Add cexp() and cexpf().

Reviewed by:	bde (earlier version)

5 files changed, 317 insertions, 2 deletions

diff --git a/lib/msun/Makefile b/lib/msun/Makefile
index 7950961..2d7d5cc 100644
--- a/lib/msun/Makefile
+++ b/lib/msun/Makefile
@@ -101,7 +101,8 @@ COMMON_SRCS+=	e_acosl.c e_asinl.c e_atan2l.c e_fmodl.c \
 .endif
 
 # C99 complex functions
-COMMON_SRCS+=	s_cimag.c s_cimagf.c s_cimagl.c s_conj.c s_conjf.c s_conjl.c \
+COMMON_SRCS+=	s_cexp.c s_cexpf.c s_cimag.c s_cimagf.c s_cimagl.c \
+	s_conj.c s_conjf.c s_conjl.c \
 	s_cproj.c s_cprojf.c s_creal.c s_crealf.c s_creall.c
 
 # FreeBSD's C library supplies these functions:
@@ -124,7 +125,7 @@ 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 \
+MAN=	acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 ceil.3 cexp.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 \
@@ -143,6 +144,7 @@ MLINKS+=atanh.3 atanhf.3
 MLINKS+=atan2.3 atan2f.3 atan2.3 atan2l.3 \
 	atan2.3 carg.3 atan2.3 cargf.3 atan2.3 cargl.3
 MLINKS+=ceil.3 ceilf.3 ceil.3 ceill.3
+MLINKS+=cexp.3 cexpf.3
 MLINKS+=cimag.3 cimagf.3 cimag.3 cimagl.3 \
 	cimag.3 conj.3 cimag.3 conjf.3 cimag.3 conjl.3 \
 	cimag.3 cproj.3 cimag.3 cprojf.3 cimag.3 cprojl.3 \
diff --git a/lib/msun/Symbol.map b/lib/msun/Symbol.map
index 69618e6..2ef5ebf 100644
--- a/lib/msun/Symbol.map
+++ b/lib/msun/Symbol.map
@@ -222,6 +222,9 @@ FBSD_1.1 {
 /* First added in 9.0-CURRENT */
 FBSD_1.2 {
 	__isnanf;
+	cexp;
+	cexpf;
 	log2;
 	log2f;
+	logl;
 };
diff --git a/lib/msun/man/cexp.3 b/lib/msun/man/cexp.3
new file mode 100644
index 0000000..407284c
--- /dev/null
+++ b/lib/msun/man/cexp.3
@@ -0,0 +1,113 @@
+.\" 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.
+.\"
+.\" $FreeBSD$
+.\"
+.Dd March 6, 2011
+.Dt CEXP 3
+.Os
+.Sh NAME
+.Nm cexp ,
+.Nm cexpf
+.Nd complex exponential functions
+.Sh LIBRARY
+.Lb libm
+.Sh SYNOPSIS
+.In complex.h
+.Ft double complex
+.Fn cexp "double complex z"
+.Ft float complex
+.Fn cexpf "float complex z"
+.Sh DESCRIPTION
+The
+.Fn cexp
+and
+.Fn cexpf
+functions compute the complex exponential of
+.Fa z ,
+also known as
+.Em cis Ns ( Ns
+.Fa z Ns )
+.Sh RETURN VALUES
+For real numbers
+.Fa x
+and
+.Fa y ,
+.Fn cexp
+behaves according to Euler's formula:
+.Bd -ragged -offset indent
+.Fn cexp "x + I*y"
+=
+.Ns ( Sy e Ns ** Ns
+.Fa x *
+.Em cos Ns ( Ns
+.Fa y Ns )) + ( Ns
+.Sy I
+*
+.Sy e Ns ** Ns
+.Fa x
+*
+.Em sin Ns ( Ns
+.Fa y Ns ))
+.Ed
+.Pp
+Generally speaking, infinities, zeroes and \*(Nas are handled as would
+be expected from this identity given the usual rules of floating-point
+arithmetic.
+However, care is taken to avoid generating \*(Nas when they are not deserved.
+For example, mathematically we expect that
+.Fo cimag
+.Fn cexp "x + I*0" Fc
+= 0 regardless of the value of
+.Fa x ,
+and
+.Fn cexp
+preserves this identity even if
+.Fa x
+is \*(If or \*(Na.
+Likewise,
+.Fn cexp "-\*(If + I*y"
+= 0 and
+.Fo creal
+.Fn cexp "\*(If + I*y" Fc
+= \*(If
+for any
+.Fa y
+(even though the latter property is only mathematically true for
+representable
+.Fa y . )
+If
+.Fa y
+is not finite, the sign of the result is indeterminate.
+.Sh SEE ALSO
+.Xr complex 3 ,
+.Xr exp 3 ,
+.Xr math 3 ,
+.Sh STANDARDS
+The
+.Fn cexp
+and
+.Fn cexpf
+functions conform to
+.St -isoC-99 .
diff --git a/lib/msun/src/s_cexp.c b/lib/msun/src/s_cexp.c
new file mode 100644
index 0000000..ecf0992
--- /dev/null
+++ b/lib/msun/src/s_cexp.c
@@ -0,0 +1,99 @@
+/*-
+ * 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  = 0x40862e42,			/* high bits of MAX_EXP * ln2 ~= 710 */
+cexp_ovfl = 0x4096b8e4,			/* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
+k         = 1799;			/* constant for reduction */
+
+static const double
+kln2      =  1246.97177782734161156;	/* k * ln2 */
+
+double complex
+cexp(double complex z)
+{
+	double x, y, exp_x;
+	uint32_t hx, hy, lx, ly;
+	int scale;
+
+	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));
+	if (hy >= 0x7ff00000) {
+		EXTRACT_WORDS(hx, lx, x);
+		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));
+		}
+	}
+
+	GET_HIGH_WORD(hx, x);
+	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).  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 = exp(x - kln2);
+		GET_HIGH_WORD(hx, exp_x);
+		SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 52) << 20));
+		scale = (hx >> 20) - (0x3ff + 52) + k;
+		return (cpack(scalbn(cos(y) * exp_x, scale),
+			scalbn(sin(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 = exp(x);
+		return (cpack(exp_x * cos(y), exp_x * sin(y)));
+	}
+}
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)));
+	}
+}