MI implementation of sqrtl(). This is very slow and should

be overridden when hardware sqrt is available.

lib/msun/src/e_sqrt.c

@@ -11,9 +11,8 @@
  * ====================================================
  */
 
-#ifndef lint
-static char rcsid[] = "$FreeBSD$";
-#endif
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
 
 /* __ieee754_sqrt(x)
  * Return correctly rounded sqrt.
@@ -85,6 +84,8 @@ static char rcsid[] = "$FreeBSD$";
  *---------------
  */
 
+#include <float.h>
+
 #include "math.h"
 #include "math_private.h"
 
@@ -187,6 +188,10 @@ __ieee754_sqrt(double x)
 	return z;
 }
 
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(sqrt, sqrtl);
+#endif
+
 /*
 Other methods  (use floating-point arithmetic)
 -------------

lib/msun/src/e_sqrtl.c

@@ -0,0 +1,159 @@
+/*-
+ * 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/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <fenv.h>
+#include <float.h>
+
+#include "fpmath.h"
+#include "math.h"
+
+/* Return (x + ulp) for normal positive x. Assumes no overflow. */
+static inline long double
+inc(long double x)
+{
+	union IEEEl2bits u;
+
+	u.e = x;
+	if (++u.bits.manl == 0) {
+		if (++u.bits.manh == 0) {
+			u.bits.exp++;
+			u.bits.manh |= LDBL_NBIT;
+		}
+	}
+	return (u.e);
+}
+
+/* Return (x - ulp) for normal positive x. Assumes no underflow. */
+static inline long double
+dec(long double x)
+{
+	union IEEEl2bits u;
+
+	u.e = x;
+	if (u.bits.manl-- == 0) {
+		if (u.bits.manh-- == LDBL_NBIT) {
+			u.bits.exp--;
+			u.bits.manh |= LDBL_NBIT;
+		}
+	}
+	return (u.e);
+}
+
+#pragma STDC FENV_ACCESS ON
+
+/*
+ * This is slow, but simple and portable. You should use hardware sqrt
+ * if possible.
+ */
+
+long double
+sqrtl(long double x)
+{
+	union IEEEl2bits u;
+	int k, r;
+	long double lo, xn;
+	fenv_t env;
+
+	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.exp == LDBL_MAX_EXP * 2 - 1)
+		return (x * x + x);
+
+	/* If x = +-0, then sqrt(x) = +-0. */
+	if ((u.bits.manh | u.bits.manl | u.bits.exp) == 0)
+		return (x);
+
+	/* If x < 0, then raise invalid and return NaN */
+	if (u.bits.sign)
+		return ((x - x) / (x - x));
+
+	feholdexcept(&env);
+
+	if (u.bits.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.exp - 0x3ffe) & 1) {	/* n is odd.     */
+		k += u.bits.exp - 0x3fff;	/* 2k = n - 1.   */
+		u.bits.exp = 0x3fff;		/* u.e in [1,2). */
+	} else {
+		k += u.bits.exp - 0x4000;	/* 2k = n - 2.   */
+		u.bits.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.manl = 0;		/* Zero out lower bits. */
+	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.exp += (k >> 1) - 1;
+
+	feclearexcept(FE_INEXACT);
+	r = fegetround();
+	fesetround(FE_TOWARDZERO);	/* Set to round-toward-zero. */
+	xn = x / u.e;			/* Chopped quotient (inexact?). */
+
+	if (!fetestexcept(FE_INEXACT)) { /* Quotient is exact. */
+		if (xn == u.e) {
+			fesetenv(&env);
+			return (u.e);
+		}
+		/* Round correctly for inputs like x = y**2 - ulp. */
+		xn = dec(xn);		/* xn = xn - ulp. */
+	}
+
+	if (r == FE_TONEAREST) {
+		xn = inc(xn);		/* xn = xn + ulp. */
+	} else if (r == FE_UPWARD) {
+		u.e = inc(u.e);		/* u.e = u.e + ulp. */
+		xn = inc(xn);		/* xn  = xn + ulp. */
+	}
+	u.e = u.e + xn;				/* Chopped sum. */
+	feupdateenv(&env);	/* Restore env and raise inexact */
+	u.bits.exp--;
+	return (u.e);
+}

lib/msun/src/math.h

@@ -468,8 +468,8 @@ long double	scalbnl(long double, int);
 long double	sinhl(long double);
 #endif
 long double	sinl(long double);
-#if 0
 long double	sqrtl(long double);
+#if 0
 long double	tanhl(long double);
 #endif
 long double	tanl(long double);