/*
* A rational number can be represented as a paired integer number;
* a/b (b>0). Where a is numerator and b is denominator. Integer a
* equals rational a/1 mathematically.
*
* In ruby, you can create rational object with Rational or to_r
* method. The return values will be irreducible.
*
* Rational(1) #=> (1/1)
* Rational(2, 3) #=> (2/3)
* Rational(4, -6) #=> (-2/3)
* 3.to_r #=> (3/1)
*
* You can also create ratioanl object from floating-point numbers or
* strings.
*
* Rational(0.3) #=> (5404319552844595/18014398509481984)
* Rational('0.3') #=> (3/10)
* Rational('2/3') #=> (2/3)
*
* 0.3.to_r #=> (5404319552844595/18014398509481984)
* '0.3'.to_r #=> (3/10)
* '2/3'.to_r #=> (2/3)
*
* A rational object is an exact number, which helps you to write
* program without any rounding errors.
*
* 10.times.inject(0){|t,| t + 0.1} #=> 0.9999999999999999
* 10.times.inject(0){|t,| t + Rational('0.1')} #=> (1/1)
*
* However, when an expression has inexact factor (numerical value or
* operation), will produce an inexact result.
*
* Rational(10) / 3 #=> (10/3)
* Rational(10) / 3.0 #=> 3.3333333333333335
*
* Rational(-8) ** Rational(1, 3)
* #=> (1.0000000000000002+1.7320508075688772i)
*/
void
Init_Rational(void)
{
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");
rb_cRational = rb_define_class("Rational", rb_cNumeric);
rb_objc_define_method(rb_cRational, "alloc", nurat_s_alloc, 0);
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_objc_define_method(rb_mKernel, "Rational", nurat_f_rational, -1);
rb_objc_define_method(rb_cRational, "numerator", nurat_numerator, 0);
rb_objc_define_method(rb_cRational, "denominator", nurat_denominator, 0);
rb_objc_define_method(rb_cRational, "+", nurat_add, 1);
rb_objc_define_method(rb_cRational, "-", nurat_sub, 1);
rb_objc_define_method(rb_cRational, "*", nurat_mul, 1);
rb_objc_define_method(rb_cRational, "/", nurat_div, 1);
rb_objc_define_method(rb_cRational, "quo", nurat_div, 1);
rb_objc_define_method(rb_cRational, "fdiv", nurat_fdiv, 1);
rb_objc_define_method(rb_cRational, "**", nurat_expt, 1);
rb_objc_define_method(rb_cRational, "<=>", nurat_cmp, 1);
rb_objc_define_method(rb_cRational, "==", nurat_eqeq_p, 1);
rb_objc_define_method(rb_cRational, "coerce", nurat_coerce, 1);
#if 0 /* NUBY */
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_objc_define_method(rb_cRational, "floor", nurat_floor_n, -1);
rb_objc_define_method(rb_cRational, "ceil", nurat_ceil_n, -1);
rb_objc_define_method(rb_cRational, "truncate", nurat_truncate_n, -1);
rb_objc_define_method(rb_cRational, "round", nurat_round_n, -1);
rb_objc_define_method(rb_cRational, "to_i", nurat_truncate, 0);
rb_objc_define_method(rb_cRational, "to_f", nurat_to_f, 0);
rb_objc_define_method(rb_cRational, "to_r", nurat_to_r, 0);
rb_objc_define_method(rb_cRational, "hash", nurat_hash, 0);
rb_objc_define_method(rb_cRational, "to_s", nurat_to_s, 0);
rb_objc_define_method(rb_cRational, "inspect", nurat_inspect, 0);
rb_objc_define_method(rb_cRational, "marshal_dump", nurat_marshal_dump, 0);
rb_objc_define_method(rb_cRational, "marshal_load", nurat_marshal_load, 1);
/* --- */
rb_objc_define_method(rb_cInteger, "gcd", rb_gcd, 1);
rb_objc_define_method(rb_cInteger, "lcm", rb_lcm, 1);
rb_objc_define_method(rb_cInteger, "gcdlcm", rb_gcdlcm, 1);
rb_objc_define_method(rb_cNumeric, "numerator", numeric_numerator, 0);
rb_objc_define_method(rb_cNumeric, "denominator", numeric_denominator, 0);
rb_objc_define_method(rb_cInteger, "numerator", integer_numerator, 0);
rb_objc_define_method(rb_cInteger, "denominator", integer_denominator, 0);
rb_objc_define_method(rb_cFloat, "numerator", float_numerator, 0);
rb_objc_define_method(rb_cFloat, "denominator", float_denominator, 0);
rb_objc_define_method(rb_cNilClass, "to_r", nilclass_to_r, 0);
rb_objc_define_method(rb_cInteger, "to_r", integer_to_r, 0);
rb_objc_define_method(rb_cFloat, "to_r", float_to_r, 0);
make_patterns();
rb_objc_define_method(rb_cString, "to_r", string_to_r, 0);
rb_objc_define_method(*(VALUE *)rb_cRational, "convert", nurat_s_convert, -1);
// rb_define_private_method(CLASS_OF(rb_cRational), "convert", nurat_s_convert, -1);
// TODO: insert NSNumber primitives
}
void
Init_Rational(void)
{
#undef rb_intern
#define rb_intern(str) rb_intern_const(str)
assert(fprintf(stderr, "assert() is now active\n"));
id_abs = rb_intern("abs");
id_cmp = rb_intern("<=>");
id_convert = rb_intern("convert");
id_equal_p = rb_intern("==");
id_expt = rb_intern("**");
id_floor = rb_intern("floor");
id_hash = rb_intern("hash");
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");
ml = (long)(log(DBL_MAX) / log(2.0) - 1);
rb_cRational = rb_define_class(RATIONAL_NAME, 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_NAME, nurat_f_rational, -1);
rb_define_method(rb_cRational, "numerator", nurat_numerator, 0);
rb_define_method(rb_cRational, "denominator", nurat_denominator, 0);
rb_define_method(rb_cRational, "+", nurat_add, 1);
rb_define_method(rb_cRational, "-", nurat_sub, 1);
rb_define_method(rb_cRational, "*", nurat_mul, 1);
rb_define_method(rb_cRational, "/", nurat_div, 1);
rb_define_method(rb_cRational, "quo", nurat_div, 1);
rb_define_method(rb_cRational, "fdiv", nurat_fdiv, 1);
rb_define_method(rb_cRational, "**", nurat_expt, 1);
rb_define_method(rb_cRational, "<=>", nurat_cmp, 1);
rb_define_method(rb_cRational, "==", nurat_equal_p, 1);
rb_define_method(rb_cRational, "coerce", nurat_coerce, 1);
rb_define_method(rb_cRational, "div", nurat_idiv, 1);
#if 0 /* NUBY */
rb_define_method(rb_cRational, "//", nurat_idiv, 1);
#endif
rb_define_method(rb_cRational, "modulo", nurat_mod, 1);
rb_define_method(rb_cRational, "%", nurat_mod, 1);
rb_define_method(rb_cRational, "divmod", nurat_divmod, 1);
#if 0
rb_define_method(rb_cRational, "quot", nurat_quot, 1);
#endif
rb_define_method(rb_cRational, "remainder", nurat_rem, 1);
#if 0
rb_define_method(rb_cRational, "quotrem", nurat_quotrem, 1);
#endif
rb_define_method(rb_cRational, "abs", nurat_abs, 0);
#if 0
rb_define_method(rb_cRational, "rational?", nurat_true, 0);
rb_define_method(rb_cRational, "exact?", nurat_true, 0);
#endif
rb_define_method(rb_cRational, "floor", nurat_floor, 0);
rb_define_method(rb_cRational, "ceil", nurat_ceil, 0);
rb_define_method(rb_cRational, "truncate", nurat_truncate, 0);
rb_define_method(rb_cRational, "round", nurat_round, 0);
rb_define_method(rb_cRational, "to_i", nurat_truncate, 0);
rb_define_method(rb_cRational, "to_f", nurat_to_f, 0);
rb_define_method(rb_cRational, "to_r", nurat_to_r, 0);
rb_define_method(rb_cRational, "hash", nurat_hash, 0);
rb_define_method(rb_cRational, "to_s", nurat_to_s, 0);
rb_define_method(rb_cRational, "inspect", nurat_inspect, 0);
rb_define_method(rb_cRational, "marshal_dump", nurat_marshal_dump, 0);
rb_define_method(rb_cRational, "marshal_load", nurat_marshal_load, 1);
/* --- */
rb_define_method(rb_cInteger, "gcd", rb_gcd, 1);
rb_define_method(rb_cInteger, "lcm", rb_lcm, 1);
rb_define_method(rb_cInteger, "gcdlcm", rb_gcdlcm, 1);
rb_define_method(rb_cNilClass, "to_r", nilclass_to_r, 0);
rb_define_method(rb_cInteger, "to_r", integer_to_r, 0);
rb_define_method(rb_cFloat, "to_r", float_to_r, 0);
make_patterns();
rb_define_method(rb_cString, "to_r", string_to_r, 0);
rb_define_private_method(CLASS_OF(rb_cRational), "convert", nurat_s_convert, -1);
}
void
Init_Rational(void)
{
assert(fprintf(stderr, "assert() is now active\n"));
id_Unify = rb_intern("Unify");
id_abs = rb_intern("abs");
id_cmp = rb_intern("<=>");
id_convert = rb_intern("convert");
id_equal_p = rb_intern("==");
id_expt = rb_intern("**");
id_floor = rb_intern("floor");
id_format = rb_intern("format");
id_idiv = rb_intern("div");
id_inspect = rb_intern("inspect");
id_negate = rb_intern("-@");
id_new = rb_intern("new");
id_new_bang = rb_intern("new!");
id_to_f = rb_intern("to_f");
id_to_i = rb_intern("to_i");
id_to_s = rb_intern("to_s");
id_truncate = rb_intern("truncate");
rb_cRational = rb_define_class(RATIONAL_NAME, rb_cNumeric);
rb_define_alloc_func(rb_cRational, nurat_s_alloc);
rb_funcall(rb_cRational, rb_intern("private_class_method"), 1,
ID2SYM(rb_intern("allocate")));
rb_define_singleton_method(rb_cRational, "new!", nurat_s_new_bang, -1);
rb_funcall(rb_cRational, rb_intern("private_class_method"), 1,
ID2SYM(rb_intern("new!")));
rb_define_singleton_method(rb_cRational, "new", nurat_s_new_m, -1);
rb_funcall(rb_cRational, rb_intern("private_class_method"), 1,
ID2SYM(rb_intern("new")));
rb_define_global_function(RATIONAL_NAME, nurat_f_rational, -1);
rb_define_method(rb_cRational, "numerator", nurat_numerator, 0);
rb_define_method(rb_cRational, "denominator", nurat_denominator, 0);
rb_define_method(rb_cRational, "+", nurat_add, 1);
rb_define_method(rb_cRational, "-", nurat_sub, 1);
rb_define_method(rb_cRational, "*", nurat_mul, 1);
rb_define_method(rb_cRational, "/", nurat_div, 1);
rb_define_method(rb_cRational, "quo", nurat_div, 1);
rb_define_method(rb_cRational, "fdiv", nurat_fdiv, 1);
rb_define_method(rb_cRational, "**", nurat_expt, 1);
rb_define_method(rb_cRational, "<=>", nurat_cmp, 1);
rb_define_method(rb_cRational, "==", nurat_equal_p, 1);
rb_define_method(rb_cRational, "coerce", nurat_coerce, 1);
rb_define_method(rb_cRational, "div", nurat_idiv, 1);
#if NUBY
rb_define_method(rb_cRational, "//", nurat_idiv, 1);
#endif
rb_define_method(rb_cRational, "modulo", nurat_mod, 1);
rb_define_method(rb_cRational, "%", nurat_mod, 1);
rb_define_method(rb_cRational, "divmod", nurat_divmod, 1);
#if 0
rb_define_method(rb_cRational, "quot", nurat_quot, 1);
#endif
rb_define_method(rb_cRational, "remainder", nurat_rem, 1);
#if 0
rb_define_method(rb_cRational, "quotrem", nurat_quotrem, 1);
#endif
rb_define_method(rb_cRational, "abs", nurat_abs, 0);
#if 0
rb_define_method(rb_cRational, "rational?", nurat_true, 0);
rb_define_method(rb_cRational, "exact?", nurat_true, 0);
#endif
rb_define_method(rb_cRational, "floor", nurat_floor, 0);
rb_define_method(rb_cRational, "ceil", nurat_ceil, 0);
rb_define_method(rb_cRational, "truncate", nurat_truncate, 0);
rb_define_method(rb_cRational, "round", nurat_round, 0);
rb_define_method(rb_cRational, "to_i", nurat_truncate, 0);
rb_define_method(rb_cRational, "to_f", nurat_to_f, 0);
rb_define_method(rb_cRational, "to_r", nurat_to_r, 0);
rb_define_method(rb_cRational, "hash", nurat_hash, 0);
rb_define_method(rb_cRational, "to_s", nurat_to_s, 0);
rb_define_method(rb_cRational, "inspect", nurat_inspect, 0);
rb_define_method(rb_cRational, "marshal_dump", nurat_marshal_dump, 0);
rb_define_method(rb_cRational, "marshal_load", nurat_marshal_load, 1);
/* --- */
rb_define_method(rb_cInteger, "gcd", rb_gcd, 1);
rb_define_method(rb_cInteger, "lcm", rb_lcm, 1);
rb_define_method(rb_cInteger, "gcdlcm", rb_gcdlcm, 1);
rb_define_method(rb_cNilClass, "to_r", nilclass_to_r, 0);
rb_define_method(rb_cInteger, "to_r", integer_to_r, 0);
rb_define_method(rb_cFloat, "to_r", float_to_r, 0);
make_patterns();
rb_define_method(rb_cString, "to_r", string_to_r, 0);
rb_define_singleton_method(rb_cRational, "convert", nurat_s_convert, -1);
rb_funcall(rb_cRational, rb_intern("private_class_method"), 1,
ID2SYM(rb_intern("convert")));
rb_include_module(rb_cRational, rb_mPrecision);
rb_define_singleton_method(rb_cRational, "induced_from",
nurat_s_induced_from, 1);
}
void
Init_Complex(void)
{
#undef rb_intern
#define rb_intern(str) rb_intern_const(str)
assert(fprintf(stderr, "assert() is now active\n"));
id_abs = rb_intern("abs");
id_abs2 = rb_intern("abs2");
id_arg = rb_intern("arg");
id_cmp = rb_intern("<=>");
id_conj = rb_intern("conj");
id_convert = rb_intern("convert");
id_denominator = rb_intern("denominator");
id_divmod = rb_intern("divmod");
id_equal_p = rb_intern("==");
id_expt = rb_intern("**");
id_floor = rb_intern("floor");
id_hash = rb_intern("hash");
id_idiv = rb_intern("div");
id_inspect = rb_intern("inspect");
id_negate = rb_intern("-@");
id_numerator = rb_intern("numerator");
id_polar = rb_intern("polar");
id_quo = rb_intern("quo");
id_real_p = rb_intern("real?");
id_to_f = rb_intern("to_f");
id_to_i = rb_intern("to_i");
id_to_r = rb_intern("to_r");
id_to_s = rb_intern("to_s");
rb_cComplex = rb_define_class(COMPLEX_NAME, rb_cNumeric);
rb_define_alloc_func(rb_cComplex, nucomp_s_alloc);
rb_undef_method(CLASS_OF(rb_cComplex), "allocate");
#if 0
rb_define_private_method(CLASS_OF(rb_cComplex), "new!", nucomp_s_new_bang, -1);
rb_define_private_method(CLASS_OF(rb_cComplex), "new", nucomp_s_new, -1);
#else
rb_undef_method(CLASS_OF(rb_cComplex), "new");
#endif
rb_define_singleton_method(rb_cComplex, "rectangular", nucomp_s_new, -1);
rb_define_singleton_method(rb_cComplex, "rect", nucomp_s_new, -1);
rb_define_singleton_method(rb_cComplex, "polar", nucomp_s_polar, 2);
rb_define_global_function(COMPLEX_NAME, nucomp_f_complex, -1);
rb_undef_method(rb_cComplex, "<");
rb_undef_method(rb_cComplex, "<=");
rb_undef_method(rb_cComplex, "<=>");
rb_undef_method(rb_cComplex, ">");
rb_undef_method(rb_cComplex, ">=");
rb_undef_method(rb_cComplex, "between?");
rb_undef_method(rb_cComplex, "divmod");
rb_undef_method(rb_cComplex, "floor");
rb_undef_method(rb_cComplex, "ceil");
rb_undef_method(rb_cComplex, "modulo");
rb_undef_method(rb_cComplex, "round");
rb_undef_method(rb_cComplex, "step");
rb_undef_method(rb_cComplex, "truncate");
#if 0 /* NUBY */
rb_undef_method(rb_cComplex, "//");
#endif
rb_define_method(rb_cComplex, "real", nucomp_real, 0);
rb_define_method(rb_cComplex, "imaginary", nucomp_imag, 0);
rb_define_method(rb_cComplex, "imag", nucomp_imag, 0);
rb_define_method(rb_cComplex, "-@", nucomp_negate, 0);
rb_define_method(rb_cComplex, "+", nucomp_add, 1);
rb_define_method(rb_cComplex, "-", nucomp_sub, 1);
rb_define_method(rb_cComplex, "*", nucomp_mul, 1);
rb_define_method(rb_cComplex, "/", nucomp_div, 1);
rb_define_method(rb_cComplex, "quo", nucomp_quo, 1);
rb_define_method(rb_cComplex, "fdiv", nucomp_fdiv, 1);
rb_define_method(rb_cComplex, "**", nucomp_expt, 1);
rb_define_method(rb_cComplex, "==", nucomp_equal_p, 1);
rb_define_method(rb_cComplex, "coerce", nucomp_coerce, 1);
rb_define_method(rb_cComplex, "abs", nucomp_abs, 0);
rb_define_method(rb_cComplex, "magnitude", nucomp_abs, 0);
rb_define_method(rb_cComplex, "abs2", nucomp_abs2, 0);
rb_define_method(rb_cComplex, "arg", nucomp_arg, 0);
rb_define_method(rb_cComplex, "angle", nucomp_arg, 0);
rb_define_method(rb_cComplex, "phase", nucomp_arg, 0);
rb_define_method(rb_cComplex, "rectangular", nucomp_rect, 0);
rb_define_method(rb_cComplex, "rect", nucomp_rect, 0);
rb_define_method(rb_cComplex, "polar", nucomp_polar, 0);
rb_define_method(rb_cComplex, "conjugate", nucomp_conj, 0);
rb_define_method(rb_cComplex, "conj", nucomp_conj, 0);
#if 0
rb_define_method(rb_cComplex, "~", nucomp_conj, 0); /* gcc */
#endif
rb_define_method(rb_cComplex, "real?", nucomp_false, 0);
#if 0
rb_define_method(rb_cComplex, "complex?", nucomp_true, 0);
rb_define_method(rb_cComplex, "exact?", nucomp_exact_p, 0);
rb_define_method(rb_cComplex, "inexact?", nucomp_inexact_p, 0);
#endif
rb_define_method(rb_cComplex, "numerator", nucomp_numerator, 0);
rb_define_method(rb_cComplex, "denominator", nucomp_denominator, 0);
rb_define_method(rb_cComplex, "hash", nucomp_hash, 0);
rb_define_method(rb_cComplex, "eql?", nucomp_eql_p, 1);
rb_define_method(rb_cComplex, "to_s", nucomp_to_s, 0);
rb_define_method(rb_cComplex, "inspect", nucomp_inspect, 0);
rb_define_method(rb_cComplex, "marshal_dump", nucomp_marshal_dump, 0);
rb_define_method(rb_cComplex, "marshal_load", nucomp_marshal_load, 1);
/* --- */
rb_define_method(rb_cComplex, "to_i", nucomp_to_i, 0);
rb_define_method(rb_cComplex, "to_f", nucomp_to_f, 0);
rb_define_method(rb_cComplex, "to_r", nucomp_to_r, 0);
rb_define_method(rb_cNilClass, "to_c", nilclass_to_c, 0);
rb_define_method(rb_cNumeric, "to_c", numeric_to_c, 0);
make_patterns();
rb_define_method(rb_cString, "to_c", string_to_c, 0);
rb_define_private_method(CLASS_OF(rb_cComplex), "convert", nucomp_s_convert, -1);
/* --- */
rb_define_method(rb_cNumeric, "real", numeric_real, 0);
rb_define_method(rb_cNumeric, "imaginary", numeric_imag, 0);
rb_define_method(rb_cNumeric, "imag", numeric_imag, 0);
rb_define_method(rb_cNumeric, "abs2", numeric_abs2, 0);
rb_define_method(rb_cNumeric, "arg", numeric_arg, 0);
rb_define_method(rb_cNumeric, "angle", numeric_arg, 0);
rb_define_method(rb_cNumeric, "phase", numeric_arg, 0);
rb_define_method(rb_cNumeric, "rectangular", numeric_rect, 0);
rb_define_method(rb_cNumeric, "rect", numeric_rect, 0);
rb_define_method(rb_cNumeric, "polar", numeric_polar, 0);
rb_define_method(rb_cNumeric, "conjugate", numeric_conj, 0);
rb_define_method(rb_cNumeric, "conj", numeric_conj, 0);
rb_define_const(rb_cComplex, "I",
f_complex_new_bang2(rb_cComplex, ZERO, ONE));
}
