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, 590 insertions, 0 deletions

diff --git a/usr/src/lib/libmvec/common/__vexp.c b/usr/src/lib/libmvec/common/__vexp.c
new file mode 100644
index 0000000000..9ab50556a1
--- /dev/null
+++ b/usr/src/lib/libmvec/common/__vexp.c
@@ -0,0 +1,590 @@
+/*
+ * 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 2005 Sun Microsystems, Inc.  All rights reserved.
+ * Use is subject to license terms.
+ */
+
+/*
+ * __vexp: double precision vector exp
+ *
+ * Algorithm:
+ *
+ * Write x = (k + j/256)ln2 + r, where k and j are integers, j >= 0,
+ * and |r| <= ln2/512.  Then exp(x) = 2^k * 2^(j/256) * exp(r).
+ * Compute exp(r) by a polynomial approximation exp(r) ~ 1 + p(r)
+ * where p(r) := r*(1+r*(B1+r*(B2+r*B3))).  From a table, obtain
+ * h and l such that h ~ 2^(j/256) to double precision and h+l
+ * ~ 2^(j/256) to well more than double precision.  Then exp(x)
+ * ~ 2^k * (h + (l + h * p(r))) to about double precision.  Note
+ * that the multiplication by 2^k requires some finagling when
+ * the result might be subnormal.
+ *
+ * Accuracy:
+ *
+ * For normal results, the largest error observed is less than
+ * 0.6 ulps.  For subnormal results, the largest error observed
+ * is 0.737 ulps.
+ */
+
+#include <sys/isa_defs.h>
+
+#ifdef _LITTLE_ENDIAN
+#define	HI(x)	*(1+(int *)&x)
+#define	LO(x)	*(unsigned *)&x
+#define	DBLWORD(x, y)	y, x
+#else
+#define	HI(x)	*(int *)&x
+#define	LO(x)	*(1+(unsigned *)&x)
+#define	DBLWORD(x, y)	x, y
+#endif
+
+#ifdef __RESTRICT
+#define	restrict _Restrict
+#else
+#define	restrict
+#endif
+
+static const double TBL[] = {
+	1.00000000000000000000e+00,  0.00000000000000000000e+00,
+	1.00271127505020252180e+00, -3.63661592869226394432e-17,
+	1.00542990111280272636e+00,  9.49918653545503175702e-17,
+	1.00815589811841754830e+00, -3.25205875608430806089e-17,
+	1.01088928605170047526e+00, -1.52347786033685771763e-17,
+	1.01363008495148942956e+00,  9.28359976818356758749e-18,
+	1.01637831491095309566e+00, -5.77217007319966002766e-17,
+	1.01913399607773791367e+00,  3.60190498225966110587e-17,
+	1.02189714865411662714e+00,  5.10922502897344389359e-17,
+	1.02466779289713572076e+00, -7.56160786848777820704e-17,
+	1.02744594911876374610e+00, -4.95607417464536982418e-17,
+	1.03023163768604097967e+00,  3.31983004108081294377e-17,
+	1.03302487902122841490e+00,  7.60083887402708848935e-18,
+	1.03582569360195719810e+00, -7.80678239133763616702e-17,
+	1.03863410196137873065e+00,  5.99627378885251061843e-17,
+	1.04145012468831610342e+00,  3.78483048028757620966e-17,
+	1.04427378242741375480e+00,  8.55188970553796365958e-17,
+	1.04710509587928979336e+00,  7.27707724310431474861e-17,
+	1.04994408580068721015e+00,  5.59293784812700258637e-17,
+	1.05279077300462642341e+00, -9.62948289902693573942e-17,
+	1.05564517836055715705e+00,  1.75932573877209198414e-18,
+	1.05850732279451276163e+00, -7.15265185663778073796e-17,
+	1.06137722728926209292e+00, -1.19735370853656575649e-17,
+	1.06425491288446449900e+00,  5.07875419861123039357e-17,
+	1.06714040067682369717e+00, -7.89985396684158212226e-17,
+	1.07003371182024187291e+00, -9.93716271128891938112e-17,
+	1.07293486752597555522e+00, -3.83966884335882380671e-18,
+	1.07584388906279104781e+00, -1.00027161511441361125e-17,
+	1.07876079775711986031e+00, -6.65666043605659260344e-17,
+	1.08168561499321524977e+00, -4.78262390299708626556e-17,
+	1.08461836221330920615e+00,  3.16615284581634611576e-17,
+	1.08755906091776965994e+00,  5.40934930782029075923e-18,
+	1.09050773266525768967e+00, -3.04678207981247114697e-17,
+	1.09346439907288583981e+00,  1.44139581472692093420e-17,
+	1.09642908181637688259e+00, -5.91993348444931582405e-17,
+	1.09940180263022191376e+00,  7.17045959970192322483e-17,
+	1.10238258330784089090e+00,  5.26603687157069438656e-17,
+	1.10537144570174117320e+00,  8.23928876050021358995e-17,
+	1.10836841172367872588e+00, -8.78681384518052661558e-17,
+	1.11137350334481754821e+00,  5.56394502666969764311e-17,
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+	1.75150335303187820735e+00, -5.12445042059672465939e-17,
+	1.75625216037329945351e+00,  2.96014069544887330703e-17,
+	1.76101384303758390359e+00, -7.94325312503922771057e-17,
+	1.76578843593327272643e+00,  9.46131501808326786660e-17,
+	1.77057597406355471392e+00,  5.96179451004055584767e-17,
+	1.77537649252652118825e+00,  6.42973179655657203396e-17,
+	1.78019002651542446181e+00, -5.28462728909161736517e-17,
+	1.78501661131893496481e+00,  1.53304001210313138184e-17,
+	1.78985628232140103755e+00, -4.15435466068334977098e-17,
+	1.79470907500310716820e+00,  1.82274584279120867698e-17,
+	1.79957502494053511732e+00, -2.52688923335889795224e-17,
+	1.80445416780662393208e+00, -5.17722240879331788328e-17,
+	1.80934653937103195886e+00, -9.03264140245002968190e-17,
+	1.81425217550039885595e+00, -9.96953153892034881983e-17,
+	1.81917111215860849427e+00,  7.40267690114583888997e-17,
+	1.82410338540705341259e+00, -1.01596278622770830650e-16,
+	1.82904903140489727420e+00,  6.88919290883569563697e-17,
+	1.83400808640934243066e+00,  3.28310722424562658722e-17,
+	1.83898058677589371079e+00,  6.91896974027251194233e-18,
+	1.84396656895862598446e+00, -5.93974202694996455028e-17,
+	1.84896606951045083811e+00,  9.02758044626108928816e-17,
+	1.85397912508338547077e+00,  9.76188749072759353840e-17,
+	1.85900577242882047990e+00, -9.52870546198994068663e-17,
+	1.86404604839778897940e+00,  6.54091268062057047791e-17,
+	1.86909998994123860427e+00, -9.93850521425506708290e-17,
+	1.87416763411029996256e+00, -6.12276341300414256164e-17,
+	1.87924901805656019427e+00, -1.62263155578358447799e-17,
+	1.88434417903233453195e+00, -8.22659312553371090551e-17,
+	1.88945315439093919352e+00, -9.00516828505912548531e-17,
+	1.89457598158696560731e+00,  3.40340353521652967060e-17,
+	1.89971269817655530332e+00, -3.85973976937851370678e-17,
+	1.90486334181767413831e+00,  6.53385751471827862895e-17,
+	1.91002795027038985154e+00, -5.90968800674406023686e-17,
+	1.91520656139714740007e+00, -1.06199460561959626376e-16,
+	1.92039921316304740273e+00,  7.11668154063031418621e-17,
+	1.92560594363612502811e+00, -9.91496376969374092749e-17,
+	1.93082679098762710623e+00,  6.16714970616910955284e-17,
+	1.93606179349229434727e+00,  1.03323859606763257448e-16,
+	1.94131098952864045160e+00, -6.63802989162148798984e-17,
+	1.94657441757923321823e+00,  6.81102234953387718436e-17,
+	1.95185211623097831790e+00, -2.19901696997935108603e-17,
+	1.95714412417540017941e+00,  8.96076779103666776760e-17,
+	1.96245048020892731699e+00,  1.09768440009135469493e-16,
+	1.96777122323317588126e+00, -1.03149280115311315109e-16,
+	1.97310639225523432039e+00, -7.45161786395603748608e-18,
+	1.97845602638795092787e+00,  4.03887531092781665750e-17,
+	1.98382016485021939189e+00, -2.20345441239106265716e-17,
+	1.98919884696726634310e+00,  8.20513263836919941553e-18,
+	1.99459211217094023461e+00,  1.79097103520026450854e-17
+};
+
+static const union {
+	unsigned	i[2];
+	double		d;
+} C[] = {
+	{ DBLWORD(0x43380000, 0x00000000) },
+	{ DBLWORD(0x40771547, 0x652b82fe) },
+	{ DBLWORD(0x3f662e42, 0xfee00000) },
+	{ DBLWORD(0x3d6a39ef, 0x35793c76) },
+	{ DBLWORD(0x3ff00000, 0x00000000) },
+	{ DBLWORD(0x3fdfffff, 0xfffffff6) },
+	{ DBLWORD(0x3fc55555, 0x721a1d14) },
+	{ DBLWORD(0x3fa55555, 0x6e0896af) },
+	{ DBLWORD(0x01000000, 0x00000000) },
+	{ DBLWORD(0x7f000000, 0x00000000) },
+	{ DBLWORD(0x40862e42, 0xfefa39ef) },
+	{ DBLWORD(0xc0874910, 0xd52d3051) },
+	{ DBLWORD(0xfff00000, 0x00000000) },
+	{ DBLWORD(0x00000000, 0x00000000) }
+};
+
+#define	round		C[0].d
+#define	invln2_256	C[1].d
+#define	ln2_256h	C[2].d
+#define	ln2_256l	C[3].d
+#define	one		C[4].d
+#define	B1		C[5].d
+#define	B2		C[6].d
+#define	B3		C[7].d
+#define	tiny		C[8].d
+#define	huge		C[9].d
+#define	othresh		C[10].d
+#define	uthresh		C[11].d
+#define	neginf		C[12].d
+#define	zero		C[13].d
+
+#define	PROCESS(N)						\
+	y##N = (x##N * invln2_256) + round;			\
+	j##N = LO(y##N);					\
+	y##N -= round;						\
+	k##N = j##N >> 8;					\
+	j##N = (j##N & 0xff) << 1;				\
+	x##N = (x##N - y##N * ln2_256h) - y##N * ln2_256l;	\
+	y##N = x##N * (one + x##N * (B1 + x##N * (B2 + x##N * B3)));	\
+	t##N = TBL[j##N];					\
+	y##N = t##N + (TBL[j##N + 1] + t##N * y##N);		\
+	if (k##N < -1021) {					\
+		HI(y##N) += (k##N + 0x3ef) << 20;		\
+		y##N *= tiny;					\
+	} else {						\
+		HI(y##N) += k##N << 20;				\
+	}							\
+	*y = y##N;						\
+	y += stridey
+
+#define	PREPROCESS(N, index, label)				\
+	hx = HI(x[0]);						\
+	ix = hx & ~0x80000000;					\
+	x##N = *x;						\
+	x += stridex;						\
+	if (ix >= 0x40862e42) {					\
+		if (ix >= 0x7ff00000) { /* x is inf or nan */	\
+			y[index] = (x##N == neginf)? zero :	\
+			    x##N * x##N;			\
+			goto label;				\
+		}						\
+		if (x##N > othresh) {				\
+			y[index] = huge * huge;			\
+			goto label;				\
+		}						\
+		if (x##N < uthresh) {				\
+			y[index] = tiny * tiny;			\
+			goto label;				\
+		}						\
+	} else if (ix < 0x3e300000) { /* |x| < 2^-28 */		\
+		y[index] = one + x##N;				\
+		goto label;					\
+	}
+
+void
+__vexp(int n, double *restrict x, int stridex, double *restrict y,
+    int stridey)
+{
+	double		x0, x1, x2, x3, x4, x5;
+	double		y0, y1, y2, y3, y4, y5;
+	double		t0, t1, t2, t3, t4, t5;
+	int		k0, k1, k2, k3, k4, k5;
+	int		j0, j1, j2, j3, j4, j5;
+	int		hx, ix;
+
+	y -= stridey;
+
+	for (;;) {
+begin:
+		if (--n < 0)
+			break;
+		y += stridey;
+
+		PREPROCESS(0, 0, begin);
+
+		if (--n < 0)
+			goto process1;
+
+		PREPROCESS(1, stridey, process1);
+
+		if (--n < 0)
+			goto process2;
+
+		PREPROCESS(2, stridey << 1, process2);
+
+		if (--n < 0)
+			goto process3;
+
+		PREPROCESS(3, (stridey << 1) + stridey, process3);
+
+		if (--n < 0)
+			goto process4;
+
+		PREPROCESS(4, stridey << 2, process4);
+
+		if (--n < 0)
+			goto process5;
+
+		PREPROCESS(5, (stridey << 2) + stridey, process5);
+
+		y0 = (x0 * invln2_256) + round;
+		y1 = (x1 * invln2_256) + round;
+		y2 = (x2 * invln2_256) + round;
+		y3 = (x3 * invln2_256) + round;
+		y4 = (x4 * invln2_256) + round;
+		y5 = (x5 * invln2_256) + round;
+
+		j0 = LO(y0);
+		j1 = LO(y1);
+		j2 = LO(y2);
+		j3 = LO(y3);
+		j4 = LO(y4);
+		j5 = LO(y5);
+
+		y0 -= round;
+		y1 -= round;
+		y2 -= round;
+		y3 -= round;
+		y4 -= round;
+		y5 -= round;
+
+		k0 = j0 >> 8;
+		k1 = j1 >> 8;
+		k2 = j2 >> 8;
+		k3 = j3 >> 8;
+		k4 = j4 >> 8;
+		k5 = j5 >> 8;
+
+		j0 = (j0 & 0xff) << 1;
+		j1 = (j1 & 0xff) << 1;
+		j2 = (j2 & 0xff) << 1;
+		j3 = (j3 & 0xff) << 1;
+		j4 = (j4 & 0xff) << 1;
+		j5 = (j5 & 0xff) << 1;
+
+		x0 = (x0 - y0 * ln2_256h) - y0 * ln2_256l;
+		x1 = (x1 - y1 * ln2_256h) - y1 * ln2_256l;
+		x2 = (x2 - y2 * ln2_256h) - y2 * ln2_256l;
+		x3 = (x3 - y3 * ln2_256h) - y3 * ln2_256l;
+		x4 = (x4 - y4 * ln2_256h) - y4 * ln2_256l;
+		x5 = (x5 - y5 * ln2_256h) - y5 * ln2_256l;
+
+		y0 = x0 * (one + x0 * (B1 + x0 * (B2 + x0 * B3)));
+		y1 = x1 * (one + x1 * (B1 + x1 * (B2 + x1 * B3)));
+		y2 = x2 * (one + x2 * (B1 + x2 * (B2 + x2 * B3)));
+		y3 = x3 * (one + x3 * (B1 + x3 * (B2 + x3 * B3)));
+		y4 = x4 * (one + x4 * (B1 + x4 * (B2 + x4 * B3)));
+		y5 = x5 * (one + x5 * (B1 + x5 * (B2 + x5 * B3)));
+
+		t0 = TBL[j0];
+		t1 = TBL[j1];
+		t2 = TBL[j2];
+		t3 = TBL[j3];
+		t4 = TBL[j4];
+		t5 = TBL[j5];
+
+		y0 = t0 + (TBL[j0 + 1] + t0 * y0);
+		y1 = t1 + (TBL[j1 + 1] + t1 * y1);
+		y2 = t2 + (TBL[j2 + 1] + t2 * y2);
+		y3 = t3 + (TBL[j3 + 1] + t3 * y3);
+		y4 = t4 + (TBL[j4 + 1] + t4 * y4);
+		y5 = t5 + (TBL[j5 + 1] + t5 * y5);
+
+		if (k0 < -1021) {
+			HI(y0) += (k0 + 0x3ef) << 20;
+			y0 *= tiny;
+		} else {
+			HI(y0) += k0 << 20;
+		}
+		if (k1 < -1021) {
+			HI(y1) += (k1 + 0x3ef) << 20;
+			y1 *= tiny;
+		} else {
+			HI(y1) += k1 << 20;
+		}
+		if (k2 < -1021) {
+			HI(y2) += (k2 + 0x3ef) << 20;
+			y2 *= tiny;
+		} else {
+			HI(y2) += k2 << 20;
+		}
+		if (k3 < -1021) {
+			HI(y3) += (k3 + 0x3ef) << 20;
+			y3 *= tiny;
+		} else {
+			HI(y3) += k3 << 20;
+		}
+		if (k4 < -1021) {
+			HI(y4) += (k4 + 0x3ef) << 20;
+			y4 *= tiny;
+		} else {
+			HI(y4) += k4 << 20;
+		}
+		if (k5 < -1021) {
+			HI(y5) += (k5 + 0x3ef) << 20;
+			y5 *= tiny;
+		} else {
+			HI(y5) += k5 << 20;
+		}
+
+		y[0] = y0;
+		y[stridey] = y1;
+		y[stridey << 1] = y2;
+		y[(stridey << 1) + stridey] = y3;
+		y[stridey << 2] = y4;
+		y[(stridey << 2) + stridey] = y5;
+		y += (stridey << 2) + stridey;
+		continue;
+
+process1:
+		PROCESS(0);
+		continue;
+
+process2:
+		PROCESS(0);
+		PROCESS(1);
+		continue;
+
+process3:
+		PROCESS(0);
+		PROCESS(1);
+		PROCESS(2);
+		continue;
+
+process4:
+		PROCESS(0);
+		PROCESS(1);
+		PROCESS(2);
+		PROCESS(3);
+		continue;
+
+process5:
+		PROCESS(0);
+		PROCESS(1);
+		PROCESS(2);
+		PROCESS(3);
+		PROCESS(4);
+	}
+}