xref: /illumos-gate/usr/src/lib/libmvec/common/__vlog.c (revision 25c28e83)
1*25c28e83SPiotr Jasiukajtis /*
2*25c28e83SPiotr Jasiukajtis  * CDDL HEADER START
3*25c28e83SPiotr Jasiukajtis  *
4*25c28e83SPiotr Jasiukajtis  * The contents of this file are subject to the terms of the
5*25c28e83SPiotr Jasiukajtis  * Common Development and Distribution License (the "License").
6*25c28e83SPiotr Jasiukajtis  * You may not use this file except in compliance with the License.
7*25c28e83SPiotr Jasiukajtis  *
8*25c28e83SPiotr Jasiukajtis  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9*25c28e83SPiotr Jasiukajtis  * or http://www.opensolaris.org/os/licensing.
10*25c28e83SPiotr Jasiukajtis  * See the License for the specific language governing permissions
11*25c28e83SPiotr Jasiukajtis  * and limitations under the License.
12*25c28e83SPiotr Jasiukajtis  *
13*25c28e83SPiotr Jasiukajtis  * When distributing Covered Code, include this CDDL HEADER in each
14*25c28e83SPiotr Jasiukajtis  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15*25c28e83SPiotr Jasiukajtis  * If applicable, add the following below this CDDL HEADER, with the
16*25c28e83SPiotr Jasiukajtis  * fields enclosed by brackets "[]" replaced with your own identifying
17*25c28e83SPiotr Jasiukajtis  * information: Portions Copyright [yyyy] [name of copyright owner]
18*25c28e83SPiotr Jasiukajtis  *
19*25c28e83SPiotr Jasiukajtis  * CDDL HEADER END
20*25c28e83SPiotr Jasiukajtis  */
21*25c28e83SPiotr Jasiukajtis /*
22*25c28e83SPiotr Jasiukajtis  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
23*25c28e83SPiotr Jasiukajtis  */
24*25c28e83SPiotr Jasiukajtis /*
25*25c28e83SPiotr Jasiukajtis  * Copyright 2005 Sun Microsystems, Inc.  All rights reserved.
26*25c28e83SPiotr Jasiukajtis  * Use is subject to license terms.
27*25c28e83SPiotr Jasiukajtis  */
28*25c28e83SPiotr Jasiukajtis 
29*25c28e83SPiotr Jasiukajtis /*
30*25c28e83SPiotr Jasiukajtis  * __vlog: double precision vector log
31*25c28e83SPiotr Jasiukajtis  *
32*25c28e83SPiotr Jasiukajtis  * Algorithm:
33*25c28e83SPiotr Jasiukajtis  *
34*25c28e83SPiotr Jasiukajtis  * Write x = 2^n z where 1 - 2^-10 <= z < 2 - 2^-9.  Let m = z
35*25c28e83SPiotr Jasiukajtis  * rounded to nine significant bits, so m = 1 + 2^-8 k, where
36*25c28e83SPiotr Jasiukajtis  * 0 <= k <= 255.  Let d = z - m.  Then
37*25c28e83SPiotr Jasiukajtis  *
38*25c28e83SPiotr Jasiukajtis  * log(x) = n log(2) + log(m) + log(1+(d/m))
39*25c28e83SPiotr Jasiukajtis  *
40*25c28e83SPiotr Jasiukajtis  * Let ln2hi = log(2) rounded to a multiple of 2^-42 and ln2lo
41*25c28e83SPiotr Jasiukajtis  * ~ log(2) - ln2hi.  From a table, obtain mh and ml such that
42*25c28e83SPiotr Jasiukajtis  * mh = log(m) rounded to a multiple of 2^-42 and ml ~ log(m) -
43*25c28e83SPiotr Jasiukajtis  * mh.  From the same table, obtain rh and rl such that rh = 1/m
44*25c28e83SPiotr Jasiukajtis  * rounded to a multiple of 2^-10 and rl ~ 1/m - rh.  For |y| <=
45*25c28e83SPiotr Jasiukajtis  * 2^-9, approximate log(1+y) by a polynomial y+p(y) where p(y)
46*25c28e83SPiotr Jasiukajtis  * := y*y*(-1/2+y*(P3+y*(P4+y*(P5+y*P6)))).  Now letting s =
47*25c28e83SPiotr Jasiukajtis  * d*rh + d*rl in double precision, we can compute the sum above
48*25c28e83SPiotr Jasiukajtis  * accurately as
49*25c28e83SPiotr Jasiukajtis  *
50*25c28e83SPiotr Jasiukajtis  * (n*ln2hi + mh) + (d*rh + (d*rl + (n*ln2lo + ml) + p(s)))
51*25c28e83SPiotr Jasiukajtis  *
52*25c28e83SPiotr Jasiukajtis  * When x is subnormal, we first scale it to the normal range,
53*25c28e83SPiotr Jasiukajtis  * adjusting n accordingly.
54*25c28e83SPiotr Jasiukajtis  *
55*25c28e83SPiotr Jasiukajtis  * Accuracy:
56*25c28e83SPiotr Jasiukajtis  *
57*25c28e83SPiotr Jasiukajtis  * The largest error observed is less than 0.8 ulps.
58*25c28e83SPiotr Jasiukajtis  */
59*25c28e83SPiotr Jasiukajtis 
60*25c28e83SPiotr Jasiukajtis #include <sys/isa_defs.h>
61*25c28e83SPiotr Jasiukajtis 
62*25c28e83SPiotr Jasiukajtis #ifdef _LITTLE_ENDIAN
63*25c28e83SPiotr Jasiukajtis #define	HI(x)	*(1+(int *)&x)
64*25c28e83SPiotr Jasiukajtis #define	LO(x)	*(unsigned *)&x
65*25c28e83SPiotr Jasiukajtis #define	HIWORD	1
66*25c28e83SPiotr Jasiukajtis #define	LOWORD	0
67*25c28e83SPiotr Jasiukajtis #else
68*25c28e83SPiotr Jasiukajtis #define	HI(x)	*(int *)&x
69*25c28e83SPiotr Jasiukajtis #define	LO(x)	*(1+(unsigned *)&x)
70*25c28e83SPiotr Jasiukajtis #define	HIWORD	0
71*25c28e83SPiotr Jasiukajtis #define	LOWORD	1
72*25c28e83SPiotr Jasiukajtis #endif
73*25c28e83SPiotr Jasiukajtis 
74*25c28e83SPiotr Jasiukajtis #ifdef __RESTRICT
75*25c28e83SPiotr Jasiukajtis #define	restrict _Restrict
76*25c28e83SPiotr Jasiukajtis #else
77*25c28e83SPiotr Jasiukajtis #define	restrict
78*25c28e83SPiotr Jasiukajtis #endif
79*25c28e83SPiotr Jasiukajtis 
80*25c28e83SPiotr Jasiukajtis static const double TBL[] = {
81*25c28e83SPiotr Jasiukajtis 	1.00000000000000000000e+00,  0.00000000000000000000e+00,
82*25c28e83SPiotr Jasiukajtis 	0.00000000000000000000e+00,  0.00000000000000000000e+00,
83*25c28e83SPiotr Jasiukajtis 	9.96093750000000000000e-01,  1.51994163424124515728e-05,
84*25c28e83SPiotr Jasiukajtis 	3.89864041562759666704e-03,  2.97263469009289512726e-14,
85*25c28e83SPiotr Jasiukajtis 	9.92187500000000000000e-01,  6.05620155038759681518e-05,
86*25c28e83SPiotr Jasiukajtis 	7.78214044203195953742e-03,  2.29894100462035112076e-14,
87*25c28e83SPiotr Jasiukajtis 	9.88281250000000000000e-01,  1.35738416988416988208e-04,
88*25c28e83SPiotr Jasiukajtis 	1.16506172200843138853e-02, -1.09039749717359319029e-13,
89*25c28e83SPiotr Jasiukajtis 	9.84375000000000000000e-01,  2.40384615384615397959e-04,
90*25c28e83SPiotr Jasiukajtis 	1.55041865359635266941e-02,  1.72745674997061065553e-15,
91*25c28e83SPiotr Jasiukajtis 	9.80468750000000000000e-01,  3.74161877394636028203e-04,
92*25c28e83SPiotr Jasiukajtis 	1.93429628432113531744e-02, -8.04185385052258635682e-14,
93*25c28e83SPiotr Jasiukajtis 	9.77539062500000000000e-01, -4.39825858778625927714e-04,
94*25c28e83SPiotr Jasiukajtis 	2.31670592816044518258e-02, -7.00735970431003565857e-14,
95*25c28e83SPiotr Jasiukajtis 	9.73632812500000000000e-01, -2.48782081749049442231e-04,
96*25c28e83SPiotr Jasiukajtis 	2.69765876983001362532e-02, -9.80605051684317662887e-14,
97*25c28e83SPiotr Jasiukajtis 	9.69726562500000000000e-01, -2.95928030303030311244e-05,
98*25c28e83SPiotr Jasiukajtis 	3.07716586667083902285e-02,  4.52981425779092882775e-14,
99*25c28e83SPiotr Jasiukajtis 	9.65820312500000000000e-01,  2.17423349056603779517e-04,
100*25c28e83SPiotr Jasiukajtis 	3.45523815067281248048e-02, -6.83913974232877736961e-14,
101*25c28e83SPiotr Jasiukajtis 	9.62890625000000000000e-01, -4.84609962406015010693e-04,
102*25c28e83SPiotr Jasiukajtis 	3.83188643020275776507e-02,  1.09021543022033016421e-13,
103*25c28e83SPiotr Jasiukajtis 	9.58984375000000000000e-01, -1.82876872659176042957e-04,
104*25c28e83SPiotr Jasiukajtis 	4.20712139207353175152e-02, -4.82631400055112824008e-14,
105*25c28e83SPiotr Jasiukajtis 	9.55078125000000000000e-01,  1.45755597014925360189e-04,
106*25c28e83SPiotr Jasiukajtis 	4.58095360313564015087e-02, -6.21983419947579227529e-14,
107*25c28e83SPiotr Jasiukajtis 	9.52148437500000000000e-01, -4.75575046468401500289e-04,
108*25c28e83SPiotr Jasiukajtis 	4.95339351223265111912e-02, -4.98803091079814255646e-14,
109*25c28e83SPiotr Jasiukajtis 	9.48242187500000000000e-01, -9.40393518518518520526e-05,
110*25c28e83SPiotr Jasiukajtis 	5.32445145188376045553e-02, -2.53216894311744497863e-14,
111*25c28e83SPiotr Jasiukajtis 	9.44335937500000000000e-01,  3.13508994464944631443e-04,
112*25c28e83SPiotr Jasiukajtis 	5.69413764001183153596e-02,  2.01093994355649575698e-14,
113*25c28e83SPiotr Jasiukajtis 	9.41406250000000000000e-01, -2.29779411764705879164e-04,
114*25c28e83SPiotr Jasiukajtis 	6.06246218164869787870e-02, -5.21362063913650408235e-14,
115*25c28e83SPiotr Jasiukajtis 	9.37500000000000000000e-01,  2.28937728937728937530e-04,
116*25c28e83SPiotr Jasiukajtis 	6.42943507054951624013e-02, -9.79051851199021608925e-14,
117*25c28e83SPiotr Jasiukajtis 	9.34570312500000000000e-01, -2.63743156934306572509e-04,
118*25c28e83SPiotr Jasiukajtis 	6.79506619085259444546e-02, -1.81950600301688149235e-14,
119*25c28e83SPiotr Jasiukajtis 	9.30664062500000000000e-01,  2.45028409090909096626e-04,
120*25c28e83SPiotr Jasiukajtis 	7.15936531869374448434e-02,  7.13730822534317801406e-14,
121*25c28e83SPiotr Jasiukajtis 	9.27734375000000000000e-01, -1.98143115942028998078e-04,
122*25c28e83SPiotr Jasiukajtis 	7.52234212375242350390e-02,  6.32906595872454402199e-14,
123*25c28e83SPiotr Jasiukajtis 	9.23828125000000000000e-01,  3.59600631768953083074e-04,
124*25c28e83SPiotr Jasiukajtis 	7.88400617077513743425e-02,  2.46501890617661192316e-14,
125*25c28e83SPiotr Jasiukajtis 	9.20898437500000000000e-01, -3.51281474820143869292e-05,
126*25c28e83SPiotr Jasiukajtis 	8.24436692109884461388e-02,  8.61451293608781447223e-14,
127*25c28e83SPiotr Jasiukajtis 	9.17968750000000000000e-01, -4.06025985663082419983e-04,
128*25c28e83SPiotr Jasiukajtis 	8.60343373417435941519e-02,  5.95592298762564263463e-14,
129*25c28e83SPiotr Jasiukajtis 	9.14062500000000000000e-01,  2.23214285714285707316e-04,
130*25c28e83SPiotr Jasiukajtis 	8.96121586897606903221e-02, -7.35577021943502867846e-14,
131*25c28e83SPiotr Jasiukajtis 	9.11132812500000000000e-01, -1.00784030249110321056e-04,
132*25c28e83SPiotr Jasiukajtis 	9.31772248541165026836e-02,  6.67870851716289831942e-14,
133*25c28e83SPiotr Jasiukajtis 	9.08203125000000000000e-01, -4.01706560283687926730e-04,
134*25c28e83SPiotr Jasiukajtis 	9.67296264584547316190e-02,  9.63806765855227740728e-14,
135*25c28e83SPiotr Jasiukajtis 	9.04296875000000000000e-01,  2.96764575971731443208e-04,
136*25c28e83SPiotr Jasiukajtis 	1.00269453163718935684e-01, -4.37863761707839790971e-14,
137*25c28e83SPiotr Jasiukajtis 	9.01367187500000000000e-01,  4.12632042253521119125e-05,
138*25c28e83SPiotr Jasiukajtis 	1.03796793681567578460e-01,  7.59863659719414144342e-14,
139*25c28e83SPiotr Jasiukajtis 	8.98437500000000000000e-01, -1.91885964912280701945e-04,
140*25c28e83SPiotr Jasiukajtis 	1.07311735789153317455e-01, -6.52667880273107116669e-14,
141*25c28e83SPiotr Jasiukajtis 	8.95507812500000000000e-01, -4.02917395104895122333e-04,
142*25c28e83SPiotr Jasiukajtis 	1.10814366340264314204e-01,  2.57999912830699022513e-14,
143*25c28e83SPiotr Jasiukajtis 	8.91601562500000000000e-01,  3.84500217770034828473e-04,
144*25c28e83SPiotr Jasiukajtis 	1.14304771280103523168e-01, -4.48895335223869926230e-14,
145*25c28e83SPiotr Jasiukajtis 	8.88671875000000000000e-01,  2.17013888888888876842e-04,
146*25c28e83SPiotr Jasiukajtis 	1.17783035656430001836e-01, -4.65472974759844472568e-14,
147*25c28e83SPiotr Jasiukajtis 	8.85742187500000000000e-01,  7.09612889273356431397e-05,
148*25c28e83SPiotr Jasiukajtis 	1.21249243632973957574e-01, -1.04272412782730081647e-13,
149*25c28e83SPiotr Jasiukajtis 	8.82812500000000000000e-01, -5.38793103448275854592e-05,
150*25c28e83SPiotr Jasiukajtis 	1.24703478501032805070e-01, -7.55692068745133691756e-14,
151*25c28e83SPiotr Jasiukajtis 	8.79882812500000000000e-01, -1.57726589347079046649e-04,
152*25c28e83SPiotr Jasiukajtis 	1.28145822691976718488e-01, -4.66803140394579609437e-14,
153*25c28e83SPiotr Jasiukajtis 	8.76953125000000000000e-01, -2.40796232876712315400e-04,
154*25c28e83SPiotr Jasiukajtis 	1.31576357788617315236e-01,  1.01957352237084734958e-13,
155*25c28e83SPiotr Jasiukajtis 	8.74023437500000000000e-01, -3.03300981228668954746e-04,
156*25c28e83SPiotr Jasiukajtis 	1.34995164537485834444e-01,  1.89961580415787680134e-14,
157*25c28e83SPiotr Jasiukajtis 	8.71093750000000000000e-01, -3.45450680272108847594e-04,
158*25c28e83SPiotr Jasiukajtis 	1.38402322859064952354e-01,  5.41833313790089940464e-14,
159*25c28e83SPiotr Jasiukajtis 	8.68164062500000000000e-01, -3.67452330508474583805e-04,
160*25c28e83SPiotr Jasiukajtis 	1.41797911860294334474e-01, -3.69845950669709681858e-14,
161*25c28e83SPiotr Jasiukajtis 	8.65234375000000000000e-01, -3.69510135135135155647e-04,
162*25c28e83SPiotr Jasiukajtis 	1.45182009844575077295e-01, -7.71800133682809851086e-14,
163*25c28e83SPiotr Jasiukajtis 	8.62304687500000000000e-01, -3.51825547138047162871e-04,
164*25c28e83SPiotr Jasiukajtis 	1.48554694323138392065e-01, -1.24915489807515996540e-15,
165*25c28e83SPiotr Jasiukajtis 	8.59375000000000000000e-01, -3.14597315436241590364e-04,
166*25c28e83SPiotr Jasiukajtis 	1.51916042025732167531e-01,  1.09807540998552379211e-13,
167*25c28e83SPiotr Jasiukajtis 	8.56445312500000000000e-01, -2.58021530100334438914e-04,
168*25c28e83SPiotr Jasiukajtis 	1.55266128911080159014e-01,  4.37925082924060541938e-14,
169*25c28e83SPiotr Jasiukajtis 	8.53515625000000000000e-01, -1.82291666666666674979e-04,
170*25c28e83SPiotr Jasiukajtis 	1.58605030176659056451e-01, -2.04723578004619553937e-14,
171*25c28e83SPiotr Jasiukajtis 	8.50585937500000000000e-01, -8.75986295681063168849e-05,
172*25c28e83SPiotr Jasiukajtis 	1.61932820269385047141e-01, -7.17939001929567730476e-14,
173*25c28e83SPiotr Jasiukajtis 	8.47656250000000000000e-01,  2.58692052980132450107e-05,
174*25c28e83SPiotr Jasiukajtis 	1.65249572895390883787e-01, -8.37209109923591205585e-14,
175*25c28e83SPiotr Jasiukajtis 	8.44726562500000000000e-01,  1.57925948844884475120e-04,
176*25c28e83SPiotr Jasiukajtis 	1.68555361029802952544e-01,  3.71439775417047191367e-15,
177*25c28e83SPiotr Jasiukajtis 	8.41796875000000000000e-01,  3.08388157894736824986e-04,
178*25c28e83SPiotr Jasiukajtis 	1.71850256926745714736e-01, -8.64923960721207091374e-14,
179*25c28e83SPiotr Jasiukajtis 	8.38867187500000000000e-01,  4.77074795081967189831e-04,
180*25c28e83SPiotr Jasiukajtis 	1.75134332127754532848e-01,  9.46151658066508147714e-14,
181*25c28e83SPiotr Jasiukajtis 	8.36914062500000000000e-01, -3.12755310457516312941e-04,
182*25c28e83SPiotr Jasiukajtis 	1.78407657472916980623e-01, -9.86835038673494943912e-14,
183*25c28e83SPiotr Jasiukajtis 	8.33984375000000000000e-01, -1.08153501628664488934e-04,
184*25c28e83SPiotr Jasiukajtis 	1.81670303107694053324e-01, -5.93750633338470149673e-14,
185*25c28e83SPiotr Jasiukajtis 	8.31054687500000000000e-01,  1.14143668831168828529e-04,
186*25c28e83SPiotr Jasiukajtis 	1.84922338494061477832e-01, -4.94851676612509959777e-14,
187*25c28e83SPiotr Jasiukajtis 	8.28125000000000000000e-01,  3.53964401294498405386e-04,
188*25c28e83SPiotr Jasiukajtis 	1.88163832418240417610e-01, -5.74307839320075599347e-14,
189*25c28e83SPiotr Jasiukajtis 	8.26171875000000000000e-01, -3.65423387096774205090e-04,
190*25c28e83SPiotr Jasiukajtis 	1.91394852999565046048e-01,  6.44085615069689207389e-14,
191*25c28e83SPiotr Jasiukajtis 	8.23242187500000000000e-01, -9.10620980707395479654e-05,
192*25c28e83SPiotr Jasiukajtis 	1.94615467699577493477e-01,  9.41653814571825038763e-14,
193*25c28e83SPiotr Jasiukajtis 	8.20312500000000000000e-01,  2.00320512820512813563e-04,
194*25c28e83SPiotr Jasiukajtis 	1.97825743329985925811e-01, -6.60454487708238395939e-14,
195*25c28e83SPiotr Jasiukajtis 	8.18359375000000000000e-01, -4.68001198083067100272e-04,
196*25c28e83SPiotr Jasiukajtis 	2.01025746060622623190e-01, -3.18818493754377370219e-14,
197*25c28e83SPiotr Jasiukajtis 	8.15429687500000000000e-01, -1.43063296178343944383e-04,
198*25c28e83SPiotr Jasiukajtis 	2.04215541428766300669e-01, -7.54091651195618882501e-14,
199*25c28e83SPiotr Jasiukajtis 	8.12500000000000000000e-01,  1.98412698412698412526e-04,
200*25c28e83SPiotr Jasiukajtis 	2.07395194345963318483e-01,  1.07268675772897325437e-13,
201*25c28e83SPiotr Jasiukajtis 	8.10546875000000000000e-01, -4.20292721518987358927e-04,
202*25c28e83SPiotr Jasiukajtis 	2.10564769107350002741e-01, -3.65071888317905767114e-16,
203*25c28e83SPiotr Jasiukajtis 	8.07617187500000000000e-01, -4.62095820189274421015e-05,
204*25c28e83SPiotr Jasiukajtis 	2.13724329397791734664e-01, -7.35958018644051430164e-14,
205*25c28e83SPiotr Jasiukajtis 	8.04687500000000000000e-01,  3.43946540880503122493e-04,
206*25c28e83SPiotr Jasiukajtis 	2.16873938300523150247e-01,  9.12093724991498410553e-14,
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545*25c28e83SPiotr Jasiukajtis 	5.24414062500000000000e-01,  1.76101434426229513973e-04,
546*25c28e83SPiotr Jasiukajtis 	6.45137961373620782979e-01, -3.60813136042255739798e-14,
547*25c28e83SPiotr Jasiukajtis 	5.23437500000000000000e-01,  7.98824130879345644567e-05,
548*25c28e83SPiotr Jasiukajtis 	6.47185044995239877608e-01,  6.96725146472247760395e-14,
549*25c28e83SPiotr Jasiukajtis 	5.22460937500000000000e-01, -1.19579081632653055071e-05,
550*25c28e83SPiotr Jasiukajtis 	6.49227946625160257099e-01, -5.04382083563449091526e-14,
551*25c28e83SPiotr Jasiukajtis 	5.21484375000000000000e-01, -9.94462830957230209915e-05,
552*25c28e83SPiotr Jasiukajtis 	6.51266683315043337643e-01, -8.52342468131615437746e-14,
553*25c28e83SPiotr Jasiukajtis 	5.20507812500000000000e-01, -1.82609247967479665321e-04,
554*25c28e83SPiotr Jasiukajtis 	6.53301272012640765752e-01,  1.04873006903856996874e-13,
555*25c28e83SPiotr Jasiukajtis 	5.19531250000000000000e-01, -2.61473123732251517670e-04,
556*25c28e83SPiotr Jasiukajtis 	6.55331729563158660312e-01, -3.10282172335227455825e-14,
557*25c28e83SPiotr Jasiukajtis 	5.18554687500000000000e-01, -3.36064018218623454786e-04,
558*25c28e83SPiotr Jasiukajtis 	6.57358072708348117885e-01,  1.19122567102055698791e-14,
559*25c28e83SPiotr Jasiukajtis 	5.17578125000000000000e-01, -4.06407828282828297722e-04,
560*25c28e83SPiotr Jasiukajtis 	6.59380318089233696810e-01, -1.05870694633429062178e-13,
561*25c28e83SPiotr Jasiukajtis 	5.16601562500000000000e-01, -4.72530241935483884957e-04,
562*25c28e83SPiotr Jasiukajtis 	6.61398482245431296178e-01, -6.62879179039074743232e-14,
563*25c28e83SPiotr Jasiukajtis 	5.14648437500000000000e-01,  4.42105759557344087183e-04,
564*25c28e83SPiotr Jasiukajtis 	6.63412581616967145237e-01,  9.91058598099467920662e-14,
565*25c28e83SPiotr Jasiukajtis 	5.13671875000000000000e-01,  3.84349899598393583006e-04,
566*25c28e83SPiotr Jasiukajtis 	6.65422632545187298092e-01, -9.68491419671810783613e-14,
567*25c28e83SPiotr Jasiukajtis 	5.12695312500000000000e-01,  3.30739604208416838882e-04,
568*25c28e83SPiotr Jasiukajtis 	6.67428651271848139004e-01,  1.08050943383646665619e-13,
569*25c28e83SPiotr Jasiukajtis 	5.11718750000000000000e-01,  2.81249999999999978750e-04,
570*25c28e83SPiotr Jasiukajtis 	6.69430653942526987521e-01,  1.02279777907416200886e-13,
571*25c28e83SPiotr Jasiukajtis 	5.10742187500000000000e-01,  2.35856412175648700539e-04,
572*25c28e83SPiotr Jasiukajtis 	6.71428656605257856427e-01,  4.44668903784876907111e-14,
573*25c28e83SPiotr Jasiukajtis 	5.09765625000000000000e-01,  1.94534362549800786662e-04,
574*25c28e83SPiotr Jasiukajtis 	6.73422675212123067467e-01,  4.36528304869414810551e-14,
575*25c28e83SPiotr Jasiukajtis 	5.08789062500000000000e-01,  1.57259567594433401650e-04,
576*25c28e83SPiotr Jasiukajtis 	6.75412725620162746054e-01,  1.39850267837821649808e-14,
577*25c28e83SPiotr Jasiukajtis 	5.07812500000000000000e-01,  1.24007936507936501053e-04,
578*25c28e83SPiotr Jasiukajtis 	6.77398823591829568613e-01, -2.34278036379790696248e-14,
579*25c28e83SPiotr Jasiukajtis 	5.06835937500000000000e-01,  9.47555693069306959140e-05,
580*25c28e83SPiotr Jasiukajtis 	6.79380984795898257289e-01, -1.00907141981183426552e-13,
581*25c28e83SPiotr Jasiukajtis 	5.05859375000000000000e-01,  6.94787549407114679145e-05,
582*25c28e83SPiotr Jasiukajtis 	6.81359224807920327294e-01, -1.72583456150091690167e-14,
583*25c28e83SPiotr Jasiukajtis 	5.04882812500000000000e-01,  4.81539694280078915244e-05,
584*25c28e83SPiotr Jasiukajtis 	6.83333559111588328960e-01,  3.23592040115024425781e-14,
585*25c28e83SPiotr Jasiukajtis 	5.03906250000000000000e-01,  3.07578740157480310692e-05,
586*25c28e83SPiotr Jasiukajtis 	6.85304003098963221419e-01, -4.38048746232309815355e-14,
587*25c28e83SPiotr Jasiukajtis 	5.02929687500000000000e-01,  1.72673133595284864178e-05,
588*25c28e83SPiotr Jasiukajtis 	6.87270572070929119946e-01,  3.11475515031130920163e-14,
589*25c28e83SPiotr Jasiukajtis 	5.01953125000000000000e-01,  7.65931372549019597214e-06,
590*25c28e83SPiotr Jasiukajtis 	6.89233281238784911693e-01,  2.40686318405286681994e-14,
591*25c28e83SPiotr Jasiukajtis 	5.00976562500000000000e-01,  1.91108121330724059841e-06,
592*25c28e83SPiotr Jasiukajtis 	6.91192145724244255689e-01, -1.02296829368141946888e-13,
593*25c28e83SPiotr Jasiukajtis };
594*25c28e83SPiotr Jasiukajtis 
595*25c28e83SPiotr Jasiukajtis static const double C[] = {
596*25c28e83SPiotr Jasiukajtis 	6.93147180559890330187e-01,
597*25c28e83SPiotr Jasiukajtis 	5.49792301870837115524e-14,
598*25c28e83SPiotr Jasiukajtis 	-0.5,
599*25c28e83SPiotr Jasiukajtis 	3.33333333332438282293284931714682042701467889609e-0001,
600*25c28e83SPiotr Jasiukajtis 	-2.49999999998669026809069285994497705748522309858e-0001,
601*25c28e83SPiotr Jasiukajtis 	2.00000758613044543658508591796951886624273250472e-0001,
602*25c28e83SPiotr Jasiukajtis 	-1.66667492411916229281646821123333564982955309481e-0001,
603*25c28e83SPiotr Jasiukajtis 	4503599627370496.0,
604*25c28e83SPiotr Jasiukajtis 	0.0
605*25c28e83SPiotr Jasiukajtis };
606*25c28e83SPiotr Jasiukajtis 
607*25c28e83SPiotr Jasiukajtis #define	ln2hi	C[0]
608*25c28e83SPiotr Jasiukajtis #define	ln2lo	C[1]
609*25c28e83SPiotr Jasiukajtis #define	mhalf	C[2]
610*25c28e83SPiotr Jasiukajtis #define	P3	C[3]
611*25c28e83SPiotr Jasiukajtis #define	P4	C[4]
612*25c28e83SPiotr Jasiukajtis #define	P5	C[5]
613*25c28e83SPiotr Jasiukajtis #define	P6	C[6]
614*25c28e83SPiotr Jasiukajtis #define	two52	C[7]
615*25c28e83SPiotr Jasiukajtis #define	zero	C[8]
616*25c28e83SPiotr Jasiukajtis 
617*25c28e83SPiotr Jasiukajtis #define	PROCESS(N)							\
618*25c28e83SPiotr Jasiukajtis 	i##N = (i##N + 0x800) & ~0xfff;					\
619*25c28e83SPiotr Jasiukajtis 	e = (i##N & 0x7ff00000) - 0x3ff00000;				\
620*25c28e83SPiotr Jasiukajtis 	z##N.i[HIWORD] -= e;						\
621*25c28e83SPiotr Jasiukajtis 	w##N.i[HIWORD] = i##N - e;					\
622*25c28e83SPiotr Jasiukajtis 	w##N.i[LOWORD] = 0;						\
623*25c28e83SPiotr Jasiukajtis 	n##N += (e >> 20);						\
624*25c28e83SPiotr Jasiukajtis 	i##N = (i##N >> 10) & 0x3fc;					\
625*25c28e83SPiotr Jasiukajtis 	d##N = z##N.d - w##N.d;					\
626*25c28e83SPiotr Jasiukajtis 	h##N = d##N * TBL[i##N];					\
627*25c28e83SPiotr Jasiukajtis 	l##N = d##N * TBL[i##N+1];					\
628*25c28e83SPiotr Jasiukajtis 	s##N = h##N + l##N;						\
629*25c28e83SPiotr Jasiukajtis 	b##N = (s##N * s##N) * (mhalf + s##N * (P3 + s##N * (P4 +	\
630*25c28e83SPiotr Jasiukajtis 	    s##N * (P5 + s##N * P6))));					\
631*25c28e83SPiotr Jasiukajtis 	*y = (n##N * ln2hi + TBL[i##N+2]) + (h##N + (l##N +		\
632*25c28e83SPiotr Jasiukajtis 	    (n##N * ln2lo + TBL[i##N+3]) + b##N));			\
633*25c28e83SPiotr Jasiukajtis 	y += stridey
634*25c28e83SPiotr Jasiukajtis 
635*25c28e83SPiotr Jasiukajtis #define	PREPROCESS(N, index, label)					\
636*25c28e83SPiotr Jasiukajtis 	i##N = HI(*x);							\
637*25c28e83SPiotr Jasiukajtis 	z##N.d = *x;							\
638*25c28e83SPiotr Jasiukajtis 	x += stridex;							\
639*25c28e83SPiotr Jasiukajtis 	n##N = 0;							\
640*25c28e83SPiotr Jasiukajtis 	if ((i##N & 0x7ff00000) == 0x7ff00000) { /* inf or NaN */	\
641*25c28e83SPiotr Jasiukajtis 		y[index] = z##N.d * ((i##N < 0)? zero : z##N.d);	\
642*25c28e83SPiotr Jasiukajtis 		goto label;						\
643*25c28e83SPiotr Jasiukajtis 	} else if (i##N < 0x00100000) { /* subnormal, negative, zero */	\
644*25c28e83SPiotr Jasiukajtis 		if (((i##N << 1) | z##N.i[LOWORD]) == 0) {		\
645*25c28e83SPiotr Jasiukajtis 			y[index] = mhalf / zero;			\
646*25c28e83SPiotr Jasiukajtis 			goto label;					\
647*25c28e83SPiotr Jasiukajtis 		} else if (i##N < 0) {					\
648*25c28e83SPiotr Jasiukajtis 			y[index] = zero / zero;				\
649*25c28e83SPiotr Jasiukajtis 			goto label;					\
650*25c28e83SPiotr Jasiukajtis 		}							\
651*25c28e83SPiotr Jasiukajtis 		z##N.d *= two52;					\
652*25c28e83SPiotr Jasiukajtis 		n##N = -52;						\
653*25c28e83SPiotr Jasiukajtis 		i##N = z##N.i[HIWORD];				\
654*25c28e83SPiotr Jasiukajtis 	}
655*25c28e83SPiotr Jasiukajtis 
656*25c28e83SPiotr Jasiukajtis void
__vlog(int n,double * restrict x,int stridex,double * restrict y,int stridey)657*25c28e83SPiotr Jasiukajtis __vlog(int n, double *restrict x, int stridex, double *restrict y,
658*25c28e83SPiotr Jasiukajtis 	int stridey)
659*25c28e83SPiotr Jasiukajtis {
660*25c28e83SPiotr Jasiukajtis 	union {
661*25c28e83SPiotr Jasiukajtis 		unsigned	i[2];
662*25c28e83SPiotr Jasiukajtis 		double		d;
663*25c28e83SPiotr Jasiukajtis 	} z0, z1, z2, z3, w0, w1, w2, w3;
664*25c28e83SPiotr Jasiukajtis 	double	b0, b1, b2, b3;
665*25c28e83SPiotr Jasiukajtis 	double	d0, d1, d2, d3;
666*25c28e83SPiotr Jasiukajtis 	double	h0, h1, h2, h3;
667*25c28e83SPiotr Jasiukajtis 	double	l0, l1, l2, l3;
668*25c28e83SPiotr Jasiukajtis 	double	s0, s1, s2, s3;
669*25c28e83SPiotr Jasiukajtis 	int	i0, i1, i2, i3, e;
670*25c28e83SPiotr Jasiukajtis 	int	n0, n1, n2, n3;
671*25c28e83SPiotr Jasiukajtis 
672*25c28e83SPiotr Jasiukajtis 	w0.i[LOWORD] = 0;
673*25c28e83SPiotr Jasiukajtis 	w1.i[LOWORD] = 0;
674*25c28e83SPiotr Jasiukajtis 	w2.i[LOWORD] = 0;
675*25c28e83SPiotr Jasiukajtis 	w3.i[LOWORD] = 0;
676*25c28e83SPiotr Jasiukajtis 
677*25c28e83SPiotr Jasiukajtis 	y -= stridey;
678*25c28e83SPiotr Jasiukajtis 
679*25c28e83SPiotr Jasiukajtis 	for (;;) {
680*25c28e83SPiotr Jasiukajtis begin:
681*25c28e83SPiotr Jasiukajtis 		y += stridey;
682*25c28e83SPiotr Jasiukajtis 
683*25c28e83SPiotr Jasiukajtis 		if (--n < 0)
684*25c28e83SPiotr Jasiukajtis 			break;
685*25c28e83SPiotr Jasiukajtis 
686*25c28e83SPiotr Jasiukajtis 		PREPROCESS(0, 0, begin);
687*25c28e83SPiotr Jasiukajtis 
688*25c28e83SPiotr Jasiukajtis 		if (--n < 0)
689*25c28e83SPiotr Jasiukajtis 			goto process1;
690*25c28e83SPiotr Jasiukajtis 
691*25c28e83SPiotr Jasiukajtis 		PREPROCESS(1, stridey, process1);
692*25c28e83SPiotr Jasiukajtis 
693*25c28e83SPiotr Jasiukajtis 		if (--n < 0)
694*25c28e83SPiotr Jasiukajtis 			goto process2;
695*25c28e83SPiotr Jasiukajtis 
696*25c28e83SPiotr Jasiukajtis 		PREPROCESS(2, (stridey << 1), process2);
697*25c28e83SPiotr Jasiukajtis 
698*25c28e83SPiotr Jasiukajtis 		if (--n < 0)
699*25c28e83SPiotr Jasiukajtis 			goto process3;
700*25c28e83SPiotr Jasiukajtis 
701*25c28e83SPiotr Jasiukajtis 		PREPROCESS(3, (stridey << 1) + stridey, process3);
702*25c28e83SPiotr Jasiukajtis 
703*25c28e83SPiotr Jasiukajtis 		i0 = (i0 + 0x800) & ~0xfff;
704*25c28e83SPiotr Jasiukajtis 		e = (i0 & 0x7ff00000) - 0x3ff00000;
705*25c28e83SPiotr Jasiukajtis 		z0.i[HIWORD] -= e;
706*25c28e83SPiotr Jasiukajtis 		w0.i[HIWORD] = i0 - e;
707*25c28e83SPiotr Jasiukajtis 		n0 += (e >> 20);
708*25c28e83SPiotr Jasiukajtis 		i0 = (i0 >> 10) & 0x3fc;
709*25c28e83SPiotr Jasiukajtis 
710*25c28e83SPiotr Jasiukajtis 		i1 = (i1 + 0x800) & ~0xfff;
711*25c28e83SPiotr Jasiukajtis 		e = (i1 & 0x7ff00000) - 0x3ff00000;
712*25c28e83SPiotr Jasiukajtis 		z1.i[HIWORD] -= e;
713*25c28e83SPiotr Jasiukajtis 		w1.i[HIWORD] = i1 - e;
714*25c28e83SPiotr Jasiukajtis 		n1 += (e >> 20);
715*25c28e83SPiotr Jasiukajtis 		i1 = (i1 >> 10) & 0x3fc;
716*25c28e83SPiotr Jasiukajtis 
717*25c28e83SPiotr Jasiukajtis 		i2 = (i2 + 0x800) & ~0xfff;
718*25c28e83SPiotr Jasiukajtis 		e = (i2 & 0x7ff00000) - 0x3ff00000;
719*25c28e83SPiotr Jasiukajtis 		z2.i[HIWORD] -= e;
720*25c28e83SPiotr Jasiukajtis 		w2.i[HIWORD] = i2 - e;
721*25c28e83SPiotr Jasiukajtis 		n2 += (e >> 20);
722*25c28e83SPiotr Jasiukajtis 		i2 = (i2 >> 10) & 0x3fc;
723*25c28e83SPiotr Jasiukajtis 
724*25c28e83SPiotr Jasiukajtis 		i3 = (i3 + 0x800) & ~0xfff;
725*25c28e83SPiotr Jasiukajtis 		e = (i3 & 0x7ff00000) - 0x3ff00000;
726*25c28e83SPiotr Jasiukajtis 		z3.i[HIWORD] -= e;
727*25c28e83SPiotr Jasiukajtis 		w3.i[HIWORD] = i3 - e;
728*25c28e83SPiotr Jasiukajtis 		n3 += (e >> 20);
729*25c28e83SPiotr Jasiukajtis 		i3 = (i3 >> 10) & 0x3fc;
730*25c28e83SPiotr Jasiukajtis 
731*25c28e83SPiotr Jasiukajtis 		d0 = z0.d - w0.d;
732*25c28e83SPiotr Jasiukajtis 		d1 = z1.d - w1.d;
733*25c28e83SPiotr Jasiukajtis 		d2 = z2.d - w2.d;
734*25c28e83SPiotr Jasiukajtis 		d3 = z3.d - w3.d;
735*25c28e83SPiotr Jasiukajtis 
736*25c28e83SPiotr Jasiukajtis 		h0 = d0 * TBL[i0];
737*25c28e83SPiotr Jasiukajtis 		h1 = d1 * TBL[i1];
738*25c28e83SPiotr Jasiukajtis 		h2 = d2 * TBL[i2];
739*25c28e83SPiotr Jasiukajtis 		h3 = d3 * TBL[i3];
740*25c28e83SPiotr Jasiukajtis 
741*25c28e83SPiotr Jasiukajtis 		l0 = d0 * TBL[i0+1];
742*25c28e83SPiotr Jasiukajtis 		l1 = d1 * TBL[i1+1];
743*25c28e83SPiotr Jasiukajtis 		l2 = d2 * TBL[i2+1];
744*25c28e83SPiotr Jasiukajtis 		l3 = d3 * TBL[i3+1];
745*25c28e83SPiotr Jasiukajtis 
746*25c28e83SPiotr Jasiukajtis 		s0 = h0 + l0;
747*25c28e83SPiotr Jasiukajtis 		s1 = h1 + l1;
748*25c28e83SPiotr Jasiukajtis 		s2 = h2 + l2;
749*25c28e83SPiotr Jasiukajtis 		s3 = h3 + l3;
750*25c28e83SPiotr Jasiukajtis 
751*25c28e83SPiotr Jasiukajtis 		b0 = (s0 * s0) * (mhalf + s0 * (P3 + s0 * (P4 +
752*25c28e83SPiotr Jasiukajtis 		    s0 * (P5 + s0 * P6))));
753*25c28e83SPiotr Jasiukajtis 		b1 = (s1 * s1) * (mhalf + s1 * (P3 + s1 * (P4 +
754*25c28e83SPiotr Jasiukajtis 		    s1 * (P5 + s1 * P6))));
755*25c28e83SPiotr Jasiukajtis 		b2 = (s2 * s2) * (mhalf + s2 * (P3 + s2 * (P4 +
756*25c28e83SPiotr Jasiukajtis 		    s2 * (P5 + s2 * P6))));
757*25c28e83SPiotr Jasiukajtis 		b3 = (s3 * s3) * (mhalf + s3 * (P3 + s3 * (P4 +
758*25c28e83SPiotr Jasiukajtis 		    s3 * (P5 + s3 * P6))));
759*25c28e83SPiotr Jasiukajtis 
760*25c28e83SPiotr Jasiukajtis 		*y = (n0 * ln2hi + TBL[i0+2]) + (h0 + (l0 +
761*25c28e83SPiotr Jasiukajtis 		    (n0 * ln2lo + TBL[i0+3]) + b0));
762*25c28e83SPiotr Jasiukajtis 		y += stridey;
763*25c28e83SPiotr Jasiukajtis 		*y = (n1 * ln2hi + TBL[i1+2]) + (h1 + (l1 +
764*25c28e83SPiotr Jasiukajtis 		    (n1 * ln2lo + TBL[i1+3]) + b1));
765*25c28e83SPiotr Jasiukajtis 		y += stridey;
766*25c28e83SPiotr Jasiukajtis 		*y = (n2 * ln2hi + TBL[