- 80-bit and quad precision trigonometric and other most

important functions: acosl, asinl, atanl, atan2l, cosl,
sinl, tanl, exp2l, frexpl, ilogbl, ldexpl, logbl, scalbnl,
fabsl, hypotl, powl, sqrtl, rintl, copysignl, nanl, fdiml,
fmaxl, fminl.  mostly taken from freebsd, needed alot of
changes to adapt.  note, these are all c versions;  and are
quite slow when architectures have, e.g. sqrt.  assembly
versions will be added afterwards
- make them .weak/__weak_alias to the double precision
versions on other archs
- no need to have two finites.  finite() and finitef() are
non-standard 3BSD obsolete versions of isfinite.  remove
from libm.  make them weak_alias in libc to __isfinite and
__isfinitef instead.  similarly make 3BSD obsolete versions
of isinf, isinff, isnan, isnanf weak_aliases to C99's
__isinf, __isinff, __isnan, __isnanf
- remove unused infinity.c.  the c library has infinities
for each supported platform
- use STRICT_ASSIGN cast hack for _kernel_rem_pio2, so that
the double version has a chance of working on i386 with
extra precision
- avoid storing multiple copies of the pi/2 array, since
it won't vary
- bump major due to removed finite/finitef.  although they
will be in libc, which anything is linked to, minor bump
might be enough
ok millert@.   tested by sthen@, jsg@, ajacoutot@, kili@, naddy@

1 files changed, 230 insertions, 0 deletions

diff --git a/lib/libm/src/e_sqrtl.c b/lib/libm/src/e_sqrtl.c
new file mode 100644
index 00000000000..7ecc83381d7
--- /dev/null
+++ b/lib/libm/src/e_sqrtl.c
@@ -0,0 +1,230 @@
+/*	$OpenBSD: e_sqrtl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $	*/
+/*-
+ * Copyright (c) 2007 Steven G. Kargl
+ * 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 unmodified, 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 ``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 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/types.h>
+#include <machine/ieee.h>
+#include <float.h>
+#include <ieeefp.h>
+#include <math.h>
+
+#ifdef EXT_IMPLICIT_NBIT
+#define	LDBL_NBIT	0
+#else /* EXT_IMPLICIT_NBIT */
+#define	LDBL_NBIT	0x80000000
+#endif /* EXT_IMPLICIT_NBIT */
+
+/* Return (x + ulp) for normal positive x. Assumes no overflow. */
+static inline long double
+inc(long double x)
+{
+	struct ieee_ext *p = (struct ieee_ext *)&x;
+
+#ifdef EXT_FRACHMBITS
+	uint64_t frach;
+
+	frach = ((uint64_t)p->ext_frach << EXT_FRACHMBITS) | p->ext_frachm;
+	frach++;
+	p->ext_frach = frach >> EXT_FRACHMBITS;
+	p->ext_frachm = frach & 0x00000000ffffffff;
+#else /* EXT_FRACHMBITS */
+	uint32_t frach;
+
+	p->ext_frach++;
+	frach = p->ext_frach;
+#endif /* EXT_FRACHMBITS */
+
+	if (frach == 0) {
+
+#ifdef EXT_FRACLMBITS
+		uint64_t fracl;
+
+		fracl = ((uint64_t)p->ext_fraclm << EXT_FRACLBITS) |
+			p->ext_fracl;
+		fracl++;
+		p->ext_fraclm = fracl >> EXT_FRACLBITS;
+		p->ext_fracl = fracl & 0x00000000ffffffff;
+#else /* EXT_FRACLMBITS */
+		uint32_t fracl;
+
+		p->ext_fracl++;
+		fracl = p->ext_fracl;
+#endif /* EXT_FRACLMBITS */
+
+		if (fracl == 0) {
+			p->ext_exp++;
+			p->ext_frach |= LDBL_NBIT;
+		}
+	}
+
+	return x;
+}
+
+/* Return (x - ulp) for normal positive x. Assumes no underflow. */
+static inline long double
+dec(long double x)
+{
+	struct ieee_ext *p = (struct ieee_ext *)&x;
+
+#ifdef EXT_FRACLMBITS
+	uint64_t fracl;
+
+	fracl = ((uint64_t)p->ext_fraclm << EXT_FRACLBITS) | p->ext_fracl;
+	fracl--;
+	p->ext_fraclm = fracl >> EXT_FRACLBITS;
+	p->ext_fracl = fracl & 0x00000000ffffffff;
+#else /* EXT_FRACLMBITS */
+	uint32_t fracl;
+
+	p->ext_fracl--;
+	fracl = p->ext_fracl;
+#endif /* EXT_FRACLMBITS */
+
+	if (fracl == 0) {
+
+#ifdef EXT_FRACHMBITS
+		uint64_t frach;
+
+		frach = ((uint64_t)p->ext_frach << EXT_FRACHMBITS) |
+			p->ext_frachm;
+		frach--;
+		p->ext_frach = frach >> EXT_FRACHMBITS;
+		p->ext_frachm = frach & 0x00000000ffffffff;
+#else /* EXT_FRACHMBITS */
+		uint32_t frach;
+
+		p->ext_frach--;
+		frach = p->ext_frach;
+#endif /* EXT_FRACHMBITS */
+
+		if (frach == LDBL_NBIT) {
+			p->ext_exp--;
+			p->ext_frach |= LDBL_NBIT;
+		}
+	}
+
+	return x;
+}
+
+/*
+ * This is slow, but simple and portable. You should use hardware sqrt
+ * if possible.
+ */
+
+long double
+sqrtl(long double x)
+{
+	union {
+		long double e;
+		struct ieee_ext bits;
+	} u;
+	int k, r;
+	long double lo, xn;
+
+	u.e = x;
+
+	/* If x = NaN, then sqrt(x) = NaN. */
+	/* If x = Inf, then sqrt(x) = Inf. */
+	/* If x = -Inf, then sqrt(x) = NaN. */
+	if (u.bits.ext_exp == LDBL_MAX_EXP * 2 - 1)
+		return (x * x + x);
+
+	/* If x = +-0, then sqrt(x) = +-0. */
+	if ((u.bits.ext_frach
+#ifdef EXT_FRACHMBITS
+		| u.bits.ext_frachm
+#endif /* EXT_FRACHMBITS */
+#ifdef EXT_FRACLMBITS
+		| u.bits.ext_fraclm
+#endif /* EXT_FRACLMBITS */
+		| u.bits.ext_fracl | u.bits.ext_exp) == 0)
+		return (x);
+
+	/* If x < 0, then raise invalid and return NaN */
+	if (u.bits.ext_sign)
+		return ((x - x) / (x - x));
+
+	if (u.bits.ext_exp == 0) {
+		/* Adjust subnormal numbers. */
+		u.e *= 0x1.0p514;
+		k = -514;
+	} else {
+		k = 0;
+	}
+	/*
+	 * u.e is a normal number, so break it into u.e = e*2^n where
+	 * u.e = (2*e)*2^2k for odd n and u.e = (4*e)*2^2k for even n.
+	 */
+	if ((u.bits.ext_exp - 0x3ffe) & 1) {	/* n is odd.     */
+		k += u.bits.ext_exp - 0x3fff;	/* 2k = n - 1.   */
+		u.bits.ext_exp = 0x3fff;	/* u.e in [1,2). */
+	} else {
+		k += u.bits.ext_exp - 0x4000;	/* 2k = n - 2.   */
+		u.bits.ext_exp = 0x4000;	/* u.e in [2,4). */
+	}
+
+	/*
+	 * Newton's iteration.
+	 * Split u.e into a high and low part to achieve additional precision.
+	 */
+	xn = sqrt(u.e);			/* 53-bit estimate of sqrtl(x). */
+#if LDBL_MANT_DIG > 100
+	xn = (xn + (u.e / xn)) * 0.5;	/* 106-bit estimate. */
+#endif
+	lo = u.e;
+	u.bits.ext_fracl = 0;		/* Zero out lower bits. */
+#ifdef EXT_FRACLMBITS
+	u.bits.ext_fraclm = 0;
+#endif /* EXT_FRACLMBITS */
+	lo = (lo - u.e) / xn;		/* Low bits divided by xn. */
+	xn = xn + (u.e / xn);		/* High portion of estimate. */
+	u.e = xn + lo;			/* Combine everything. */
+	u.bits.ext_exp += (k >> 1) - 1;
+
+	fpsetsticky(fpgetsticky() & ~FP_X_IMP);
+	r = fpsetround(FP_RZ);		/* Set to round-toward-zero. */
+	xn = x / u.e;			/* Chopped quotient (inexact?). */
+
+	if (!(fpgetsticky() & FP_X_IMP)) { /* Quotient is exact. */
+		if (xn == u.e) {
+			fpsetround(r);
+			return (u.e);
+		}
+		/* Round correctly for inputs like x = y**2 - ulp. */
+		xn = dec(xn);		/* xn = xn - ulp. */
+	}
+
+	if (r == FP_RN) {
+		xn = inc(xn);		/* xn = xn + ulp. */
+	} else if (r == FP_RP) {
+		u.e = inc(u.e);		/* u.e = u.e + ulp. */
+		xn = inc(xn);		/* xn  = xn + ulp. */
+	}
+	u.e = u.e + xn;			/* Chopped sum. */
+	fpsetround(r);			/* Restore env and raise inexact */
+	u.bits.ext_exp--;
+	return (u.e);
+}