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Commit | Line | Data |
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f7eac6eb | 1 | /* |
e4d82761 | 2 | * IBM Accurate Mathematical Library |
aeb25823 | 3 | * written by International Business Machines Corp. |
b168057a | 4 | * Copyright (C) 2001-2015 Free Software Foundation, Inc. |
f7eac6eb | 5 | * |
e4d82761 UD |
6 | * This program is free software; you can redistribute it and/or modify |
7 | * it under the terms of the GNU Lesser General Public License as published by | |
cc7375ce | 8 | * the Free Software Foundation; either version 2.1 of the License, or |
e4d82761 | 9 | * (at your option) any later version. |
f7eac6eb | 10 | * |
e4d82761 UD |
11 | * This program is distributed in the hope that it will be useful, |
12 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
c6c6dd48 | 14 | * GNU Lesser General Public License for more details. |
f7eac6eb | 15 | * |
e4d82761 | 16 | * You should have received a copy of the GNU Lesser General Public License |
59ba27a6 | 17 | * along with this program; if not, see <http://www.gnu.org/licenses/>. |
f7eac6eb | 18 | */ |
e4d82761 UD |
19 | /***************************************************************************/ |
20 | /* MODULE_NAME: upow.c */ | |
21 | /* */ | |
22 | /* FUNCTIONS: upow */ | |
23 | /* power1 */ | |
0ac5ae23 | 24 | /* my_log2 */ |
e4d82761 UD |
25 | /* log1 */ |
26 | /* checkint */ | |
27 | /* FILES NEEDED: dla.h endian.h mpa.h mydefs.h */ | |
28 | /* halfulp.c mpexp.c mplog.c slowexp.c slowpow.c mpa.c */ | |
0ac5ae23 | 29 | /* uexp.c upow.c */ |
e4d82761 UD |
30 | /* root.tbl uexp.tbl upow.tbl */ |
31 | /* An ultimate power routine. Given two IEEE double machine numbers y,x */ | |
32 | /* it computes the correctly rounded (to nearest) value of x^y. */ | |
33 | /* Assumption: Machine arithmetic operations are performed in */ | |
34 | /* round to nearest mode of IEEE 754 standard. */ | |
35 | /* */ | |
36 | /***************************************************************************/ | |
4da6db51 | 37 | #include <math.h> |
e4d82761 UD |
38 | #include "endian.h" |
39 | #include "upow.h" | |
c8b3296b | 40 | #include <dla.h> |
e4d82761 UD |
41 | #include "mydefs.h" |
42 | #include "MathLib.h" | |
43 | #include "upow.tbl" | |
1ed0291c | 44 | #include <math_private.h> |
b7cd39e8 | 45 | #include <fenv.h> |
f7eac6eb | 46 | |
31d3cc00 UD |
47 | #ifndef SECTION |
48 | # define SECTION | |
49 | #endif | |
50 | ||
d7dd9453 | 51 | static const double huge = 1.0e300, tiny = 1.0e-300; |
f7eac6eb | 52 | |
88576635 SP |
53 | double __exp1 (double x, double xx, double error); |
54 | static double log1 (double x, double *delta, double *error); | |
55 | static double my_log2 (double x, double *delta, double *error); | |
56 | double __slowpow (double x, double y, double z); | |
57 | static double power1 (double x, double y); | |
58 | static int checkint (double x); | |
f7eac6eb | 59 | |
88576635 SP |
60 | /* An ultimate power routine. Given two IEEE double machine numbers y, x it |
61 | computes the correctly rounded (to nearest) value of X^y. */ | |
31d3cc00 UD |
62 | double |
63 | SECTION | |
88576635 SP |
64 | __ieee754_pow (double x, double y) |
65 | { | |
66 | double z, a, aa, error, t, a1, a2, y1, y2; | |
67 | mynumber u, v; | |
e4d82761 | 68 | int k; |
88576635 SP |
69 | int4 qx, qy; |
70 | v.x = y; | |
71 | u.x = x; | |
72 | if (v.i[LOW_HALF] == 0) | |
73 | { /* of y */ | |
74 | qx = u.i[HIGH_HALF] & 0x7fffffff; | |
75 | /* Is x a NaN? */ | |
76 | if (((qx == 0x7ff00000) && (u.i[LOW_HALF] != 0)) || (qx > 0x7ff00000)) | |
77 | return x; | |
78 | if (y == 1.0) | |
79 | return x; | |
80 | if (y == 2.0) | |
81 | return x * x; | |
82 | if (y == -1.0) | |
83 | return 1.0 / x; | |
84 | if (y == 0) | |
85 | return 1.0; | |
86 | } | |
e4d82761 | 87 | /* else */ |
88576635 SP |
88 | if (((u.i[HIGH_HALF] > 0 && u.i[HIGH_HALF] < 0x7ff00000) || /* x>0 and not x->0 */ |
89 | (u.i[HIGH_HALF] == 0 && u.i[LOW_HALF] != 0)) && | |
90 | /* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */ | |
91 | (v.i[HIGH_HALF] & 0x7fffffff) < 0x4ff00000) | |
92 | { /* if y<-1 or y>1 */ | |
93 | double retval; | |
b7cd39e8 | 94 | |
4da6db51 JM |
95 | { |
96 | SET_RESTORE_ROUND (FE_TONEAREST); | |
b7cd39e8 | 97 | |
4da6db51 JM |
98 | /* Avoid internal underflow for tiny y. The exact value of y does |
99 | not matter if |y| <= 2**-64. */ | |
100 | if (ABS (y) < 0x1p-64) | |
101 | y = y < 0 ? -0x1p-64 : 0x1p-64; | |
102 | z = log1 (x, &aa, &error); /* x^y =e^(y log (X)) */ | |
103 | t = y * CN; | |
104 | y1 = t - (t - y); | |
105 | y2 = y - y1; | |
106 | t = z * CN; | |
107 | a1 = t - (t - z); | |
108 | a2 = (z - a1) + aa; | |
109 | a = y1 * a1; | |
110 | aa = y2 * a1 + y * a2; | |
111 | a1 = a + aa; | |
112 | a2 = (a - a1) + aa; | |
113 | error = error * ABS (y); | |
114 | t = __exp1 (a1, a2, 1.9e16 * error); /* return -10 or 0 if wasn't computed exactly */ | |
115 | retval = (t > 0) ? t : power1 (x, y); | |
116 | } | |
b7cd39e8 | 117 | |
4da6db51 JM |
118 | if (__isinf (retval)) |
119 | retval = huge * huge; | |
120 | else if (retval == 0) | |
121 | retval = tiny * tiny; | |
88576635 SP |
122 | return retval; |
123 | } | |
f7eac6eb | 124 | |
88576635 SP |
125 | if (x == 0) |
126 | { | |
127 | if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0) | |
128 | || (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000) /* NaN */ | |
129 | return y; | |
130 | if (ABS (y) > 1.0e20) | |
131 | return (y > 0) ? 0 : 1.0 / 0.0; | |
132 | k = checkint (y); | |
133 | if (k == -1) | |
134 | return y < 0 ? 1.0 / x : x; | |
135 | else | |
136 | return y < 0 ? 1.0 / 0.0 : 0.0; /* return 0 */ | |
137 | } | |
8f3edfee | 138 | |
88576635 SP |
139 | qx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */ |
140 | qy = v.i[HIGH_HALF] & 0x7fffffff; /* no sign */ | |
8f3edfee | 141 | |
88576635 | 142 | if (qx >= 0x7ff00000 && (qx > 0x7ff00000 || u.i[LOW_HALF] != 0)) /* NaN */ |
8b43a0c9 | 143 | return x; |
88576635 | 144 | if (qy >= 0x7ff00000 && (qy > 0x7ff00000 || v.i[LOW_HALF] != 0)) /* NaN */ |
8b43a0c9 | 145 | return x == 1.0 ? 1.0 : y; |
8f3edfee | 146 | |
e4d82761 | 147 | /* if x<0 */ |
88576635 SP |
148 | if (u.i[HIGH_HALF] < 0) |
149 | { | |
150 | k = checkint (y); | |
151 | if (k == 0) | |
152 | { | |
153 | if (qy == 0x7ff00000) | |
154 | { | |
155 | if (x == -1.0) | |
156 | return 1.0; | |
157 | else if (x > -1.0) | |
158 | return v.i[HIGH_HALF] < 0 ? INF.x : 0.0; | |
159 | else | |
160 | return v.i[HIGH_HALF] < 0 ? 0.0 : INF.x; | |
161 | } | |
162 | else if (qx == 0x7ff00000) | |
163 | return y < 0 ? 0.0 : INF.x; | |
164 | return (x - x) / (x - x); /* y not integer and x<0 */ | |
165 | } | |
8f3edfee | 166 | else if (qx == 0x7ff00000) |
88576635 SP |
167 | { |
168 | if (k < 0) | |
169 | return y < 0 ? nZERO.x : nINF.x; | |
170 | else | |
171 | return y < 0 ? 0.0 : INF.x; | |
172 | } | |
173 | /* if y even or odd */ | |
4da6db51 JM |
174 | if (k == 1) |
175 | return __ieee754_pow (-x, y); | |
176 | else | |
177 | { | |
178 | double retval; | |
179 | { | |
180 | SET_RESTORE_ROUND (FE_TONEAREST); | |
181 | retval = -__ieee754_pow (-x, y); | |
182 | } | |
183 | if (__isinf (retval)) | |
184 | retval = -huge * huge; | |
185 | else if (retval == 0) | |
186 | retval = -tiny * tiny; | |
187 | return retval; | |
188 | } | |
ca58f1db | 189 | } |
e4d82761 | 190 | /* x>0 */ |
f7eac6eb | 191 | |
88576635 | 192 | if (qx == 0x7ff00000) /* x= 2^-0x3ff */ |
d91da4ce | 193 | return y > 0 ? x : 0; |
f14bd805 | 194 | |
88576635 SP |
195 | if (qy > 0x45f00000 && qy < 0x7ff00000) |
196 | { | |
197 | if (x == 1.0) | |
198 | return 1.0; | |
199 | if (y > 0) | |
200 | return (x > 1.0) ? huge * huge : tiny * tiny; | |
201 | if (y < 0) | |
202 | return (x < 1.0) ? huge * huge : tiny * tiny; | |
203 | } | |
f7eac6eb | 204 | |
88576635 SP |
205 | if (x == 1.0) |
206 | return 1.0; | |
207 | if (y > 0) | |
208 | return (x > 1.0) ? INF.x : 0; | |
209 | if (y < 0) | |
210 | return (x < 1.0) ? INF.x : 0; | |
211 | return 0; /* unreachable, to make the compiler happy */ | |
e4d82761 | 212 | } |
88576635 | 213 | |
af968f62 | 214 | #ifndef __ieee754_pow |
0ac5ae23 | 215 | strong_alias (__ieee754_pow, __pow_finite) |
af968f62 | 216 | #endif |
f7eac6eb | 217 | |
88576635 | 218 | /* Compute x^y using more accurate but more slow log routine. */ |
31d3cc00 UD |
219 | static double |
220 | SECTION | |
88576635 SP |
221 | power1 (double x, double y) |
222 | { | |
223 | double z, a, aa, error, t, a1, a2, y1, y2; | |
224 | z = my_log2 (x, &aa, &error); | |
225 | t = y * CN; | |
226 | y1 = t - (t - y); | |
e4d82761 | 227 | y2 = y - y1; |
88576635 SP |
228 | t = z * CN; |
229 | a1 = t - (t - z); | |
e4d82761 | 230 | a2 = z - a1; |
88576635 SP |
231 | a = y * z; |
232 | aa = ((y1 * a1 - a) + y1 * a2 + y2 * a1) + y2 * a2 + aa * y; | |
233 | a1 = a + aa; | |
234 | a2 = (a - a1) + aa; | |
235 | error = error * ABS (y); | |
236 | t = __exp1 (a1, a2, 1.9e16 * error); | |
237 | return (t >= 0) ? t : __slowpow (x, y, z); | |
e4d82761 | 238 | } |
f7eac6eb | 239 | |
88576635 SP |
240 | /* Compute log(x) (x is left argument). The result is the returned double + the |
241 | parameter DELTA. The result is bounded by ERROR. */ | |
31d3cc00 UD |
242 | static double |
243 | SECTION | |
88576635 SP |
244 | log1 (double x, double *delta, double *error) |
245 | { | |
246 | int i, j, m; | |
247 | double uu, vv, eps, nx, e, e1, e2, t, t1, t2, res, add = 0; | |
248 | mynumber u, v; | |
27692f89 | 249 | #ifdef BIG_ENDI |
88576635 | 250 | mynumber /**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */ |
27692f89 | 251 | #else |
88576635 SP |
252 | # ifdef LITTLE_ENDI |
253 | mynumber /**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */ | |
254 | # endif | |
27692f89 | 255 | #endif |
ba1ffaa1 | 256 | |
e4d82761 UD |
257 | u.x = x; |
258 | m = u.i[HIGH_HALF]; | |
259 | *error = 0; | |
260 | *delta = 0; | |
88576635 SP |
261 | if (m < 0x00100000) /* 1<x<2^-1007 */ |
262 | { | |
263 | x = x * t52.x; | |
264 | add = -52.0; | |
265 | u.x = x; | |
266 | m = u.i[HIGH_HALF]; | |
267 | } | |
f7eac6eb | 268 | |
88576635 SP |
269 | if ((m & 0x000fffff) < 0x0006a09e) |
270 | { | |
271 | u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000; | |
272 | two52.i[LOW_HALF] = (m >> 20); | |
273 | } | |
e4d82761 | 274 | else |
88576635 SP |
275 | { |
276 | u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3fe00000; | |
277 | two52.i[LOW_HALF] = (m >> 20) + 1; | |
278 | } | |
f7eac6eb | 279 | |
e4d82761 UD |
280 | v.x = u.x + bigu.x; |
281 | uu = v.x - bigu.x; | |
88576635 SP |
282 | i = (v.i[LOW_HALF] & 0x000003ff) << 2; |
283 | if (two52.i[LOW_HALF] == 1023) /* nx = 0 */ | |
284 | { | |
285 | if (i > 1192 && i < 1208) /* |x-1| < 1.5*2**-10 */ | |
286 | { | |
e4d82761 | 287 | t = x - 1.0; |
88576635 SP |
288 | t1 = (t + 5.0e6) - 5.0e6; |
289 | t2 = t - t1; | |
290 | e1 = t - 0.5 * t1 * t1; | |
291 | e2 = (t * t * t * (r3 + t * (r4 + t * (r5 + t * (r6 + t | |
292 | * (r7 + t * r8))))) | |
293 | - 0.5 * t2 * (t + t1)); | |
294 | res = e1 + e2; | |
295 | *error = 1.0e-21 * ABS (t); | |
296 | *delta = (e1 - res) + e2; | |
e4d82761 | 297 | return res; |
88576635 | 298 | } /* |x-1| < 1.5*2**-10 */ |
e4d82761 | 299 | else |
88576635 SP |
300 | { |
301 | v.x = u.x * (ui.x[i] + ui.x[i + 1]) + bigv.x; | |
302 | vv = v.x - bigv.x; | |
303 | j = v.i[LOW_HALF] & 0x0007ffff; | |
304 | j = j + j + j; | |
305 | eps = u.x - uu * vv; | |
306 | e1 = eps * ui.x[i]; | |
307 | e2 = eps * (ui.x[i + 1] + vj.x[j] * (ui.x[i] + ui.x[i + 1])); | |
308 | e = e1 + e2; | |
309 | e2 = ((e1 - e) + e2); | |
310 | t = ui.x[i + 2] + vj.x[j + 1]; | |
311 | t1 = t + e; | |
312 | t2 = ((((t - t1) + e) + (ui.x[i + 3] + vj.x[j + 2])) + e2 + e * e | |
313 | * (p2 + e * (p3 + e * p4))); | |
314 | res = t1 + t2; | |
e4d82761 | 315 | *error = 1.0e-24; |
88576635 | 316 | *delta = (t1 - res) + t2; |
e4d82761 | 317 | return res; |
88576635 SP |
318 | } |
319 | } /* nx = 0 */ | |
320 | else /* nx != 0 */ | |
321 | { | |
e4d82761 | 322 | eps = u.x - uu; |
88576635 SP |
323 | nx = (two52.x - two52e.x) + add; |
324 | e1 = eps * ui.x[i]; | |
325 | e2 = eps * ui.x[i + 1]; | |
326 | e = e1 + e2; | |
327 | e2 = (e1 - e) + e2; | |
328 | t = nx * ln2a.x + ui.x[i + 2]; | |
329 | t1 = t + e; | |
330 | t2 = ((((t - t1) + e) + nx * ln2b.x + ui.x[i + 3] + e2) + e * e | |
331 | * (q2 + e * (q3 + e * (q4 + e * (q5 + e * q6))))); | |
332 | res = t1 + t2; | |
e4d82761 | 333 | *error = 1.0e-21; |
88576635 | 334 | *delta = (t1 - res) + t2; |
e4d82761 | 335 | return res; |
88576635 | 336 | } /* nx != 0 */ |
e4d82761 UD |
337 | } |
338 | ||
88576635 SP |
339 | /* Slower but more accurate routine of log. The returned result is double + |
340 | DELTA. The result is bounded by ERROR. */ | |
31d3cc00 UD |
341 | static double |
342 | SECTION | |
88576635 SP |
343 | my_log2 (double x, double *delta, double *error) |
344 | { | |
345 | int i, j, m; | |
346 | double uu, vv, eps, nx, e, e1, e2, t, t1, t2, res, add = 0; | |
347 | double ou1, ou2, lu1, lu2, ov, lv1, lv2, a, a1, a2; | |
348 | double y, yy, z, zz, j1, j2, j7, j8; | |
58985aa9 | 349 | #ifndef DLA_FMS |
88576635 | 350 | double j3, j4, j5, j6; |
a1a87169 | 351 | #endif |
88576635 | 352 | mynumber u, v; |
27692f89 | 353 | #ifdef BIG_ENDI |
88576635 | 354 | mynumber /**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */ |
27692f89 | 355 | #else |
88576635 SP |
356 | # ifdef LITTLE_ENDI |
357 | mynumber /**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */ | |
358 | # endif | |
27692f89 | 359 | #endif |
e4d82761 UD |
360 | |
361 | u.x = x; | |
362 | m = u.i[HIGH_HALF]; | |
363 | *error = 0; | |
364 | *delta = 0; | |
88576635 SP |
365 | add = 0; |
366 | if (m < 0x00100000) | |
367 | { /* x < 2^-1022 */ | |
368 | x = x * t52.x; | |
369 | add = -52.0; | |
370 | u.x = x; | |
371 | m = u.i[HIGH_HALF]; | |
372 | } | |
f7eac6eb | 373 | |
88576635 SP |
374 | if ((m & 0x000fffff) < 0x0006a09e) |
375 | { | |
376 | u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000; | |
377 | two52.i[LOW_HALF] = (m >> 20); | |
378 | } | |
e4d82761 | 379 | else |
88576635 SP |
380 | { |
381 | u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3fe00000; | |
382 | two52.i[LOW_HALF] = (m >> 20) + 1; | |
383 | } | |
e4d82761 UD |
384 | |
385 | v.x = u.x + bigu.x; | |
386 | uu = v.x - bigu.x; | |
88576635 | 387 | i = (v.i[LOW_HALF] & 0x000003ff) << 2; |
e4d82761 | 388 | /*------------------------------------- |x-1| < 2**-11------------------------------- */ |
88576635 SP |
389 | if ((two52.i[LOW_HALF] == 1023) && (i == 1200)) |
390 | { | |
e4d82761 | 391 | t = x - 1.0; |
88576635 SP |
392 | EMULV (t, s3, y, yy, j1, j2, j3, j4, j5); |
393 | ADD2 (-0.5, 0, y, yy, z, zz, j1, j2); | |
394 | MUL2 (t, 0, z, zz, y, yy, j1, j2, j3, j4, j5, j6, j7, j8); | |
395 | MUL2 (t, 0, y, yy, z, zz, j1, j2, j3, j4, j5, j6, j7, j8); | |
e4d82761 | 396 | |
88576635 SP |
397 | e1 = t + z; |
398 | e2 = ((((t - e1) + z) + zz) + t * t * t | |
399 | * (ss3 + t * (s4 + t * (s5 + t * (s6 + t * (s7 + t * s8)))))); | |
400 | res = e1 + e2; | |
401 | *error = 1.0e-25 * ABS (t); | |
402 | *delta = (e1 - res) + e2; | |
e4d82761 | 403 | return res; |
88576635 | 404 | } |
e4d82761 UD |
405 | /*----------------------------- |x-1| > 2**-11 -------------------------- */ |
406 | else | |
88576635 SP |
407 | { /*Computing log(x) according to log table */ |
408 | nx = (two52.x - two52e.x) + add; | |
e4d82761 | 409 | ou1 = ui.x[i]; |
88576635 SP |
410 | ou2 = ui.x[i + 1]; |
411 | lu1 = ui.x[i + 2]; | |
412 | lu2 = ui.x[i + 3]; | |
413 | v.x = u.x * (ou1 + ou2) + bigv.x; | |
414 | vv = v.x - bigv.x; | |
415 | j = v.i[LOW_HALF] & 0x0007ffff; | |
416 | j = j + j + j; | |
417 | eps = u.x - uu * vv; | |
418 | ov = vj.x[j]; | |
419 | lv1 = vj.x[j + 1]; | |
420 | lv2 = vj.x[j + 2]; | |
421 | a = (ou1 + ou2) * (1.0 + ov); | |
422 | a1 = (a + 1.0e10) - 1.0e10; | |
423 | a2 = a * (1.0 - a1 * uu * vv); | |
424 | e1 = eps * a1; | |
425 | e2 = eps * a2; | |
426 | e = e1 + e2; | |
427 | e2 = (e1 - e) + e2; | |
428 | t = nx * ln2a.x + lu1 + lv1; | |
429 | t1 = t + e; | |
430 | t2 = ((((t - t1) + e) + (lu2 + lv2 + nx * ln2b.x + e2)) + e * e | |
431 | * (p2 + e * (p3 + e * p4))); | |
432 | res = t1 + t2; | |
e4d82761 | 433 | *error = 1.0e-27; |
88576635 | 434 | *delta = (t1 - res) + t2; |
e4d82761 | 435 | return res; |
88576635 | 436 | } |
e4d82761 | 437 | } |
f7eac6eb | 438 | |
88576635 SP |
439 | /* This function receives a double x and checks if it is an integer. If not, |
440 | it returns 0, else it returns 1 if even or -1 if odd. */ | |
31d3cc00 UD |
441 | static int |
442 | SECTION | |
88576635 SP |
443 | checkint (double x) |
444 | { | |
445 | union | |
446 | { | |
447 | int4 i[2]; | |
448 | double x; | |
449 | } u; | |
450 | int k, m, n; | |
e4d82761 | 451 | u.x = x; |
88576635 SP |
452 | m = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */ |
453 | if (m >= 0x7ff00000) | |
454 | return 0; /* x is +/-inf or NaN */ | |
455 | if (m >= 0x43400000) | |
456 | return 1; /* |x| >= 2**53 */ | |
457 | if (m < 0x40000000) | |
458 | return 0; /* |x| < 2, can not be 0 or 1 */ | |
e4d82761 | 459 | n = u.i[LOW_HALF]; |
88576635 SP |
460 | k = (m >> 20) - 1023; /* 1 <= k <= 52 */ |
461 | if (k == 52) | |
462 | return (n & 1) ? -1 : 1; /* odd or even */ | |
463 | if (k > 20) | |
464 | { | |
465 | if (n << (k - 20)) | |
466 | return 0; /* if not integer */ | |
467 | return (n << (k - 21)) ? -1 : 1; | |
468 | } | |
469 | if (n) | |
470 | return 0; /*if not integer */ | |
471 | if (k == 20) | |
472 | return (m & 1) ? -1 : 1; | |
473 | if (m << (k + 12)) | |
474 | return 0; | |
475 | return (m << (k + 11)) ? -1 : 1; | |
f7eac6eb | 476 | } |