patch-2.4.6 linux/arch/mips64/math-emu/dp_sqrt.c

• Lines: 168
• Date: Mon Jul 2 13:56:40 2001
• Orig file: v2.4.5/linux/arch/mips64/math-emu/dp_sqrt.c
• Orig date: Wed Dec 31 16:00:00 1969

diff -u --recursive --new-file v2.4.5/linux/arch/mips64/math-emu/dp_sqrt.c linux/arch/mips64/math-emu/dp_sqrt.c
@@ -0,0 +1,167 @@
+/* IEEE754 floating point arithmetic
+ * double precision square root
+ */
+/*
+ * MIPS floating point support
+ * Copyright (C) 1994-2000 Algorithmics Ltd.  All rights reserved.
+ * http://www.algor.co.uk
+ *
+ * ########################################################################
+ *
+ *  This program is free software; you can distribute it and/or modify it
+ *  under the terms of the GNU General Public License (Version 2) as
+ *  published by the Free Software Foundation.
+ *
+ *  This program is distributed in the hope it will be useful, but WITHOUT
+ *  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+ *  FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+ *  for more details.
+ *
+ *  You should have received a copy of the GNU General Public License along
+ *  with this program; if not, write to the Free Software Foundation, Inc.,
+ *  59 Temple Place - Suite 330, Boston MA 02111-1307, USA.
+ *
+ * ########################################################################
+ */
+
+
+#include "ieee754dp.h"
+
+static const struct ieee754dp_konst knan = {
+#if (defined(BYTE_ORDER) && BYTE_ORDER == LITTLE_ENDIAN) || defined(__MIPSEL__)
+	0, 0, DP_EBIAS + DP_EMAX + 1, 0
+#else
+	0, DP_EBIAS + DP_EMAX + 1, 0, 0
+#endif
+};
+
+#define nan	((ieee754dp)knan)
+
+static const unsigned table[] = {
+	0, 1204, 3062, 5746, 9193, 13348, 18162, 23592,
+	29598, 36145, 43202, 50740, 58733, 67158, 75992,
+	85215, 83599, 71378, 60428, 50647, 41945, 34246,
+	27478, 21581, 16499, 12183, 8588, 5674, 3403,
+	1742, 661, 130
+};
+
+ieee754dp ieee754dp_sqrt(ieee754dp x)
+{
+	struct ieee754_csr oldcsr;
+	ieee754dp y, z, t;
+	unsigned scalx, yh;
+	COMPXDP;
+
+	EXPLODEXDP;
+
+	/* x == INF or NAN? */
+	switch (xc) {
+	case IEEE754_CLASS_QNAN:
+	case IEEE754_CLASS_SNAN:
+		/* sqrt(Nan) = Nan */
+		return ieee754dp_nanxcpt(x, "sqrt");
+	case IEEE754_CLASS_ZERO:
+		/* sqrt(0) = 0 */
+		return x;
+	case IEEE754_CLASS_INF:
+		if (xs)
+			/* sqrt(-Inf) = Nan */
+			return ieee754dp_nanxcpt(nan, "sqrt");
+		/* sqrt(+Inf) = Inf */
+		return x;
+	case IEEE754_CLASS_DNORM:
+		DPDNORMX;
+		/* fall through */
+	case IEEE754_CLASS_NORM:
+		if (xs)
+			/* sqrt(-x) = Nan */
+			return ieee754dp_nanxcpt(nan, "sqrt");
+		break;
+	}
+
+	/* save old csr; switch off INX enable & flag; set RN rounding */
+	oldcsr = ieee754_csr;
+	ieee754_csr.mx &= ~IEEE754_INEXACT;
+	ieee754_csr.sx &= ~IEEE754_INEXACT;
+	ieee754_csr.rm = IEEE754_RN;
+
+	/* adjust exponent to prevent overflow */
+	scalx = 0;
+	if (xe > 512) {		/* x > 2**-512? */
+		xe -= 512;	/* x = x / 2**512 */
+		scalx += 256;
+	} else if (xe < -512) {	/* x < 2**-512? */
+		xe += 512;	/* x = x * 2**512 */
+		scalx -= 256;
+	}
+
+	y = x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
+
+	/* magic initial approximation to almost 8 sig. bits */
+	yh = y.bits >> 32;
+	yh = (yh >> 1) + 0x1ff80000;
+	yh = yh - table[(yh >> 15) & 31];
+	y.bits = ((unsigned long long) yh << 32) | (y.bits & 0xffffffff);
+
+	/* Heron's rule once with correction to improve to ~18 sig. bits */
+	/* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */
+	t = ieee754dp_div(x, y);
+	y = ieee754dp_add(y, t);
+	y.bits -= 0x0010000600000000LL;
+	y.bits &= 0xffffffff00000000LL;
+
+	/* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */
+	/* t=y*y; z=t;  pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */
+	z = t = ieee754dp_mul(y, y);
+	t.parts.bexp += 0x001;
+	t = ieee754dp_add(t, z);
+	z = ieee754dp_mul(ieee754dp_sub(x, z), y);
+
+	/* t=z/(t+x) ;  pt[n0]+=0x00100000; y+=t; */
+	t = ieee754dp_div(z, ieee754dp_add(t, x));
+	t.parts.bexp += 0x001;
+	y = ieee754dp_add(y, t);
+
+	/* twiddle last bit to force y correctly rounded */
+
+	/* set RZ, clear INEX flag */
+	ieee754_csr.rm = IEEE754_RZ;
+	ieee754_csr.sx &= ~IEEE754_INEXACT;
+
+	/* t=x/y; ...chopped quotient, possibly inexact */
+	t = ieee754dp_div(x, y);
+
+	if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) {
+
+		if (!(ieee754_csr.sx & IEEE754_INEXACT))
+			/* t = t-ulp */
+			t.bits -= 1;
+
+		/* add inexact to result status */
+		oldcsr.cx |= IEEE754_INEXACT;
+		oldcsr.sx |= IEEE754_INEXACT;
+
+		switch (oldcsr.rm) {
+		case IEEE754_RP:
+			y.bits += 1;
+			/* drop through */
+		case IEEE754_RN:
+			t.bits += 1;
+			break;
+		}
+
+		/* y=y+t; ...chopped sum */
+		y = ieee754dp_add(y, t);
+
+		/* adjust scalx for correctly rounded sqrt(x) */
+		scalx -= 1;
+	}
+
+	/* py[n0]=py[n0]+scalx; ...scale back y */
+	y.parts.bexp += scalx;
+
+	/* restore rounding mode, possibly set inexact */
+	ieee754_csr = oldcsr;
+
+	return y;
+}