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1 /*-------------------------------------------------------------------------
2  * drawElements Base Portability Library
3  * -------------------------------------
4  *
5  * Copyright 2014 The Android Open Source Project
6  *
7  * Licensed under the Apache License, Version 2.0 (the "License");
8  * you may not use this file except in compliance with the License.
9  * You may obtain a copy of the License at
10  *
11  *      http://www.apache.org/licenses/LICENSE-2.0
12  *
13  * Unless required by applicable law or agreed to in writing, software
14  * distributed under the License is distributed on an "AS IS" BASIS,
15  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
16  * See the License for the specific language governing permissions and
17  * limitations under the License.
18  *
19  *//*!
20  * \file
21  * \brief 32-bit integer math.
22  *//*--------------------------------------------------------------------*/
23 
24 #include "deInt32.h"
25 
26 DE_BEGIN_EXTERN_C
27 
28 const deInt8 g_clzLUT[256] =
29 {
30 	8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4,
31 	3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
32 	2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
33 	2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
34 	1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
35 	1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
36 	1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
37 	1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
38 	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
39 	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
40 	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
41 	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
42 	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
43 	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
44 	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
45 	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
46 };
47 
48 const deInt8 g_ctzLUT[256] =
49 {
50 	8, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
51 	4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
52 	5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
53 	4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
54 	6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
55 	4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
56 	5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
57 	4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
58 	7, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
59 	4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
60 	5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
61 	4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
62 	6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
63 	4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
64 	5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
65 	4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
66 };
67 
68 /*--------------------------------------------------------------------*//*!
69  * \brief Compute the reciprocal of an integer.
70  * \param a		Input value.
71  * \param rcp	Pointer to resulting reciprocal "mantissa" value.
72  * \param exp	Pointer to resulting exponent value.
73  *
74  * The returned value is split into an exponent part and a mantissa part for
75  * practical reasons. The actual reciprocal can be computed with the formula:
76  * result = exp2(exp) * rcp / (1<<DE_RCP_FRAC_BITS).
77  *//*--------------------------------------------------------------------*/
deRcp32(deUint32 a,deUint32 * rcp,int * exp)78 void deRcp32 (deUint32 a, deUint32* rcp, int* exp)
79 {
80 	enum { RCP_LUT_BITS = 8 };
81 	static const deUint32 s_rcpLUT[1<<RCP_LUT_BITS] =
82 	{
83 		0x40000000, 0x3fc03fc0, 0x3f80fe03, 0x3f423954,
84 		0x3f03f03f, 0x3ec62159, 0x3e88cb3c, 0x3e4bec88,
85 		0x3e0f83e0, 0x3dd38ff0, 0x3d980f66, 0x3d5d00f5,
86 		0x3d226357, 0x3ce8354b, 0x3cae7592, 0x3c7522f3,
87 		0x3c3c3c3c, 0x3c03c03c, 0x3bcbadc7, 0x3b9403b9,
88 		0x3b5cc0ed, 0x3b25e446, 0x3aef6ca9, 0x3ab95900,
89 		0x3a83a83a, 0x3a4e5947, 0x3a196b1e, 0x39e4dcb8,
90 		0x39b0ad12, 0x397cdb2c, 0x3949660a, 0x39164cb5,
91 		0x38e38e38, 0x38b129a2, 0x387f1e03, 0x384d6a72,
92 		0x381c0e07, 0x37eb07dd, 0x37ba5713, 0x3789facb,
93 		0x3759f229, 0x372a3c56, 0x36fad87b, 0x36cbc5c7,
94 		0x369d0369, 0x366e9095, 0x36406c80, 0x36129663,
95 		0x35e50d79, 0x35b7d0ff, 0x358ae035, 0x355e3a5f,
96 		0x3531dec0, 0x3505cca2, 0x34da034d, 0x34ae820e,
97 		0x34834834, 0x3458550f, 0x342da7f2, 0x34034034,
98 		0x33d91d2a, 0x33af3e2e, 0x3385a29d, 0x335c49d4,
99 		0x33333333, 0x330a5e1b, 0x32e1c9f0, 0x32b97617,
100 		0x329161f9, 0x32698cff, 0x3241f693, 0x321a9e24,
101 		0x31f3831f, 0x31cca4f5, 0x31a6031a, 0x317f9d00,
102 		0x3159721e, 0x313381ec, 0x310dcbe1, 0x30e84f79,
103 		0x30c30c30, 0x309e0184, 0x30792ef5, 0x30549403,
104 		0x30303030, 0x300c0300, 0x2fe80bfa, 0x2fc44aa2,
105 		0x2fa0be82, 0x2f7d6724, 0x2f5a4411, 0x2f3754d7,
106 		0x2f149902, 0x2ef21023, 0x2ecfb9c8, 0x2ead9584,
107 		0x2e8ba2e8, 0x2e69e18a, 0x2e4850fe, 0x2e26f0db,
108 		0x2e05c0b8, 0x2de4c02d, 0x2dc3eed6, 0x2da34c4d,
109 		0x2d82d82d, 0x2d629215, 0x2d4279a2, 0x2d228e75,
110 		0x2d02d02d, 0x2ce33e6c, 0x2cc3d8d4, 0x2ca49f0a,
111 		0x2c8590b2, 0x2c66ad71, 0x2c47f4ee, 0x2c2966d0,
112 		0x2c0b02c0, 0x2becc868, 0x2bceb771, 0x2bb0cf87,
113 		0x2b931057, 0x2b75798c, 0x2b580ad6, 0x2b3ac3e2,
114 		0x2b1da461, 0x2b00ac02, 0x2ae3da78, 0x2ac72f74,
115 		0x2aaaaaaa, 0x2a8e4bcd, 0x2a721291, 0x2a55fead,
116 		0x2a3a0fd5, 0x2a1e45c2, 0x2a02a02a, 0x29e71ec5,
117 		0x29cbc14e, 0x29b0877d, 0x2995710e, 0x297a7dbb,
118 		0x295fad40, 0x2944ff5a, 0x292a73c7, 0x29100a44,
119 		0x28f5c28f, 0x28db9c68, 0x28c1978f, 0x28a7b3c5,
120 		0x288df0ca, 0x28744e61, 0x285acc4b, 0x28416a4c,
121 		0x28282828, 0x280f05a2, 0x27f6027f, 0x27dd1e85,
122 		0x27c45979, 0x27abb323, 0x27932b48, 0x277ac1b2,
123 		0x27627627, 0x274a4870, 0x27323858, 0x271a45a6,
124 		0x27027027, 0x26eab7a3, 0x26d31be7, 0x26bb9cbf,
125 		0x26a439f6, 0x268cf359, 0x2675c8b6, 0x265eb9da,
126 		0x2647c694, 0x2630eeb1, 0x261a3202, 0x26039055,
127 		0x25ed097b, 0x25d69d43, 0x25c04b80, 0x25aa1402,
128 		0x2593f69b, 0x257df31c, 0x2568095a, 0x25523925,
129 		0x253c8253, 0x2526e4b7, 0x25116025, 0x24fbf471,
130 		0x24e6a171, 0x24d166f9, 0x24bc44e1, 0x24a73afd,
131 		0x24924924, 0x247d6f2e, 0x2468acf1, 0x24540245,
132 		0x243f6f02, 0x242af300, 0x24168e18, 0x24024024,
133 		0x23ee08fb, 0x23d9e878, 0x23c5de76, 0x23b1eace,
134 		0x239e0d5b, 0x238a45f8, 0x23769480, 0x2362f8cf,
135 		0x234f72c2, 0x233c0233, 0x2328a701, 0x23156107,
136 		0x23023023, 0x22ef1432, 0x22dc0d12, 0x22c91aa1,
137 		0x22b63cbe, 0x22a37347, 0x2290be1c, 0x227e1d1a,
138 		0x226b9022, 0x22591713, 0x2246b1ce, 0x22346033,
139 		0x22222222, 0x220ff77c, 0x21fde021, 0x21ebdbf5,
140 		0x21d9ead7, 0x21c80cab, 0x21b64151, 0x21a488ac,
141 		0x2192e29f, 0x21814f0d, 0x216fcdd8, 0x215e5ee4,
142 		0x214d0214, 0x213bb74d, 0x212a7e72, 0x21195766,
143 		0x21084210, 0x20f73e53, 0x20e64c14, 0x20d56b38,
144 		0x20c49ba5, 0x20b3dd40, 0x20a32fef, 0x20929398,
145 		0x20820820, 0x20718d6f, 0x2061236a, 0x2050c9f8,
146 		0x20408102, 0x2030486c, 0x20202020, 0x20100804
147 	};
148 
149 	DE_STATIC_ASSERT(DE_LENGTH_OF_ARRAY(s_rcpLUT) == (1<<RCP_LUT_BITS));
150 
151 	int			shift		= deClz32(a);
152 	deUint32	normalized	= (deUint32)a << shift; /* Highest bit is always 1. */
153 	int			lookupNdx	= (normalized >> (31 - RCP_LUT_BITS)) & ((1<<RCP_LUT_BITS)-1); /* Discard high bit, leave 8 next highest bits to lowest bits of normalized. */
154 	deUint32	result;
155 	deUint32	tmp;
156 
157 	/* Must be non-negative. */
158 	DE_ASSERT(a > 0);
159 
160 	/* First approximation from lookup table. */
161 	DE_ASSERT(lookupNdx >= 0 && lookupNdx < (1<<RCP_LUT_BITS));
162 	result = s_rcpLUT[lookupNdx];
163 
164 	/* Newton-Raphson iteration for improved accuracy (has 16 bits of accuracy afterwards). */
165 	tmp		= deSafeMuluAsr32(result, normalized, 31);
166 	result	= deSafeMuluAsr32(result, (2u<<DE_RCP_FRAC_BITS) - tmp, DE_RCP_FRAC_BITS);
167 
168 	/* Second Newton-Raphson iteration (now has full accuracy). */
169 	tmp		= deSafeMuluAsr32(result, normalized, 31);
170 	result	= deSafeMuluAsr32(result, (2u<<DE_RCP_FRAC_BITS) - tmp, DE_RCP_FRAC_BITS);
171 
172 	/* Return results. */
173 	*rcp = result;
174 	*exp = 31 - shift;
175 }
176 
177 DE_END_EXTERN_C
178