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Diffstat (limited to 'ruby_1_9_3/rational.c')
-rw-r--r-- | ruby_1_9_3/rational.c | 2409 |
1 files changed, 0 insertions, 2409 deletions
diff --git a/ruby_1_9_3/rational.c b/ruby_1_9_3/rational.c deleted file mode 100644 index 8aced2aee8..0000000000 --- a/ruby_1_9_3/rational.c +++ /dev/null @@ -1,2409 +0,0 @@ -/* - rational.c: Coded by Tadayoshi Funaba 2008-2011 - - This implementation is based on Keiju Ishitsuka's Rational library - which is written in ruby. -*/ - -#include "ruby.h" -#include "internal.h" -#include <math.h> -#include <float.h> - -#ifdef HAVE_IEEEFP_H -#include <ieeefp.h> -#endif - -#define NDEBUG -#include <assert.h> - -#define ZERO INT2FIX(0) -#define ONE INT2FIX(1) -#define TWO INT2FIX(2) - -VALUE rb_cRational; - -static ID id_abs, id_cmp, id_convert, id_eqeq_p, id_expt, id_fdiv, - id_floor, id_idiv, id_inspect, id_integer_p, id_negate, id_to_f, - id_to_i, id_to_s, id_truncate; - -#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) - -inline static VALUE -f_to_i(VALUE x) -{ - if (TYPE(x) == T_STRING) - return rb_str_to_inum(x, 10, 0); - return rb_funcall(x, id_to_i, 0); -} -inline static VALUE -f_to_f(VALUE x) -{ - if (TYPE(x) == T_STRING) - return DBL2NUM(rb_str_to_dbl(x, 0)); - return rb_funcall(x, id_to_f, 0); -} - -fun1(to_s) -fun1(truncate) - -inline static VALUE -f_eqeq_p(VALUE x, VALUE y) -{ - if (FIXNUM_P(x) && FIXNUM_P(y)) - return f_boolcast(FIX2LONG(x) == FIX2LONG(y)); - return rb_funcall(x, id_eqeq_p, 1, y); -} - -fun2(expt) -fun2(fdiv) -fun2(idiv) - -#define f_expt10(x) f_expt(INT2FIX(10), x) - -inline static VALUE -f_negative_p(VALUE x) -{ - if (FIXNUM_P(x)) - return f_boolcast(FIX2LONG(x) < 0); - return rb_funcall(x, '<', 1, ZERO); -} - -#define f_positive_p(x) (!f_negative_p(x)) - -inline static VALUE -f_zero_p(VALUE x) -{ - switch (TYPE(x)) { - case T_FIXNUM: - return f_boolcast(FIX2LONG(x) == 0); - case T_BIGNUM: - return Qfalse; - case T_RATIONAL: - { - VALUE num = RRATIONAL(x)->num; - - return f_boolcast(FIXNUM_P(num) && FIX2LONG(num) == 0); - } - } - return rb_funcall(x, id_eqeq_p, 1, ZERO); -} - -#define f_nonzero_p(x) (!f_zero_p(x)) - -inline static VALUE -f_one_p(VALUE x) -{ - switch (TYPE(x)) { - case T_FIXNUM: - return f_boolcast(FIX2LONG(x) == 1); - case T_BIGNUM: - return Qfalse; - case T_RATIONAL: - { - VALUE num = RRATIONAL(x)->num; - VALUE den = RRATIONAL(x)->den; - - return f_boolcast(FIXNUM_P(num) && FIX2LONG(num) == 1 && - FIXNUM_P(den) && FIX2LONG(den) == 1); - } - } - return rb_funcall(x, id_eqeq_p, 1, ONE); -} - -inline static VALUE -f_kind_of_p(VALUE x, VALUE c) -{ - return rb_obj_is_kind_of(x, c); -} - -inline static VALUE -k_numeric_p(VALUE x) -{ - return f_kind_of_p(x, rb_cNumeric); -} - -inline static VALUE -k_integer_p(VALUE x) -{ - return f_kind_of_p(x, rb_cInteger); -} - -inline static VALUE -k_float_p(VALUE x) -{ - return f_kind_of_p(x, rb_cFloat); -} - -inline static VALUE -k_rational_p(VALUE x) -{ - return f_kind_of_p(x, rb_cRational); -} - -#define k_exact_p(x) (!k_float_p(x)) -#define k_inexact_p(x) k_float_p(x) - -#define k_exact_zero_p(x) (k_exact_p(x) && f_zero_p(x)) -#define k_exact_one_p(x) (k_exact_p(x) && f_one_p(x)) - -#ifndef NDEBUG -#define f_gcd f_gcd_orig -#endif - -inline static long -i_gcd(long x, long y) -{ - if (x < 0) - x = -x; - if (y < 0) - y = -y; - - if (x == 0) - return y; - if (y == 0) - return x; - - while (x > 0) { - long t = x; - x = y % x; - y = t; - } - return y; -} - -inline static VALUE -f_gcd(VALUE x, VALUE y) -{ - VALUE z; - - if (FIXNUM_P(x) && FIXNUM_P(y)) - return LONG2NUM(i_gcd(FIX2LONG(x), FIX2LONG(y))); - - if (f_negative_p(x)) - x = f_negate(x); - if (f_negative_p(y)) - y = f_negate(y); - - if (f_zero_p(x)) - return y; - if (f_zero_p(y)) - return x; - - for (;;) { - if (FIXNUM_P(x)) { - if (FIX2LONG(x) == 0) - return y; - if (FIXNUM_P(y)) - return LONG2NUM(i_gcd(FIX2LONG(x), FIX2LONG(y))); - } - z = x; - x = f_mod(y, x); - y = z; - } - /* 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 0") - -#if 0 -static VALUE -nurat_s_new_bang(int argc, VALUE *argv, VALUE klass) -{ - VALUE num, den; - - switch (rb_scan_args(argc, argv, "11", &num, &den)) { - case 1: - if (!k_integer_p(num)) - num = f_to_i(num); - den = ONE; - break; - default: - if (!k_integer_p(num)) - num = f_to_i(num); - if (!k_integer_p(den)) - den = f_to_i(den); - - switch (FIX2INT(f_cmp(den, ZERO))) { - case -1: - num = f_negate(num); - den = f_negate(den); - break; - case 0: - rb_raise_zerodiv(); - break; - } - break; - } - - return nurat_s_new_internal(klass, num, den); -} -#endif - -inline static VALUE -f_rational_new_bang1(VALUE klass, VALUE x) -{ - return nurat_s_new_internal(klass, x, ONE); -} - -inline static VALUE -f_rational_new_bang2(VALUE klass, VALUE x, VALUE y) -{ - assert(f_positive_p(y)); - assert(f_nonzero_p(y)); - return nurat_s_new_internal(klass, x, y); -} - -#ifdef CANONICALIZATION_FOR_MATHN -#define CANON -#endif - -#ifdef CANON -static int canonicalization = 0; - -RUBY_FUNC_EXPORTED void -nurat_canonicalization(int f) -{ - canonicalization = f; -} -#endif - -inline static void -nurat_int_check(VALUE num) -{ - switch (TYPE(num)) { - case T_FIXNUM: - case T_BIGNUM: - break; - default: - if (!k_numeric_p(num) || !f_integer_p(num)) - rb_raise(rb_eTypeError, "not an integer"); - } -} - -inline static VALUE -nurat_int_value(VALUE num) -{ - nurat_int_check(num); - if (!k_integer_p(num)) - num = f_to_i(num); - return num; -} - -inline static VALUE -nurat_s_canonicalize_internal(VALUE klass, VALUE num, VALUE den) -{ - VALUE gcd; - - switch (FIX2INT(f_cmp(den, ZERO))) { - case -1: - num = f_negate(num); - den = f_negate(den); - break; - case 0: - rb_raise_zerodiv(); - break; - } - - gcd = f_gcd(num, den); - num = f_idiv(num, gcd); - den = f_idiv(den, gcd); - -#ifdef CANON - if (f_one_p(den) && canonicalization) - return num; -#endif - return nurat_s_new_internal(klass, num, den); -} - -inline static VALUE -nurat_s_canonicalize_internal_no_reduce(VALUE klass, VALUE num, VALUE den) -{ - switch (FIX2INT(f_cmp(den, ZERO))) { - case -1: - num = f_negate(num); - den = f_negate(den); - break; - case 0: - rb_raise_zerodiv(); - break; - } - -#ifdef CANON - if (f_one_p(den) && canonicalization) - return num; -#endif - return nurat_s_new_internal(klass, num, den); -} - -static VALUE -nurat_s_new(int argc, VALUE *argv, VALUE klass) -{ - VALUE num, den; - - switch (rb_scan_args(argc, argv, "11", &num, &den)) { - case 1: - num = nurat_int_value(num); - den = ONE; - break; - default: - num = nurat_int_value(num); - den = nurat_int_value(den); - break; - } - - return nurat_s_canonicalize_internal(klass, num, den); -} - -inline static VALUE -f_rational_new1(VALUE klass, VALUE x) -{ - assert(!k_rational_p(x)); - return nurat_s_canonicalize_internal(klass, x, ONE); -} - -inline static VALUE -f_rational_new2(VALUE klass, VALUE x, VALUE y) -{ - assert(!k_rational_p(x)); - assert(!k_rational_p(y)); - return nurat_s_canonicalize_internal(klass, x, y); -} - -inline static VALUE -f_rational_new_no_reduce1(VALUE klass, VALUE x) -{ - assert(!k_rational_p(x)); - return nurat_s_canonicalize_internal_no_reduce(klass, x, ONE); -} - -inline static VALUE -f_rational_new_no_reduce2(VALUE klass, VALUE x, VALUE y) -{ - assert(!k_rational_p(x)); - assert(!k_rational_p(y)); - return nurat_s_canonicalize_internal_no_reduce(klass, x, y); -} - -/* - * call-seq: - * Rational(x[, y]) -> numeric - * - * Returns 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. - * - * For example: - * - * Rational(7).numerator #=> 7 - * Rational(7, 1).numerator #=> 7 - * 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 (always positive). - * - * For example: - * - * Rational(7).denominator #=> 1 - * Rational(7, 1).denominator #=> 1 - * Rational(9, -4).denominator #=> 4 - * Rational(-2, -10).denominator #=> 5 - * rat.numerator.gcd(rat.denominator) #=> 1 - */ -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; - volatile 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_eqeq_p(r, f_mul(LONG2NUM(x), LONG2NUM(y)))); - return r; -} -#endif - -inline static VALUE -f_addsub(VALUE self, VALUE anum, VALUE aden, VALUE bnum, VALUE bden, int k) -{ - VALUE num, den; - - if (FIXNUM_P(anum) && FIXNUM_P(aden) && - FIXNUM_P(bnum) && FIXNUM_P(bden)) { - long an = FIX2LONG(anum); - long ad = FIX2LONG(aden); - long bn = FIX2LONG(bnum); - long bd = FIX2LONG(bden); - long ig = i_gcd(ad, bd); - - VALUE g = LONG2NUM(ig); - VALUE a = f_imul(an, bd / ig); - VALUE b = f_imul(bn, ad / ig); - VALUE c; - - if (k == '+') - c = f_add(a, b); - else - c = f_sub(a, b); - - b = f_idiv(aden, g); - g = f_gcd(c, g); - num = f_idiv(c, g); - a = f_idiv(bden, g); - den = f_mul(a, b); - } - else { - VALUE g = f_gcd(aden, bden); - VALUE a = f_mul(anum, f_idiv(bden, g)); - VALUE b = f_mul(bnum, f_idiv(aden, g)); - VALUE c; - - if (k == '+') - c = f_add(a, b); - else - c = f_sub(a, b); - - b = f_idiv(aden, g); - g = f_gcd(c, g); - num = f_idiv(c, g); - a = f_idiv(bden, g); - den = f_mul(a, b); - } - return f_rational_new_no_reduce2(CLASS_OF(self), num, den); -} - -/* - * call-seq: - * rat + numeric -> numeric - * - * Performs addition. - * - * 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 - */ -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 - * - * Performs subtraction. - * - * 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 - */ -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 - * - * Performs multiplication. - * - * 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 - */ -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 - * rat.quo(numeric) -> numeric - * - * Performs division. - * - * 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 - */ -static VALUE -nurat_div(VALUE self, VALUE other) -{ - switch (TYPE(other)) { - case T_FIXNUM: - case T_BIGNUM: - if (f_zero_p(other)) - rb_raise_zerodiv(); - { - get_dat1(self); - - return f_muldiv(self, - dat->num, dat->den, - other, ONE, '/'); - } - case T_FLOAT: - { - double x = RFLOAT_VALUE(other), den; - get_dat1(self); - - if (isnan(x)) return DBL2NUM(NAN); - if (isinf(x)) return INT2FIX(0); - if (x != 0.0 && modf(x, &den) == 0.0) { - return rb_rational_raw2(dat->num, f_mul(rb_dbl2big(den), dat->den)); - } - } - return rb_funcall(f_to_f(self), '/', 1, other); - case T_RATIONAL: - if (f_zero_p(other)) - rb_raise_zerodiv(); - { - get_dat2(self, other); - - if (f_one_p(self)) - return f_rational_new_no_reduce2(CLASS_OF(self), - bdat->den, bdat->num); - - return f_muldiv(self, - adat->num, adat->den, - bdat->num, bdat->den, '/'); - } - default: - return rb_num_coerce_bin(self, other, '/'); - } -} - -/* - * call-seq: - * rat.fdiv(numeric) -> float - * - * Performs division and returns the value as a float. - * - * For example: - * - * Rational(2, 3).fdiv(1) #=> 0.6666666666666666 - * Rational(2, 3).fdiv(0.5) #=> 1.3333333333333333 - * Rational(2).fdiv(3) #=> 0.6666666666666666 - */ -static VALUE -nurat_fdiv(VALUE self, VALUE other) -{ - if (f_zero_p(other)) - return f_div(self, f_to_f(other)); - return f_to_f(f_div(self, other)); -} - -/* - * call-seq: - * rat ** numeric -> numeric - * - * Performs exponentiation. - * - * For example: - * - * Rational(2) ** Rational(3) #=> (8/1) - * Rational(10) ** -2 #=> (1/100) - * Rational(10) ** -2.0 #=> 0.01 - * Rational(-4) ** Rational(1,2) #=> (1.2246063538223773e-16+2.0i) - * Rational(1, 2) ** 0 #=> (1/1) - * Rational(1, 2) ** 0.0 #=> 1.0 - */ -static VALUE -nurat_expt(VALUE self, VALUE other) -{ - if (k_numeric_p(other) && k_exact_zero_p(other)) - return f_rational_new_bang1(CLASS_OF(self), ONE); - - if (k_rational_p(other)) { - get_dat1(other); - - if (f_one_p(dat->den)) - other = dat->num; /* c14n */ - } - - switch (TYPE(other)) { - case T_FIXNUM: - { - VALUE num, den; - - get_dat1(self); - - switch (FIX2INT(f_cmp(other, ZERO))) { - case 1: - num = f_expt(dat->num, other); - den = f_expt(dat->den, other); - break; - case -1: - num = f_expt(dat->den, f_negate(other)); - den = f_expt(dat->num, f_negate(other)); - break; - default: - num = ONE; - den = ONE; - break; - } - return f_rational_new2(CLASS_OF(self), num, den); - } - case T_BIGNUM: - rb_warn("in a**b, b may be too big"); - /* fall through */ - case T_FLOAT: - case T_RATIONAL: - 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 or nil - * - * Performs comparison and returns -1, 0, or +1. - * - * For example: - * - * Rational(2, 3) <=> Rational(2, 3) #=> 0 - * Rational(5) <=> 5 #=> 0 - * Rational(2,3) <=> Rational(1,3) #=> 1 - * Rational(1,3) <=> 1 #=> -1 - * Rational(1,3) <=> 0.3 #=> 1 - */ -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); /* c14n */ - return f_cmp(self, f_rational_new_bang1(CLASS_OF(self), other)); - } - case T_FLOAT: - return f_cmp(f_to_f(self), other); - case T_RATIONAL: - { - VALUE num1, num2; - - get_dat2(self, other); - - if (FIXNUM_P(adat->num) && FIXNUM_P(adat->den) && - FIXNUM_P(bdat->num) && FIXNUM_P(bdat->den)) { - num1 = f_imul(FIX2LONG(adat->num), FIX2LONG(bdat->den)); - num2 = f_imul(FIX2LONG(bdat->num), FIX2LONG(adat->den)); - } - else { - num1 = f_mul(adat->num, bdat->den); - num2 = f_mul(bdat->num, adat->den); - } - return f_cmp(f_sub(num1, num2), ZERO); - } - default: - return rb_num_coerce_cmp(self, other, id_cmp); - } -} - -/* - * call-seq: - * rat == object -> true or false - * - * Returns true if rat equals object numerically. - * - * For example: - * - * Rational(2, 3) == Rational(2, 3) #=> true - * Rational(5) == 5 #=> true - * Rational(0) == 0.0 #=> true - * Rational('1/3') == 0.33 #=> false - * Rational('1/2') == '1/2' #=> false - */ -static VALUE -nurat_eqeq_p(VALUE self, VALUE other) -{ - switch (TYPE(other)) { - case T_FIXNUM: - case T_BIGNUM: - { - get_dat1(self); - - if (f_zero_p(dat->num) && f_zero_p(other)) - return Qtrue; - - if (!FIXNUM_P(dat->den)) - return Qfalse; - if (FIX2LONG(dat->den) != 1) - return Qfalse; - if (f_eqeq_p(dat->num, other)) - return Qtrue; - return Qfalse; - } - case T_FLOAT: - return f_eqeq_p(f_to_f(self), other); - case T_RATIONAL: - { - get_dat2(self, other); - - if (f_zero_p(adat->num) && f_zero_p(bdat->num)) - return Qtrue; - - return f_boolcast(f_eqeq_p(adat->num, bdat->num) && - f_eqeq_p(adat->den, bdat->den)); - } - default: - return f_eqeq_p(other, self); - } -} - -/* :nodoc: */ -static VALUE -nurat_coerce(VALUE self, VALUE other) -{ - switch (TYPE(other)) { - case T_FIXNUM: - case T_BIGNUM: - return rb_assoc_new(f_rational_new_bang1(CLASS_OF(self), other), self); - case T_FLOAT: - return rb_assoc_new(other, f_to_f(self)); - case T_RATIONAL: - return rb_assoc_new(other, self); - case T_COMPLEX: - if (k_exact_zero_p(RCOMPLEX(other)->imag)) - return rb_assoc_new(f_rational_new_bang1 - (CLASS_OF(self), RCOMPLEX(other)->real), self); - else - return rb_assoc_new(other, rb_Complex(self, INT2FIX(0))); - } - - rb_raise(rb_eTypeError, "%s can't be coerced into %s", - rb_obj_classname(other), rb_obj_classname(self)); - return Qnil; -} - -#if 0 -/* :nodoc: */ -static VALUE -nurat_idiv(VALUE self, VALUE other) -{ - return f_idiv(self, other); -} - -/* :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 the truncated value as an integer. - * - * 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 -f_round_common(int argc, VALUE *argv, VALUE self, VALUE (*func)(VALUE)) -{ - VALUE n, b, s; - - if (argc == 0) - return (*func)(self); - - rb_scan_args(argc, argv, "01", &n); - - if (!k_integer_p(n)) - rb_raise(rb_eTypeError, "not an integer"); - - b = f_expt10(n); - s = f_mul(self, b); - - 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 truncated value (toward negative infinity). - * - * For example: - * - * Rational(3).floor #=> 3 - * Rational(2, 3).floor #=> 0 - * Rational(-3, 2).floor #=> -1 - * - * decimal - 1 2 3 . 4 5 6 - * ^ ^ ^ ^ ^ ^ - * precision -3 -2 -1 0 +1 +2 - * - * '%f' % Rational('-123.456').floor(+1) #=> "-123.500000" - * '%f' % Rational('-123.456').floor(-1) #=> "-130.000000" - */ -static VALUE -nurat_floor_n(int argc, VALUE *argv, VALUE self) -{ - return f_round_common(argc, argv, self, nurat_floor); -} - -/* - * call-seq: - * rat.ceil -> integer - * rat.ceil(precision=0) -> rational - * - * Returns the truncated value (toward positive infinity). - * - * For example: - * - * Rational(3).ceil #=> 3 - * Rational(2, 3).ceil #=> 1 - * Rational(-3, 2).ceil #=> -1 - * - * decimal - 1 2 3 . 4 5 6 - * ^ ^ ^ ^ ^ ^ - * precision -3 -2 -1 0 +1 +2 - * - * '%f' % Rational('-123.456').ceil(+1) #=> "-123.400000" - * '%f' % Rational('-123.456').ceil(-1) #=> "-120.000000" - */ -static VALUE -nurat_ceil_n(int argc, VALUE *argv, VALUE self) -{ - return f_round_common(argc, argv, self, nurat_ceil); -} - -/* - * call-seq: - * rat.truncate -> integer - * rat.truncate(precision=0) -> rational - * - * Returns the truncated value (toward zero). - * - * For example: - * - * Rational(3).truncate #=> 3 - * Rational(2, 3).truncate #=> 0 - * Rational(-3, 2).truncate #=> -1 - * - * decimal - 1 2 3 . 4 5 6 - * ^ ^ ^ ^ ^ ^ - * precision -3 -2 -1 0 +1 +2 - * - * '%f' % Rational('-123.456').truncate(+1) #=> "-123.400000" - * '%f' % Rational('-123.456').truncate(-1) #=> "-120.000000" - */ -static VALUE -nurat_truncate_n(int argc, VALUE *argv, VALUE self) -{ - return f_round_common(argc, argv, self, nurat_truncate); -} - -/* - * call-seq: - * rat.round -> integer - * rat.round(precision=0) -> rational - * - * Returns the truncated value (toward the nearest integer; - * 0.5 => 1; -0.5 => -1). - * - * For example: - * - * Rational(3).round #=> 3 - * Rational(2, 3).round #=> 1 - * Rational(-3, 2).round #=> -2 - * - * decimal - 1 2 3 . 4 5 6 - * ^ ^ ^ ^ ^ ^ - * precision -3 -2 -1 0 +1 +2 - * - * '%f' % Rational('-123.456').round(+1) #=> "-123.500000" - * '%f' % Rational('-123.456').round(-1) #=> "-120.000000" - */ -static VALUE -nurat_round_n(int argc, VALUE *argv, VALUE self) -{ - return f_round_common(argc, argv, self, nurat_round); -} - -/* - * call-seq: - * rat.to_f -> float - * - * Return the value as a float. - * - * 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. - * - * For example: - * - * Rational(2).to_r #=> (2/1) - * Rational(-8, 6).to_r #=> (-4/3) - */ -static VALUE -nurat_to_r(VALUE self) -{ - return self; -} - -#define id_ceil rb_intern("ceil") -#define f_ceil(x) rb_funcall((x), id_ceil, 0) - -#define id_quo rb_intern("quo") -#define f_quo(x,y) rb_funcall((x), id_quo, 1, (y)) - -#define f_reciprocal(x) f_quo(ONE, (x)) - -/* - The algorithm here is the method described in CLISP. Bruno Haible has - graciously given permission to use this algorithm. He says, "You can use - it, if you present the following explanation of the algorithm." - - Algorithm (recursively presented): - If x is a rational number, return x. - If x = 0.0, return 0. - If x < 0.0, return (- (rationalize (- x))). - If x > 0.0: - Call (integer-decode-float x). It returns a m,e,s=1 (mantissa, - exponent, sign). - If m = 0 or e >= 0: return x = m*2^e. - Search a rational number between a = (m-1/2)*2^e and b = (m+1/2)*2^e - with smallest possible numerator and denominator. - Note 1: If m is a power of 2, we ought to take a = (m-1/4)*2^e. - But in this case the result will be x itself anyway, regardless of - the choice of a. Therefore we can simply ignore this case. - Note 2: At first, we need to consider the closed interval [a,b]. - but since a and b have the denominator 2^(|e|+1) whereas x itself - has a denominator <= 2^|e|, we can restrict the search to the open - interval (a,b). - So, for given a and b (0 < a < b) we are searching a rational number - y with a <= y <= b. - Recursive algorithm fraction_between(a,b): - c := (ceiling a) - if c < b - then return c ; because a <= c < b, c integer - else - ; a is not integer (otherwise we would have had c = a < b) - k := c-1 ; k = floor(a), k < a < b <= k+1 - return y = k + 1/fraction_between(1/(b-k), 1/(a-k)) - ; note 1 <= 1/(b-k) < 1/(a-k) - - You can see that we are actually computing a continued fraction expansion. - - Algorithm (iterative): - If x is rational, return x. - Call (integer-decode-float x). It returns a m,e,s (mantissa, - exponent, sign). - If m = 0 or e >= 0, return m*2^e*s. (This includes the case x = 0.0.) - Create rational numbers a := (2*m-1)*2^(e-1) and b := (2*m+1)*2^(e-1) - (positive and already in lowest terms because the denominator is a - power of two and the numerator is odd). - Start a continued fraction expansion - p[-1] := 0, p[0] := 1, q[-1] := 1, q[0] := 0, i := 0. - Loop - c := (ceiling a) - if c >= b - then k := c-1, partial_quotient(k), (a,b) := (1/(b-k),1/(a-k)), - goto Loop - finally partial_quotient(c). - Here partial_quotient(c) denotes the iteration - i := i+1, p[i] := c*p[i-1]+p[i-2], q[i] := c*q[i-1]+q[i-2]. - At the end, return s * (p[i]/q[i]). - This rational number is already in lowest terms because - p[i]*q[i-1]-p[i-1]*q[i] = (-1)^i. -*/ - -static void -nurat_rationalize_internal(VALUE a, VALUE b, VALUE *p, VALUE *q) -{ - VALUE c, k, t, p0, p1, p2, q0, q1, q2; - - p0 = ZERO; - p1 = ONE; - q0 = ONE; - q1 = ZERO; - - while (1) { - c = f_ceil(a); - if (f_lt_p(c, b)) - break; - k = f_sub(c, ONE); - p2 = f_add(f_mul(k, p1), p0); - q2 = f_add(f_mul(k, q1), q0); - t = f_reciprocal(f_sub(b, k)); - b = f_reciprocal(f_sub(a, k)); - a = t; - p0 = p1; - q0 = q1; - p1 = p2; - q1 = q2; - } - *p = f_add(f_mul(c, p1), p0); - *q = f_add(f_mul(c, q1), q0); -} - -/* - * call-seq: - * rat.rationalize -> self - * rat.rationalize(eps) -> rational - * - * Returns a simpler approximation of the value if an optional - * argument eps is given (rat-|eps| <= result <= rat+|eps|), self - * otherwise. - * - * For example: - * - * r = Rational(5033165, 16777216) - * r.rationalize #=> (5033165/16777216) - * r.rationalize(Rational('0.01')) #=> (3/10) - * r.rationalize(Rational('0.1')) #=> (1/3) - */ -static VALUE -nurat_rationalize(int argc, VALUE *argv, VALUE self) -{ - VALUE e, a, b, p, q; - - if (argc == 0) - return self; - - if (f_negative_p(self)) - return f_negate(nurat_rationalize(argc, argv, f_abs(self))); - - rb_scan_args(argc, argv, "01", &e); - e = f_abs(e); - a = f_sub(self, e); - b = f_add(self, e); - - if (f_eqeq_p(a, b)) - return self; - - nurat_rationalize_internal(a, b, &p, &q); - return f_rational_new2(CLASS_OF(self), p, q); -} - -/* :nodoc: */ -static VALUE -nurat_hash(VALUE self) -{ - st_index_t v, h[2]; - VALUE n; - - get_dat1(self); - n = rb_hash(dat->num); - h[0] = NUM2LONG(n); - n = rb_hash(dat->den); - h[1] = NUM2LONG(n); - v = rb_memhash(h, sizeof(h)); - return LONG2FIX(v); -} - -static VALUE -f_format(VALUE self, VALUE (*func)(VALUE)) -{ - VALUE s; - get_dat1(self); - - s = (*func)(dat->num); - rb_str_cat2(s, "/"); - rb_str_concat(s, (*func)(dat->den)); - - return s; -} - -/* - * call-seq: - * rat.to_s -> string - * - * Returns the value as a string. - * - * 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 f_format(self, f_to_s); -} - -/* - * call-seq: - * rat.inspect -> string - * - * Returns the value as a string for inspection. - * - * For example: - * - * Rational(2).inspect #=> "(2/1)" - * Rational(-8, 6).inspect #=> "(-4/3)" - * Rational('0.5').inspect #=> "(1/2)" - */ -static VALUE -nurat_inspect(VALUE self) -{ - VALUE s; - - s = rb_usascii_str_new2("("); - rb_str_concat(s, f_format(self, f_inspect)); - rb_str_cat2(s, ")"); - - return s; -} - -/* :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); - Check_Type(a, T_ARRAY); - if (RARRAY_LEN(a) != 2) - rb_raise(rb_eArgError, "marshaled rational must have an array whose length is 2 but %ld", RARRAY_LEN(a)); - 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_rational_reciprocal(VALUE x) -{ - get_dat1(x); - return f_rational_new_no_reduce2(CLASS_OF(x), dat->den, dat->num); -} - -/* - * call-seq: - * int.gcd(int2) -> integer - * - * Returns the greatest common divisor (always positive). 0.gcd(x) - * and x.gcd(0) return abs(x). - * - * For example: - * - * 2.gcd(2) #=> 2 - * 3.gcd(-7) #=> 1 - * ((1<<31)-1).gcd((1<<61)-1) #=> 1 - */ -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 (always positive). 0.lcm(x) and - * x.lcm(0) return zero. - * - * For example: - * - * 2.lcm(2) #=> 2 - * 3.lcm(-7) #=> 21 - * ((1<<31)-1).lcm((1<<61)-1) #=> 4951760154835678088235319297 - */ -VALUE -rb_lcm(VALUE self, VALUE other) -{ - other = nurat_int_value(other); - return f_lcm(self, other); -} - -/* - * call-seq: - * int.gcdlcm(int2) -> array - * - * Returns an array; [int.gcd(int2), int.lcm(int2)]. - * - * For example: - * - * 2.gcdlcm(2) #=> [2, 2] - * 3.gcdlcm(-7) #=> [1, 21] - * ((1<<31)-1).gcdlcm((1<<61)-1) #=> [1, 4951760154835678088235319297] - */ -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. - */ -static VALUE -numeric_numerator(VALUE self) -{ - return f_numerator(f_to_r(self)); -} - -/* - * call-seq: - * num.denominator -> integer - * - * Returns the denominator (always positive). - */ -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.denominator -> 1 - * - * Returns 1. - */ -static VALUE -integer_denominator(VALUE self) -{ - return INT2FIX(1); -} - -/* - * call-seq: - * flo.numerator -> integer - * - * Returns the numerator. The result is machine dependent. - * - * For example: - * - * n = 0.3.numerator #=> 5404319552844595 - * d = 0.3.denominator #=> 18014398509481984 - * 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 (always positive). The result is machine - * dependent. - * - * See 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 zero as a rational. - */ -static VALUE -nilclass_to_r(VALUE self) -{ - return rb_rational_new1(INT2FIX(0)); -} - -/* - * call-seq: - * nil.rationalize([eps]) -> (0/1) - * - * Returns zero as a rational. An optional argument eps is always - * ignored. - */ -static VALUE -nilclass_rationalize(int argc, VALUE *argv, VALUE self) -{ - rb_scan_args(argc, argv, "01", NULL); - return nilclass_to_r(self); -} - -/* - * call-seq: - * int.to_r -> rational - * - * Returns the value as a rational. - * - * For example: - * - * 1.to_r #=> (1/1) - * (1<<64).to_r #=> (18446744073709551616/1) - */ -static VALUE -integer_to_r(VALUE self) -{ - return rb_rational_new1(self); -} - -/* - * call-seq: - * int.rationalize([eps]) -> rational - * - * Returns the value as a rational. An optional argument eps is - * always ignored. - */ -static VALUE -integer_rationalize(int argc, VALUE *argv, VALUE self) -{ - rb_scan_args(argc, argv, "01", NULL); - return integer_to_r(self); -} - -static void -float_decode_internal(VALUE self, VALUE *rf, VALUE *rn) -{ - double f; - int n; - - f = frexp(RFLOAT_VALUE(self), &n); - f = ldexp(f, DBL_MANT_DIG); - n -= DBL_MANT_DIG; - *rf = rb_dbl2big(f); - *rn = INT2FIX(n); -} - -#if 0 -static VALUE -float_decode(VALUE self) -{ - VALUE f, n; - - float_decode_internal(self, &f, &n); - return rb_assoc_new(f, n); -} -#endif - -#define id_lshift rb_intern("<<") -#define f_lshift(x,n) rb_funcall((x), id_lshift, 1, (n)) - -/* - * call-seq: - * flt.to_r -> rational - * - * Returns the value as a rational. - * - * NOTE: 0.3.to_r isn't the same as '0.3'.to_r. The latter is - * equivalent to '3/10'.to_r, but the former isn't so. - * - * 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) - */ -static VALUE -float_to_r(VALUE self) -{ - VALUE f, n; - - float_decode_internal(self, &f, &n); -#if FLT_RADIX == 2 - { - long ln = FIX2LONG(n); - - if (ln == 0) - return f_to_r(f); - if (ln > 0) - return f_to_r(f_lshift(f, n)); - ln = -ln; - return rb_rational_new2(f, f_lshift(ONE, INT2FIX(ln))); - } -#else - return f_to_r(f_mul(f, f_expt(INT2FIX(FLT_RADIX), n))); -#endif -} - -/* - * call-seq: - * flt.rationalize([eps]) -> rational - * - * Returns a simpler approximation of the value (flt-|eps| <= result - * <= flt+|eps|). if eps is not given, it will be chosen - * automatically. - * - * For example: - * - * 0.3.rationalize #=> (3/10) - * 1.333.rationalize #=> (1333/1000) - * 1.333.rationalize(0.01) #=> (4/3) - */ -static VALUE -float_rationalize(int argc, VALUE *argv, VALUE self) -{ - VALUE e, a, b, p, q; - - if (f_negative_p(self)) - return f_negate(float_rationalize(argc, argv, f_abs(self))); - - rb_scan_args(argc, argv, "01", &e); - - if (argc != 0) { - e = f_abs(e); - a = f_sub(self, e); - b = f_add(self, e); - } - else { - VALUE f, n; - - float_decode_internal(self, &f, &n); - if (f_zero_p(f) || f_positive_p(n)) - return rb_rational_new1(f_lshift(f, n)); - -#if FLT_RADIX == 2 - a = rb_rational_new2(f_sub(f_mul(TWO, f), ONE), - f_lshift(ONE, f_sub(ONE, n))); - b = rb_rational_new2(f_add(f_mul(TWO, f), ONE), - f_lshift(ONE, f_sub(ONE, n))); -#else - a = rb_rational_new2(f_sub(f_mul(INT2FIX(FLT_RADIX), f), - INT2FIX(FLT_RADIX - 1)), - f_expt(INT2FIX(FLT_RADIX), f_sub(ONE, n))); - b = rb_rational_new2(f_add(f_mul(INT2FIX(FLT_RADIX), f), - INT2FIX(FLT_RADIX - 1)), - f_expt(INT2FIX(FLT_RADIX), f_sub(ONE, n))); -#endif - } - - if (f_eqeq_p(a, b)) - return f_to_r(self); - - nurat_rationalize_internal(a, b, &p, &q); - return rb_rational_new2(p, q); -} - -static VALUE rat_pat, an_e_pat, a_dot_pat, underscores_pat, an_underscore; - -#define WS "\\s*" -#define DIGITS "(?:[0-9](?:_[0-9]|[0-9])*)" -#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_split rb_intern("split") -#define f_split(x,y) rb_funcall((x), id_split, 1, (y)) - -#include <ctype.h> - -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 = rb_reg_nth_match(1, m); - VALUE nu = rb_reg_nth_match(2, m); - VALUE de = rb_reg_nth_match(3, m); - VALUE re = rb_reg_match_post(m); - - { - VALUE a; - - if (!strpbrk(RSTRING_PTR(nu), "eE")) { - ifp = nu; /* not a copy */ - exp = Qnil; - } - else { - 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]; - } - - if (!strchr(RSTRING_PTR(ifp), '.')) { - ip = ifp; /* not a copy */ - fp = Qnil; - } - else { - 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 = RSTRING_PTR(fp); - long count = 0; - VALUE l; - - while (*p) { - if (rb_isdigit(*p)) - count++; - p++; - } - l = f_expt10(LONG2NUM(count)); - v = f_mul(v, l); - v = f_add(v, f_to_i(fp)); - v = f_div(v, l); - } - if (!NIL_P(si) && *RSTRING_PTR(si) == '-') - v = f_negate(v); - if (!NIL_P(exp)) - v = f_mul(v, f_expt10(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 which denotes the string form. The parser - * ignores leading whitespaces and trailing garbage. Any digit - * sequences can be separated by an underscore. Returns zero for null - * or garbage string. - * - * NOTE: '0.3'.to_r isn't the same as 0.3.to_r. The former is - * equivalent to '3/10'.to_r, but the latter isn't so. - * - * For example: - * - * ' 2 '.to_r #=> (2/1) - * '300/2'.to_r #=> (150/1) - * '-9.2'.to_r #=> (-46/5) - * '-9.2e2'.to_r #=> (-920/1) - * '1_234_567'.to_r #=> (1234567/1) - * '21 june 09'.to_r #=> (21/1) - * '21/06/09'.to_r #=> (7/2) - * 'bwv 1079'.to_r #=> (0/1) - */ -static VALUE -string_to_r(VALUE self) -{ - VALUE s, a, a1, 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); - - a1 = RARRAY_PTR(a)[0]; - if (!NIL_P(a1)) { - if (TYPE(a1) == T_FLOAT) - rb_raise(rb_eFloatDomainError, "Infinity"); - return a1; - } - 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_zero_p(RCOMPLEX(a1)->imag)) - a1 = RCOMPLEX(a1)->real; - } - - switch (TYPE(a2)) { - case T_COMPLEX: - if (k_exact_zero_p(RCOMPLEX(a2)->imag)) - a2 = RCOMPLEX(a2)->real; - } - - backref = rb_backref_get(); - rb_match_busy(backref); - - switch (TYPE(a1)) { - case T_FIXNUM: - case T_BIGNUM: - break; - case T_FLOAT: - a1 = f_to_r(a1); - break; - case T_STRING: - a1 = string_to_r_strict(a1); - break; - } - - switch (TYPE(a2)) { - case T_FIXNUM: - case T_BIGNUM: - break; - case T_FLOAT: - a2 = f_to_r(a2); - break; - case T_STRING: - a2 = string_to_r_strict(a2); - break; - } - - rb_backref_set(backref); - - switch (TYPE(a1)) { - case T_RATIONAL: - if (argc == 1 || (k_exact_one_p(a2))) - return a1; - } - - if (argc == 1) { - if (!(k_numeric_p(a1) && k_integer_p(a1))) - return rb_convert_type(a1, T_RATIONAL, "Rational", "to_r"); - } - else { - if ((k_numeric_p(a1) && k_numeric_p(a2)) && - (!f_integer_p(a1) || !f_integer_p(a2))) - return f_div(a1, a2); - } - - { - VALUE argv2[2]; - argv2[0] = a1; - argv2[1] = a2; - return nurat_s_new(argc, argv2, klass); - } -} - -/* - * 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, to_r or - * rationalize 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 rational 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) - * 0.3.rationalize #=> (3/10) - * - * 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) -{ -#undef rb_intern -#define rb_intern(str) rb_intern_const(str) - - assert(fprintf(stderr, "assert() is now active\n")); - - id_abs = rb_intern("abs"); - id_cmp = rb_intern("<=>"); - id_convert = rb_intern("convert"); - id_eqeq_p = rb_intern("=="); - id_expt = rb_intern("**"); - id_fdiv = rb_intern("fdiv"); - id_floor = rb_intern("floor"); - id_idiv = rb_intern("div"); - id_inspect = rb_intern("inspect"); - id_integer_p = rb_intern("integer?"); - id_negate = rb_intern("-@"); - id_to_f = rb_intern("to_f"); - id_to_i = rb_intern("to_i"); - id_to_s = rb_intern("to_s"); - id_truncate = rb_intern("truncate"); - - rb_cRational = rb_define_class("Rational", rb_cNumeric); - - rb_define_alloc_func(rb_cRational, nurat_s_alloc); - rb_undef_method(CLASS_OF(rb_cRational), "allocate"); - -#if 0 - rb_define_private_method(CLASS_OF(rb_cRational), "new!", nurat_s_new_bang, -1); - rb_define_private_method(CLASS_OF(rb_cRational), "new", nurat_s_new, -1); -#else - rb_undef_method(CLASS_OF(rb_cRational), "new"); -#endif - - rb_define_global_function("Rational", nurat_f_rational, -1); - - rb_define_method(rb_cRational, "numerator", nurat_numerator, 0); - rb_define_method(rb_cRational, "denominator", nurat_denominator, 0); - - rb_define_method(rb_cRational, "+", nurat_add, 1); - rb_define_method(rb_cRational, "-", nurat_sub, 1); - rb_define_method(rb_cRational, "*", nurat_mul, 1); - rb_define_method(rb_cRational, "/", nurat_div, 1); - rb_define_method(rb_cRational, "quo", nurat_div, 1); - rb_define_method(rb_cRational, "fdiv", nurat_fdiv, 1); - rb_define_method(rb_cRational, "**", nurat_expt, 1); - - rb_define_method(rb_cRational, "<=>", nurat_cmp, 1); - rb_define_method(rb_cRational, "==", nurat_eqeq_p, 1); - rb_define_method(rb_cRational, "coerce", nurat_coerce, 1); - -#if 0 /* 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, "rationalize", nurat_rationalize, -1); - - rb_define_method(rb_cRational, "hash", nurat_hash, 0); - - rb_define_method(rb_cRational, "to_s", nurat_to_s, 0); - rb_define_method(rb_cRational, "inspect", nurat_inspect, 0); - - rb_define_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_cNilClass, "rationalize", nilclass_rationalize, -1); - rb_define_method(rb_cInteger, "to_r", integer_to_r, 0); - rb_define_method(rb_cInteger, "rationalize", integer_rationalize, -1); - rb_define_method(rb_cFloat, "to_r", float_to_r, 0); - rb_define_method(rb_cFloat, "rationalize", float_rationalize, -1); - - 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: -*/ |