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annotate libquadmath/printf/mul.c @ 158:494b0b89df80 default tip

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Mon, 25 May 2020 18:13:55 +0900
parents 561a7518be6b
children
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rev   line source
68
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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1 /* mpn_mul -- Multiply two natural numbers.
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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2
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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3 Copyright (C) 1991, 1993, 1994, 1996 Free Software Foundation, Inc.
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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4
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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5 This file is part of the GNU MP Library.
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parents:
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6
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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7 The GNU MP Library is free software; you can redistribute it and/or modify
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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8 it under the terms of the GNU Lesser General Public License as published by
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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9 the Free Software Foundation; either version 2.1 of the License, or (at your
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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10 option) any later version.
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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11
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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12 The GNU MP Library is distributed in the hope that it will be useful, but
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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13 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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14 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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15 License for more details.
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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16
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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17 You should have received a copy of the GNU Lesser General Public License
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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18 along with the GNU MP Library; see the file COPYING.LIB. If not, write to
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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19 the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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20 MA 02111-1307, USA. */
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parents:
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21
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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22 #include <config.h>
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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23 #include "gmp-impl.h"
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24
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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25 /* Multiply the natural numbers u (pointed to by UP, with USIZE limbs)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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26 and v (pointed to by VP, with VSIZE limbs), and store the result at
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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27 PRODP. USIZE + VSIZE limbs are always stored, but if the input
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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28 operands are normalized. Return the most significant limb of the
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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29 result.
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30
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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31 NOTE: The space pointed to by PRODP is overwritten before finished
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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32 with U and V, so overlap is an error.
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33
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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34 Argument constraints:
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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35 1. USIZE >= VSIZE.
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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36 2. PRODP != UP and PRODP != VP, i.e. the destination
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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37 must be distinct from the multiplier and the multiplicand. */
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38
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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39 /* If KARATSUBA_THRESHOLD is not already defined, define it to a
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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40 value which is good on most machines. */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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41 #ifndef KARATSUBA_THRESHOLD
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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42 #define KARATSUBA_THRESHOLD 32
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parents:
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43 #endif
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44
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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45 mp_limb_t
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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46 #if __STDC__
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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47 mpn_mul (mp_ptr prodp,
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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48 mp_srcptr up, mp_size_t usize,
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49 mp_srcptr vp, mp_size_t vsize)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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50 #else
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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51 mpn_mul (prodp, up, usize, vp, vsize)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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52 mp_ptr prodp;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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53 mp_srcptr up;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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54 mp_size_t usize;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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55 mp_srcptr vp;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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56 mp_size_t vsize;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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57 #endif
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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58 {
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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59 mp_ptr prod_endp = prodp + usize + vsize - 1;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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60 mp_limb_t cy;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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61 mp_ptr tspace;
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62
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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63 if (vsize < KARATSUBA_THRESHOLD)
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64 {
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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65 /* Handle simple cases with traditional multiplication.
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66
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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67 This is the most critical code of the entire function. All
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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68 multiplies rely on this, both small and huge. Small ones arrive
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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69 here immediately. Huge ones arrive here as this is the base case
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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70 for Karatsuba's recursive algorithm below. */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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71 mp_size_t i;
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72 mp_limb_t cy_limb;
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73 mp_limb_t v_limb;
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74
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75 if (vsize == 0)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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76 return 0;
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77
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78 /* Multiply by the first limb in V separately, as the result can be
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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79 stored (not added) to PROD. We also avoid a loop for zeroing. */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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80 v_limb = vp[0];
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81 if (v_limb <= 1)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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82 {
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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83 if (v_limb == 1)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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84 MPN_COPY (prodp, up, usize);
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85 else
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86 MPN_ZERO (prodp, usize);
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87 cy_limb = 0;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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88 }
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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89 else
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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90 cy_limb = mpn_mul_1 (prodp, up, usize, v_limb);
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91
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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92 prodp[usize] = cy_limb;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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93 prodp++;
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94
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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95 /* For each iteration in the outer loop, multiply one limb from
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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96 U with one limb from V, and add it to PROD. */
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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97 for (i = 1; i < vsize; i++)
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98 {
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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99 v_limb = vp[i];
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100 if (v_limb <= 1)
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101 {
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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102 cy_limb = 0;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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103 if (v_limb == 1)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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104 cy_limb = mpn_add_n (prodp, prodp, up, usize);
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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105 }
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parents:
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106 else
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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107 cy_limb = mpn_addmul_1 (prodp, up, usize, v_limb);
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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108
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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109 prodp[usize] = cy_limb;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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110 prodp++;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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111 }
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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112 return cy_limb;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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113 }
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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114
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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115 tspace = (mp_ptr) alloca (2 * vsize * BYTES_PER_MP_LIMB);
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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116 MPN_MUL_N_RECURSE (prodp, up, vp, vsize, tspace);
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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117
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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118 prodp += vsize;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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119 up += vsize;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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120 usize -= vsize;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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121 if (usize >= vsize)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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122 {
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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123 mp_ptr tp = (mp_ptr) alloca (2 * vsize * BYTES_PER_MP_LIMB);
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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124 do
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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125 {
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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126 MPN_MUL_N_RECURSE (tp, up, vp, vsize, tspace);
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127 cy = mpn_add_n (prodp, prodp, tp, vsize);
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128 mpn_add_1 (prodp + vsize, tp + vsize, vsize, cy);
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129 prodp += vsize;
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130 up += vsize;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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131 usize -= vsize;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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132 }
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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133 while (usize >= vsize);
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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134 }
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135
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136 /* True: usize < vsize. */
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137
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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138 /* Make life simple: Recurse. */
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139
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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140 if (usize != 0)
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
parents:
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141 {
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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142 mpn_mul (tspace, vp, vsize, up, usize);
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143 cy = mpn_add_n (prodp, prodp, tspace, vsize);
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144 mpn_add_1 (prodp + vsize, tspace + vsize, usize, cy);
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145 }
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146
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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147 return *prod_endp;
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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148 }