1 /* mpn_invert_limb -- Invert a normalized limb.
2
3 Copyright 1991, 2000, 2001 Free Software Foundation, Inc.
4
5 This file is part of the GNU MP Library.
6
7 The GNU MP Library is free software; you can redistribute it and/or modify
8 it under the terms of either:
9
10 * the GNU Lesser General Public License as published by the Free
11 Software Foundation; either version 3 of the License, or (at your
12 option) any later version.
13
14 or
15
16 * the GNU General Public License as published by the Free Software
17 Foundation; either version 2 of the License, or (at your option) any
18 later version.
19
20 or both in parallel, as here.
21
22 The GNU MP Library is distributed in the hope that it will be useful, but
23 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
24 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
25 for more details.
26
27 You should have received copies of the GNU General Public License and the
28 GNU Lesser General Public License along with the GNU MP Library. If not,
29 see https://www.gnu.org/licenses/. */
30
31 #include "gmp.h"
32 #include "gmp-impl.h"
33 #include "longlong.h"
34
35 /*
36 This is needed to make configure define HAVE_NATIVE_mpn_invert_limb:
37 PROLOGUE(mpn_invert_limb)
38 */
39
40 static const unsigned short int approx_tab[0x100] =
41 {
42 /* 0x400, */
43 0x3ff,
44 0x3fc, 0x3f8, 0x3f4, 0x3f0, 0x3ec, 0x3e8, 0x3e4,
45 0x3e0, 0x3dd, 0x3d9, 0x3d5, 0x3d2, 0x3ce, 0x3ca, 0x3c7,
46 0x3c3, 0x3c0, 0x3bc, 0x3b9, 0x3b5, 0x3b2, 0x3ae, 0x3ab,
47 0x3a8, 0x3a4, 0x3a1, 0x39e, 0x39b, 0x397, 0x394, 0x391,
48 0x38e, 0x38b, 0x387, 0x384, 0x381, 0x37e, 0x37b, 0x378,
49 0x375, 0x372, 0x36f, 0x36c, 0x369, 0x366, 0x364, 0x361,
50 0x35e, 0x35b, 0x358, 0x355, 0x353, 0x350, 0x34d, 0x34a,
51 0x348, 0x345, 0x342, 0x340, 0x33d, 0x33a, 0x338, 0x335,
52 0x333, 0x330, 0x32e, 0x32b, 0x329, 0x326, 0x324, 0x321,
53 0x31f, 0x31c, 0x31a, 0x317, 0x315, 0x313, 0x310, 0x30e,
54 0x30c, 0x309, 0x307, 0x305, 0x303, 0x300, 0x2fe, 0x2fc,
55 0x2fa, 0x2f7, 0x2f5, 0x2f3, 0x2f1, 0x2ef, 0x2ec, 0x2ea,
56 0x2e8, 0x2e6, 0x2e4, 0x2e2, 0x2e0, 0x2de, 0x2dc, 0x2da,
57 0x2d8, 0x2d6, 0x2d4, 0x2d2, 0x2d0, 0x2ce, 0x2cc, 0x2ca,
58 0x2c8, 0x2c6, 0x2c4, 0x2c2, 0x2c0, 0x2be, 0x2bc, 0x2bb,
59 0x2b9, 0x2b7, 0x2b5, 0x2b3, 0x2b1, 0x2b0, 0x2ae, 0x2ac,
60 0x2aa, 0x2a8, 0x2a7, 0x2a5, 0x2a3, 0x2a1, 0x2a0, 0x29e,
61 0x29c, 0x29b, 0x299, 0x297, 0x295, 0x294, 0x292, 0x291,
62 0x28f, 0x28d, 0x28c, 0x28a, 0x288, 0x287, 0x285, 0x284,
63 0x282, 0x280, 0x27f, 0x27d, 0x27c, 0x27a, 0x279, 0x277,
64 0x276, 0x274, 0x273, 0x271, 0x270, 0x26e, 0x26d, 0x26b,
65 0x26a, 0x268, 0x267, 0x265, 0x264, 0x263, 0x261, 0x260,
66 0x25e, 0x25d, 0x25c, 0x25a, 0x259, 0x257, 0x256, 0x255,
67 0x253, 0x252, 0x251, 0x24f, 0x24e, 0x24d, 0x24b, 0x24a,
68 0x249, 0x247, 0x246, 0x245, 0x243, 0x242, 0x241, 0x240,
69 0x23e, 0x23d, 0x23c, 0x23b, 0x239, 0x238, 0x237, 0x236,
70 0x234, 0x233, 0x232, 0x231, 0x230, 0x22e, 0x22d, 0x22c,
71 0x22b, 0x22a, 0x229, 0x227, 0x226, 0x225, 0x224, 0x223,
72 0x222, 0x220, 0x21f, 0x21e, 0x21d, 0x21c, 0x21b, 0x21a,
73 0x219, 0x218, 0x216, 0x215, 0x214, 0x213, 0x212, 0x211,
74 0x210, 0x20f, 0x20e, 0x20d, 0x20c, 0x20b, 0x20a, 0x209,
75 0x208, 0x207, 0x206, 0x205, 0x204, 0x203, 0x202, 0x201,
76 };
77
78 /* iteration: z = 2z-(z**2)d */
79
80 mp_limb_t
mpn_invert_limb(mp_limb_t d)81 mpn_invert_limb (mp_limb_t d)
82 {
83 mp_limb_t z, z2l, z2h, tl, th;
84 mp_limb_t xh, xl;
85 mp_limb_t zh, zl;
86
87 #if GMP_LIMB_BITS == 32
88 z = approx_tab[(d >> 23) - 0x100] << 6; /* z < 2^16 */
89
90 z2l = z * z; /* z2l < 2^32 */
91 umul_ppmm (th, tl, z2l, d);
92 z = (z << 17) - (th << 1);
93 #endif
94 #if GMP_LIMB_BITS == 64
95 z = approx_tab[(d >> 55) - 0x100] << 6; /* z < 2^16 */
96
97 z2l = z * z; /* z2l < 2^32 */
98 th = z2l * (d >> 32); /* th < 2^64 */
99 z = (z << 17) - (th >> 31); /* z < 2^32 */
100
101 z2l = z * z;
102 umul_ppmm (th, tl, z2l, d);
103 z = (z << 33) - (th << 1);
104 #endif
105
106 umul_ppmm (z2h, z2l, z, z);
107 umul_ppmm (th, tl, z2h, d);
108 umul_ppmm (xh, xl, z2l, d);
109 tl += xh;
110 th += tl < xh;
111 th = (th << 2) | (tl >> GMP_LIMB_BITS - 2);
112 tl = tl << 2;
113 sub_ddmmss (zh, zl, z << 2, 0, th, tl);
114
115 umul_ppmm (xh, xl, d, zh);
116 xh += d; /* add_ssaaaa (xh, xl, xh, xl, d, 0); */
117 if (~xh != 0)
118 {
119 add_ssaaaa (xh, xl, xh, xl, 0, d);
120 zh++;
121 }
122
123 add_ssaaaa (xh, xl, xh, xl, 0, d);
124 if (xh != 0)
125 zh++;
126
127 return zh;
128 }
129