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authorLinus Torvalds <torvalds@ppc970.osdl.org>2005-04-16 15:20:36 -0700
committerLinus Torvalds <torvalds@ppc970.osdl.org>2005-04-16 15:20:36 -0700
commit1da177e4c3f41524e886b7f1b8a0c1fc7321cac2 (patch)
tree0bba044c4ce775e45a88a51686b5d9f90697ea9d /arch/mips/math-emu/dp_sqrt.c
Linux-2.6.12-rc2v2.6.12-rc2
Initial git repository build. I'm not bothering with the full history, even though we have it. We can create a separate "historical" git archive of that later if we want to, and in the meantime it's about 3.2GB when imported into git - space that would just make the early git days unnecessarily complicated, when we don't have a lot of good infrastructure for it. Let it rip!
Diffstat (limited to 'arch/mips/math-emu/dp_sqrt.c')
-rw-r--r--arch/mips/math-emu/dp_sqrt.c165
1 files changed, 165 insertions, 0 deletions
diff --git a/arch/mips/math-emu/dp_sqrt.c b/arch/mips/math-emu/dp_sqrt.c
new file mode 100644
index 00000000000..c35e871ae97
--- /dev/null
+++ b/arch/mips/math-emu/dp_sqrt.c
@@ -0,0 +1,165 @@
+/* IEEE754 floating point arithmetic
+ * double precision square root
+ */
+/*
+ * MIPS floating point support
+ * Copyright (C) 1994-2000 Algorithmics Ltd.
+ * 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 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;
+ CLEARCX;
+ FLUSHXDP;
+
+ /* x == INF or NAN? */
+ switch (xc) {
+ case IEEE754_CLASS_QNAN:
+ /* sqrt(Nan) = Nan */
+ return ieee754dp_nanxcpt(x, "sqrt");
+ case IEEE754_CLASS_SNAN:
+ SETCX(IEEE754_INVALID_OPERATION);
+ return ieee754dp_nanxcpt(ieee754dp_indef(), "sqrt");
+ case IEEE754_CLASS_ZERO:
+ /* sqrt(0) = 0 */
+ return x;
+ case IEEE754_CLASS_INF:
+ if (xs) {
+ /* sqrt(-Inf) = Nan */
+ SETCX(IEEE754_INVALID_OPERATION);
+ return ieee754dp_nanxcpt(ieee754dp_indef(), "sqrt");
+ }
+ /* sqrt(+Inf) = Inf */
+ return x;
+ case IEEE754_CLASS_DNORM:
+ DPDNORMX;
+ /* fall through */
+ case IEEE754_CLASS_NORM:
+ if (xs) {
+ /* sqrt(-x) = Nan */
+ SETCX(IEEE754_INVALID_OPERATION);
+ return ieee754dp_nanxcpt(ieee754dp_indef(), "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 = ((u64) 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;
+}