mpi-div.c 5.9 KB

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  1. /* mpi-div.c - MPI functions
  2. * Copyright (C) 1994, 1996, 1998, 2001, 2002,
  3. * 2003 Free Software Foundation, Inc.
  4. *
  5. * This file is part of Libgcrypt.
  6. *
  7. * Note: This code is heavily based on the GNU MP Library.
  8. * Actually it's the same code with only minor changes in the
  9. * way the data is stored; this is to support the abstraction
  10. * of an optional secure memory allocation which may be used
  11. * to avoid revealing of sensitive data due to paging etc.
  12. */
  13. #include "mpi-internal.h"
  14. #include "longlong.h"
  15. void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den);
  16. void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor);
  17. void mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor)
  18. {
  19. int divisor_sign = divisor->sign;
  20. MPI temp_divisor = NULL;
  21. /* We need the original value of the divisor after the remainder has been
  22. * preliminary calculated. We have to copy it to temporary space if it's
  23. * the same variable as REM.
  24. */
  25. if (rem == divisor) {
  26. temp_divisor = mpi_copy(divisor);
  27. divisor = temp_divisor;
  28. }
  29. mpi_tdiv_r(rem, dividend, divisor);
  30. if (((divisor_sign?1:0) ^ (dividend->sign?1:0)) && rem->nlimbs)
  31. mpi_add(rem, rem, divisor);
  32. if (temp_divisor)
  33. mpi_free(temp_divisor);
  34. }
  35. void mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor)
  36. {
  37. MPI tmp = mpi_alloc(mpi_get_nlimbs(quot));
  38. mpi_fdiv_qr(quot, tmp, dividend, divisor);
  39. mpi_free(tmp);
  40. }
  41. void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor)
  42. {
  43. int divisor_sign = divisor->sign;
  44. MPI temp_divisor = NULL;
  45. if (quot == divisor || rem == divisor) {
  46. temp_divisor = mpi_copy(divisor);
  47. divisor = temp_divisor;
  48. }
  49. mpi_tdiv_qr(quot, rem, dividend, divisor);
  50. if ((divisor_sign ^ dividend->sign) && rem->nlimbs) {
  51. mpi_sub_ui(quot, quot, 1);
  52. mpi_add(rem, rem, divisor);
  53. }
  54. if (temp_divisor)
  55. mpi_free(temp_divisor);
  56. }
  57. /* If den == quot, den needs temporary storage.
  58. * If den == rem, den needs temporary storage.
  59. * If num == quot, num needs temporary storage.
  60. * If den has temporary storage, it can be normalized while being copied,
  61. * i.e no extra storage should be allocated.
  62. */
  63. void mpi_tdiv_r(MPI rem, MPI num, MPI den)
  64. {
  65. mpi_tdiv_qr(NULL, rem, num, den);
  66. }
  67. void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den)
  68. {
  69. mpi_ptr_t np, dp;
  70. mpi_ptr_t qp, rp;
  71. mpi_size_t nsize = num->nlimbs;
  72. mpi_size_t dsize = den->nlimbs;
  73. mpi_size_t qsize, rsize;
  74. mpi_size_t sign_remainder = num->sign;
  75. mpi_size_t sign_quotient = num->sign ^ den->sign;
  76. unsigned int normalization_steps;
  77. mpi_limb_t q_limb;
  78. mpi_ptr_t marker[5];
  79. int markidx = 0;
  80. /* Ensure space is enough for quotient and remainder.
  81. * We need space for an extra limb in the remainder, because it's
  82. * up-shifted (normalized) below.
  83. */
  84. rsize = nsize + 1;
  85. mpi_resize(rem, rsize);
  86. qsize = rsize - dsize; /* qsize cannot be bigger than this. */
  87. if (qsize <= 0) {
  88. if (num != rem) {
  89. rem->nlimbs = num->nlimbs;
  90. rem->sign = num->sign;
  91. MPN_COPY(rem->d, num->d, nsize);
  92. }
  93. if (quot) {
  94. /* This needs to follow the assignment to rem, in case the
  95. * numerator and quotient are the same.
  96. */
  97. quot->nlimbs = 0;
  98. quot->sign = 0;
  99. }
  100. return;
  101. }
  102. if (quot)
  103. mpi_resize(quot, qsize);
  104. /* Read pointers here, when reallocation is finished. */
  105. np = num->d;
  106. dp = den->d;
  107. rp = rem->d;
  108. /* Optimize division by a single-limb divisor. */
  109. if (dsize == 1) {
  110. mpi_limb_t rlimb;
  111. if (quot) {
  112. qp = quot->d;
  113. rlimb = mpihelp_divmod_1(qp, np, nsize, dp[0]);
  114. qsize -= qp[qsize - 1] == 0;
  115. quot->nlimbs = qsize;
  116. quot->sign = sign_quotient;
  117. } else
  118. rlimb = mpihelp_mod_1(np, nsize, dp[0]);
  119. rp[0] = rlimb;
  120. rsize = rlimb != 0?1:0;
  121. rem->nlimbs = rsize;
  122. rem->sign = sign_remainder;
  123. return;
  124. }
  125. if (quot) {
  126. qp = quot->d;
  127. /* Make sure QP and NP point to different objects. Otherwise the
  128. * numerator would be gradually overwritten by the quotient limbs.
  129. */
  130. if (qp == np) { /* Copy NP object to temporary space. */
  131. np = marker[markidx++] = mpi_alloc_limb_space(nsize);
  132. MPN_COPY(np, qp, nsize);
  133. }
  134. } else /* Put quotient at top of remainder. */
  135. qp = rp + dsize;
  136. normalization_steps = count_leading_zeros(dp[dsize - 1]);
  137. /* Normalize the denominator, i.e. make its most significant bit set by
  138. * shifting it NORMALIZATION_STEPS bits to the left. Also shift the
  139. * numerator the same number of steps (to keep the quotient the same!).
  140. */
  141. if (normalization_steps) {
  142. mpi_ptr_t tp;
  143. mpi_limb_t nlimb;
  144. /* Shift up the denominator setting the most significant bit of
  145. * the most significant word. Use temporary storage not to clobber
  146. * the original contents of the denominator.
  147. */
  148. tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
  149. mpihelp_lshift(tp, dp, dsize, normalization_steps);
  150. dp = tp;
  151. /* Shift up the numerator, possibly introducing a new most
  152. * significant word. Move the shifted numerator in the remainder
  153. * meanwhile.
  154. */
  155. nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
  156. if (nlimb) {
  157. rp[nsize] = nlimb;
  158. rsize = nsize + 1;
  159. } else
  160. rsize = nsize;
  161. } else {
  162. /* The denominator is already normalized, as required. Copy it to
  163. * temporary space if it overlaps with the quotient or remainder.
  164. */
  165. if (dp == rp || (quot && (dp == qp))) {
  166. mpi_ptr_t tp;
  167. tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
  168. MPN_COPY(tp, dp, dsize);
  169. dp = tp;
  170. }
  171. /* Move the numerator to the remainder. */
  172. if (rp != np)
  173. MPN_COPY(rp, np, nsize);
  174. rsize = nsize;
  175. }
  176. q_limb = mpihelp_divrem(qp, 0, rp, rsize, dp, dsize);
  177. if (quot) {
  178. qsize = rsize - dsize;
  179. if (q_limb) {
  180. qp[qsize] = q_limb;
  181. qsize += 1;
  182. }
  183. quot->nlimbs = qsize;
  184. quot->sign = sign_quotient;
  185. }
  186. rsize = dsize;
  187. MPN_NORMALIZE(rp, rsize);
  188. if (normalization_steps && rsize) {
  189. mpihelp_rshift(rp, rp, rsize, normalization_steps);
  190. rsize -= rp[rsize - 1] == 0?1:0;
  191. }
  192. rem->nlimbs = rsize;
  193. rem->sign = sign_remainder;
  194. while (markidx) {
  195. markidx--;
  196. mpi_free_limb_space(marker[markidx]);
  197. }
  198. }