693 Opensource replacement of sunwlibm

Reviewed by: Igor Kozhukhov ikozhukhov@gmail.com
Reviewed by: Keith M Wesolowski <keith.wesolowski@joyent.com>
Reviewed by: Richard Lowe <richlowe@richlowe.net>
Approved by: Dan McDonald <danmcd@omniti.com>

1 files changed, 479 insertions, 0 deletions

diff --git a/usr/src/lib/libm/common/Q/sqrtl.c b/usr/src/lib/libm/common/Q/sqrtl.c
new file mode 100644
index 0000000000..30c8f5e097
--- /dev/null
+++ b/usr/src/lib/libm/common/Q/sqrtl.c
@@ -0,0 +1,479 @@
+/*
+ * CDDL HEADER START
+ *
+ * The contents of this file are subject to the terms of the
+ * Common Development and Distribution License (the "License").
+ * You may not use this file except in compliance with the License.
+ *
+ * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
+ * or http://www.opensolaris.org/os/licensing.
+ * See the License for the specific language governing permissions
+ * and limitations under the License.
+ *
+ * When distributing Covered Code, include this CDDL HEADER in each
+ * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
+ * If applicable, add the following below this CDDL HEADER, with the
+ * fields enclosed by brackets "[]" replaced with your own identifying
+ * information: Portions Copyright [yyyy] [name of copyright owner]
+ *
+ * CDDL HEADER END
+ */
+
+/*
+ * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
+ */
+/*
+ * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
+ * Use is subject to license terms.
+ */
+
+#pragma weak sqrtl = __sqrtl
+
+#include "libm.h"
+#include "longdouble.h"
+
+extern int __swapTE(int);
+extern int __swapEX(int);
+extern enum fp_direction_type __swapRD(enum fp_direction_type);
+
+/*
+ * in struct longdouble, msw consists of
+ *	unsigned short	sgn:1;
+ *	unsigned short	exp:15;
+ *	unsigned short	frac1:16;
+ */
+
+#ifdef __LITTLE_ENDIAN
+
+/* array indices used to access words within a double */
+#define	HIWORD	1
+#define	LOWORD	0
+
+/* structure used to access words within a quad */
+union longdouble {
+	struct {
+		unsigned int	frac4;
+		unsigned int	frac3;
+		unsigned int	frac2;
+		unsigned int	msw;
+	} l;
+	long double	d;
+};
+
+/* default NaN returned for sqrt(neg) */
+static const union longdouble
+	qnan = { 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff };
+
+/* signalling NaN used to raise invalid */
+static const union {
+	unsigned u[2];
+	double d;
+} snan = { 0, 0x7ff00001 };
+
+#else
+
+/* array indices used to access words within a double */
+#define	HIWORD	0
+#define	LOWORD	1
+
+/* structure used to access words within a quad */
+union longdouble {
+	struct {
+		unsigned int	msw;
+		unsigned int	frac2;
+		unsigned int	frac3;
+		unsigned int	frac4;
+	} l;
+	long double	d;
+};
+
+/* default NaN returned for sqrt(neg) */
+static const union longdouble
+	qnan = { 0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff };
+
+/* signalling NaN used to raise invalid */
+static const union {
+	unsigned u[2];
+	double d;
+} snan = { 0x7ff00001, 0 };
+
+#endif /* __LITTLE_ENDIAN */
+
+
+static const double
+	zero = 0.0,
+	half = 0.5,
+	one = 1.0,
+	huge = 1.0e300,
+	tiny = 1.0e-300,
+	two36 = 6.87194767360000000000e+10,
+	two30 = 1.07374182400000000000e+09,
+	two6 = 6.40000000000000000000e+01,
+	two4 = 1.60000000000000000000e+01,
+	twom18 = 3.81469726562500000000e-06,
+	twom28 = 3.72529029846191406250e-09,
+	twom42 = 2.27373675443232059479e-13,
+	twom60 = 8.67361737988403547206e-19,
+	twom62 = 2.16840434497100886801e-19,
+	twom66 = 1.35525271560688054251e-20,
+	twom90 = 8.07793566946316088742e-28,
+	twom113 = 9.62964972193617926528e-35,
+	twom124 = 4.70197740328915003187e-38;
+
+
+/*
+*	Extract the exponent and normalized significand (represented as
+*	an array of five doubles) from a finite, nonzero quad.
+*/
+static int
+__q_unpack(const union longdouble *x, double *s)
+{
+	union {
+		double			d;
+		unsigned int	l[2];
+	} u;
+	double			b;
+	unsigned int	lx, w[3];
+	int				ex;
+
+	/* get the normalized significand and exponent */
+	ex = (int) ((x->l.msw & 0x7fffffff) >> 16);
+	lx = x->l.msw & 0xffff;
+	if (ex)
+	{
+		lx |= 0x10000;
+		w[0] = x->l.frac2;
+		w[1] = x->l.frac3;
+		w[2] = x->l.frac4;
+	}
+	else
+	{
+		if (lx | (x->l.frac2 & 0xfffe0000))
+		{
+			w[0] = x->l.frac2;
+			w[1] = x->l.frac3;
+			w[2] = x->l.frac4;
+			ex = 1;
+		}
+		else if (x->l.frac2 | (x->l.frac3 & 0xfffe0000))
+		{
+			lx = x->l.frac2;
+			w[0] = x->l.frac3;
+			w[1] = x->l.frac4;
+			w[2] = 0;
+			ex = -31;
+		}
+		else if (x->l.frac3 | (x->l.frac4 & 0xfffe0000))
+		{
+			lx = x->l.frac3;
+			w[0] = x->l.frac4;
+			w[1] = w[2] = 0;
+			ex = -63;
+		}
+		else
+		{
+			lx = x->l.frac4;
+			w[0] = w[1] = w[2] = 0;
+			ex = -95;
+		}
+		while ((lx & 0x10000) == 0)
+		{
+			lx = (lx << 1) | (w[0] >> 31);
+			w[0] = (w[0] << 1) | (w[1] >> 31);
+			w[1] = (w[1] << 1) | (w[2] >> 31);
+			w[2] <<= 1;
+			ex--;
+		}
+	}
+
+	/* extract the significand into five doubles */
+	u.l[HIWORD] = 0x42300000;
+	u.l[LOWORD] = 0;
+	b = u.d;
+	u.l[LOWORD] = lx;
+	s[0] = u.d - b;
+
+	u.l[HIWORD] = 0x40300000;
+	u.l[LOWORD] = 0;
+	b = u.d;
+	u.l[LOWORD] = w[0] & 0xffffff00;
+	s[1] = u.d - b;
+
+	u.l[HIWORD] = 0x3e300000;
+	u.l[LOWORD] = 0;
+	b = u.d;
+	u.l[HIWORD] |= w[0] & 0xff;
+	u.l[LOWORD] = w[1] & 0xffff0000;
+	s[2] = u.d - b;
+
+	u.l[HIWORD] = 0x3c300000;
+	u.l[LOWORD] = 0;
+	b = u.d;
+	u.l[HIWORD] |= w[1] & 0xffff;
+	u.l[LOWORD] = w[2] & 0xff000000;
+	s[3] = u.d - b;
+
+	u.l[HIWORD] = 0x3c300000;
+	u.l[LOWORD] = 0;
+	b = u.d;
+	u.l[LOWORD] = w[2] & 0xffffff;
+	s[4] = u.d - b;
+
+	return ex - 0x3fff;
+}
+
+
+/*
+*	Pack an exponent and array of three doubles representing a finite,
+*	nonzero number into a quad.  Assume the sign is already there and
+*	the rounding mode has been fudged accordingly.
+*/
+static void
+__q_pack(const double *z, int exp, enum fp_direction_type rm,
+	union longdouble *x, int *inexact)
+{
+	union {
+		double			d;
+		unsigned int	l[2];
+	} u;
+	double			s[3], t, t2;
+	unsigned int	msw, frac2, frac3, frac4;
+
+	/* bias exponent and strip off integer bit */
+	exp += 0x3fff;
+	s[0] = z[0] - one;
+	s[1] = z[1];
+	s[2] = z[2];
+
+	/*
+	 * chop the significand to obtain the fraction;
+	 * use round-to-minus-infinity to ensure chopping
+	 */
+	(void) __swapRD(fp_negative);
+
+	/* extract the first eighty bits of fraction */
+	t = s[1] + s[2];
+	u.d = two36 + (s[0] + t);
+	msw = u.l[LOWORD];
+	s[0] -= (u.d - two36);
+
+	u.d = two4 + (s[0] + t);
+	frac2 = u.l[LOWORD];
+	s[0] -= (u.d - two4);
+
+	u.d = twom28 + (s[0] + t);
+	frac3 = u.l[LOWORD];
+	s[0] -= (u.d - twom28);
+
+	/* condense the remaining fraction; errors here won't matter */
+	t = s[0] + s[1];
+	s[1] = ((s[0] - t) + s[1]) + s[2];
+	s[0] = t;
+
+	/* get the last word of fraction */
+	u.d = twom60 + (s[0] + s[1]);
+	frac4 = u.l[LOWORD];
+	s[0] -= (u.d - twom60);
+
+	/*
+	 * keep track of what's left for rounding; note that
+	 * t2 will be non-negative due to rounding mode
+	 */
+	t = s[0] + s[1];
+	t2 = (s[0] - t) + s[1];
+
+	if (t != zero)
+	{
+		*inexact = 1;
+
+		/* decide whether to round the fraction up */
+		if (rm == fp_positive || (rm == fp_nearest && (t > twom113 ||
+			(t == twom113 && (t2 != zero || frac4 & 1)))))
+		{
+			/* round up and renormalize if necessary */
+			if (++frac4 == 0)
+				if (++frac3 == 0)
+					if (++frac2 == 0)
+						if (++msw == 0x10000)
+						{
+							msw = 0;
+							exp++;
+						}
+		}
+	}
+
+	/* assemble the result */
+	x->l.msw |= msw | (exp << 16);
+	x->l.frac2 = frac2;
+	x->l.frac3 = frac3;
+	x->l.frac4 = frac4;
+}
+
+
+/*
+*	Compute the square root of x and place the TP result in s.
+*/
+static void
+__q_tp_sqrt(const double *x, double *s)
+{
+	double	c, rr, r[3], tt[3], t[5];
+
+	/* approximate the divisor for the Newton iteration */
+	c = sqrt((x[0] + x[1]) + x[2]);
+	rr = half / c;
+
+	/* compute the first five "digits" of the square root */
+	t[0] = (c + two30) - two30;
+	tt[0] = t[0] + t[0];
+	r[0] = ((x[0] - t[0] * t[0]) + x[1]) + x[2];
+
+	t[1] = (rr * (r[0] + x[3]) + two6) - two6;
+	tt[1] = t[1] + t[1];
+	r[0] -= tt[0] * t[1];
+	r[1] = x[3] - t[1] * t[1];
+	c = (r[1] + twom18) - twom18;
+	r[0] += c;
+	r[1] = (r[1] - c) + x[4];
+
+	t[2] = (rr * (r[0] + r[1]) + twom18) - twom18;
+	tt[2] = t[2] + t[2];
+	r[0] -= tt[0] * t[2];
+	r[1] -= tt[1] * t[2];
+	c = (r[1] + twom42) - twom42;
+	r[0] += c;
+	r[1] = (r[1] - c) - t[2] * t[2];
+
+	t[3] = (rr * (r[0] + r[1]) + twom42) - twom42;
+	r[0] = ((r[0] - tt[0] * t[3]) + r[1]) - tt[1] * t[3];
+	r[1] = -tt[2] * t[3];
+	c = (r[1] + twom90) - twom90;
+	r[0] += c;
+	r[1] = (r[1] - c) - t[3] * t[3];
+
+	t[4] = (rr * (r[0] + r[1]) + twom66) - twom66;
+
+	/* here we just need to get the sign of the remainder */
+	c = (((((r[0] - tt[0] * t[4]) - tt[1] * t[4]) + r[1])
+		- tt[2] * t[4]) - (t[3] + t[3]) * t[4]) - t[4] * t[4];
+
+	/* reduce to three doubles */
+	t[0] += t[1];
+	t[1] = t[2] + t[3];
+	t[2] = t[4];
+
+	/* if the third term might lie on a rounding boundary, perturb it */
+	if (c != zero && t[2] == (twom62 + t[2]) - twom62)
+	{
+		if (c < zero)
+			t[2] -= twom124;
+		else
+			t[2] += twom124;
+	}
+
+	/* condense the square root */
+	c = t[1] + t[2];
+	t[2] += (t[1] - c);
+	t[1] = c;
+	c = t[0] + t[1];
+	s[1] = t[1] + (t[0] - c);
+	s[0] = c;
+	if (s[1] == zero)
+	{
+		c = s[0] + t[2];
+		s[1] = t[2] + (s[0] - c);
+		s[0] = c;
+		s[2] = zero;
+	}
+	else
+	{
+		c = s[1] + t[2];
+		s[2] = t[2] + (s[1] - c);
+		s[1] = c;
+	}
+}
+
+
+long double
+sqrtl(long double ldx)
+{
+	union	longdouble		x;
+	volatile double			t;
+	double					xx[5], zz[3];
+	enum fp_direction_type	rm;
+	int				ex, inexact, exc, traps;
+
+	/* clear cexc */
+	t = zero;
+	t -= zero;
+
+	/* check for zero operand */
+	x.d = ldx;
+	if (!((x.l.msw & 0x7fffffff) | x.l.frac2 | x.l.frac3 | x.l.frac4))
+		return ldx;
+
+	/* handle nan and inf cases */
+	if ((x.l.msw & 0x7fffffff) >= 0x7fff0000)
+	{
+		if ((x.l.msw & 0xffff) | x.l.frac2 | x.l.frac3 | x.l.frac4)
+		{
+			if (!(x.l.msw & 0x8000))
+			{
+				/* snan, signal invalid */
+				t += snan.d;
+			}
+			x.l.msw |= 0x8000;
+			return x.d;
+		}
+		if (x.l.msw & 0x80000000)
+		{
+			/* sqrt(-inf), signal invalid */
+			t = -one;
+			t = sqrt(t);
+			return qnan.d;
+		}
+		/* sqrt(inf), return inf */
+		return x.d;
+	}
+
+	/* handle negative numbers */
+	if (x.l.msw & 0x80000000)
+	{
+		t = -one;
+		t = sqrt(t);
+		return qnan.d;
+	}
+
+	/* now x is finite, positive */
+
+	traps = __swapTE(0);
+	exc = __swapEX(0);
+	rm = __swapRD(fp_nearest);
+
+	ex = __q_unpack(&x, xx);
+	if (ex & 1)
+	{
+		/* make exponent even */
+		xx[0] += xx[0];
+		xx[1] += xx[1];
+		xx[2] += xx[2];
+		xx[3] += xx[3];
+		xx[4] += xx[4];
+		ex--;
+	}
+	__q_tp_sqrt(xx, zz);
+
+	/* put everything together */
+	x.l.msw = 0;
+	inexact = 0;
+	__q_pack(zz, ex >> 1, rm, &x, &inexact);
+
+	(void) __swapRD(rm);
+	(void) __swapEX(exc);
+	(void) __swapTE(traps);
+	if (inexact)
+	{
+		t = huge;
+		t += tiny;
+	}
+	return x.d;
+}