Implement and document csqrt(3) and csqrtf(3).

2 files changed, 192 insertions, 0 deletions

diff --git a/lib/msun/src/s_csqrt.c b/lib/msun/src/s_csqrt.c
new file mode 100644
index 0000000..3b1e187
--- /dev/null
+++ b/lib/msun/src/s_csqrt.c
@@ -0,0 +1,104 @@
+/*-
+ * 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 <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <complex.h>
+#include <math.h>
+
+#include "math_private.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 a = creal(z), b = cimag(z);
+	double t;
+	double complex result;
+	int scale;
+
+	/* 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(t, 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 (a >= THRESH || 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)
+	    return (result * 2);
+	else
+	    return (result);
+}
diff --git a/lib/msun/src/s_csqrtf.c b/lib/msun/src/s_csqrtf.c
new file mode 100644
index 0000000..cc5485a
--- /dev/null
+++ b/lib/msun/src/s_csqrtf.c
@@ -0,0 +1,88 @@
+/*-
+ * 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 <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <complex.h>
+#include <math.h>
+
+#include "math_private.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
+
+float complex
+csqrtf(float complex z)
+{
+	float a = crealf(z), b = cimagf(z);
+	double t;
+
+	/* Handle special cases. */
+	if (z == 0)
+		return (cpackf(0, b));
+	if (isinf(b))
+		return (cpackf(INFINITY, b));
+	if (isnan(a)) {
+		t = (b - b) / (b - b);	/* raise invalid if b is not a NaN */
+		return (cpackf(t, t));	/* return NaN + NaN i */
+	}
+	if (isinf(a)) {
+		/*
+		 * csqrtf(inf + nan i)  = inf +  nan i
+		 * csqrtf(inf + y i)    = inf +  0 i
+		 * csqrtf(-inf + nan i) = nan +- inf i
+		 * csqrtf(-inf + y i)   = 0   +  inf i
+		 */
+		if (signbit(a))
+			return (cpackf(fabsf(b - b), copysignf(a, b)));
+		else
+			return (cpackf(a, copysignf(b - b, b)));
+	}
+	/*
+	 * The remaining special case (b is NaN) is handled just fine by
+	 * the normal code path below.
+	 */
+
+	/*
+	 * We compute t in double precision to avoid overflow and to
+	 * provide correct rounding in nearly all cases.
+	 * This is Algorithm 312, CACM vol 10, Oct 1967.
+	 */
+	if (a >= 0) {
+		t = sqrt((a + hypot(a, b)) * 0.5);
+		return (cpackf(t, b / (2.0 * t)));
+	} else {
+		t = sqrt((-a + hypot(a, b)) * 0.5);
+		return (cpackf(fabsf(b) / (2.0 * t), copysignf(t, b)));
+	}
+}