[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
[Guile-commits] GNU Guile branch, stable-2.0, updated. v2.0.9-41-g620c13
From: |
Mark H Weaver |
Subject: |
[Guile-commits] GNU Guile branch, stable-2.0, updated. v2.0.9-41-g620c13e |
Date: |
Sun, 21 Jul 2013 10:54:52 +0000 |
This is an automated email from the git hooks/post-receive script. It was
generated because a ref change was pushed to the repository containing
the project "GNU Guile".
http://git.savannah.gnu.org/cgit/guile.git/commit/?id=620c13e8fc02060e0af8fa38398ee4de745d41e9
The branch, stable-2.0 has been updated
via 620c13e8fc02060e0af8fa38398ee4de745d41e9 (commit)
from 824b9ad8b792ab42c5cc614d66462dfaab489075 (commit)
Those revisions listed above that are new to this repository have
not appeared on any other notification email; so we list those
revisions in full, below.
- Log -----------------------------------------------------------------
commit 620c13e8fc02060e0af8fa38398ee4de745d41e9
Author: Mark H Weaver <address@hidden>
Date: Sat Jul 20 12:29:02 2013 -0400
Rewrite 'rationalize' to fix bugs and improve efficiency.
Fixes <http://bugs.gnu.org/14905>.
Reported by GÃ¶ran Weinholt <address@hidden>.
* libguile/numbers.c (scm_rationalize): Rewrite. Previously an
incorrect algorithm was used which failed in many cases.
* test-suite/tests/numbers.test (rationalize): Add tests.
-----------------------------------------------------------------------
Summary of changes:
libguile/numbers.c | 247 +++++++++++++++++++++++++++++------------
test-suite/tests/numbers.test | 29 +++++
2 files changed, 203 insertions(+), 73 deletions(-)
diff --git a/libguile/numbers.c b/libguile/numbers.c
index 5ee1fc7..b7b91ac 100644
--- a/libguile/numbers.c
+++ b/libguile/numbers.c
@@ -9391,89 +9391,190 @@ SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0,
{
SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real");
SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real");
- eps = scm_abs (eps);
- if (scm_is_false (scm_positive_p (eps)))
- {
- /* eps is either zero or a NaN */
- if (scm_is_true (scm_nan_p (eps)))
- return scm_nan ();
- else if (SCM_INEXACTP (eps))
- return scm_exact_to_inexact (x);
- else
- return x;
- }
- else if (scm_is_false (scm_finite_p (eps)))
- {
- if (scm_is_true (scm_finite_p (x)))
- return flo0;
- else
- return scm_nan ();
- }
- else if (scm_is_false (scm_finite_p (x))) /* checks for both inf and nan */
- return x;
- else if (scm_is_false (scm_less_p (scm_floor (scm_sum (x, eps)),
- scm_ceiling (scm_difference (x, eps)))))
+
+ if (SCM_UNLIKELY (!scm_is_exact (eps) || !scm_is_exact (x)))
{
- /* There's an integer within range; we want the one closest to zero */
- if (scm_is_false (scm_less_p (eps, scm_abs (x))))
- {
- /* zero is within range */
- if (SCM_INEXACTP (x) || SCM_INEXACTP (eps))
- return flo0;
- else
- return SCM_INUM0;
- }
- else if (scm_is_true (scm_positive_p (x)))
- return scm_ceiling (scm_difference (x, eps));
+ if (SCM_UNLIKELY (scm_is_false (scm_finite_p (eps))))
+ {
+ if (scm_is_false (scm_nan_p (eps)) && scm_is_true (scm_finite_p (x)))
+ return flo0;
+ else
+ return scm_nan ();
+ }
+ else if (SCM_UNLIKELY (scm_is_false (scm_finite_p (x))))
+ return x;
else
- return scm_floor (scm_sum (x, eps));
- }
- else
- {
- /* Use continued fractions to find closest ratio. All
- arithmetic is done with exact numbers.
+ return scm_exact_to_inexact
+ (scm_rationalize (scm_inexact_to_exact (x),
+ scm_inexact_to_exact (eps)));
+ }
+ else
+ {
+ /* X and EPS are exact rationals.
+
+ The code that follows is equivalent to the following Scheme code:
+
+ (define (exact-rationalize x eps)
+ (let ((n1 (if (negative? x) -1 1))
+ (x (abs x))
+ (eps (abs eps)))
+ (let ((lo (- x eps))
+ (hi (+ x eps)))
+ (if (<= lo 0)
+ 0
+ (let loop ((nlo (numerator lo)) (dlo (denominator lo))
+ (nhi (numerator hi)) (dhi (denominator hi))
+ (n1 n1) (d1 0) (n2 0) (d2 1))
+ (let-values (((qlo rlo) (floor/ nlo dlo))
+ ((qhi rhi) (floor/ nhi dhi)))
+ (let ((n0 (+ n2 (* n1 qlo)))
+ (d0 (+ d2 (* d1 qlo))))
+ (cond ((zero? rlo) (/ n0 d0))
+ ((< qlo qhi) (/ (+ n0 n1) (+ d0 d1)))
+ (else (loop dhi rhi dlo rlo n0 d0 n1
d1))))))))))
*/
- SCM ex = scm_inexact_to_exact (x);
- SCM int_part = scm_floor (ex);
- SCM tt = SCM_INUM1;
- SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0;
- SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0;
- SCM rx;
- int i = 0;
+ int n1_init = 1;
+ SCM lo, hi;
- ex = scm_difference (ex, int_part); /* x = x-int_part */
- rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */
+ eps = scm_abs (eps);
+ if (scm_is_true (scm_negative_p (x)))
+ {
+ n1_init = -1;
+ x = scm_difference (x, SCM_UNDEFINED);
+ }
- /* We stop after a million iterations just to be absolutely sure
- that we don't go into an infinite loop. The process normally
- converges after less than a dozen iterations.
- */
+ /* X and EPS are non-negative exact rationals. */
- while (++i < 1000000)
- {
- a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */
- b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */
- if (scm_is_false (scm_zero_p (b)) && /* b != 0 */
- scm_is_false
- (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))),
- eps))) /* abs(x-a/b) <= eps */
- {
- SCM res = scm_sum (int_part, scm_divide (a, b));
- if (SCM_INEXACTP (x) || SCM_INEXACTP (eps))
- return scm_exact_to_inexact (res);
- else
- return res;
- }
- rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */
- SCM_UNDEFINED);
- tt = scm_floor (rx); /* tt = floor (rx) */
- a2 = a1;
- b2 = b1;
- a1 = a;
- b1 = b;
- }
- scm_num_overflow (s_scm_rationalize);
+ lo = scm_difference (x, eps);
+ hi = scm_sum (x, eps);
+
+ if (scm_is_false (scm_positive_p (lo)))
+ /* If zero is included in the interval, return it.
+ It is the simplest rational of all. */
+ return SCM_INUM0;
+ else
+ {
+ SCM result;
+ mpz_t n0, d0, n1, d1, n2, d2;
+ mpz_t nlo, dlo, nhi, dhi;
+ mpz_t qlo, rlo, qhi, rhi;
+
+ /* LO and HI are positive exact rationals. */
+
+ /* Our approach here follows the method described by Alan
+ Bawden in a message entitled "(rationalize x y)" on the
+ rrrs-authors mailing list, dated 16 Feb 1988 14:08:28 EST:
+
+
http://groups.csail.mit.edu/mac/ftpdir/scheme-mail/HTML/rrrs-1988/msg00063.html
+
+ In brief, we compute the continued fractions of the two
+ endpoints of the interval (LO and HI). The continued
+ fraction of the result consists of the common prefix of the
+ continued fractions of LO and HI, plus one final term. The
+ final term of the result is the smallest integer contained
+ in the interval between the remainders of LO and HI after
+ the common prefix has been removed.
+
+ The following code lazily computes the continued fraction
+ representations of LO and HI, and simultaneously converts
+ the continued fraction of the result into a rational
+ number. We use MPZ functions directly to avoid type
+ dispatch and GC allocation during the loop. */
+
+ mpz_inits (n0, d0, n1, d1, n2, d2,
+ nlo, dlo, nhi, dhi,
+ qlo, rlo, qhi, rhi,
+ NULL);
+
+ /* The variables N1, D1, N2 and D2 are used to compute the
+ resulting rational from its continued fraction. At each
+ step, N2/D2 and N1/D1 are the last two convergents. They
+ are normally initialized to 0/1 and 1/0, respectively.
+ However, if we negated X then we must negate the result as
+ well, and we do that by initializing N1/D1 to -1/0. */
+ mpz_set_si (n1, n1_init);
+ mpz_set_ui (d1, 0);
+ mpz_set_ui (n2, 0);
+ mpz_set_ui (d2, 1);
+
+ /* The variables NLO, DLO, NHI, and DHI are used to lazily
+ compute the continued fraction representations of LO and HI
+ using Euclid's algorithm. Initially, NLO/DLO == LO and
+ NHI/DHI == HI. */
+ scm_to_mpz (scm_numerator (lo), nlo);
+ scm_to_mpz (scm_denominator (lo), dlo);
+ scm_to_mpz (scm_numerator (hi), nhi);
+ scm_to_mpz (scm_denominator (hi), dhi);
+
+ /* As long as we're using exact arithmetic, the following loop
+ is guaranteed to terminate. */
+ for (;;)
+ {
+ /* Compute the next terms (QLO and QHI) of the continued
+ fractions of LO and HI. */
+ mpz_fdiv_qr (qlo, rlo, nlo, dlo); /* QLO <-- floor (NLO/DLO),
RLO <-- NLO - QLO * DLO */
+ mpz_fdiv_qr (qhi, rhi, nhi, dhi); /* QHI <-- floor (NHI/DHI),
RHI <-- NHI - QHI * DHI */
+
+ /* The next term of the result will be either QLO or
+ QLO+1. Here we compute the next convergent of the
+ result based on the assumption that QLO is the next
+ term. If that turns out to be wrong, we'll adjust
+ these later by adding N1 to N0 and D1 to D0. */
+ mpz_set (n0, n2); mpz_addmul (n0, n1, qlo); /* N0 <-- N2 + (QLO
* N1) */
+ mpz_set (d0, d2); mpz_addmul (d0, d1, qlo); /* D0 <-- D2 + (QLO
* D1) */
+
+ /* We stop iterating when an integer is contained in the
+ interval between the remainders NLO/DLO and NHI/DHI.
+ There are two cases to consider: either NLO/DLO == QLO
+ is an integer (indicated by RLO == 0), or QLO < QHI. */
+ if (mpz_sgn (rlo) == 0 || mpz_cmp (qlo, qhi)
+ != 0) break;
+
+ /* Efficiently shuffle variables around for the next
+ iteration. First we shift the recent convergents. */
+ mpz_swap (n2, n1); mpz_swap (n1, n0); /* N2 <-- N1 <-- N0 */
+ mpz_swap (d2, d1); mpz_swap (d1, d0); /* D2 <-- D1 <-- D0 */
+
+ /* The following shuffling is a bit confusing, so some
+ explanation is in order. Conceptually, we're doing a
+ couple of things here. After substracting the floor of
+ NLO/DLO, the remainder is RLO/DLO. The rest of the
+ continued fraction will represent the remainder's
+ reciprocal DLO/RLO. Similarly for the HI endpoint.
+ So in the next iteration, the new endpoints will be
+ DLO/RLO and DHI/RHI. However, when we take the
+ reciprocals of these endpoints, their order is
+ switched. So in summary, we want NLO/DLO <-- DHI/RHI
+ and NHI/DHI <-- DLO/RLO. */
+ mpz_swap (nlo, dhi); mpz_swap (dhi, rlo); /* NLO <-- DHI <-- RLO
*/
+ mpz_swap (nhi, dlo); mpz_swap (dlo, rhi); /* NHI <-- DLO <-- RHI
*/
+ }
+
+ /* There is now an integer in the interval [NLO/DLO NHI/DHI].
+ The last term of the result will be the smallest integer in
+ that interval, which is ceiling(NLO/DLO). We have already
+ computed floor(NLO/DLO) in QLO, so now we adjust QLO to be
+ equal to the ceiling. */
+ if (mpz_sgn (rlo) != 0)
+ {
+ /* If RLO is non-zero, then NLO/DLO is not an integer and
+ the next term will be QLO+1. QLO was used in the
+ computation of N0 and D0 above. Here we adjust N0 and
+ D0 to be based on QLO+1 instead of QLO. */
+ mpz_add (n0, n0, n1); /* N0 <-- N0 + N1 */
+ mpz_add (d0, d0, d1); /* D0 <-- D0 + D1 */
+ }
+
+ /* The simplest rational in the interval is N0/D0 */
+ result = scm_i_make_ratio_already_reduced (scm_from_mpz (n0),
+ scm_from_mpz (d0));
+ mpz_clears (n0, d0, n1, d1, n2, d2,
+ nlo, dlo, nhi, dhi,
+ qlo, rlo, qhi, rhi,
+ NULL);
+ return result;
+ }
}
}
#undef FUNC_NAME
diff --git a/test-suite/tests/numbers.test b/test-suite/tests/numbers.test
index a36d493..ffbbea2 100644
--- a/test-suite/tests/numbers.test
+++ b/test-suite/tests/numbers.test
@@ -1431,6 +1431,35 @@
(pass-if (eqv? 1/3 (rationalize 3/10 -1/10)))
(pass-if (eqv? -1/3 (rationalize -3/10 -1/10)))
+ ;; Prior to Guile 2.0.10, rationalize used a faulty algorithm that
+ ;; incorrectly returned 2/3 and -2/3 in the following cases.
+ (pass-if (eqv? 1/2 (rationalize #e+0.67 1/4)))
+ (pass-if (eqv? -1/2 (rationalize #e-0.67 1/4)))
+
+ (pass-if (eqv? 1 (rationalize #e+0.67 1/3)))
+ (pass-if (eqv? -1 (rationalize #e-0.67 1/3)))
+
+ (pass-if (eqv? 1/2 (rationalize #e+0.66 1/3)))
+ (pass-if (eqv? -1/2 (rationalize #e-0.66 1/3)))
+
+ (pass-if (eqv? 1 (rationalize #e+0.67 2/3)))
+ (pass-if (eqv? -1 (rationalize #e-0.67 2/3)))
+
+ (pass-if (eqv? 0 (rationalize #e+0.66 2/3)))
+ (pass-if (eqv? 0 (rationalize #e-0.66 2/3)))
+
+ ;; Prior to Guile 2.0.10, rationalize used a faulty algorithm that
+ ;; incorrectly computed the following approximations of PI.
+ (with-test-prefix "pi"
+ (define *pi*
#e3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679)
+ (pass-if (eqv? 16/5 (rationalize *pi* 1/10)))
+ (pass-if (eqv? 201/64 (rationalize *pi* 1/1000)))
+ (pass-if (eqv? 75948/24175 (rationalize *pi* (expt 10 -7))))
+ (pass-if (eqv? 100798/32085 (rationalize *pi* (expt 10 -8))))
+ (pass-if (eqv? 58466453/18610450 (rationalize *pi* (expt 10 -14))))
+ (pass-if (eqv?
2307954651196778721982809475299879198775111361078/734644782339796933783743757007944508986600750685
+ (rationalize *pi* (expt 10 -95)))))
+
(pass-if (test-eqv? (/ 1.0 3) (rationalize 0.3 1/10)))
(pass-if (test-eqv? (/ -1.0 3) (rationalize -0.3 1/10)))
(pass-if (test-eqv? (/ 1.0 3) (rationalize 0.3 -1/10)))
hooks/post-receive
--
GNU Guile
[Prev in Thread] |
Current Thread |
[Next in Thread] |
- [Guile-commits] GNU Guile branch, stable-2.0, updated. v2.0.9-41-g620c13e,
Mark H Weaver <=