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1 | .file "exp2f.s" |
2 | ||
3 | ||
4 | // Copyright (c) 2000 - 2005, Intel Corporation | |
5 | // All rights reserved. | |
6 | // | |
d5efd131 MF |
7 | // |
8 | // Redistribution and use in source and binary forms, with or without | |
9 | // modification, are permitted provided that the following conditions are | |
10 | // met: | |
11 | // | |
12 | // * Redistributions of source code must retain the above copyright | |
13 | // notice, this list of conditions and the following disclaimer. | |
14 | // | |
15 | // * Redistributions in binary form must reproduce the above copyright | |
16 | // notice, this list of conditions and the following disclaimer in the | |
17 | // documentation and/or other materials provided with the distribution. | |
18 | // | |
19 | // * The name of Intel Corporation may not be used to endorse or promote | |
20 | // products derived from this software without specific prior written | |
21 | // permission. | |
22 | ||
23 | // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | |
24 | // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | |
25 | // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR | |
26 | // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS | |
27 | // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, | |
28 | // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, | |
29 | // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR | |
30 | // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY | |
31 | // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING | |
32 | // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS | |
33 | // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | |
34 | // | |
35 | // Intel Corporation is the author of this code, and requests that all | |
36 | // problem reports or change requests be submitted to it directly at | |
37 | // http://www.intel.com/software/products/opensource/libraries/num.htm. | |
38 | // | |
39 | // History | |
40 | //============================================================== | |
41 | // 08/25/00 Initial version | |
42 | // 05/20/02 Cleaned up namespace and sf0 syntax | |
43 | // 09/05/02 Improved performance and accuracy | |
44 | // 01/17/03 Fixed to call error support when x=128.0 | |
45 | // 03/31/05 Reformatted delimiters between data tables | |
46 | // | |
47 | // API | |
48 | //============================================================== | |
49 | // float exp2f(float) | |
50 | // | |
51 | // Overview of operation | |
52 | //============================================================== | |
53 | // Background | |
54 | // | |
55 | // Implementation | |
56 | // | |
57 | // Let x= (K + fh + fl + r), where | |
58 | // K is an integer, fh= 0.b1 b2 b3 b4 b5, | |
59 | // fl= 2^{-5}* 0.b6 b7 b8 b8 b10 (fh, fl >= 0), | |
60 | // and |r|<2^{-11} | |
61 | // Th is a table that stores 2^fh (32 entries) rounded to | |
62 | // double extended precision (only mantissa is stored) | |
63 | // Tl is a table that stores 2^fl (32 entries) rounded to | |
64 | // double extended precision (only mantissa is stored) | |
65 | // | |
66 | // 2^x is approximated as | |
67 | // 2^K * Th [ f ] * Tl [ f ] * (1+c1*r+c2*r^2) | |
68 | ||
69 | // Note: We use the following trick to speed up conversion from FP to integer: | |
70 | // | |
71 | // Let x = K + r, where K is an integer, and |r| <= 0.5 | |
72 | // Let N be the number of significand bits for the FP format used | |
73 | // ( N=64 for double-extended, N=53 for double) | |
74 | // | |
75 | // Then let y = 1.5 * 2^(N-1) + x for RN mode | |
76 | // K = y - 1.5 * 2^(N-1) | |
77 | // r = x - K | |
78 | // | |
79 | // If we want to obtain the integer part and the first m fractional bits of x, | |
80 | // we can use the same trick, but with a constant of 1.5 * 2^(N-1-m): | |
81 | // | |
82 | // Let x = K + f + r | |
83 | // f = 0.b_1 b_2 ... b_m | |
84 | // |r| <= 2^(-m-1) | |
85 | // | |
86 | // Then let y = 1.5 * 2^(N-1-m) + x for RN mode | |
87 | // (K+f) = y - 1.5 * 2^(N-1-m) | |
88 | // r = x - K | |
89 | ||
90 | ||
91 | // Special values | |
92 | //============================================================== | |
93 | // exp2(0)= 1 | |
94 | // exp2(+inf)= inf | |
95 | // exp2(-inf)= 0 | |
96 | // | |
97 | ||
98 | // Registers used | |
99 | //============================================================== | |
100 | // r2-r3, r14-r40 | |
101 | // f6-f15, f32-f45 | |
102 | // p6-p8, p12 | |
103 | // | |
104 | ||
105 | ||
106 | GR_TBL_START = r2 | |
107 | GR_LOG_TBL = r3 | |
108 | ||
109 | GR_OF_LIMIT = r14 | |
110 | GR_UF_LIMIT = r15 | |
111 | GR_EXP_CORR = r16 | |
112 | GR_F_low = r17 | |
113 | GR_F_high = r18 | |
114 | GR_K = r19 | |
115 | GR_Flow_ADDR = r20 | |
116 | ||
117 | GR_BIAS = r21 | |
118 | GR_Fh = r22 | |
119 | GR_Fh_ADDR = r23 | |
120 | GR_EXPMAX = r24 | |
121 | GR_EMIN = r25 | |
122 | ||
123 | GR_ROUNDVAL = r26 | |
124 | GR_MASK = r27 | |
125 | GR_KF0 = r28 | |
126 | GR_MASK_low = r29 | |
127 | GR_COEFF_START = r30 | |
128 | ||
129 | GR_SAVE_B0 = r33 | |
130 | GR_SAVE_PFS = r34 | |
131 | GR_SAVE_GP = r35 | |
132 | GR_SAVE_SP = r36 | |
133 | ||
134 | GR_Parameter_X = r37 | |
135 | GR_Parameter_Y = r38 | |
136 | GR_Parameter_RESULT = r39 | |
137 | GR_Parameter_TAG = r40 | |
138 | ||
139 | ||
140 | FR_X = f10 | |
141 | FR_Y = f1 | |
142 | FR_RESULT = f8 | |
143 | ||
144 | ||
145 | FR_COEFF1 = f6 | |
146 | FR_COEFF2 = f7 | |
147 | FR_R = f9 | |
148 | ||
149 | FR_KF0 = f12 | |
150 | FR_UF_LIMIT = f15 | |
151 | ||
152 | FR_OF_LIMIT = f32 | |
153 | FR_EXPMIN = f33 | |
154 | FR_ROUNDVAL = f34 | |
155 | FR_KF = f35 | |
156 | ||
157 | FR_2_TO_K = f36 | |
158 | FR_T_low = f37 | |
159 | FR_T_high = f38 | |
160 | ||
161 | FR_P12 = f41 | |
162 | FR_T_low_K = f42 | |
163 | FR_T = f44 | |
164 | FR_P = f45 | |
165 | ||
166 | ||
167 | // Data tables | |
168 | //============================================================== | |
169 | ||
170 | RODATA | |
171 | ||
172 | .align 16 | |
173 | ||
174 | LOCAL_OBJECT_START(poly_coeffs) | |
175 | ||
176 | data8 0xb17217f7d1cf79ab, 0x00003ffe // C_1 | |
177 | data8 0xf5fdeffc162c7541, 0x00003ffc // C_2 | |
178 | LOCAL_OBJECT_END(poly_coeffs) | |
179 | ||
180 | ||
181 | LOCAL_OBJECT_START(T_table) | |
182 | ||
183 | // 2^{0.00000 b6 b7 b8 b9 b10} | |
184 | data8 0x8000000000000000, 0x8016302f17467628 | |
185 | data8 0x802c6436d0e04f50, 0x80429c17d77c18ed | |
186 | data8 0x8058d7d2d5e5f6b0, 0x806f17687707a7af | |
187 | data8 0x80855ad965e88b83, 0x809ba2264dada76a | |
188 | data8 0x80b1ed4fd999ab6c, 0x80c83c56b50cf77f | |
189 | data8 0x80de8f3b8b85a0af, 0x80f4e5ff089f763e | |
190 | data8 0x810b40a1d81406d4, 0x81219f24a5baa59d | |
191 | data8 0x813801881d886f7b, 0x814e67cceb90502c | |
192 | data8 0x8164d1f3bc030773, 0x817b3ffd3b2f2e47 | |
193 | data8 0x8191b1ea15813bfd, 0x81a827baf7838b78 | |
194 | data8 0x81bea1708dde6055, 0x81d51f0b8557ec1c | |
195 | data8 0x81eba08c8ad4536f, 0x820225f44b55b33b | |
196 | data8 0x8218af4373fc25eb, 0x822f3c7ab205c89a | |
197 | data8 0x8245cd9ab2cec048, 0x825c62a423d13f0c | |
198 | data8 0x8272fb97b2a5894c, 0x828998760d01faf3 | |
199 | data8 0x82a0393fe0bb0ca8, 0x82b6ddf5dbc35906 | |
200 | // | |
201 | // 2^{0.b1 b2 b3 b4 b5} | |
202 | data8 0x8000000000000000, 0x82cd8698ac2ba1d7 | |
203 | data8 0x85aac367cc487b14, 0x88980e8092da8527 | |
204 | data8 0x8b95c1e3ea8bd6e6, 0x8ea4398b45cd53c0 | |
205 | data8 0x91c3d373ab11c336, 0x94f4efa8fef70961 | |
206 | data8 0x9837f0518db8a96f, 0x9b8d39b9d54e5538 | |
207 | data8 0x9ef5326091a111ad, 0xa27043030c496818 | |
208 | data8 0xa5fed6a9b15138ea, 0xa9a15ab4ea7c0ef8 | |
209 | data8 0xad583eea42a14ac6, 0xb123f581d2ac258f | |
210 | data8 0xb504f333f9de6484, 0xb8fbaf4762fb9ee9 | |
211 | data8 0xbd08a39f580c36be, 0xc12c4cca66709456 | |
212 | data8 0xc5672a115506dadd, 0xc9b9bd866e2f27a2 | |
213 | data8 0xce248c151f8480e3, 0xd2a81d91f12ae45a | |
214 | data8 0xd744fccad69d6af4, 0xdbfbb797daf23755 | |
215 | data8 0xe0ccdeec2a94e111, 0xe5b906e77c8348a8 | |
216 | data8 0xeac0c6e7dd24392e, 0xefe4b99bdcdaf5cb | |
217 | data8 0xf5257d152486cc2c, 0xfa83b2db722a033a | |
218 | LOCAL_OBJECT_END(T_table) | |
219 | ||
220 | ||
221 | ||
222 | .section .text | |
ba5b14c7 | 223 | WEAK_LIBM_ENTRY(exp2f) |
d5efd131 MF |
224 | |
225 | ||
226 | {.mfi | |
227 | alloc r32= ar.pfs, 1, 4, 4, 0 | |
228 | // will continue only for non-zero normal/denormal numbers | |
229 | fclass.nm p12, p0= f8, 0x1b | |
230 | // GR_TBL_START= pointer to C_1...C_2 followed by T_table | |
231 | addl GR_TBL_START= @ltoff(poly_coeffs), gp | |
232 | } | |
233 | {.mlx | |
234 | mov GR_OF_LIMIT= 0xffff + 7 // Exponent of overflow limit | |
235 | movl GR_ROUNDVAL= 0x5a400000 // 1.5*2^(63-10) (SP) | |
236 | } | |
237 | ;; | |
238 | ||
239 | // Form special constant 1.5*2^(63-10) to give integer part and first 10 | |
240 | // fractional bits of x | |
241 | {.mfi | |
242 | setf.s FR_ROUNDVAL= GR_ROUNDVAL // Form special constant | |
243 | fcmp.lt.s1 p6, p8= f8, f0 // X<0 ? | |
244 | nop.i 0 | |
245 | } | |
246 | {.mfb | |
247 | ld8 GR_COEFF_START= [ GR_TBL_START ] // Load pointer to coeff table | |
248 | nop.f 0 | |
249 | (p12) br.cond.spnt SPECIAL_exp2 // Branch if nan, inf, zero | |
250 | } | |
251 | ;; | |
252 | ||
253 | {.mlx | |
254 | setf.exp FR_OF_LIMIT= GR_OF_LIMIT // Set overflow limit | |
255 | movl GR_UF_LIMIT= 0xc3160000 // (-2^7-22) = -150 | |
256 | } | |
257 | ;; | |
258 | ||
259 | {.mfi | |
260 | ldfe FR_COEFF1= [ GR_COEFF_START ], 16 // load C_1 | |
261 | fma.s0 f8= f8, f1, f0 // normalize x | |
262 | nop.i 0 | |
263 | } | |
264 | ;; | |
265 | ||
266 | {.mmi | |
267 | ldfe FR_COEFF2= [ GR_COEFF_START ], 16 // load C_2 | |
268 | setf.s FR_UF_LIMIT= GR_UF_LIMIT // Set underflow limit | |
269 | mov GR_EXP_CORR= 0xffff-126 | |
270 | } | |
271 | ;; | |
272 | ||
273 | {.mfi | |
274 | nop.m 0 | |
275 | fma.s1 FR_KF0= f8, f1, FR_ROUNDVAL // y= x + 1.5*2^(63-10) | |
276 | nop.i 0 | |
277 | } | |
278 | ;; | |
279 | ||
280 | {.mfi | |
281 | mov GR_MASK= 1023 | |
282 | fms.s1 FR_KF= FR_KF0, f1, FR_ROUNDVAL // (K+f) | |
283 | mov GR_MASK_low= 31 | |
284 | } | |
285 | ;; | |
286 | ||
287 | {.mfi | |
288 | getf.sig GR_KF0= FR_KF0 // (K+f)*2^10= round_to_int(y) | |
289 | fcmp.ge.s1 p12, p7= f8, FR_OF_LIMIT // x >= overflow threshold ? | |
290 | add GR_LOG_TBL= 256, GR_COEFF_START // Pointer to high T_table | |
291 | } | |
292 | ;; | |
293 | ||
294 | {.mmi | |
295 | and GR_F_low= GR_KF0, GR_MASK_low // f_low | |
296 | and GR_F_high= GR_MASK, GR_KF0 // f_high*32 | |
297 | shr GR_K= GR_KF0, 10 // K | |
298 | } | |
299 | ;; | |
300 | ||
301 | {.mmi | |
302 | shladd GR_Flow_ADDR= GR_F_low, 3, GR_COEFF_START // address of 2^{f_low} | |
303 | add GR_BIAS= GR_K, GR_EXP_CORR // K= bias-2*63 | |
304 | shr GR_Fh= GR_F_high, 5 // f_high | |
305 | } | |
306 | ;; | |
307 | ||
308 | {.mfi | |
309 | setf.exp FR_2_TO_K= GR_BIAS // 2^{K-126} | |
310 | fnma.s1 FR_R= FR_KF, f1, f8 // r= x - (K+f) | |
311 | shladd GR_Fh_ADDR= GR_Fh, 3, GR_LOG_TBL // address of 2^{f_high} | |
312 | } | |
313 | {.mlx | |
314 | ldf8 FR_T_low= [ GR_Flow_ADDR ] // load T_low= 2^{f_low} | |
315 | movl GR_EMIN= 0xc2fc0000 // EMIN= -126 | |
316 | } | |
317 | ;; | |
318 | ||
319 | {.mfi | |
320 | ldf8 FR_T_high= [ GR_Fh_ADDR ] // load T_high= 2^{f_high} | |
321 | (p7) fcmp.lt.s1 p12, p7= f8, FR_UF_LIMIT // x<underflow threshold ? | |
322 | nop.i 0 | |
323 | } | |
324 | ;; | |
325 | ||
326 | {.mfb | |
327 | setf.s FR_EXPMIN= GR_EMIN // FR_EXPMIN= EMIN | |
328 | fma.s1 FR_P12= FR_COEFF2, FR_R, FR_COEFF1 // P12= C_1+C_2*r | |
329 | (p12) br.cond.spnt OUT_RANGE_exp2 | |
330 | } | |
331 | ;; | |
332 | ||
333 | {.mfi | |
334 | nop.m 0 | |
335 | fma.s1 FR_T_low_K= FR_T_low, FR_2_TO_K, f0 // T= 2^{K-126}*T_low | |
336 | nop.i 0 | |
337 | } | |
338 | ;; | |
339 | ||
340 | {.mfi | |
341 | nop.m 0 | |
342 | fma.s1 FR_P= FR_R, FR_P12, f0 // P= P12+r | |
343 | nop.i 0 | |
344 | } | |
345 | ;; | |
346 | ||
347 | {.mfi | |
348 | nop.m 0 | |
349 | fma.s1 FR_T= FR_T_low_K, FR_T_high, f0 // T= T*T_high | |
350 | nop.i 0 | |
351 | } | |
352 | ;; | |
353 | ||
354 | {.mfi | |
355 | nop.m 0 | |
356 | fcmp.lt.s0 p6, p8= f8, FR_EXPMIN // underflow (x<EMIN) ? | |
357 | nop.i 0 | |
358 | } | |
359 | ;; | |
360 | ||
361 | {.mfb | |
362 | nop.m 0 | |
363 | fma.s.s0 f8= FR_P, FR_T, FR_T // result= T+T*P | |
364 | (p8) br.ret.sptk b0 // return | |
365 | } | |
366 | ;; | |
367 | ||
368 | {.mfb | |
369 | (p6) mov GR_Parameter_TAG= 164 | |
370 | nop.f 0 | |
371 | (p6) br.cond.sptk __libm_error_region | |
372 | } | |
373 | ;; | |
374 | ||
375 | ||
376 | SPECIAL_exp2: | |
377 | {.mfi | |
378 | nop.m 0 | |
379 | fclass.m p6, p0= f8, 0x22 // x= -Infinity ? | |
380 | nop.i 0 | |
381 | } | |
382 | ;; | |
383 | ||
384 | {.mfi | |
385 | nop.m 0 | |
386 | fclass.m p7, p0= f8, 0x21 // x= +Infinity ? | |
387 | nop.i 0 | |
388 | } | |
389 | ;; | |
390 | ||
391 | {.mfi | |
392 | nop.m 0 | |
393 | fclass.m p8, p0= f8, 0x7 // x= +/-Zero ? | |
394 | nop.i 0 | |
395 | } | |
396 | {.mfb | |
397 | nop.m 0 | |
398 | (p6) mov f8= f0 // exp2(-Infinity)= 0 | |
399 | (p6) br.ret.spnt b0 | |
400 | } | |
401 | ;; | |
402 | ||
403 | {.mfb | |
404 | nop.m 0 | |
405 | nop.f 0 | |
406 | (p7) br.ret.spnt b0 // exp2(+Infinity)= +Infinity | |
407 | } | |
408 | ;; | |
409 | ||
410 | {.mfb | |
411 | nop.m 0 | |
412 | (p8) mov f8= f1 // exp2(+/-0)= 1 | |
413 | (p8) br.ret.spnt b0 | |
414 | } | |
415 | ;; | |
416 | ||
417 | {.mfb | |
418 | nop.m 0 | |
419 | fma.s.s0 f8= f8, f1, f0 // Remaining cases: NaNs | |
420 | br.ret.sptk b0 | |
421 | } | |
422 | ;; | |
423 | ||
424 | ||
425 | OUT_RANGE_exp2: | |
426 | ||
427 | // overflow: p8= 1 | |
428 | ||
429 | {.mii | |
430 | (p8) mov GR_EXPMAX= 0x1fffe | |
431 | nop.i 0 | |
432 | nop.i 0 | |
433 | } | |
434 | ;; | |
435 | ||
436 | {.mmb | |
437 | (p8) mov GR_Parameter_TAG= 163 | |
438 | (p8) setf.exp FR_R= GR_EXPMAX | |
439 | nop.b 999 | |
440 | } | |
441 | ;; | |
442 | ||
443 | {.mfi | |
444 | nop.m 999 | |
445 | (p8) fma.s.s0 f8= FR_R, FR_R, f0 // Create overflow | |
446 | nop.i 999 | |
447 | } | |
448 | // underflow: p6= 1 | |
449 | {.mii | |
450 | (p6) mov GR_Parameter_TAG= 164 | |
451 | (p6) mov GR_EXPMAX= 1 | |
452 | nop.i 0 | |
453 | } | |
454 | ;; | |
455 | ||
456 | {.mmb | |
457 | nop.m 0 | |
458 | (p6) setf.exp FR_R= GR_EXPMAX | |
459 | nop.b 999 | |
460 | } | |
461 | ;; | |
462 | ||
463 | {.mfb | |
464 | nop.m 999 | |
465 | (p6) fma.s.s0 f8= FR_R, FR_R, f0 // Create underflow | |
466 | nop.b 0 | |
467 | } | |
468 | ;; | |
469 | ||
ba5b14c7 | 470 | WEAK_LIBM_END(exp2f) |
c191f64c | 471 | libm_alias_float_other (__exp2, exp2) |
f5f0f526 | 472 | #ifdef SHARED |
ba5b14c7 | 473 | .symver exp2f,exp2f@@GLIBC_2.27 |
f5f0f526 SN |
474 | .weak __exp2f_compat |
475 | .set __exp2f_compat,__exp2f | |
476 | .symver __exp2f_compat,exp2f@GLIBC_2.2 | |
477 | #endif | |
d5efd131 MF |
478 | |
479 | ||
480 | LOCAL_LIBM_ENTRY(__libm_error_region) | |
481 | ||
482 | .prologue | |
483 | {.mfi | |
484 | add GR_Parameter_Y= -32, sp // Parameter 2 value | |
485 | nop.f 0 | |
486 | .save ar.pfs, GR_SAVE_PFS | |
487 | mov GR_SAVE_PFS= ar.pfs // Save ar.pfs | |
488 | } | |
489 | ||
490 | {.mfi | |
491 | .fframe 64 | |
492 | add sp= -64, sp // Create new stack | |
493 | nop.f 0 | |
494 | mov GR_SAVE_GP= gp // Save gp | |
495 | } | |
496 | ;; | |
497 | ||
498 | {.mmi | |
499 | stfs [ GR_Parameter_Y ]= FR_Y, 16 // STORE Parameter 2 on stack | |
500 | add GR_Parameter_X= 16, sp // Parameter 1 address | |
501 | .save b0, GR_SAVE_B0 | |
502 | mov GR_SAVE_B0= b0 // Save b0 | |
503 | } | |
504 | ;; | |
505 | ||
506 | .body | |
507 | {.mib | |
508 | stfs [ GR_Parameter_X ]= FR_X // STORE Parameter 1 on stack | |
509 | add GR_Parameter_RESULT= 0, GR_Parameter_Y // Parameter 3 address | |
510 | nop.b 0 | |
511 | } | |
512 | {.mib | |
513 | stfs [ GR_Parameter_Y ]= FR_RESULT // STORE Parameter 3 on stack | |
514 | add GR_Parameter_Y= -16, GR_Parameter_Y | |
515 | br.call.sptk b0= __libm_error_support# // Call error handling function | |
516 | } | |
517 | ;; | |
518 | ||
519 | {.mmi | |
520 | add GR_Parameter_RESULT= 48, sp | |
521 | nop.m 0 | |
522 | nop.i 0 | |
523 | } | |
524 | ;; | |
525 | ||
526 | {.mmi | |
527 | ldfs f8= [ GR_Parameter_RESULT ] // Get return result off stack | |
528 | .restore sp | |
529 | add sp= 64, sp // Restore stack pointer | |
530 | mov b0= GR_SAVE_B0 // Restore return address | |
531 | } | |
532 | ;; | |
533 | ||
534 | {.mib | |
535 | mov gp= GR_SAVE_GP // Restore gp | |
536 | mov ar.pfs= GR_SAVE_PFS // Restore ar.pfs | |
537 | br.ret.sptk b0 // Return | |
538 | } | |
539 | ;; | |
540 | ||
541 | ||
542 | LOCAL_LIBM_END(__libm_error_region) | |
543 | ||
544 | .type __libm_error_support#, @function | |
545 | .global __libm_error_support# |