static Lisp_Object
rounding_driver (Lisp_Object arg, Lisp_Object divisor,
double (*double_round) (double),
- EMACS_INT (*int_round2) (EMACS_INT, EMACS_INT),
+ void (*int_divide) (mpz_t, mpz_t const, mpz_t const),
const char *name)
{
- CHECK_FIXNUM_OR_FLOAT (arg);
+ CHECK_NUMBER (arg);
double d;
if (NILP (divisor))
}
else
{
- CHECK_FIXNUM_OR_FLOAT (divisor);
+ CHECK_NUMBER (divisor);
if (!FLOATP (arg) && !FLOATP (divisor))
{
- if (XFIXNUM (divisor) == 0)
+ if (EQ (divisor, make_fixnum (0)))
xsignal0 (Qarith_error);
- return make_fixnum (int_round2 (XFIXNUM (arg), XFIXNUM (divisor)));
+ mpz_t d, q;
+ mpz_init (d);
+ mpz_init (q);
+ int_divide (q,
+ (FIXNUMP (arg)
+ ? (mpz_set_intmax (q, XFIXNUM (arg)), q)
+ : XBIGNUM (arg)->value),
+ (FIXNUMP (divisor)
+ ? (mpz_set_intmax (d, XFIXNUM (divisor)), d)
+ : XBIGNUM (divisor)->value));
+ Lisp_Object result = make_number (q);
+ mpz_clear (d);
+ mpz_clear (q);
+ return result;
}
double f1 = FLOATP (arg) ? XFLOAT_DATA (arg) : XFIXNUM (arg);
xsignal2 (Qrange_error, build_string (name), arg);
}
-static EMACS_INT
-ceiling2 (EMACS_INT i1, EMACS_INT i2)
-{
- return i1 / i2 + ((i1 % i2 != 0) & ((i1 < 0) == (i2 < 0)));
-}
-
-static EMACS_INT
-floor2 (EMACS_INT i1, EMACS_INT i2)
-{
- return i1 / i2 - ((i1 % i2 != 0) & ((i1 < 0) != (i2 < 0)));
-}
-
-static EMACS_INT
-truncate2 (EMACS_INT i1, EMACS_INT i2)
-{
- return i1 / i2;
-}
-
-static EMACS_INT
-round2 (EMACS_INT i1, EMACS_INT i2)
-{
- /* The C language's division operator gives us one remainder R, but
- we want the remainder R1 on the other side of 0 if R1 is closer
- to 0 than R is; because we want to round to even, we also want R1
- if R and R1 are the same distance from 0 and if C's quotient is
- odd. */
- EMACS_INT q = i1 / i2;
- EMACS_INT r = i1 % i2;
- EMACS_INT abs_r = eabs (r);
- EMACS_INT abs_r1 = eabs (i2) - abs_r;
- return q + (abs_r + (q & 1) <= abs_r1 ? 0 : (i2 ^ r) < 0 ? -1 : 1);
+static void
+rounddiv_q (mpz_t q, mpz_t const n, mpz_t const d)
+{
+ /* mpz_tdiv_qr gives us one remainder R, but we want the remainder
+ R1 on the other side of 0 if R1 is closer to 0 than R is; because
+ we want to round to even, we also want R1 if R and R1 are the
+ same distance from 0 and if the quotient is odd.
+
+ If we were using EMACS_INT arithmetic instead of bignums,
+ the following code could look something like this:
+
+ q = n / d;
+ r = n % d;
+ neg_d = d < 0;
+ neg_r = r < 0;
+ r = eabs (r);
+ abs_r1 = eabs (d) - r;
+ if (abs_r1 < r + (q & 1))
+ q += neg_d == neg_r ? 1 : -1; */
+
+ mpz_t r, abs_r1;
+ mpz_init (r);
+ mpz_init (abs_r1);
+ mpz_tdiv_qr (q, r, n, d);
+ bool neg_d = mpz_sgn (d) < 0;
+ bool neg_r = mpz_sgn (r) < 0;
+ mpz_abs (r, r);
+ mpz_abs (abs_r1, d);
+ mpz_sub (abs_r1, abs_r1, r);
+ if (mpz_cmp (abs_r1, r) < (mpz_odd_p (q) != 0))
+ (neg_d == neg_r ? mpz_add_ui : mpz_sub_ui) (q, q, 1);
+ mpz_clear (r);
+ mpz_clear (abs_r1);
}
/* The code uses emacs_rint, so that it works to undefine HAVE_RINT
With optional DIVISOR, return the smallest integer no less than ARG/DIVISOR. */)
(Lisp_Object arg, Lisp_Object divisor)
{
- return rounding_driver (arg, divisor, ceil, ceiling2, "ceiling");
+ return rounding_driver (arg, divisor, ceil, mpz_cdiv_q, "ceiling");
}
DEFUN ("floor", Ffloor, Sfloor, 1, 2, 0,
With optional DIVISOR, return the largest integer no greater than ARG/DIVISOR. */)
(Lisp_Object arg, Lisp_Object divisor)
{
- return rounding_driver (arg, divisor, floor, floor2, "floor");
+ return rounding_driver (arg, divisor, floor, mpz_fdiv_q, "floor");
}
DEFUN ("round", Fround, Sround, 1, 2, 0,
systems, but 2 on others. */)
(Lisp_Object arg, Lisp_Object divisor)
{
- return rounding_driver (arg, divisor, emacs_rint, round2, "round");
+ return rounding_driver (arg, divisor, emacs_rint, rounddiv_q, "round");
}
DEFUN ("truncate", Ftruncate, Struncate, 1, 2, 0,
With optional DIVISOR, truncate ARG/DIVISOR. */)
(Lisp_Object arg, Lisp_Object divisor)
{
- return rounding_driver (arg, divisor, trunc, truncate2, "truncate");
+ return rounding_driver (arg, divisor, trunc, mpz_tdiv_q, "truncate");
}
(ert-deftest bignum-mod ()
(should (= 0 (mod (1+ most-positive-fixnum) 2.0))))
+(ert-deftest bignum-round ()
+ (let ((ns (list (* most-positive-fixnum most-negative-fixnum)
+ (1- most-negative-fixnum) most-negative-fixnum
+ (1+ most-negative-fixnum) -2 1 1 2
+ (1- most-positive-fixnum) most-positive-fixnum
+ (1+ most-positive-fixnum)
+ (* most-positive-fixnum most-positive-fixnum))))
+ (dolist (n ns)
+ (dolist (d ns)
+ (let ((q (/ n d))
+ (r (% n d))
+ (same-sign (eq (< n 0) (< d 0))))
+ (should (= (ceiling n d)
+ (+ q (if (and same-sign (not (zerop r))) 1 0))))
+ (should (= (floor n d)
+ (- q (if (and (not same-sign) (not (zerop r))) 1 0))))
+ (should (= (truncate n d) q))
+ (let ((cdelta (abs (- n (* d (ceiling n d)))))
+ (fdelta (abs (- n (* d (floor n d)))))
+ (rdelta (abs (- n (* d (round n d))))))
+ (should (<= rdelta cdelta))
+ (should (<= rdelta fdelta))
+ (should (if (zerop r)
+ (= 0 cdelta fdelta rdelta)
+ (or (/= cdelta fdelta)
+ (zerop (% (round n d) 2)))))))))))
+
(provide 'floatfns-tests)