source/libs/gmp/gmp-src/mpn/cray/ieee/invert_limb.c

   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
  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 }