>From baa6ae8724fd4cd7631164a89bf8eed4ff79cfc0 Mon Sep 17 00:00:00 2001
From: Paul Eggert <address@hidden>
Date: Wed, 5 Sep 2018 00:21:02 -0700
Subject: [PATCH] Improve (round FIXNUM FIXNUM) performance

* src/floatfns.c (rounding_driver):
New arg fixnum_divide.  All callers changed.
(ceiling2, floor2, truncate2, round2): New functions.
Not that new, actually; these are essentially taken from Emacs 26.
(Fceiling, Ffloor, Fround, Ftruncate): Use them.
---
 src/floatfns.c | 74 +++++++++++++++++++++++++++++++++++---------------
 1 file changed, 52 insertions(+), 22 deletions(-)

diff --git a/src/floatfns.c b/src/floatfns.c
index 13ab7b0359..dc7236353c 100644
--- a/src/floatfns.c
+++ b/src/floatfns.c
@@ -339,6 +339,7 @@ static Lisp_Object
 rounding_driver (Lisp_Object arg, Lisp_Object divisor,
 		 double (*double_round) (double),
 		 void (*int_divide) (mpz_t, mpz_t const, mpz_t const),
+		 EMACS_INT (*fixnum_divide) (EMACS_INT, EMACS_INT),
 		 const char *name)
 {
   CHECK_NUMBER (arg);
@@ -357,8 +358,14 @@ rounding_driver (Lisp_Object arg, Lisp_Object divisor,
 	{
 	  /* Divide as integers.  Converting to double might lose
 	     info, even for fixnums; also see the FIXME below.  */
-	  if (EQ (divisor, make_fixnum (0)))
-	    xsignal0 (Qarith_error);
+	  if (FIXNUMP (divisor))
+	    {
+	      if (XFIXNUM (divisor) == 0)
+		xsignal0 (Qarith_error);
+	      if (FIXNUMP (arg))
+		return make_int (fixnum_divide (XFIXNUM (arg),
+						XFIXNUM (divisor)));
+	    }
 	  int_divide (mpz[0],
 		      *bignum_integer (&mpz[0], arg),
 		      *bignum_integer (&mpz[1], divisor));
@@ -387,26 +394,47 @@ rounding_driver (Lisp_Object arg, Lisp_Object divisor,
   return double_to_bignum (dr);
 }
 
-static void
-rounddiv_q (mpz_t q, mpz_t const n, mpz_t const d)
+static EMACS_INT
+ceiling2 (EMACS_INT n, EMACS_INT 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.
+  return n / d + ((n % d != 0) & ((n < 0) == (d < 0)));
+}
 
-     If we were using EMACS_INT arithmetic instead of bignums,
-     the following code could look something like this:
+static EMACS_INT
+floor2 (EMACS_INT n, EMACS_INT d)
+{
+  return n / d - ((n % d != 0) & ((n < 0) != (d < 0)));
+}
 
-     q = n / d;
-     r = n % d;
-     neg_d = d < 0;
-     neg_r = r < 0;
-     abs_r = eabs (r);
-     abs_r1 = eabs (d) - abs_r;
-     if (abs_r1 < abs_r + (q & 1))
-       q += neg_d == neg_r ? 1 : -1;  */
+static EMACS_INT
+truncate2 (EMACS_INT n, EMACS_INT d)
+{
+  return n / d;
+}
 
+static EMACS_INT
+round2 (EMACS_INT n, EMACS_INT d)
+{
+  /* The C language's division operator gives us the remainder R
+     corresponding to truncated division, 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 truncated quotient is odd.  */
+  EMACS_INT q = n / d;
+  EMACS_INT r = n % d;
+  bool neg_d = d < 0;
+  bool neg_r = r < 0;
+  EMACS_INT abs_r = eabs (r);
+  EMACS_INT abs_r1 = eabs (d) - abs_r;
+  if (abs_r1 < abs_r + (q & 1))
+    q += neg_d == neg_r ? 1 : -1;
+  return q;
+}
+
+static void
+rounddiv_q (mpz_t q, mpz_t const n, mpz_t const d)
+{
+  /* Mimic the source code of round2, using mpz_t instead of EMACS_INT.  */
   mpz_t *r = &mpz[2], *abs_r = r, *abs_r1 = &mpz[3];
   mpz_tdiv_qr (q, *r, n, d);
   bool neg_d = mpz_sgn (d) < 0;
@@ -446,7 +474,7 @@ This rounds the value towards +inf.
 With optional DIVISOR, return the smallest integer no less than ARG/DIVISOR.  */)
   (Lisp_Object arg, Lisp_Object divisor)
 {
-  return rounding_driver (arg, divisor, ceil, mpz_cdiv_q, "ceiling");
+  return rounding_driver (arg, divisor, ceil, mpz_cdiv_q, ceiling2, "ceiling");
 }
 
 DEFUN ("floor", Ffloor, Sfloor, 1, 2, 0,
@@ -455,7 +483,7 @@ This rounds the value towards -inf.
 With optional DIVISOR, return the largest integer no greater than ARG/DIVISOR.  */)
   (Lisp_Object arg, Lisp_Object divisor)
 {
-  return rounding_driver (arg, divisor, floor, mpz_fdiv_q, "floor");
+  return rounding_driver (arg, divisor, floor, mpz_fdiv_q, floor2, "floor");
 }
 
 DEFUN ("round", Fround, Sround, 1, 2, 0,
@@ -468,7 +496,8 @@ your machine.  For example, (round 2.5) can return 3 on some
 systems, but 2 on others.  */)
   (Lisp_Object arg, Lisp_Object divisor)
 {
-  return rounding_driver (arg, divisor, emacs_rint, rounddiv_q, "round");
+  return rounding_driver (arg, divisor, emacs_rint, rounddiv_q, round2,
+			  "round");
 }
 
 /* Since rounding_driver truncates anyway, no need to call 'trunc'.  */
@@ -484,7 +513,8 @@ Rounds ARG toward zero.
 With optional DIVISOR, truncate ARG/DIVISOR.  */)
   (Lisp_Object arg, Lisp_Object divisor)
 {
-  return rounding_driver (arg, divisor, identity, mpz_tdiv_q, "truncate");
+  return rounding_driver (arg, divisor, identity, mpz_tdiv_q, truncate2,
+			  "truncate");
 }
 
 
-- 
2.17.1