--- a/lib/fmod.c
+++ b/lib/fmod.c
@@ -14,59 +14,347 @@
    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.  */
 
-#include <config.h>
+#if ! defined USE_LONG_DOUBLE
+# include <config.h>
+#endif
 
 /* Specification.  */
 #include <math.h>
 
-double
-fmod (double x, double y)
+#include <float.h>
+#include <stdlib.h>
+
+#ifdef USE_LONG_DOUBLE
+# define FMOD fmodl
+# define DOUBLE long double
+# define MANT_DIG LDBL_MANT_DIG
+# define L_(literal) literal##L
+# define FREXP frexpl
+# define LDEXP ldexpl
+# define FABS fabsl
+# define TRUNC truncl
+# define ISNAN isnanl
+#else
+# define FMOD fmod
+# define DOUBLE double
+# define MANT_DIG DBL_MANT_DIG
+# define L_(literal) literal
+# define FREXP frexp
+# define LDEXP ldexp
+# define FABS fabs
+# define TRUNC trunc
+# define ISNAN isnand
+#endif
+
+/* MSVC with option -fp:strict refuses to compile constant initializers that
+   contain floating-point operations.  Pacify this compiler.  */
+#ifdef _MSC_VER
+# pragma fenv_access (off)
+#endif
+
+#undef NAN
+#if defined _MSC_VER
+static DOUBLE zero;
+# define NAN (zero / zero)
+#else
+# define NAN (L_(0.0) / L_(0.0))
+#endif
+
+/* To avoid rounding errors during the computation of x - q * y,
+   there are three possibilities:
+     - Use fma (- q, y, x).
+     - Have q be a single bit at a time, and compute x - q * y
+       through a subtraction.
+     - Have q be at most MANT_DIG/2 bits at a time, and compute
+       x - q * y by splitting y into two halves:
+       y = y1 * 2^(MANT_DIG/2) + y0
+       x - q * y = (x - q * y1 * 2^MANT_DIG/2) - q * y0.
+   The latter is probably the most efficient.  */
+
+/* Number of bits in a limb.  */
+#define LIMB_BITS (MANT_DIG / 2)
+
+/* 2^LIMB_BITS.  */
+static const DOUBLE TWO_LIMB_BITS =
+  /* Assume LIMB_BITS <= 3 * 31.
+     Use the identity
+       n = floor(n/3) + floor((n+1)/3) + floor((n+2)/3).  */
+  (DOUBLE) (1U << (LIMB_BITS / 3))
+  * (DOUBLE) (1U << ((LIMB_BITS + 1) / 3))
+  * (DOUBLE) (1U << ((LIMB_BITS + 2) / 3));
+
+/* 2^-LIMB_BITS.  */
+static const DOUBLE TWO_LIMB_BITS_INVERSE =
+  /* Assume LIMB_BITS <= 3 * 31.
+     Use the identity
+       n = floor(n/3) + floor((n+1)/3) + floor((n+2)/3).  */
+  L_(1.0) / ((DOUBLE) (1U << (LIMB_BITS / 3))
+             * (DOUBLE) (1U << ((LIMB_BITS + 1) / 3))
+             * (DOUBLE) (1U << ((LIMB_BITS + 2) / 3)));
+
+DOUBLE
+FMOD (DOUBLE x, DOUBLE y)
 {
-  if (isinf (y))
-    return x;
+  if (isfinite (x) && isfinite (y) && y != L_(0.0))
+    {
+      if (x == L_(0.0))
+        /* Return x, regardless of the sign of y.  */
+        return x;
+
+      {
+        int negate = ((!signbit (x)) ^ (!signbit (y)));
+
+        /* Take the absolute value of x and y.  */
+        x = FABS (x);
+        y = FABS (y);
+
+        /* Trivial case that requires no computation.  */
+        if (x < y)
+          return (negate ? - x : x);
+
+        {
+          int yexp;
+          DOUBLE ym;
+          DOUBLE y1;
+          DOUBLE y0;
+          int k;
+          DOUBLE x2;
+          DOUBLE x1;
+          DOUBLE x0;
+
+          /* Write y = 2^yexp * (y1 * 2^-LIMB_BITS + y0 * 2^-(2*LIMB_BITS))
+             where y1 is an integer, 2^(LIMB_BITS-1) <= y1 < 2^LIMB_BITS,
+             y1 has at most LIMB_BITS bits,
+             0 <= y0 < 2^LIMB_BITS,
+             y0 has at most (MANT_DIG + 1) / 2 bits.  */
+          ym = FREXP (y, &yexp);
+          ym = ym * TWO_LIMB_BITS;
+          y1 = TRUNC (ym);
+          y0 = (ym - y1) * TWO_LIMB_BITS;
+
+          /* Write
+               x = 2^(yexp+(k-3)*LIMB_BITS)
+                   * (x2 * 2^(2*LIMB_BITS) + x1 * 2^LIMB_BITS + x0)
+             where x2, x1, x0 are each integers >= 0, < 2^LIMB_BITS.  */
+          {
+            int xexp;
+            DOUBLE xm = FREXP (x, &xexp);
+            /* Since we know x >= y, we know xexp >= yexp.  */
+            xexp -= yexp;
+            /* Compute k = ceil(xexp / LIMB_BITS).  */
+            k = (xexp + LIMB_BITS - 1) / LIMB_BITS;
+            /* Note: (k - 1) * LIMB_BITS + 1 <= xexp <= k * LIMB_BITS.  */
+            /* Note: 0.5 <= xm < 1.0.  */
+            xm = LDEXP (xm, xexp - (k - 1) * LIMB_BITS);
+            /* Note: Now xm < 2^(xexp - (k - 1) * LIMB_BITS) <= 2^LIMB_BITS
+               and xm >= 0.5 * 2^(xexp - (k - 1) * LIMB_BITS) >= 1.0
+               and xm has at most MANT_DIG <= 2*LIMB_BITS+1 bits.  */
+            x2 = TRUNC (xm);
+            x1 = (xm - x2) * TWO_LIMB_BITS;
+            /* Split off x0 from x1 later.  */
+          }
+
+          /* Test whether [x2,x1,0] >= 2^LIMB_BITS * [y1,y0].  */
+          if (x2 > y1 || (x2 == y1 && x1 >= y0))
+            {
+              /* Subtract 2^LIMB_BITS * [y1,y0] from [x2,x1,0].  */
+              x2 -= y1;
+              x1 -= y0;
+              if (x1 < L_(0.0))
+                {
+                  if (!(x2 >= L_(1.0)))
+                    abort ();
+                  x2 -= L_(1.0);
+                  x1 += TWO_LIMB_BITS;
+                }
+            }
+
+          /* Split off x0 from x1.  */
+          {
+            DOUBLE x1int = TRUNC (x1);
+            x0 = TRUNC ((x1 - x1int) * TWO_LIMB_BITS);
+            x1 = x1int;
+          }
+
+          for (; k > 0; k--)
+            {
+              /* Multiprecision division of the limb sequence [x2,x1,x0]
+                 by [y1,y0].  */
+              /* Here [x2,x1,x0] < 2^LIMB_BITS * [y1,y0].  */
+              /* The first guess takes into account only [x2,x1] and [y1].
+
+                 By Knuth's theorem, we know that
+                   q* = min (floor ([x2,x1] / [y1]), 2^LIMB_BITS - 1)
+                 and
+                   q = floor ([x2,x1,x0] / [y1,y0])
+                 are not far away:
+                   q* - 2 <= q <= q* + 1.
+
+                 Proof:
+                 a) q* * y1 <= floor ([x2,x1] / [y1]) * y1 <= [x2,x1].
+                    Hence
+                    [x2,x1,x0] - q* * [y1,y0]
+                      = 2^LIMB_BITS * ([x2,x1] - q* * [y1]) + x0 - q* * y0
+                      >= x0 - q* * y0
+                      >= - q* * y0
+                      > - 2^(2*LIMB_BITS)
+                      >= - 2 * [y1,y0]
+                    So
+                      [x2,x1,x0] > (q* - 2) * [y1,y0].
+                 b) If q* = floor ([x2,x1] / [y1]), then
+                      [x2,x1] < (q* + 1) * y1
+                    Hence
+                    [x2,x1,x0] - q* * [y1,y0]
+                      = 2^LIMB_BITS * ([x2,x1] - q* * [y1]) + x0 - q* * y0
+                      <= 2^LIMB_BITS * (y1 - 1) + x0 - q* * y0
+                      <= 2^LIMB_BITS * (2^LIMB_BITS-2) + (2^LIMB_BITS-1) - 0
+                      < 2^(2*LIMB_BITS)
+                      <= 2 * [y1,y0]
+                    So
+                      [x2,x1,x0] < (q* + 2) * [y1,y0].
+                    and so
+                      q < q* + 2
+                    which implies
+                      q <= q* + 1.
+                    In the other case, q* = 2^LIMB_BITS - 1.  Then trivially
+                      q < 2^LIMB_BITS = q* + 1.
+
+                 We know that floor ([x2,x1] / [y1]) >= 2^LIMB_BITS if and
+                 only if x2 >= y1.  */
+              DOUBLE q =
+                (x2 >= y1
+                 ? TWO_LIMB_BITS - L_(1.0)
+                 : TRUNC ((x2 * TWO_LIMB_BITS + x1) / y1));
+              if (q > L_(0.0))
+                {
+                  /* Compute
+                     [x2,x1,x0] - q* * [y1,y0]
+                       = 2^LIMB_BITS * ([x2,x1] - q* * [y1]) + x0 - q* * y0.  */
+                  DOUBLE q_y1 = q * y1; /* exact, at most 2*LIMB_BITS bits */
+                  DOUBLE q_y1_1 = TRUNC (q_y1 * TWO_LIMB_BITS_INVERSE);
+                  DOUBLE q_y1_0 = q_y1 - q_y1_1 * TWO_LIMB_BITS;
+                  DOUBLE q_y0 = q * y0; /* exact, at most MANT_DIG bits */
+                  DOUBLE q_y0_1 = TRUNC (q_y0 * TWO_LIMB_BITS_INVERSE);
+                  DOUBLE q_y0_0 = q_y0 - q_y0_1 * TWO_LIMB_BITS;
+                  x2 -= q_y1_1;
+                  x1 -= q_y1_0;
+                  x1 -= q_y0_1;
+                  x0 -= q_y0_0;
+                  /* Move negative carry from x0 to x1 and from x1 to x2.  */
+                  if (x0 < L_(0.0))
+                    {
+                      x0 += TWO_LIMB_BITS;
+                      x1 -= L_(1.0);
+                    }
+                  if (x1 < L_(0.0))
+                    {
+                      x1 += TWO_LIMB_BITS;
+                      x2 -= L_(1.0);
+                      if (x1 < L_(0.0)) /* not sure this can happen */
+                        {
+                          x1 += TWO_LIMB_BITS;
+                          x2 -= L_(1.0);
+                        }
+                    }
+                  if (x2 < L_(0.0))
+                    {
+                      /* Reduce q by 1.  */
+                      x1 += y1;
+                      x0 += y0;
+                      /* Move overflow from x0 to x1 and from x1 to x0.  */
+                      if (x0 >= TWO_LIMB_BITS)
+                        {
+                          x0 -= TWO_LIMB_BITS;
+                          x1 += L_(1.0);
+                        }
+                      if (x1 >= TWO_LIMB_BITS)
+                        {
+                          x1 -= TWO_LIMB_BITS;
+                          x2 += L_(1.0);
+                        }
+                      if (x2 < L_(0.0))
+                        {
+                          /* Reduce q by 1 again.  */
+                          x1 += y1;
+                          x0 += y0;
+                          /* Move overflow from x0 to x1 and from x1 to x0.  */
+                          if (x0 >= TWO_LIMB_BITS)
+                            {
+                              x0 -= TWO_LIMB_BITS;
+                              x1 += L_(1.0);
+                            }
+                          if (x1 >= TWO_LIMB_BITS)
+                            {
+                              x1 -= TWO_LIMB_BITS;
+                              x2 += L_(1.0);
+                            }
+                          if (x2 < L_(0.0))
+                            /* Shouldn't happen, because we proved that
+                               q >= q* - 2.  */
+                            abort ();
+                        }
+                    }
+                }
+              if (x2 > L_(0.0)
+                  || x1 > y1
+                  || (x1 == y1 && x0 >= y0))
+                {
+                  /* Increase q by 1.  */
+                  x1 -= y1;
+                  x0 -= y0;
+                  /* Move negative carry from x0 to x1 and from x1 to x2.  */
+                  if (x0 < L_(0.0))
+                    {
+                      x0 += TWO_LIMB_BITS;
+                      x1 -= L_(1.0);
+                    }
+                  if (x1 < L_(0.0))
+                    {
+                      x1 += TWO_LIMB_BITS;
+                      x2 -= L_(1.0);
+                    }
+                  if (x2 < L_(0.0))
+                    abort ();
+                  if (x2 > L_(0.0)
+                      || x1 > y1
+                      || (x1 == y1 && x0 >= y0))
+                    /* Shouldn't happen, because we proved that
+                       q <= q* + 1.  */
+                    abort ();
+                }
+              /* Here [x2,x1,x0] < [y1,y0].  */
+              /* Next round.  */
+              x2 = x1;
+#if (MANT_DIG + 1) / 2 > LIMB_BITS /* y0 can have a fractional bit */
+              x1 = TRUNC (x0);
+              x0 = (x0 - x1) * TWO_LIMB_BITS;
+#else
+              x1 = x0;
+              x0 = L_(0.0);
+#endif
+              /* Here [x2,x1,x0] < 2^LIMB_BITS * [y1,y0].  */
+            }
+          /* Here k = 0.
+             The result is
+               2^(yexp-3*LIMB_BITS)
+               * (x2 * 2^(2*LIMB_BITS) + x1 * 2^LIMB_BITS + x0).  */
+          {
+            DOUBLE r =
+              LDEXP ((x2 * TWO_LIMB_BITS + x1) * TWO_LIMB_BITS + x0,
+                     yexp - 3 * LIMB_BITS);
+            return (negate ? - r : r);
+          }
+        }
+      }
+    }
   else
     {
-      double q = - trunc (x / y);
-      double r = fma (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 = fma (q, y, x);
-              else if (r >= y)
-                q -= 1, r = fma (q, y, x);
-            }
-          else
-            {
-              /* Expect - y < r <= 0.  */
-              if (r > 0)
-                q -= 1, r = fma (q, y, x);
-              else if (r <= - y)
-                q += 1, r = fma (q, y, x);
-            }
-        }
+      if (ISNAN (x) || ISNAN (y))
+        return x + y; /* NaN */
+      else if (isinf (y))
+        return x;
       else
-        {
-          if (x >= 0)
-            {
-              /* Expect 0 <= r < - y.  */
-              if (r < 0)
-                q -= 1, r = fma (q, y, x);
-              else if (r >= - y)
-                q += 1, r = fma (q, y, x);
-            }
-          else
-            {
-              /* Expect y < r <= 0.  */
-              if (r > 0)
-                q += 1, r = fma (q, y, x);
-              else if (r <= y)
-                q -= 1, r = fma (q, y, x);
-            }
-        }
-      return r;
+        /* x infinite or y zero */
+        return NAN;
     }
 }