New __sqr function as a faster special case of __mul

ChangeLog

@@ -1,3 +1,16 @@
+2013-02-14  Siddhesh Poyarekar  <siddhesh@redhat.com>
+
+	* sysdeps/ieee754/dbl-64/mpa.c (__sqr): New function.
+	* sysdeps/ieee754/dbl-64/mpa.h (__sqr): Declare.
+	* sysdeps/ieee754/dbl-64/mpexp.c (__mpexp): use __sqr instead
+	of __mul for squares.
+	* sysdeps/powerpc/powerpc32/power4/fpu/mpa.c (__sqr): New
+	function
+	* sysdeps/powerpc/powerpc64/power4/fpu/mpa.c (__sqr):
+	Likewise.
+	* sysdeps/x86_64/fpu/multiarch/mpa-avx.c: Define __sqr.
+	* sysdeps/x86_64/fpu/multiarch/mpa-fma4.c: Likewise.
+
 2013-02-13  Joseph Myers  <joseph@codesourcery.com>
 
 	[BZ #13550]

sysdeps/ieee754/dbl-64/mpa.c

@@ -702,6 +702,97 @@ __mul (const mp_no *x, const mp_no *y, mp_no *z, int p)
   Z[0] = X[0] * Y[0];
 }
 
+/* Square *X and store result in *Y.  X and Y may not overlap.  For P in
+   [1, 2, 3], the exact result is truncated to P digits.  In case P > 3 the
+   error is bounded by 1.001 ULP.  This is a faster special case of
+   multiplication.  */
+void
+SECTION
+__sqr (const mp_no *x, mp_no *y, int p)
+{
+  long i, j, k, ip;
+  double u, yk;
+
+  /* Is z=0?  */
+  if (__glibc_unlikely (X[0] == ZERO))
+    {
+      Y[0] = ZERO;
+      return;
+    }
+
+  /* We need not iterate through all X's since it's pointless to
+     multiply zeroes.  */
+  for (ip = p; ip > 0; ip--)
+    if (X[ip] != ZERO)
+      break;
+
+  k = (__glibc_unlikely (p < 3)) ? p + p : p + 3;
+
+  while (k > 2 * ip + 1)
+    Y[k--] = ZERO;
+
+  yk = ZERO;
+
+  while (k > p)
+    {
+      double yk2 = 0.0;
+      long lim = k / 2;
+
+      if (k % 2 == 0)
+        {
+	  yk += X[lim] * X[lim];
+	  lim--;
+	}
+
+      for (i = k - p, j = p; i <= lim; i++, j--)
+	yk2 += X[i] * X[j];
+
+      yk += 2.0 * yk2;
+
+      u = (yk + CUTTER) - CUTTER;
+      if (u > yk)
+	u -= RADIX;
+      Y[k--] = yk - u;
+      yk = u * RADIXI;
+    }
+
+  while (k > 1)
+    {
+      double yk2 = 0.0;
+      long lim = k / 2;
+
+      if (k % 2 == 0)
+        {
+	  yk += X[lim] * X[lim];
+	  lim--;
+	}
+
+      for (i = 1, j = k - 1; i <= lim; i++, j--)
+	yk2 += X[i] * X[j];
+
+      yk += 2.0 * yk2;
+
+      u = (yk + CUTTER) - CUTTER;
+      if (u > yk)
+	u -= RADIX;
+      Y[k--] = yk - u;
+      yk = u * RADIXI;
+    }
+  Y[k] = yk;
+
+  /* Squares are always positive.  */
+  Y[0] = 1.0;
+
+  EY = 2 * EX;
+  /* Is there a carry beyond the most significant digit?  */
+  if (__glibc_unlikely (Y[1] == ZERO))
+    {
+      for (i = 1; i <= p; i++)
+	Y[i] = Y[i + 1];
+      EY--;
+    }
+}
+
 /* Invert *X and store in *Y.  Relative error bound:
    - For P = 2: 1.001 * R ^ (1 - P)
    - For P = 3: 1.063 * R ^ (1 - P)

sysdeps/ieee754/dbl-64/mpa.h

@@ -115,6 +115,7 @@ void __dbl_mp (double, mp_no *, int);
 void __add (const mp_no *, const mp_no *, mp_no *, int);
 void __sub (const mp_no *, const mp_no *, mp_no *, int);
 void __mul (const mp_no *, const mp_no *, mp_no *, int);
+void __sqr (const mp_no *, mp_no *, int);
 void __dvd (const mp_no *, const mp_no *, mp_no *, int);
 
 extern void __mpatan (mp_no *, mp_no *, int);

sysdeps/ieee754/dbl-64/mpexp.c

@@ -145,14 +145,14 @@ __mpexp (mp_no *x, mp_no *y, int p)
   /* Raise polynomial value to the power of 2**m. Put result in y.  */
   for (k = 0, j = 0; k < m;)
     {
-      __mul (&mpt2, &mpt2, &mpt1, p);
+      __sqr (&mpt2, &mpt1, p);
       k++;
       if (k == m)
 	{
 	  j = 1;
 	  break;
 	}
-      __mul (&mpt1, &mpt1, &mpt2, p);
+      __sqr (&mpt1, &mpt2, p);
       k++;
     }
   if (j)

sysdeps/powerpc/powerpc32/power4/fpu/mpa.c

@@ -687,6 +687,106 @@ __mul (const mp_no *x, const mp_no *y, mp_no *z, int p)
   return;
 }
 
+/* Square *X and store result in *Y.  X and Y may not overlap.  For P in
+   [1, 2, 3], the exact result is truncated to P digits.  In case P > 3 the
+   error is bounded by 1.001 ULP.  This is a faster special case of
+   multiplication.  */
+void
+__sqr (const mp_no *x, mp_no *y, int p)
+{
+  long i, j, k, ip;
+  double u, yk;
+
+  /* Is z=0?  */
+  if (__glibc_unlikely (X[0] == ZERO))
+    {
+      Y[0] = ZERO;
+      return;
+    }
+
+  /* We need not iterate through all X's since it's pointless to
+     multiply zeroes.  */
+  for (ip = p; ip > 0; ip--)
+    if (X[ip] != ZERO)
+      break;
+
+  k = (__glibc_unlikely (p < 3)) ? p + p : p + 3;
+
+  while (k > 2 * ip + 1)
+    Y[k--] = ZERO;
+
+  yk = ZERO;
+
+  while (k > p)
+    {
+      double yk2 = 0.0;
+      long lim = k / 2;
+
+      if (k % 2 == 0)
+        {
+	  yk += X[lim] * X[lim];
+	  lim--;
+	}
+
+      /* In __mul, this loop (and the one within the next while loop) run
+         between a range to calculate the mantissa as follows:
+
+         Z[k] = X[k] * Y[n] + X[k+1] * Y[n-1] ... + X[n-1] * Y[k+1]
+		+ X[n] * Y[k]
+
+         For X == Y, we can get away with summing halfway and doubling the
+	 result.  For cases where the range size is even, the mid-point needs
+	 to be added separately (above).  */
+      for (i = k - p, j = p; i <= lim; i++, j--)
+	yk2 += X[i] * X[j];
+
+      yk += 2.0 * yk2;
+
+      u = (yk + CUTTER) - CUTTER;
+      if (u > yk)
+	u -= RADIX;
+      Y[k--] = yk - u;
+      yk = u * RADIXI;
+    }
+
+  while (k > 1)
+    {
+      double yk2 = 0.0;
+      long lim = k / 2;
+
+      if (k % 2 == 0)
+        {
+	  yk += X[lim] * X[lim];
+	  lim--;
+	}
+
+      /* Likewise for this loop.  */
+      for (i = 1, j = k - 1; i <= lim; i++, j--)
+	yk2 += X[i] * X[j];
+
+      yk += 2.0 * yk2;
+
+      u = (yk + CUTTER) - CUTTER;
+      if (u > yk)
+	u -= RADIX;
+      Y[k--] = yk - u;
+      yk = u * RADIXI;
+    }
+  Y[k] = yk;
+
+  /* Squares are always positive.  */
+  Y[0] = 1.0;
+
+  EY = 2 * EX;
+  /* Is there a carry beyond the most significant digit?  */
+  if (__glibc_unlikely (Y[1] == ZERO))
+    {
+      for (i = 1; i <= p; i++)
+	Y[i] = Y[i + 1];
+      EY--;
+    }
+}
+
 /* Invert *X and store in *Y.  Relative error bound:
    - For P = 2: 1.001 * R ^ (1 - P)
    - For P = 3: 1.063 * R ^ (1 - P)

sysdeps/powerpc/powerpc64/power4/fpu/mpa.c

@@ -687,6 +687,106 @@ __mul (const mp_no *x, const mp_no *y, mp_no *z, int p)
   return;
 }
 
+/* Square *X and store result in *Y.  X and Y may not overlap.  For P in
+   [1, 2, 3], the exact result is truncated to P digits.  In case P > 3 the
+   error is bounded by 1.001 ULP.  This is a faster special case of
+   multiplication.  */
+void
+__sqr (const mp_no *x, mp_no *y, int p)
+{
+  long i, j, k, ip;
+  double u, yk;
+
+  /* Is z=0?  */
+  if (__glibc_unlikely (X[0] == ZERO))
+    {
+      Y[0] = ZERO;
+      return;
+    }
+
+  /* We need not iterate through all X's since it's pointless to
+     multiply zeroes.  */
+  for (ip = p; ip > 0; ip--)
+    if (X[ip] != ZERO)
+      break;
+
+  k = (__glibc_unlikely (p < 3)) ? p + p : p + 3;
+
+  while (k > 2 * ip + 1)
+    Y[k--] = ZERO;
+
+  yk = ZERO;
+
+  while (k > p)
+    {
+      double yk2 = 0.0;
+      long lim = k / 2;
+
+      if (k % 2 == 0)
+        {
+	  yk += X[lim] * X[lim];
+	  lim--;
+	}
+
+      /* In __mul, this loop (and the one within the next while loop) run
+         between a range to calculate the mantissa as follows:
+
+         Z[k] = X[k] * Y[n] + X[k+1] * Y[n-1] ... + X[n-1] * Y[k+1]
+		+ X[n] * Y[k]
+
+         For X == Y, we can get away with summing halfway and doubling the
+	 result.  For cases where the range size is even, the mid-point needs
+	 to be added separately (above).  */
+      for (i = k - p, j = p; i <= lim; i++, j--)
+	yk2 += X[i] * X[j];
+
+      yk += 2.0 * yk2;
+
+      u = (yk + CUTTER) - CUTTER;
+      if (u > yk)
+	u -= RADIX;
+      Y[k--] = yk - u;
+      yk = u * RADIXI;
+    }
+
+  while (k > 1)
+    {
+      double yk2 = 0.0;
+      long lim = k / 2;
+
+      if (k % 2 == 0)
+        {
+	  yk += X[lim] * X[lim];
+	  lim--;
+	}
+
+      /* Likewise for this loop.  */
+      for (i = 1, j = k - 1; i <= lim; i++, j--)
+	yk2 += X[i] * X[j];
+
+      yk += 2.0 * yk2;
+
+      u = (yk + CUTTER) - CUTTER;
+      if (u > yk)
+	u -= RADIX;
+      Y[k--] = yk - u;
+      yk = u * RADIXI;
+    }
+  Y[k] = yk;
+
+  /* Squares are always positive.  */
+  Y[0] = 1.0;
+
+  EY = 2 * EX;
+  /* Is there a carry beyond the most significant digit?  */
+  if (__glibc_unlikely (Y[1] == ZERO))
+    {
+      for (i = 1; i <= p; i++)
+	Y[i] = Y[i + 1];
+      EY--;
+    }
+}
+
 /* Invert *X and store in *Y.  Relative error bound:
    - For P = 2: 1.001 * R ^ (1 - P)
    - For P = 3: 1.063 * R ^ (1 - P)

sysdeps/x86_64/fpu/multiarch/mpa-avx.c

@@ -1,5 +1,6 @@
 #define __add __add_avx
 #define __mul __mul_avx
+#define __sqr __sqr_avx
 #define __sub __sub_avx
 #define __dbl_mp __dbl_mp_avx
 #define __dvd __dvd_avx

sysdeps/x86_64/fpu/multiarch/mpa-fma4.c

@@ -1,5 +1,6 @@
 #define __add __add_fma4
 #define __mul __mul_fma4
+#define __sqr __sqr_fma4
 #define __sub __sub_fma4
 #define __dbl_mp __dbl_mp_fma4
 #define __dvd __dvd_fma4