initial cmath code and minor libm.h update

[libm] / src / cmath / cexp.c

diff --git a/src/cmath/cexp.c b/src/cmath/cexp.c
new file mode 100644 (file)
index 0000000..3b8bb75
--- /dev/null
+++ b/src/cmath/cexp.c
@@ -0,0 +1,83 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_cexp.c */
+/*-
+ * Copyright (c) 2011 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"
+
+static const uint32_t
+exp_ovfl  = 0x40862e42,  /* high bits of MAX_EXP * ln2 ~= 710 */
+cexp_ovfl = 0x4096b8e4;  /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
+
+double complex cexp(double complex z)
+{
+       double x, y, exp_x;
+       uint32_t hx, hy, lx, ly;
+
+       x = creal(z);
+       y = cimag(z);
+
+       EXTRACT_WORDS(hy, ly, y);
+       hy &= 0x7fffffff;
+
+       /* cexp(x + I 0) = exp(x) + I 0 */
+       if ((hy | ly) == 0)
+               return cpack(exp(x), y);
+       EXTRACT_WORDS(hx, lx, x);
+       /* cexp(0 + I y) = cos(y) + I sin(y) */
+       if (((hx & 0x7fffffff) | lx) == 0)
+               return cpack(cos(y), sin(y));
+
+       if (hy >= 0x7ff00000) {
+               if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) {
+                       /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
+                       return cpack(y - y, y - y);
+               } else if (hx & 0x80000000) {
+                       /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
+                       return cpack(0.0, 0.0);
+               } else {
+                       /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
+                       return cpack(x, y - y);
+               }
+       }
+
+       if (hx >= exp_ovfl && hx <= cexp_ovfl) {
+               /*
+                * x is between 709.7 and 1454.3, so we must scale to avoid
+                * overflow in exp(x).
+                */
+               return __ldexp_cexp(z, 0);
+       } else {
+               /*
+                * Cases covered here:
+                *  -  x < exp_ovfl and exp(x) won't overflow (common case)
+                *  -  x > cexp_ovfl, so exp(x) * s overflows for all s > 0
+                *  -  x = +-Inf (generated by exp())
+                *  -  x = NaN (spurious inexact exception from y)
+                */
+               exp_x = exp(x);
+               return cpack(exp_x * cos(y), exp_x * sin(y));
+       }
+}