```   1 /*
3  *
4  * The contents of this file are subject to the terms of the
6  * You may not use this file except in compliance with the License.
7  *
8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9  * or http://www.opensolaris.org/os/licensing.
10  * See the License for the specific language governing permissions
11  * and limitations under the License.
12  *
13  * When distributing Covered Code, include this CDDL HEADER in each
15  * If applicable, add the following below this CDDL HEADER, with the
16  * fields enclosed by brackets "[]" replaced with your own identifying
18  *
20  */
21
22 /*
24  */
25 /*
27  * Use is subject to license terms.
28  */
29
30 #include <sys/isa_defs.h>
31 #include "libm_inlines.h"
32
33 #ifdef _LITTLE_ENDIAN
34 #define HI(x)   *(1+(int*)x)
35 #define LO(x)   *(unsigned*)x
36 #else
37 #define HI(x)   *(int*)x
38 #define LO(x)   *(1+(unsigned*)x)
39 #endif
40
41 #ifdef __RESTRICT
42 #define restrict _Restrict
43 #else
44 #define restrict
45 #endif
46
47 /* float rhypotf(float x, float y)
48  *
49  * Method :
50  *      1. Special cases:
51  *              for x or y = Inf                        => 0;
52  *              for x or y = NaN                        => QNaN;
53  *              for x and y = 0                         => +Inf + divide-by-zero;
54  *      2. Computes d = x * x + y * y;
55  *      3. Computes reciprocal square root from:
56  *              d = m * 2**n
57  *      Where:
58  *              m = [0.5, 2),
59  *              n = ((exponent + 1) & ~1).
60  *      Then:
61  *              rsqrtf(d) = 1/sqrt( m * 2**n ) = (2 ** (-n/2)) * (1/sqrt(m))
62  *      4. Computes 1/sqrt(m) from:
63  *              1/sqrt(m) = (1/sqrt(m0)) * (1/sqrt(1 + (1/m0)*dm))
64  *      Where:
65  *              m = m0 + dm,
66  *              m0 = 0.5 * (1 + k/64) for m = [0.5,         0.5+127/256), k = [0, 63];
67  *              m0 = 1.0 * (0 + k/64) for m = [0.5+127/256, 1.0+127/128), k = [64, 127];
68  *      Then:
69  *              1/sqrt(m0), 1/m0 are looked up in a table,
70  *              1/sqrt(1 + (1/m0)*dm) is computed using approximation:
71  *                      1/sqrt(1 + z) = ((a3 * z + a2) * z + a1) * z + a0
72  *                      where z = [-1/64, 1/64].
73  *
74  * Accuracy:
75  *      The maximum relative error for the approximating
76  *      polynomial is 2**(-27.87).
77  *      Maximum error observed: less than 0.535 ulp after 3.000.000.000
78  *      results.
79  */
80
81 #pragma align 32 (__vlibm_TBL_rhypotf)
82
83 static const double __vlibm_TBL_rhypotf[] = {
84 /*
85  i = [0,63]
86  TBL[2*i+0] = 1.0 / (*(double*)&(0x3ff0000000000000LL + (i << 46)));
87  TBL[2*i+1] = (double)(0.5/sqrtl(2) / sqrtl(*(double*)&(0x3ff0000000000000LL + (i << 46))));
88  TBL[128+2*i+0] = 1.0 / (*(double*)&(0x3ff0000000000000LL + (i << 46)));
89  TBL[128+2*i+1] = (double)(0.25 / sqrtl(*(double*)&(0x3ff0000000000000LL + (i << 46))));
90 */
91  1.0000000000000000000e+00, 3.5355339059327378637e-01,
92  9.8461538461538467004e-01, 3.5082320772281166965e-01,
93  9.6969696969696972388e-01, 3.4815531191139570399e-01,
94  9.5522388059701490715e-01, 3.4554737023254405992e-01,
95  9.4117647058823528106e-01, 3.4299717028501769400e-01,
96  9.2753623188405798228e-01, 3.4050261230349943009e-01,
97  9.1428571428571425717e-01, 3.3806170189140660742e-01,
98  9.0140845070422537244e-01, 3.3567254331867563133e-01,
99  8.8888888888888883955e-01, 3.3333333333333331483e-01,
100  8.7671232876712323900e-01, 3.3104235544094717802e-01,
101  8.6486486486486491287e-01, 3.2879797461071458287e-01,
102  8.5333333333333338810e-01, 3.2659863237109043599e-01,
103  8.4210526315789469010e-01, 3.2444284226152508843e-01,
104  8.3116883116883122362e-01, 3.2232918561015211356e-01,
105  8.2051282051282048435e-01, 3.2025630761017426229e-01,
106  8.1012658227848100001e-01, 3.1822291367029204023e-01,
107  8.0000000000000004441e-01, 3.1622776601683794118e-01,
108  7.9012345679012341293e-01, 3.1426968052735443360e-01,
109  7.8048780487804880757e-01, 3.1234752377721214378e-01,
110  7.7108433734939763049e-01, 3.1046021028253312224e-01,
111  7.6190476190476186247e-01, 3.0860669992418382490e-01,
112  7.5294117647058822484e-01, 3.0678599553894819740e-01,
113  7.4418604651162789665e-01, 3.0499714066520933198e-01,
114  7.3563218390804596680e-01, 3.0323921743156134756e-01,
115  7.2727272727272729291e-01, 3.0151134457776362918e-01,
116  7.1910112359550559802e-01, 2.9981267559834456904e-01,
117  7.1111111111111113825e-01, 2.9814239699997197031e-01,
118  7.0329670329670335160e-01, 2.9649972666444046610e-01,
119  6.9565217391304345895e-01, 2.9488391230979427160e-01,
120  6.8817204301075274309e-01, 2.9329423004270660513e-01,
121  6.8085106382978721751e-01, 2.9172998299578911663e-01,
122  6.7368421052631577428e-01, 2.9019050004400465115e-01,
123  6.6666666666666662966e-01, 2.8867513459481286553e-01,
124  6.5979381443298967813e-01, 2.8718326344709527165e-01,
125  6.5306122448979586625e-01, 2.8571428571428569843e-01,
126  6.4646464646464651960e-01, 2.8426762180748055275e-01,
127  6.4000000000000001332e-01, 2.8284271247461900689e-01,
128  6.3366336633663367106e-01, 2.8143901789211672737e-01,
129  6.2745098039215685404e-01, 2.8005601680560193723e-01,
130  6.2135922330097081989e-01, 2.7869320571664707442e-01,
131  6.1538461538461541878e-01, 2.7735009811261457369e-01,
132  6.0952380952380957879e-01, 2.7602622373694168934e-01,
133  6.0377358490566035432e-01, 2.7472112789737807015e-01,
134  5.9813084112149528249e-01, 2.7343437080986532361e-01,
135  5.9259259259259255970e-01, 2.7216552697590867815e-01,
136  5.8715596330275232617e-01, 2.7091418459143856712e-01,
137  5.8181818181818178992e-01, 2.6967994498529684888e-01,
138  5.7657657657657657158e-01, 2.6846242208560971987e-01,
139  5.7142857142857139685e-01, 2.6726124191242439654e-01,
140  5.6637168141592919568e-01, 2.6607604209509572168e-01,
141  5.6140350877192979340e-01, 2.6490647141300877054e-01,
142  5.5652173913043478937e-01, 2.6375218935831479250e-01,
143  5.5172413793103447510e-01, 2.6261286571944508772e-01,
144  5.4700854700854706358e-01, 2.6148818018424535570e-01,
145  5.4237288135593220151e-01, 2.6037782196164771520e-01,
146  5.3781512605042014474e-01, 2.5928148942086576278e-01,
147  5.3333333333333332593e-01, 2.5819888974716115326e-01,
148  5.2892561983471075848e-01, 2.5712973861329002645e-01,
149  5.2459016393442625681e-01, 2.5607375986579195004e-01,
150  5.2032520325203257539e-01, 2.5503068522533534068e-01,
151  5.1612903225806450180e-01, 2.5400025400038100942e-01,
152  5.1200000000000001066e-01, 2.5298221281347033074e-01,
153  5.0793650793650790831e-01, 2.5197631533948483540e-01,
154  5.0393700787401574104e-01, 2.5098232205526344041e-01,
155  1.0000000000000000000e+00, 2.5000000000000000000e-01,
156  9.8461538461538467004e-01, 2.4806946917841690703e-01,
157  9.6969696969696972388e-01, 2.4618298195866547551e-01,
158  9.5522388059701490715e-01, 2.4433888871261044695e-01,
159  9.4117647058823528106e-01, 2.4253562503633296910e-01,
160  9.2753623188405798228e-01, 2.4077170617153839660e-01,
161  9.1428571428571425717e-01, 2.3904572186687872426e-01,
162  9.0140845070422537244e-01, 2.3735633163877067897e-01,
163  8.8888888888888883955e-01, 2.3570226039551583908e-01,
164  8.7671232876712323900e-01, 2.3408229439226113655e-01,
165  8.6486486486486491287e-01, 2.3249527748763856860e-01,
166  8.5333333333333338810e-01, 2.3094010767585029797e-01,
167  8.4210526315789469010e-01, 2.2941573387056177213e-01,
168  8.3116883116883122362e-01, 2.2792115291927589338e-01,
169  8.2051282051282048435e-01, 2.2645540682891915352e-01,
170  8.1012658227848100001e-01, 2.2501758018520479077e-01,
171  8.0000000000000004441e-01, 2.2360679774997896385e-01,
172  7.9012345679012341293e-01, 2.2222222222222220989e-01,
173  7.8048780487804880757e-01, 2.2086305214969309541e-01,
174  7.7108433734939763049e-01, 2.1952851997938069295e-01,
175  7.6190476190476186247e-01, 2.1821789023599238999e-01,
176  7.5294117647058822484e-01, 2.1693045781865616384e-01,
177  7.4418604651162789665e-01, 2.1566554640687682354e-01,
178  7.3563218390804596680e-01, 2.1442250696755896233e-01,
179  7.2727272727272729291e-01, 2.1320071635561044232e-01,
180  7.1910112359550559802e-01, 2.1199957600127200541e-01,
181  7.1111111111111113825e-01, 2.1081851067789195153e-01,
182  7.0329670329670335160e-01, 2.0965696734438366011e-01,
183  6.9565217391304345895e-01, 2.0851441405707477061e-01,
184  6.8817204301075274309e-01, 2.0739033894608505104e-01,
185  6.8085106382978721751e-01, 2.0628424925175867233e-01,
186  6.7368421052631577428e-01, 2.0519567041703082322e-01,
187  6.6666666666666662966e-01, 2.0412414523193150862e-01,
188  6.5979381443298967813e-01, 2.0306923302672380549e-01,
189  6.5306122448979586625e-01, 2.0203050891044216364e-01,
190  6.4646464646464651960e-01, 2.0100756305184241945e-01,
191  6.4000000000000001332e-01, 2.0000000000000001110e-01,
192  6.3366336633663367106e-01, 1.9900743804199783060e-01,
193  6.2745098039215685404e-01, 1.9802950859533485772e-01,
194  6.2135922330097081989e-01, 1.9706585563285863860e-01,
195  6.1538461538461541878e-01, 1.9611613513818404453e-01,
196  6.0952380952380957879e-01, 1.9518001458970662965e-01,
197  6.0377358490566035432e-01, 1.9425717247145282696e-01,
198  5.9813084112149528249e-01, 1.9334729780913270658e-01,
199  5.9259259259259255970e-01, 1.9245008972987526219e-01,
200  5.8715596330275232617e-01, 1.9156525704423027490e-01,
201  5.8181818181818178992e-01, 1.9069251784911847580e-01,
202  5.7657657657657657158e-01, 1.8983159915049979682e-01,
203  5.7142857142857139685e-01, 1.8898223650461362655e-01,
204  5.6637168141592919568e-01, 1.8814417367671945613e-01,
205  5.6140350877192979340e-01, 1.8731716231633879777e-01,
206  5.5652173913043478937e-01, 1.8650096164806276300e-01,
207  5.5172413793103447510e-01, 1.8569533817705186074e-01,
208  5.4700854700854706358e-01, 1.8490006540840969729e-01,
209  5.4237288135593220151e-01, 1.8411492357966466327e-01,
210  5.3781512605042014474e-01, 1.8333969940564226464e-01,
211  5.3333333333333332593e-01, 1.8257418583505535814e-01,
212  5.2892561983471075848e-01, 1.8181818181818182323e-01,
213  5.2459016393442625681e-01, 1.8107149208503706128e-01,
214  5.2032520325203257539e-01, 1.8033392693348646030e-01,
215  5.1612903225806450180e-01, 1.7960530202677491007e-01,
216  5.1200000000000001066e-01, 1.7888543819998317663e-01,
217  5.0793650793650790831e-01, 1.7817416127494958844e-01,
218  5.0393700787401574104e-01, 1.7747130188322274291e-01,
219 };
220
221 extern float fabsf(float);
222
223 static const double
224         A0 = 9.99999997962321453275e-01,
225         A1 =-4.99999998166077580600e-01,
226         A2 = 3.75066768969515586277e-01,
227         A3 =-3.12560092408808548438e-01;
228
229 static void
230 __vrhypotf_n(int n, float * restrict px, int stridex, float * restrict py,
231         int stridey, float * restrict pz, int stridez);
232
233 #pragma no_inline(__vrhypotf_n)
234
235 #define RETURN(ret)                                             \
236 {                                                               \
237         *pz = (ret);                                            \
238         pz += stridez;                                          \
239         if (n_n == 0)                                           \
240         {                                                       \
241                 spx = px; spy = py; spz = pz;                   \
242                 ay0 = *(int*)py;                                \
243                 continue;                                       \
244         }                                                       \
245         n--;                                                    \
246         break;                                                  \
247 }
248
249
250 void
251 __vrhypotf(int n, float * restrict px, int stridex, float * restrict py,
252         int stridey, float * restrict pz, int stridez)
253 {
254         float           *spx, *spy, *spz;
255         int             ax0, ay0, n_n;
256         float           res, x0, y0;
257
258         while (n > 1)
259         {
260                 n_n = 0;
261                 spx = px;
262                 spy = py;
263                 spz = pz;
264                 ax0 = *(int*)px;
265                 ay0 = *(int*)py;
266                 for (; n > 1 ; n--)
267                 {
268                         ax0 &= 0x7fffffff;
269                         ay0 &= 0x7fffffff;
270
271                         px += stridex;
272
273                         if (ax0 >= 0x7f800000 || ay0 >= 0x7f800000)       /* X or Y = NaN or Inf  */
274                         {
275                                 x0 = *(px - stridex);
276                                 y0 = *py;
277                                 res = fabsf(x0) + fabsf(y0);
278                                 if (ax0 == 0x7f800000) res = 0.0f;
279                                 else if (ay0 == 0x7f800000) res = 0.0f;
280                                 ax0 = *(int*)px;
281                                 py += stridey;
282                                 RETURN (res)
283                         }
284                         ax0 = *(int*)px;
285                         py += stridey;
286                         if (ay0 == 0)           /* Y = 0        */
287                         {
288                                 int tx = *(int*)(px - stridex) & 0x7fffffff;
289                                 if (tx == 0)    /* X = 0        */
290                                 {
291                                         RETURN (1.0f / 0.0f)
292                                 }
293                         }
294                         pz += stridez;
295                         n_n++;
296                         ay0 = *(int*)py;
297                 }
298                 if (n_n > 0)
299                         __vrhypotf_n(n_n, spx, stridex, spy, stridey, spz, stridez);
300         }
301         if (n > 0)
302         {
303                 ax0 = *(int*)px;
304                 ay0 = *(int*)py;
305                 x0 = *px;
306                 y0 = *py;
307
308                 ax0 &= 0x7fffffff;
309                 ay0 &= 0x7fffffff;
310
311                 if (ax0 >= 0x7f800000 || ay0 >= 0x7f800000)       /* X or Y = NaN or Inf  */
312                 {
313                         res = fabsf(x0) + fabsf(y0);
314                         if (ax0 == 0x7f800000) res = 0.0f;
315                         else if (ay0 == 0x7f800000) res = 0.0f;
316                         *pz = res;
317                 }
318                 else if (ax0 == 0 && ay0 == 0)  /* X and Y = 0  */
319                 {
320                         *pz = 1.0f / 0.0f;
321                 }
322                 else
323                 {
324                         double          xx0, res0, hyp0, h_hi0 = 0, dbase0 = 0;
325                         int             ibase0, si0, hyp0h;
326
327                         hyp0 = x0 * (double)x0 + y0 * (double)y0;
328
329                         ibase0 = HI(&hyp0);
330
331                         HI(&dbase0) = (0x60000000 - ((ibase0 & 0x7fe00000) >> 1));
332
333                         hyp0h = (ibase0 & 0x000fffff) | 0x3ff00000;
334                         HI(&hyp0) = hyp0h;
335                         HI(&h_hi0) = hyp0h & 0x7fffc000;
336
337                         ibase0 >>= 10;
338                         si0 = ibase0 & 0x7f0;
339                         xx0 = ((double*)((char*)__vlibm_TBL_rhypotf + si0))[0];
340
341                         xx0 = (hyp0 - h_hi0) * xx0;
342                         res0 = ((double*)((char*)__vlibm_TBL_rhypotf + si0))[1];
343                         res0 *= (((A3 * xx0 + A2) * xx0 + A1) * xx0 + A0);
344                         res0 *= dbase0;
345                         *pz = res0;
346                 }
347         }
348 }
349
350 static void
351 __vrhypotf_n(int n, float * restrict px, int stridex, float * restrict py,
352         int stridey, float * restrict pz, int stridez)
353 {
354         double          xx0, res0, hyp0, h_hi0 = 0, dbase0 = 0;
355         double          xx1, res1, hyp1, h_hi1 = 0, dbase1 = 0;
356         double          xx2, res2, hyp2, h_hi2 = 0, dbase2 = 0;
357         float           x0, y0;
358         float           x1, y1;
359         float           x2, y2;
360         int             ibase0, si0, hyp0h;
361         int             ibase1, si1, hyp1h;
362         int             ibase2, si2, hyp2h;
363
364         for (; n > 2 ; n -= 3)
365         {
366                 x0 = *px;
367                 px += stridex;
368                 x1 = *px;
369                 px += stridex;
370                 x2 = *px;
371                 px += stridex;
372
373                 y0 = *py;
374                 py += stridey;
375                 y1 = *py;
376                 py += stridey;
377                 y2 = *py;
378                 py += stridey;
379
380                 hyp0 = x0 * (double)x0 + y0 * (double)y0;
381                 hyp1 = x1 * (double)x1 + y1 * (double)y1;
382                 hyp2 = x2 * (double)x2 + y2 * (double)y2;
383
384                 ibase0 = HI(&hyp0);
385                 ibase1 = HI(&hyp1);
386                 ibase2 = HI(&hyp2);
387
388                 HI(&dbase0) = (0x60000000 - ((ibase0 & 0x7fe00000) >> 1));
389                 HI(&dbase1) = (0x60000000 - ((ibase1 & 0x7fe00000) >> 1));
390                 HI(&dbase2) = (0x60000000 - ((ibase2 & 0x7fe00000) >> 1));
391
392                 hyp0h = (ibase0 & 0x000fffff) | 0x3ff00000;
393                 hyp1h = (ibase1 & 0x000fffff) | 0x3ff00000;
394                 hyp2h = (ibase2 & 0x000fffff) | 0x3ff00000;
395                 HI(&hyp0) = hyp0h;
396                 HI(&hyp1) = hyp1h;
397                 HI(&hyp2) = hyp2h;
398                 HI(&h_hi0) = hyp0h & 0x7fffc000;
399                 HI(&h_hi1) = hyp1h & 0x7fffc000;
400                 HI(&h_hi2) = hyp2h & 0x7fffc000;
401
402                 ibase0 >>= 10;
403                 ibase1 >>= 10;
404                 ibase2 >>= 10;
405                 si0 = ibase0 & 0x7f0;
406                 si1 = ibase1 & 0x7f0;
407                 si2 = ibase2 & 0x7f0;
408                 xx0 = ((double*)((char*)__vlibm_TBL_rhypotf + si0))[0];
409                 xx1 = ((double*)((char*)__vlibm_TBL_rhypotf + si1))[0];
410                 xx2 = ((double*)((char*)__vlibm_TBL_rhypotf + si2))[0];
411
412                 xx0 = (hyp0 - h_hi0) * xx0;
413                 xx1 = (hyp1 - h_hi1) * xx1;
414                 xx2 = (hyp2 - h_hi2) * xx2;
415                 res0 = ((double*)((char*)__vlibm_TBL_rhypotf + si0))[1];
416                 res1 = ((double*)((char*)__vlibm_TBL_rhypotf + si1))[1];
417                 res2 = ((double*)((char*)__vlibm_TBL_rhypotf + si2))[1];
418                 res0 *= (((A3 * xx0 + A2) * xx0 + A1) * xx0 + A0);
419                 res1 *= (((A3 * xx1 + A2) * xx1 + A1) * xx1 + A0);
420                 res2 *= (((A3 * xx2 + A2) * xx2 + A1) * xx2 + A0);
421                 res0 *= dbase0;
422                 res1 *= dbase1;
423                 res2 *= dbase2;
424                 *pz = res0;
425                 pz += stridez;
426                 *pz = res1;
427                 pz += stridez;
428                 *pz = res2;
429                 pz += stridez;
430         }
431
432         for (; n > 0 ; n--)
433         {
434                 x0 = *px;
435                 px += stridex;
436
437                 y0 = *py;
438                 py += stridey;
439
440                 hyp0 = x0 * (double)x0 + y0 * (double)y0;
441
442                 ibase0 = HI(&hyp0);
443
444                 HI(&dbase0) = (0x60000000 - ((ibase0 & 0x7fe00000) >> 1));
445
446                 hyp0h = (ibase0 & 0x000fffff) | 0x3ff00000;
447                 HI(&hyp0) = hyp0h;
448                 HI(&h_hi0) = hyp0h & 0x7fffc000;
449
450                 ibase0 >>= 10;
451                 si0 = ibase0 & 0x7f0;
452                 xx0 = ((double*)((char*)__vlibm_TBL_rhypotf + si0))[0];
453
454                 xx0 = (hyp0 - h_hi0) * xx0;
455                 res0 = ((double*)((char*)__vlibm_TBL_rhypotf + si0))[1];
456                 res0 *= (((A3 * xx0 + A2) * xx0 + A1) * xx0 + A0);
457                 res0 *= dbase0;
458                 *pz = res0;
459                 pz += stridez;
460         }
461 }
```