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1 | .file "exp_m1.s" |
2 | ||
0ecb606c JJ |
3 | |
4 | // Copyright (c) 2000 - 2005, Intel Corporation | |
8da2915d | 5 | // All rights reserved. |
0ecb606c JJ |
6 | // |
7 | // Contributed 2000 by the Intel Numerics Group, Intel Corporation | |
aeb25823 AJ |
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. | |
0ecb606c JJ |
23 | |
24 | // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | |
25 | // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | |
8da2915d | 26 | // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
0ecb606c | 27 | // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS |
8da2915d | 28 | // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
0ecb606c JJ |
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 | |
8da2915d | 32 | // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING |
0ecb606c JJ |
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. | |
8da2915d | 35 | // |
0ecb606c JJ |
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 | // 04/04/00 Unwind support added | |
44 | // 08/15/00 Bundle added after call to __libm_error_support to properly | |
8da2915d | 45 | // set [the previously overwritten] GR_Parameter_RESULT. |
0ecb606c JJ |
46 | // 07/07/01 Improved speed of all paths |
47 | // 05/20/02 Cleaned up namespace and sf0 syntax | |
48 | // 11/20/02 Improved speed, algorithm based on exp | |
49 | // 03/31/05 Reformatted delimiters between data tables | |
50 | ||
51 | // API | |
52 | //============================================================== | |
53 | // double expm1(double) | |
54 | ||
55 | // Overview of operation | |
56 | //============================================================== | |
57 | // 1. Inputs of Nan, Inf, Zero, NatVal handled with special paths | |
58 | // | |
59 | // 2. |x| < 2^-60 | |
60 | // Result = x, computed by x + x*x to handle appropriate flags and rounding | |
61 | // | |
62 | // 3. 2^-60 <= |x| < 2^-2 | |
63 | // Result determined by 13th order Taylor series polynomial | |
64 | // expm1f(x) = x + Q2*x^2 + ... + Q13*x^13 | |
65 | // | |
66 | // 4. x < -48.0 | |
67 | // Here we know result is essentially -1 + eps, where eps only affects | |
68 | // rounded result. Set I. | |
69 | // | |
70 | // 5. x >= 709.7827 | |
71 | // Result overflows. Set I, O, and call error support | |
8da2915d | 72 | // |
0ecb606c JJ |
73 | // 6. 2^-2 <= x < 709.7827 or -48.0 <= x < -2^-2 |
74 | // This is the main path. The algorithm is described below: | |
8da2915d | 75 | |
0ecb606c JJ |
76 | // Take the input x. w is "how many log2/128 in x?" |
77 | // w = x * 128/log2 | |
78 | // n = int(w) | |
79 | // x = n log2/128 + r + delta | |
80 | ||
81 | // n = 128M + index_1 + 2^4 index_2 | |
82 | // x = M log2 + (log2/128) index_1 + (log2/8) index_2 + r + delta | |
83 | ||
84 | // exp(x) = 2^M 2^(index_1/128) 2^(index_2/8) exp(r) exp(delta) | |
85 | // Construct 2^M | |
86 | // Get 2^(index_1/128) from table_1; | |
87 | // Get 2^(index_2/8) from table_2; | |
88 | // Calculate exp(r) by series by 5th order polynomial | |
89 | // r = x - n (log2/128)_high | |
90 | // delta = - n (log2/128)_low | |
91 | // Calculate exp(delta) as 1 + delta | |
92 | ||
93 | ||
94 | // Special values | |
95 | //============================================================== | |
96 | // expm1(+0) = +0.0 | |
97 | // expm1(-0) = -0.0 | |
98 | ||
99 | // expm1(+qnan) = +qnan | |
100 | // expm1(-qnan) = -qnan | |
101 | // expm1(+snan) = +qnan | |
102 | // expm1(-snan) = -qnan | |
103 | ||
104 | // expm1(-inf) = -1.0 | |
105 | // expm1(+inf) = +inf | |
106 | ||
107 | // Overflow and Underflow | |
108 | //======================= | |
109 | // expm1(x) = largest double normal when | |
110 | // x = 709.7827 = 40862e42fefa39ef | |
111 | // | |
112 | // Underflow is handled as described in case 2 above. | |
113 | ||
114 | ||
115 | // Registers used | |
116 | //============================================================== | |
117 | // Floating Point registers used: | |
118 | // f8, input | |
119 | // f9 -> f15, f32 -> f75 | |
120 | ||
121 | // General registers used: | |
122 | // r14 -> r40 | |
123 | ||
124 | // Predicate registers used: | |
125 | // p6 -> p15 | |
126 | ||
127 | // Assembly macros | |
128 | //============================================================== | |
129 | ||
130 | rRshf = r14 | |
131 | rAD_TB1 = r15 | |
132 | rAD_T1 = r15 | |
133 | rAD_TB2 = r16 | |
134 | rAD_T2 = r16 | |
135 | rAD_Ln2_lo = r17 | |
136 | rAD_P = r17 | |
137 | ||
138 | rN = r18 | |
139 | rIndex_1 = r19 | |
140 | rIndex_2_16 = r20 | |
141 | ||
142 | rM = r21 | |
143 | rBiased_M = r21 | |
144 | rIndex_1_16 = r22 | |
145 | rSignexp_x = r23 | |
146 | rExp_x = r24 | |
147 | rSig_inv_ln2 = r25 | |
148 | ||
149 | rAD_Q1 = r26 | |
150 | rAD_Q2 = r27 | |
151 | rTmp = r27 | |
152 | rExp_bias = r28 | |
153 | rExp_mask = r29 | |
154 | rRshf_2to56 = r30 | |
155 | ||
156 | rGt_ln = r31 | |
157 | rExp_2tom56 = r31 | |
158 | ||
159 | ||
160 | GR_SAVE_B0 = r33 | |
161 | GR_SAVE_PFS = r34 | |
162 | GR_SAVE_GP = r35 | |
163 | GR_SAVE_SP = r36 | |
164 | ||
165 | GR_Parameter_X = r37 | |
166 | GR_Parameter_Y = r38 | |
167 | GR_Parameter_RESULT = r39 | |
168 | GR_Parameter_TAG = r40 | |
169 | ||
170 | ||
171 | FR_X = f10 | |
172 | FR_Y = f1 | |
173 | FR_RESULT = f8 | |
174 | ||
175 | fRSHF_2TO56 = f6 | |
176 | fINV_LN2_2TO63 = f7 | |
177 | fW_2TO56_RSH = f9 | |
178 | f2TOM56 = f11 | |
179 | fP5 = f12 | |
180 | fP54 = f50 | |
181 | fP5432 = f50 | |
182 | fP4 = f13 | |
183 | fP3 = f14 | |
184 | fP32 = f14 | |
185 | fP2 = f15 | |
186 | ||
187 | fLn2_by_128_hi = f33 | |
188 | fLn2_by_128_lo = f34 | |
189 | ||
190 | fRSHF = f35 | |
191 | fNfloat = f36 | |
192 | fW = f37 | |
193 | fR = f38 | |
194 | fF = f39 | |
195 | ||
196 | fRsq = f40 | |
197 | fRcube = f41 | |
198 | ||
199 | f2M = f42 | |
200 | fS1 = f43 | |
201 | fT1 = f44 | |
202 | ||
203 | fMIN_DBL_OFLOW_ARG = f45 | |
204 | fMAX_DBL_MINUS_1_ARG = f46 | |
205 | fMAX_DBL_NORM_ARG = f47 | |
206 | fP_lo = f51 | |
207 | fP_hi = f52 | |
208 | fP = f53 | |
209 | fS = f54 | |
210 | ||
211 | fNormX = f56 | |
212 | ||
213 | fWre_urm_f8 = f57 | |
214 | ||
215 | fGt_pln = f58 | |
216 | fTmp = f58 | |
217 | ||
218 | fS2 = f59 | |
219 | fT2 = f60 | |
220 | fSm1 = f61 | |
221 | ||
222 | fXsq = f62 | |
223 | fX6 = f63 | |
224 | fX4 = f63 | |
225 | fQ7 = f64 | |
226 | fQ76 = f64 | |
227 | fQ7654 = f64 | |
228 | fQ765432 = f64 | |
229 | fQ6 = f65 | |
230 | fQ5 = f66 | |
231 | fQ54 = f66 | |
232 | fQ4 = f67 | |
233 | fQ3 = f68 | |
234 | fQ32 = f68 | |
235 | fQ2 = f69 | |
236 | fQD = f70 | |
237 | fQDC = f70 | |
238 | fQDCBA = f70 | |
239 | fQDCBA98 = f70 | |
240 | fQDCBA98765432 = f70 | |
241 | fQC = f71 | |
242 | fQB = f72 | |
243 | fQBA = f72 | |
244 | fQA = f73 | |
245 | fQ9 = f74 | |
246 | fQ98 = f74 | |
247 | fQ8 = f75 | |
248 | ||
249 | // Data tables | |
250 | //============================================================== | |
251 | ||
252 | RODATA | |
253 | .align 16 | |
254 | ||
255 | // ************* DO NOT CHANGE ORDER OF THESE TABLES ******************** | |
256 | ||
257 | // double-extended 1/ln(2) | |
258 | // 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88 | |
259 | // 3fff b8aa 3b29 5c17 f0bc | |
260 | // For speed the significand will be loaded directly with a movl and setf.sig | |
261 | // and the exponent will be bias+63 instead of bias+0. Thus subsequent | |
262 | // computations need to scale appropriately. | |
263 | // The constant 128/ln(2) is needed for the computation of w. This is also | |
264 | // obtained by scaling the computations. | |
265 | // | |
266 | // Two shifting constants are loaded directly with movl and setf.d. | |
267 | // 1. fRSHF_2TO56 = 1.1000..00 * 2^(63-7) | |
268 | // This constant is added to x*1/ln2 to shift the integer part of | |
269 | // x*128/ln2 into the rightmost bits of the significand. | |
270 | // The result of this fma is fW_2TO56_RSH. | |
271 | // 2. fRSHF = 1.1000..00 * 2^(63) | |
272 | // This constant is subtracted from fW_2TO56_RSH * 2^(-56) to give | |
273 | // the integer part of w, n, as a floating-point number. | |
274 | // The result of this fms is fNfloat. | |
275 | ||
276 | ||
277 | LOCAL_OBJECT_START(exp_Table_1) | |
278 | data8 0x40862e42fefa39f0 // smallest dbl overflow arg | |
279 | data8 0xc048000000000000 // approx largest arg for minus one result | |
280 | data8 0x40862e42fefa39ef // largest dbl arg to give normal dbl result | |
281 | data8 0x0 // pad | |
282 | data8 0xb17217f7d1cf79ab , 0x00003ff7 // ln2/128 hi | |
283 | data8 0xc9e3b39803f2f6af , 0x00003fb7 // ln2/128 lo | |
284 | // | |
285 | // Table 1 is 2^(index_1/128) where | |
286 | // index_1 goes from 0 to 15 | |
287 | // | |
288 | data8 0x8000000000000000 , 0x00003FFF | |
289 | data8 0x80B1ED4FD999AB6C , 0x00003FFF | |
290 | data8 0x8164D1F3BC030773 , 0x00003FFF | |
291 | data8 0x8218AF4373FC25EC , 0x00003FFF | |
292 | data8 0x82CD8698AC2BA1D7 , 0x00003FFF | |
293 | data8 0x8383594EEFB6EE37 , 0x00003FFF | |
294 | data8 0x843A28C3ACDE4046 , 0x00003FFF | |
295 | data8 0x84F1F656379C1A29 , 0x00003FFF | |
296 | data8 0x85AAC367CC487B15 , 0x00003FFF | |
297 | data8 0x8664915B923FBA04 , 0x00003FFF | |
298 | data8 0x871F61969E8D1010 , 0x00003FFF | |
299 | data8 0x87DB357FF698D792 , 0x00003FFF | |
300 | data8 0x88980E8092DA8527 , 0x00003FFF | |
301 | data8 0x8955EE03618E5FDD , 0x00003FFF | |
302 | data8 0x8A14D575496EFD9A , 0x00003FFF | |
303 | data8 0x8AD4C6452C728924 , 0x00003FFF | |
304 | LOCAL_OBJECT_END(exp_Table_1) | |
305 | ||
306 | // Table 2 is 2^(index_1/8) where | |
307 | // index_2 goes from 0 to 7 | |
308 | LOCAL_OBJECT_START(exp_Table_2) | |
309 | data8 0x8000000000000000 , 0x00003FFF | |
310 | data8 0x8B95C1E3EA8BD6E7 , 0x00003FFF | |
311 | data8 0x9837F0518DB8A96F , 0x00003FFF | |
312 | data8 0xA5FED6A9B15138EA , 0x00003FFF | |
313 | data8 0xB504F333F9DE6484 , 0x00003FFF | |
314 | data8 0xC5672A115506DADD , 0x00003FFF | |
315 | data8 0xD744FCCAD69D6AF4 , 0x00003FFF | |
316 | data8 0xEAC0C6E7DD24392F , 0x00003FFF | |
317 | LOCAL_OBJECT_END(exp_Table_2) | |
318 | ||
319 | ||
320 | LOCAL_OBJECT_START(exp_p_table) | |
321 | data8 0x3f8111116da21757 //P5 | |
322 | data8 0x3fa55555d787761c //P4 | |
323 | data8 0x3fc5555555555414 //P3 | |
324 | data8 0x3fdffffffffffd6a //P2 | |
325 | LOCAL_OBJECT_END(exp_p_table) | |
326 | ||
327 | LOCAL_OBJECT_START(exp_Q1_table) | |
328 | data8 0x3de6124613a86d09 // QD = 1/13! | |
329 | data8 0x3e21eed8eff8d898 // QC = 1/12! | |
330 | data8 0x3ec71de3a556c734 // Q9 = 1/9! | |
331 | data8 0x3efa01a01a01a01a // Q8 = 1/8! | |
332 | data8 0x8888888888888889,0x3ff8 // Q5 = 1/5! | |
333 | data8 0xaaaaaaaaaaaaaaab,0x3ffc // Q3 = 1/3! | |
334 | data8 0x0,0x0 // Pad to avoid bank conflicts | |
335 | LOCAL_OBJECT_END(exp_Q1_table) | |
336 | ||
337 | LOCAL_OBJECT_START(exp_Q2_table) | |
338 | data8 0x3e5ae64567f544e4 // QB = 1/11! | |
339 | data8 0x3e927e4fb7789f5c // QA = 1/10! | |
340 | data8 0x3f2a01a01a01a01a // Q7 = 1/7! | |
341 | data8 0x3f56c16c16c16c17 // Q6 = 1/6! | |
342 | data8 0xaaaaaaaaaaaaaaab,0x3ffa // Q4 = 1/4! | |
343 | data8 0x8000000000000000,0x3ffe // Q2 = 1/2! | |
344 | LOCAL_OBJECT_END(exp_Q2_table) | |
8da2915d UD |
345 | |
346 | ||
0ecb606c JJ |
347 | .section .text |
348 | GLOBAL_IEEE754_ENTRY(expm1) | |
8da2915d | 349 | |
0ecb606c JJ |
350 | { .mlx |
351 | getf.exp rSignexp_x = f8 // Must recompute if x unorm | |
352 | movl rSig_inv_ln2 = 0xb8aa3b295c17f0bc // signif of 1/ln2 | |
8da2915d | 353 | } |
0ecb606c JJ |
354 | { .mlx |
355 | addl rAD_TB1 = @ltoff(exp_Table_1), gp | |
356 | movl rRshf_2to56 = 0x4768000000000000 // 1.10000 2^(63+56) | |
8da2915d | 357 | } |
0ecb606c | 358 | ;; |
8da2915d | 359 | |
0ecb606c JJ |
360 | // We do this fnorm right at the beginning to normalize |
361 | // any input unnormals so that SWA is not taken. | |
8da2915d | 362 | { .mfi |
0ecb606c JJ |
363 | ld8 rAD_TB1 = [rAD_TB1] |
364 | fclass.m p6,p0 = f8,0x0b // Test for x=unorm | |
365 | mov rExp_mask = 0x1ffff | |
8da2915d | 366 | } |
8da2915d | 367 | { .mfi |
0ecb606c JJ |
368 | mov rExp_bias = 0xffff |
369 | fnorm.s1 fNormX = f8 | |
370 | mov rExp_2tom56 = 0xffff-56 | |
8da2915d UD |
371 | } |
372 | ;; | |
373 | ||
0ecb606c JJ |
374 | // Form two constants we need |
375 | // 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128 | |
376 | // 1.1000..000 * 2^(63+63-7) to right shift int(w) into the significand | |
8da2915d | 377 | |
0ecb606c JJ |
378 | { .mfi |
379 | setf.sig fINV_LN2_2TO63 = rSig_inv_ln2 // form 1/ln2 * 2^63 | |
380 | fclass.m p8,p0 = f8,0x07 // Test for x=0 | |
381 | nop.i 0 | |
8da2915d | 382 | } |
8da2915d | 383 | { .mlx |
0ecb606c JJ |
384 | setf.d fRSHF_2TO56 = rRshf_2to56 // Form 1.100 * 2^(63+56) |
385 | movl rRshf = 0x43e8000000000000 // 1.10000 2^63 for rshift | |
8da2915d UD |
386 | } |
387 | ;; | |
388 | ||
8da2915d | 389 | { .mfi |
0ecb606c JJ |
390 | setf.exp f2TOM56 = rExp_2tom56 // form 2^-56 for scaling Nfloat |
391 | fclass.m p9,p0 = f8,0x22 // Test for x=-inf | |
392 | add rAD_TB2 = 0x140, rAD_TB1 // Point to Table 2 | |
8da2915d | 393 | } |
8da2915d | 394 | { .mib |
0ecb606c JJ |
395 | add rAD_Q1 = 0x1e0, rAD_TB1 // Point to Q table for small path |
396 | add rAD_Ln2_lo = 0x30, rAD_TB1 // Point to ln2_by_128_lo | |
397 | (p6) br.cond.spnt EXPM1_UNORM // Branch if x unorm | |
8da2915d UD |
398 | } |
399 | ;; | |
400 | ||
0ecb606c | 401 | EXPM1_COMMON: |
8da2915d | 402 | { .mfi |
0ecb606c JJ |
403 | ldfpd fMIN_DBL_OFLOW_ARG, fMAX_DBL_MINUS_1_ARG = [rAD_TB1],16 |
404 | fclass.m p10,p0 = f8,0x1e1 // Test for x=+inf, NaN, NaT | |
405 | add rAD_Q2 = 0x50, rAD_Q1 // Point to Q table for small path | |
8da2915d | 406 | } |
0ecb606c JJ |
407 | { .mfb |
408 | nop.m 0 | |
409 | nop.f 0 | |
410 | (p8) br.ret.spnt b0 // Exit for x=0, return x | |
8da2915d | 411 | } |
0ecb606c | 412 | ;; |
8da2915d UD |
413 | |
414 | { .mfi | |
0ecb606c JJ |
415 | ldfd fMAX_DBL_NORM_ARG = [rAD_TB1],16 |
416 | nop.f 0 | |
417 | and rExp_x = rExp_mask, rSignexp_x // Biased exponent of x | |
8da2915d | 418 | } |
0ecb606c JJ |
419 | { .mfb |
420 | setf.d fRSHF = rRshf // Form right shift const 1.100 * 2^63 | |
421 | (p9) fms.d.s0 f8 = f0,f0,f1 // quick exit for x=-inf | |
422 | (p9) br.ret.spnt b0 | |
8da2915d | 423 | } |
0ecb606c | 424 | ;; |
8da2915d UD |
425 | |
426 | { .mfi | |
0ecb606c JJ |
427 | ldfpd fQD, fQC = [rAD_Q1], 16 // Load coeff for small path |
428 | nop.f 0 | |
429 | sub rExp_x = rExp_x, rExp_bias // True exponent of x | |
8da2915d | 430 | } |
0ecb606c JJ |
431 | { .mfb |
432 | ldfpd fQB, fQA = [rAD_Q2], 16 // Load coeff for small path | |
433 | (p10) fma.d.s0 f8 = f8, f1, f0 // For x=+inf, NaN, NaT | |
434 | (p10) br.ret.spnt b0 // Exit for x=+inf, NaN, NaT | |
8da2915d | 435 | } |
0ecb606c | 436 | ;; |
8da2915d UD |
437 | |
438 | { .mfi | |
0ecb606c JJ |
439 | ldfpd fQ9, fQ8 = [rAD_Q1], 16 // Load coeff for small path |
440 | fma.s1 fXsq = fNormX, fNormX, f0 // x*x for small path | |
441 | cmp.gt p7, p8 = -2, rExp_x // Test |x| < 2^(-2) | |
8da2915d | 442 | } |
8da2915d | 443 | { .mfi |
0ecb606c JJ |
444 | ldfpd fQ7, fQ6 = [rAD_Q2], 16 // Load coeff for small path |
445 | nop.f 0 | |
446 | nop.i 0 | |
8da2915d | 447 | } |
0ecb606c | 448 | ;; |
8da2915d UD |
449 | |
450 | { .mfi | |
0ecb606c JJ |
451 | ldfe fQ5 = [rAD_Q1], 16 // Load coeff for small path |
452 | nop.f 0 | |
453 | nop.i 0 | |
8da2915d | 454 | } |
0ecb606c JJ |
455 | { .mib |
456 | ldfe fQ4 = [rAD_Q2], 16 // Load coeff for small path | |
457 | (p7) cmp.gt.unc p6, p7 = -60, rExp_x // Test |x| < 2^(-60) | |
458 | (p7) br.cond.spnt EXPM1_SMALL // Branch if 2^-60 <= |x| < 2^-2 | |
8da2915d | 459 | } |
0ecb606c | 460 | ;; |
8da2915d | 461 | |
0ecb606c JJ |
462 | // W = X * Inv_log2_by_128 |
463 | // By adding 1.10...0*2^63 we shift and get round_int(W) in significand. | |
464 | // We actually add 1.10...0*2^56 to X * Inv_log2 to do the same thing. | |
8da2915d UD |
465 | |
466 | { .mfi | |
0ecb606c JJ |
467 | ldfe fLn2_by_128_hi = [rAD_TB1],32 |
468 | fma.s1 fW_2TO56_RSH = fNormX, fINV_LN2_2TO63, fRSHF_2TO56 | |
469 | nop.i 0 | |
8da2915d | 470 | } |
8da2915d | 471 | { .mfb |
0ecb606c JJ |
472 | ldfe fLn2_by_128_lo = [rAD_Ln2_lo] |
473 | (p6) fma.d.s0 f8 = f8, f8, f8 // If x < 2^-60, result=x+x*x | |
474 | (p6) br.ret.spnt b0 // Exit if x < 2^-60 | |
8da2915d | 475 | } |
0ecb606c | 476 | ;; |
8da2915d | 477 | |
0ecb606c JJ |
478 | // Divide arguments into the following categories: |
479 | // Certain minus one p11 - -inf < x <= MAX_DBL_MINUS_1_ARG | |
480 | // Possible Overflow p14 - MAX_DBL_NORM_ARG < x < MIN_DBL_OFLOW_ARG | |
481 | // Certain Overflow p15 - MIN_DBL_OFLOW_ARG <= x < +inf | |
8da2915d | 482 | // |
0ecb606c JJ |
483 | // If the input is really a double arg, then there will never be "Possible |
484 | // Overflow" arguments. | |
8da2915d UD |
485 | // |
486 | ||
0ecb606c | 487 | // After that last load, rAD_TB1 points to the beginning of table 1 |
8da2915d UD |
488 | |
489 | { .mfi | |
0ecb606c JJ |
490 | nop.m 0 |
491 | fcmp.ge.s1 p15,p14 = fNormX,fMIN_DBL_OFLOW_ARG | |
492 | nop.i 0 | |
8da2915d | 493 | } |
0ecb606c | 494 | ;; |
8da2915d UD |
495 | |
496 | { .mfi | |
0ecb606c JJ |
497 | add rAD_P = 0x80, rAD_TB2 |
498 | fcmp.le.s1 p11,p0 = fNormX,fMAX_DBL_MINUS_1_ARG | |
499 | nop.i 0 | |
8da2915d | 500 | } |
0ecb606c | 501 | ;; |
8da2915d UD |
502 | |
503 | { .mfb | |
0ecb606c JJ |
504 | ldfpd fP5, fP4 = [rAD_P] ,16 |
505 | (p14) fcmp.gt.unc.s1 p14,p0 = fNormX,fMAX_DBL_NORM_ARG | |
506 | (p15) br.cond.spnt EXPM1_CERTAIN_OVERFLOW | |
8da2915d UD |
507 | } |
508 | ;; | |
509 | ||
0ecb606c JJ |
510 | // Nfloat = round_int(W) |
511 | // The signficand of fW_2TO56_RSH contains the rounded integer part of W, | |
512 | // as a twos complement number in the lower bits (that is, it may be negative). | |
513 | // That twos complement number (called N) is put into rN. | |
8da2915d | 514 | |
0ecb606c JJ |
515 | // Since fW_2TO56_RSH is scaled by 2^56, it must be multiplied by 2^-56 |
516 | // before the shift constant 1.10000 * 2^63 is subtracted to yield fNfloat. | |
517 | // Thus, fNfloat contains the floating point version of N | |
8da2915d | 518 | |
0ecb606c JJ |
519 | { .mfb |
520 | ldfpd fP3, fP2 = [rAD_P] | |
521 | fms.s1 fNfloat = fW_2TO56_RSH, f2TOM56, fRSHF | |
522 | (p11) br.cond.spnt EXPM1_CERTAIN_MINUS_ONE | |
8da2915d UD |
523 | } |
524 | ;; | |
525 | ||
8da2915d | 526 | { .mfi |
0ecb606c JJ |
527 | getf.sig rN = fW_2TO56_RSH |
528 | nop.f 0 | |
529 | nop.i 0 | |
8da2915d UD |
530 | } |
531 | ;; | |
532 | ||
0ecb606c JJ |
533 | // rIndex_1 has index_1 |
534 | // rIndex_2_16 has index_2 * 16 | |
535 | // rBiased_M has M | |
536 | // rIndex_1_16 has index_1 * 16 | |
8da2915d | 537 | |
0ecb606c JJ |
538 | // r = x - Nfloat * ln2_by_128_hi |
539 | // f = 1 - Nfloat * ln2_by_128_lo | |
8da2915d | 540 | { .mfi |
0ecb606c JJ |
541 | and rIndex_1 = 0x0f, rN |
542 | fnma.s1 fR = fNfloat, fLn2_by_128_hi, fNormX | |
543 | shr rM = rN, 0x7 | |
8da2915d | 544 | } |
8da2915d | 545 | { .mfi |
0ecb606c JJ |
546 | and rIndex_2_16 = 0x70, rN |
547 | fnma.s1 fF = fNfloat, fLn2_by_128_lo, f1 | |
548 | nop.i 0 | |
8da2915d | 549 | } |
0ecb606c | 550 | ;; |
8da2915d | 551 | |
0ecb606c JJ |
552 | // rAD_T1 has address of T1 |
553 | // rAD_T2 has address if T2 | |
8da2915d UD |
554 | |
555 | { .mmi | |
0ecb606c JJ |
556 | add rBiased_M = rExp_bias, rM |
557 | add rAD_T2 = rAD_TB2, rIndex_2_16 | |
558 | shladd rAD_T1 = rIndex_1, 4, rAD_TB1 | |
8da2915d | 559 | } |
0ecb606c | 560 | ;; |
8da2915d | 561 | |
0ecb606c JJ |
562 | // Create Scale = 2^M |
563 | // Load T1 and T2 | |
8da2915d | 564 | { .mmi |
0ecb606c JJ |
565 | setf.exp f2M = rBiased_M |
566 | ldfe fT2 = [rAD_T2] | |
567 | nop.i 0 | |
8da2915d | 568 | } |
0ecb606c | 569 | ;; |
8da2915d UD |
570 | |
571 | { .mfi | |
0ecb606c JJ |
572 | ldfe fT1 = [rAD_T1] |
573 | fmpy.s0 fTmp = fLn2_by_128_lo, fLn2_by_128_lo // Force inexact | |
574 | nop.i 0 | |
8da2915d | 575 | } |
0ecb606c | 576 | ;; |
8da2915d UD |
577 | |
578 | { .mfi | |
0ecb606c JJ |
579 | nop.m 0 |
580 | fma.s1 fP54 = fR, fP5, fP4 | |
581 | nop.i 0 | |
8da2915d | 582 | } |
8da2915d | 583 | { .mfi |
0ecb606c JJ |
584 | nop.m 0 |
585 | fma.s1 fP32 = fR, fP3, fP2 | |
586 | nop.i 0 | |
8da2915d | 587 | } |
0ecb606c | 588 | ;; |
8da2915d UD |
589 | |
590 | { .mfi | |
0ecb606c JJ |
591 | nop.m 0 |
592 | fma.s1 fRsq = fR, fR, f0 | |
593 | nop.i 0 | |
8da2915d | 594 | } |
0ecb606c | 595 | ;; |
8da2915d UD |
596 | |
597 | { .mfi | |
0ecb606c JJ |
598 | nop.m 0 |
599 | fma.s1 fP5432 = fRsq, fP54, fP32 | |
600 | nop.i 0 | |
8da2915d | 601 | } |
0ecb606c | 602 | ;; |
8da2915d UD |
603 | |
604 | { .mfi | |
0ecb606c JJ |
605 | nop.m 0 |
606 | fma.s1 fS2 = fF,fT2,f0 | |
607 | nop.i 0 | |
8da2915d | 608 | } |
8da2915d | 609 | { .mfi |
0ecb606c JJ |
610 | nop.m 0 |
611 | fma.s1 fS1 = f2M,fT1,f0 | |
612 | nop.i 0 | |
8da2915d | 613 | } |
0ecb606c | 614 | ;; |
8da2915d UD |
615 | |
616 | { .mfi | |
0ecb606c JJ |
617 | nop.m 0 |
618 | fma.s1 fP = fRsq, fP5432, fR | |
619 | nop.i 0 | |
8da2915d | 620 | } |
0ecb606c | 621 | ;; |
8da2915d UD |
622 | |
623 | { .mfi | |
0ecb606c JJ |
624 | nop.m 0 |
625 | fms.s1 fSm1 = fS1,fS2,f1 // S - 1.0 | |
626 | nop.i 0 | |
8da2915d | 627 | } |
8da2915d | 628 | { .mfb |
0ecb606c JJ |
629 | nop.m 0 |
630 | fma.s1 fS = fS1,fS2,f0 | |
631 | (p14) br.cond.spnt EXPM1_POSSIBLE_OVERFLOW | |
8da2915d | 632 | } |
0ecb606c | 633 | ;; |
8da2915d UD |
634 | |
635 | { .mfb | |
0ecb606c JJ |
636 | nop.m 0 |
637 | fma.d.s0 f8 = fS, fP, fSm1 | |
638 | br.ret.sptk b0 // Normal path exit | |
8da2915d | 639 | } |
0ecb606c | 640 | ;; |
8da2915d | 641 | |
0ecb606c JJ |
642 | // Here if 2^-60 <= |x| <2^-2 |
643 | // Compute 13th order polynomial | |
644 | EXPM1_SMALL: | |
645 | { .mmf | |
646 | ldfe fQ3 = [rAD_Q1], 16 | |
647 | ldfe fQ2 = [rAD_Q2], 16 | |
648 | fma.s1 fX4 = fXsq, fXsq, f0 | |
8da2915d | 649 | } |
0ecb606c | 650 | ;; |
8da2915d UD |
651 | |
652 | { .mfi | |
0ecb606c JJ |
653 | nop.m 0 |
654 | fma.s1 fQDC = fQD, fNormX, fQC | |
655 | nop.i 0 | |
8da2915d | 656 | } |
8da2915d | 657 | { .mfi |
0ecb606c JJ |
658 | nop.m 0 |
659 | fma.s1 fQBA = fQB, fNormX, fQA | |
660 | nop.i 0 | |
8da2915d | 661 | } |
0ecb606c | 662 | ;; |
8da2915d UD |
663 | |
664 | { .mfi | |
0ecb606c JJ |
665 | nop.m 0 |
666 | fma.s1 fQ98 = fQ9, fNormX, fQ8 | |
667 | nop.i 0 | |
8da2915d | 668 | } |
8da2915d | 669 | { .mfi |
0ecb606c JJ |
670 | nop.m 0 |
671 | fma.s1 fQ76= fQ7, fNormX, fQ6 | |
672 | nop.i 0 | |
8da2915d | 673 | } |
0ecb606c | 674 | ;; |
8da2915d UD |
675 | |
676 | { .mfi | |
0ecb606c JJ |
677 | nop.m 0 |
678 | fma.s1 fQ54 = fQ5, fNormX, fQ4 | |
679 | nop.i 0 | |
8da2915d | 680 | } |
0ecb606c | 681 | ;; |
8da2915d UD |
682 | |
683 | { .mfi | |
0ecb606c JJ |
684 | nop.m 0 |
685 | fma.s1 fX6 = fX4, fXsq, f0 | |
686 | nop.i 0 | |
8da2915d | 687 | } |
8da2915d | 688 | { .mfi |
0ecb606c JJ |
689 | nop.m 0 |
690 | fma.s1 fQ32= fQ3, fNormX, fQ2 | |
691 | nop.i 0 | |
8da2915d | 692 | } |
0ecb606c | 693 | ;; |
8da2915d UD |
694 | |
695 | { .mfi | |
0ecb606c JJ |
696 | nop.m 0 |
697 | fma.s1 fQDCBA = fQDC, fXsq, fQBA | |
698 | nop.i 0 | |
8da2915d | 699 | } |
8da2915d | 700 | { .mfi |
0ecb606c JJ |
701 | nop.m 0 |
702 | fma.s1 fQ7654 = fQ76, fXsq, fQ54 | |
703 | nop.i 0 | |
8da2915d | 704 | } |
0ecb606c | 705 | ;; |
8da2915d UD |
706 | |
707 | { .mfi | |
0ecb606c JJ |
708 | nop.m 0 |
709 | fma.s1 fQDCBA98 = fQDCBA, fXsq, fQ98 | |
710 | nop.i 0 | |
8da2915d | 711 | } |
8da2915d | 712 | { .mfi |
0ecb606c JJ |
713 | nop.m 0 |
714 | fma.s1 fQ765432 = fQ7654, fXsq, fQ32 | |
715 | nop.i 0 | |
8da2915d | 716 | } |
0ecb606c | 717 | ;; |
8da2915d UD |
718 | |
719 | { .mfi | |
0ecb606c JJ |
720 | nop.m 0 |
721 | fma.s1 fQDCBA98765432 = fQDCBA98, fX6, fQ765432 | |
722 | nop.i 0 | |
8da2915d | 723 | } |
0ecb606c | 724 | ;; |
8da2915d | 725 | |
0ecb606c JJ |
726 | { .mfb |
727 | nop.m 0 | |
728 | fma.d.s0 f8 = fQDCBA98765432, fXsq, fNormX | |
729 | br.ret.sptk b0 // Exit small branch | |
8da2915d | 730 | } |
0ecb606c | 731 | ;; |
8da2915d | 732 | |
8da2915d | 733 | |
0ecb606c | 734 | EXPM1_POSSIBLE_OVERFLOW: |
8da2915d | 735 | |
0ecb606c JJ |
736 | // Here if fMAX_DBL_NORM_ARG < x < fMIN_DBL_OFLOW_ARG |
737 | // This cannot happen if input is a double, only if input higher precision. | |
738 | // Overflow is a possibility, not a certainty. | |
8da2915d | 739 | |
0ecb606c JJ |
740 | // Recompute result using status field 2 with user's rounding mode, |
741 | // and wre set. If result is larger than largest double, then we have | |
742 | // overflow | |
8da2915d UD |
743 | |
744 | { .mfi | |
0ecb606c JJ |
745 | mov rGt_ln = 0x103ff // Exponent for largest dbl + 1 ulp |
746 | fsetc.s2 0x7F,0x42 // Get user's round mode, set wre | |
747 | nop.i 0 | |
8da2915d | 748 | } |
0ecb606c | 749 | ;; |
8da2915d UD |
750 | |
751 | { .mfi | |
0ecb606c JJ |
752 | setf.exp fGt_pln = rGt_ln // Create largest double + 1 ulp |
753 | fma.d.s2 fWre_urm_f8 = fS, fP, fSm1 // Result with wre set | |
754 | nop.i 0 | |
8da2915d | 755 | } |
0ecb606c | 756 | ;; |
8da2915d UD |
757 | |
758 | { .mfi | |
0ecb606c JJ |
759 | nop.m 0 |
760 | fsetc.s2 0x7F,0x40 // Turn off wre in sf2 | |
761 | nop.i 0 | |
8da2915d | 762 | } |
0ecb606c | 763 | ;; |
8da2915d UD |
764 | |
765 | { .mfi | |
0ecb606c JJ |
766 | nop.m 0 |
767 | fcmp.ge.s1 p6, p0 = fWre_urm_f8, fGt_pln // Test for overflow | |
768 | nop.i 0 | |
8da2915d | 769 | } |
0ecb606c | 770 | ;; |
8da2915d | 771 | |
0ecb606c JJ |
772 | { .mfb |
773 | nop.m 0 | |
774 | nop.f 0 | |
775 | (p6) br.cond.spnt EXPM1_CERTAIN_OVERFLOW // Branch if overflow | |
8da2915d | 776 | } |
0ecb606c | 777 | ;; |
8da2915d UD |
778 | |
779 | { .mfb | |
0ecb606c JJ |
780 | nop.m 0 |
781 | fma.d.s0 f8 = fS, fP, fSm1 | |
782 | br.ret.sptk b0 // Exit if really no overflow | |
8da2915d | 783 | } |
0ecb606c | 784 | ;; |
8da2915d | 785 | |
0ecb606c JJ |
786 | EXPM1_CERTAIN_OVERFLOW: |
787 | { .mmi | |
788 | sub rTmp = rExp_mask, r0, 1 | |
789 | ;; | |
790 | setf.exp fTmp = rTmp | |
791 | nop.i 0 | |
8da2915d | 792 | } |
0ecb606c | 793 | ;; |
8da2915d UD |
794 | |
795 | { .mfi | |
0ecb606c JJ |
796 | alloc r32=ar.pfs,1,4,4,0 |
797 | fmerge.s FR_X = f8,f8 | |
798 | nop.i 0 | |
8da2915d | 799 | } |
8da2915d | 800 | { .mfb |
0ecb606c JJ |
801 | mov GR_Parameter_TAG = 41 |
802 | fma.d.s0 FR_RESULT = fTmp, fTmp, f0 // Set I,O and +INF result | |
803 | br.cond.sptk __libm_error_region | |
8da2915d | 804 | } |
0ecb606c | 805 | ;; |
8da2915d | 806 | |
0ecb606c JJ |
807 | // Here if x unorm |
808 | EXPM1_UNORM: | |
8da2915d | 809 | { .mfb |
0ecb606c JJ |
810 | getf.exp rSignexp_x = fNormX // Must recompute if x unorm |
811 | fcmp.eq.s0 p6, p0 = f8, f0 // Set D flag | |
812 | br.cond.sptk EXPM1_COMMON | |
8da2915d | 813 | } |
0ecb606c | 814 | ;; |
8da2915d | 815 | |
0ecb606c JJ |
816 | // here if result will be -1 and inexact, x <= -48.0 |
817 | EXPM1_CERTAIN_MINUS_ONE: | |
818 | { .mmi | |
819 | mov rTmp = 1 | |
820 | ;; | |
821 | setf.exp fTmp = rTmp | |
822 | nop.i 0 | |
8da2915d | 823 | } |
0ecb606c | 824 | ;; |
8da2915d | 825 | |
8da2915d | 826 | { .mfb |
0ecb606c JJ |
827 | nop.m 0 |
828 | fms.d.s0 FR_RESULT = fTmp, fTmp, f1 // Set I, rounded -1+eps result | |
829 | br.ret.sptk b0 | |
8da2915d | 830 | } |
0ecb606c JJ |
831 | ;; |
832 | ||
833 | GLOBAL_IEEE754_END(expm1) | |
8da2915d | 834 | |
0ecb606c JJ |
835 | |
836 | LOCAL_LIBM_ENTRY(__libm_error_region) | |
8da2915d | 837 | .prologue |
8da2915d UD |
838 | { .mfi |
839 | add GR_Parameter_Y=-32,sp // Parameter 2 value | |
840 | nop.f 0 | |
841 | .save ar.pfs,GR_SAVE_PFS | |
842 | mov GR_SAVE_PFS=ar.pfs // Save ar.pfs | |
843 | } | |
844 | { .mfi | |
845 | .fframe 64 | |
0ecb606c | 846 | add sp=-64,sp // Create new stack |
8da2915d | 847 | nop.f 0 |
0ecb606c | 848 | mov GR_SAVE_GP=gp // Save gp |
8da2915d | 849 | };; |
8da2915d UD |
850 | { .mmi |
851 | stfd [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack | |
0ecb606c | 852 | add GR_Parameter_X = 16,sp // Parameter 1 address |
8da2915d | 853 | .save b0, GR_SAVE_B0 |
0ecb606c | 854 | mov GR_SAVE_B0=b0 // Save b0 |
8da2915d | 855 | };; |
8da2915d | 856 | .body |
8da2915d | 857 | { .mib |
0ecb606c | 858 | stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack |
8da2915d | 859 | add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address |
0ecb606c | 860 | nop.b 0 |
8da2915d UD |
861 | } |
862 | { .mib | |
0ecb606c | 863 | stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack |
8da2915d | 864 | add GR_Parameter_Y = -16,GR_Parameter_Y |
0ecb606c | 865 | br.call.sptk b0=__libm_error_support# // Call error handling function |
8da2915d UD |
866 | };; |
867 | { .mmi | |
8da2915d | 868 | add GR_Parameter_RESULT = 48,sp |
0ecb606c JJ |
869 | nop.m 0 |
870 | nop.i 0 | |
8da2915d | 871 | };; |
8da2915d UD |
872 | { .mmi |
873 | ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack | |
874 | .restore sp | |
875 | add sp = 64,sp // Restore stack pointer | |
876 | mov b0 = GR_SAVE_B0 // Restore return address | |
877 | };; | |
878 | { .mib | |
879 | mov gp = GR_SAVE_GP // Restore gp | |
880 | mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs | |
881 | br.ret.sptk b0 // Return | |
882 | };; | |
883 | ||
0ecb606c | 884 | LOCAL_LIBM_END(__libm_error_region) |
8da2915d UD |
885 | .type __libm_error_support#,@function |
886 | .global __libm_error_support# |