Annotation of OpenXM_contrib/gmp/mpfr/round_prec.c, Revision 1.1.1.1
1.1 ohara 1: /* mpfr_round_raw_generic, mpfr_round_raw2, mpfr_round_raw, mpfr_round_prec,
2: mpfr_can_round, mpfr_can_round_raw -- various rounding functions
3:
4: Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc.
5:
6: This file is part of the MPFR Library.
7:
8: The MPFR Library is free software; you can redistribute it and/or modify
9: it under the terms of the GNU Lesser General Public License as published by
10: the Free Software Foundation; either version 2.1 of the License, or (at your
11: option) any later version.
12:
13: The MPFR Library is distributed in the hope that it will be useful, but
14: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15: or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
16: License for more details.
17:
18: You should have received a copy of the GNU Lesser General Public License
19: along with the MPFR Library; see the file COPYING.LIB. If not, write to
20: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
21: MA 02111-1307, USA. */
22:
23: #include "gmp.h"
24: #include "gmp-impl.h"
25: #include "mpfr.h"
26: #include "mpfr-impl.h"
27:
28: #if (BITS_PER_MP_LIMB & (BITS_PER_MP_LIMB - 1))
29: #error "BITS_PER_MP_LIMB must be a power of 2"
30: #endif
31:
32: /*
33: * If flag = 0, puts in y the value of xp (with precision xprec and
34: * sign 1 if negative=0, -1 otherwise) rounded to precision yprec and
35: * direction rnd_mode. Supposes x is not zero nor NaN nor +/- Infinity
36: * (i.e. *xp != 0). If inexp != NULL, computes the inexact flag of the
37: * rounding.
38: *
39: * In case of even rounding when rnd = GMP_RNDN, returns 2 or -2.
40: *
41: * If flag = 1, just returns whether one should add 1 or not for rounding.
42: *
43: * Note: yprec may be < MPFR_PREC_MIN; in particular, it may be equal
44: * to 1. In this case, the even rounding is done away from 0, which is
45: * a natural generalization. Indeed, a number with 1-bit precision can
46: * be seen as a denormalized number with more precision.
47: */
48:
49: int
50: mpfr_round_raw_generic(mp_limb_t *yp, mp_limb_t *xp, mp_prec_t xprec,
51: int neg, mp_prec_t yprec, mp_rnd_t rnd_mode,
52: int *inexp, int flag)
53: {
54: mp_size_t xsize, nw;
55: mp_limb_t himask, lomask;
56: int rw, carry = 0;
57:
58: xsize = (xprec-1)/BITS_PER_MP_LIMB + 1;
59:
60: nw = yprec / BITS_PER_MP_LIMB;
61: rw = yprec & (BITS_PER_MP_LIMB - 1);
62:
63: if (flag && !inexp && (rnd_mode==GMP_RNDZ || xprec <= yprec
64: || (rnd_mode==GMP_RNDU && neg)
65: || (rnd_mode==GMP_RNDD && neg==0)))
66: return 0;
67:
68: if (rw)
69: {
70: nw++;
71: lomask = ((MP_LIMB_T_ONE << (BITS_PER_MP_LIMB - rw)) - MP_LIMB_T_ONE);
72: himask = ~lomask;
73: }
74: else
75: {
76: lomask = -1;
77: himask = -1;
78: }
79: MPFR_ASSERTN(nw >= 1);
80:
81: if (xprec <= yprec)
82: { /* No rounding is necessary. */
83: /* if yp=xp, maybe an overlap: MPN_COPY_DECR is ok when src <= dst */
84: MPFR_ASSERTN(nw >= xsize);
85: if (inexp)
86: *inexp = 0;
87: if (flag)
88: return 0;
89: MPN_COPY_DECR(yp + (nw - xsize), xp, xsize);
90: MPN_ZERO(yp, nw - xsize);
91: }
92: else
93: {
94: mp_limb_t sb;
95:
96: if ((rnd_mode == GMP_RNDU && neg) ||
97: (rnd_mode == GMP_RNDD && !neg))
98: rnd_mode = GMP_RNDZ;
99:
100: if (inexp || rnd_mode != GMP_RNDZ)
101: {
102: mp_size_t k;
103:
104: k = xsize - nw;
105: if (!rw)
106: k--;
107: MPFR_ASSERTN(k >= 0);
108: sb = xp[k] & lomask; /* First non-significant bits */
109: if (rnd_mode == GMP_RNDN)
110: {
111: mp_limb_t rbmask = MP_LIMB_T_ONE << (BITS_PER_MP_LIMB - rw - 1);
112: if (sb & rbmask) /* rounding bit */
113: sb &= ~rbmask; /* it is 1, clear it */
114: else
115: rnd_mode = GMP_RNDZ; /* it is 0, behave like rounding to 0 */
116: }
117: while (sb == 0 && k > 0)
118: sb = xp[--k];
119: if (rnd_mode == GMP_RNDN)
120: { /* rounding to nearest, with rounding bit = 1 */
121: if (sb == 0) /* Even rounding. */
122: {
123: sb = xp[xsize - nw] & (himask ^ (himask << 1));
124: if (inexp)
125: *inexp = ((neg != 0) ^ (sb != 0))
126: ? MPFR_EVEN_INEX : -MPFR_EVEN_INEX;
127: }
128: else /* sb != 0 */
129: {
130: if (inexp)
131: *inexp = (neg == 0) ? 1 : -1;
132: }
133: }
134: else if (inexp)
135: *inexp = sb == 0 ? 0
136: : (((neg != 0) ^ (rnd_mode != GMP_RNDZ)) ? 1 : -1);
137: }
138: else
139: sb = 0;
140:
141: if (flag)
142: return sb != 0 && rnd_mode != GMP_RNDZ;
143:
144: if (sb != 0 && rnd_mode != GMP_RNDZ)
145: carry = mpn_add_1(yp, xp + xsize - nw, nw,
146: rw ? MP_LIMB_T_ONE << (BITS_PER_MP_LIMB - rw) : 1);
147: else
148: MPN_COPY_INCR(yp, xp + xsize - nw, nw);
149:
150: yp[0] &= himask;
151: }
152:
153: return carry;
154: }
155:
156: int
157: mpfr_round_prec (mpfr_ptr x, mp_rnd_t rnd_mode, mp_prec_t prec)
158: {
159: mp_limb_t *tmp, *xp;
160: int carry, inexact;
161: mp_prec_t nw;
162: TMP_DECL(marker);
163:
164: MPFR_ASSERTN(prec >= MPFR_PREC_MIN && prec <= MPFR_PREC_MAX);
165:
166: nw = 1 + (prec - 1) / BITS_PER_MP_LIMB; /* needed allocated limbs */
167:
168: /* check if x has enough allocated space for the mantissa */
169: if (nw > MPFR_ABSSIZE(x))
170: {
171: MPFR_MANT(x) = (mp_ptr) (*__gmp_reallocate_func)
172: (MPFR_MANT(x), (size_t) MPFR_ABSSIZE(x) * BYTES_PER_MP_LIMB,
173: (size_t) nw * BYTES_PER_MP_LIMB);
174: MPFR_SET_ABSSIZE(x, nw); /* new number of allocated limbs */
175: }
176:
177: if (MPFR_IS_NAN(x))
178: MPFR_RET_NAN;
179:
180: if (MPFR_IS_INF(x))
181: return 0; /* infinity is exact */
182:
183: /* x is a real number */
184:
185: TMP_MARK(marker);
186: tmp = TMP_ALLOC (nw * BYTES_PER_MP_LIMB);
187: xp = MPFR_MANT(x);
188: carry = mpfr_round_raw (tmp, xp, MPFR_PREC(x), MPFR_SIGN(x) < 0,
189: prec, rnd_mode, &inexact);
190: MPFR_PREC(x) = prec;
191:
192: if (carry)
193: {
194: mp_exp_t exp = MPFR_EXP(x);
195:
196: if (exp == __mpfr_emax)
197: (void) mpfr_set_overflow(x, rnd_mode, MPFR_SIGN(x));
198: else
199: {
200: MPFR_EXP(x)++;
201: xp[nw - 1] = GMP_LIMB_HIGHBIT;
202: if (nw - 1 > 0)
203: MPN_ZERO(xp, nw - 1);
204: }
205: }
206: else
207: MPN_COPY(xp, tmp, nw);
208:
209: TMP_FREE(marker);
210: return inexact;
211: }
212:
213: /* assumption: BITS_PER_MP_LIMB is a power of 2 */
214:
215: /* assuming b is an approximation of x in direction rnd1
216: with error at most 2^(MPFR_EXP(b)-err), returns 1 if one is
217: able to round exactly x to precision prec with direction rnd2,
218: and 0 otherwise.
219:
220: Side effects: none.
221: */
222:
223: int
224: mpfr_can_round (mpfr_ptr b, mp_exp_t err, mp_rnd_t rnd1,
225: mp_rnd_t rnd2, mp_prec_t prec)
226: {
227: return MPFR_IS_ZERO(b) ? 0 : /* we cannot round if b=0 */
228: mpfr_can_round_raw (MPFR_MANT(b),
229: (MPFR_PREC(b) - 1)/BITS_PER_MP_LIMB + 1,
230: MPFR_SIGN(b), err, rnd1, rnd2, prec);
231: }
232:
233: int
234: mpfr_can_round_raw (mp_limb_t *bp, mp_size_t bn, int neg, mp_exp_t err0,
235: mp_rnd_t rnd1, mp_rnd_t rnd2, mp_prec_t prec)
236: {
237: mp_prec_t err;
238: mp_size_t k, k1, tn;
239: int s, s1;
240: mp_limb_t cc, cc2;
241: mp_limb_t *tmp;
242: TMP_DECL(marker);
243:
244: if (err0 < 0 || (mp_exp_unsigned_t) err0 <= prec)
245: return 0; /* can't round */
246:
247: neg = neg <= 0;
248:
249: /* if the error is smaller than ulp(b), then anyway it will propagate
250: up to ulp(b) */
251: err = ((mp_exp_unsigned_t) err0 > (mp_prec_t) bn * BITS_PER_MP_LIMB) ?
252: (mp_prec_t) bn * BITS_PER_MP_LIMB : err0;
253:
254: /* warning: if k = m*BITS_PER_MP_LIMB, consider limb m-1 and not m */
255: k = (err - 1) / BITS_PER_MP_LIMB;
256: s = err % BITS_PER_MP_LIMB;
257: if (s)
258: s = BITS_PER_MP_LIMB - s;
259: /* the error corresponds to bit s in limb k, the most significant limb
260: being limb 0 */
261: k1 = (prec - 1) / BITS_PER_MP_LIMB;
262: s1 = prec % BITS_PER_MP_LIMB;
263: if (s1)
264: s1 = BITS_PER_MP_LIMB - s1;
265:
266: /* the last significant bit is bit s1 in limb k1 */
267:
268: /* don't need to consider the k1 most significant limbs */
269: k -= k1;
270: bn -= k1;
271: prec -= (mp_prec_t) k1 * BITS_PER_MP_LIMB;
272: /* if when adding or subtracting (1 << s) in bp[bn-1-k], it does not
273: change bp[bn-1] >> s1, then we can round */
274:
275: if (rnd1 == GMP_RNDU)
276: if (neg)
277: rnd1 = GMP_RNDZ;
278:
279: if (rnd1 == GMP_RNDD)
280: rnd1 = neg ? GMP_RNDU : GMP_RNDZ;
281:
282: /* in the sequel, RNDU = towards infinity, RNDZ = towards zero */
283:
284: TMP_MARK(marker);
285: tn = bn;
286: k++; /* since we work with k+1 everywhere */
287: tmp = TMP_ALLOC(tn * BYTES_PER_MP_LIMB);
288: if (bn > k)
289: MPN_COPY (tmp, bp, bn - k);
290:
291: if (rnd1 != GMP_RNDN)
292: { /* GMP_RNDZ or GMP_RNDU */
293: cc = (bp[bn - 1] >> s1) & 1;
294: cc ^= mpfr_round_raw2(bp, bn, neg, rnd2, prec);
295:
296: /* now round b +/- 2^(MPFR_EXP(b)-err) */
297: cc2 = rnd1 == GMP_RNDZ ?
298: mpn_add_1 (tmp + bn - k, bp + bn - k, k, MP_LIMB_T_ONE << s) :
299: mpn_sub_1 (tmp + bn - k, bp + bn - k, k, MP_LIMB_T_ONE << s);
300: }
301: else
302: { /* GMP_RNDN */
303: /* first round b+2^(MPFR_EXP(b)-err) */
304: cc = mpn_add_1 (tmp + bn - k, bp + bn - k, k, MP_LIMB_T_ONE << s);
305: cc = (tmp[bn - 1] >> s1) & 1; /* gives 0 when cc=1 */
306: cc ^= mpfr_round_raw2 (tmp, bn, neg, rnd2, prec);
307:
308: /* now round b-2^(MPFR_EXP(b)-err) */
309: cc2 = mpn_sub_1 (tmp + bn - k, bp + bn - k, k, MP_LIMB_T_ONE << s);
310: }
311:
312: if (cc2 && cc)
313: {
314: TMP_FREE(marker);
315: return 0;
316: }
317:
318: cc2 = (tmp[bn - 1] >> s1) & 1;
319: cc2 ^= mpfr_round_raw2 (tmp, bn, neg, rnd2, prec);
320:
321: TMP_FREE(marker);
322: return cc == cc2;
323: }
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