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1 | .file "libm_ldexp.s" |
2 | ||
3 | ||
4 | // Copyright (c) 2000 - 2003, 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. | |
23 | ||
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 | // 02/02/00 Initial version | |
43 | // 01/26/01 ldexp completely reworked and now standalone version | |
44 | // 01/04/02 Added handling for int 32 or 64 bits | |
45 | // 05/20/02 Cleaned up namespace and sf0 syntax | |
46 | // 02/10/03 Reordered header: .section, .global, .proc, .align | |
47 | // 08/04/03 Improved performance | |
48 | // | |
49 | // API | |
50 | //============================================================== | |
51 | // double __libm_ldexp (double x, int n, int int_type) | |
52 | // input floating point f8 and int n (r33), int int_type (r34) | |
53 | // output floating point f8 | |
54 | // | |
55 | // int_type = 0 if int is 32 bits | |
56 | // int_type = 1 if int is 64 bits | |
57 | // | |
58 | // Returns x* 2**n using an fma and detects overflow | |
59 | // and underflow. | |
60 | // | |
61 | // | |
62 | // Strategy: | |
63 | // Compute biased exponent of result exp_Result = N + exp_X | |
64 | // Break into ranges: | |
65 | // exp_Result > 0x103fe -> Certain overflow | |
66 | // exp_Result = 0x103fe -> Possible overflow | |
67 | // 0x0fc01 <= exp_Result < 0x103fe -> No over/underflow (main path) | |
68 | // 0x0fc01 - 52 <= exp_Result < 0x0fc01 -> Possible underflow | |
69 | // exp_Result < 0x0fc01 - 52 -> Certain underflow | |
70 | ||
71 | FR_Big = f6 | |
72 | FR_NBig = f7 | |
73 | FR_Floating_X = f8 | |
74 | FR_Result = f8 | |
75 | FR_Result2 = f9 | |
76 | FR_Result3 = f10 | |
77 | FR_Norm_X = f11 | |
78 | FR_Two_N = f12 | |
79 | ||
80 | GR_neg_ov_limit= r14 | |
81 | GR_N_Biased = r15 | |
82 | GR_Big = r16 | |
83 | GR_NBig = r17 | |
84 | GR_exp_Result = r18 | |
85 | GR_pos_ov_limit= r19 | |
86 | GR_Bias = r20 | |
87 | GR_N_as_int = r21 | |
88 | GR_signexp_X = r22 | |
89 | GR_exp_X = r23 | |
90 | GR_exp_mask = r24 | |
91 | GR_max_exp = r25 | |
92 | GR_min_exp = r26 | |
93 | GR_min_den_exp = r27 | |
94 | ||
95 | GR_SAVE_B0 = r32 | |
96 | GR_SAVE_GP = r33 | |
97 | GR_SAVE_PFS = r34 | |
98 | GR_Parameter_X = r35 | |
99 | GR_Parameter_Y = r36 | |
100 | GR_Parameter_RESULT = r37 | |
101 | GR_Tag = r38 | |
102 | ||
103 | .section .text | |
104 | GLOBAL_LIBM_ENTRY(__libm_ldexp) | |
105 | ||
106 | // | |
107 | // Is x NAN, INF, ZERO, +-? | |
108 | // Build the exponent Bias | |
109 | // | |
110 | { .mfi | |
111 | getf.exp GR_signexp_X = FR_Floating_X // Get signexp of x | |
112 | fclass.m p6,p0 = FR_Floating_X, 0xe7 // @snan | @qnan | @inf | @zero | |
113 | mov GR_Bias = 0x0ffff | |
114 | } | |
115 | // | |
116 | // Normalize x | |
117 | // Is integer type 32 bits? | |
118 | // | |
119 | { .mfi | |
120 | mov GR_Big = 35000 // If N this big then certain overflow | |
121 | fnorm.s1 FR_Norm_X = FR_Floating_X | |
122 | cmp.eq p8,p9 = r34,r0 | |
123 | } | |
124 | ;; | |
125 | ||
126 | // Sign extend N if int is 32 bits | |
127 | { .mfi | |
128 | (p9) mov GR_N_as_int = r33 // Copy N if int is 64 bits | |
129 | fclass.m p9,p0 = FR_Floating_X, 0x0b // Test for x=unorm | |
130 | (p8) sxt4 GR_N_as_int = r33 // Sign extend N if int is 32 bits | |
131 | } | |
132 | { .mfi | |
133 | mov GR_NBig = -35000 // If N this small then certain underflow | |
134 | nop.f 0 | |
135 | mov GR_max_exp = 0x103fe // Exponent of maximum double | |
136 | } | |
137 | ;; | |
138 | ||
139 | // Create biased exponent for 2**N | |
140 | { .mfi | |
141 | add GR_N_Biased = GR_Bias,GR_N_as_int | |
142 | nop.f 0 | |
143 | cmp.ge p7, p0 = GR_N_as_int, GR_Big // Certain overflow? | |
144 | } | |
145 | { .mib | |
146 | cmp.le p8, p0 = GR_N_as_int, GR_NBig // Certain underflow? | |
147 | mov GR_min_exp = 0x0fc01 // Exponent of minimum double | |
148 | (p9) br.cond.spnt LDEXP_UNORM // Branch if x=unorm | |
149 | } | |
150 | ;; | |
151 | ||
152 | LDEXP_COMMON: | |
153 | // Main path continues. Also return here from x=unorm path. | |
154 | // Create 2**N | |
155 | .pred.rel "mutex",p7,p8 | |
156 | { .mfi | |
157 | setf.exp FR_Two_N = GR_N_Biased | |
158 | nop.f 0 | |
159 | (p7) mov GR_N_as_int = GR_Big // Limit max N | |
160 | } | |
161 | { .mfi | |
162 | (p8) mov GR_N_as_int = GR_NBig // Limit min N | |
163 | nop.f 0 | |
164 | (p8) cmp.eq p7,p0 = r0,r0 // Set p7 if |N| big | |
165 | } | |
166 | ;; | |
167 | ||
168 | // | |
169 | // Create biased exponent for 2**N for N big | |
170 | // Is N zero? | |
171 | // | |
172 | { .mfi | |
173 | (p7) add GR_N_Biased = GR_Bias,GR_N_as_int | |
174 | nop.f 0 | |
175 | cmp.eq.or p6,p0 = r33,r0 | |
176 | } | |
177 | { .mfi | |
178 | mov GR_pos_ov_limit = 0x103ff // Exponent for positive overflow | |
179 | nop.f 0 | |
180 | mov GR_exp_mask = 0x1ffff // Exponent mask | |
181 | } | |
182 | ;; | |
183 | ||
184 | // | |
185 | // Create 2**N for N big | |
186 | // Return x when N = 0 or X = Nan, Inf, Zero | |
187 | // | |
188 | { .mfi | |
189 | (p7) setf.exp FR_Two_N = GR_N_Biased | |
190 | nop.f 0 | |
191 | mov GR_min_den_exp = 0x0fc01 - 52 // Exponent of min denorm dble | |
192 | } | |
193 | { .mfb | |
194 | and GR_exp_X = GR_exp_mask, GR_signexp_X | |
195 | (p6) fma.d.s0 FR_Result = FR_Floating_X, f1, f0 | |
196 | (p6) br.ret.spnt b0 | |
197 | } | |
198 | ;; | |
199 | ||
200 | // | |
201 | // Raise Denormal operand flag with compare | |
202 | // Compute biased result exponent | |
203 | // | |
204 | { .mfi | |
205 | add GR_exp_Result = GR_exp_X, GR_N_as_int | |
206 | fcmp.ge.s0 p0,p11 = FR_Floating_X,f0 | |
207 | mov GR_neg_ov_limit = 0x303ff // Exponent for negative overflow | |
208 | } | |
209 | ;; | |
210 | ||
211 | // | |
212 | // Do final operation | |
213 | // | |
214 | { .mfi | |
215 | cmp.lt p7,p6 = GR_exp_Result, GR_max_exp // Test no overflow | |
216 | fma.d.s0 FR_Result = FR_Two_N,FR_Norm_X,f0 | |
217 | cmp.lt p9,p0 = GR_exp_Result, GR_min_den_exp // Test sure underflow | |
218 | } | |
219 | { .mfb | |
220 | nop.m 0 | |
221 | nop.f 0 | |
222 | (p9) br.cond.spnt LDEXP_UNDERFLOW // Branch if certain underflow | |
223 | } | |
224 | ;; | |
225 | ||
226 | { .mib | |
227 | (p6) cmp.gt.unc p6,p8 = GR_exp_Result, GR_max_exp // Test sure overflow | |
228 | (p7) cmp.ge.unc p7,p9 = GR_exp_Result, GR_min_exp // Test no over/underflow | |
229 | (p7) br.ret.sptk b0 // Return from main path | |
230 | } | |
231 | ;; | |
232 | ||
233 | { .bbb | |
234 | (p6) br.cond.spnt LDEXP_OVERFLOW // Branch if certain overflow | |
235 | (p8) br.cond.spnt LDEXP_POSSIBLE_OVERFLOW // Branch if possible overflow | |
236 | (p9) br.cond.spnt LDEXP_POSSIBLE_UNDERFLOW // Branch if possible underflow | |
237 | } | |
238 | ;; | |
239 | ||
240 | // Here if possible underflow. | |
241 | // Resulting exponent: 0x0fc01-52 <= exp_Result < 0x0fc01 | |
242 | LDEXP_POSSIBLE_UNDERFLOW: | |
243 | // | |
244 | // Here if possible overflow. | |
245 | // Resulting exponent: 0x103fe = exp_Result | |
246 | LDEXP_POSSIBLE_OVERFLOW: | |
247 | ||
248 | // Set up necessary status fields | |
249 | // | |
250 | // S0 user supplied status | |
251 | // S2 user supplied status + WRE + TD (Overflows) | |
252 | // S3 user supplied status + FZ + TD (Underflows) | |
253 | // | |
254 | { .mfi | |
255 | nop.m 0 | |
256 | fsetc.s3 0x7F,0x41 | |
257 | nop.i 0 | |
258 | } | |
259 | { .mfi | |
260 | nop.m 0 | |
261 | fsetc.s2 0x7F,0x42 | |
262 | nop.i 0 | |
263 | } | |
264 | ;; | |
265 | ||
266 | // | |
267 | // Do final operation with s2 and s3 | |
268 | // | |
269 | { .mfi | |
270 | setf.exp FR_NBig = GR_neg_ov_limit | |
271 | fma.d.s3 FR_Result3 = FR_Two_N,FR_Norm_X,f0 | |
272 | nop.i 0 | |
273 | } | |
274 | { .mfi | |
275 | setf.exp FR_Big = GR_pos_ov_limit | |
276 | fma.d.s2 FR_Result2 = FR_Two_N,FR_Norm_X,f0 | |
277 | nop.i 0 | |
278 | } | |
279 | ;; | |
280 | ||
281 | // Check for overflow or underflow. | |
282 | // Restore s3 | |
283 | // Restore s2 | |
284 | // | |
285 | { .mfi | |
286 | nop.m 0 | |
287 | fsetc.s3 0x7F,0x40 | |
288 | nop.i 0 | |
289 | } | |
290 | { .mfi | |
291 | nop.m 0 | |
292 | fsetc.s2 0x7F,0x40 | |
293 | nop.i 0 | |
294 | } | |
295 | ;; | |
296 | ||
297 | // | |
298 | // Is the result zero? | |
299 | // | |
300 | { .mfi | |
301 | nop.m 0 | |
302 | fclass.m p6, p0 = FR_Result3, 0x007 | |
303 | nop.i 0 | |
304 | } | |
305 | { .mfi | |
306 | nop.m 0 | |
307 | fcmp.ge.s1 p7, p8 = FR_Result2 , FR_Big | |
308 | nop.i 0 | |
309 | } | |
310 | ;; | |
311 | ||
312 | // | |
313 | // Detect masked underflow - Tiny + Inexact Only | |
314 | // | |
315 | { .mfi | |
316 | nop.m 0 | |
317 | (p6) fcmp.neq.unc.s1 p6, p0 = FR_Result , FR_Result2 | |
318 | nop.i 0 | |
319 | } | |
320 | ;; | |
321 | ||
322 | // | |
323 | // Is result bigger the allowed range? | |
324 | // Branch out for underflow | |
325 | // | |
326 | { .mfb | |
327 | nop.m 0 | |
328 | (p8) fcmp.le.unc.s1 p9, p10 = FR_Result2 , FR_NBig | |
329 | (p6) br.cond.spnt LDEXP_UNDERFLOW | |
330 | } | |
331 | ;; | |
332 | ||
333 | // | |
334 | // Branch out for overflow | |
335 | // | |
336 | { .bbb | |
337 | (p7) br.cond.spnt LDEXP_OVERFLOW | |
338 | (p9) br.cond.spnt LDEXP_OVERFLOW | |
339 | br.ret.sptk b0 // Return from main path. | |
340 | } | |
341 | ;; | |
342 | ||
343 | // Here if result overflows | |
344 | LDEXP_OVERFLOW: | |
345 | { .mib | |
346 | alloc r32=ar.pfs,3,0,4,0 | |
347 | addl GR_Tag = 146, r0 // Set error tag for overflow | |
348 | br.cond.sptk __libm_error_region // Call error support for overflow | |
349 | } | |
350 | ;; | |
351 | ||
352 | // Here if result underflows | |
353 | LDEXP_UNDERFLOW: | |
354 | { .mib | |
355 | alloc r32=ar.pfs,3,0,4,0 | |
356 | addl GR_Tag = 147, r0 // Set error tag for underflow | |
357 | br.cond.sptk __libm_error_region // Call error support for underflow | |
358 | } | |
359 | ;; | |
360 | ||
361 | // Here if x=unorm | |
362 | LDEXP_UNORM: | |
363 | { .mib | |
364 | getf.exp GR_signexp_X = FR_Norm_X // Get signexp of normalized x | |
365 | nop.i 0 | |
366 | br.cond.sptk LDEXP_COMMON // Return to main path | |
367 | } | |
368 | ;; | |
369 | ||
370 | ||
371 | GLOBAL_LIBM_END(__libm_ldexp) | |
372 | LOCAL_LIBM_ENTRY(__libm_error_region) | |
373 | ||
374 | // | |
375 | // Get stack address of N | |
376 | // | |
377 | .prologue | |
378 | { .mfi | |
379 | add GR_Parameter_Y=-32,sp | |
380 | nop.f 0 | |
381 | .save ar.pfs,GR_SAVE_PFS | |
382 | mov GR_SAVE_PFS=ar.pfs | |
383 | } | |
384 | // | |
385 | // Adjust sp | |
386 | // | |
387 | { .mfi | |
388 | .fframe 64 | |
389 | add sp=-64,sp | |
390 | nop.f 0 | |
391 | mov GR_SAVE_GP=gp | |
392 | };; | |
393 | ||
394 | // | |
395 | // Store N on stack in correct position | |
396 | // Locate the address of x on stack | |
397 | // | |
398 | { .mmi | |
399 | st8 [GR_Parameter_Y] = GR_N_as_int,16 | |
400 | add GR_Parameter_X = 16,sp | |
401 | .save b0, GR_SAVE_B0 | |
402 | mov GR_SAVE_B0=b0 | |
403 | };; | |
404 | ||
405 | // | |
406 | // Store x on the stack. | |
407 | // Get address for result on stack. | |
408 | // | |
409 | .body | |
410 | { .mib | |
411 | stfd [GR_Parameter_X] = FR_Norm_X | |
412 | add GR_Parameter_RESULT = 0,GR_Parameter_Y | |
413 | nop.b 0 | |
414 | } | |
415 | { .mib | |
416 | stfd [GR_Parameter_Y] = FR_Result | |
417 | add GR_Parameter_Y = -16,GR_Parameter_Y | |
418 | br.call.sptk b0=__libm_error_support# | |
419 | };; | |
420 | ||
421 | // | |
422 | // Get location of result on stack | |
423 | // | |
424 | { .mmi | |
425 | add GR_Parameter_RESULT = 48,sp | |
426 | nop.m 0 | |
427 | nop.i 0 | |
428 | };; | |
429 | ||
430 | // | |
431 | // Get the new result | |
432 | // | |
433 | { .mmi | |
434 | ldfd FR_Result = [GR_Parameter_RESULT] | |
435 | .restore sp | |
436 | add sp = 64,sp | |
437 | mov b0 = GR_SAVE_B0 | |
438 | };; | |
439 | ||
440 | // | |
441 | // Restore gp, ar.pfs and return | |
442 | // | |
443 | { .mib | |
444 | mov gp = GR_SAVE_GP | |
445 | mov ar.pfs = GR_SAVE_PFS | |
446 | br.ret.sptk b0 | |
447 | };; | |
448 | ||
449 | LOCAL_LIBM_END(__libm_error_region) | |
450 | ||
451 | .type __libm_error_support#,@function | |
452 | .global __libm_error_support# |