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1/*
2 * log2f.s
3 *
4 * by Ian Ollmann
5 *
6 * Copyright � 2007 Apple Inc. All Rights Reserved.
7 */
8
9#include <machine/asm.h>
10#include "abi.h"
11
12.const
13.align 4
14
15// 256 entry of Lookup table of values used for log2 calculation, generated as:
16//
17// [ollmia:/tmp] iano% cat main.c
18// #include <stdio.h>
19// #include <stdint.h>
20// #include <math.h>
21//
22// int main (void)
23// {
24//
25// int i;
26//
27// for( i = 0; i < 256; i++ )
28// {
29// double d = (double) i / 256.0 + 1.0;
30// union
31// {
32// double d;
33// uint64_t u;
34// }u, u2;
35//
36// u.d = log2l( (long double) d );
37// u2.d = 1.0 / d;
38//
39// printf( "0x%llx, 0x%llx,\t//log2(%7.5f), 1/%7.5f\n", u.u, u2.u, d, d );
40// }
41//
42// return 0;
43// }
44
45log2f_table: .quad 0x0, 0x3ff0000000000000 //log2(1.00000), 1/1.00000
46 .quad 0x3f7709c46d7aac77, 0x3fefe01fe01fe020 //log2(1.00391), 1/1.00391
47 .quad 0x3f86fe50b6ef0851, 0x3fefc07f01fc07f0 //log2(1.00781), 1/1.00781
48 .quad 0x3f91363117a97b0c, 0x3fefa11caa01fa12 //log2(1.01172), 1/1.01172
49 .quad 0x3f96e79685c2d22a, 0x3fef81f81f81f820 //log2(1.01562), 1/1.01562
50 .quad 0x3f9c9363ba850f86, 0x3fef6310aca0dbb5 //log2(1.01953), 1/1.01953
51 .quad 0x3fa11cd1d5133413, 0x3fef44659e4a4271 //log2(1.02344), 1/1.02344
52 .quad 0x3fa3ed3094685a26, 0x3fef25f644230ab5 //log2(1.02734), 1/1.02734
53 .quad 0x3fa6bad3758efd87, 0x3fef07c1f07c1f08 //log2(1.03125), 1/1.03125
54 .quad 0x3fa985bfc3495194, 0x3feee9c7f8458e02 //log2(1.03516), 1/1.03516
55 .quad 0x3fac4dfab90aab5f, 0x3feecc07b301ecc0 //log2(1.03906), 1/1.03906
56 .quad 0x3faf1389833253a0, 0x3feeae807aba01eb //log2(1.04297), 1/1.04297
57 .quad 0x3fb0eb389fa29f9b, 0x3fee9131abf0b767 //log2(1.04688), 1/1.04688
58 .quad 0x3fb24b5b7e135a3d, 0x3fee741aa59750e4 //log2(1.05078), 1/1.05078
59 .quad 0x3fb3aa2fdd27f1c3, 0x3fee573ac901e574 //log2(1.05469), 1/1.05469
60 .quad 0x3fb507b836033bb7, 0x3fee3a9179dc1a73 //log2(1.05859), 1/1.05859
61 .quad 0x3fb663f6fac91316, 0x3fee1e1e1e1e1e1e //log2(1.06250), 1/1.06250
62 .quad 0x3fb7beee96b8a281, 0x3fee01e01e01e01e //log2(1.06641), 1/1.06641
63 .quad 0x3fb918a16e46335b, 0x3fede5d6e3f8868a //log2(1.07031), 1/1.07031
64 .quad 0x3fba7111df348494, 0x3fedca01dca01dca //log2(1.07422), 1/1.07422
65 .quad 0x3fbbc84240adabba, 0x3fedae6076b981db //log2(1.07812), 1/1.07812
66 .quad 0x3fbd1e34e35b82da, 0x3fed92f2231e7f8a //log2(1.08203), 1/1.08203
67 .quad 0x3fbe72ec117fa5b2, 0x3fed77b654b82c34 //log2(1.08594), 1/1.08594
68 .quad 0x3fbfc66a0f0b00a5, 0x3fed5cac807572b2 //log2(1.08984), 1/1.08984
69 .quad 0x3fc08c588cda79e4, 0x3fed41d41d41d41d //log2(1.09375), 1/1.09375
70 .quad 0x3fc134e1b489062e, 0x3fed272ca3fc5b1a //log2(1.09766), 1/1.09766
71 .quad 0x3fc1dcd197552b7b, 0x3fed0cb58f6ec074 //log2(1.10156), 1/1.10156
72 .quad 0x3fc284294b07a640, 0x3fecf26e5c44bfc6 //log2(1.10547), 1/1.10547
73 .quad 0x3fc32ae9e278ae1a, 0x3fecd85689039b0b //log2(1.10938), 1/1.10938
74 .quad 0x3fc3d1146d9a8a64, 0x3fecbe6d9601cbe7 //log2(1.11328), 1/1.11328
75 .quad 0x3fc476a9f983f74d, 0x3feca4b3055ee191 //log2(1.11719), 1/1.11719
76 .quad 0x3fc51bab907a5c8a, 0x3fec8b265afb8a42 //log2(1.12109), 1/1.12109
77 .quad 0x3fc5c01a39fbd688, 0x3fec71c71c71c71c //log2(1.12500), 1/1.12500
78 .quad 0x3fc663f6fac91316, 0x3fec5894d10d4986 //log2(1.12891), 1/1.12891
79 .quad 0x3fc70742d4ef027f, 0x3fec3f8f01c3f8f0 //log2(1.13281), 1/1.13281
80 .quad 0x3fc7a9fec7d05ddf, 0x3fec26b5392ea01c //log2(1.13672), 1/1.13672
81 .quad 0x3fc84c2bd02f03b3, 0x3fec0e070381c0e0 //log2(1.14062), 1/1.14062
82 .quad 0x3fc8edcae8352b6c, 0x3febf583ee868d8b //log2(1.14453), 1/1.14453
83 .quad 0x3fc98edd077e70df, 0x3febdd2b899406f7 //log2(1.14844), 1/1.14844
84 .quad 0x3fca2f632320b86b, 0x3febc4fd65883e7b //log2(1.15234), 1/1.15234
85 .quad 0x3fcacf5e2db4ec94, 0x3febacf914c1bad0 //log2(1.15625), 1/1.15625
86 .quad 0x3fcb6ecf175f95e9, 0x3feb951e2b18ff23 //log2(1.16016), 1/1.16016
87 .quad 0x3fcc0db6cdd94dee, 0x3feb7d6c3dda338b //log2(1.16406), 1/1.16406
88 .quad 0x3fccac163c770dc9, 0x3feb65e2e3beee05 //log2(1.16797), 1/1.16797
89 .quad 0x3fcd49ee4c325970, 0x3feb4e81b4e81b4f //log2(1.17188), 1/1.17188
90 .quad 0x3fcde73fe3b1480f, 0x3feb37484ad806ce //log2(1.17578), 1/1.17578
91 .quad 0x3fce840be74e6a4d, 0x3feb2036406c80d9 //log2(1.17969), 1/1.17969
92 .quad 0x3fcf205339208f27, 0x3feb094b31d922a4 //log2(1.18359), 1/1.18359
93 .quad 0x3fcfbc16b902680a, 0x3feaf286bca1af28 //log2(1.18750), 1/1.18750
94 .quad 0x3fd02baba24d0664, 0x3feadbe87f94905e //log2(1.19141), 1/1.19141
95 .quad 0x3fd0790adbb03009, 0x3feac5701ac5701b //log2(1.19531), 1/1.19531
96 .quad 0x3fd0c62975542a8f, 0x3feaaf1d2f87ebfd //log2(1.19922), 1/1.19922
97 .quad 0x3fd11307dad30b76, 0x3fea98ef606a63be //log2(1.20312), 1/1.20312
98 .quad 0x3fd15fa676bb08ff, 0x3fea82e65130e159 //log2(1.20703), 1/1.20703
99 .quad 0x3fd1ac05b291f070, 0x3fea6d01a6d01a6d //log2(1.21094), 1/1.21094
100 .quad 0x3fd1f825f6d88e13, 0x3fea574107688a4a //log2(1.21484), 1/1.21484
101 .quad 0x3fd24407ab0e073a, 0x3fea41a41a41a41a //log2(1.21875), 1/1.21875
102 .quad 0x3fd28fab35b32683, 0x3fea2c2a87c51ca0 //log2(1.22266), 1/1.22266
103 .quad 0x3fd2db10fc4d9aaf, 0x3fea16d3f97a4b02 //log2(1.22656), 1/1.22656
104 .quad 0x3fd32639636b2836, 0x3fea01a01a01a01a //log2(1.23047), 1/1.23047
105 .quad 0x3fd37124cea4cded, 0x3fe9ec8e951033d9 //log2(1.23438), 1/1.23438
106 .quad 0x3fd3bbd3a0a1dcfb, 0x3fe9d79f176b682d //log2(1.23828), 1/1.23828
107 .quad 0x3fd406463b1b0449, 0x3fe9c2d14ee4a102 //log2(1.24219), 1/1.24219
108 .quad 0x3fd4507cfedd4fc4, 0x3fe9ae24ea5510da //log2(1.24609), 1/1.24609
109 .quad 0x3fd49a784bcd1b8b, 0x3fe999999999999a //log2(1.25000), 1/1.25000
110 .quad 0x3fd4e43880e8fb6a, 0x3fe9852f0d8ec0ff //log2(1.25391), 1/1.25391
111 .quad 0x3fd52dbdfc4c96b3, 0x3fe970e4f80cb872 //log2(1.25781), 1/1.25781
112 .quad 0x3fd577091b3378cb, 0x3fe95cbb0be377ae //log2(1.26172), 1/1.26172
113 .quad 0x3fd5c01a39fbd688, 0x3fe948b0fcd6e9e0 //log2(1.26562), 1/1.26562
114 .quad 0x3fd608f1b42948ae, 0x3fe934c67f9b2ce6 //log2(1.26953), 1/1.26953
115 .quad 0x3fd6518fe4677ba7, 0x3fe920fb49d0e229 //log2(1.27344), 1/1.27344
116 .quad 0x3fd699f5248cd4b8, 0x3fe90d4f120190d5 //log2(1.27734), 1/1.27734
117 .quad 0x3fd6e221cd9d0cde, 0x3fe8f9c18f9c18fa //log2(1.28125), 1/1.28125
118 .quad 0x3fd72a1637cbc183, 0x3fe8e6527af1373f //log2(1.28516), 1/1.28516
119 .quad 0x3fd771d2ba7efb3c, 0x3fe8d3018d3018d3 //log2(1.28906), 1/1.28906
120 .quad 0x3fd7b957ac51aac4, 0x3fe8bfce8062ff3a //log2(1.29297), 1/1.29297
121 .quad 0x3fd800a563161c54, 0x3fe8acb90f6bf3aa //log2(1.29688), 1/1.29688
122 .quad 0x3fd847bc33d8618e, 0x3fe899c0f601899c //log2(1.30078), 1/1.30078
123 .quad 0x3fd88e9c72e0b226, 0x3fe886e5f0abb04a //log2(1.30469), 1/1.30469
124 .quad 0x3fd8d54673b5c372, 0x3fe87427bcc092b9 //log2(1.30859), 1/1.30859
125 .quad 0x3fd91bba891f1709, 0x3fe8618618618618 //log2(1.31250), 1/1.31250
126 .quad 0x3fd961f90527409c, 0x3fe84f00c2780614 //log2(1.31641), 1/1.31641
127 .quad 0x3fd9a802391e232f, 0x3fe83c977ab2bedd //log2(1.32031), 1/1.32031
128 .quad 0x3fd9edd6759b25e0, 0x3fe82a4a0182a4a0 //log2(1.32422), 1/1.32422
129 .quad 0x3fda33760a7f6051, 0x3fe8181818181818 //log2(1.32812), 1/1.32812
130 .quad 0x3fda78e146f7bef4, 0x3fe8060180601806 //log2(1.33203), 1/1.33203
131 .quad 0x3fdabe18797f1f49, 0x3fe7f405fd017f40 //log2(1.33594), 1/1.33594
132 .quad 0x3fdb031befe06434, 0x3fe7e225515a4f1d //log2(1.33984), 1/1.33984
133 .quad 0x3fdb47ebf73882a1, 0x3fe7d05f417d05f4 //log2(1.34375), 1/1.34375
134 .quad 0x3fdb8c88dbf8867a, 0x3fe7beb3922e017c //log2(1.34766), 1/1.34766
135 .quad 0x3fdbd0f2e9e79031, 0x3fe7ad2208e0ecc3 //log2(1.35156), 1/1.35156
136 .quad 0x3fdc152a6c24cae6, 0x3fe79baa6bb6398b //log2(1.35547), 1/1.35547
137 .quad 0x3fdc592fad295b56, 0x3fe78a4c8178a4c8 //log2(1.35938), 1/1.35938
138 .quad 0x3fdc9d02f6ca47b4, 0x3fe77908119ac60d //log2(1.36328), 1/1.36328
139 .quad 0x3fdce0a4923a587d, 0x3fe767dce434a9b1 //log2(1.36719), 1/1.36719
140 .quad 0x3fdd2414c80bf27d, 0x3fe756cac201756d //log2(1.37109), 1/1.37109
141 .quad 0x3fdd6753e032ea0f, 0x3fe745d1745d1746 //log2(1.37500), 1/1.37500
142 .quad 0x3fddaa6222064fb9, 0x3fe734f0c541fe8d //log2(1.37891), 1/1.37891
143 .quad 0x3fdded3fd442364c, 0x3fe724287f46debc //log2(1.38281), 1/1.38281
144 .quad 0x3fde2fed3d097298, 0x3fe713786d9c7c09 //log2(1.38672), 1/1.38672
145 .quad 0x3fde726aa1e754d2, 0x3fe702e05c0b8170 //log2(1.39062), 1/1.39062
146 .quad 0x3fdeb4b847d15bce, 0x3fe6f26016f26017 //log2(1.39453), 1/1.39453
147 .quad 0x3fdef6d67328e220, 0x3fe6e1f76b4337c7 //log2(1.39844), 1/1.39844
148 .quad 0x3fdf38c567bcc541, 0x3fe6d1a62681c861 //log2(1.40234), 1/1.40234
149 .quad 0x3fdf7a8568cb06cf, 0x3fe6c16c16c16c17 //log2(1.40625), 1/1.40625
150 .quad 0x3fdfbc16b902680a, 0x3fe6b1490aa31a3d //log2(1.41016), 1/1.41016
151 .quad 0x3fdffd799a83ff9b, 0x3fe6a13cd1537290 //log2(1.41406), 1/1.41406
152 .quad 0x3fe01f57277264e0, 0x3fe691473a88d0c0 //log2(1.41797), 1/1.41797
153 .quad 0x3fe03fda8b97997f, 0x3fe6816816816817 //log2(1.42188), 1/1.42188
154 .quad 0x3fe0604719f24eb2, 0x3fe6719f3601671a //log2(1.42578), 1/1.42578
155 .quad 0x3fe0809cf27f703d, 0x3fe661ec6a5122f9 //log2(1.42969), 1/1.42969
156 .quad 0x3fe0a0dc34f8e1fc, 0x3fe6524f853b4aa3 //log2(1.43359), 1/1.43359
157 .quad 0x3fe0c10500d63aa6, 0x3fe642c8590b2164 //log2(1.43750), 1/1.43750
158 .quad 0x3fe0e117754d7c11, 0x3fe63356b88ac0de //log2(1.44141), 1/1.44141
159 .quad 0x3fe10113b153c8ea, 0x3fe623fa77016240 //log2(1.44531), 1/1.44531
160 .quad 0x3fe120f9d39e1807, 0x3fe614b36831ae94 //log2(1.44922), 1/1.44922
161 .quad 0x3fe140c9faa1e544, 0x3fe6058160581606 //log2(1.45312), 1/1.45312
162 .quad 0x3fe160844495e006, 0x3fe5f66434292dfc //log2(1.45703), 1/1.45703
163 .quad 0x3fe18028cf72976a, 0x3fe5e75bb8d015e7 //log2(1.46094), 1/1.46094
164 .quad 0x3fe19fb7b8f32421, 0x3fe5d867c3ece2a5 //log2(1.46484), 1/1.46484
165 .quad 0x3fe1bf311e95d00e, 0x3fe5c9882b931057 //log2(1.46875), 1/1.46875
166 .quad 0x3fe1de951d9cbba6, 0x3fe5babcc647fa91 //log2(1.47266), 1/1.47266
167 .quad 0x3fe1fde3d30e8126, 0x3fe5ac056b015ac0 //log2(1.47656), 1/1.47656
168 .quad 0x3fe21d1d5bb6d59a, 0x3fe59d61f123ccaa //log2(1.48047), 1/1.48047
169 .quad 0x3fe23c41d42727c8, 0x3fe58ed2308158ed //log2(1.48438), 1/1.48438
170 .quad 0x3fe25b5158b73d04, 0x3fe5805601580560 //log2(1.48828), 1/1.48828
171 .quad 0x3fe27a4c0585cbf8, 0x3fe571ed3c506b3a //log2(1.49219), 1/1.49219
172 .quad 0x3fe29931f6791560, 0x3fe56397ba7c52e2 //log2(1.49609), 1/1.49609
173 .quad 0x3fe2b803473f7ad1, 0x3fe5555555555555 //log2(1.50000), 1/1.50000
174 .quad 0x3fe2d6c013501380, 0x3fe54725e6bb82fe //log2(1.50391), 1/1.50391
175 .quad 0x3fe2f56875eb3f26, 0x3fe5390948f40feb //log2(1.50781), 1/1.50781
176 .quad 0x3fe313fc8a1b36f2, 0x3fe52aff56a8054b //log2(1.51172), 1/1.51172
177 .quad 0x3fe3327c6ab49ca7, 0x3fe51d07eae2f815 //log2(1.51562), 1/1.51562
178 .quad 0x3fe350e8325707d9, 0x3fe50f22e111c4c5 //log2(1.51953), 1/1.51953
179 .quad 0x3fe36f3ffb6d9162, 0x3fe5015015015015 //log2(1.52344), 1/1.52344
180 .quad 0x3fe38d83e02f5d09, 0x3fe4f38f62dd4c9b //log2(1.52734), 1/1.52734
181 .quad 0x3fe3abb3faa02167, 0x3fe4e5e0a72f0539 //log2(1.53125), 1/1.53125
182 .quad 0x3fe3c9d06490ae12, 0x3fe4d843bedc2c4c //log2(1.53516), 1/1.53516
183 .quad 0x3fe3e7d9379f7016, 0x3fe4cab88725af6e //log2(1.53906), 1/1.53906
184 .quad 0x3fe405ce8d38f4bc, 0x3fe4bd3edda68fe1 //log2(1.54297), 1/1.54297
185 .quad 0x3fe423b07e986aa9, 0x3fe4afd6a052bf5b //log2(1.54688), 1/1.54688
186 .quad 0x3fe4417f24c82165, 0x3fe4a27fad76014a //log2(1.55078), 1/1.55078
187 .quad 0x3fe45f3a98a20739, 0x3fe49539e3b2d067 //log2(1.55469), 1/1.55469
188 .quad 0x3fe47ce2f2d02587, 0x3fe4880522014880 //log2(1.55859), 1/1.55859
189 .quad 0x3fe49a784bcd1b8b, 0x3fe47ae147ae147b //log2(1.56250), 1/1.56250
190 .quad 0x3fe4b7fabbe49795, 0x3fe46dce34596066 //log2(1.56641), 1/1.56641
191 .quad 0x3fe4d56a5b33cec4, 0x3fe460cbc7f5cf9a //log2(1.57031), 1/1.57031
192 .quad 0x3fe4f2c741a9f33e, 0x3fe453d9e2c776ca //log2(1.57422), 1/1.57422
193 .quad 0x3fe510118708a8f9, 0x3fe446f86562d9fb //log2(1.57812), 1/1.57812
194 .quad 0x3fe52d4942e47909, 0x3fe43a2730abee4d //log2(1.58203), 1/1.58203
195 .quad 0x3fe54a6e8ca5438e, 0x3fe42d6625d51f87 //log2(1.58594), 1/1.58594
196 .quad 0x3fe567817b86b02c, 0x3fe420b5265e5951 //log2(1.58984), 1/1.58984
197 .quad 0x3fe5848226989d34, 0x3fe4141414141414 //log2(1.59375), 1/1.59375
198 .quad 0x3fe5a170a4bf8d5c, 0x3fe40782d10e6566 //log2(1.59766), 1/1.59766
199 .quad 0x3fe5be4d0cb51435, 0x3fe3fb013fb013fb //log2(1.60156), 1/1.60156
200 .quad 0x3fe5db177508413c, 0x3fe3ee8f42a5af07 //log2(1.60547), 1/1.60547
201 .quad 0x3fe5f7cff41e09af, 0x3fe3e22cbce4a902 //log2(1.60938), 1/1.60938
202 .quad 0x3fe61476a031b109, 0x3fe3d5d991aa75c6 //log2(1.61328), 1/1.61328
203 .quad 0x3fe6310b8f553048, 0x3fe3c995a47babe7 //log2(1.61719), 1/1.61719
204 .quad 0x3fe64d8ed7719bf0, 0x3fe3bd60d9232955 //log2(1.62109), 1/1.62109
205 .quad 0x3fe66a008e4788cc, 0x3fe3b13b13b13b14 //log2(1.62500), 1/1.62500
206 .quad 0x3fe68660c96f6f87, 0x3fe3a524387ac822 //log2(1.62891), 1/1.62891
207 .quad 0x3fe6a2af9e5a0f0a, 0x3fe3991c2c187f63 //log2(1.63281), 1/1.63281
208 .quad 0x3fe6beed2250cdae, 0x3fe38d22d366088e //log2(1.63672), 1/1.63672
209 .quad 0x3fe6db196a76194a, 0x3fe3813813813814 //log2(1.64062), 1/1.64062
210 .quad 0x3fe6f7348bc5c618, 0x3fe3755bd1c945ee //log2(1.64453), 1/1.64453
211 .quad 0x3fe7133e9b156c7c, 0x3fe3698df3de0748 //log2(1.64844), 1/1.64844
212 .quad 0x3fe72f37ad14c5b0, 0x3fe35dce5f9f2af8 //log2(1.65234), 1/1.65234
213 .quad 0x3fe74b1fd64e0754, 0x3fe3521cfb2b78c1 //log2(1.65625), 1/1.65625
214 .quad 0x3fe766f72b263dee, 0x3fe34679ace01346 //log2(1.66016), 1/1.66016
215 .quad 0x3fe782bdbfdda657, 0x3fe33ae45b57bcb2 //log2(1.66406), 1/1.66406
216 .quad 0x3fe79e73a8900620, 0x3fe32f5ced6a1dfa //log2(1.66797), 1/1.66797
217 .quad 0x3fe7ba18f93502e4, 0x3fe323e34a2b10bf //log2(1.67188), 1/1.67188
218 .quad 0x3fe7d5adc5a078a4, 0x3fe3187758e9ebb6 //log2(1.67578), 1/1.67578
219 .quad 0x3fe7f1322182cf16, 0x3fe30d190130d190 //log2(1.67969), 1/1.67969
220 .quad 0x3fe80ca620694df9, 0x3fe301c82ac40260 //log2(1.68359), 1/1.68359
221 .quad 0x3fe82809d5be7073, 0x3fe2f684bda12f68 //log2(1.68750), 1/1.68750
222 .quad 0x3fe8435d54ca3774, 0x3fe2eb4ea1fed14b //log2(1.69141), 1/1.69141
223 .quad 0x3fe85ea0b0b27b26, 0x3fe2e025c04b8097 //log2(1.69531), 1/1.69531
224 .quad 0x3fe879d3fc7b3b71, 0x3fe2d50a012d50a0 //log2(1.69922), 1/1.69922
225 .quad 0x3fe894f74b06ef8b, 0x3fe2c9fb4d812ca0 //log2(1.70312), 1/1.70312
226 .quad 0x3fe8b00aaf16d4a9, 0x3fe2bef98e5a3711 //log2(1.70703), 1/1.70703
227 .quad 0x3fe8cb0e3b4b3bbe, 0x3fe2b404ad012b40 //log2(1.71094), 1/1.71094
228 .quad 0x3fe8e6020223d661, 0x3fe2a91c92f3c105 //log2(1.71484), 1/1.71484
229 .quad 0x3fe900e6160002cd, 0x3fe29e4129e4129e //log2(1.71875), 1/1.71875
230 .quad 0x3fe91bba891f1709, 0x3fe293725bb804a5 //log2(1.72266), 1/1.72266
231 .quad 0x3fe9367f6da0ab2f, 0x3fe288b01288b013 //log2(1.72656), 1/1.72656
232 .quad 0x3fe95134d584e2e3, 0x3fe27dfa38a1ce4d //log2(1.73047), 1/1.73047
233 .quad 0x3fe96bdad2acb5f6, 0x3fe27350b8812735 //log2(1.73438), 1/1.73438
234 .quad 0x3fe9867176da382f, 0x3fe268b37cd60127 //log2(1.73828), 1/1.73828
235 .quad 0x3fe9a0f8d3b0e050, 0x3fe25e22708092f1 //log2(1.74219), 1/1.74219
236 .quad 0x3fe9bb70fab5ce4d, 0x3fe2539d7e9177b2 //log2(1.74609), 1/1.74609
237 .quad 0x3fe9d5d9fd5010b3, 0x3fe2492492492492 //log2(1.75000), 1/1.75000
238 .quad 0x3fe9f033ecc8e956, 0x3fe23eb79717605b //log2(1.75391), 1/1.75391
239 .quad 0x3fea0a7eda4c112d, 0x3fe23456789abcdf //log2(1.75781), 1/1.75781
240 .quad 0x3fea24bad6e7fb77, 0x3fe22a0122a0122a //log2(1.76172), 1/1.76172
241 .quad 0x3fea3ee7f38e181f, 0x3fe21fb78121fb78 //log2(1.76562), 1/1.76562
242 .quad 0x3fea590641131564, 0x3fe21579804855e6 //log2(1.76953), 1/1.76953
243 .quad 0x3fea7315d02f20c8, 0x3fe20b470c67c0d9 //log2(1.77344), 1/1.77344
244 .quad 0x3fea8d16b17e2745, 0x3fe2012012012012 //log2(1.77734), 1/1.77734
245 .quad 0x3feaa708f58014d3, 0x3fe1f7047dc11f70 //log2(1.78125), 1/1.78125
246 .quad 0x3feac0ecac99133b, 0x3fe1ecf43c7fb84c //log2(1.78516), 1/1.78516
247 .quad 0x3feadac1e711c833, 0x3fe1e2ef3b3fb874 //log2(1.78906), 1/1.78906
248 .quad 0x3feaf488b51792d6, 0x3fe1d8f5672e4abd //log2(1.79297), 1/1.79297
249 .quad 0x3feb0e4126bcc86c, 0x3fe1cf06ada2811d //log2(1.79688), 1/1.79688
250 .quad 0x3feb27eb4bf8f08a, 0x3fe1c522fc1ce059 //log2(1.80078), 1/1.80078
251 .quad 0x3feb418734a9008c, 0x3fe1bb4a4046ed29 //log2(1.80469), 1/1.80469
252 .quad 0x3feb5b14f08f9666, 0x3fe1b17c67f2bae3 //log2(1.80859), 1/1.80859
253 .quad 0x3feb74948f5532da, 0x3fe1a7b9611a7b96 //log2(1.81250), 1/1.81250
254 .quad 0x3feb8e0620887309, 0x3fe19e0119e0119e //log2(1.81641), 1/1.81641
255 .quad 0x3feba769b39e4964, 0x3fe19453808ca29c //log2(1.82031), 1/1.82031
256 .quad 0x3febc0bf57f23606, 0x3fe18ab083902bdb //log2(1.82422), 1/1.82422
257 .quad 0x3febda071cc67e6e, 0x3fe1811811811812 //log2(1.82812), 1/1.82812
258 .quad 0x3febf341114464a7, 0x3fe1778a191bd684 //log2(1.83203), 1/1.83203
259 .quad 0x3fec0c6d447c5dd3, 0x3fe16e0689427379 //log2(1.83594), 1/1.83594
260 .quad 0x3fec258bc5664829, 0x3fe1648d50fc3201 //log2(1.83984), 1/1.83984
261 .quad 0x3fec3e9ca2e1a055, 0x3fe15b1e5f75270d //log2(1.84375), 1/1.84375
262 .quad 0x3fec579febb5b658, 0x3fe151b9a3fdd5c9 //log2(1.84766), 1/1.84766
263 .quad 0x3fec7095ae91e1c7, 0x3fe1485f0e0acd3b //log2(1.85156), 1/1.85156
264 .quad 0x3fec897dfa0db58e, 0x3fe13f0e8d344724 //log2(1.85547), 1/1.85547
265 .quad 0x3feca258dca93316, 0x3fe135c81135c811 //log2(1.85938), 1/1.85938
266 .quad 0x3fecbb2664ccfcf6, 0x3fe12c8b89edc0ac //log2(1.86328), 1/1.86328
267 .quad 0x3fecd3e6a0ca8907, 0x3fe12358e75d3033 //log2(1.86719), 1/1.86719
268 .quad 0x3fecec999edc5203, 0x3fe11a3019a74826 //log2(1.87109), 1/1.87109
269 .quad 0x3fed053f6d260896, 0x3fe1111111111111 //log2(1.87500), 1/1.87500
270 .quad 0x3fed1dd819b4c3f1, 0x3fe107fbbe011080 //log2(1.87891), 1/1.87891
271 .quad 0x3fed3663b27f31d5, 0x3fe0fef010fef011 //log2(1.88281), 1/1.88281
272 .quad 0x3fed4ee24565c62b, 0x3fe0f5edfab325a2 //log2(1.88672), 1/1.88672
273 .quad 0x3fed6753e032ea0f, 0x3fe0ecf56be69c90 //log2(1.89062), 1/1.89062
274 .quad 0x3fed7fb8909b2a6c, 0x3fe0e40655826011 //log2(1.89453), 1/1.89453
275 .quad 0x3fed9810643d6615, 0x3fe0db20a88f4696 //log2(1.89844), 1/1.89844
276 .quad 0x3fedb05b68a2fb65, 0x3fe0d24456359e3a //log2(1.90234), 1/1.90234
277 .quad 0x3fedc899ab3ff56c, 0x3fe0c9714fbcda3b //log2(1.90625), 1/1.90625
278 .quad 0x3fede0cb397338a4, 0x3fe0c0a7868b4171 //log2(1.91016), 1/1.91016
279 .quad 0x3fedf8f02086af2c, 0x3fe0b7e6ec259dc8 //log2(1.91406), 1/1.91406
280 .quad 0x3fee11086daf7496, 0x3fe0af2f722eecb5 //log2(1.91797), 1/1.91797
281 .quad 0x3fee29142e0e0140, 0x3fe0a6810a6810a7 //log2(1.92188), 1/1.92188
282 .quad 0x3fee41136eae553d, 0x3fe09ddba6af8360 //log2(1.92578), 1/1.92578
283 .quad 0x3fee59063c8822ce, 0x3fe0953f39010954 //log2(1.92969), 1/1.92969
284 .quad 0x3fee70eca47ef86f, 0x3fe08cabb37565e2 //log2(1.93359), 1/1.93359
285 .quad 0x3fee88c6b3626a73, 0x3fe0842108421084 //log2(1.93750), 1/1.93750
286 .quad 0x3feea09475ee3c3a, 0x3fe07b9f29b8eae2 //log2(1.94141), 1/1.94141
287 .quad 0x3feeb855f8ca88fb, 0x3fe073260a47f7c6 //log2(1.94531), 1/1.94531
288 .quad 0x3feed00b488bec23, 0x3fe06ab59c7912fb //log2(1.94922), 1/1.94922
289 .quad 0x3feee7b471b3a950, 0x3fe0624dd2f1a9fc //log2(1.95312), 1/1.95312
290 .quad 0x3feeff5180afd3e4, 0x3fe059eea0727586 //log2(1.95703), 1/1.95703
291 .quad 0x3fef16e281db7630, 0x3fe05197f7d73404 //log2(1.96094), 1/1.96094
292 .quad 0x3fef2e67817eb845, 0x3fe04949cc1664c5 //log2(1.96484), 1/1.96484
293 .quad 0x3fef45e08bcf0655, 0x3fe0410410410410 //log2(1.96875), 1/1.96875
294 .quad 0x3fef5d4dacef36be, 0x3fe038c6b78247fc //log2(1.97266), 1/1.97266
295 .quad 0x3fef74aef0efafae, 0x3fe03091b51f5e1a //log2(1.97656), 1/1.97656
296 .quad 0x3fef8c0463ce8c69, 0x3fe02864fc7729e9 //log2(1.98047), 1/1.98047
297 .quad 0x3fefa34e1177c233, 0x3fe0204081020408 //log2(1.98438), 1/1.98438
298 .quad 0x3fefba8c05c544df, 0x3fe0182436517a37 //log2(1.98828), 1/1.98828
299 .quad 0x3fefd1be4c7f2af9, 0x3fe0101010101010 //log2(1.99219), 1/1.99219
300 .quad 0x3fefe8e4f15bd1a0, 0x3fe0080402010080 //log2(1.99609), 1/1.99609
301
302.literal8
303.align 3
304one: .double 1.0
305onehalf: .double 0.5
306onethird: .quad 0x3fd5555555555555 // 1/3
307onequarter: .double 0.25
308onefifth: .double 0.2
309onesixth: .quad 0x3fc5555555555555
310recip_log2: .quad 0x3ff71547652b82fe // 1.0 / ln(2)
311
312.text
313
314#if defined( __x86_64__ )
315 #define RELATIVE_ADDR( _a) (_a)( %rip )
316 #define RELATIVE_ADDR_B( _a) (_a)( %rip )
317 #define RELATIVE_ADDR2( _a, _i, _step) ( %r8, _i, _step )
318#elif defined( __i386__ )
319 #define RELATIVE_ADDR( _a) (_a)-rel_addr( CX_P )
320 #define RELATIVE_ADDR_B( _a) (_a)-rel_addr_b( CX_P )
321 #define RELATIVE_ADDR2( _a, _i, _step) (_a)-rel_addr( CX_P, _i, _step )
322
323//a short routine to get the local address
324.align 4
325log2f_pic: movl (%esp), %ecx //copy address of local_addr to %ecx
326 ret
327#else
328 #error arch not supported
329#endif
330
331//
332// log2f -- overall approach
333//
334// We break up log2f(x) as follows:
335//
336// i = ilogb(x) //integer part of the result
337// m = scalbn( x, -i ) //mantissa has range 1.0 <= m < 2.0
338//
339// log2f(x) = i + log2f(m)
340//
341// We further break down m as :
342//
343// m = (1+a/256.0)(1+r) a = high 8 explicit bits of mantissa(m)
344// log2f(m) = log2(1+a/256.0) + log2(1+r)
345//
346// We use the high 8 bits of the mantissa to look up log2(1+a/256.0) in log2f_table above
347// We calculate 1+r as:
348//
349// 1+r = m * (1 /(1+a/256.0))
350//
351// We can lookup (from the same table) the value of 1/(1+a/256.0) based on a too.
352//
353// So the whole calculation is:
354//
355// log2f(x) = i + log2(1+a/256.0) + log2(1+r) = i + log2f_table[a][0] + log2f( m * log2f_table[a][1] )
356//
357// The third term is calculated using the Taylor series:
358//
359// log(x+1) = x - x**2/2 + x**3/3
360//
361// Adding one more term produces excellent results, but this is good enough to get within 0.519028 ulps
362// for the entire single precision number range and saves 7 cycles.
363//
364// The edge case code is done in integer to avoid setting flags, and because it is faster that way.
365//
366
367ENTRY( log2f )
368//read argument into %eax
369#if defined( __i386__ )
370 movl FRAME_SIZE( STACKP ), %eax
371#else
372 movd %xmm0, %eax
373#endif
374
375 //Get exceptional cases out of the way
376 //push NaNs around to negative
377 movl %eax, %ecx // set aside x
378 addl $0x00800000, %eax // push Infs, NaNs negative
379 xorps %xmm1, %xmm1 // 0.0f
380 cmpl $0x00800000, %eax // if( x <= 0 or Inf, NaN )
381 jle 2f // goto 2
382
383 //Check for narrow range near 1 where 3rd order Taylor series is not enough
384 subl $0x3ff80000, %eax // subtract low value in our range (+0x00800000)
385 cmpl $0x000d8000, %eax // check to see if we are in the range
386 jb 7f
387
388 movl $-127, %edx // bias of float
389 cmpl $0x00800000, %ecx // if isnormal( x )
390 jae 1f // goto 1
391
392 //deal with denormal
393 subl $126, %edx // set aside -126 as a bias adjustment (was 0 )
394 orl $0x3f800000, %ecx // multiply low bits by 2**127 by oring in 1.0
395 movl $0x3f800000, %eax // prepare 1.0f
396 movd %ecx, %xmm3 // copy to vr
397 movd %eax, %xmm4 // copy to vr
398 subss %xmm4, %xmm3 // (x | 2**127) - 1.0f
399 movd %xmm3, %ecx // copy normalized scaled number back to %ecx
400
4011: //normal operand
402 movl %ecx, %eax // x
403 andl $0x7f800000, %ecx // exponent of x
404 cmpl %ecx, %eax // is this a power of 2?
405 je 6f // early out for power of 2, saves inexact flag for exact cases
406
407 //non-power of two
408 xorl %ecx, %eax // mask off exponent
409 shrl $23, %ecx // push exponent to unit precision
410 addl %edx, %ecx // remove bias from exponent part
411 movl %eax, %edx // set aside mantissa bits
412 cvtsi2sd %ecx, %xmm0 // move integer part of the result to xmm0.
413 andl $0x00007fff, %eax // isolate low bits of mantissa
414 andl $0x007f8000, %edx // isolate high bits of mantissa
415 orl $0x3f800000, %eax // set exponent of the mantissa to 0 + bias
416 shrl $(15-4), %edx
417 movd %eax, %xmm1 // move reduced mantissa to xmm0 (1+r)
418 cvtss2sd %xmm1, %xmm1
419
420//do PIC
421#if defined( __i386__ )
422 calll log2f_pic // set %ecx to point to local_addr
423rel_addr:
424#else
425 andq $0xff0, %rdx
426#endif
427
428 subsd RELATIVE_ADDR( one ), %xmm1 // r = (1+r) - 1.0
429
430 //load the address of the log2f_table
431 lea RELATIVE_ADDR(log2f_table), AX_P
432
433 mulsd 8( AX_P, DX_P, 1), %xmm1 // r *= 1 / (1+a)
434
435 //Do a relatively small/cheap Taylor series: log2(r+1) = (r - 0.5rr + (1/3)rrr)/ln(2)
436 movsd RELATIVE_ADDR( onethird), %xmm3 // 1/3
437 movapd %xmm1, %xmm2 // r
438 mulsd %xmm1, %xmm3 // (1/3)r
439 mulsd %xmm2, %xmm2 // rr
440 subsd RELATIVE_ADDR( onehalf),%xmm3 // -0.5 + (1/3)r
441 mulsd %xmm2, %xmm3 // -0.5rr + (1/3)rrr
442 addsd %xmm1, %xmm3 // r - 0.5rr + (1/3)rrr
443 mulsd RELATIVE_ADDR( recip_log2 ), %xmm3 // (r - 0.5rr + (1/3)rrr)/ln(2)
444 addsd ( AX_P, DX_P, 1), %xmm3 // log2(1+a) + (r - 0.5rr + (1/3)rrr)/ln(2)
445 addsd %xmm3, %xmm0 // add in integer part
446 cvtsd2ss %xmm0, %xmm0 // round to float
447
448#if defined( __i386__ )
449 movss %xmm0, FRAME_SIZE(STACKP)
450 flds FRAME_SIZE(STACKP)
451#endif
452 ret
453
454
4552: //special case code for negative, NaN or 0
456#if defined( __i386__ )
457 movss FRAME_SIZE( STACKP ), %xmm0
458#endif
459 ucomiss %xmm1, %xmm0 //test for x == 0
460 jb 4f //NaN or negative
461
462 //We imagine that 0.0, Inf are the most common cases, so those falls through
463 ja 3f //Infinity, just return inf
464
465 //We need to return -Inf for zero and set div/0 flag
466 pcmpeqb %xmm0, %xmm0 // -1U
467 cvtdq2ps %xmm0, %xmm0 // -1.0f
468 divss %xmm1, %xmm0 // -1.0f / 0 = -Inf + div/0 flag
469#if defined( __i386__ )
470 movss %xmm0, FRAME_SIZE(STACKP)
471#endif
4723:
473#if defined( __i386__ )
474 flds FRAME_SIZE(STACKP)
475#endif
476 ret
477
4784: jp 5f // handle NaN elsewhere
479
480 //negative number, return NaN and set invalid
481 pcmpeqb %xmm0, %xmm0 // -1U
482 pslld $23, %xmm0 // 0xff800000, -inf
483 mulss %xmm1, %xmm0 // 0 * -inf = NaN, set invalid
484#if defined( __i386__ )
485 movss %xmm0, FRAME_SIZE(STACKP)
486 flds FRAME_SIZE(STACKP)
487#endif
488 ret
489
490 //Its a NaN
4915:
492#if defined( __i386__ )
493 flds FRAME_SIZE(STACKP ) //load the NaN
494 fadd %st(0), %st(0) //quiet it
495#else
496 addss %xmm0, %xmm0
497#endif
498 ret
499
5006: //early out for power of 2
501 shrl $23, %eax
502 addl %edx, %eax
503#if defined( __i386__ )
504 movl %eax, FRAME_SIZE( STACKP )
505 fildl FRAME_SIZE(STACKP)
506#else
507 cvtsi2ss %eax, %xmm0
508#endif
509 ret
510
5117:
512#if defined( __i386__ )
513 cvtss2sd FRAME_SIZE(STACKP), %xmm2 // convert to double
514 xorps %xmm0, %xmm0 // zero xmm0
515
516//do PIC
517 calll log2f_pic // set %ecx to point to local_addr
518rel_addr_b:
519#else
520 cvtss2sd %xmm0, %xmm2 // convert to double
521#endif
522
523 subsd RELATIVE_ADDR_B( one ), %xmm2 // r = x - 1.0
524 movapd %xmm2, %xmm1 // r again
525 mulsd %xmm2, %xmm2
526
527 //Do a more expensive Taylor series: log2(r+1) = (r - 0.5rr + (1/3)rrr - 0.25rrrr + 0.2rrrrr - 1/6rrrrrr)/ln(2)
528 movsd RELATIVE_ADDR_B( onesixth ), %xmm4 // 1/6
529 movsd RELATIVE_ADDR_B( onefifth ), %xmm3 // 0.2
530 mulsd %xmm2, %xmm4 // 1/6rr
531 mulsd %xmm2, %xmm3 // 0.2rr
532 addsd RELATIVE_ADDR_B( onequarter ), %xmm4 // 0.25 + 1/6rr
533 addsd RELATIVE_ADDR_B( onethird ), %xmm3 // 1/3 _ 0.2rr
534 mulsd %xmm2, %xmm4 // 0.25rr + 1/6rrrr
535 mulsd %xmm2, %xmm3
536 addsd RELATIVE_ADDR_B( onehalf ), %xmm4
537 addsd RELATIVE_ADDR_B( one ), %xmm3
538 mulsd %xmm2, %xmm4
539 mulsd %xmm1, %xmm3
540 subsd %xmm4, %xmm3
541 mulsd RELATIVE_ADDR_B( recip_log2 ), %xmm3 // ( r - 0.5rr + 1/3rrr - 0.25rrrr + 0.2rrrrr - 1/6rrrrrr ) / ln(2)
542
543 cvtsd2ss %xmm3, %xmm0 // round to float
544
545#if defined( __i386__ )
546 movss %xmm0, FRAME_SIZE(STACKP)
547 flds FRAME_SIZE(STACKP)
548#endif
549 ret