update gcc-4.6
author Nobuyasu Oshiro Sun, 21 Aug 2011 07:07:55 +0900 04ced10e8804
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```--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/libquadmath/math/complex.c	Sun Aug 21 07:07:55 2011 +0900
@@ -0,0 +1,210 @@
+
+
+#define REALPART(z) (__real__(z))
+#define IMAGPART(z) (__imag__(z))
+#define COMPLEX_ASSIGN(z_, r_, i_) {__real__(z_) = (r_); __imag__(z_) = (i_);}
+
+
+// Horrible... GCC doesn't know how to multiply or divide these
+// __complex128 things. We have to do it on our own.
+// Protect it around macros so, some day, we can switch it on
+
+#if 0
+
+# define C128_MULT(x,y) ((x)*(y))
+# define C128_DIV(x,y) ((x)/(y))
+
+#else
+
+#define C128_MULT(x,y) mult_c128(x,y)
+#define C128_DIV(x,y) div_c128(x,y)
+
+static inline __complex128 mult_c128 (__complex128 x, __complex128 y)
+{
+  __float128 r1 = REALPART(x), i1 = IMAGPART(x);
+  __float128 r2 = REALPART(y), i2 = IMAGPART(y);
+  __complex128 res;
+  COMPLEX_ASSIGN(res, r1*r2 - i1*i2, i2*r1 + i1*r2);
+  return res;
+}
+
+
+// Careful: the algorithm for the division sucks. A lot.
+static inline __complex128 div_c128 (__complex128 x, __complex128 y)
+{
+  __float128 n = hypotq (REALPART (y), IMAGPART (y));
+  __float128 r1 = REALPART(x), i1 = IMAGPART(x);
+  __float128 r2 = REALPART(y), i2 = IMAGPART(y);
+  __complex128 res;
+  COMPLEX_ASSIGN(res, r1*r2 + i1*i2, i1*r2 - i2*r1);
+  return res / n;
+}
+
+#endif
+
+
+
+__float128
+cabsq (__complex128 z)
+{
+  return hypotq (REALPART (z), IMAGPART (z));
+}
+
+
+__complex128
+cexpq (__complex128 z)
+{
+  __float128 a, b;
+  __complex128 v;
+
+  a = REALPART (z);
+  b = IMAGPART (z);
+  COMPLEX_ASSIGN (v, cosq (b), sinq (b));
+  return expq (a) * v;
+}
+
+
+__complex128
+cexpiq (__float128 x)
+{
+  __complex128 v;
+  COMPLEX_ASSIGN (v, cosq (x), sinq (x));
+  return v;
+}
+
+
+__float128
+cargq (__complex128 z)
+{
+  return atan2q (IMAGPART (z), REALPART (z));
+}
+
+
+__complex128
+clogq (__complex128 z)
+{
+  __complex128 v;
+  COMPLEX_ASSIGN (v, logq (cabsq (z)), cargq (z));
+  return v;
+}
+
+
+__complex128
+clog10q (__complex128 z)
+{
+  __complex128 v;
+  COMPLEX_ASSIGN (v, log10q (cabsq (z)), cargq (z));
+  return v;
+}
+
+
+__complex128
+cpowq (__complex128 base, __complex128 power)
+{
+  return cexpq (C128_MULT(power, clogq (base)));
+}
+
+
+__complex128
+csinq (__complex128 a)
+{
+  __float128 r = REALPART (a), i = IMAGPART (a);
+  __complex128 v;
+  COMPLEX_ASSIGN (v, sinq (r) * coshq (i), cosq (r) * sinhq (i));
+  return v;
+}
+
+
+__complex128
+csinhq (__complex128 a)
+{
+  __float128 r = REALPART (a), i = IMAGPART (a);
+  __complex128 v;
+  COMPLEX_ASSIGN (v, sinhq (r) * cosq (i), coshq (r) * sinq (i));
+  return v;
+}
+
+
+__complex128
+ccosq (__complex128 a)
+{
+  __float128 r = REALPART (a), i = IMAGPART (a);
+  __complex128 v;
+  COMPLEX_ASSIGN (v, cosq (r) * coshq (i), - (sinq (r) * sinhq (i)));
+  return v;
+}
+
+
+__complex128
+ccoshq (__complex128 a)
+{
+  __float128 r = REALPART (a), i = IMAGPART (a);
+  __complex128 v;
+  COMPLEX_ASSIGN (v, coshq (r) * cosq (i),  sinhq (r) * sinq (i));
+  return v;
+}
+
+
+__complex128
+ctanq (__complex128 a)
+{
+  __float128 rt = tanq (REALPART (a)), it = tanhq (IMAGPART (a));
+  __complex128 n, d;
+  COMPLEX_ASSIGN (n, rt, it);
+  COMPLEX_ASSIGN (d, 1, - (rt * it));
+  return C128_DIV(n,d);
+}
+
+
+__complex128
+ctanhq (__complex128 a)
+{
+  __float128 rt = tanhq (REALPART (a)), it = tanq (IMAGPART (a));
+  __complex128 n, d;
+  COMPLEX_ASSIGN (n, rt, it);
+  COMPLEX_ASSIGN (d, 1, rt * it);
+  return C128_DIV(n,d);
+}
+
+
+/* Square root algorithm from glibc.  */
+__complex128
+csqrtq (__complex128 z)
+{
+  __float128 re = REALPART(z), im = IMAGPART(z);
+  __complex128 v;
+
+  if (im == 0)
+  {
+    if (re < 0)
+    {
+      COMPLEX_ASSIGN (v, 0, copysignq (sqrtq (-re), im));
+    }
+    else
+    {
+      COMPLEX_ASSIGN (v, fabsq (sqrtq (re)), copysignq (0, im));
+    }
+  }
+  else if (re == 0)
+  {
+    __float128 r = sqrtq (0.5 * fabsq (im));
+    COMPLEX_ASSIGN (v, r, copysignq (r, im));
+  }
+  else
+  {
+    __float128 d = hypotq (re, im);
+    __float128 r, s;
+
+    /* Use the identity   2  Re res  Im res = Im x
+	to avoid cancellation error in  d +/- Re x.  */
+    if (re > 0)
+      r = sqrtq (0.5 * d + 0.5 * re), s = (0.5 * im) / r;
+    else
+      s = sqrtq (0.5 * d - 0.5 * re), r = fabsq ((0.5 * im) / s);
+
+    COMPLEX_ASSIGN (v, r, copysignq (s, im));
+  }
+  return v;
+}
+```