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1 /* mpf_div_2exp -- Divide a float by 2^n. | |
2 | |
3 Copyright 1993, 1994, 1996, 2000, 2001, 2002, 2004 Free Software Foundation, | |
4 Inc. | |
5 | |
6 This file is part of the GNU MP Library. | |
7 | |
8 The GNU MP 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 3 of the License, or (at your | |
11 option) any later version. | |
12 | |
13 The GNU MP 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 GNU MP Library. If not, see http://www.gnu.org/licenses/. */ | |
20 | |
21 #include "gmp.h" | |
22 #include "gmp-impl.h" | |
23 | |
24 | |
25 /* Multiples of GMP_NUMB_BITS in exp simply mean an amount subtracted from | |
26 EXP(u) to set EXP(r). The remainder exp%GMP_NUMB_BITS is then a right | |
27 shift for the limb data. | |
28 | |
29 If exp%GMP_NUMB_BITS == 0 then there's no shifting, we effectively just | |
30 do an mpz_set with changed EXP(r). Like mpz_set we take prec+1 limbs in | |
31 this case. Although just prec would suffice, it's nice to have | |
32 mpf_div_2exp with exp==0 come out the same as mpz_set. | |
33 | |
34 When shifting we take up to prec many limbs from the input. Our shift is | |
35 cy = mpn_rshift (PTR(r)+1, PTR(u)+k, ...), where k is the number of low | |
36 limbs dropped from u, and the carry out is stored to PTR(r)[0]. We don't | |
37 try to work extra bits from PTR(u)[k-1] (when k>=1 makes it available) | |
38 into that low carry limb. Just prec limbs (with the high non-zero) from | |
39 the input is enough bits for the application requested precision, no need | |
40 to do extra work. | |
41 | |
42 If r==u the shift will have overlapping operands. When k>=1 (ie. when | |
43 usize > prec), the overlap is in the style supported by rshift (ie. dst | |
44 <= src). | |
45 | |
46 But when r==u and k==0 (ie. usize <= prec), we would have an invalid | |
47 overlap (mpn_rshift (rp+1, rp, ...)). In this case we must instead use | |
48 mpn_lshift (PTR(r), PTR(u), size, NUMB-shift). An lshift by NUMB-shift | |
49 bits gives identical data of course, it's just its overlap restrictions | |
50 which differ. | |
51 | |
52 In both shift cases, the resulting data is abs_usize+1 limbs. "adj" is | |
53 used to add +1 to that size if the high is non-zero (it may of course | |
54 have become zero by the shifting). EXP(u) is the exponent just above | |
55 those abs_usize+1 limbs, so it gets -1+adj, which means -1 if the high is | |
56 zero, or no change if the high is non-zero. | |
57 | |
58 Enhancements: | |
59 | |
60 The way mpn_lshift is used means successive mpf_div_2exp calls on the | |
61 same operand will accumulate low zero limbs, until prec+1 limbs is | |
62 reached. This is wasteful for subsequent operations. When abs_usize <= | |
63 prec, we should test the low exp%GMP_NUMB_BITS many bits of PTR(u)[0], | |
64 ie. those which would be shifted out by an mpn_rshift. If they're zero | |
65 then use that mpn_rshift. */ | |
66 | |
67 void | |
68 mpf_div_2exp (mpf_ptr r, mpf_srcptr u, unsigned long int exp) | |
69 { | |
70 mp_srcptr up; | |
71 mp_ptr rp = r->_mp_d; | |
72 mp_size_t usize; | |
73 mp_size_t abs_usize; | |
74 mp_size_t prec = r->_mp_prec; | |
75 mp_exp_t uexp = u->_mp_exp; | |
76 | |
77 usize = u->_mp_size; | |
78 | |
79 if (UNLIKELY (usize == 0)) | |
80 { | |
81 r->_mp_size = 0; | |
82 r->_mp_exp = 0; | |
83 return; | |
84 } | |
85 | |
86 abs_usize = ABS (usize); | |
87 up = u->_mp_d; | |
88 | |
89 if (exp % GMP_NUMB_BITS == 0) | |
90 { | |
91 prec++; /* retain more precision here as we don't need | |
92 to account for carry-out here */ | |
93 if (abs_usize > prec) | |
94 { | |
95 up += abs_usize - prec; | |
96 abs_usize = prec; | |
97 } | |
98 if (rp != up) | |
99 MPN_COPY_INCR (rp, up, abs_usize); | |
100 r->_mp_exp = uexp - exp / GMP_NUMB_BITS; | |
101 } | |
102 else | |
103 { | |
104 mp_limb_t cy_limb; | |
105 mp_size_t adj; | |
106 if (abs_usize > prec) | |
107 { | |
108 up += abs_usize - prec; | |
109 abs_usize = prec; | |
110 /* Use mpn_rshift since mpn_lshift operates downwards, and we | |
111 therefore would clobber part of U before using that part, in case | |
112 R is the same variable as U. */ | |
113 cy_limb = mpn_rshift (rp + 1, up, abs_usize, exp % GMP_NUMB_BITS); | |
114 rp[0] = cy_limb; | |
115 adj = rp[abs_usize] != 0; | |
116 } | |
117 else | |
118 { | |
119 cy_limb = mpn_lshift (rp, up, abs_usize, | |
120 GMP_NUMB_BITS - exp % GMP_NUMB_BITS); | |
121 rp[abs_usize] = cy_limb; | |
122 adj = cy_limb != 0; | |
123 } | |
124 | |
125 abs_usize += adj; | |
126 r->_mp_exp = uexp - exp / GMP_NUMB_BITS - 1 + adj; | |
127 } | |
128 r->_mp_size = usize >= 0 ? abs_usize : -abs_usize; | |
129 } | |
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