1 /*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
5 * Common Development and Distribution License (the "License").
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
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21
22 /*
23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 */
25 /*
26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 * Use is subject to license terms.
28 */
29
30 #pragma weak remquol = __remquol
31
32 #include "libm.h"
33 #include "libm_synonyms.h"
34 #if defined(__SUNPRO_C)
35 #include <sunmath.h> /* fabsl */
36 #endif
37 /* INDENT OFF */
38 static const int
39 is = -0x7fffffff - 1,
40 im = 0x0000ffff,
41 iu = 0x00010000;
42
43 static const long double zero = 0.0L, one = 1.0L;
44 /* INDENT ON */
45
46 #if defined(__sparc)
47 #define __H0(x) ((int *) &x)[0]
48 #define __H1(x) ((int *) &x)[1]
49 #define __H2(x) ((int *) &x)[2]
50 #define __H3(x) ((int *) &x)[3]
51 #else
52 #error Unsupported architecture
53 #endif
54
55 /*
56 * On entrance: *quo is initialized to 0, x finite and y non-zero & ordered
57 */
58 static long double
59 fmodquol(long double x, long double y, int *quo) {
60 long double a, b;
61 int n, ix, iy, k, sx, sq, m;
62 int hx;
63 int x0, y0, z0, carry;
64 unsigned x1, x2, x3, y1, y2, y3, z1, z2, z3;
65
66 hx = __H0(x);
67 x1 = __H1(x);
68 x2 = __H2(x);
69 x3 = __H3(x);
70 y0 = __H0(y);
71 y1 = __H1(y);
72 y2 = __H2(y);
73 y3 = __H3(y);
74
75 sx = hx & is;
76 sq = (hx ^ y0) & is;
77 x0 = hx ^ sx;
78 y0 &= ~0x80000000;
79
80 a = fabsl(x);
81 b = fabsl(y);
82 if (a <= b) {
83 if (a < b)
84 return (x);
85 else {
86 *quo = 1 + (sq >> 30);
87 return (zero * x);
88 }
89 }
90 /* determine ix = ilogbl(x) */
91 if (x0 < iu) { /* subnormal x */
92 ix = 0;
93 ix = -16382;
94 while (x0 == 0) {
95 ix -= 16;
96 x0 = x1 >> 16;
97 x1 = (x1 << 16) | (x2 >> 16);
98 x2 = (x2 << 16) | (x3 >> 16);
99 x3 = (x3 << 16);
100 }
101 while (x0 < iu) {
102 ix -= 1;
103 x0 = (x0 << 1) | (x1 >> 31);
104 x1 = (x1 << 1) | (x2 >> 31);
105 x2 = (x2 << 1) | (x3 >> 31);
106 x3 <<= 1;
107 }
108 } else {
109 ix = (x0 >> 16) - 16383;
110 x0 = iu | (x0 & im);
111 }
112
113 /* determine iy = ilogbl(y) */
114 if (y0 < iu) { /* subnormal y */
115 iy = -16382;
116 while (y0 == 0) {
117 iy -= 16;
118 y0 = y1 >> 16;
119 y1 = (y1 << 16) | (y2 >> 16);
120 y2 = (y2 << 16) | (y3 >> 16);
121 y3 = (y3 << 16);
122 }
123 while (y0 < iu) {
124 iy -= 1;
125 y0 = (y0 << 1) | (y1 >> 31);
126 y1 = (y1 << 1) | (y2 >> 31);
127 y2 = (y2 << 1) | (y3 >> 31);
128 y3 <<= 1;
129 }
130 } else {
131 iy = (y0 >> 16) - 16383;
132 y0 = iu | (y0 & im);
133 }
134
135
136 /* fix point fmod */
137 n = ix - iy;
138 m = 0;
139 while (n--) {
140 while (x0 == 0 && n >= 16) {
141 m <<= 16;
142 n -= 16;
143 x0 = x1 >> 16;
144 x1 = (x1 << 16) | (x2 >> 16);
145 x2 = (x2 << 16) | (x3 >> 16);
146 x3 = (x3 << 16);
147 }
148 while (x0 < iu && n >= 1) {
149 m += m;
150 n -= 1;
151 x0 = (x0 << 1) | (x1 >> 31);
152 x1 = (x1 << 1) | (x2 >> 31);
153 x2 = (x2 << 1) | (x3 >> 31);
154 x3 = (x3 << 1);
155 }
156 carry = 0;
157 z3 = x3 - y3;
158 carry = z3 > x3;
159 if (carry == 0) {
160 z2 = x2 - y2;
161 carry = z2 > x2;
162 } else {
163 z2 = x2 - y2 - 1;
164 carry = z2 >= x2;
165 }
166 if (carry == 0) {
167 z1 = x1 - y1;
168 carry = z1 > x1;
169 } else {
170 z1 = x1 - y1 - 1;
171 carry = z1 >= x1;
172 }
173 z0 = x0 - y0 - carry;
174 if (z0 < 0) { /* double x */
175 x0 = x0 + x0 + ((x1 & is) != 0);
176 x1 = x1 + x1 + ((x2 & is) != 0);
177 x2 = x2 + x2 + ((x3 & is) != 0);
178 x3 = x3 + x3;
179 m += m;
180 } else {
181 m += 1;
182 if (z0 == 0) {
183 if ((z1 | z2 | z3) == 0) {
184 /* 0: we are done */
185 if (n < 31)
186 m <<= (1 + n);
187 else
188 m = 0;
189 m &= ~0x80000000;
190 *quo = sq >= 0 ? m : -m;
191 __H0(a) = hx & is;
192 __H1(a) = __H2(a) = __H3(a) = 0;
193 return (a);
194 }
195 }
196 /* x = z << 1 */
197 z0 = z0 + z0 + ((z1 & is) != 0);
198 z1 = z1 + z1 + ((z2 & is) != 0);
199 z2 = z2 + z2 + ((z3 & is) != 0);
200 z3 = z3 + z3;
201 x0 = z0;
202 x1 = z1;
203 x2 = z2;
204 x3 = z3;
205 m += m;
206 }
207 }
208 carry = 0;
209 z3 = x3 - y3;
210 carry = z3 > x3;
211 if (carry == 0) {
212 z2 = x2 - y2;
213 carry = z2 > x2;
214 } else {
215 z2 = x2 - y2 - 1;
216 carry = z2 >= x2;
217 }
218 if (carry == 0) {
219 z1 = x1 - y1;
220 carry = z1 > x1;
221 } else {
222 z1 = x1 - y1 - 1;
223 carry = z1 >= x1;
224 }
225 z0 = x0 - y0 - carry;
226 if (z0 >= 0) {
227 x0 = z0;
228 x1 = z1;
229 x2 = z2;
230 x3 = z3;
231 m += 1;
232 }
233 m &= ~0x80000000;
234 *quo = sq >= 0 ? m : -m;
235
236 /* convert back to floating value and restore the sign */
237 if ((x0 | x1 | x2 | x3) == 0) {
238 __H0(a) = hx & is;
239 __H1(a) = __H2(a) = __H3(a) = 0;
240 return (a);
241 }
242 while (x0 < iu) {
243 if (x0 == 0) {
244 iy -= 16;
245 x0 = x1 >> 16;
246 x1 = (x1 << 16) | (x2 >> 16);
247 x2 = (x2 << 16) | (x3 >> 16);
248 x3 = (x3 << 16);
249 } else {
250 x0 = x0 + x0 + ((x1 & is) != 0);
251 x1 = x1 + x1 + ((x2 & is) != 0);
252 x2 = x2 + x2 + ((x3 & is) != 0);
253 x3 = x3 + x3;
254 iy -= 1;
255 }
256 }
257
258 /* normalize output */
259 if (iy >= -16382) {
260 __H0(a) = sx | (x0 - iu) | ((iy + 16383) << 16);
261 __H1(a) = x1;
262 __H2(a) = x2;
263 __H3(a) = x3;
264 } else { /* subnormal output */
265 n = -16382 - iy;
266 k = n & 31;
267 if (k <= 16) {
268 x3 = (x2 << (32 - k)) | (x3 >> k);
269 x2 = (x1 << (32 - k)) | (x2 >> k);
270 x1 = (x0 << (32 - k)) | (x1 >> k);
271 x0 >>= k;
272 } else {
273 x3 = (x2 << (32 - k)) | (x3 >> k);
274 x2 = (x1 << (32 - k)) | (x2 >> k);
275 x1 = (x0 << (32 - k)) | (x1 >> k);
276 x0 = 0;
277 }
278 while (n >= 32) {
279 n -= 32;
280 x3 = x2;
281 x2 = x1;
282 x1 = x0;
283 x0 = 0;
284 }
285 __H0(a) = x0 | sx;
286 __H1(a) = x1;
287 __H2(a) = x2;
288 __H3(a) = x3;
289 a *= one;
290 }
291 return (a);
292 }
293
294 long double
295 remquol(long double x, long double y, int *quo) {
296 int hx, hy, sx, sq;
297 long double v;
298
299 hx = __H0(x); /* high word of x */
300 hy = __H0(y); /* high word of y */
301 sx = hx & is; /* sign of x */
302 sq = (hx ^ hy) & is; /* sign of x/y */
303 hx ^= sx; /* |x| */
304 hy &= ~0x80000000;
305
306 /* purge off exception values */
307 *quo = 0;
308 /* y=0, y is NaN, x is NaN or inf */
309 if (y == 0.0L || y != y || hx >= 0x7fff0000)
310 return ((x * y) / (x * y));
311
312 y = fabsl(y);
313 x = fabsl(x);
314 if (hy <= 0x7ffdffff) {
315 x = fmodquol(x, y + y, quo);
316 *quo = ((*quo) & 0x3fffffff) << 1;
317 }
318 if (hy < 0x00020000) {
319 if (x + x > y) {
320 *quo += 1;
321 if (x == y)
322 x = zero;
323 else
324 x -= y;
325 if (x + x >= y) {
326 x -= y;
327 *quo += 1;
328 }
329 }
330 } else {
331 v = 0.5L * y;
332 if (x > v) {
333 *quo += 1;
334 if (x == y)
335 x = zero;
336 else
337 x -= y;
338 if (x >= v) {
339 x -= y;
340 *quo += 1;
341 }
342 }
343 }
344 if (sq != 0)
345 *quo = -(*quo);
346 return (sx == 0 ? x : -x);
347 }