i4lib

i4lib, a MATLAB code which contains many utility routines for integer 32 bit arithmetic.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

i4lib is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and an Octave version and a Python version.

Related Programs:

c8lib, a MATLAB code which implements certain elementary functions for "C8" or complex 64 bit variables;

i4lib_test

l4lib, a MATLAB code which contains many utility routines, using one byte logical (L4) variables.

quaternions, a MATLAB code which carries out some simple arithmetic operations for quaternions.

r8lib, a MATLAB code which contains many utility routines, using real 64 bit arithmetic.

Reference:

1. Milton Abramowitz, Irene Stegun,
   Handbook of Mathematical Functions,
   National Bureau of Standards, 1964,
   ISBN: 0-486-61272-4,
   LC: QA47.A34.
2. Thomas Cormen, Charles Leiserson, Ronald Rivest,
   Introduction to Algorithms,
   MIT Press, 2001,
   ISBN: 0262032937,
   LC: QA76.C662.
3. Albert Nijenhuis, Herbert Wilf,
   Combinatorial Algorithms for Computers and Calculators,
   Second Edition,
   Academic Press, 1978,
   ISBN: 0-12-519260-6,
   LC: QA164.N54.

Source Code:

• boolean_to_string.m, returns "True" or "False", given a boolean value.
• get_key.m, returns a random key for the random number generator.
• i4_abs.m, returns the absolute value of an I4;
• i4_and.m, returns the AND of two I4's;
• i4_bclr.m, sets a given bit of an I4 to 0.
• i4_bit_hi1.m, returns the location of the highest 1 bit in an I4;
• i4_bit_lo0.m, returns the location of the lowest 0 bit in an I4;
• i4_bit_lo1.m, returns the location of the lowest 1 bit in an I4;
• i4_bit_reverse.m, reverses the bits of an I4.
• i4_bset.m, sets a given bit of an I4 to 1.
• i4_btest.m, is true if bit POS of I is a 1.
• i4_btest_test.m
• i4_ceiling.m, rounds an R8 up to the nearest I4;
• i4_characteristic.m, gives the characteristic for an I4;
• i4_choose.m, computes the binomial coefficient C(N,K) as an I4;
• i4_choose_check.m, checks whether the binomial coefficient C(N,K) can be computed without overflow;
• i4_choose_log.m, computes the logarithm of the binomial coefficient C(N,K);
• i4_div_rounded.m, computes the rounded result of I4 division.
• i4_division.m, computes the rounded result of I4 division.
• i4_divp.m, returns the smallest multiple of J greater than or equal to an I4;
• i4_factorial.m, computes the factorial of an I4;
• i4_factorial_log.m, computes the logarithm of N!;
• i4_factorial2.m, computes the double factorial as an I4;
• i4_factorial2_values.m, returns selected values of the double factorial function..
• i4_fall.m, computes a falling factorial as an I4.
• i4_fall_values.m, returns selected values of the falling factorial function..
• i4_floor.m, computes the "floor" of an I4.
• i4_fraction.m, computes a ratio and returns an I4 result.
• i4_gcd.m, returns the greatest common divisor of two I4's;
• i4_gcdb.m, returns the greatest common divisor of the form K^N of two I4's;
• i4_huge.m, returns a huge I4;
• i4_huge_normalizer.m, returns the "normalizer" for I4_HUGE.
• i4_is_even.m, is true if an I4 is even;
• i4_is_integer.m, is true if an I4 is an integer value;
• i4_is_odd.m, is true if an I4 is odd;
• i4_is_power_of_2.m, is true if an I4 is a power of 2;
• i4_is_power_of_10.m, is true if an I4 is a power of 10;
• i4_is_prime.m, is true if an I4 is prime number;
• i4_lcm.m, returns the least common multiple of two I4's;
• i4_lcm_12n.m, returns the least common multiple of the integer from 1 to N;
• i4_log_2.m, returns the integer part of the logarithm base 2 of an I4;
• i4_log_10.m, returns the integer part of the logarithm base 10 of an I4;
• i4_log_i4.m, logarithm of an I4 to an I4 base;
• i4_log_r8.m, logarithm of an I4 to an R8 base;
• i4_mant.m, returns the mantissa of a real number as an I4;
• i4_max.m, returns the maximum of two I4's;
• i4_min.m, returns the minimum of two I4's;
• i4_mod_inv.m, computes the inverse of an I4 modulo another I4.
• i4_moddiv.m, breaks an I4 into a multiple of a divisor and a remainder;
• i4_modp.m, returns the nonnegative remainder of I4 division;
• i4_not.m, returns the NOT of an I4 with respect to a maximum value;
• i4_or.m, returns the OR of two I4's;
• i4_power.m, returns the value of the J-th power of an I4;
• i4_rise.m, computes a rising factorial as an I4;
• i4_rise_values.m, returns selected values of the rising factorial function;
• i4_sign.m, returns the sign of an I4.
• i4_sign3.m, returns the three-way sign of an I4.
• i4_swap.m, swaps two I4's.
• i4_swap3.m, swaps three I4's;
• i4_to_angle.m, maps I4's to points on a circle;
• i4_to_digits_binary.m, determines the last N binary digits of an I4;
• i4_to_digits_decimal.m, determines the last N decimal digits of an I4;
• i4_to_fac.m, converts an I4 into a product of prime factors;
• i4_to_halton.m, converts an I4 to the I-th Halton number;
• i4_to_isbn.m, converts an I4 to its ISBN representation;
• i4_to_l4.m, converts an I4 to an L4;
• i4_to_pascal.m, converts an I4 to a pair of indices in Pascal's triangle;
• i4_to_pascal_degree.m, converts an I4 to the degree (sum) of the corresponding pair of indices in Pascal's triangle;
• i4_to_triangle_lower.m, converts an I4 to a pair of indices in a lower triangle;
• i4_to_triangle_upper.m, converts an I4 to a pair of indices in an upper triangle;
• i4_uniform_ab.m, returns a pseudorandom I4 between A and B;
• i4_unswap3.m, unswaps three I4's;
• i4_walsh_1d.m, evaluates the Walsh function;
• i4_width.m, returns the printing "width" of an I4;
• i4_wrap.m, forces an I4 to lie between given limits;
• i4_xor.m, returns the exclusive OR of two I4's;
• i4block_print.m, prints an I4BLOCK;
• i4col_compare.m, compares two columns of an I4COL;
• i4col_find.m, searches an I4COL for a given column vector;
• i4col_find_item.m, searches an I4COL for a given scalar value;
• i4col_find_pair_wrap.m, wrap-searches an I4COL for a pair of values;
• i4col_first_index.m, indexes the first occurrence of values in an I4COL.
• i4col_sort_a.m, ascending sorts the columns of an I4COL;
• i4col_sort_d.m, descending sorts the columns of an I4COL;
• i4col_sort2_a.m, ascending sorts the elements of each column of an I4COL;
• i4col_sorted_singleton_count.m, counts the number of singletons in a sorted I4COL;
• i4col_sorted_unique.m, returns the unique elements in a sorted I4COL;
• i4col_sorted_unique_count.m, counts the number of unique elements in a sorted I4COL;
• i4col_swap.m, swaps two columns of an I4COL;
• i4i4_sort_a.m, ascending sorts a pair of integers;
• i4i4i4_sort_a.m, ascending sorts a triple of integers;
• i4int_to_r8int.m, maps an I4 interval to an R8 interval;
• i4list_print.m, prints an I4LIST.
• i4mat_border_add.m, adds a "border" to an I4MAT.
• i4mat_border_cut.m, cuts the "border" of an I4MAT.
• i4mat_elim.m, performs exact Gauss elimination on an I4MAT;
• i4mat_flip_cols.m, flips the columns in an I4MAT;
• i4mat_flip_rows.m, flips the rows in an I4MAT;
• i4mat_histogram.m, returns a histogram of the entries of an I4MAT;
• i4mat_indicator.m, returns the indicator matrix as an I4MAT.
• i4mat_is_binary.m, is true if an I4MAT has only 0 and 1 entries;
• i4mat_is_integer.m, is TRUE if all entries of an I4MAT are actually integers;
• i4mat_l1_inverse.m, returns the inverse of a unit lower triangular I4MAT;
• i4mat_max.m, returns the maximum element in an I4MAT.
• i4mat_max_index.m, returns the location of the maximum element of an I4MAT;
• i4mat_min.m, returns the minimum element in an I4MAT.
• i4mat_min_index.m, returns the location of the minimum element of an I4MAT;
• i4mat_perm.m, applies a permutation to the rows and columns of an I4MAT;
• i4mat_perm_uniform.m, selects a random permutation of an I4MAT;
• i4mat_perm2.m, applies a row and a column permutation to an I4MAT;
• i4mat_perm2_uniform.m, selects random row and column permutations of an I4MAT;
• i4mat_print.m, prints an I4MAT;
• i4mat_print_some.m, prints some of an I4MAT;
• i4mat_product_elementwise.m, computes the elementwise product of two I4MAT's.
• i4mat_rank.m, computes the rank of an I4MAT;
• i4mat_ref.m, returns the integer row echelon form of an I4MAT.
• i4mat_row_reduce.m, divides out a common factor in one row of an I4MAT.
• i4mat_row_swap.m, swaps two rows of an I4MAT.
• i4mat_rref.m, returns the integer reduced row echelon form of an I4MAT.
• i4mat_rref_solve_binary.m, seeks binary solutions (if any) of an integer row reduced echelon form linear system.
• i4mat_rref_solve_binary_nz.m, seeks binary solutions (if any) of an integer row reduced echelon form linear system, but only consider solutions with exactly NZ nonzeros.
• i4mat_rref_system.m, considers an underdetermined integer linear system A*x=b, and uses the integer row reduced echelon form (IRREF) to find the solvable augmented linear system, with degrees of freedom indicated.
• i4mat_sum.m, returns the sum of the entries of an I4MAT.
• i4mat_transpose.m, transposes an I4MAT;
• i4mat_transpose_print.m, prints an I4MAT, transposed;
• i4mat_transpose_print_some.m, prints some of an I4MAT, transposed;
• i4mat_u_solve.m, solves an upper triangular linear system involving only integer values.
• i4mat_u1_inverse.m, returns the inverse of a unit upper triangular I4MAT;
• i4mat_uniform_ab.m, returns an I4MAT of pseudorandom values;
• i4mat_width.m, returns the printing width of an I4MAT;
• i4row_compare.m, compares two rows of an I4ROW.
• i4row_find_item.m, searches the rows of an I4ROW for a given value.
• i4row_find_pair_wrap.m, searches the rows of an I4ROW for a given pair of values.
• i4row_max.m, returns the row maximums of an I4ROW.
• i4row_mean.m, returns the row means of an I4ROW.
• i4row_min.m, returns the row minimums of an I4ROW.
• i4row_sort_a.m, ascending sorts the rows of an I4ROW.
• i4row_sort_rotate_ascending.m, ascending sorts each row of an i4row, with respect to the lexicographic ordering, and allowing only rotations of vector elements.
• i4row_sort_d.m, descending sorts the rows of an I4ROW.
• i4row_sort2_d.m, descending sorts the rows of an I4ROW.
• i4row_sorted_unique.m, returns the unique rows of an I4ROW.
• i4row_sorted_unique_count.m, counts the unique rows of an I4ROW.
• i4row_sum.m, returns the row sums of an I4ROW.
• i4row_swap.m, swaps two rows of an I4ROW.
• i4row_variance.m, returns the row variances of an I4ROW.
• i4rows_to_i4mat.m, copies data from a rowwise vector to a columnwise doubly-indexed array.
• i4vec_add.m, returns C = A + B for I4VEC's.
• i4vec_amax.m, returns the maximum absolute value of an entry in an I4VEC;
• i4vec_amax_index.m, returns the index of the maximum absolute value of an entry in an I4VEC;
• i4vec_amin.m, returns the minimum absolute value of an entry in an I4VEC;
• i4vec_amin_index.m, returns the index of the minimum absolute value of an entry in an I4VEC;
• i4vec_aminz.m, returns the minimum nonzero absolute value of an entry in an I4VEC;
• i4vec_aminz_index.m, returns the index of the minimum nonzero absolute value of an entry in an I4VEC;
• i4vec_ascend_sub.m, returns the longest ascending subsequence of an I4VEC;
• i4vec_binary_next.m, returns the next binary vector.
• i4vec_bracket.m, searches a sorted I4VEC for successive brackets of a value;
• i4vec_choose.m, evaluates the generalized binomial coefficient.
• i4vec_compare.m, compares two I4VEC's;
• i4vec_concatenate.m, concatenates two I4VEC's;
• i4vec_cum.m, returns the cumulative sums of an I4VEC;
• i4vec_cum0.m, returns the cumulative sums of an I4VEC;
• i4vec_decrement.m, decrements an I4VEC;
• i4vec_direct_product.m, forms the elements of the direct product of I4VEC's.
• i4vec_direct_product2.m, forms the elements of the direct product of I4VEC's.
• i4vec_dot_product.m, computes the dot product of two I4VEC's.
• i4vec_eq.m, is TRUE if A1 == A2.
• i4vec_find.m, indexes the first occurrence of a specific value in an I4VEC.
• i4vec_first_index.m, indexes the first occurrence of values in an I4VEC.
• i4vec_frac.m, finds the K-th smallest entry of an I4VEC;
• i4vec_gcd.m, returns the greatest common divisor of the entries of an I4VEC;
• i4vec_ge.m, is TRUE if A1 ≥ A2, for integer vectors A1 and A2, with respect to the lexicographic ordering.
• i4vec_gt.m, is TRUE if A1 %gt; A2, for integer vectors A1 and A2, with respect to the lexicographic ordering.
• i4vec_heap_a.m, sets an I4VEC to a ascending heap;
• i4vec_heap_d.m, sets an I4VEC to a descending heap;
• i4vec_heap_d_extract.m, extracts the maximum value from a descending heap.
• i4vec_heap_d_insert.m, inserts a new value into a descending heap.
• i4vec_heap_d_max.m, returns the maximum value in a descending heap of integers.
• i4vec_histogram.m, returns a histogram of the entries of an I4VEC;
• i4vec_histogram_masked.m, returns a histogram of a masked I4VEC;
• i4vec_identity_row.m, returns a row of the identity matrix as an I4VEC.
• i4vec_imin.m, returns the index of the minimum entry in an I4VEC.
• i4vec_increment.m, increments an I4VEC;
• i4vec_index.m, returns the first location of a given value in an I4VEC.
• i4vec_index_delete_all.m, deletes all occurrences of a value from an indexed sorted list;
• i4vec_index_delete_dupes.m, deletes duplicates from an indexed sorted list.
• i4vec_index_delete_one.m, deletes one copy of a value from an indexed sorted list.
• i4vec_index_insert.m, inserts a value in an indexed sorted list.
• i4vec_index_insert_unique.m, inserts a unique value in an indexed sorted list.
• i4vec_index_order.m, sorts an integer vector using an index vector.
• i4vec_index_search.m, searches for a value in an indexed sorted list.
• i4vec_indexed_heap_d.m, creates a descending heap from an indexed I4VEC.
• i4vec_indexed_heap_d_extract.m, extracts from heap descending indexed I4VEC.
• i4vec_indexed_heap_d_insert.m, inserts value into heap descending indexed I4VEC.
• i4vec_indexed_heap_d_max.m, maximum value in heap descending indexed I4VEC.
• i4vec_indicator0.m, sets an I4VEC to the indicator vector.
• i4vec_indicator1.m, sets an I4VEC to the indicator vector.
• i4vec_insert.m, inserts a value at a particular location in an I4VEC.
• i4vec_is_ascending.m, is true if an I4VEC is ascending;
• i4vec_is_binary.m, is true if an I4VEC has only 0 and 1 entries;
• i4vec_is_coprime.m, is true if all pairs of entries of an I4VEC are coprime;
• i4vec_is_descending.m, is true if an I4VEC is descending;
• i4vec_is_distinct.m, is true if the entries of an I4VEC are distinct;
• i4vec_is_equal.m, is true if two I4VEC's are equal.
• i4vec_is_even_all.m, is true if all entries of an I4VEC are even.
• i4vec_is_even_any.m, is true if any entries of an I4VEC are even.
• i4vec_is_integer.m, is true if an I4VEC is all integer values;
• i4vec_is_lt_any.m, is true if any A is less than B, for I4VEC's.
• i4vec_is_negative_any.m, is true if any entry of an I4VEC is negative;
• i4vec_is_nonpositive_all.m, is true if all entries of an I4VEC are nonpositive;
• i4vec_is_nonzero_any.m, is true if any entry of an I4VEC is nonzero;
• i4vec_is_odd_all.m, is true if all entries of an I4VEC are odd.
• i4vec_is_odd_any.m, is true if any entries of an I4VEC are odd.
• i4vec_is_one.m, is true if all entries of an I4VEC are 1;
• i4vec_is_permutation.m, is true if I4VEC is a permutation of the integer 1 through N.
• i4vec_is_zero.m, is true if all entries of an I4VEC are 0;
• i4vec_lcm.m, returns the lowest common multiple of the entries of an I4VEC;
• i4vec_le.m, is TRUE if A1 ≤ A2, for integer vectors A1 and A2, with respect to the lexicographic ordering.
• i4vec_lt.m, is TRUE if A1 < A2, for integer vectors A1 and A2, with respect to the lexicographic ordering.
• i4vec_max.m, returns the maximum entry in an I4VEC;
• i4vec_max_index.m, returns the index of the maximum entry in an I4VEC;
• i4vec_max_index_last.m, returns the index of the last maximum entry in an I4VEC;
• i4vec_mean.m, returns the mean of an I4VEC;
• i4vec_mean_i4.m, returns the I4 mean of an I4VEC;
• i4vec_median.m, returns the median of an I4VEC;
• i4vec_merge_a.m, merges two ascending-sorted I4VEC's;
• i4vec_min.m, returns the minimum entry in an I4VEC;
• i4vec_min_index.m, returns the index of the minimum entry in an I4VEC;
• i4vec_min_mv.m, determines U(1:N) /\ V for vectors U and a single vector V.
• i4vec_ne.m, is TRUE if A1 =/= A2, for integer vectors A1 and A2.
• i4vec_negone.m, returns an I4VEC of -1's;
• i4vec_nonzero_count.m, counts the nonzero entries in an I4VEC;
• i4vec_nonzero_first.m, left shifts the nonzero entries in an I4VEC;
• i4vec_norm_l0.m, returns the l0 "norm" of an I4VEC;
• i4vec_one.m, returns an I4VEC of 1's;
• i4vec_order_type.m, determines if an I4VEC is (non)strictly ascending/descending;
• i4vec_part.m, partitions an integer into N nearly equal parts;
• i4vec_part_quick_a.m, reorders an I4VEC as part of a quicksort;
• i4vec_permute.m, permutes an I4VEC in place;
• i4vec_permute_uniform.m, randomly permutes an I4VEC in place;
• i4vec_print.m, prints an I4VEC;
• i4vec_print_mask.m, prints masked elements of an I4VEC;
• i4vec_print_part.m, prints part of an I4VEC;
• i4vec_print_select.m, prints selected elements of an I4VEC;
• i4vec_print_some.m, prints some of an I4VEC;
• i4vec_red.m, divides out common factors in an I4VEC;
• i4vec_reverse.m, reverses the order of the entries of an I4VEC;
• i4vec_rotate.m, "rotates" the entries of an I4VEC by M positions;
• i4vec_run_count.m, counts the runs in an I4VEC;
• i4vec_search_binary_a.m, uses binary search on an ascending sorted I4VEC;
• i4vec_search_binary_d.m, uses binary search on a descending sorted I4VEC;
• i4vec_sort_bubble_a.m, ascending sorts an I4VEC using bubble sort;
• i4vec_sort_bubble_d.m, descending sorts an I4VEC using bubble sort;
• i4vec_sort_heap_a.m, ascending sorts an I4VEC using heap sort;
• i4vec_sort_heap_d.m, descending sorts an I4VEC using heap sort;
• i4vec_sort_heap_index_a.m, computes an index vector to ascending sort an I4VEC;
• i4vec_sort_heap_index_d.m, computes an index vector to descending sort an I4VEC;
• i4vec_sort_insert_a.m, ascending sorts an I4VEC using insertion sort;
• i4vec_sort_insert_d.m, descending sorts an I4VEC using insertion sort;
• i4vec_sort_quick_a.m, ascending sorts an I4VEC using quick sort;
• i4vec_sort_shell_a.m, ascending sorts an I4VEC using Shell's sort;
• i4vec_sorted_undex.m, returns unique sorted indexes for a sorted I4VEC.
• i4vec_sorted_unique.m, returns the unique elements in a sorted I4VEC;
• i4vec_sorted_unique_count.m, counts the number of unique elements in a sorted I4VEC;
• i4vec_sorted_unique_hist.m, creates a histogram of the unique elements in a sorted I4VEC;
• i4vec_split_unsort.m, "splits" an unsorted I4VEC based on a splitting value;
• i4vec_std.m, returns the standard deviation of an I4VEC;
• i4vec_sum.m, sums the entries of an I4VEC.
• i4vec_sum_vec.m, computes the pairwise sum of two I4VEC's.
• i4vec_swap.m, swaps two I4VEC's;
• i4vec_transpose_print.m, prints an I4VEC "transposed";
• i4vec_undex.m, returns unique sorted indexes for an I4VEC.
• i4vec_uniform_ab.m, returns a pseudorandom I4VEC in a given range;
• i4vec_unique_count.m, counts the number of unique elements in an unsorted I4VEC;
• i4vec_unique_index.m
• i4vec_value_index.m, indexes I4VEC entries equal to a given value;
• i4vec_value_num.m, counts I4VEC entries equal to a given value;
• i4vec_variance.m, returns the variance of an I4VEC;
• i4vec_width.m, returns the "width" of an I4VEC;
• i4vec_wrap.m, wraps the entries of an I4VEC between LO and HI;
• i4vec2_compare.m, compares pairs of integers stored in two vectors;
• i4vec2_print.m, prints a pair of I4VECs.
• i4vec2_sort_a.m, ascending sorts an I4VEC2;
• i4vec2_sort_d.m, descending sorts an I4VEC2;
• i4vec2_sort_insert_a.m, uses insertion to ascending sort an I4VEC2;
• i4vec2_sorted_unique.m, finds unique elements in a sorted I4VEC2;
• i4vec2_sorted_unique_count.m, counts unique elements in a sorted I4VEC2;
• intspace.m, returns N roughly equally spaced integers between A and B;
• ksub_next4.m, selects the next subset of size K from a set of size N.
• l4_to_i4.m, converts an L4 to an I4;
• l4_xor.m, evaluates the exclusive OR of two L4's.
• pascal_to_i4.m, converts a pair of indices in Pascal's triangle to a linear index;
• perm0_check.m, checks a permutation of (0,...,N-1)
• perm0_uniform.m, selects a random permutation of 0, ...,N-1;
• perm1_check.m, checks a permutation of (1,...,N);
• perm1_uniform.m, selects a random permutation of 1, ..., N;
• permutation_symbol.m, evaluates the Levi-Civita permutation symbol.
• prime.m, a list of prime numbers.
• r8_uniform_ab.m, returns a random R8 between given limits.
• r8vec_is_integer.m, is true if all entries of an R8VEC are integers;
• r8vec_print.m, prints an R8VEC;
• sort_heap_external.m, external sorts a list of values into ascending order;
• triangle_lower_to_i4.m, converts a pair of indices in a lower triangle to an I4.
• triangle_upper_to_i4.m, converts a pair of indices in an upper triangle to an I4.