1/*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
5 * Common Development and Distribution License (the "License").
6 * You may not use this file except in compliance with the License.
7 *
8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 * or http://www.opensolaris.org/os/licensing.
10 * See the License for the specific language governing permissions
11 * and limitations under the License.
12 *
13 * When distributing Covered Code, include this CDDL HEADER in each
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21
22/*
23 * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
24 */
25/*
26 * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
27 * Use is subject to license terms.
28 */
29
30#ifdef __RESTRICT
31#define restrict _Restrict
32#else
33#define restrict
34#endif
35
36/* float logf(float x)
37 *
38 * Method :
39 *	1. Special cases:
40 *		for x is negative, -Inf => QNaN + invalid;
41 *		for x = 0		=> -Inf + divide-by-zero;
42 *		for x = +Inf		=> Inf;
43 *		for x = NaN		=> QNaN.
44 *	2. Computes logarithm from:
45 *		x = m * 2**n => log(x) = n * log(2) + log(m),
46 *		m = [1, 2).
47 *	Let m = m0 + dm, where m0 = 1 + k / 32,
48 *		k = [0, 32],
49 *		dm = [-1/64, 1/64].
50 *	Then log(m) = log(m0 + dm) = log(m0) + log(1+y),
51 *		where y = dm*(1/m0), y = [-1/66, 1/64].
52 *	Then
53 *		1/m0 is looked up in a table of 1, 1/(1+1/32), ..., 1/(1+32/32);
54 *		log(m0) is looked up in a table of log(1), log(1+1/32),
55 *		..., log(1+32/32).
56 *		log(1+y) is computed using approximation:
57 *		log(1+y) = ((a3*y + a2)*y + a1)*y*y + y.
58 * Accuracy:
59 *	The maximum relative error for the approximating
60 *	polynomial is 2**(-28.41).  All calculations are of
61 *	double precision.
62 *	Maximum error observed: less than 0.545 ulp for the
63 *	whole float type range.
64 */
65
66static const double __TBL_logf[] = {
67	/* __TBL_logf[2*i] = log(1+i/32), i = [0, 32] */
68	/* __TBL_logf[2*i+1] = 2**(-23)/(1+i/32), i = [0, 32] */
690.000000000000000000e+00, 1.192092895507812500e-07, 3.077165866675368733e-02,
701.155968868371212153e-07, 6.062462181643483994e-02, 1.121969784007352926e-07,
718.961215868968713805e-02, 1.089913504464285680e-07, 1.177830356563834557e-01,
721.059638129340277719e-07, 1.451820098444978890e-01, 1.030999260979729787e-07,
731.718502569266592284e-01, 1.003867701480263102e-07, 1.978257433299198675e-01,
749.781275040064102225e-08, 2.231435513142097649e-01, 9.536743164062500529e-08,
752.478361639045812692e-01, 9.304139672256097884e-08, 2.719337154836417580e-01,
769.082612537202380448e-08, 2.954642128938358980e-01, 8.871388989825581272e-08,
773.184537311185345887e-01, 8.669766512784091150e-08, 3.409265869705931928e-01,
788.477105034722222546e-08, 3.629054936893684746e-01, 8.292820142663043248e-08,
793.844116989103320559e-01, 8.116377160904255122e-08, 4.054651081081643849e-01,
807.947285970052082892e-08, 4.260843953109000881e-01, 7.785096460459183052e-08,
814.462871026284195297e-01, 7.629394531250000159e-08, 4.660897299245992387e-01,
827.479798560049019504e-08, 4.855078157817008244e-01, 7.335956280048077330e-08,
835.045560107523953119e-01, 7.197542010613207272e-08, 5.232481437645478684e-01,
847.064254195601851460e-08, 5.415972824327444091e-01, 6.935813210227272390e-08,
855.596157879354226594e-01, 6.811959402901785336e-08, 5.773153650348236132e-01,
866.692451343201754014e-08, 5.947071077466927758e-01, 6.577064251077586116e-08,
876.118015411059929409e-01, 6.465588585805084723e-08, 6.286086594223740942e-01,
886.357828776041666578e-08, 6.451379613735847007e-01, 6.253602074795082293e-08,
896.613984822453650159e-01, 6.152737525201612732e-08, 6.773988235918061429e-01,
906.055075024801586965e-08, 6.931471805599452862e-01, 5.960464477539062500e-08
91};
92
93static const double
94	K3 = -2.49887584306188944706e-01,
95	K2 =  3.33368809981254554946e-01,
96	K1 = -5.00000008402474976565e-01;
97
98static const union {
99	int	i;
100	float	f;
101} inf = { 0x7f800000 };
102
103#define INF	inf.f
104
105#define PROCESS(N)								\
106	iy##N = ival##N & 0x007fffff;						\
107	ival##N = (iy##N + 0x20000) & 0xfffc0000;				\
108	i##N  = ival##N >> 17;							\
109	iy##N = iy##N - ival##N;						\
110	ty##N = LN2 * (double) exp##N + __TBL_logf[i##N];			\
111	yy##N = (double) iy##N * __TBL_logf[i##N + 1];				\
112	yy##N = ((K3 * yy##N + K2) * yy##N + K1) * yy##N * yy##N + yy##N;	\
113	y[0] = (float)(yy##N + ty##N);						\
114	y += stridey;
115
116#define PREPROCESS(N, index, label)						\
117	ival##N = *(int*)x;							\
118	value = x[0];								\
119	x += stridex;								\
120	exp##N = (ival##N >> 23) - 127;						\
121	if ((ival##N & 0x7fffffff) >= 0x7f800000) /* X = NaN or Inf */	\
122	{									\
123		y[index] = value + INF;						\
124		goto label;							\
125	}									\
126	if (ival##N < 0x00800000)						\
127	{									\
128		if (ival##N > 0)	/* X = denormal */			\
129		{								\
130			value = (float) ival##N;				\
131			ival##N = *(int*) &value;				\
132			exp##N = (ival##N >> 23) - (127 + 149);			\
133		}								\
134		else								\
135		{								\
136			value = 0.0f;						\
137			y[index] = ((ival##N & 0x7fffffff) == 0) ?		\
138				-1.0f / value : value / value;			\
139			goto label;						\
140		}								\
141	}
142
143void
144__vlogf(int n, float * restrict x, int stridex, float * restrict y,
145	int stridey)
146{
147	double	LN2 = __TBL_logf[64];		/* log(2) = 0.6931471805599453094 	*/
148	double	yy0, yy1, yy2, yy3, yy4;
149	double	ty0, ty1, ty2, ty3, ty4;
150	float	value;
151	int	i0, i1, i2, i3, i4;
152	int	ival0, ival1, ival2, ival3, ival4;
153	int	exp0, exp1, exp2, exp3, exp4;
154	int	iy0, iy1, iy2, iy3, iy4;
155
156	y -= stridey;
157
158	for (; ;)
159	{
160begin:
161		y += stridey;
162
163		if (--n < 0)
164			break;
165
166		PREPROCESS(0, 0, begin)
167
168		if (--n < 0)
169			goto process1;
170
171		PREPROCESS(1, stridey, process1)
172
173		if (--n < 0)
174			goto process2;
175
176		PREPROCESS(2, (stridey << 1), process2)
177
178		if (--n < 0)
179			goto process3;
180
181		PREPROCESS(3, (stridey << 1) + stridey, process3)
182
183		if (--n < 0)
184			goto process4;
185
186		PREPROCESS(4, (stridey << 2), process4)
187
188		iy0 = ival0 & 0x007fffff;
189		iy1 = ival1 & 0x007fffff;
190		iy2 = ival2 & 0x007fffff;
191		iy3 = ival3 & 0x007fffff;
192		iy4 = ival4 & 0x007fffff;
193
194		ival0 = (iy0 + 0x20000) & 0xfffc0000;
195		ival1 = (iy1 + 0x20000) & 0xfffc0000;
196		ival2 = (iy2 + 0x20000) & 0xfffc0000;
197		ival3 = (iy3 + 0x20000) & 0xfffc0000;
198		ival4 = (iy4 + 0x20000) & 0xfffc0000;
199
200		i0 = ival0 >> 17;
201		i1 = ival1 >> 17;
202		i2 = ival2 >> 17;
203		i3 = ival3 >> 17;
204		i4 = ival4 >> 17;
205
206		iy0 = iy0 - ival0;
207		iy1 = iy1 - ival1;
208		iy2 = iy2 - ival2;
209		iy3 = iy3 - ival3;
210		iy4 = iy4 - ival4;
211
212		ty0 = LN2 * (double) exp0 + __TBL_logf[i0];
213		ty1 = LN2 * (double) exp1 + __TBL_logf[i1];
214		ty2 = LN2 * (double) exp2 + __TBL_logf[i2];
215		ty3 = LN2 * (double) exp3 + __TBL_logf[i3];
216		ty4 = LN2 * (double) exp4 + __TBL_logf[i4];
217
218		yy0 = (double) iy0 * __TBL_logf[i0 + 1];
219		yy1 = (double) iy1 * __TBL_logf[i1 + 1];
220		yy2 = (double) iy2 * __TBL_logf[i2 + 1];
221		yy3 = (double) iy3 * __TBL_logf[i3 + 1];
222		yy4 = (double) iy4 * __TBL_logf[i4 + 1];
223
224		yy0 = ((K3 * yy0 + K2) * yy0 + K1) * yy0 * yy0 + yy0;
225		yy1 = ((K3 * yy1 + K2) * yy1 + K1) * yy1 * yy1 + yy1;
226		yy2 = ((K3 * yy2 + K2) * yy2 + K1) * yy2 * yy2 + yy2;
227		yy3 = ((K3 * yy3 + K2) * yy3 + K1) * yy3 * yy3 + yy3;
228		yy4 = ((K3 * yy4 + K2) * yy4 + K1) * yy4 * yy4 + yy4;
229
230		y[0] = (float)(yy0 + ty0);
231		y += stridey;
232		y[0] = (float)(yy1 + ty1);
233		y += stridey;
234		y[0] = (float)(yy2 + ty2);
235		y += stridey;
236		y[0] = (float)(yy3 + ty3);
237		y += stridey;
238		y[0] = (float)(yy4 + ty4);
239		continue;
240
241process1:
242		PROCESS(0)
243		continue;
244
245process2:
246		PROCESS(0)
247		PROCESS(1)
248		continue;
249
250process3:
251		PROCESS(0)
252		PROCESS(1)
253		PROCESS(2)
254		continue;
255
256process4:
257		PROCESS(0)
258		PROCESS(1)
259		PROCESS(2)
260		PROCESS(3)
261	}
262}
263