/* rational.c: Coded by Tadayoshi Funaba 2008 This implementation is based on Keiju Ishitsuka's Rational library which is written in ruby. */ #include "ruby.h" #include #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_floor, id_hash, 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); } binop(xor, '^') fun1(abs) fun1(floor) fun1(hash) 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(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); } static VALUE nurat_numerator(VALUE self) { get_dat1(self); return dat->num; } static VALUE nurat_denominator(VALUE self) { get_dat1(self); return dat->den; } #ifndef NDEBUG #define f_imul f_imul_orig #endif inline static VALUE f_imul(long a, long b) { VALUE r; long c; if (a == 0 || b == 0) return ZERO; else if (a == 1) return LONG2NUM(b); else if (b == 1) return LONG2NUM(a); c = a * b; r = LONG2NUM(c); if (NUM2LONG(r) != c || (c / a) != b) r = rb_big_mul(rb_int2big(a), rb_int2big(b)); return r; } #ifndef NDEBUG #undef f_imul inline static VALUE f_imul(long x, long y) { VALUE r = f_imul_orig(x, y); assert(f_equal_p(r, f_mul(LONG2NUM(x), LONG2NUM(y)))); return r; } #endif inline static VALUE f_addsub(VALUE self, VALUE anum, VALUE aden, VALUE bnum, VALUE bden, int k) { VALUE num, den; if (FIXNUM_P(anum) && FIXNUM_P(aden) && FIXNUM_P(bnum) && FIXNUM_P(bden)) { long an = FIX2LONG(anum); long ad = FIX2LONG(aden); long bn = FIX2LONG(bnum); long bd = FIX2LONG(bden); long ig = i_gcd(ad, bd); VALUE g = LONG2NUM(ig); VALUE a = f_imul(an, bd / ig); VALUE b = f_imul(bn, ad / ig); VALUE c; if (k == '+') c = f_add(a, b); else c = f_sub(a, b); b = f_idiv(aden, g); g = f_gcd(c, g); num = f_idiv(c, g); a = f_idiv(bden, g); den = f_mul(a, b); } else { VALUE g = f_gcd(aden, bden); VALUE a = f_mul(anum, f_idiv(bden, g)); VALUE b = f_mul(bnum, f_idiv(aden, g)); VALUE c; if (k == '+') c = f_add(a, b); else c = f_sub(a, b); b = f_idiv(aden, g); g = f_gcd(c, g); num = f_idiv(c, g); a = f_idiv(bden, g); den = f_mul(a, b); } return f_rational_new_no_reduce2(CLASS_OF(self), num, den); } static VALUE nurat_add(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: { get_dat1(self); return f_addsub(self, dat->num, dat->den, other, ONE, '+'); } case T_FLOAT: return f_add(f_to_f(self), other); case T_RATIONAL: { get_dat2(self, other); return f_addsub(self, adat->num, adat->den, bdat->num, bdat->den, '+'); } default: return rb_num_coerce_bin(self, other, '+'); } } static VALUE nurat_sub(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: { get_dat1(self); return f_addsub(self, dat->num, dat->den, other, ONE, '-'); } case T_FLOAT: return f_sub(f_to_f(self), other); case T_RATIONAL: { get_dat2(self, other); return f_addsub(self, adat->num, adat->den, bdat->num, bdat->den, '-'); } default: return rb_num_coerce_bin(self, other, '-'); } } inline static VALUE f_muldiv(VALUE self, VALUE anum, VALUE aden, VALUE bnum, VALUE bden, int k) { VALUE num, den; if (k == '/') { VALUE t; if (f_negative_p(bnum)) { anum = f_negate(anum); bnum = f_negate(bnum); } t = bnum; bnum = bden; bden = t; } if (FIXNUM_P(anum) && FIXNUM_P(aden) && FIXNUM_P(bnum) && FIXNUM_P(bden)) { long an = FIX2LONG(anum); long ad = FIX2LONG(aden); long bn = FIX2LONG(bnum); long bd = FIX2LONG(bden); long g1 = i_gcd(an, bd); long g2 = i_gcd(ad, bn); num = f_imul(an / g1, bn / g2); den = f_imul(ad / g2, bd / g1); } else { VALUE g1 = f_gcd(anum, bden); VALUE g2 = f_gcd(aden, bnum); num = f_mul(f_idiv(anum, g1), f_idiv(bnum, g2)); den = f_mul(f_idiv(aden, g2), f_idiv(bden, g1)); } return f_rational_new_no_reduce2(CLASS_OF(self), num, den); } static VALUE nurat_mul(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: { get_dat1(self); return f_muldiv(self, dat->num, dat->den, other, ONE, '*'); } case T_FLOAT: return f_mul(f_to_f(self), other); case T_RATIONAL: { get_dat2(self, other); return f_muldiv(self, adat->num, adat->den, bdat->num, bdat->den, '*'); } default: return rb_num_coerce_bin(self, other, '*'); } } 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, '/'); } } static VALUE nurat_fdiv(VALUE self, VALUE other) { return f_div(f_to_f(self), other); } static VALUE nurat_expt(VALUE self, VALUE other) { if (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: return f_expt(f_to_f(self), other); default: return rb_num_coerce_bin(self, other, id_expt); } } static VALUE nurat_cmp(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: { get_dat1(self); if (FIXNUM_P(dat->den) && FIX2LONG(dat->den) == 1) return f_cmp(dat->num, other); return f_cmp(self, f_rational_new_bang1(CLASS_OF(self), other)); } case T_FLOAT: return f_cmp(f_to_f(self), other); case T_RATIONAL: { VALUE num1, num2; get_dat2(self, other); if (FIXNUM_P(adat->num) && FIXNUM_P(adat->den) && FIXNUM_P(bdat->num) && FIXNUM_P(bdat->den)) { num1 = f_imul(FIX2LONG(adat->num), FIX2LONG(bdat->den)); num2 = f_imul(FIX2LONG(bdat->num), FIX2LONG(adat->den)); } else { num1 = f_mul(adat->num, bdat->den); num2 = f_mul(bdat->num, adat->den); } return f_cmp(f_sub(num1, num2), ZERO); } default: return rb_num_coerce_bin(self, other, id_cmp); } } static VALUE nurat_equal_p(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: { get_dat1(self); if (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; } static VALUE nurat_idiv(VALUE self, VALUE other) { return f_floor(f_div(self, other)); } static VALUE nurat_mod(VALUE self, VALUE other) { VALUE val = f_floor(f_div(self, other)); return f_sub(self, f_mul(other, val)); } static VALUE nurat_divmod(VALUE self, VALUE other) { VALUE val = f_floor(f_div(self, other)); return rb_assoc_new(val, f_sub(self, f_mul(other, val))); } #if 0 static VALUE nurat_quot(VALUE self, VALUE other) { return f_truncate(f_div(self, other)); } #endif static VALUE nurat_rem(VALUE self, VALUE other) { VALUE val = f_truncate(f_div(self, other)); return f_sub(self, f_mul(other, val)); } #if 0 static VALUE nurat_quotrem(VALUE self, VALUE other) { VALUE val = f_truncate(f_div(self, other)); return rb_assoc_new(val, f_sub(self, f_mul(other, val))); } #endif static VALUE nurat_abs(VALUE self) { if (f_positive_p(self)) return self; return f_negate(self); } #if 0 static VALUE nurat_true(VALUE self) { return Qtrue; } #endif static VALUE nurat_floor(VALUE self) { get_dat1(self); return f_idiv(dat->num, dat->den); } static VALUE nurat_ceil(VALUE self) { get_dat1(self); return f_negate(f_idiv(f_negate(dat->num), dat->den)); } static VALUE nurat_truncate(VALUE self) { get_dat1(self); if (f_negative_p(dat->num)) return f_negate(f_idiv(f_negate(dat->num), dat->den)); return f_idiv(dat->num, dat->den); } static VALUE nurat_round(VALUE self) { get_dat1(self); if (f_negative_p(dat->num)) { VALUE num, den; num = f_negate(dat->num); num = f_add(f_mul(num, TWO), dat->den); den = f_mul(dat->den, TWO); return f_negate(f_idiv(num, den)); } else { VALUE num = f_add(f_mul(dat->num, TWO), dat->den); VALUE den = f_mul(dat->den, TWO); return f_idiv(num, den); } } #define f_size(x) rb_funcall(x, rb_intern("size"), 0) #define f_rshift(x,y) rb_funcall(x, rb_intern(">>"), 1, y) inline static long i_ilog2(VALUE x) { long q, r, fx; assert(!f_lt_p(x, ONE)); q = (NUM2LONG(f_size(x)) - sizeof(long)) * 8 + 1; if (q > 0) x = f_rshift(x, LONG2NUM(q)); fx = NUM2LONG(x); r = -1; while (fx) { fx >>= 1; r += 1; } return q + r; } static long ml; static VALUE nurat_to_f(VALUE self) { VALUE num, den; int minus = 0; long nl, dl, ne, de; int e; double f; { get_dat1(self); if (f_zero_p(dat->num)) return rb_float_new(0.0); num = dat->num; den = dat->den; } if (f_negative_p(num)) { num = f_negate(num); minus = 1; } nl = i_ilog2(num); dl = i_ilog2(den); 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_warning("%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_warning("%s out of Float range", rb_obj_classname(self)); return rb_float_new(f); } static VALUE nurat_to_r(VALUE self) { return self; } static VALUE nurat_hash(VALUE self) { get_dat1(self); return f_xor(f_hash(dat->num), f_hash(dat->den)); } 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; } static VALUE nurat_to_s(VALUE self) { return nurat_format(self, f_to_s); } 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; } static VALUE nurat_marshal_dump(VALUE self) { VALUE a; get_dat1(self); a = rb_assoc_new(dat->num, dat->den); rb_copy_generic_ivar(a, self); return a; } static VALUE nurat_marshal_load(VALUE self, VALUE a) { 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; } /* --- */ VALUE rb_gcd(VALUE self, VALUE other) { other = nurat_int_value(other); return f_gcd(self, other); } VALUE rb_lcm(VALUE self, VALUE other) { other = nurat_int_value(other); return f_lcm(self, other); } VALUE rb_gcdlcm(VALUE self, VALUE other) { other = nurat_int_value(other); return rb_assoc_new(f_gcd(self, other), f_lcm(self, other)); } VALUE rb_rational_raw(VALUE x, VALUE y) { return nurat_s_new_internal(rb_cRational, x, y); } VALUE rb_rational_new(VALUE x, VALUE y) { return nurat_s_canonicalize_internal(rb_cRational, x, y); } static VALUE nurat_s_convert(int argc, VALUE *argv, VALUE klass); VALUE rb_Rational(VALUE x, VALUE y) { VALUE a[2]; a[0] = x; a[1] = y; return nurat_s_convert(2, a, rb_cRational); } #define id_numerator rb_intern("numerator") #define f_numerator(x) rb_funcall(x, id_numerator, 0) #define id_denominator rb_intern("denominator") #define f_denominator(x) rb_funcall(x, id_denominator, 0) #define id_to_r rb_intern("to_r") #define f_to_r(x) rb_funcall(x, id_to_r, 0) static VALUE numeric_numerator(VALUE self) { return f_numerator(f_to_r(self)); } static VALUE numeric_denominator(VALUE self) { return f_denominator(f_to_r(self)); } static VALUE integer_numerator(VALUE self) { return self; } static VALUE integer_denominator(VALUE self) { return INT2FIX(1); } static VALUE float_numerator(VALUE self) { double d = RFLOAT_VALUE(self); if (isinf(d) || isnan(d)) return self; return rb_call_super(0, 0); } static VALUE float_denominator(VALUE self) { double d = RFLOAT_VALUE(self); if (isinf(d) || isnan(d)) return INT2FIX(1); return rb_call_super(0, 0); } static VALUE nilclass_to_r(VALUE self) { return rb_rational_new1(INT2FIX(0)); } static VALUE 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 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 Rational: %s", StringValuePtr(s)); } return RARRAY_PTR(a)[0]; } #define id_gsub rb_intern("gsub") #define f_gsub(x,y,z) rb_funcall(x, id_gsub, 2, y, z) static VALUE string_to_r(VALUE self) { VALUE s, 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); 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) && !f_integer_p(a1)) return a1; } else { if ((k_numeric_p(a1) && k_numeric_p(a2)) && (!f_integer_p(a1) || !f_integer_p(a2))) return f_div(a1, a2); } { VALUE argv2[2]; argv2[0] = a1; argv2[1] = a2; return nurat_s_new(argc, argv2, klass); } } void Init_Rational(void) { #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", 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); 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_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: */