i4lib

i4lib, an Octave code which contains many utility routines for I4 or "single precision integer" arithmetic.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

i4lib is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Programs:

i4lib_test

c4lib, an Octave code which implements certain elementary functions for single precision complex (C4) variables.

c8lib, an Octave code which implements certain elementary functions for "C8" or double precision complex variables;

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

quaternions, an Octave code which carries out some simple arithmetic operations for quaternions.

r8lib, an Octave code which contains many utility routines, using "R8" or "double precision real" 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_seed.m, returns a random seed 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_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_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_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_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_pairwise_prime.m, is true if the entries of an I4VEC are pairwise prime;
• 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_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_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_shift_circular.m, performs a k-step circular shift on an 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_sorted_unique.m, finds unique elements in a sorted I4VEC2;
• i4vec2_sorted_unique_count.m, counts unique elements in a sorted I4VEC2;
• 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_gamma_log.m, returns the logarithm of the gamma function.
• 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;
• timestamp.m, prints the current YMDHMS date as a timestamp;
• 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.