, 1073741789)) + assert_equal(Rational(2, 1073741789), + Rational(2, 3) * Rational(3, 1073741789)) + assert_equal(Rational(2147483578, 9), + Rational(2, 3) / Rational(3, 1073741789)) + assert_equal(Rational(1073741791, 3), + Rational(2, 3) + Rational(1073741789, 3)) + assert_equal(Rational(-357913929, 1), + Rational(2, 3) - Rational(1073741789, 3)) + assert_equal(Rational(2147483578, 9), + Rational(2, 3) * Rational(1073741789, 3)) + assert_equal(Rational(2, 1073741789), + Rational(2, 3) / Rational(1073741789, 3)) + assert_equal(Rational(2147483663, 3221225481), + Rational(2, 3) + Rational(3, 1073741827)) + assert_equal(Rational(2147483645, 3221225481), + Rational(2, 3) - Rational(3, 1073741827)) + assert_equal(Rational(2, 1073741827), + Rational(2, 3) * Rational(3, 1073741827)) + assert_equal(Rational(2147483654, 9), + Rational(2, 3) / Rational(3, 1073741827)) + assert_equal(Rational(357913943, 1), + Rational(2, 3) + Rational(1073741827, 3)) + assert_equal(Rational(-1073741825, 3), + Rational(2, 3) - Rational(1073741827, 3)) + assert_equal(Rational(2147483654, 9), + Rational(2, 3) * Rational(1073741827, 3)) + assert_equal(Rational(2, 1073741827), + Rational(2, 3) / Rational(1073741827, 3)) + assert_equal(Rational(5368709021, 3221225481), + Rational(2, 3) + Rational(1073741789, 1073741827)) + assert_equal(Rational(-1073741713, 3221225481), + Rational(2, 3) - Rational(1073741789, 1073741827)) + assert_equal(Rational(2147483578, 3221225481), + Rational(2, 3) * Rational(1073741789, 1073741827)) + assert_equal(Rational(2147483654, 3221225367), + Rational(2, 3) / Rational(1073741789, 1073741827)) + assert_equal(Rational(5368709059, 3221225367), + Rational(2, 3) + Rational(1073741827, 1073741789)) + assert_equal(Rational(-1073741903, 3221225367), + Rational(2, 3) - Rational(1073741827, 1073741789)) + assert_equal(Rational(2147483654, 3221225367), + Rational(2, 3) * Rational(1073741827, 1073741789)) + assert_equal(Rational(2147483578, 3221225481), + Rational(2, 3) / Rational(1073741827, 1073741789)) + assert_equal(Rational(5, 2), + Rational(3, 2) + Rational(1, 1)) + assert_equal(Rational(1, 2), + Rational(3, 2) - Rational(1, 1)) + assert_equal(Rational(3, 2), + Rational(3, 2) * Rational(1, 1)) + assert_equal(Rational(3, 2), + Rational(3, 2) / Rational(1, 1)) + assert_equal(Rational(7, 2), + Rational(3, 2) + Rational(2, 1)) + assert_equal(Rational(-1, 2), + Rational(3, 2) - Rational(2, 1)) + assert_equal(Rational(3, 1), + Rational(3, 2) * Rational(2, 1)) + assert_equal(Rational(3, 4), + Rational(3, 2) / Rational(2, 1)) + assert_equal(Rational(9, 2), + Rational(3, 2) + Rational(3, 1)) + assert_equal(Rational(-3, 2), + Rational(3, 2) - Rational(3, 1)) + assert_equal(Rational(9, 2), + Rational(3, 2) * Rational(3, 1)) + assert_equal(Rational(1, 2), + Rational(3, 2) / Rational(3, 1)) + assert_equal(Rational(2147483581, 2), + Rational(3, 2) + Rational(1073741789, 1)) + assert_equal(Rational(-2147483575, 2), + Rational(3, 2) - Rational(1073741789, 1)) + assert_equal(Rational(3221225367, 2), + Rational(3, 2) * Rational(1073741789, 1)) + assert_equal(Rational(3, 2147483578), + Rational(3, 2) / Rational(1073741789, 1)) + assert_equal(Rational(2147483657, 2), + Rational(3, 2) + Rational(1073741827, 1)) + assert_equal(Rational(-2147483651, 2), + Rational(3, 2) - Rational(1073741827, 1)) + assert_equal(Rational(3221225481, 2), + Rational(3, 2) * Rational(1073741827, 1)) + assert_equal(Rational(3, 2147483654), + Rational(3, 2) / Rational(1073741827, 1)) + assert_equal(Rational(13, 6), + Rational(3, 2) + Rational(2, 3)) + assert_equal(Rational(5, 6), + Rational(3, 2) - Rational(2, 3)) + assert_equal(Rational(1, 1), + Rational(3, 2) * Rational(2, 3)) + assert_equal(Rational(9, 4), + Rational(3, 2) / Rational(2, 3)) + assert_equal(Rational(3, 1), + Rational(3, 2) + Rational(3, 2)) + assert_equal(Rational(0, 1), + Rational(3, 2) - Rational(3, 2)) + assert_equal(Rational(9, 4), + Rational(3, 2) * Rational(3, 2)) + assert_equal(Rational(1, 1), + Rational(3, 2) / Rational(3, 2)) + assert_equal(Rational(3221225373, 2147483578), + Rational(3, 2) + Rational(3, 1073741789)) + assert_equal(Rational(3221225361, 2147483578), + Rational(3, 2) - Rational(3, 1073741789)) + assert_equal(Rational(9, 2147483578), + Rational(3, 2) * Rational(3, 1073741789)) + assert_equal(Rational(1073741789, 2), + Rational(3, 2) / Rational(3, 1073741789)) + assert_equal(Rational(2147483587, 6), + Rational(3, 2) + Rational(1073741789, 3)) + assert_equal(Rational(-2147483569, 6), + Rational(3, 2) - Rational(1073741789, 3)) + assert_equal(Rational(1073741789, 2), + Rational(3, 2) * Rational(1073741789, 3)) + assert_equal(Rational(9, 2147483578), + Rational(3, 2) / Rational(1073741789, 3)) + assert_equal(Rational(3221225487, 2147483654), + Rational(3, 2) + Rational(3, 1073741827)) + assert_equal(Rational(3221225475, 2147483654), + Rational(3, 2) - Rational(3, 1073741827)) + assert_equal(Rational(9, 2147483654), + Rational(3, 2) * Rational(3, 1073741827)) + assert_equal(Rational(1073741827, 2), + Rational(3, 2) / Rational(3, 1073741827)) + assert_equal(Rational(2147483663, 6), + Rational(3, 2) + Rational(1073741827, 3)) + assert_equal(Rational(-2147483645, 6), + Rational(3, 2) - Rational(1073741827, 3)) + assert_equal(Rational(1073741827, 2), + Rational(3, 2) * Rational(1073741827, 3)) + assert_equal(Rational(9, 2147483654), + Rational(3, 2) / Rational(1073741827, 3)) + assert_equal(Rational(5368709059, 2147483654), + Rational(3, 2) + Rational(1073741789, 1073741827)) + assert_equal(Rational(1073741903, 2147483654), + Rational(3, 2) - Rational(1073741789, 1073741827)) + assert_equal(Rational(3221225367, 2147483654), + Rational(3, 2) * Rational(1073741789, 1073741827)) + assert_equal(Rational(3221225481, 2147483578), + Rational(3, 2) / Rational(1073741789, 1073741827)) + assert_equal(Rational(5368709021, 2147483578), + Rational(3, 2) + Rational(1073741827, 1073741789)) + assert_equal(Rational(1073741713, 2147483578), + Rational(3, 2) - Rational(1073741827, 1073741789)) + assert_equal(Rational(3221225481, 2147483578), + Rational(3, 2) * Rational(1073741827, 1073741789)) + assert_equal(Rational(3221225367, 2147483654), + Rational(3, 2) / Rational(1073741827, 1073741789)) + assert_equal(Rational(1073741792, 1073741789), + Rational(3, 1073741789) + Rational(1, 1)) + assert_equal(Rational(-1073741786, 1073741789), + Rational(3, 1073741789) - Rational(1, 1)) + assert_equal(Rational(3, 1073741789), + Rational(3, 1073741789) * Rational(1, 1)) + assert_equal(Rational(3, 1073741789), + Rational(3, 1073741789) / Rational(1, 1)) + assert_equal(Rational(2147483581, 1073741789), + Rational(3, 1073741789) + Rational(2, 1)) + assert_equal(Rational(-2147483575, 1073741789), + Rational(3, 1073741789) - Rational(2, 1)) + assert_equal(Rational(6, 1073741789), + Rational(3, 1073741789) * Rational(2, 1)) + assert_equal(Rational(3, 2147483578), + Rational(3, 1073741789) / Rational(2, 1)) + assert_equal(Rational(3221225370, 1073741789), + Rational(3, 1073741789) + Rational(3, 1)) + assert_equal(Rational(-3221225364, 1073741789), + Rational(3, 1073741789) - Rational(3, 1)) + assert_equal(Rational(9, 1073741789), + Rational(3, 1073741789) * Rational(3, 1)) + assert_equal(Rational(1, 1073741789), + Rational(3, 1073741789) / Rational(3, 1)) + assert_equal(Rational(1152921429444920524, 1073741789), + Rational(3, 1073741789) + Rational(1073741789, 1)) + assert_equal(Rational(-1152921429444920518, 1073741789), + Rational(3, 1073741789) - Rational(1073741789, 1)) + assert_equal(Rational(3, 1), + Rational(3, 1073741789) * Rational(1073741789, 1)) + assert_equal(Rational(3, 1152921429444920521), + Rational(3, 1073741789) / Rational(1073741789, 1)) + assert_equal(Rational(1152921470247108506, 1073741789), + Rational(3, 1073741789) + Rational(1073741827, 1)) + assert_equal(Rational(-1152921470247108500, 1073741789), + Rational(3, 1073741789) - Rational(1073741827, 1)) + assert_equal(Rational(3221225481, 1073741789), + Rational(3, 1073741789) * Rational(1073741827, 1)) + assert_equal(Rational(3, 1152921470247108503), + Rational(3, 1073741789) / Rational(1073741827, 1)) + assert_equal(Rational(2147483587, 3221225367), + Rational(3, 1073741789) + Rational(2, 3)) + assert_equal(Rational(-2147483569, 3221225367), + Rational(3, 1073741789) - Rational(2, 3)) + assert_equal(Rational(2, 1073741789), + Rational(3, 1073741789) * Rational(2, 3)) + assert_equal(Rational(9, 2147483578), + Rational(3, 1073741789) / Rational(2, 3)) + assert_equal(Rational(3221225373, 2147483578), + Rational(3, 1073741789) + Rational(3, 2)) + assert_equal(Rational(-3221225361, 2147483578), + Rational(3, 1073741789) - Rational(3, 2)) + assert_equal(Rational(9, 2147483578), + Rational(3, 1073741789) * Rational(3, 2)) + assert_equal(Rational(2, 1073741789), + Rational(3, 1073741789) / Rational(3, 2)) + assert_equal(Rational(6, 1073741789), + Rational(3, 1073741789) + Rational(3, 1073741789)) + assert_equal(Rational(0, 1), + Rational(3, 1073741789) - Rational(3, 1073741789)) + assert_equal(Rational(9, 1152921429444920521), + Rational(3, 1073741789) * Rational(3, 1073741789)) + assert_equal(Rational(1, 1), + Rational(3, 1073741789) / Rational(3, 1073741789)) + assert_equal(Rational(1152921429444920530, 3221225367), + Rational(3, 1073741789) + Rational(1073741789, 3)) + assert_equal(Rational(-1152921429444920512, 3221225367), + Rational(3, 1073741789) - Rational(1073741789, 3)) + assert_equal(Rational(1, 1), + Rational(3, 1073741789) * Rational(1073741789, 3)) + assert_equal(Rational(9, 1152921429444920521), + Rational(3, 1073741789) / Rational(1073741789, 3)) + assert_equal(Rational(6442450848, 1152921470247108503), + Rational(3, 1073741789) + Rational(3, 1073741827)) + assert_equal(Rational(114, 1152921470247108503), + Rational(3, 1073741789) - Rational(3, 1073741827)) + assert_equal(Rational(9, 1152921470247108503), + Rational(3, 1073741789) * Rational(3, 1073741827)) + assert_equal(Rational(1073741827, 1073741789), + Rational(3, 1073741789) / Rational(3, 1073741827)) + assert_equal(Rational(1152921470247108512, 3221225367), + Rational(3, 1073741789) + Rational(1073741827, 3)) + assert_equal(Rational(-1152921470247108494, 3221225367), + Rational(3, 1073741789) - Rational(1073741827, 3)) + assert_equal(Rational(1073741827, 1073741789), + Rational(3, 1073741789) * Rational(1073741827, 3)) + assert_equal(Rational(9, 1152921470247108503), + Rational(3, 1073741789) / Rational(1073741827, 3)) + assert_equal(Rational(1152921432666146002, 1152921470247108503), + Rational(3, 1073741789) + Rational(1073741789, 1073741827)) + assert_equal(Rational(-1152921426223695040, 1152921470247108503), + Rational(3, 1073741789) - Rational(1073741789, 1073741827)) + assert_equal(Rational(3, 1073741827), + Rational(3, 1073741789) * Rational(1073741789, 1073741827)) + assert_equal(Rational(3221225481, 1152921429444920521), + Rational(3, 1073741789) / Rational(1073741789, 1073741827)) + assert_equal(Rational(1073741830, 1073741789), + Rational(3, 1073741789) + Rational(1073741827, 1073741789)) + assert_equal(Rational(-1073741824, 1073741789), + Rational(3, 1073741789) - Rational(1073741827, 1073741789)) + assert_equal(Rational(3221225481, 1152921429444920521), + Rational(3, 1073741789) * Rational(1073741827, 1073741789)) + assert_equal(Rational(3, 1073741827), + Rational(3, 1073741789) / Rational(1073741827, 1073741789)) + assert_equal(Rational(1073741792, 3), + Rational(1073741789, 3) + Rational(1, 1)) + assert_equal(Rational(1073741786, 3), + Rational(1073741789, 3) - Rational(1, 1)) + assert_equal(Rational(1073741789, 3), + Rational(1073741789, 3) * Rational(1, 1)) + assert_equal(Rational(1073741789, 3), + Rational(1073741789, 3) / Rational(1, 1)) + assert_equal(Rational(1073741795, 3), + Rational(1073741789, 3) + Rational(2, 1)) + assert_equal(Rational(1073741783, 3), + Rational(1073741789, 3) - Rational(2, 1)) + assert_equal(Rational(2147483578, 3), + Rational(1073741789, 3) * Rational(2, 1)) + assert_equal(Rational(1073741789, 6), + Rational(1073741789, 3) / Rational(2, 1)) + assert_equal(Rational(1073741798, 3), + Rational(1073741789, 3) + Rational(3, 1)) + assert_equal(Rational(1073741780, 3), + Rational(1073741789, 3) - Rational(3, 1)) + assert_equal(Rational(1073741789, 1), + Rational(1073741789, 3) * Rational(3, 1)) + assert_equal(Rational(1073741789, 9), + Rational(1073741789, 3) / Rational(3, 1)) + assert_equal(Rational(4294967156, 3), + Rational(1073741789, 3) + Rational(1073741789, 1)) + assert_equal(Rational(-2147483578, 3), + Rational(1073741789, 3) - Rational(1073741789, 1)) + assert_equal(Rational(1152921429444920521, 3), + Rational(1073741789, 3) * Rational(1073741789, 1)) + assert_equal(Rational(1, 3), + Rational(1073741789, 3) / Rational(1073741789, 1)) + assert_equal(Rational(4294967270, 3), + Rational(1073741789, 3) + Rational(1073741827, 1)) + assert_equal(Rational(-2147483692, 3), + Rational(1073741789, 3) - Rational(1073741827, 1)) + assert_equal(Rational(1152921470247108503, 3), + Rational(1073741789, 3) * Rational(1073741827, 1)) + assert_equal(Rational(1073741789, 3221225481), + Rational(1073741789, 3) / Rational(1073741827, 1)) + assert_equal(Rational(1073741791, 3), + Rational(1073741789, 3) + Rational(2, 3)) + assert_equal(Rational(357913929, 1), + Rational(1073741789, 3) - Rational(2, 3)) + assert_equal(Rational(2147483578, 9), + Rational(1073741789, 3) * Rational(2, 3)) + assert_equal(Rational(1073741789, 2), + Rational(1073741789, 3) / Rational(2, 3)) + assert_equal(Rational(2147483587, 6), + Rational(1073741789, 3) + Rational(3, 2)) + assert_equal(Rational(2147483569, 6), + Rational(1073741789, 3) - Rational(3, 2)) + assert_equal(Rational(1073741789, 2), + Rational(1073741789, 3) * Rational(3, 2)) + assert_equal(Rational(2147483578, 9), + Rational(1073741789, 3) / Rational(3, 2)) + assert_equal(Rational(1152921429444920530, 3221225367), + Rational(1073741789, 3) + Rational(3, 1073741789)) + assert_equal(Rational(1152921429444920512, 3221225367), + Rational(1073741789, 3) - Rational(3, 1073741789)) + assert_equal(Rational(1, 1), + Rational(1073741789, 3) * Rational(3, 1073741789)) + assert_equal(Rational(1152921429444920521, 9), + Rational(1073741789, 3) / Rational(3, 1073741789)) + assert_equal(Rational(2147483578, 3), + Rational(1073741789, 3) + Rational(1073741789, 3)) + assert_equal(Rational(0, 1), + Rational(1073741789, 3) - Rational(1073741789, 3)) + assert_equal(Rational(1152921429444920521, 9), + Rational(1073741789, 3) * Rational(1073741789, 3)) + assert_equal(Rational(1, 1), + Rational(1073741789, 3) / Rational(1073741789, 3)) + assert_equal(Rational(1152921470247108512, 3221225481), + Rational(1073741789, 3) + Rational(3, 1073741827)) + assert_equal(Rational(1152921470247108494, 3221225481), + Rational(1073741789, 3) - Rational(3, 1073741827)) + assert_equal(Rational(1073741789, 1073741827), + Rational(1073741789, 3) * Rational(3, 1073741827)) + assert_equal(Rational(1152921470247108503, 9), + Rational(1073741789, 3) / Rational(3, 1073741827)) + assert_equal(Rational(715827872, 1), + Rational(1073741789, 3) + Rational(1073741827, 3)) + assert_equal(Rational(-38, 3), + Rational(1073741789, 3) - Rational(1073741827, 3)) + assert_equal(Rational(1152921470247108503, 9), + Rational(1073741789, 3) * Rational(1073741827, 3)) + assert_equal(Rational(1073741789, 1073741827), + Rational(1073741789, 3) / Rational(1073741827, 3)) + assert_equal(Rational(1152921473468333870, 3221225481), + Rational(1073741789, 3) + Rational(1073741789, 1073741827)) + assert_equal(Rational(1152921467025883136, 3221225481), + Rational(1073741789, 3) - Rational(1073741789, 1073741827)) + assert_equal(Rational(1152921429444920521, 3221225481), + Rational(1073741789, 3) * Rational(1073741789, 1073741827)) + assert_equal(Rational(1073741827, 3), + Rational(1073741789, 3) / Rational(1073741789, 1073741827)) + assert_equal(Rational(1152921432666146002, 3221225367), + Rational(1073741789, 3) + Rational(1073741827, 1073741789)) + assert_equal(Rational(1152921426223695040, 3221225367), + Rational(1073741789, 3) - Rational(1073741827, 1073741789)) + assert_equal(Rational(1073741827, 3), + Rational(1073741789, 3) * Rational(1073741827, 1073741789)) + assert_equal(Rational(1152921429444920521, 3221225481), + Rational(1073741789, 3) / Rational(1073741827, 1073741789)) + assert_equal(Rational(1073741830, 1073741827), + Rational(3, 1073741827) + Rational(1, 1)) + assert_equal(Rational(-1073741824, 1073741827), + Rational(3, 1073741827) - Rational(1, 1)) + assert_equal(Rational(3, 1073741827), + Rational(3, 1073741827) * Rational(1, 1)) + assert_equal(Rational(3, 1073741827), + Rational(3, 1073741827) / Rational(1, 1)) + assert_equal(Rational(2147483657, 1073741827), + Rational(3, 1073741827) + Rational(2, 1)) + assert_equal(Rational(-2147483651, 1073741827), + Rational(3, 1073741827) - Rational(2, 1)) + assert_equal(Rational(6, 1073741827), + Rational(3, 1073741827) * Rational(2, 1)) + assert_equal(Rational(3, 2147483654), + Rational(3, 1073741827) / Rational(2, 1)) + assert_equal(Rational(3221225484, 1073741827), + Rational(3, 1073741827) + Rational(3, 1)) + assert_equal(Rational(-3221225478, 1073741827), + Rational(3, 1073741827) - Rational(3, 1)) + assert_equal(Rational(9, 1073741827), + Rational(3, 1073741827) * Rational(3, 1)) + assert_equal(Rational(1, 1073741827), + Rational(3, 1073741827) / Rational(3, 1)) + assert_equal(Rational(1152921470247108506, 1073741827), + Rational(3, 1073741827) + Rational(1073741789, 1)) + assert_equal(Rational(-1152921470247108500, 1073741827), + Rational(3, 1073741827) - Rational(1073741789, 1)) + assert_equal(Rational(3221225367, 1073741827), + Rational(3, 1073741827) * Rational(1073741789, 1)) + assert_equal(Rational(3, 1152921470247108503), + Rational(3, 1073741827) / Rational(1073741789, 1)) + assert_equal(Rational(1152921511049297932, 1073741827), + Rational(3, 1073741827) + Rational(1073741827, 1)) + assert_equal(Rational(-1152921511049297926, 1073741827), + Rational(3, 1073741827) - Rational(1073741827, 1)) + assert_equal(Rational(3, 1), + Rational(3, 1073741827) * Rational(1073741827, 1)) + assert_equal(Rational(3, 1152921511049297929), + Rational(3, 1073741827) / Rational(1073741827, 1)) + assert_equal(Rational(2147483663, 3221225481), + Rational(3, 1073741827) + Rational(2, 3)) + assert_equal(Rational(-2147483645, 3221225481), + Rational(3, 1073741827) - Rational(2, 3)) + assert_equal(Rational(2, 1073741827), + Rational(3, 1073741827) * Rational(2, 3)) + assert_equal(Rational(9, 2147483654), + Rational(3, 1073741827) / Rational(2, 3)) + assert_equal(Rational(3221225487, 2147483654), + Rational(3, 1073741827) + Rational(3, 2)) + assert_equal(Rational(-3221225475, 2147483654), + Rational(3, 1073741827) - Rational(3, 2)) + assert_equal(Rational(9, 2147483654), + Rational(3, 1073741827) * Rational(3, 2)) + assert_equal(Rational(2, 1073741827), + Rational(3, 1073741827) / Rational(3, 2)) + assert_equal(Rational(6442450848, 1152921470247108503), + Rational(3, 1073741827) + Rational(3, 1073741789)) + assert_equal(Rational(-114, 1152921470247108503), + Rational(3, 1073741827) - Rational(3, 1073741789)) + assert_equal(Rational(9, 1152921470247108503), + Rational(3, 1073741827) * Rational(3, 1073741789)) + assert_equal(Rational(1073741789, 1073741827), + Rational(3, 1073741827) / Rational(3, 1073741789)) + assert_equal(Rational(1152921470247108512, 3221225481), + Rational(3, 1073741827) + Rational(1073741789, 3)) + assert_equal(Rational(-1152921470247108494, 3221225481), + Rational(3, 1073741827) - Rational(1073741789, 3)) + assert_equal(Rational(1073741789, 1073741827), + Rational(3, 1073741827) * Rational(1073741789, 3)) + assert_equal(Rational(9, 1152921470247108503), + Rational(3, 1073741827) / Rational(1073741789, 3)) + assert_equal(Rational(6, 1073741827), + Rational(3, 1073741827) + Rational(3, 1073741827)) + assert_equal(Rational(0, 1), + Rational(3, 1073741827) - Rational(3, 1073741827)) + assert_equal(Rational(9, 1152921511049297929), + Rational(3, 1073741827) * Rational(3, 1073741827)) + assert_equal(Rational(1, 1), + Rational(3, 1073741827) / Rational(3, 1073741827)) + assert_equal(Rational(1152921511049297938, 3221225481), + Rational(3, 1073741827) + Rational(1073741827, 3)) + assert_equal(Rational(-1152921511049297920, 3221225481), + Rational(3, 1073741827) - Rational(1073741827, 3)) + assert_equal(Rational(1, 1), + Rational(3, 1073741827) * Rational(1073741827, 3)) + assert_equal(Rational(9, 1152921511049297929), + Rational(3, 1073741827) / Rational(1073741827, 3)) + assert_equal(Rational(1073741792, 1073741827), + Rational(3, 1073741827) + Rational(1073741789, 1073741827)) + assert_equal(Rational(-1073741786, 1073741827), + Rational(3, 1073741827) - Rational(1073741789, 1073741827)) + assert_equal(Rational(3221225367, 1152921511049297929), + Rational(3, 1073741827) * Rational(1073741789, 1073741827)) + assert_equal(Rational(3, 1073741789), + Rational(3, 1073741827) / Rational(1073741789, 1073741827)) + assert_equal(Rational(1152921514270523296, 1152921470247108503), + Rational(3, 1073741827) + Rational(1073741827, 1073741789)) + assert_equal(Rational(-1152921507828072562, 1152921470247108503), + Rational(3, 1073741827) - Rational(1073741827, 1073741789)) + assert_equal(Rational(3, 1073741789), + Rational(3, 1073741827) * Rational(1073741827, 1073741789)) + assert_equal(Rational(3221225367, 1152921511049297929), + Rational(3, 1073741827) / Rational(1073741827, 1073741789)) + assert_equal(Rational(1073741830, 3), + Rational(1073741827, 3) + Rational(1, 1)) + assert_equal(Rational(1073741824, 3), + Rational(1073741827, 3) - Rational(1, 1)) + assert_equal(Rational(1073741827, 3), + Rational(1073741827, 3) * Rational(1, 1)) + assert_equal(Rational(1073741827, 3), + Rational(1073741827, 3) / Rational(1, 1)) + assert_equal(Rational(1073741833, 3), + Rational(1073741827, 3) + Rational(2, 1)) + assert_equal(Rational(1073741821, 3), + Rational(1073741827, 3) - Rational(2, 1)) + assert_equal(Rational(2147483654, 3), + Rational(1073741827, 3) * Rational(2, 1)) + assert_equal(Rational(1073741827, 6), + Rational(1073741827, 3) / Rational(2, 1)) + assert_equal(Rational(1073741836, 3), + Rational(1073741827, 3) + Rational(3, 1)) + assert_equal(Rational(1073741818, 3), + Rational(1073741827, 3) - Rational(3, 1)) + assert_equal(Rational(1073741827, 1), + Rational(1073741827, 3) * Rational(3, 1)) + assert_equal(Rational(1073741827, 9), + Rational(1073741827, 3) / Rational(3, 1)) + assert_equal(Rational(4294967194, 3), + Rational(1073741827, 3) + Rational(1073741789, 1)) + assert_equal(Rational(-2147483540, 3), + Rational(1073741827, 3) - Rational(1073741789, 1)) + assert_equal(Rational(1152921470247108503, 3), + Rational(1073741827, 3) * Rational(1073741789, 1)) + assert_equal(Rational(1073741827, 3221225367), + Rational(1073741827, 3) / Rational(1073741789, 1)) + assert_equal(Rational(4294967308, 3), + Rational(1073741827, 3) + Rational(1073741827, 1)) + assert_equal(Rational(-2147483654, 3), + Rational(1073741827, 3) - Rational(1073741827, 1)) + assert_equal(Rational(1152921511049297929, 3), + Rational(1073741827, 3) * Rational(1073741827, 1)) + assert_equal(Rational(1, 3), + Rational(1073741827, 3) / Rational(1073741827, 1)) + assert_equal(Rational(357913943, 1), + Rational(1073741827, 3) + Rational(2, 3)) + assert_equal(Rational(1073741825, 3), + Rational(1073741827, 3) - Rational(2, 3)) + assert_equal(Rational(2147483654, 9), + Rational(1073741827, 3) * Rational(2, 3)) + assert_equal(Rational(1073741827, 2), + Rational(1073741827, 3) / Rational(2, 3)) + assert_equal(Rational(2147483663, 6), + Rational(1073741827, 3) + Rational(3, 2)) + assert_equal(Rational(2147483645, 6), + Rational(1073741827, 3) - Rational(3, 2)) + assert_equal(Rational(1073741827, 2), + Rational(1073741827, 3) * Rational(3, 2)) + assert_equal(Rational(2147483654, 9), + Rational(1073741827, 3) / Rational(3, 2)) + assert_equal(Rational(1152921470247108512, 3221225367), + Rational(1073741827, 3) + Rational(3, 1073741789)) + assert_equal(Rational(1152921470247108494, 3221225367), + Rational(1073741827, 3) - Rational(3, 1073741789)) + assert_equal(Rational(1073741827, 1073741789), + Rational(1073741827, 3) * Rational(3, 1073741789)) + assert_equal(Rational(1152921470247108503, 9), + Rational(1073741827, 3) / Rational(3, 1073741789)) + assert_equal(Rational(715827872, 1), + Rational(1073741827, 3) + Rational(1073741789, 3)) + assert_equal(Rational(38, 3), + Rational(1073741827, 3) - Rational(1073741789, 3)) + assert_equal(Rational(1152921470247108503, 9), + Rational(1073741827, 3) * Rational(1073741789, 3)) + assert_equal(Rational(1073741827, 1073741789), + Rational(1073741827, 3) / Rational(1073741789, 3)) + assert_equal(Rational(1152921511049297938, 3221225481), + Rational(1073741827, 3) + Rational(3, 1073741827)) + assert_equal(Rational(1152921511049297920, 3221225481), + Rational(1073741827, 3) - Rational(3, 1073741827)) + assert_equal(Rational(1, 1), + Rational(1073741827, 3) * Rational(3, 1073741827)) + assert_equal(Rational(1152921511049297929, 9), + Rational(1073741827, 3) / Rational(3, 1073741827)) + assert_equal(Rational(2147483654, 3), + Rational(1073741827, 3) + Rational(1073741827, 3)) + assert_equal(Rational(0, 1), + Rational(1073741827, 3) - Rational(1073741827, 3)) + assert_equal(Rational(1152921511049297929, 9), + Rational(1073741827, 3) * Rational(1073741827, 3)) + assert_equal(Rational(1, 1), + Rational(1073741827, 3) / Rational(1073741827, 3)) + assert_equal(Rational(1152921514270523296, 3221225481), + Rational(1073741827, 3) + Rational(1073741789, 1073741827)) + assert_equal(Rational(1152921507828072562, 3221225481), + Rational(1073741827, 3) - Rational(1073741789, 1073741827)) + assert_equal(Rational(1073741789, 3), + Rational(1073741827, 3) * Rational(1073741789, 1073741827)) + assert_equal(Rational(1152921511049297929, 3221225367), + Rational(1073741827, 3) / Rational(1073741789, 1073741827)) + assert_equal(Rational(1152921473468333984, 3221225367), + Rational(1073741827, 3) + Rational(1073741827, 1073741789)) + assert_equal(Rational(1152921467025883022, 3221225367), + Rational(1073741827, 3) - Rational(1073741827, 1073741789)) + assert_equal(Rational(1152921511049297929, 3221225367), + Rational(1073741827, 3) * Rational(1073741827, 1073741789)) + assert_equal(Rational(1073741789, 3), + Rational(1073741827, 3) / Rational(1073741827, 1073741789)) + assert_equal(Rational(2147483616, 1073741827), + Rational(1073741789, 1073741827) + Rational(1, 1)) + assert_equal(Rational(-38, 1073741827), + Rational(1073741789, 1073741827) - Rational(1, 1)) + assert_equal(Rational(1073741789, 1073741827), + Rational(1073741789, 1073741827) * Rational(1, 1)) + assert_equal(Rational(1073741789, 1073741827), + Rational(1073741789, 1073741827) / Rational(1, 1)) + assert_equal(Rational(3221225443, 1073741827), + Rational(1073741789, 1073741827) + Rational(2, 1)) + assert_equal(Rational(-1073741865, 1073741827), + Rational(1073741789, 1073741827) - Rational(2, 1)) + assert_equal(Rational(2147483578, 1073741827), + Rational(1073741789, 1073741827) * Rational(2, 1)) + assert_equal(Rational(1073741789, 2147483654), + Rational(1073741789, 1073741827) / Rational(2, 1)) + assert_equal(Rational(4294967270, 1073741827), + Rational(1073741789, 1073741827) + Rational(3, 1)) + assert_equal(Rational(-2147483692, 1073741827), + Rational(1073741789, 1073741827) - Rational(3, 1)) + assert_equal(Rational(3221225367, 1073741827), + Rational(1073741789, 1073741827) * Rational(3, 1)) + assert_equal(Rational(1073741789, 3221225481), + Rational(1073741789, 1073741827) / Rational(3, 1)) + assert_equal(Rational(1152921471320850292, 1073741827), + Rational(1073741789, 1073741827) + Rational(1073741789, 1)) + assert_equal(Rational(-1152921469173366714, 1073741827), + Rational(1073741789, 1073741827) - Rational(1073741789, 1)) + assert_equal(Rational(1152921429444920521, 1073741827), + Rational(1073741789, 1073741827) * Rational(1073741789, 1)) + assert_equal(Rational(1, 1073741827), + Rational(1073741789, 1073741827) / Rational(1073741789, 1)) + assert_equal(Rational(1152921512123039718, 1073741827), + Rational(1073741789, 1073741827) + Rational(1073741827, 1)) + assert_equal(Rational(-1152921509975556140, 1073741827), + Rational(1073741789, 1073741827) - Rational(1073741827, 1)) + assert_equal(Rational(1073741789, 1), + Rational(1073741789, 1073741827) * Rational(1073741827, 1)) + assert_equal(Rational(1073741789, 1152921511049297929), + Rational(1073741789, 1073741827) / Rational(1073741827, 1)) + assert_equal(Rational(5368709021, 3221225481), + Rational(1073741789, 1073741827) + Rational(2, 3)) + assert_equal(Rational(1073741713, 3221225481), + Rational(1073741789, 1073741827) - Rational(2, 3)) + assert_equal(Rational(2147483578, 3221225481), + Rational(1073741789, 1073741827) * Rational(2, 3)) + assert_equal(Rational(3221225367, 2147483654), + Rational(1073741789, 1073741827) / Rational(2, 3)) + assert_equal(Rational(5368709059, 2147483654), + Rational(1073741789, 1073741827) + Rational(3, 2)) + assert_equal(Rational(-1073741903, 2147483654), + Rational(1073741789, 1073741827) - Rational(3, 2)) + assert_equal(Rational(3221225367, 2147483654), + Rational(1073741789, 1073741827) * Rational(3, 2)) + assert_equal(Rational(2147483578, 3221225481), + Rational(1073741789, 1073741827) / Rational(3, 2)) + assert_equal(Rational(1152921432666146002, 1152921470247108503), + Rational(1073741789, 1073741827) + Rational(3, 1073741789)) + assert_equal(Rational(1152921426223695040, 1152921470247108503), + Rational(1073741789, 1073741827) - Rational(3, 1073741789)) + assert_equal(Rational(3, 1073741827), + Rational(1073741789, 1073741827) * Rational(3, 1073741789)) + assert_equal(Rational(1152921429444920521, 3221225481), + Rational(1073741789, 1073741827) / Rational(3, 1073741789)) + assert_equal(Rational(1152921473468333870, 3221225481), + Rational(1073741789, 1073741827) + Rational(1073741789, 3)) + assert_equal(Rational(-1152921467025883136, 3221225481), + Rational(1073741789, 1073741827) - Rational(1073741789, 3)) + assert_equal(Rational(1152921429444920521, 3221225481), + Rational(1073741789, 1073741827) * Rational(1073741789, 3)) + assert_equal(Rational(3, 1073741827), + Rational(1073741789, 1073741827) / Rational(1073741789, 3)) + assert_equal(Rational(1073741792, 1073741827), + Rational(1073741789, 1073741827) + Rational(3, 1073741827)) + assert_equal(Rational(1073741786, 1073741827), + Rational(1073741789, 1073741827) - Rational(3, 1073741827)) + assert_equal(Rational(3221225367, 1152921511049297929), + Rational(1073741789, 1073741827) * Rational(3, 1073741827)) + assert_equal(Rational(1073741789, 3), + Rational(1073741789, 1073741827) / Rational(3, 1073741827)) + assert_equal(Rational(1152921514270523296, 3221225481), + Rational(1073741789, 1073741827) + Rational(1073741827, 3)) + assert_equal(Rational(-1152921507828072562, 3221225481), + Rational(1073741789, 1073741827) - Rational(1073741827, 3)) + assert_equal(Rational(1073741789, 3), + Rational(1073741789, 1073741827) * Rational(1073741827, 3)) + assert_equal(Rational(3221225367, 1152921511049297929), + Rational(1073741789, 1073741827) / Rational(1073741827, 3)) + assert_equal(Rational(2147483578, 1073741827), + Rational(1073741789, 1073741827) + Rational(1073741789, 1073741827)) + assert_equal(Rational(0, 1), + Rational(1073741789, 1073741827) - Rational(1073741789, 1073741827)) + assert_equal(Rational(1152921429444920521, 1152921511049297929), + Rational(1073741789, 1073741827) * Rational(1073741789, 1073741827)) + assert_equal(Rational(1, 1), + Rational(1073741789, 1073741827) / Rational(1073741789, 1073741827)) + assert_equal(Rational(2305842940494218450, 1152921470247108503), + Rational(1073741789, 1073741827) + Rational(1073741827, 1073741789)) + assert_equal(Rational(-81604377408, 1152921470247108503), + Rational(1073741789, 1073741827) - Rational(1073741827, 1073741789)) + assert_equal(Rational(1, 1), + Rational(1073741789, 1073741827) * Rational(1073741827, 1073741789)) + assert_equal(Rational(1152921429444920521, 1152921511049297929), + Rational(1073741789, 1073741827) / Rational(1073741827, 1073741789)) + assert_equal(Rational(2147483616, 1073741789), + Rational(1073741827, 1073741789) + Rational(1, 1)) + assert_equal(Rational(38, 1073741789), + Rational(1073741827, 1073741789) - Rational(1, 1)) + assert_equal(Rational(1073741827, 1073741789), + Rational(1073741827, 1073741789) * Rational(1, 1)) + assert_equal(Rational(1073741827, 1073741789), + Rational(1073741827, 1073741789) / Rational(1, 1)) + assert_equal(Rational(3221225405, 1073741789), + Rational(1073741827, 1073741789) + Rational(2, 1)) + assert_equal(Rational(-1073741751, 1073741789), + Rational(1073741827, 1073741789) - Rational(2, 1)) + assert_equal(Rational(2147483654, 1073741789), + Rational(1073741827, 1073741789) * Rational(2, 1)) + assert_equal(Rational(1073741827, 2147483578), + Rational(1073741827, 1073741789) / Rational(2, 1)) + assert_equal(Rational(4294967194, 1073741789), + Rational(1073741827, 1073741789) + Rational(3, 1)) + assert_equal(Rational(-2147483540, 1073741789), + Rational(1073741827, 1073741789) - Rational(3, 1)) + assert_equal(Rational(3221225481, 1073741789), + Rational(1073741827, 1073741789) * Rational(3, 1)) + assert_equal(Rational(1073741827, 3221225367), + Rational(1073741827, 1073741789) / Rational(3, 1)) + assert_equal(Rational(1152921430518662348, 1073741789), + Rational(1073741827, 1073741789) + Rational(1073741789, 1)) + assert_equal(Rational(-1152921428371178694, 1073741789), + Rational(1073741827, 1073741789) - Rational(1073741789, 1)) + assert_equal(Rational(1073741827, 1), + Rational(1073741827, 1073741789) * Rational(1073741789, 1)) + assert_equal(Rational(1073741827, 1152921429444920521), + Rational(1073741827, 1073741789) / Rational(1073741789, 1)) + assert_equal(Rational(1152921471320850330, 1073741789), + Rational(1073741827, 1073741789) + Rational(1073741827, 1)) + assert_equal(Rational(-1152921469173366676, 1073741789), + Rational(1073741827, 1073741789) - Rational(1073741827, 1)) + assert_equal(Rational(1152921511049297929, 1073741789), + Rational(1073741827, 1073741789) * Rational(1073741827, 1)) + assert_equal(Rational(1, 1073741789), + Rational(1073741827, 1073741789) / Rational(1073741827, 1)) + assert_equal(Rational(5368709059, 3221225367), + Rational(1073741827, 1073741789) + Rational(2, 3)) + assert_equal(Rational(1073741903, 3221225367), + Rational(1073741827, 1073741789) - Rational(2, 3)) + assert_equal(Rational(2147483654, 3221225367), + Rational(1073741827, 1073741789) * Rational(2, 3)) + assert_equal(Rational(3221225481, 2147483578), + Rational(1073741827, 1073741789) / Rational(2, 3)) + assert_equal(Rational(5368709021, 2147483578), + Rational(1073741827, 1073741789) + Rational(3, 2)) + assert_equal(Rational(-1073741713, 2147483578), + Rational(1073741827, 1073741789) - Rational(3, 2)) + assert_equal(Rational(3221225481, 2147483578), + Rational(1073741827, 1073741789) * Rational(3, 2)) + assert_equal(Rational(2147483654, 3221225367), + Rational(1073741827, 1073741789) / Rational(3, 2)) + assert_equal(Rational(1073741830, 1073741789), + Rational(1073741827, 1073741789) + Rational(3, 1073741789)) + assert_equal(Rational(1073741824, 1073741789), + Rational(1073741827, 1073741789) - Rational(3, 1073741789)) + assert_equal(Rational(3221225481, 1152921429444920521), + Rational(1073741827, 1073741789) * Rational(3, 1073741789)) + assert_equal(Rational(1073741827, 3), + Rational(1073741827, 1073741789) / Rational(3, 1073741789)) + assert_equal(Rational(1152921432666146002, 3221225367), + Rational(1073741827, 1073741789) + Rational(1073741789, 3)) + assert_equal(Rational(-1152921426223695040, 3221225367), + Rational(1073741827, 1073741789) - Rational(1073741789, 3)) + assert_equal(Rational(1073741827, 3), + Rational(1073741827, 1073741789) * Rational(1073741789, 3)) + assert_equal(Rational(3221225481, 1152921429444920521), + Rational(1073741827, 1073741789) / Rational(1073741789, 3)) + assert_equal(Rational(1152921514270523296, 1152921470247108503), + Rational(1073741827, 1073741789) + Rational(3, 1073741827)) + assert_equal(Rational(1152921507828072562, 1152921470247108503), + Rational(1073741827, 1073741789) - Rational(3, 1073741827)) + assert_equal(Rational(3, 1073741789), + Rational(1073741827, 1073741789) * Rational(3, 1073741827)) + assert_equal(Rational(1152921511049297929, 3221225367), + Rational(1073741827, 1073741789) / Rational(3, 1073741827)) + assert_equal(Rational(1152921473468333984, 3221225367), + Rational(1073741827, 1073741789) + Rational(1073741827, 3)) + assert_equal(Rational(-1152921467025883022, 3221225367), + Rational(1073741827, 1073741789) - Rational(1073741827, 3)) + assert_equal(Rational(1152921511049297929, 3221225367), + Rational(1073741827, 1073741789) * Rational(1073741827, 3)) + assert_equal(Rational(3, 1073741789), + Rational(1073741827, 1073741789) / Rational(1073741827, 3)) + assert_equal(Rational(2305842940494218450, 1152921470247108503), + Rational(1073741827, 1073741789) + Rational(1073741789, 1073741827)) + assert_equal(Rational(81604377408, 1152921470247108503), + Rational(1073741827, 1073741789) - Rational(1073741789, 1073741827)) + assert_equal(Rational(1, 1), + Rational(1073741827, 1073741789) * Rational(1073741789, 1073741827)) + assert_equal(Rational(1152921511049297929, 1152921429444920521), + Rational(1073741827, 1073741789) / Rational(1073741789, 1073741827)) + assert_equal(Rational(2147483654, 1073741789), + Rational(1073741827, 1073741789) + Rational(1073741827, 1073741789)) + assert_equal(Rational(0, 1), + Rational(1073741827, 1073741789) - Rational(1073741827, 1073741789)) + assert_equal(Rational(1152921511049297929, 1152921429444920521), + Rational(1073741827, 1073741789) * Rational(1073741827, 1073741789)) + assert_equal(Rational(1, 1), + Rational(1073741827, 1073741789) / Rational(1073741827, 1073741789)) + end + +end |