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

4 files changed, 290 insertions, 2 deletions

diff --git a/lib/msun/Makefile b/lib/msun/Makefile
index 8a04ef2..eaad0f6 100644
--- a/lib/msun/Makefile
+++ b/lib/msun/Makefile
@@ -40,7 +40,8 @@ COMMON_SRCS= b_exp.c b_log.c b_tgamma.c \
 	k_tan.c k_tanf.c \
 	s_asinh.c s_asinhf.c s_atan.c s_atanf.c s_carg.c s_cargf.c \
 	s_cbrt.c s_cbrtf.c s_ceil.c s_ceilf.c s_ceill.c \
-	s_copysign.c s_copysignf.c s_cos.c s_cosf.c s_erf.c s_erff.c \
+	s_copysign.c s_copysignf.c s_cos.c s_cosf.c \
+	s_csqrt.c s_csqrtf.c s_erf.c s_erff.c \
 	s_exp2.c s_exp2f.c s_expm1.c s_expm1f.c s_fabsf.c s_fdim.c \
 	s_finite.c s_finitef.c \
 	s_floor.c s_floorf.c s_floorl.c s_fma.c s_fmaf.c \
@@ -93,7 +94,7 @@ SRCS=	${COMMON_SRCS} ${ARCH_SRCS}
 INCS=	fenv.h math.h
 
 MAN=	acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 ceil.3 \
-	cimag.3 copysign.3 cos.3 cosh.3 erf.3 exp.3 fabs.3 fdim.3 \
+	cimag.3 copysign.3 cos.3 cosh.3 csqrt.3 erf.3 exp.3 fabs.3 fdim.3 \
 	feclearexcept.3 feenableexcept.3 fegetenv.3 \
 	fegetround.3 fenv.3 floor.3 \
 	fma.3 fmax.3 fmod.3 hypot.3 ieee.3 ieee_test.3 ilogb.3 j0.3 \
@@ -114,6 +115,7 @@ MLINKS+=cimag.3 cimagf.3 cimag.3 cimagl.3 \
 MLINKS+=copysign.3 copysignf.3 copysign.3 copysignl.3
 MLINKS+=cos.3 cosf.3
 MLINKS+=cosh.3 coshf.3
+MLINKS+=csqrt.3 csqrtf.3
 MLINKS+=erf.3 erfc.3 erf.3 erff.3 erf.3 erfcf.3
 MLINKS+=exp.3 expm1.3 exp.3 log.3 exp.3 log10.3 exp.3 log1p.3 exp.3 pow.3 \
 	exp.3 exp2.3 exp.3 exp2f.3 exp.3 expf.3 \
diff --git a/lib/msun/man/csqrt.3 b/lib/msun/man/csqrt.3
new file mode 100644
index 0000000..132b314
--- /dev/null
+++ b/lib/msun/man/csqrt.3
@@ -0,0 +1,94 @@
+.\" 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.
+.\"
+.\" $FreeBSD$
+.\"
+.Dd December 14, 2007
+.Dt CSQRT 3
+.Os
+.Sh NAME
+.Nm csqrt ,
+.Nm csqrtf
+.Nd complex square root functions
+.Sh LIBRARY
+.Lb libm
+.Sh SYNOPSIS
+.In complex.h
+.Ft double complex
+.Fn csqrt "double complex z"
+.Ft float complex
+.Fn csqrtf "float complex z"
+.Sh DESCRIPTION
+The
+.Fn csqrt
+and
+.Fn csqrtf
+functions compute the square root of
+.Fa z
+in the complex plane, with a branch cut along the negative real axis.
+In other words,
+.Fn csqrt
+and
+.Fn csqrtf
+always return the square root whose real part is non-negative.
+.Sh RETURN VALUES
+These functions return the requested square root.
+The square root of 0 is
+.Li +0 \*(Pm 0 ,
+where the imaginary parts of the input and respective result have
+the same sign.
+For infinities and \*(Nas, the following rules apply, with the
+earlier rules having precedence:
+.Bl -column -offset indent "-\*(If + \*(Na*I" "\*(If \*(Pm \*(If*I  " "(for all k)"
+.Em Input	Result
+k + \*(If*I	\*(If + \*(If*I	(for all k)
+-\*(If + \*(Na*I	\*(Na \*(Pm \*(If*I
+\*(If + \*(Na*I	\*(If + \*(Na*I
+k + \*(Na*I	\*(Na + \*(Na*I
+\*(Na + k*I	\*(Na + \*(Na*I
+-\*(If + k*I	+0 + \*(If*I
+\*(If + k*I	\*(If + 0*I
+.El
+.Pp
+For numbers with negative imaginary parts, the above special cases
+apply given the identity:
+.Dl csqrt(conj(z) = conj(sqrt(z))
+Note that the sign of \*(Na is indeterminate.
+Also, if the real or imaginary part of the input is finite and
+an \*(Na is generated, an invalid exception will be thrown.
+.Sh SEE ALSO
+.Xr cabs 3 ,
+.Xr fenv 3 ,
+.Xr math 3 ,
+.Sh STANDARDS
+The
+.Fn csqrt
+and
+.Fn csqrtf
+functions conform to
+.St -isoC-99 .
+.Sh BUGS
+For
+.Fn csqrt ,
+inexact results are not correctly rounded in general.
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)));
+	}
+}