Merge common usage of mul_split function

A number of files share identical code for the
mul_split function.

This moves the duplicated function mul_split into its
own header, and refactors the fma usage into a single
selection macro.  Likewise, mul_split when used by a
long double implementation is renamed mul_splitl for
clarity.

11 files changed, 22 insertions, 346 deletions

diff --git a/sysdeps/ieee754/dbl-64/gamma_product.c b/sysdeps/ieee754/dbl-64/gamma_product.c
index 7ae144a..51407b1 100644
--- a/sysdeps/ieee754/dbl-64/gamma_product.c
+++ b/sysdeps/ieee754/dbl-64/gamma_product.c
@@ -18,37 +18,7 @@
 
 #include <math.h>
 #include <math_private.h>
-#include <float.h>
-
-/* Calculate X * Y exactly and store the result in *HI + *LO.  It is
-   given that the values are small enough that no overflow occurs and
-   large enough (or zero) that no underflow occurs.  */
-
-static void
-mul_split (double *hi, double *lo, double x, double y)
-{
-#ifdef __FP_FAST_FMA
-  /* Fast built-in fused multiply-add.  */
-  *hi = x * y;
-  *lo = __builtin_fma (x, y, -*hi);
-#elif defined FP_FAST_FMA
-  /* Fast library fused multiply-add, compiler before GCC 4.6.  */
-  *hi = x * y;
-  *lo = __fma (x, y, -*hi);
-#else
-  /* Apply Dekker's algorithm.  */
-  *hi = x * y;
-# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
-  double x1 = x * C;
-  double y1 = y * C;
-# undef C
-  x1 = (x - x1) + x1;
-  y1 = (y - y1) + y1;
-  double x2 = x - x1;
-  double y2 = y - y1;
-  *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
-#endif
-}
+#include <mul_split.h>
 
 /* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
    - 1, in the form R * (1 + *EPS) where the return value R is an
diff --git a/sysdeps/ieee754/dbl-64/lgamma_product.c b/sysdeps/ieee754/dbl-64/lgamma_product.c
index d956575..fa89337 100644
--- a/sysdeps/ieee754/dbl-64/lgamma_product.c
+++ b/sysdeps/ieee754/dbl-64/lgamma_product.c
@@ -18,37 +18,7 @@
 
 #include <math.h>
 #include <math_private.h>
-#include <float.h>
-
-/* Calculate X * Y exactly and store the result in *HI + *LO.  It is
-   given that the values are small enough that no overflow occurs and
-   large enough (or zero) that no underflow occurs.  */
-
-static void
-mul_split (double *hi, double *lo, double x, double y)
-{
-#ifdef __FP_FAST_FMA
-  /* Fast built-in fused multiply-add.  */
-  *hi = x * y;
-  *lo = __builtin_fma (x, y, -*hi);
-#elif defined FP_FAST_FMA
-  /* Fast library fused multiply-add, compiler before GCC 4.6.  */
-  *hi = x * y;
-  *lo = __fma (x, y, -*hi);
-#else
-  /* Apply Dekker's algorithm.  */
-  *hi = x * y;
-# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
-  double x1 = x * C;
-  double y1 = y * C;
-# undef C
-  x1 = (x - x1) + x1;
-  y1 = (y - y1) + y1;
-  double x2 = x - x1;
-  double y2 = y - y1;
-  *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
-#endif
-}
+#include <mul_split.h>
 
 /* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
    1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1.  X is such that
diff --git a/sysdeps/ieee754/dbl-64/x2y2m1.c b/sysdeps/ieee754/dbl-64/x2y2m1.c
index 9607888..7505215 100644
--- a/sysdeps/ieee754/dbl-64/x2y2m1.c
+++ b/sysdeps/ieee754/dbl-64/x2y2m1.c
@@ -18,7 +18,7 @@
 
 #include <math.h>
 #include <math_private.h>
-#include <float.h>
+#include <mul_split.h>
 #include <stdlib.h>
 
 /* Calculate X + Y exactly and store the result in *HI + *LO.  It is
@@ -33,36 +33,6 @@ add_split (double *hi, double *lo, double x, double y)
   *lo = (x - *hi) + y;
 }
 
-/* Calculate X * Y exactly and store the result in *HI + *LO.  It is
-   given that the values are small enough that no overflow occurs and
-   large enough (or zero) that no underflow occurs.  */
-
-static void
-mul_split (double *hi, double *lo, double x, double y)
-{
-#ifdef __FP_FAST_FMA
-  /* Fast built-in fused multiply-add.  */
-  *hi = x * y;
-  *lo = __builtin_fma (x, y, -*hi);
-#elif defined FP_FAST_FMA
-  /* Fast library fused multiply-add, compiler before GCC 4.6.  */
-  *hi = x * y;
-  *lo = __fma (x, y, -*hi);
-#else
-  /* Apply Dekker's algorithm.  */
-  *hi = x * y;
-# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
-  double x1 = x * C;
-  double y1 = y * C;
-# undef C
-  x1 = (x - x1) + x1;
-  y1 = (y - y1) + y1;
-  double x2 = x - x1;
-  double y2 = y - y1;
-  *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
-#endif
-}
-
 /* Compare absolute values of floating-point values pointed to by P
    and Q for qsort.  */
 
diff --git a/sysdeps/ieee754/ldbl-128/gamma_productl.c b/sysdeps/ieee754/ldbl-128/gamma_productl.c
index 849b57d..8ad0452 100644
--- a/sysdeps/ieee754/ldbl-128/gamma_productl.c
+++ b/sysdeps/ieee754/ldbl-128/gamma_productl.c
@@ -18,37 +18,7 @@
 
 #include <math.h>
 #include <math_private.h>
-#include <float.h>
-
-/* Calculate X * Y exactly and store the result in *HI + *LO.  It is
-   given that the values are small enough that no overflow occurs and
-   large enough (or zero) that no underflow occurs.  */
-
-static inline void
-mul_split (long double *hi, long double *lo, long double x, long double y)
-{
-#ifdef __FP_FAST_FMAL
-  /* Fast built-in fused multiply-add.  */
-  *hi = x * y;
-  *lo = __builtin_fmal (x, y, -*hi);
-#elif defined FP_FAST_FMAL
-  /* Fast library fused multiply-add, compiler before GCC 4.6.  */
-  *hi = x * y;
-  *lo = __fmal (x, y, -*hi);
-#else
-  /* Apply Dekker's algorithm.  */
-  *hi = x * y;
-# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
-  long double x1 = x * C;
-  long double y1 = y * C;
-# undef C
-  x1 = (x - x1) + x1;
-  y1 = (y - y1) + y1;
-  long double x2 = x - x1;
-  long double y2 = y - y1;
-  *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
-#endif
-}
+#include <mul_splitl.h>
 
 /* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
    - 1, in the form R * (1 + *EPS) where the return value R is an
@@ -68,7 +38,7 @@ __gamma_productl (long double x, long double x_eps, int n, long double *eps)
     {
       *eps += x_eps / (x + i);
       long double lo;
-      mul_split (&ret, &lo, ret, x + i);
+      mul_splitl (&ret, &lo, ret, x + i);
       *eps += lo / ret;
     }
   return ret;
diff --git a/sysdeps/ieee754/ldbl-128/lgamma_productl.c b/sysdeps/ieee754/ldbl-128/lgamma_productl.c
index de67cbe..9aa0137 100644
--- a/sysdeps/ieee754/ldbl-128/lgamma_productl.c
+++ b/sysdeps/ieee754/ldbl-128/lgamma_productl.c
@@ -18,37 +18,7 @@
 
 #include <math.h>
 #include <math_private.h>
-#include <float.h>
-
-/* Calculate X * Y exactly and store the result in *HI + *LO.  It is
-   given that the values are small enough that no overflow occurs and
-   large enough (or zero) that no underflow occurs.  */
-
-static void
-mul_split (long double *hi, long double *lo, long double x, long double y)
-{
-#ifdef __FP_FAST_FMAL
-  /* Fast built-in fused multiply-add.  */
-  *hi = x * y;
-  *lo = __builtin_fmal (x, y, -*hi);
-#elif defined FP_FAST_FMAL
-  /* Fast library fused multiply-add, compiler before GCC 4.6.  */
-  *hi = x * y;
-  *lo = __fmal (x, y, -*hi);
-#else
-  /* Apply Dekker's algorithm.  */
-  *hi = x * y;
-# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
-  long double x1 = x * C;
-  long double y1 = y * C;
-# undef C
-  x1 = (x - x1) + x1;
-  y1 = (y - y1) + y1;
-  long double x2 = x - x1;
-  long double y2 = y - y1;
-  *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
-#endif
-}
+#include <mul_splitl.h>
 
 /* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
    1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1.  X is such that
@@ -65,11 +35,11 @@ __lgamma_productl (long double t, long double x, long double x_eps, int n)
       long double xi = x + i;
       long double quot = t / xi;
       long double mhi, mlo;
-      mul_split (&mhi, &mlo, quot, xi);
+      mul_splitl (&mhi, &mlo, quot, xi);
       long double quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi);
       /* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1.  */
       long double rhi, rlo;
-      mul_split (&rhi, &rlo, ret, quot);
+      mul_splitl (&rhi, &rlo, ret, quot);
       long double rpq = ret + quot;
       long double rpq_eps = (ret - rpq) + quot;
       long double nret = rpq + rhi;
diff --git a/sysdeps/ieee754/ldbl-128/x2y2m1l.c b/sysdeps/ieee754/ldbl-128/x2y2m1l.c
index 733742d..4e97885 100644
--- a/sysdeps/ieee754/ldbl-128/x2y2m1l.c
+++ b/sysdeps/ieee754/ldbl-128/x2y2m1l.c
@@ -18,9 +18,10 @@
 
 #include <math.h>
 #include <math_private.h>
-#include <float.h>
+#include <mul_splitl.h>
 #include <stdlib.h>
 
+
 /* Calculate X + Y exactly and store the result in *HI + *LO.  It is
    given that |X| >= |Y| and the values are small enough that no
    overflow occurs.  */
@@ -33,36 +34,6 @@ add_split (long double *hi, long double *lo, long double x, long double y)
   *lo = (x - *hi) + y;
 }
 
-/* Calculate X * Y exactly and store the result in *HI + *LO.  It is
-   given that the values are small enough that no overflow occurs and
-   large enough (or zero) that no underflow occurs.  */
-
-static inline void
-mul_split (long double *hi, long double *lo, long double x, long double y)
-{
-#ifdef __FP_FAST_FMAL
-  /* Fast built-in fused multiply-add.  */
-  *hi = x * y;
-  *lo = __builtin_fmal (x, y, -*hi);
-#elif defined FP_FAST_FMAL
-  /* Fast library fused multiply-add, compiler before GCC 4.6.  */
-  *hi = x * y;
-  *lo = __fmal (x, y, -*hi);
-#else
-  /* Apply Dekker's algorithm.  */
-  *hi = x * y;
-# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
-  long double x1 = x * C;
-  long double y1 = y * C;
-# undef C
-  x1 = (x - x1) + x1;
-  y1 = (y - y1) + y1;
-  long double x2 = x - x1;
-  long double y2 = y - y1;
-  *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
-#endif
-}
-
 /* Compare absolute values of floating-point values pointed to by P
    and Q for qsort.  */
 
@@ -88,8 +59,8 @@ __x2y2m1l (long double x, long double y)
 {
   long double vals[5];
   SET_RESTORE_ROUNDL (FE_TONEAREST);
-  mul_split (&vals[1], &vals[0], x, x);
-  mul_split (&vals[3], &vals[2], y, y);
+  mul_splitl (&vals[1], &vals[0], x, x);
+  mul_splitl (&vals[3], &vals[2], y, y);
   vals[4] = -1.0L;
   qsort (vals, 5, sizeof (long double), compare);
   /* Add up the values so that each element of VALS has absolute value
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_fmal.c b/sysdeps/ieee754/ldbl-128ibm/s_fmal.c
index 177a048..1405763 100644
--- a/sysdeps/ieee754/ldbl-128ibm/s_fmal.c
+++ b/sysdeps/ieee754/ldbl-128ibm/s_fmal.c
@@ -22,6 +22,7 @@
 #include <math.h>
 #include <math_private.h>
 #include <math_ldbl_opt.h>
+#include <mul_split.h>
 #include <stdlib.h>
 
 /* Calculate X + Y exactly and store the result in *HI + *LO.  It is
@@ -36,32 +37,6 @@ add_split (double *hi, double *lo, double x, double y)
   *lo = (x - *hi) + y;
 }
 
-/* Calculate X * Y exactly and store the result in *HI + *LO.  It is
-   given that the values are small enough that no overflow occurs and
-   large enough (or zero) that no underflow occurs.  */
-
-static void
-mul_split (double *hi, double *lo, double x, double y)
-{
-#ifdef __FP_FAST_FMA
-  /* Fast built-in fused multiply-add.  */
-  *hi = x * y;
-  *lo = __builtin_fma (x, y, -*hi);
-#else
-  /* Apply Dekker's algorithm.  */
-  *hi = x * y;
-# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
-  double x1 = x * C;
-  double y1 = y * C;
-# undef C
-  x1 = (x - x1) + x1;
-  y1 = (y - y1) + y1;
-  double x2 = x - x1;
-  double y2 = y - y1;
-  *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
-#endif
-}
-
 /* Value with extended range, used in intermediate computations.  */
 typedef struct
 {
diff --git a/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c b/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c
index da2e929..a8b4895 100644
--- a/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c
+++ b/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c
@@ -18,7 +18,7 @@
 
 #include <math.h>
 #include <math_private.h>
-#include <float.h>
+#include <mul_split.h>
 #include <stdlib.h>
 
 /* Calculate X + Y exactly and store the result in *HI + *LO.  It is
@@ -33,36 +33,6 @@ add_split (double *hi, double *lo, double x, double y)
   *lo = (x - *hi) + y;
 }
 
-/* Calculate X * Y exactly and store the result in *HI + *LO.  It is
-   given that the values are small enough that no overflow occurs and
-   large enough (or zero) that no underflow occurs.  */
-
-static inline void
-mul_split (double *hi, double *lo, double x, double y)
-{
-#ifdef __FP_FAST_FMA
-  /* Fast built-in fused multiply-add.  */
-  *hi = x * y;
-  *lo = __builtin_fma (x, y, -*hi);
-#elif defined FP_FAST_FMA
-  /* Fast library fused multiply-add, compiler before GCC 4.6.  */
-  *hi = x * y;
-  *lo = __fma (x, y, -*hi);
-#else
-  /* Apply Dekker's algorithm.  */
-  *hi = x * y;
-# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
-  double x1 = x * C;
-  double y1 = y * C;
-# undef C
-  x1 = (x - x1) + x1;
-  y1 = (y - y1) + y1;
-  double x2 = x - x1;
-  double y2 = y - y1;
-  *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
-#endif
-}
-
 /* Compare absolute values of floating-point values pointed to by P
    and Q for qsort.  */
 
diff --git a/sysdeps/ieee754/ldbl-96/gamma_productl.c b/sysdeps/ieee754/ldbl-96/gamma_productl.c
index 849b57d..8ad0452 100644
--- a/sysdeps/ieee754/ldbl-96/gamma_productl.c
+++ b/sysdeps/ieee754/ldbl-96/gamma_productl.c
@@ -18,37 +18,7 @@
 
 #include <math.h>
 #include <math_private.h>
-#include <float.h>
-
-/* Calculate X * Y exactly and store the result in *HI + *LO.  It is
-   given that the values are small enough that no overflow occurs and
-   large enough (or zero) that no underflow occurs.  */
-
-static inline void
-mul_split (long double *hi, long double *lo, long double x, long double y)
-{
-#ifdef __FP_FAST_FMAL
-  /* Fast built-in fused multiply-add.  */
-  *hi = x * y;
-  *lo = __builtin_fmal (x, y, -*hi);
-#elif defined FP_FAST_FMAL
-  /* Fast library fused multiply-add, compiler before GCC 4.6.  */
-  *hi = x * y;
-  *lo = __fmal (x, y, -*hi);
-#else
-  /* Apply Dekker's algorithm.  */
-  *hi = x * y;
-# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
-  long double x1 = x * C;
-  long double y1 = y * C;
-# undef C
-  x1 = (x - x1) + x1;
-  y1 = (y - y1) + y1;
-  long double x2 = x - x1;
-  long double y2 = y - y1;
-  *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
-#endif
-}
+#include <mul_splitl.h>
 
 /* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
    - 1, in the form R * (1 + *EPS) where the return value R is an
@@ -68,7 +38,7 @@ __gamma_productl (long double x, long double x_eps, int n, long double *eps)
     {
       *eps += x_eps / (x + i);
       long double lo;
-      mul_split (&ret, &lo, ret, x + i);
+      mul_splitl (&ret, &lo, ret, x + i);
       *eps += lo / ret;
     }
   return ret;
diff --git a/sysdeps/ieee754/ldbl-96/lgamma_productl.c b/sysdeps/ieee754/ldbl-96/lgamma_productl.c
index de67cbe..9aa0137 100644
--- a/sysdeps/ieee754/ldbl-96/lgamma_productl.c
+++ b/sysdeps/ieee754/ldbl-96/lgamma_productl.c
@@ -18,37 +18,7 @@
 
 #include <math.h>
 #include <math_private.h>
-#include <float.h>
-
-/* Calculate X * Y exactly and store the result in *HI + *LO.  It is
-   given that the values are small enough that no overflow occurs and
-   large enough (or zero) that no underflow occurs.  */
-
-static void
-mul_split (long double *hi, long double *lo, long double x, long double y)
-{
-#ifdef __FP_FAST_FMAL
-  /* Fast built-in fused multiply-add.  */
-  *hi = x * y;
-  *lo = __builtin_fmal (x, y, -*hi);
-#elif defined FP_FAST_FMAL
-  /* Fast library fused multiply-add, compiler before GCC 4.6.  */
-  *hi = x * y;
-  *lo = __fmal (x, y, -*hi);
-#else
-  /* Apply Dekker's algorithm.  */
-  *hi = x * y;
-# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
-  long double x1 = x * C;
-  long double y1 = y * C;
-# undef C
-  x1 = (x - x1) + x1;
-  y1 = (y - y1) + y1;
-  long double x2 = x - x1;
-  long double y2 = y - y1;
-  *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
-#endif
-}
+#include <mul_splitl.h>
 
 /* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
    1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1.  X is such that
@@ -65,11 +35,11 @@ __lgamma_productl (long double t, long double x, long double x_eps, int n)
       long double xi = x + i;
       long double quot = t / xi;
       long double mhi, mlo;
-      mul_split (&mhi, &mlo, quot, xi);
+      mul_splitl (&mhi, &mlo, quot, xi);
       long double quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi);
       /* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1.  */
       long double rhi, rlo;
-      mul_split (&rhi, &rlo, ret, quot);
+      mul_splitl (&rhi, &rlo, ret, quot);
       long double rpq = ret + quot;
       long double rpq_eps = (ret - rpq) + quot;
       long double nret = rpq + rhi;
diff --git a/sysdeps/ieee754/ldbl-96/x2y2m1l.c b/sysdeps/ieee754/ldbl-96/x2y2m1l.c
index 733742d..b86ba1c 100644
--- a/sysdeps/ieee754/ldbl-96/x2y2m1l.c
+++ b/sysdeps/ieee754/ldbl-96/x2y2m1l.c
@@ -18,7 +18,7 @@
 
 #include <math.h>
 #include <math_private.h>
-#include <float.h>
+#include <mul_splitl.h>
 #include <stdlib.h>
 
 /* Calculate X + Y exactly and store the result in *HI + *LO.  It is
@@ -33,36 +33,6 @@ add_split (long double *hi, long double *lo, long double x, long double y)
   *lo = (x - *hi) + y;
 }
 
-/* Calculate X * Y exactly and store the result in *HI + *LO.  It is
-   given that the values are small enough that no overflow occurs and
-   large enough (or zero) that no underflow occurs.  */
-
-static inline void
-mul_split (long double *hi, long double *lo, long double x, long double y)
-{
-#ifdef __FP_FAST_FMAL
-  /* Fast built-in fused multiply-add.  */
-  *hi = x * y;
-  *lo = __builtin_fmal (x, y, -*hi);
-#elif defined FP_FAST_FMAL
-  /* Fast library fused multiply-add, compiler before GCC 4.6.  */
-  *hi = x * y;
-  *lo = __fmal (x, y, -*hi);
-#else
-  /* Apply Dekker's algorithm.  */
-  *hi = x * y;
-# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
-  long double x1 = x * C;
-  long double y1 = y * C;
-# undef C
-  x1 = (x - x1) + x1;
-  y1 = (y - y1) + y1;
-  long double x2 = x - x1;
-  long double y2 = y - y1;
-  *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
-#endif
-}
-
 /* Compare absolute values of floating-point values pointed to by P
    and Q for qsort.  */
 
@@ -88,8 +58,8 @@ __x2y2m1l (long double x, long double y)
 {
   long double vals[5];
   SET_RESTORE_ROUNDL (FE_TONEAREST);
-  mul_split (&vals[1], &vals[0], x, x);
-  mul_split (&vals[3], &vals[2], y, y);
+  mul_splitl (&vals[1], &vals[0], x, x);
+  mul_splitl (&vals[3], &vals[2], y, y);
   vals[4] = -1.0L;
   qsort (vals, 5, sizeof (long double), compare);
   /* Add up the values so that each element of VALS has absolute value