fe_mul.c 10 KB

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  1. #include "fe.h"
  2. #include "crypto_int64.h"
  3. /*
  4. h = f * g
  5. Can overlap h with f or g.
  6. Preconditions:
  7. |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
  8. |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
  9. Postconditions:
  10. |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
  11. */
  12. /*
  13. Notes on implementation strategy:
  14. Using schoolbook multiplication.
  15. Karatsuba would save a little in some cost models.
  16. Most multiplications by 2 and 19 are 32-bit precomputations;
  17. cheaper than 64-bit postcomputations.
  18. There is one remaining multiplication by 19 in the carry chain;
  19. one *19 precomputation can be merged into this,
  20. but the resulting data flow is considerably less clean.
  21. There are 12 carries below.
  22. 10 of them are 2-way parallelizable and vectorizable.
  23. Can get away with 11 carries, but then data flow is much deeper.
  24. With tighter constraints on inputs can squeeze carries into int32.
  25. */
  26. void fe_mul(fe h,const fe f,const fe g)
  27. {
  28. crypto_int32 f0 = f[0];
  29. crypto_int32 f1 = f[1];
  30. crypto_int32 f2 = f[2];
  31. crypto_int32 f3 = f[3];
  32. crypto_int32 f4 = f[4];
  33. crypto_int32 f5 = f[5];
  34. crypto_int32 f6 = f[6];
  35. crypto_int32 f7 = f[7];
  36. crypto_int32 f8 = f[8];
  37. crypto_int32 f9 = f[9];
  38. crypto_int32 g0 = g[0];
  39. crypto_int32 g1 = g[1];
  40. crypto_int32 g2 = g[2];
  41. crypto_int32 g3 = g[3];
  42. crypto_int32 g4 = g[4];
  43. crypto_int32 g5 = g[5];
  44. crypto_int32 g6 = g[6];
  45. crypto_int32 g7 = g[7];
  46. crypto_int32 g8 = g[8];
  47. crypto_int32 g9 = g[9];
  48. crypto_int32 g1_19 = 19 * g1; /* 1.959375*2^29 */
  49. crypto_int32 g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
  50. crypto_int32 g3_19 = 19 * g3;
  51. crypto_int32 g4_19 = 19 * g4;
  52. crypto_int32 g5_19 = 19 * g5;
  53. crypto_int32 g6_19 = 19 * g6;
  54. crypto_int32 g7_19 = 19 * g7;
  55. crypto_int32 g8_19 = 19 * g8;
  56. crypto_int32 g9_19 = 19 * g9;
  57. crypto_int32 f1_2 = 2 * f1;
  58. crypto_int32 f3_2 = 2 * f3;
  59. crypto_int32 f5_2 = 2 * f5;
  60. crypto_int32 f7_2 = 2 * f7;
  61. crypto_int32 f9_2 = 2 * f9;
  62. crypto_int64 f0g0 = f0 * (crypto_int64) g0;
  63. crypto_int64 f0g1 = f0 * (crypto_int64) g1;
  64. crypto_int64 f0g2 = f0 * (crypto_int64) g2;
  65. crypto_int64 f0g3 = f0 * (crypto_int64) g3;
  66. crypto_int64 f0g4 = f0 * (crypto_int64) g4;
  67. crypto_int64 f0g5 = f0 * (crypto_int64) g5;
  68. crypto_int64 f0g6 = f0 * (crypto_int64) g6;
  69. crypto_int64 f0g7 = f0 * (crypto_int64) g7;
  70. crypto_int64 f0g8 = f0 * (crypto_int64) g8;
  71. crypto_int64 f0g9 = f0 * (crypto_int64) g9;
  72. crypto_int64 f1g0 = f1 * (crypto_int64) g0;
  73. crypto_int64 f1g1_2 = f1_2 * (crypto_int64) g1;
  74. crypto_int64 f1g2 = f1 * (crypto_int64) g2;
  75. crypto_int64 f1g3_2 = f1_2 * (crypto_int64) g3;
  76. crypto_int64 f1g4 = f1 * (crypto_int64) g4;
  77. crypto_int64 f1g5_2 = f1_2 * (crypto_int64) g5;
  78. crypto_int64 f1g6 = f1 * (crypto_int64) g6;
  79. crypto_int64 f1g7_2 = f1_2 * (crypto_int64) g7;
  80. crypto_int64 f1g8 = f1 * (crypto_int64) g8;
  81. crypto_int64 f1g9_38 = f1_2 * (crypto_int64) g9_19;
  82. crypto_int64 f2g0 = f2 * (crypto_int64) g0;
  83. crypto_int64 f2g1 = f2 * (crypto_int64) g1;
  84. crypto_int64 f2g2 = f2 * (crypto_int64) g2;
  85. crypto_int64 f2g3 = f2 * (crypto_int64) g3;
  86. crypto_int64 f2g4 = f2 * (crypto_int64) g4;
  87. crypto_int64 f2g5 = f2 * (crypto_int64) g5;
  88. crypto_int64 f2g6 = f2 * (crypto_int64) g6;
  89. crypto_int64 f2g7 = f2 * (crypto_int64) g7;
  90. crypto_int64 f2g8_19 = f2 * (crypto_int64) g8_19;
  91. crypto_int64 f2g9_19 = f2 * (crypto_int64) g9_19;
  92. crypto_int64 f3g0 = f3 * (crypto_int64) g0;
  93. crypto_int64 f3g1_2 = f3_2 * (crypto_int64) g1;
  94. crypto_int64 f3g2 = f3 * (crypto_int64) g2;
  95. crypto_int64 f3g3_2 = f3_2 * (crypto_int64) g3;
  96. crypto_int64 f3g4 = f3 * (crypto_int64) g4;
  97. crypto_int64 f3g5_2 = f3_2 * (crypto_int64) g5;
  98. crypto_int64 f3g6 = f3 * (crypto_int64) g6;
  99. crypto_int64 f3g7_38 = f3_2 * (crypto_int64) g7_19;
  100. crypto_int64 f3g8_19 = f3 * (crypto_int64) g8_19;
  101. crypto_int64 f3g9_38 = f3_2 * (crypto_int64) g9_19;
  102. crypto_int64 f4g0 = f4 * (crypto_int64) g0;
  103. crypto_int64 f4g1 = f4 * (crypto_int64) g1;
  104. crypto_int64 f4g2 = f4 * (crypto_int64) g2;
  105. crypto_int64 f4g3 = f4 * (crypto_int64) g3;
  106. crypto_int64 f4g4 = f4 * (crypto_int64) g4;
  107. crypto_int64 f4g5 = f4 * (crypto_int64) g5;
  108. crypto_int64 f4g6_19 = f4 * (crypto_int64) g6_19;
  109. crypto_int64 f4g7_19 = f4 * (crypto_int64) g7_19;
  110. crypto_int64 f4g8_19 = f4 * (crypto_int64) g8_19;
  111. crypto_int64 f4g9_19 = f4 * (crypto_int64) g9_19;
  112. crypto_int64 f5g0 = f5 * (crypto_int64) g0;
  113. crypto_int64 f5g1_2 = f5_2 * (crypto_int64) g1;
  114. crypto_int64 f5g2 = f5 * (crypto_int64) g2;
  115. crypto_int64 f5g3_2 = f5_2 * (crypto_int64) g3;
  116. crypto_int64 f5g4 = f5 * (crypto_int64) g4;
  117. crypto_int64 f5g5_38 = f5_2 * (crypto_int64) g5_19;
  118. crypto_int64 f5g6_19 = f5 * (crypto_int64) g6_19;
  119. crypto_int64 f5g7_38 = f5_2 * (crypto_int64) g7_19;
  120. crypto_int64 f5g8_19 = f5 * (crypto_int64) g8_19;
  121. crypto_int64 f5g9_38 = f5_2 * (crypto_int64) g9_19;
  122. crypto_int64 f6g0 = f6 * (crypto_int64) g0;
  123. crypto_int64 f6g1 = f6 * (crypto_int64) g1;
  124. crypto_int64 f6g2 = f6 * (crypto_int64) g2;
  125. crypto_int64 f6g3 = f6 * (crypto_int64) g3;
  126. crypto_int64 f6g4_19 = f6 * (crypto_int64) g4_19;
  127. crypto_int64 f6g5_19 = f6 * (crypto_int64) g5_19;
  128. crypto_int64 f6g6_19 = f6 * (crypto_int64) g6_19;
  129. crypto_int64 f6g7_19 = f6 * (crypto_int64) g7_19;
  130. crypto_int64 f6g8_19 = f6 * (crypto_int64) g8_19;
  131. crypto_int64 f6g9_19 = f6 * (crypto_int64) g9_19;
  132. crypto_int64 f7g0 = f7 * (crypto_int64) g0;
  133. crypto_int64 f7g1_2 = f7_2 * (crypto_int64) g1;
  134. crypto_int64 f7g2 = f7 * (crypto_int64) g2;
  135. crypto_int64 f7g3_38 = f7_2 * (crypto_int64) g3_19;
  136. crypto_int64 f7g4_19 = f7 * (crypto_int64) g4_19;
  137. crypto_int64 f7g5_38 = f7_2 * (crypto_int64) g5_19;
  138. crypto_int64 f7g6_19 = f7 * (crypto_int64) g6_19;
  139. crypto_int64 f7g7_38 = f7_2 * (crypto_int64) g7_19;
  140. crypto_int64 f7g8_19 = f7 * (crypto_int64) g8_19;
  141. crypto_int64 f7g9_38 = f7_2 * (crypto_int64) g9_19;
  142. crypto_int64 f8g0 = f8 * (crypto_int64) g0;
  143. crypto_int64 f8g1 = f8 * (crypto_int64) g1;
  144. crypto_int64 f8g2_19 = f8 * (crypto_int64) g2_19;
  145. crypto_int64 f8g3_19 = f8 * (crypto_int64) g3_19;
  146. crypto_int64 f8g4_19 = f8 * (crypto_int64) g4_19;
  147. crypto_int64 f8g5_19 = f8 * (crypto_int64) g5_19;
  148. crypto_int64 f8g6_19 = f8 * (crypto_int64) g6_19;
  149. crypto_int64 f8g7_19 = f8 * (crypto_int64) g7_19;
  150. crypto_int64 f8g8_19 = f8 * (crypto_int64) g8_19;
  151. crypto_int64 f8g9_19 = f8 * (crypto_int64) g9_19;
  152. crypto_int64 f9g0 = f9 * (crypto_int64) g0;
  153. crypto_int64 f9g1_38 = f9_2 * (crypto_int64) g1_19;
  154. crypto_int64 f9g2_19 = f9 * (crypto_int64) g2_19;
  155. crypto_int64 f9g3_38 = f9_2 * (crypto_int64) g3_19;
  156. crypto_int64 f9g4_19 = f9 * (crypto_int64) g4_19;
  157. crypto_int64 f9g5_38 = f9_2 * (crypto_int64) g5_19;
  158. crypto_int64 f9g6_19 = f9 * (crypto_int64) g6_19;
  159. crypto_int64 f9g7_38 = f9_2 * (crypto_int64) g7_19;
  160. crypto_int64 f9g8_19 = f9 * (crypto_int64) g8_19;
  161. crypto_int64 f9g9_38 = f9_2 * (crypto_int64) g9_19;
  162. crypto_int64 h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
  163. crypto_int64 h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
  164. crypto_int64 h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
  165. crypto_int64 h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
  166. crypto_int64 h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
  167. crypto_int64 h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
  168. crypto_int64 h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38;
  169. crypto_int64 h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19;
  170. crypto_int64 h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38;
  171. crypto_int64 h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ;
  172. crypto_int64 carry0;
  173. crypto_int64 carry1;
  174. crypto_int64 carry2;
  175. crypto_int64 carry3;
  176. crypto_int64 carry4;
  177. crypto_int64 carry5;
  178. crypto_int64 carry6;
  179. crypto_int64 carry7;
  180. crypto_int64 carry8;
  181. crypto_int64 carry9;
  182. /*
  183. |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
  184. i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
  185. |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
  186. i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
  187. */
  188. carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
  189. carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
  190. /* |h0| <= 2^25 */
  191. /* |h4| <= 2^25 */
  192. /* |h1| <= 1.71*2^59 */
  193. /* |h5| <= 1.71*2^59 */
  194. carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
  195. carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
  196. /* |h1| <= 2^24; from now on fits into int32 */
  197. /* |h5| <= 2^24; from now on fits into int32 */
  198. /* |h2| <= 1.41*2^60 */
  199. /* |h6| <= 1.41*2^60 */
  200. carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
  201. carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
  202. /* |h2| <= 2^25; from now on fits into int32 unchanged */
  203. /* |h6| <= 2^25; from now on fits into int32 unchanged */
  204. /* |h3| <= 1.71*2^59 */
  205. /* |h7| <= 1.71*2^59 */
  206. carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
  207. carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
  208. /* |h3| <= 2^24; from now on fits into int32 unchanged */
  209. /* |h7| <= 2^24; from now on fits into int32 unchanged */
  210. /* |h4| <= 1.72*2^34 */
  211. /* |h8| <= 1.41*2^60 */
  212. carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
  213. carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
  214. /* |h4| <= 2^25; from now on fits into int32 unchanged */
  215. /* |h8| <= 2^25; from now on fits into int32 unchanged */
  216. /* |h5| <= 1.01*2^24 */
  217. /* |h9| <= 1.71*2^59 */
  218. carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
  219. /* |h9| <= 2^24; from now on fits into int32 unchanged */
  220. /* |h0| <= 1.1*2^39 */
  221. carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
  222. /* |h0| <= 2^25; from now on fits into int32 unchanged */
  223. /* |h1| <= 1.01*2^24 */
  224. h[0] = h0;
  225. h[1] = h1;
  226. h[2] = h2;
  227. h[3] = h3;
  228. h[4] = h4;
  229. h[5] = h5;
  230. h[6] = h6;
  231. h[7] = h7;
  232. h[8] = h8;
  233. h[9] = h9;
  234. }