initial cmath code and minor libm.h update

[libm] / src / cmath / csqrt.c

diff --git a/src/cmath/csqrt.c b/src/cmath/csqrt.c
new file mode 100644 (file)
index 0000000..21fb879
--- /dev/null
+++ b/src/cmath/csqrt.c
@@ -0,0 +1,100 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_csqrt.c */
+/*-
+ * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+#include "libm.h"
+
+/*
+ * gcc doesn't implement complex multiplication or division correctly,
+ * so we need to handle infinities specially. We turn on this pragma to
+ * notify conforming c99 compilers that the fast-but-incorrect code that
+ * gcc generates is acceptable, since the special cases have already been
+ * handled.
+ */
+#pragma STDC CX_LIMITED_RANGE ON
+
+/* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */
+#define THRESH  0x1.a827999fcef32p+1022
+
+double complex csqrt(double complex z)
+{
+       double complex result;
+       double a, b;
+       double t;
+       int scale;
+
+       a = creal(z);
+       b = cimag(z);
+
+       /* Handle special cases. */
+       if (z == 0)
+               return cpack(0, b);
+       if (isinf(b))
+               return cpack(INFINITY, b);
+       if (isnan(a)) {
+               t = (b - b) / (b - b);  /* raise invalid if b is not a NaN */
+               return cpack(a, t);   /* return NaN + NaN i */
+       }
+       if (isinf(a)) {
+               /*
+                * csqrt(inf + NaN i)  = inf +  NaN i
+                * csqrt(inf + y i)    = inf +  0 i
+                * csqrt(-inf + NaN i) = NaN +- inf i
+                * csqrt(-inf + y i)   = 0   +  inf i
+                */
+               if (signbit(a))
+                       return cpack(fabs(b - b), copysign(a, b));
+               else
+                       return cpack(a, copysign(b - b, b));
+       }
+       /*
+        * The remaining special case (b is NaN) is handled just fine by
+        * the normal code path below.
+        */
+
+       /* Scale to avoid overflow. */
+       if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
+               a *= 0.25;
+               b *= 0.25;
+               scale = 1;
+       } else {
+               scale = 0;
+       }
+
+       /* Algorithm 312, CACM vol 10, Oct 1967. */
+       if (a >= 0) {
+               t = sqrt((a + hypot(a, b)) * 0.5);
+               result = cpack(t, b / (2 * t));
+       } else {
+               t = sqrt((-a + hypot(a, b)) * 0.5);
+               result = cpack(fabs(b) / (2 * t), copysign(t, b));
+       }
+
+       /* Rescale. */
+       if (scale)
+               result *= 2;
+       return result;
+}