Add cexp() and cexpf().

Reviewed by:	bde (earlier version)

1 files changed, 98 insertions, 0 deletions

diff --git a/lib/msun/src/s_cexpf.c b/lib/msun/src/s_cexpf.c
new file mode 100644
index 0000000..4ea3931
--- /dev/null
+++ b/lib/msun/src/s_cexpf.c
@@ -0,0 +1,98 @@
+/*-
+ * 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 <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <complex.h>
+#include <math.h>
+
+#include "math_private.h"
+
+static const uint32_t
+exp_ovfl  = 0x42b17218,		/* MAX_EXP * ln2 ~= 88.722839355 */
+cexp_ovfl = 0x43400074,		/* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
+k         = 235;		/* constant for reduction */
+
+static const float
+kln2      =  162.88958740f;	/* k * ln2 */
+
+float complex
+cexpf(float complex z)
+{
+	float x, y, exp_x;
+	uint32_t hx, hy;
+	int scale;
+
+	x = crealf(z);
+	y = cimagf(z);
+
+	GET_FLOAT_WORD(hy, y);
+	hy &= 0x7fffffff;
+
+	/* cexp(x + I 0) = exp(x) + I 0 */
+	if (hy == 0)
+		return (cpackf(expf(x), y));
+	GET_FLOAT_WORD(hx, x);
+	if (hy >= 0x7f800000) {
+		if ((hx & 0x7fffffff) != 0x7f800000) {
+			/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
+			return (cpackf(y - y, y - y));
+		} else if (hx & 0x80000000) {
+			/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
+			return (cpackf(0.0, 0.0));
+		} else {
+			/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
+			return (cpackf(x, y - y));
+		}
+	}
+
+	if (hx >= exp_ovfl && hx <= cexp_ovfl) {
+		/*
+		 * x is between 88.7 and 192, so we must scale to avoid
+		 * overflow in expf(x).  We use exp(x) = exp(x - kln2) * 2**k,
+		 * carefully chosen to minimize |exp(kln2) - 2**k|.  We also
+		 * scale the exponent of exp(x) to MANT_DIG to avoid loss of
+		 * accuracy due to underflow if sin(y) is tiny.
+		 */
+		exp_x = expf(x - kln2);
+		GET_FLOAT_WORD(hx, exp_x);
+		SET_FLOAT_WORD(exp_x, (hx & 0x7fffff) | ((0x7f + 23) << 23));
+		scale = (hx >> 23) - (0x7f + 23) + k;
+		return (cpackf(scalbnf(cosf(y) * exp_x, scale),
+			scalbnf(sinf(y) * exp_x, scale)));
+	} 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 = expf(x);
+		return (cpackf(exp_x * cosf(y), exp_x * sinf(y)));
+	}
+}