- replace dtoa w/ David's gdtoa, version 2008-03-15

- provide proper dtoa locks
- use the real strtof implementation
- add strtold, __hdtoa, __hldtoa
- add %a/%A support
- don't lose precision in printf, don't round to double anymore
- implement extended-precision versions of libc functions: fpclassify,
isnan, isinf, signbit, isnormal, isfinite, now that the ieee.h is
fixed
- separate vax versions of strtof, and __hdtoa
- add complex math support.  added functions: cacos, casin, catan,
ccos, csin, ctan, cacosh, casinh, catanh, ccosh, csinh, ctanh, cexp,
clog, cabs, cpow, csqrt, carg, cimag, conj, cproj, creal, cacosf,
casinf, catanf, ccosf, csinf, ctanf, cacoshf, casinhf, catanhf,
ccoshf, csinhf, ctanhf, cexpf, clogf, cabsf, cpowf, csqrtf, cargf,
cimagf, conjf, cprojf, crealf
- add fdim, fmax, fmin
- add log2. (adapted implementation e_log.c.  could be more acruate
& faster, but it's good enough for now)
- remove wrappers & cruft in libm, supposed to work-around mistakes
in SVID, etc.;  use ieee versions.  fixes issues in python 2.6 for
djm@
- make _digittoint static
- proper definitions for i386, and amd64 in ieee.h
- sh, powerpc don't really have extended-precision
- add missing definitions for mips64 (quad), m{6,8}k (96-bit) float.h
for LDBL_*
- merge lead to frac for m{6,8}k, for gdtoa to work properly
- add FRAC*BITS & EXT_TO_ARRAY32 definitions in ieee.h, for hdtoa&ldtoa
to use
- add EXT_IMPLICIT_NBIT definition, which indicates implicit
normalization bit
- add regression tests for libc: fpclassify and printf
- arith.h & gd_qnan.h definitions
- update ieee.h: hppa doesn't have quad-precision, hppa64 does
- add missing prototypes to gdtoaimp
- on 64-bit platforms make sure gdtoa doesn't use a long when it
really wants an int
- etc., what i may have forgotten...
- bump libm major, due to removed&changed symbols
- no libc bump, since this is riding on djm's libc major crank from
a day ago

discussed with / requested by / testing theo, sthen@, djm@, jsg@,
merdely@, jsing@, tedu@, brad@, jakemsr@, and others.
looks good to millert@
parts of the diff ok kettenis@

this commit does not include:
- man page changes

1 files changed, 131 insertions, 0 deletions

diff --git a/lib/libm/src/s_csqrt.c b/lib/libm/src/s_csqrt.c
new file mode 100644
index 00000000000..3ed4aa56076
--- /dev/null
+++ b/lib/libm/src/s_csqrt.c
@@ -0,0 +1,131 @@
+/*	$OpenBSD: s_csqrt.c,v 1.1 2008/09/07 20:36:09 martynas Exp $	*/
+/*
+ * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
+ *
+ * Permission to use, copy, modify, and distribute this software for any
+ * purpose with or without fee is hereby granted, provided that the above
+ * copyright notice and this permission notice appear in all copies.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
+ * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
+ * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
+ * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
+ * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
+ * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ */
+
+/*							csqrt()
+ *
+ *	Complex square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double complex csqrt();
+ * double complex z, w;
+ *
+ * w = csqrt (z);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy,  r = |z|, then
+ *
+ *                       1/2
+ * Re w  =  [ (r + x)/2 ]   ,
+ *
+ *                       1/2
+ * Im w  =  [ (r - x)/2 ]   .
+ *
+ * Cancellation error in r-x or r+x is avoided by using the
+ * identity  2 Re w Im w  =  y.
+ *
+ * Note that -w is also a square root of z.  The root chosen
+ * is always in the right half plane and Im w has the same sign as y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10     25000       3.2e-17     9.6e-18
+ *    IEEE      -10,+10   1,000,000     2.9e-16     6.1e-17
+ *
+ */
+
+#include <complex.h>
+#include <math.h>
+
+double complex
+csqrt(double complex z)
+{
+	double complex w;
+	double x, y, r, t, scale;
+
+	x = creal (z);
+	y = cimag (z);
+
+	if (y == 0.0) {
+		if (x == 0.0) {
+			w = 0.0 + y * I;
+		}
+		else {
+			r = fabs (x);
+			r = sqrt (r);
+			if (x < 0.0) {
+				w = 0.0 + r * I;
+			}
+			else {
+				w = r + y * I;
+			}
+		}
+		return (w);
+	}
+	if (x == 0.0) {
+		r = fabs (y);
+		r = sqrt (0.5*r);
+		if (y > 0)
+			w = r + r * I;
+		else
+			w = r - r * I;
+		return (w);
+	}
+	/* Rescale to avoid internal overflow or underflow.  */
+	if ((fabs(x) > 4.0) || (fabs(y) > 4.0)) {
+		x *= 0.25;
+		y *= 0.25;
+		scale = 2.0;
+	}
+	else {
+		x *= 1.8014398509481984e16;  /* 2^54 */
+		y *= 1.8014398509481984e16;
+		scale = 7.450580596923828125e-9; /* 2^-27 */
+#if 0
+		x *= 4.0;
+		y *= 4.0;
+		scale = 0.5;
+#endif
+	}
+	w = x + y * I;
+	r = cabs(w);
+	if (x > 0) {
+		t = sqrt(0.5 * r + 0.5 * x);
+		r = scale * fabs((0.5 * y) / t);
+		t *= scale;
+	}
+	else {
+		r = sqrt( 0.5 * r - 0.5 * x );
+		t = scale * fabs( (0.5 * y) / r );
+		r *= scale;
+	}
+	if (y < 0)
+		w = t - r * I;
+	else
+		w = t + r * I;
+	return (w);
+}