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1 .file "exp10l.s"
4 // Copyright (c) 2000 - 2004, Intel Corporation
5 // All rights reserved.
6 //
7 // Contributed 2000 by the Intel Numerics Group, Intel Corporation
8 //
9 // Redistribution and use in source and binary forms, with or without
10 // modification, are permitted provided that the following conditions are
11 // met:
12 //
13 // * Redistributions of source code must retain the above copyright
14 // notice, this list of conditions and the following disclaimer.
15 //
16 // * Redistributions in binary form must reproduce the above copyright
17 // notice, this list of conditions and the following disclaimer in the
18 // documentation and/or other materials provided with the distribution.
19 //
20 // * The name of Intel Corporation may not be used to endorse or promote
21 // products derived from this software without specific prior written
22 // permission.
24 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
25 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
26 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
27 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
28 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
29 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
30 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
31 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
32 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
33 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
34 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
35 //
36 // Intel Corporation is the author of this code, and requests that all
37 // problem reports or change requests be submitted to it directly at
38 // http://www.intel.com/software/products/opensource/libraries/num.htm.
39 //
40 // History
41 //==============================================================
42 // 08/25/00 Initial version
43 // 05/20/02 Cleaned up namespace and sf0 syntax
44 // 02/06/03 Reordered header: .section, .global, .proc, .align
45 // 05/08/03 Reformatted assembly source; corrected overflow result for round to
46 // -inf and round to zero; exact results now don't set inexact flag
47 // 12/16/04 Call error handling on underflow.
48 //
49 // API
50 //==============================================================
51 // long double exp10l(long double)
52 //
53 // Overview of operation
54 //==============================================================
55 // Background
56 //
57 // Implementation
58 //
59 // Let x= (K + f + r)/log2(10), where
60 // K is an integer, f= 0.b1 b2... b8 (f>= 0),
61 // and |r|<2^{-9}
62 // T is a table that stores 2^f (256 entries) rounded to
63 // double extended precision (only mantissa is stored)
64 // D stores (2^f/T [ f ] - 1), rounded to single precision
65 //
66 // 10^x is approximated as
67 // 2^K * T [ f ] * ((1+c1*r+c2*r^2+...+c6*r^6)*(1+c1*e)+D [ f ] ),
68 // where e= log2(10)_lo*x+(log2(10)_hi*x-RN(log2(10)_hi*x))
69 //
73 // Special values
74 //==============================================================
75 // exp10(0)= 1
76 // exp10(+inf)= inf
77 // exp10(-inf)= 0
78 //
81 // Registers used
82 //==============================================================
83 // f6-f15, f32-f63
84 // r14-r30, r32-r40
85 // p6-p8, p11-p14
86 //
89 FR_X = f10
90 FR_Y = f1
91 FR_RESULT = f8
93 FR_COEFF1 = f6
94 FR_COEFF2 = f7
95 FR_KF0 = f9
96 FR_LOG10 = f10
97 FR_CONST1 = f11
98 FR_XL10 = f12
99 FR_COEFF3 = f13
100 FR_COEFF4 = f14
101 FR_UF_TEST = f15
102 FR_OF_TEST = f32
103 FR_L10_LOW = f33
104 FR_COEFF5 = f34
105 FR_COEFF6 = f35
106 FR_L10 = f36
107 FR_C_L10 = f37
108 FR_XL10_H = f38
109 FR_XL10_L = f39
110 FR_KF = f40
111 FR_E = f41
112 FR_T = f42
113 FR_D = f43
114 FR_EXP_M_63 = f44
115 FR_R = f45
116 FR_E1 = f46
117 FR_COEFF2 = f47
118 FR_P34 = f48
119 FR_P56 = f49
120 FR_R2 = f50
121 FR_RE = f51
122 FR_D1 = f52
123 FR_P36 = f53
124 FR_R3E = f54
125 FR_P1 = f55
126 FR_P = f56
127 FR_T1 = f57
128 FR_XINT = f58
129 FR_XINTF = f59
130 FR_4 = f60
131 FR_28 = f61
132 FR_32 = f62
133 FR_SNORM_LIMIT = f63
136 GR_ADDR0 = r14
137 GR_D_ADDR = r15
138 GR_ADDR = r16
139 GR_B63 = r17
140 GR_KBITS = r18
141 GR_F = r19
142 GR_K = r20
143 GR_D = r21
144 GR_BM63 = r22
145 GR_T = r23
146 GR_CONST1 = r24
147 GR_EMIN = r25
148 GR_CONST2 = r26
149 GR_BM8 = r27
150 GR_SREG = r28
151 GR_4_BIAS = r29
152 GR_32_BIAS = r30
154 GR_SAVE_B0 = r33
155 GR_SAVE_PFS = r34
156 GR_SAVE_GP = r35
157 GR_SAVE_SP = r36
159 GR_Parameter_X = r37
160 GR_Parameter_Y = r38
161 GR_Parameter_RESULT= r39
162 GR_Parameter_TAG = r40
165 // Data tables
166 //==============================================================
168 RODATA
170 .align 16
172 LOCAL_OBJECT_START(poly_coeffs)
174 data8 0xd49a784bcd1b8afe, 0x00004008 // log2(10)*2^8
175 data8 0x9a209a84fbcff798, 0x0000400b // overflow threshold
176 data8 0xb17217f7d1cf79ab, 0x00003ffe // C_1
177 data8 0xf5fdeffc162c7541, 0x00003ffc // C_2
178 data8 0x3fac6b08d704a0c0 // C_3
179 data8 0x3f83b2ab6fba4e77 // C_4
180 data8 0x3f55d87fe78a6731 // C_5
181 data8 0x3f2430912f86c787 // C_6
182 data8 0x9257edfe9b5fb698, 0x00003fbf // log2(10)_low (bits 64...127)
183 data8 0x9a1bc98027a81918, 0x0000c00b // Smallest normal threshold
184 LOCAL_OBJECT_END(poly_coeffs)
187 LOCAL_OBJECT_START(T_table)
189 // 2^{0.b1 b2 b3 b4 b5 b6 b7 b8}
190 data8 0x8000000000000000, 0x8058d7d2d5e5f6b1
191 data8 0x80b1ed4fd999ab6c, 0x810b40a1d81406d4
192 data8 0x8164d1f3bc030773, 0x81bea1708dde6056
193 data8 0x8218af4373fc25ec, 0x8272fb97b2a5894c
194 data8 0x82cd8698ac2ba1d7, 0x83285071e0fc4547
195 data8 0x8383594eefb6ee37, 0x83dea15b9541b132
196 data8 0x843a28c3acde4046, 0x8495efb3303efd30
197 data8 0x84f1f656379c1a29, 0x854e3cd8f9c8c95d
198 data8 0x85aac367cc487b15, 0x86078a2f23642a9f
199 data8 0x8664915b923fba04, 0x86c1d919caef5c88
200 data8 0x871f61969e8d1010, 0x877d2afefd4e256c
201 data8 0x87db357ff698d792, 0x88398146b919f1d4
202 data8 0x88980e8092da8527, 0x88f6dd5af155ac6b
203 data8 0x8955ee03618e5fdd, 0x89b540a7902557a4
204 data8 0x8a14d575496efd9a, 0x8a74ac9a79896e47
205 data8 0x8ad4c6452c728924, 0x8b3522a38e1e1032
206 data8 0x8b95c1e3ea8bd6e7, 0x8bf6a434adde0085
207 data8 0x8c57c9c4646f4dde, 0x8cb932c1bae97a95
208 data8 0x8d1adf5b7e5ba9e6, 0x8d7ccfc09c50e2f8
209 data8 0x8ddf042022e69cd6, 0x8e417ca940e35a01
210 data8 0x8ea4398b45cd53c0, 0x8f073af5a2013520
211 data8 0x8f6a8117e6c8e5c4, 0x8fce0c21c6726481
212 data8 0x9031dc431466b1dc, 0x9095f1abc540ca6b
213 data8 0x90fa4c8beee4b12b, 0x915eed13c89689d3
214 data8 0x91c3d373ab11c336, 0x9228ffdc10a051ad
215 data8 0x928e727d9531f9ac, 0x92f42b88f673aa7c
216 data8 0x935a2b2f13e6e92c, 0x93c071a0eef94bc1
217 data8 0x9426ff0fab1c04b6, 0x948dd3ac8ddb7ed3
218 data8 0x94f4efa8fef70961, 0x955c5336887894d5
219 data8 0x95c3fe86d6cc7fef, 0x962bf1cbb8d97560
220 data8 0x96942d3720185a00, 0x96fcb0fb20ac4ba3
221 data8 0x97657d49f17ab08e, 0x97ce9255ec4357ab
222 data8 0x9837f0518db8a96f, 0x98a1976f7597e996
223 data8 0x990b87e266c189aa, 0x9975c1dd47518c77
224 data8 0x99e0459320b7fa65, 0x9a4b13371fd166ca
225 data8 0x9ab62afc94ff864a, 0x9b218d16f441d63d
226 data8 0x9b8d39b9d54e5539, 0x9bf93118f3aa4cc1
227 data8 0x9c6573682ec32c2d, 0x9cd200db8a0774cb
228 data8 0x9d3ed9a72cffb751, 0x9dabfdff6367a2aa
229 data8 0x9e196e189d472420, 0x9e872a276f0b98ff
230 data8 0x9ef5326091a111ae, 0x9f6386f8e28ba651
231 data8 0x9fd228256400dd06, 0xa041161b3d0121be
232 data8 0xa0b0510fb9714fc2, 0xa11fd9384a344cf7
233 data8 0xa18faeca8544b6e4, 0xa1ffd1fc25cea188
234 data8 0xa27043030c496819, 0xa2e102153e918f9e
235 data8 0xa3520f68e802bb93, 0xa3c36b345991b47c
236 data8 0xa43515ae09e6809e, 0xa4a70f0c95768ec5
237 data8 0xa5195786be9ef339, 0xa58bef536dbeb6ee
238 data8 0xa5fed6a9b15138ea, 0xa6720dc0be08a20c
239 data8 0xa6e594cfeee86b1e, 0xa7596c0ec55ff55b
240 data8 0xa7cd93b4e965356a, 0xa8420bfa298f70d1
241 data8 0xa8b6d5167b320e09, 0xa92bef41fa77771b
242 data8 0xa9a15ab4ea7c0ef8, 0xaa1717a7b5693979
243 data8 0xaa8d2652ec907629, 0xab0386ef48868de1
244 data8 0xab7a39b5a93ed337, 0xabf13edf162675e9
245 data8 0xac6896a4be3fe929, 0xace0413ff83e5d04
246 data8 0xad583eea42a14ac6, 0xadd08fdd43d01491
247 data8 0xae493452ca35b80e, 0xaec22c84cc5c9465
248 data8 0xaf3b78ad690a4375, 0xafb51906e75b8661
249 data8 0xb02f0dcbb6e04584, 0xb0a957366fb7a3c9
250 data8 0xb123f581d2ac2590, 0xb19ee8e8c94feb09
251 data8 0xb21a31a66618fe3b, 0xb295cff5e47db4a4
252 data8 0xb311c412a9112489, 0xb38e0e38419fae18
253 data8 0xb40aaea2654b9841, 0xb487a58cf4a9c180
254 data8 0xb504f333f9de6484, 0xb58297d3a8b9f0d2
255 data8 0xb60093a85ed5f76c, 0xb67ee6eea3b22b8f
256 data8 0xb6fd91e328d17791, 0xb77c94c2c9d725e9
257 data8 0xb7fbefca8ca41e7c, 0xb87ba337a1743834
258 data8 0xb8fbaf4762fb9ee9, 0xb97c143756844dbf
259 data8 0xb9fcd2452c0b9deb, 0xba7de9aebe5fea09
260 data8 0xbaff5ab2133e45fb, 0xbb81258d5b704b6f
261 data8 0xbc034a7ef2e9fb0d, 0xbc85c9c560e7b269
262 data8 0xbd08a39f580c36bf, 0xbd8bd84bb67ed483
263 data8 0xbe0f6809860993e2, 0xbe935317fc378238
264 data8 0xbf1799b67a731083, 0xbf9c3c248e2486f8
265 data8 0xc0213aa1f0d08db0, 0xc0a6956e8836ca8d
266 data8 0xc12c4cca66709456, 0xc1b260f5ca0fbb33
267 data8 0xc238d2311e3d6673, 0xc2bfa0bcfad907c9
268 data8 0xc346ccda24976407, 0xc3ce56c98d21b15d
269 data8 0xc4563ecc5334cb33, 0xc4de8523c2c07baa
270 data8 0xc5672a115506dadd, 0xc5f02dd6b0bbc3d9
271 data8 0xc67990b5aa245f79, 0xc70352f04336c51e
272 data8 0xc78d74c8abb9b15d, 0xc817f681416452b2
273 data8 0xc8a2d85c8ffe2c45, 0xc92e1a9d517f0ecc
274 data8 0xc9b9bd866e2f27a3, 0xca45c15afcc72624
275 data8 0xcad2265e4290774e, 0xcb5eecd3b38597c9
276 data8 0xcbec14fef2727c5d, 0xcc799f23d11510e5
277 data8 0xcd078b86503dcdd2, 0xcd95da6a9ff06445
278 data8 0xce248c151f8480e4, 0xceb3a0ca5dc6a55d
279 data8 0xcf4318cf191918c1, 0xcfd2f4683f94eeb5
280 data8 0xd06333daef2b2595, 0xd0f3d76c75c5db8d
281 data8 0xd184df6251699ac6, 0xd2164c023056bcab
282 data8 0xd2a81d91f12ae45a, 0xd33a5457a3029054
283 data8 0xd3ccf099859ac379, 0xd45ff29e0972c561
284 data8 0xd4f35aabcfedfa1f, 0xd5872909ab75d18a
285 data8 0xd61b5dfe9f9bce07, 0xd6aff9d1e13ba2fe
286 data8 0xd744fccad69d6af4, 0xd7da67311797f56a
287 data8 0xd870394c6db32c84, 0xd9067364d44a929c
288 data8 0xd99d15c278afd7b6, 0xda3420adba4d8704
289 data8 0xdacb946f2ac9cc72, 0xdb63714f8e295255
290 data8 0xdbfbb797daf23755, 0xdc9467913a4f1c92
291 data8 0xdd2d818508324c20, 0xddc705bcd378f7f0
292 data8 0xde60f4825e0e9124, 0xdefb4e1f9d1037f2
293 data8 0xdf9612deb8f04420, 0xe031430a0d99e627
294 data8 0xe0ccdeec2a94e111, 0xe168e6cfd3295d23
295 data8 0xe2055afffe83d369, 0xe2a23bc7d7d91226
296 data8 0xe33f8972be8a5a51, 0xe3dd444c46499619
297 data8 0xe47b6ca0373da88d, 0xe51a02ba8e26d681
298 data8 0xe5b906e77c8348a8, 0xe658797368b3a717
299 data8 0xe6f85aaaee1fce22, 0xe798aadadd5b9cbf
300 data8 0xe8396a503c4bdc68, 0xe8da9958464b42ab
301 data8 0xe97c38406c4f8c57, 0xea1e4756550eb27b
302 data8 0xeac0c6e7dd24392f, 0xeb63b74317369840
303 data8 0xec0718b64c1cbddc, 0xecaaeb8ffb03ab41
304 data8 0xed4f301ed9942b84, 0xedf3e6b1d418a491
305 data8 0xee990f980da3025b, 0xef3eab20e032bc6b
306 data8 0xefe4b99bdcdaf5cb, 0xf08b3b58cbe8b76a
307 data8 0xf13230a7ad094509, 0xf1d999d8b7708cc1
308 data8 0xf281773c59ffb13a, 0xf329c9233b6bae9c
309 data8 0xf3d28fde3a641a5b, 0xf47bcbbe6db9fddf
310 data8 0xf5257d152486cc2c, 0xf5cfa433e6537290
311 data8 0xf67a416c733f846e, 0xf7255510c4288239
312 data8 0xf7d0df730ad13bb9, 0xf87ce0e5b2094d9c
313 data8 0xf92959bb5dd4ba74, 0xf9d64a46eb939f35
314 data8 0xfa83b2db722a033a, 0xfb3193cc4227c3f4
315 data8 0xfbdfed6ce5f09c49, 0xfc8ec01121e447bb
316 data8 0xfd3e0c0cf486c175, 0xfdedd1b496a89f35
317 data8 0xfe9e115c7b8f884c, 0xff4ecb59511ec8a5
318 LOCAL_OBJECT_END(T_table)
321 LOCAL_OBJECT_START(D_table)
322 data4 0x00000000, 0x9f55c08f, 0x1e93ffa3, 0x1dcd43a8
323 data4 0x1f751f79, 0x9f3cdd88, 0x9f43d155, 0x1eda222c
324 data4 0x1ef35513, 0x9f597895, 0x9e698881, 0x1ec71073
325 data4 0x1e50e371, 0x9dc01e19, 0x1de74133, 0x1e2f028c
326 data4 0x9edefb47, 0x1ebbac48, 0x9e8b0330, 0x9e9e9314
327 data4 0x1edc1d11, 0x1f098529, 0x9f52827c, 0x1f50050d
328 data4 0x1f301e8e, 0x1f5b64d1, 0x9f45e3ee, 0x9ef64d6d
329 data4 0x1d6ec5e8, 0x9e61ad9a, 0x1d44ccbb, 0x9e4a8bbb
330 data4 0x9cf11576, 0x9dcce7e7, 0x9d02ac90, 0x1f26ccf0
331 data4 0x9f0877c6, 0x9ddd62ae, 0x9f4b7fc3, 0x1ea8ef6b
332 data4 0x1ea4378d, 0x1ef6fc38, 0x1db99fd9, 0x1f22bf6f
333 data4 0x1f53e172, 0x1e85504a, 0x9f37cc75, 0x1f0c5e17
334 data4 0x1dde8aac, 0x9cb42bb2, 0x1e153cd7, 0x1eb62bba
335 data4 0x9e9b941b, 0x9ea80e3c, 0x1f508823, 0x1ec3fd36
336 data4 0x1e9ffaa1, 0x1e21e2eb, 0x9d948b1d, 0x9e8ac93a
337 data4 0x1ef7ee6f, 0x9e80dda3, 0x1f0814be, 0x1dc5ddfe
338 data4 0x1eedb9d1, 0x9f2aaa26, 0x9ea5b0fc, 0x1edf702e
339 data4 0x9e391201, 0x1f1316bb, 0x1ea27fb7, 0x9e05ed18
340 data4 0x9f199ed2, 0x1ee7fd7c, 0x1f003db6, 0x9eac3793
341 data4 0x9e5b8c10, 0x9f3af17c, 0x1bc9a8be, 0x1ee3c004
342 data4 0x9f19b1b2, 0x9f242ce9, 0x9ce67dd1, 0x9e4f6275
343 data4 0x1e20742c, 0x1eb9328a, 0x9f477153, 0x1d969718
344 data4 0x9f1e6c43, 0x1f2f67f4, 0x9f39c7e4, 0x9e3c4feb
345 data4 0x1da3956b, 0x9e7c685d, 0x1f280911, 0x9f0d8afb
346 data4 0x1e314b40, 0x9eb4f250, 0x9f1a34ad, 0x1ef5d5e7
347 data4 0x9f145496, 0x1e604827, 0x9f1e5195, 0x1e9c1fc0
348 data4 0x1efde521, 0x1e69b385, 0x1f316830, 0x9f244eae
349 data4 0x1f1787ec, 0x9e939971, 0x1f0bb393, 0x9f0511d6
350 data4 0x1ed919de, 0x1d8b7b28, 0x1e5ca4a9, 0x1e7c357b
351 data4 0x9e3ff8e8, 0x1eef53b5, 0x9ed22ed7, 0x1f16659b
352 data4 0x9f2db102, 0x9e2c6a78, 0x1f328d7d, 0x9f2fec3c
353 data4 0x1eb395bd, 0x9f242b84, 0x9e2683e6, 0x1ed71e68
354 data4 0x1efd1df5, 0x9e9eeafd, 0x9ed2249c, 0x1eef129a
355 data4 0x1d1ea44c, 0x9e81f7ff, 0x1eaf77c9, 0x9ee7a285
356 data4 0x1e1864ed, 0x9ee7edbb, 0x9e15a27d, 0x9ae61655
357 data4 0x1f1ff1a2, 0x1da29755, 0x9e5f46fb, 0x1e901236
358 data4 0x9eecfb9b, 0x9f204d2f, 0x1ec64685, 0x9eb809bd
359 data4 0x9e0026c5, 0x1d9f1da1, 0x1f142b49, 0x9f20f22e
360 data4 0x1f24b067, 0x1f185a4c, 0x9f09765c, 0x9ece902f
361 data4 0x1e2ca5db, 0x1e6de464, 0x9f071f67, 0x1f1518c3
362 data4 0x1ea13ded, 0x1f0b8414, 0x1edb6ad4, 0x9e548740
363 data4 0x9ea10efb, 0x1ee48a60, 0x1e7954c5, 0x9edad013
364 data4 0x9f21517d, 0x9e9b6e0c, 0x9ee7f9a6, 0x9ebd4298
365 data4 0x9d65b24e, 0x1eed751f, 0x9f1573ea, 0x9d430377
366 data4 0x9e13fc0c, 0x1e47008a, 0x1e3d5c1d, 0x1ef41a91
367 data4 0x9e4a4ef7, 0x9e952f18, 0x1d620566, 0x1d9b8d33
368 data4 0x1db06247, 0x1e94b31e, 0x1f0730ad, 0x9d79ffb4
369 data4 0x1ed64d51, 0x9e91fd11, 0x9e28d35a, 0x9dea0ed9
370 data4 0x1e891def, 0x9ee28ac0, 0x1e1db99b, 0x9ee1ce38
371 data4 0x9bdd9bca, 0x1eb72cb9, 0x9e8c53c6, 0x1e0df6ca
372 data4 0x1e8f2ccd, 0x9e9b0886, 0x1eeb3bc7, 0x1ec7e772
373 data4 0x9e210776, 0x9daf246c, 0x1ea1f151, 0x1ece4dc6
374 data4 0x1ce741c8, 0x1ed3c88f, 0x9ec9a4fd, 0x9e0c8d30
375 data4 0x1d2fbb26, 0x9ef212a7, 0x1ee44f1c, 0x9e445550
376 data4 0x1e075f77, 0x9d9291a3, 0x1f09c2ee, 0x9e012c88
377 data4 0x1f057d62, 0x9e7bb0dc, 0x9d8758ee, 0x1ee8d6c1
378 data4 0x9e509a57, 0x9e4ca7b7, 0x1e2cb341, 0x9ec35106
379 data4 0x1ecf3baf, 0x1e11781c, 0x1ea0cc78, 0x1eb75ca6
380 data4 0x1e961e1a, 0x1eb88853, 0x1e7abf50, 0x1ee38704
381 data4 0x9dc5ab0f, 0x1afe197b, 0x9ec07523, 0x9d9b7f78
382 data4 0x1f011618, 0x1ed43b0b, 0x9f035945, 0x9e3fd014
383 data4 0x9bbda5cd, 0x9e83f8ab, 0x1e58a928, 0x1e392d61
384 data4 0x1efdbb52, 0x1ee310a8, 0x9ec7ecc1, 0x1e8c9ed6
385 data4 0x9ef82dee, 0x9e70545b, 0x9ea53fc4, 0x1e40f419
386 LOCAL_OBJECT_END(D_table)
390 .section .text
391 GLOBAL_IEEE754_ENTRY(exp10l)
393 {.mfi
394 alloc GR_SREG = ar.pfs, 1, 4, 4, 0
395 // will continue only for normal/denormal numbers
396 fclass.nm.unc p12, p7 = f8, 0x1b
397 // GR_ADDR0 = pointer to log2(10), C_1...C_6 followed by T_table
398 addl GR_ADDR0 = @ltoff(poly_coeffs), gp ;;
399 }
401 {.mfi
402 // load start address for C_1...C_6 followed by T_table
403 ld8 GR_ADDR0 = [ GR_ADDR0 ]
404 // X<0 ?
405 fcmp.lt.s1 p6, p8 = f8, f0
406 // GR_BM8 = bias-8
407 mov GR_BM8 = 0xffff-8
408 }
409 {.mlx
410 nop.m 0
411 // GR_EMIN = (-2^14-62)*2^{8}
412 movl GR_EMIN = 0xca807c00 ;;
413 }
415 {.mmb
416 // FR_CONST1 = 2^{-8}
417 setf.exp FR_CONST1 = GR_BM8
418 // load log2(10)*2^8
419 ldfe FR_LOG10 = [ GR_ADDR0 ], 16
420 (p12) br.cond.spnt SPECIAL_EXP10 ;;
421 }
423 {.mmf
424 setf.s FR_UF_TEST = GR_EMIN
425 // load overflow threshold
426 ldfe FR_OF_TEST = [ GR_ADDR0 ], 16
427 // normalize x
428 fma.s0 f8 = f8, f1, f0 ;;
429 }
431 {.mmi
432 // load C_1
433 ldfe FR_COEFF1 = [ GR_ADDR0 ], 16 ;;
434 // load C_2
435 ldfe FR_COEFF2 = [ GR_ADDR0 ], 16
436 nop.i 0 ;;
437 }
439 {.mmf
440 // GR_D_ADDR = pointer to D table
441 add GR_D_ADDR = 2048-64+96+32, GR_ADDR0
442 // load C_3, C_4
443 ldfpd FR_COEFF3, FR_COEFF4 = [ GR_ADDR0 ], 16
444 // y = x*log2(10)*2^8
445 fma.s1 FR_XL10 = f8, FR_LOG10, f0 ;;
446 }
448 {.mfi
449 // load C_5, C_6
450 ldfpd FR_COEFF5, FR_COEFF6 = [ GR_ADDR0 ], 16
451 // get int(x)
452 fcvt.fx.trunc.s1 FR_XINT = f8
453 nop.i 0
454 }
455 {.mfi
456 nop.m 0
457 // FR_LOG10 = log2(10)
458 fma.s1 FR_L10 = FR_LOG10, FR_CONST1, f0
459 nop.i 0 ;;
460 }
462 {.mfi
463 // load log2(10)_low
464 ldfe FR_L10_LOW = [ GR_ADDR0 ], 16
465 // y0 = x*log2(10) = x*log2(10)_hi
466 fma.s1 FR_LOG10 = f8, FR_L10, f0
467 mov GR_EMIN = 0xffff-63
468 }
469 {.mfi
470 mov GR_32_BIAS = 0xffff + 5
471 // (K+f)*2^8 = round_to_int(y)
472 fcvt.fx.s1 FR_KF0 = FR_XL10
473 mov GR_4_BIAS = 0xffff + 2;;
474 }
476 {.mfi
477 // load smallest normal limit
478 ldfe FR_SNORM_LIMIT = [ GR_ADDR0 ], 16
479 // x>overflow threshold ?
480 fcmp.gt.s1 p12, p7 = f8, FR_OF_TEST
481 nop.i 0 ;;
482 }
484 {.mfi
485 setf.exp FR_32 = GR_32_BIAS
486 // x<underflow threshold ?
487 (p7) fcmp.lt.s1 p12, p7 = FR_XL10, FR_UF_TEST
488 nop.i 0 ;;
489 }
491 {.mfi
492 setf.exp FR_4 = GR_4_BIAS
493 fcvt.xf FR_XINTF = FR_XINT
494 nop.i 0
495 }
496 {.mfi
497 nop.m 0
498 // FR_L10 = log2(10)_h*x-RN(log2(10)_h*x)
499 fms.s1 FR_L10 = f8, FR_L10, FR_LOG10
500 nop.i 0 ;;
501 }
503 {.mfi
504 getf.sig GR_BM8 = FR_KF0
505 fcvt.xf FR_KF0 = FR_KF0
506 mov GR_CONST2 = 255 ;;
507 }
509 {.mfi
510 // GR_CONST2 = f
511 and GR_CONST2 = GR_CONST2, GR_BM8
512 // FR_L10_LOW = e = log2(10)_l*x+(log2(10)_h*x-RN(log2(10)_h*x))
513 fma.s1 FR_L10_LOW = FR_L10_LOW, f8, FR_L10
514 // GR_BM8 = K
515 shr GR_BM8 = GR_BM8, 8 ;;
516 }
518 {.mmi
519 // address of D
520 shladd GR_D_ADDR = GR_CONST2, 2, GR_D_ADDR
521 // K+ = bias-63
522 add GR_BM8 = GR_BM8, GR_EMIN
523 // address of T
524 shladd GR_ADDR0 = GR_CONST2, 3, GR_ADDR0 ;;
525 }
527 {.mfb
528 // load D
529 ldfs FR_OF_TEST = [ GR_D_ADDR ]
530 // is input an integer ?
531 fcmp.eq.s1 p13, p14 = f8, FR_XINTF
532 (p12) br.cond.spnt OUT_RANGE_EXP10 ;;
533 }
535 {.mmf
536 // load T
537 ldf8 FR_UF_TEST = [ GR_ADDR0 ]
538 // FR_XL10 = 2^{K-63}
539 setf.exp FR_XL10 = GR_BM8
540 // r = x*log2(10)_hi-2^{-10}* [ (K+f)*2^{10} ]
541 fnma.s1 FR_KF0 = FR_KF0, FR_CONST1, FR_LOG10 ;;
542 }
544 {.mfi
545 nop.m 0
546 // get 28.0
547 fms.s1 FR_28 = FR_32, f1, FR_4
548 nop.i 0
549 }
550 {.mfi
551 nop.m 0
552 // E = 1+C_1*e
553 fma.s1 FR_L10 = FR_L10_LOW, FR_COEFF1, f1
554 nop.i 0 ;;
555 }
557 {.mfi
558 nop.m 0
559 // P12 = C_1+C_2*r
560 fma.s1 FR_COEFF2 = FR_COEFF2, FR_KF0, FR_COEFF1
561 nop.i 0
562 }
563 {.mfi
564 nop.m 0
565 // P34 = C_3+C_4*r
566 fma.s1 FR_COEFF4 = FR_COEFF4, FR_KF0, FR_COEFF3
567 nop.i 0 ;;
568 }
570 {.mfi
571 nop.m 0
572 // P56 = C_5+C_6*r
573 fma.s1 FR_COEFF5 = FR_COEFF6, FR_KF0, FR_COEFF5
574 nop.i 0
575 }
576 {.mfi
577 nop.m 0
578 // GR_ADDR0 = r*r
579 fma.s1 FR_COEFF3 = FR_KF0, FR_KF0, f0
580 nop.i 0 ;;
581 }
583 {.mfi
584 nop.m 0
585 // if input is integer, is it positive ?
586 (p13) fcmp.ge.s1 p13, p14 = f8, f0
587 nop.i 0
588 }
589 {.mfi
590 nop.m 0
591 // r' = r*E
592 fma.s1 FR_KF0 = FR_KF0, FR_L10, f0
593 nop.i 0 ;;
594 }
596 {.mfi
597 nop.m 0
598 // D' = D+C_1*e
599 fma.s1 FR_OF_TEST = FR_L10_LOW, FR_COEFF1, FR_OF_TEST
600 nop.i 0 ;;
601 }
603 {.mfi
604 nop.m 0
605 // test if x >= smallest normal limit
606 fcmp.ge.s1 p11, p0 = f8, FR_SNORM_LIMIT
607 nop.i 0 ;;
608 }
610 {.mfi
611 nop.m 0
612 // P36 = P34+r2*P56
613 fma.s1 FR_COEFF4 = FR_COEFF5, FR_COEFF3, FR_COEFF4
614 nop.i 0
615 }
616 {.mfi
617 nop.m 0
618 // GR_D_ADDR = r'*r2
619 fma.s1 FR_COEFF3 = FR_COEFF3, FR_KF0, f0
620 nop.i 0 ;;
621 }
623 {.mfi
624 nop.m 0
625 // is input below 28.0 ?
626 (p13) fcmp.lt.s1 p13, p14 = f8, FR_28
627 nop.i 0
628 }
629 {.mfi
630 nop.m 0
631 // P' = P12*r'+D'
632 fma.s1 FR_COEFF2 = FR_COEFF2, FR_KF0, FR_OF_TEST
633 nop.i 0 ;;
634 }
636 {.mfi
637 nop.m 0
638 // P = P'+r3*P36
639 fma.s1 FR_COEFF3 = FR_COEFF3, FR_COEFF4, FR_COEFF2
640 nop.i 0
641 }
642 {.mfi
643 nop.m 0
644 // T = 2^{K-63}*T
645 fma.s1 FR_UF_TEST = FR_UF_TEST, FR_XL10, f0
646 nop.i 0 ;;
647 }
649 .pred.rel "mutex",p13,p14
650 {.mfi
651 nop.m 0
652 (p13) fma.s1 f8 = FR_COEFF3, FR_UF_TEST, FR_UF_TEST
653 nop.i 0
654 }
655 {.mfb
656 nop.m 0
657 // result = T+T*P
658 (p14) fma.s0 f8 = FR_COEFF3, FR_UF_TEST, FR_UF_TEST
659 // return
660 (p11) br.ret.sptk b0 ;; // return, if result normal
661 }
663 // Here if result in denormal range (and not zero)
664 {.mib
665 nop.m 0
666 mov GR_Parameter_TAG= 264
667 br.cond.sptk __libm_error_region // Branch to error handling
668 }
669 ;;
671 SPECIAL_EXP10:
673 {.mfi
674 nop.m 0
675 // x = -Infinity ?
676 fclass.m p6, p0 = f8, 0x22
677 nop.i 0 ;;
678 }
680 {.mfi
681 nop.m 0
682 // x = +Infinity ?
683 fclass.m p7, p0 = f8, 0x21
684 nop.i 0 ;;
685 }
687 {.mfi
688 nop.m 0
689 // x = +/-Zero ?
690 fclass.m p8, p0 = f8, 0x7
691 nop.i 0
692 }
693 {.mfb
694 nop.m 0
695 // exp10(-Infinity) = 0
696 (p6) mov f8 = f0
697 (p6) br.ret.spnt b0 ;;
698 }
700 {.mfb
701 nop.m 0
702 // exp10(+Infinity) = +Infinity
703 nop.f 0
704 (p7) br.ret.spnt b0 ;;
705 }
707 {.mfb
708 nop.m 0
709 // exp10(+/-0) = 1
710 (p8) mov f8 = f1
711 (p8) br.ret.spnt b0 ;;
712 }
714 {.mfb
715 nop.m 0
716 // Remaining cases: NaNs
717 fma.s0 f8 = f8, f1, f0
718 br.ret.sptk b0 ;;
719 }
722 OUT_RANGE_EXP10:
724 // underflow: p6 = 1
725 // overflow: p8 = 1
727 .pred.rel "mutex",p6,p8
728 {.mmi
729 (p8) mov GR_CONST1 = 0x1fffe
730 (p6) mov GR_CONST1 = 1
731 nop.i 0
732 }
733 ;;
735 {.mii
736 setf.exp FR_KF0 = GR_CONST1
737 (p8) mov GR_Parameter_TAG = 165
738 (p6) mov GR_Parameter_TAG = 264
739 }
740 ;;
742 {.mfb
743 nop.m 999
744 fma.s0 f8 = FR_KF0, FR_KF0, f0 // Create overflow/underflow
745 br.cond.sptk __libm_error_region // Branch to error handling
746 }
747 ;;
749 GLOBAL_IEEE754_END(exp10l)
750 weak_alias (exp10l, pow10l)
753 LOCAL_LIBM_ENTRY(__libm_error_region)
754 .prologue
755 {.mfi
756 add GR_Parameter_Y = -32, sp // Parameter 2 value
757 nop.f 0
758 .save ar.pfs, GR_SAVE_PFS
759 mov GR_SAVE_PFS = ar.pfs // Save ar.pfs
760 }
762 {.mfi
763 .fframe 64
764 add sp = -64, sp // Create new stack
765 nop.f 0
766 mov GR_SAVE_GP = gp ;; // Save gp
767 }
769 {.mmi
770 stfe [ GR_Parameter_Y ] = FR_Y, 16 // STORE Parameter 2 on stack
771 add GR_Parameter_X = 16, sp // Parameter 1 address
772 .save b0, GR_SAVE_B0
773 mov GR_SAVE_B0 = b0 ;; // Save b0
774 }
776 .body
777 {.mib
778 stfe [ GR_Parameter_X ] = FR_X // STORE Parameter 1 on stack
779 add GR_Parameter_RESULT = 0, GR_Parameter_Y // Parameter 3 address
780 nop.b 0
781 }
782 {.mib
783 stfe [ GR_Parameter_Y ] = FR_RESULT // STORE Parameter 3 on stack
784 add GR_Parameter_Y = -16, GR_Parameter_Y
785 br.call.sptk b0 = __libm_error_support# ;; // Call error handling function
786 }
788 {.mmi
789 add GR_Parameter_RESULT = 48, sp
790 nop.m 0
791 nop.i 0 ;;
792 }
794 {.mmi
795 ldfe f8 = [ GR_Parameter_RESULT ] // Get return result off stack
796 .restore sp
797 add sp = 64, sp // Restore stack pointer
798 mov b0 = GR_SAVE_B0 ;; // Restore return address
799 }
801 {.mib
802 mov gp = GR_SAVE_GP // Restore gp
803 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
804 br.ret.sptk b0 ;; // Return
805 }
808 LOCAL_LIBM_END(__libm_error_region)
809 .type __libm_error_support#, @function
810 .global __libm_error_support#