| blob | 5edd877db94301b9a45541d8009fc1e1ea8373f2 |
1 .file "exp10.s"
4 // Copyright (c) 2000 - 2005, Intel Corporation
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7 //
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35 // Intel Corporation is the author of this code, and requests that all
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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 // 09/06/02 Improved performance; no inexact flags on exact cases
44 // 01/29/03 Added missing } to bundle templates
45 // 12/16/04 Call error handling on underflow.
46 // 03/31/05 Reformatted delimiters between data tables
47 //
48 // API
49 //==============================================================
50 // double exp10(double)
51 //
52 // Overview of operation
53 //==============================================================
54 // Background
55 //
56 // Implementation
57 //
58 // Let x= (K + fh + fl + r)/log2(10), where
59 // K is an integer, fh= 0.b1 b2 b3 b4 b5,
60 // fl= 2^{-5}* 0.b6 b7 b8 b8 b10 (fh, fl >= 0),
61 // and |r|<2^{-11}
62 // Th is a table that stores 2^fh (32 entries) rounded to
63 // double extended precision (only mantissa is stored)
64 // Tl is a table that stores 2^fl (32 entries) rounded to
65 // double extended precision (only mantissa is stored)
66 //
67 // 10^x is approximated as
68 // 2^K * Th [ f ] * Tl [ f ] * (1+c1*e+c1*r+c2*r^2+c3*r^3+c4*r^4),
69 // where e= (x*log2(10)_hi-RN(x*log2(10)_hi))+log2(10)_lo*x
71 // Note there are only 22 non-zero values that produce an exact result:
72 // 1.0, 2.0, ... 22.0.
73 // We test for these cases and use s1 to avoid setting the inexact flag.
75 // Special values
76 //==============================================================
77 // exp10(0)= 1
78 // exp10(+inf)= inf
79 // exp10(-inf)= 0
80 //
82 // Registers used
83 //==============================================================
84 // r2-r3, r14-r40
85 // f6-f15, f32-f52
86 // p6-p12
87 //
89 #include <shlib-compat.h>
92 GR_TBL_START = r2
93 GR_LOG_TBL = r3
95 GR_OF_LIMIT = r14
96 GR_UF_LIMIT = r15
97 GR_EXP_CORR = r16
98 GR_F_low = r17
99 GR_F_high = r18
100 GR_K = r19
101 GR_Flow_ADDR = r20
103 GR_BIAS = r21
104 GR_Fh = r22
105 GR_Fh_ADDR = r23
106 GR_EXPMAX = r24
107 GR_BIAS53 = r25
109 GR_ROUNDVAL = r26
110 GR_SNORM_LIMIT = r26
111 GR_MASK = r27
112 GR_KF0 = r28
113 GR_MASK_low = r29
114 GR_COEFF_START = r30
115 GR_exact_limit = r31
117 GR_SAVE_B0 = r33
118 GR_SAVE_PFS = r34
119 GR_SAVE_GP = r35
120 GR_SAVE_SP = r36
122 GR_Parameter_X = r37
123 GR_Parameter_Y = r38
124 GR_Parameter_RESULT = r39
125 GR_Parameter_TAG = r40
128 FR_X = f10
129 FR_Y = f1
130 FR_RESULT = f8
133 FR_COEFF1 = f6
134 FR_COEFF2 = f7
135 FR_R = f9
136 FR_LOG2_10 = f10
138 FR_2P53 = f11
139 FR_KF0 = f12
140 FR_COEFF3 = f13
141 FR_COEFF4 = f14
142 FR_UF_LIMIT = f15
144 FR_OF_LIMIT = f32
145 FR_DX_L210 = f33
146 FR_ROUNDVAL = f34
147 FR_KF = f35
149 FR_2_TO_K = f36
150 FR_T_low = f37
151 FR_T_high = f38
152 FR_P34 = f39
153 FR_R2 = f40
155 FR_P12 = f41
156 FR_T_low_K = f42
157 FR_P14 = f43
158 FR_T = f44
159 FR_P = f45
161 FR_L2_10_low = f46
162 FR_L2_10_high = f47
163 FR_E0 = f48
164 FR_E = f49
165 FR_exact_limit = f50
167 FR_int_x = f51
168 FR_SNORM_LIMIT = f52
171 // Data tables
172 //==============================================================
174 RODATA
176 .align 16
178 LOCAL_OBJECT_START(poly_coeffs)
180 data8 0xd49a784bcd1b8afe, 0x00003fcb // log2(10)*2^(10-63)
181 data8 0x9257edfe9b5fb698, 0x3fbf // log2(10)_low (bits 64...127)
182 data8 0x3fac6b08d704a0c0, 0x3f83b2ab6fba4e77 // C_3 and C_4
183 data8 0xb17217f7d1cf79ab, 0x00003ffe // C_1
184 data8 0xf5fdeffc162c7541, 0x00003ffc // C_2
185 LOCAL_OBJECT_END(poly_coeffs)
188 LOCAL_OBJECT_START(T_table)
190 // 2^{0.00000 b6 b7 b8 b9 b10}
191 data8 0x8000000000000000, 0x8016302f17467628
192 data8 0x802c6436d0e04f50, 0x80429c17d77c18ed
193 data8 0x8058d7d2d5e5f6b0, 0x806f17687707a7af
194 data8 0x80855ad965e88b83, 0x809ba2264dada76a
195 data8 0x80b1ed4fd999ab6c, 0x80c83c56b50cf77f
196 data8 0x80de8f3b8b85a0af, 0x80f4e5ff089f763e
197 data8 0x810b40a1d81406d4, 0x81219f24a5baa59d
198 data8 0x813801881d886f7b, 0x814e67cceb90502c
199 data8 0x8164d1f3bc030773, 0x817b3ffd3b2f2e47
200 data8 0x8191b1ea15813bfd, 0x81a827baf7838b78
201 data8 0x81bea1708dde6055, 0x81d51f0b8557ec1c
202 data8 0x81eba08c8ad4536f, 0x820225f44b55b33b
203 data8 0x8218af4373fc25eb, 0x822f3c7ab205c89a
204 data8 0x8245cd9ab2cec048, 0x825c62a423d13f0c
205 data8 0x8272fb97b2a5894c, 0x828998760d01faf3
206 data8 0x82a0393fe0bb0ca8, 0x82b6ddf5dbc35906
207 //
208 // 2^{0.b1 b2 b3 b4 b5}
209 data8 0x8000000000000000, 0x82cd8698ac2ba1d7
210 data8 0x85aac367cc487b14, 0x88980e8092da8527
211 data8 0x8b95c1e3ea8bd6e6, 0x8ea4398b45cd53c0
212 data8 0x91c3d373ab11c336, 0x94f4efa8fef70961
213 data8 0x9837f0518db8a96f, 0x9b8d39b9d54e5538
214 data8 0x9ef5326091a111ad, 0xa27043030c496818
215 data8 0xa5fed6a9b15138ea, 0xa9a15ab4ea7c0ef8
216 data8 0xad583eea42a14ac6, 0xb123f581d2ac258f
217 data8 0xb504f333f9de6484, 0xb8fbaf4762fb9ee9
218 data8 0xbd08a39f580c36be, 0xc12c4cca66709456
219 data8 0xc5672a115506dadd, 0xc9b9bd866e2f27a2
220 data8 0xce248c151f8480e3, 0xd2a81d91f12ae45a
221 data8 0xd744fccad69d6af4, 0xdbfbb797daf23755
222 data8 0xe0ccdeec2a94e111, 0xe5b906e77c8348a8
223 data8 0xeac0c6e7dd24392e, 0xefe4b99bdcdaf5cb
224 data8 0xf5257d152486cc2c, 0xfa83b2db722a033a
225 LOCAL_OBJECT_END(T_table)
229 .section .text
230 GLOBAL_IEEE754_ENTRY(exp10)
233 {.mfi
234 alloc r32= ar.pfs, 1, 4, 4, 0
235 // will continue only for non-zero normal/denormal numbers
236 fclass.nm.unc p12, p7= f8, 0x1b
237 mov GR_BIAS53= 0xffff+63-10
238 }
239 {.mlx
240 // GR_TBL_START= pointer to log2(10), C_1...C_4 followed by T_table
241 addl GR_TBL_START= @ltoff(poly_coeffs), gp
242 movl GR_ROUNDVAL= 0x3fc00000 // 1.5 (SP)
243 }
244 ;;
246 {.mfi
247 ld8 GR_COEFF_START= [ GR_TBL_START ] // Load pointer to coeff table
248 fcmp.lt.s1 p6, p8= f8, f0 // X<0 ?
249 nop.i 0
250 }
251 ;;
253 {.mlx
254 setf.exp FR_2P53= GR_BIAS53 // 2^{63-10}
255 movl GR_UF_LIMIT= 0xc07439b746e36b52 // (-2^10-51) / log2(10)
256 }
257 {.mlx
258 setf.s FR_ROUNDVAL= GR_ROUNDVAL
259 movl GR_OF_LIMIT= 0x40734413509f79fe // Overflow threshold
260 }
261 ;;
263 {.mlx
264 ldfe FR_LOG2_10= [ GR_COEFF_START ], 16 // load log2(10)*2^(10-63)
265 movl GR_SNORM_LIMIT= 0xc0733a7146f72a41 // Smallest normal threshold
266 }
267 {.mib
268 nop.m 0
269 nop.i 0
270 (p12) br.cond.spnt SPECIAL_exp10 // Branch if nan, inf, zero
271 }
272 ;;
274 {.mmf
275 ldfe FR_L2_10_low= [ GR_COEFF_START ], 16 // load log2(10)_low
276 setf.d FR_OF_LIMIT= GR_OF_LIMIT // Set overflow limit
277 fma.s0 f8= f8, f1, f0 // normalize x
278 }
279 ;;
281 {.mfi
282 ldfpd FR_COEFF3, FR_COEFF4= [ GR_COEFF_START ], 16 // load C_3, C_4
283 (p8) fcvt.fx.s1 FR_int_x = f8 // Convert x to integer
284 nop.i 0
285 }
286 {.mfi
287 setf.d FR_UF_LIMIT= GR_UF_LIMIT // Set underflow limit
288 fma.s1 FR_KF0= f8, FR_LOG2_10, FR_ROUNDVAL // y= (x*log2(10)*2^10 +
289 // 1.5*2^63) * 2^(-63)
290 mov GR_EXP_CORR= 0xffff-126
291 }
292 ;;
294 {.mfi
295 setf.d FR_SNORM_LIMIT= GR_SNORM_LIMIT // Set smallest normal limit
296 fma.s1 FR_L2_10_high= FR_LOG2_10, FR_2P53, f0 // FR_LOG2_10= log2(10)_hi
297 nop.i 0
298 }
299 ;;
301 {.mfi
302 ldfe FR_COEFF1= [ GR_COEFF_START ], 16 // load C_1
303 fms.s1 FR_KF= FR_KF0, f1, FR_ROUNDVAL // (K+f)*2^(10-63)
304 mov GR_MASK= 1023
305 }
306 ;;
308 {.mfi
309 ldfe FR_COEFF2= [ GR_COEFF_START ], 16 // load C_2
310 fma.s1 FR_LOG2_10= f8, FR_L2_10_high, f0 // y0= x*log2(10)_hi
311 mov GR_MASK_low= 31
312 }
313 ;;
315 {.mlx
316 getf.sig GR_KF0= FR_KF0 // (K+f)*2^10= round_to_int(y)
317 (p8) movl GR_exact_limit= 0x41b00000 // Largest x for exact result,
318 // +22.0
319 }
320 ;;
322 {.mfi
323 add GR_LOG_TBL= 256, GR_COEFF_START // Pointer to high T_table
324 fcmp.gt.s1 p12, p7= f8, FR_OF_LIMIT // x>overflow threshold ?
325 nop.i 0
326 }
327 ;;
329 {.mfi
330 (p8) setf.s FR_exact_limit = GR_exact_limit // Largest x for exact result
331 (p8) fcvt.xf FR_int_x = FR_int_x // Integral part of x
332 shr GR_K= GR_KF0, 10 // K
333 }
334 {.mfi
335 and GR_F_high= GR_MASK, GR_KF0 // f_high*32
336 fnma.s1 FR_R= FR_KF, FR_2P53, FR_LOG2_10 // r= x*log2(10)-2^{63-10}*
337 // [ (K+f)*2^{10-63} ]
338 and GR_F_low= GR_KF0, GR_MASK_low // f_low
339 }
340 ;;
342 {.mmi
343 shladd GR_Flow_ADDR= GR_F_low, 3, GR_COEFF_START // address of 2^{f_low}
344 add GR_BIAS= GR_K, GR_EXP_CORR // K= bias-2*63
345 shr GR_Fh= GR_F_high, 5 // f_high
346 }
347 ;;
349 {.mfi
350 setf.exp FR_2_TO_K= GR_BIAS // 2^{K-126}
351 (p7) fcmp.lt.s1 p12, p7= f8, FR_UF_LIMIT // x<underflow threshold ?
352 shladd GR_Fh_ADDR= GR_Fh, 3, GR_LOG_TBL // address of 2^{f_high}
353 }
354 {.mfi
355 ldf8 FR_T_low= [ GR_Flow_ADDR ] // load T_low= 2^{f_low}
356 fms.s1 FR_DX_L210= f8, FR_L2_10_high, FR_LOG2_10 // x*log2(10)_hi-
357 // RN(x*log2(10)_hi)
358 nop.i 0
359 }
360 ;;
362 {.mfi
363 ldf8 FR_T_high= [ GR_Fh_ADDR ] // load T_high= 2^{f_high}
364 fma.s1 FR_P34= FR_COEFF4, FR_R, FR_COEFF3 // P34= C_3+C_4*r
365 nop.i 0
366 }
367 {.mfb
368 nop.m 0
369 fma.s1 FR_R2= FR_R, FR_R, f0 // r*r
370 (p12) br.cond.spnt OUT_RANGE_exp10
371 }
372 ;;
374 {.mfi
375 nop.m 0
376 // e= (x*log2(10)_hi-RN(x*log2(10)_hi))+log2(10)_lo*x
377 fma.s1 FR_E0= f8, FR_L2_10_low, FR_DX_L210
378 cmp.eq p7,p9= r0,r0 // Assume inexact result
379 }
380 {.mfi
381 nop.m 0
382 fma.s1 FR_P12= FR_COEFF2, FR_R, FR_COEFF1 // P12= C_1+C_2*r
383 nop.i 0
384 }
385 ;;
387 {.mfi
388 nop.m 0
389 (p8) fcmp.eq.s1 p9,p7= FR_int_x, f8 // Test x positive integer
390 nop.i 0
391 }
392 {.mfi
393 nop.m 0
394 fma.s1 FR_T_low_K= FR_T_low, FR_2_TO_K, f0 // T= 2^{K-126}*T_low
395 nop.i 0
396 }
397 ;;
399 {.mfi
400 nop.m 0
401 fcmp.ge.s1 p11,p0= f8, FR_SNORM_LIMIT // Test x for normal range
402 nop.i 0
403 }
404 ;;
406 {.mfi
407 nop.m 0
408 fma.s1 FR_E= FR_E0, FR_COEFF1, f0 // E= C_1*e
409 nop.i 0
410 }
411 {.mfi
412 nop.m 0
413 fma.s1 FR_P14= FR_R2, FR_P34, FR_P12 // P14= P12+r2*P34
414 nop.i 0
415 }
416 ;;
418 // If x a positive integer, will it produce an exact result?
419 // p7 result will be inexact
420 // p9 result will be exact
421 {.mfi
422 nop.m 0
423 (p9) fcmp.le.s1 p9,p7= f8, FR_exact_limit // Test x gives exact result
424 nop.i 0
425 }
426 {.mfi
427 nop.m 0
428 fma.s1 FR_T= FR_T_low_K, FR_T_high, f0 // T= T*T_high
429 nop.i 0
430 }
431 ;;
433 {.mfi
434 nop.m 0
435 fma.s1 FR_P= FR_P14, FR_R, FR_E // P= P14*r+E
436 nop.i 0
437 }
438 ;;
440 .pred.rel "mutex",p7,p9
441 {.mfi
442 nop.m 0
443 (p7) fma.d.s0 f8= FR_P, FR_T, FR_T // result= T+T*P, inexact set
444 nop.i 0
445 }
446 {.mfb
447 nop.m 0
448 (p9) fma.d.s1 f8= FR_P, FR_T, FR_T // result= T+T*P, exact use s1
449 (p11) br.ret.sptk b0 // return, if result normal
450 }
451 ;;
453 // Here if result in denormal range (and not zero)
454 {.mib
455 nop.m 0
456 mov GR_Parameter_TAG= 265
457 br.cond.sptk __libm_error_region // Branch to error handling
458 }
459 ;;
461 SPECIAL_exp10:
462 {.mfi
463 nop.m 0
464 fclass.m p6, p0= f8, 0x22 // x= -Infinity ?
465 nop.i 0
466 }
467 ;;
469 {.mfi
470 nop.m 0
471 fclass.m p7, p0= f8, 0x21 // x= +Infinity ?
472 nop.i 0
473 }
474 ;;
476 {.mfi
477 nop.m 0
478 fclass.m p8, p0= f8, 0x7 // x= +/-Zero ?
479 nop.i 0
480 }
481 {.mfb
482 nop.m 0
483 (p6) mov f8= f0 // exp10(-Infinity)= 0
484 (p6) br.ret.spnt b0
485 }
486 ;;
488 {.mfb
489 nop.m 0
490 nop.f 0
491 (p7) br.ret.spnt b0 // exp10(+Infinity)= +Infinity
492 }
493 ;;
495 {.mfb
496 nop.m 0
497 (p8) mov f8= f1 // exp10(+/-0)= 1
498 (p8) br.ret.spnt b0
499 }
500 ;;
502 {.mfb
503 nop.m 0
504 fma.d.s0 f8= f8, f1, f0 // Remaining cases: NaNs
505 br.ret.sptk b0
506 }
507 ;;
510 OUT_RANGE_exp10:
512 // underflow: p6= 1
513 // overflow: p8= 1
515 .pred.rel "mutex",p6,p8
516 {.mmi
517 (p8) mov GR_EXPMAX= 0x1fffe
518 (p6) mov GR_EXPMAX= 1
519 nop.i 0
520 }
521 ;;
523 {.mii
524 setf.exp FR_R= GR_EXPMAX
525 (p8) mov GR_Parameter_TAG= 166
526 (p6) mov GR_Parameter_TAG= 265
527 }
528 ;;
530 {.mfb
531 nop.m 0
532 fma.d.s0 f8= FR_R, FR_R, f0 // Create overflow/underflow
533 br.cond.sptk __libm_error_region // Branch to error handling
534 }
535 ;;
537 GLOBAL_IEEE754_END(exp10)
538 libm_alias_double_other (__exp10, exp10)
539 #if SHLIB_COMPAT (libm, GLIBC_2_1, GLIBC_2_27)
540 compat_symbol (libm, exp10, pow10, GLIBC_2_2)
541 #endif
544 LOCAL_LIBM_ENTRY(__libm_error_region)
546 .prologue
547 {.mfi
548 add GR_Parameter_Y= -32, sp // Parameter 2 value
549 nop.f 0
550 .save ar.pfs, GR_SAVE_PFS
551 mov GR_SAVE_PFS= ar.pfs // Save ar.pfs
552 }
554 {.mfi
555 .fframe 64
556 add sp= -64, sp // Create new stack
557 nop.f 0
558 mov GR_SAVE_GP= gp // Save gp
559 }
560 ;;
562 {.mmi
563 stfd [ GR_Parameter_Y ]= FR_Y, 16 // STORE Parameter 2 on stack
564 add GR_Parameter_X= 16, sp // Parameter 1 address
565 .save b0, GR_SAVE_B0
566 mov GR_SAVE_B0= b0 // Save b0
567 }
568 ;;
570 .body
571 {.mib
572 stfd [ GR_Parameter_X ]= FR_X // STORE Parameter 1 on stack
573 add GR_Parameter_RESULT= 0, GR_Parameter_Y // Parameter 3 address
574 nop.b 0
575 }
576 {.mib
577 stfd [ GR_Parameter_Y ]= FR_RESULT // STORE Parameter 3 on stack
578 add GR_Parameter_Y= -16, GR_Parameter_Y
579 br.call.sptk b0= __libm_error_support# // Call error handling function
580 }
581 ;;
583 {.mmi
584 add GR_Parameter_RESULT= 48, sp
585 nop.m 0
586 nop.i 0
587 }
588 ;;
590 {.mmi
591 ldfd f8= [ GR_Parameter_RESULT ] // Get return result off stack
592 .restore sp
593 add sp= 64, sp // Restore stack pointer
594 mov b0= GR_SAVE_B0 // Restore return address
595 }
596 ;;
598 {.mib
599 mov gp= GR_SAVE_GP // Restore gp
600 mov ar.pfs= GR_SAVE_PFS // Restore ar.pfs
601 br.ret.sptk b0 // Return
602 }
603 ;;
606 LOCAL_LIBM_END(__libm_error_region)
608 .type __libm_error_support#, @function
609 .global __libm_error_support#