@@ -140,20 +140,40 @@ static inline void bc_standard_sqrt(bc_num *num, size_t rscale, size_t num_calc_
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bc_convert_to_vector_with_zero_pad (n_vector , nend , n_full_len , n_extend_zeros );
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- /* Prepare guess_vector (Temporary implementation) */
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- for (size_t i = 0 ; i < guess_arr_size - 2 ; i ++ ) {
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- guess_vector [i ] = BC_VECTOR_BOUNDARY_NUM - 1 ;
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+ /* Prepare guess_vector. Use bc_fast_sqrt_vector to quickly obtain a highly accurate initial value. */
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+ size_t n_top_len_for_initial_guess = SIZEOF_SIZE_T == 8 ? 18 : 10 ;
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+
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+ /* Set the number of digits of num to be used as the initial value for Newton's method.
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+ * Just as the square roots of 1000 and 100 differ significantly, the number of digits
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+ * to "ignore" here must be even. */
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+ if (num_calc_full_len & 1 ) {
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+ n_top_len_for_initial_guess -- ;
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}
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- if (guess_full_len % BC_VECTOR_SIZE == 0 ) {
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- guess_vector [guess_arr_size - 2 ] = BC_VECTOR_BOUNDARY_NUM - 1 ;
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- } else {
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- guess_vector [guess_arr_size - 2 ] = 0 ;
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- for (size_t i = 0 ; i < guess_full_len % BC_VECTOR_SIZE ; i ++ ) {
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- guess_vector [guess_arr_size - 2 ] *= BASE ;
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- guess_vector [guess_arr_size - 2 ] += 9 ;
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- }
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+ BC_VECTOR n_top = n_vector [n_arr_size - 1 ];
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+ size_t n_top_index = n_arr_size - 2 ;
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+ size_t count = n_top_len_for_initial_guess - num_calc_full_len % BC_VECTOR_SIZE ;
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+ while (count >= BC_VECTOR_SIZE ) {
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+ n_top *= BC_VECTOR_SIZE ;
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+ n_top += n_vector [n_top_index -- ];
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+ count -= BC_VECTOR_SIZE ;
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}
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- guess_vector [guess_arr_size - 1 ] = 0 ;
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+ if (count > 0 ) {
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+ n_top *= BC_POW_10_LUT [count ];
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+ n_top += n_vector [n_top_index ] / BC_POW_10_LUT [BC_VECTOR_SIZE - count ];
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+ }
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+
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+ for (size_t i = 0 ; i < guess_arr_size ; i ++ ) {
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+ guess_vector [i ] = 0 ;
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+ }
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+ BC_VECTOR initial_guess = bc_fast_sqrt_vector (n_top );
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+
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+ size_t initial_guess_len = SIZEOF_SIZE_T == 8 ? 9 : 5 ;
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+ size_t guess_top_vector_len = guess_full_len % BC_VECTOR_SIZE == 0 ? BC_VECTOR_SIZE : guess_full_len % BC_VECTOR_SIZE ;
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+ size_t guess_len_diff = initial_guess_len - guess_top_vector_len ;
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+ guess_vector [guess_arr_size - 2 ] = initial_guess / BC_POW_10_LUT [guess_len_diff ];
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+ initial_guess %= BC_POW_10_LUT [guess_len_diff ];
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+ guess_vector [guess_arr_size - 3 ] = initial_guess * BC_POW_10_LUT [BC_VECTOR_SIZE - guess_len_diff ];
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+
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guess1_vector [guess_arr_size - 1 ] = 0 ;
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size_t quot_size = n_arr_size - (guess_arr_size - 1 ) + 1 ;
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