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