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* complex.c (nucomp_rationalize) added. [experimental]
* rational.c ({nurat,nilclass,integer,float}_rationalize) ditto.
git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@24565 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
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@ -1,3 +1,9 @@
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Mon Aug 17 08:14:26 2009 Tadayoshi Funaba <tadf@dotrb.org>
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* complex.c (nucomp_rationalize) added. [experimental]
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* rational.c ({nurat,nilclass,integer,float}_rationalize) ditto.
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Mon Aug 17 08:11:53 2009 Tadayoshi Funaba <tadf@dotrb.org>
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* lib/cmath.rb: use num#i.
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15
complex.c
15
complex.c
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@ -1377,6 +1377,20 @@ nucomp_to_r(VALUE self)
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return f_to_r(dat->real);
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}
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/*
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* call-seq:
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* cmp.rationalize([eps]) -> rational
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*
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* Returns the value as a rational if possible. An optional argument
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* eps is always ignored.
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*/
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static VALUE
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nucomp_rationalize(int argc, VALUE *argv, VALUE self)
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{
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rb_scan_args(argc, argv, "01", NULL);
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return nucomp_to_r(self);
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}
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/*
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* call-seq:
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* nil.to_c -> (0+0i)
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@ -1967,6 +1981,7 @@ Init_Complex(void)
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rb_define_method(rb_cComplex, "to_i", nucomp_to_i, 0);
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rb_define_method(rb_cComplex, "to_f", nucomp_to_f, 0);
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rb_define_method(rb_cComplex, "to_r", nucomp_to_r, 0);
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rb_define_method(rb_cComplex, "rationalize", nucomp_rationalize, -1);
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rb_define_method(rb_cNilClass, "to_c", nilclass_to_c, 0);
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rb_define_method(rb_cNumeric, "to_c", numeric_to_c, 0);
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225
rational.c
225
rational.c
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@ -1356,6 +1356,141 @@ nurat_to_r(VALUE self)
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return self;
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}
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#define id_ceil rb_intern("ceil")
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#define f_ceil(x) rb_funcall(x, id_ceil, 0)
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#define id_quo rb_intern("quo")
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#define f_quo(x,y) rb_funcall(x, id_quo, 1, y)
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#define f_reciprocal(x) f_quo(ONE, x)
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/*
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The algorithm here is the method described in CLISP. Bruno Haible has
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graciously given permission to use this algorithm. He says, "You can use
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it, if you present the following explanation of the algorithm."
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Algorithm (recursively presented):
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If x is a rational number, return x.
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If x = 0.0, return 0.
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If x < 0.0, return (- (rationalize (- x))).
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If x > 0.0:
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Call (integer-decode-float x). It returns a m,e,s=1 (mantissa,
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exponent, sign).
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If m = 0 or e >= 0: return x = m*2^e.
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Search a rational number between a = (m-1/2)*2^e and b = (m+1/2)*2^e
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with smallest possible numerator and denominator.
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Note 1: If m is a power of 2, we ought to take a = (m-1/4)*2^e.
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But in this case the result will be x itself anyway, regardless of
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the choice of a. Therefore we can simply ignore this case.
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Note 2: At first, we need to consider the closed interval [a,b].
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but since a and b have the denominator 2^(|e|+1) whereas x itself
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has a denominator <= 2^|e|, we can restrict the seach to the open
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interval (a,b).
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So, for given a and b (0 < a < b) we are searching a rational number
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y with a <= y <= b.
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Recursive algorithm fraction_between(a,b):
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c := (ceiling a)
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if c < b
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then return c ; because a <= c < b, c integer
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else
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; a is not integer (otherwise we would have had c = a < b)
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k := c-1 ; k = floor(a), k < a < b <= k+1
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return y = k + 1/fraction_between(1/(b-k), 1/(a-k))
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; note 1 <= 1/(b-k) < 1/(a-k)
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You can see that we are actually computing a continued fraction expansion.
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Algorithm (iterative):
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If x is rational, return x.
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Call (integer-decode-float x). It returns a m,e,s (mantissa,
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exponent, sign).
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If m = 0 or e >= 0, return m*2^e*s. (This includes the case x = 0.0.)
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Create rational numbers a := (2*m-1)*2^(e-1) and b := (2*m+1)*2^(e-1)
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(positive and already in lowest terms because the denominator is a
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power of two and the numerator is odd).
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Start a continued fraction expansion
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p[-1] := 0, p[0] := 1, q[-1] := 1, q[0] := 0, i := 0.
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Loop
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c := (ceiling a)
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if c >= b
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then k := c-1, partial_quotient(k), (a,b) := (1/(b-k),1/(a-k)),
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goto Loop
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finally partial_quotient(c).
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Here partial_quotient(c) denotes the iteration
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i := i+1, p[i] := c*p[i-1]+p[i-2], q[i] := c*q[i-1]+q[i-2].
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At the end, return s * (p[i]/q[i]).
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This rational number is already in lowest terms because
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p[i]*q[i-1]-p[i-1]*q[i] = (-1)^i.
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*/
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static void
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nurat_rationalize_internal(VALUE a, VALUE b, VALUE *p, VALUE *q)
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{
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VALUE c, k, t, p0, p1, p2, q0, q1, q2;
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p0 = ZERO;
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p1 = ONE;
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q0 = ONE;
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q1 = ZERO;
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while (1) {
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c = f_ceil(a);
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if (f_lt_p(c, b))
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break;
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k = f_sub(c, ONE);
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p2 = f_add(f_mul(k, p1), p0);
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q2 = f_add(f_mul(k, q1), q0);
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t = f_reciprocal(f_sub(b, k));
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b = f_reciprocal(f_sub(a, k));
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a = t;
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p0 = p1;
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q0 = q1;
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p1 = p2;
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q1 = q2;
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}
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*p = f_add(f_mul(c, p1), p0);
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*q = f_add(f_mul(c, q1), q0);
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}
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/*
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* call-seq:
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* rat.rationalize -> self
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* rat.rationalize(eps) -> rational
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*
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* Returns a simpler approximation of the value if an optional
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* argument eps is given (rat-|eps| <= result <= rat+|eps|), self
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* otherwise.
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*
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* For example:
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*
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* r = Rational(5033165, 16777216)
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* r.rationalize #=> (5033165/16777216)
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* r.rationalize(Rational('0.01')) #=> (3/10)
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* r.rationalize(Rational('0.1')) #=> (1/3)
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*/
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static VALUE
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nurat_rationalize(int argc, VALUE *argv, VALUE self)
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{
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VALUE e, a, b, p, q;
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if (argc == 0)
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return self;
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if (f_negative_p(self))
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return f_negate(nurat_rationalize(argc, argv, f_abs(self)));
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rb_scan_args(argc, argv, "01", &e);
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e = f_abs(e);
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a = f_sub(self, e);
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b = f_add(self, e);
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if (f_eqeq_p(a, b))
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return self;
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nurat_rationalize_internal(a, b, &p, &q);
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return f_rational_new2(CLASS_OF(self), p, q);
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}
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/* :nodoc: */
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static VALUE
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nurat_hash(VALUE self)
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@ -1653,6 +1788,20 @@ nilclass_to_r(VALUE self)
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return rb_rational_new1(INT2FIX(0));
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}
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/*
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* call-seq:
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* nil.rationalize([eps]) -> (0/1)
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*
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* Returns zero as a rational. An optional argument eps is always
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* ignored.
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*/
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static VALUE
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nilclass_rationalize(int argc, VALUE *argv, VALUE self)
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{
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rb_scan_args(argc, argv, "01", NULL);
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return nilclass_to_r(self);
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}
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/*
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* call-seq:
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* int.to_r -> rational
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@ -1670,6 +1819,20 @@ integer_to_r(VALUE self)
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return rb_rational_new1(self);
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}
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/*
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* call-seq:
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* int.rationalize([eps]) -> rational
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*
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* Returns the value as a rational. An optional argument eps is
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* always ignored.
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*/
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static VALUE
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integer_rationalize(int argc, VALUE *argv, VALUE self)
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{
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rb_scan_args(argc, argv, "01", NULL);
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return integer_to_r(self);
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}
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static void
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float_decode_internal(VALUE self, VALUE *rf, VALUE *rn)
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{
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@ -1735,6 +1898,64 @@ float_to_r(VALUE self)
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#endif
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}
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/*
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* call-seq:
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* flt.rationalize([eps]) -> rational
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*
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* Returns a simpler approximation of the value (flt-|eps| <= result
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* <= flt+|eps|). if eps is not given, it will be chosen
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* automatically.
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*
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* For example:
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*
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* 0.3.rationalize #=> (3/10)
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* 1.333.rationalize #=> (1333/1000)
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* 1.333.rationalize(0.01) #=> (4/3)
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*/
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static VALUE
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float_rationalize(int argc, VALUE *argv, VALUE self)
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{
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VALUE e, a, b, p, q;
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if (f_negative_p(self))
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return f_negate(float_rationalize(argc, argv, f_abs(self)));
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rb_scan_args(argc, argv, "01", &e);
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if (argc != 0) {
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e = f_abs(e);
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a = f_sub(self, e);
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b = f_add(self, e);
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}
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else {
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VALUE f, n;
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float_decode_internal(self, &f, &n);
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if (f_zero_p(f) || f_positive_p(n))
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return rb_rational_new1(f_lshift(f, n));
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#if FLT_RADIX == 2
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a = rb_rational_new2(f_sub(f_mul(TWO, f), ONE),
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f_lshift(ONE, f_sub(ONE, n)));
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b = rb_rational_new2(f_add(f_mul(TWO, f), ONE),
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f_lshift(ONE, f_sub(ONE, n)));
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#else
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a = rb_rational_new2(f_sub(f_mul(INT2FIX(FLT_RADIX), f),
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INT2FIX(FLT_RADIX - 1)),
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f_expt(INT2FIX(FLT_RADIX), f_sub(ONE, n)));
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b = rb_rational_new2(f_add(f_mul(INT2FIX(FLT_RADIX), f),
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INT2FIX(FLT_RADIX - 1)),
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f_expt(INT2FIX(FLT_RADIX), f_sub(ONE, n)));
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#endif
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}
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if (f_eqeq_p(a, b))
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return f_to_r(self);
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nurat_rationalize_internal(a, b, &p, &q);
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return rb_rational_new2(p, q);
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}
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static VALUE rat_pat, an_e_pat, a_dot_pat, underscores_pat, an_underscore;
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#define WS "\\s*"
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@ -2103,6 +2324,7 @@ Init_Rational(void)
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rb_define_method(rb_cRational, "to_i", nurat_truncate, 0);
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rb_define_method(rb_cRational, "to_f", nurat_to_f, 0);
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rb_define_method(rb_cRational, "to_r", nurat_to_r, 0);
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rb_define_method(rb_cRational, "rationalize", nurat_rationalize, -1);
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rb_define_method(rb_cRational, "hash", nurat_hash, 0);
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@ -2128,8 +2350,11 @@ Init_Rational(void)
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rb_define_method(rb_cFloat, "denominator", float_denominator, 0);
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rb_define_method(rb_cNilClass, "to_r", nilclass_to_r, 0);
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rb_define_method(rb_cNilClass, "rationalize", nilclass_rationalize, -1);
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rb_define_method(rb_cInteger, "to_r", integer_to_r, 0);
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rb_define_method(rb_cInteger, "rationalize", integer_rationalize, -1);
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rb_define_method(rb_cFloat, "to_r", float_to_r, 0);
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rb_define_method(rb_cFloat, "rationalize", float_rationalize, -1);
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make_patterns();
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@ -964,6 +964,61 @@ class Rational_Test < Test::Unit::TestCase
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end
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end
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def test_rationalize
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c = nil.rationalize
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assert_equal([0,1], [c.numerator, c.denominator])
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c = 0.rationalize
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assert_equal([0,1], [c.numerator, c.denominator])
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c = 1.rationalize
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assert_equal([1,1], [c.numerator, c.denominator])
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c = 1.1.rationalize
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assert_equal([11, 10], [c.numerator, c.denominator])
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c = Rational(1,2).rationalize
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assert_equal([1,2], [c.numerator, c.denominator])
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assert_equal(nil.rationalize(Rational(1,10)), Rational(0))
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assert_equal(0.rationalize(Rational(1,10)), Rational(0))
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assert_equal(10.rationalize(Rational(1,10)), Rational(10))
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r = 0.3333
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assert_equal(r.rationalize, Rational(3333, 10000))
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assert_equal(r.rationalize(Rational(1,10)), Rational(1,3))
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assert_equal(r.rationalize(Rational(-1,10)), Rational(1,3))
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r = Rational(5404319552844595,18014398509481984)
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assert_equal(r.rationalize, r)
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assert_equal(r.rationalize(Rational(1,10)), Rational(1,3))
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assert_equal(r.rationalize(Rational(-1,10)), Rational(1,3))
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r = -0.3333
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assert_equal(r.rationalize, Rational(-3333, 10000))
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assert_equal(r.rationalize(Rational(1,10)), Rational(-1,3))
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assert_equal(r.rationalize(Rational(-1,10)), Rational(-1,3))
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r = Rational(-5404319552844595,18014398509481984)
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assert_equal(r.rationalize, r)
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assert_equal(r.rationalize(Rational(1,10)), Rational(-1,3))
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assert_equal(r.rationalize(Rational(-1,10)), Rational(-1,3))
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if @complex
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if @keiju
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else
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assert_raise(RangeError){Complex(1,2).rationalize}
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end
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end
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if (0.0/0).nan?
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assert_raise(FloatDomainError){(0.0/0).rationalize}
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end
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if (1.0/0).infinite?
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assert_raise(FloatDomainError){(1.0/0).rationalize}
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end
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end
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def test_gcdlcm
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assert_equal(7, 91.gcd(-49))
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assert_equal(5, 5.gcd(0))
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