Re: new module 'fmodl'

[Bruno Haible]

> long double
> fmodl (long double x, long double y)
> {
>   long double i = truncl (x / y);
>   return fmal (- i, y, x);
> }

Oops, 1 bug in 2 lines of code, is a bad ratio. I was not thinking at the
effects of rounding errors. This should fix it:


2012-02-25  Bruno Haible  <address@hidden>

        fmodl, remainder*: Avoid wrong results due to rounding errors.
        * lib/fmodl.c (fmodl): Correct the result if it is not within the
        expected bounds.
        * lib/remainderf.c (remainderf): Likewise.
        * lib/remainder.c (remainder): Likewise.
        * lib/remainderl.c (remainderl): Likewise.

--- lib/fmodl.c.orig    Sun Feb 26 00:31:10 2012
+++ lib/fmodl.c Sat Feb 25 23:28:43 2012
@@ -32,8 +32,48 @@
 long double
 fmodl (long double x, long double y)
 {
-  long double i = truncl (x / y);
-  return fmal (- i, y, x);
+  long double q = - truncl (x / y);
+  long double r = fmal (q, y, x); /* = x + q * y, computed in one step */
+  /* Correct possible rounding errors in the quotient x / y.  */
+  if (y >= 0)
+    {
+      if (x >= 0)
+        {
+          /* Expect 0 <= r < y.  */
+          if (r < 0)
+            q += 1, r = fmal (q, y, x);
+          else if (r >= y)
+            q -= 1, r = fmal (q, y, x);
+        }
+      else
+        {
+          /* Expect - y < r <= 0.  */
+          if (r > 0)
+            q -= 1, r = fmal (q, y, x);
+          else if (r <= - y)
+            q += 1, r = fmal (q, y, x);
+        }
+    }
+  else
+    {
+      if (x >= 0)
+        {
+          /* Expect 0 <= r < - y.  */
+          if (r < 0)
+            q -= 1, r = fmal (q, y, x);
+          else if (r >= - y)
+            q += 1, r = fmal (q, y, x);
+        }
+      else
+        {
+          /* Expect y < r <= 0.  */
+          if (r > 0)
+            q += 1, r = fmal (q, y, x);
+          else if (r <= y)
+            q -= 1, r = fmal (q, y, x);
+        }
+    }
+  return r;
 }
 
 #endif
--- lib/remainder.c.orig        Sun Feb 26 00:31:10 2012
+++ lib/remainder.c     Sat Feb 25 23:31:24 2012
@@ -22,6 +22,25 @@
 double
 remainder (double x, double y)
 {
-  double i = round (x / y);
-  return fma (- i, y, x);
+  double q = - round (x / y);
+  double r = fma (q, y, x); /* = x + q * y, computed in one step */
+  /* Correct possible rounding errors in the quotient x / y.  */
+  double half_y = 0.5L * y;
+  if (y >= 0)
+    {
+      /* Expect -y/2 <= r <= y/2.  */
+      if (r > half_y)
+        q -= 1, r = fma (q, y, x);
+      else if (r < - half_y)
+        q += 1, r = fma (q, y, x);
+    }
+  else
+    {
+      /* Expect y/2 <= r <= -y/2.  */
+      if (r > - half_y)
+        q += 1, r = fma (q, y, x);
+      else if (r < half_y)
+        q -= 1, r = fma (q, y, x);
+    }
+  return r;
 }
--- lib/remainderf.c.orig       Sun Feb 26 00:31:10 2012
+++ lib/remainderf.c    Sat Feb 25 23:31:24 2012
@@ -25,7 +25,26 @@
 #if HAVE_REMAINDER
   return (float) remainder ((double) x, (double) y);
 #else
-  float i = roundf (x / y);
-  return fmaf (- i, y, x);
+  float q = - roundf (x / y);
+  float r = fmaf (q, y, x); /* = x + q * y, computed in one step */
+  /* Correct possible rounding errors in the quotient x / y.  */
+  float half_y = 0.5L * y;
+  if (y >= 0)
+    {
+      /* Expect -y/2 <= r <= y/2.  */
+      if (r > half_y)
+        q -= 1, r = fmaf (q, y, x);
+      else if (r < - half_y)
+        q += 1, r = fmaf (q, y, x);
+    }
+  else
+    {
+      /* Expect y/2 <= r <= -y/2.  */
+      if (r > - half_y)
+        q += 1, r = fmaf (q, y, x);
+      else if (r < half_y)
+        q -= 1, r = fmaf (q, y, x);
+    }
+  return r;
 #endif
 }
--- lib/remainderl.c.orig       Sun Feb 26 00:31:10 2012
+++ lib/remainderl.c    Sat Feb 25 23:31:24 2012
@@ -32,8 +32,27 @@
 long double
 remainderl (long double x, long double y)
 {
-  long double i = roundl (x / y);
-  return fmal (- i, y, x);
+  long double q = - roundl (x / y);
+  long double r = fmal (q, y, x); /* = x + q * y, computed in one step */
+  /* Correct possible rounding errors in the quotient x / y.  */
+  long double half_y = 0.5L * y;
+  if (y >= 0)
+    {
+      /* Expect -y/2 <= r <= y/2.  */
+      if (r > half_y)
+        q -= 1, r = fmal (q, y, x);
+      else if (r < - half_y)
+        q += 1, r = fmal (q, y, x);
+    }
+  else
+    {
+      /* Expect y/2 <= r <= -y/2.  */
+      if (r > - half_y)
+        q += 1, r = fmal (q, y, x);
+      else if (r < half_y)
+        q -= 1, r = fmal (q, y, x);
+    }
+  return r;
 }
 
 #endif