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-impl.h"
32 #include "longlong.h"
33
34 /*
35 This is needed to make configure define HAVE_NATIVE_mpn_invert_limb:
36 PROLOGUE(mpn_invert_limb)
37 */
38
39 static const unsigned short int approx_tab[0x100] =
40 {
41 /* 0x400, */
42 0x3ff,
43 0x3fc, 0x3f8, 0x3f4, 0x3f0, 0x3ec, 0x3e8, 0x3e4,
44 0x3e0, 0x3dd, 0x3d9, 0x3d5, 0x3d2, 0x3ce, 0x3ca, 0x3c7,
45 0x3c3, 0x3c0, 0x3bc, 0x3b9, 0x3b5, 0x3b2, 0x3ae, 0x3ab,
46 0x3a8, 0x3a4, 0x3a1, 0x39e, 0x39b, 0x397, 0x394, 0x391,
47 0x38e, 0x38b, 0x387, 0x384, 0x381, 0x37e, 0x37b, 0x378,
48 0x375, 0x372, 0x36f, 0x36c, 0x369, 0x366, 0x364, 0x361,
49 0x35e, 0x35b, 0x358, 0x355, 0x353, 0x350, 0x34d, 0x34a,
50 0x348, 0x345, 0x342, 0x340, 0x33d, 0x33a, 0x338, 0x335,
51 0x333, 0x330, 0x32e, 0x32b, 0x329, 0x326, 0x324, 0x321,
52 0x31f, 0x31c, 0x31a, 0x317, 0x315, 0x313, 0x310, 0x30e,
53 0x30c, 0x309, 0x307, 0x305, 0x303, 0x300, 0x2fe, 0x2fc,
54 0x2fa, 0x2f7, 0x2f5, 0x2f3, 0x2f1, 0x2ef, 0x2ec, 0x2ea,
55 0x2e8, 0x2e6, 0x2e4, 0x2e2, 0x2e0, 0x2de, 0x2dc, 0x2da,
56 0x2d8, 0x2d6, 0x2d4, 0x2d2, 0x2d0, 0x2ce, 0x2cc, 0x2ca,
57 0x2c8, 0x2c6, 0x2c4, 0x2c2, 0x2c0, 0x2be, 0x2bc, 0x2bb,
58 0x2b9, 0x2b7, 0x2b5, 0x2b3, 0x2b1, 0x2b0, 0x2ae, 0x2ac,
59 0x2aa, 0x2a8, 0x2a7, 0x2a5, 0x2a3, 0x2a1, 0x2a0, 0x29e,
60 0x29c, 0x29b, 0x299, 0x297, 0x295, 0x294, 0x292, 0x291,
61 0x28f, 0x28d, 0x28c, 0x28a, 0x288, 0x287, 0x285, 0x284,
62 0x282, 0x280, 0x27f, 0x27d, 0x27c, 0x27a, 0x279, 0x277,
63 0x276, 0x274, 0x273, 0x271, 0x270, 0x26e, 0x26d, 0x26b,
64 0x26a, 0x268, 0x267, 0x265, 0x264, 0x263, 0x261, 0x260,
65 0x25e, 0x25d, 0x25c, 0x25a, 0x259, 0x257, 0x256, 0x255,
66 0x253, 0x252, 0x251, 0x24f, 0x24e, 0x24d, 0x24b, 0x24a,
67 0x249, 0x247, 0x246, 0x245, 0x243, 0x242, 0x241, 0x240,
68 0x23e, 0x23d, 0x23c, 0x23b, 0x239, 0x238, 0x237, 0x236,
69 0x234, 0x233, 0x232, 0x231, 0x230, 0x22e, 0x22d, 0x22c,
70 0x22b, 0x22a, 0x229, 0x227, 0x226, 0x225, 0x224, 0x223,
71 0x222, 0x220, 0x21f, 0x21e, 0x21d, 0x21c, 0x21b, 0x21a,
72 0x219, 0x218, 0x216, 0x215, 0x214, 0x213, 0x212, 0x211,
73 0x210, 0x20f, 0x20e, 0x20d, 0x20c, 0x20b, 0x20a, 0x209,
74 0x208, 0x207, 0x206, 0x205, 0x204, 0x203, 0x202, 0x201,
75 };
76
77 /* iteration: z = 2z-(z**2)d */
78
79 mp_limb_t
80 mpn_invert_limb (mp_limb_t d)
81 {
82 mp_limb_t z, z2l, z2h, tl, th;
83 mp_limb_t xh, xl;
84 mp_limb_t zh, zl;
85
86 #if GMP_LIMB_BITS == 32
87 z = approx_tab[(d >> 23) - 0x100] << 6; /* z < 2^16 */
88
89 z2l = z * z; /* z2l < 2^32 */
90 umul_ppmm (th, tl, z2l, d);
91 z = (z << 17) - (th << 1);
92 #endif
93 #if GMP_LIMB_BITS == 64
94 z = approx_tab[(d >> 55) - 0x100] << 6; /* z < 2^16 */
95
96 z2l = z * z; /* z2l < 2^32 */
97 th = z2l * (d >> 32); /* th < 2^64 */
98 z = (z << 17) - (th >> 31); /* z < 2^32 */
99
100 z2l = z * z;
101 umul_ppmm (th, tl, z2l, d);
102 z = (z << 33) - (th << 1);
103 #endif
104
105 umul_ppmm (z2h, z2l, z, z);
106 umul_ppmm (th, tl, z2h, d);
107 umul_ppmm (xh, xl, z2l, d);
108 tl += xh;
109 th += tl < xh;
110 th = (th << 2) | (tl >> GMP_LIMB_BITS - 2);
111 tl = tl << 2;
112 sub_ddmmss (zh, zl, z << 2, 0, th, tl);
113
114 umul_ppmm (xh, xl, d, zh);
115 xh += d; /* add_ssaaaa (xh, xl, xh, xl, d, 0); */
116 if (~xh != 0)
117 {
118 add_ssaaaa (xh, xl, xh, xl, 0, d);
119 zh++;
120 }
121
122 add_ssaaaa (xh, xl, xh, xl, 0, d);
123 if (xh != 0)
124 zh++;
125
126 return zh;
127 }