I4LIB
A Single Precision Integer Arithmetic Utility Library

I4LIB is a MATLAB library which contains many utility routines for "I4" or "single precision integer" arithmetic.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL 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.

Related Programs:

C8LIB, a MATLAB library which implements certain elementary functions for "C8" or double precision complex variables;

R8LIB, a MATLAB library which contains many utility routines, using "R8" or "double precision real" arithmetic.

SUBPAK, a MATLAB library which contains many utility routines;

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:

• get_seed.m, returns a random seed for the random number generator.
• 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_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_div_rounded.m, computes the rounded result of I4 division.
• i4_divp.m, returns the smallest multiple of J greater than or equal to I;
• i4_even.m, is TRUE if an I4 is even;
• i4_factorial.m, computes N! for small values of N;
• i4_factorial2.m, computes the double factorial for small values of N;
• 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_power_of_2.m, returns TRUE if I is a power of 2;
• i4_is_prime.m, returns TRUE if I is prime number;
• i4_lcm.m, returns the least common multiple of two integers;
• i4_log_2.m, returns the integer part of the logarithm base 2 of an integer;
• i4_log_10.m, returns the integer part of the logarithm base 10 of an integer;
• 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;
• i4_mod_inv.m, computes the inverse of an I4 modulo another I4.
• i4_moddiv.m, breaks a number into a multiple of a divisor and a remainder;
• i4_modp.m, returns the nonnegative remainder of integer division;
• i4_odd.m, is TRUE if an integer is odd;
• i4_power.m, returns the value of the J-th power of I;
• i4_sign.m, returns the sign of an integer.
• i4_swap.m, swaps two integer values.
• i4_swap3.m, swaps three integers;
• i4_to_angle.m, maps integers to points on a circle;
• i4_to_digits_binary.m, determines the last N binary digits of an integer;
• i4_to_digits_decimal.m, determines the last N decimal digits of an integer;
• i4_to_fac.m, converts an integer into a product of prime factors;
• i4_to_halton.m, converts an integer I to the I-th Halton number;
• i4_to_isbn.m, converts an I4 to its ISBN representation;
• i4_to_l.m, converts an I4 to a logical value;
• i4_uniform_ab.m, returns a pseudorandom I4 between A and B;
• i4_unswap3.m, unswaps three integers;
• i4_walsh_1d.m, evaluates the Walsh function;
• i4_width.m, returns the "width" of an integer;
• i4_wrap.m, forces an integer to lie between given limits;
• i4_xor.m, returns the exclusive OR of two integers;
• 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_sort2_a.m, ascending sorts the elements of each column of an I4COL;
• i4col_sort_d.m, descending sorts the columns 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_l1_inverse.m, returns the inverse of a unit lower triangular I4MAT;
• i4mat_max_index.m, returns the location of the maximum element of 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_red.m, divides out common factors iin a row or column of an I4MAT;
• i4mat_transpose_print.m, prints an I4MAT, transposed;
• i4mat_transpose_print_some.m, prints some of an I4MAT, transposed;
• i4mat_u1_inverse.m, returns the inverse of a unit upper triangular I4MAT;
• i4mat_uniform_ab.m, returns an I4MAT of pseudorandom values;
• 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.
• 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_any_lt.m, returns TRUE if any A is less than B, for I4VEC's.
• i4vec_any_negative.m, is true if any entry of an I4VEC is negative;
• i4vec_any_nonzero.m, is true if any entry of an I4VEC is nonzero;
• i4vec_ascend_sub.m, returns the longest ascending subsequence of an I4VEC;
• i4vec_ascends.m, returns TRUE if an I4VEC is ascending;
• i4vec_bracket.m, searches a sorted I4VEC for successive brackets of a value;
• i4vec_compare.m, compares two I4VEC's;
• i4vec_cum.m, returns the cumulative sums of an I4VEC;
• i4vec_cum0.m, returns the cumulative sums of an I4VEC;
• i4vec_descends.m, returns TRUE if an I4VEC is descending;
• 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 two I4VEC's are equal.
• i4vec_even_all.m, is TRUE if all entries of an I4VEC are even.
• i4vec_even_any.m, is TRUE if any entries of an I4VEC are even.
• 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_delete.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_imin.m, returns the index of the minimum entry in 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_indicator.m, sets an I4VEC to the indicator vector.
• i4vec_insert.m, inserts a value at a particular location in an I4VEC.
• i4vec_lcm.m, returns the lowest common multiple of the entries of an I4VEC;
• i4vec_mask_print.m, prints a masked 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_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_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_odd_all.m, is TRUE if all entries of an I4VEC are odd.
• i4vec_odd_any.m, is TRUE if any entries of an I4VEC are odd.
• i4vec_order_type.m, determines if an I4VEC is (non)strictly ascending/descending;
• i4vec_pairwise_prime.m, is TRUE if the entries of an I4VEC are pairwise prime;
• 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_part.m, prints part 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;
• 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_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_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;
• i4vec2_compare.m, compares pairs of integers stored in two vectors;
• i4vec2_print.m, prints a pair of integer vectors.
• 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;
• l_to_i4.m, converts a logical value to an I4;
• perm_check.m, checks that a vector represents a permutation;
• perm_uniform.m, selects a random permutation of N objects;
• sort_heap_external.m, external sorts a list of values into ascending order;
• timestamp.m, prints the current YMDHMS date as a timestamp;

Examples and Tests:

• i4lib_test.m, runs all the tests;
• i4lib_test_output.txt, the output file;
• i4lib_test01.m, tests I4_BIT_HI1;
• i4lib_test02.m, tests I4_BIT_LO0;
• i4lib_test03.m, tests I4_BIT_LO1;
• i4lib_test04.m, tests I4_BIT_REVERSE;
• i4lib_test05.m, tests I4_CHARACTERISTIC;
• i4lib_test06.m, tests I4_DIV_ROUNDED;
• i4lib_test07.m, tests I4_DIVP;
• i4lib_test08.m, tests I4_GCD;
• i4lib_test09.m, tests I4_HUGE;
• i4lib_test10.m, tests I4_HUGE_NORMALIZER;
• i4lib_test11.m, tests I4_IS_PRIME;
• i4lib_test12.m, tests I4_LCM;
• i4lib_test13.m, tests I4_LOG_10;
• i4lib_test14.m, tests I4_LOG_2;
• i4lib_test15.m, tests I4_LOG_I4;
• i4lib_test16.m, tests I4_LOG_R8;
• i4lib_test17.m, tests I4_MANT.
• i4lib_test18.m, tests I4_MODDIV;
• i4lib_test19.m, tests I4_MODP;
• i4lib_test20.m, tests I4_SIGN;
• i4lib_test21.m, tests I4_SWAP;
• i4lib_test22.m, tests I4_WALSH_1D;
• i4lib_test23.m, tests I4_WRAP;
• i4lib_test24.m, tests I4_XOR;
• i4lib_test245.m, tests I4BLOCK_PRINT;
• i4lib_test25.m, tests I4COL_FIND_ITEM;
• i4lib_test26.m, tests I4COL_FIND_PAIR_WRAP;
• i4lib_test27.m, tests I4COL_SORT_A and I4COL_SORT_D;
• i4lib_test28.m, tests I4COL_SORT2_A;
• i4lib_test29.m, tests I4COL_SORTED_SINGLETON_COUNT;
• i4lib_test30.m, tests I4COL_SORTED_UNIQUE_COUNT;
• i4lib_test31.m, tests I4MAT_ELIM and I4MAT_RED;
• i4lib_test32.m, tests I4MAT_MAX_INDEX and I4MAT_MIN_INDEX.
• i4lib_test33.m, tests I4MAT_L1_INVERSE;
• i4lib_test34.m, tests I4MAT_PERM_UNIFORM;
• i4lib_test35.m, tests I4MAT_U1_INVERSE;
• i4lib_test36.m, tests I4ROW_MAX and I4ROW_MIN.
• i4lib_test37.m, tests I4ROW_MEAN and I4ROW_SUM;
• i4lib_test38.m, tests I4ROW_SORT_A;
• i4lib_test39.m, tests I4ROW_SORT_D and I4ROW_SORT2_D;
• i4lib_test40.m, tests I4ROW_SWAP;
• i4lib_test41.m, tests I4ROW_VARIANCE.
• i4lib_test42.m, tests I4VEC_AMAX;
• i4lib_test43.m, tests I4VEC_AMIN.
• i4lib_test44.m, tests I4VEC_AMINZ and I4VEC_AMINZ_INDEX;
• i4lib_test45.m, tests I4VEC_AMAX_INDEX and I4VEC_AMIN_INDEX;
• i4lib_test46.m, tests I4VEC_MAX_INDEX, I4VEC_MAX_INDEX_LAST and I4VEC_INDEX;
• i4lib_test47.m, tests I4VEC_ASCEND_SUB.
• i4lib_test48.m, tests I4VEC_ASCENDS.
• i4lib_test49.m, tests I4VEC_BRACKET and I4VEC_INSERT.
• i4lib_test50.m, tests I4VEC_CUM.
• i4lib_test51.m, tests I4VEC_DESCENDS.
• i4lib_test52.m, tests I4VEC_DIRECT_PRODUCT;
• i4lib_test53.m, tests I4VEC_DIRECT_PRODUCT2;
• i4lib_test54.m, tests I4VEC_FRAC;
• i4lib_test55.m, tests I4VEC_HEAP_A and I4VEC_HEAP_D.
• i4lib_test56.m, tests I4VEC_HEAP_D_EXTRACT, I4VEC_HEAP_D_INSERT and I4VEC_HEAP_D_MAX.
• i4lib_test57.m, tests I4VEC_HISTOGRAM;
• i4lib_test58.m, tests I4VEC_INDEX_INSERT_UNIQUE and I4VEC_INDEX_SEARCH.
• i4lib_test59.m, tests I4VEC_INDEX_INSERT, I4VEC_INDEX_DELETE_DUPES, I4VEC_INDEX_DELETE_ALL.
• i4lib_test60.m, tests I4VEC_INDEX_INSERT_UNIQUE and I4VEC_INDEX_ORDER.
• i4lib_test602.m, tests I4VEC_INDEXED_HEAP_D.
• i4lib_test605.m, tests I4VEC_INDEXED_HEAP_D_EXTRACT and others.
• i4lib_test61.m, tests I4VEC_INDICATOR;
• i4lib_test62.m, tests I4VEC_MAX and I4VEC_MIN.
• i4lib_test63.m, tests I4VEC_MEAN and I4VEC_MEDIAN;
• i4lib_test64.m, tests I4VEC_MERGE_A;
• i4lib_test65.m, tests I4VEC_NONZERO_COUNT.
• i4lib_test66.m, tests I4VEC_NONZERO_FIRST.
• i4lib_test67.m, tests I4VEC_ORDER_TYPE.
• i4lib_test68.m, tests I4VEC_PAIRWISE_PRIME.
• i4lib_test69.m, tests I4VEC_PART.
• i4lib_test70.m, tests I4VEC_PART_QUICK_A.
• i4lib_test71.m, tests I4VEC_PERMUTE.
• i4lib_test72.m, tests I4VEC_REVERSE.
• i4lib_test73.m, tests I4VEC_RUN_COUNT.
• i4lib_test74.m, tests I4VEC_SEARCH_BINARY_A;
• i4lib_test75.m, tests I4VEC_SORT_BUBBLE_A and I4VEC_SORTED_UNIQUE_HIST.
• i4lib_test76.m, tests I4VEC_SORT_HEAP_A.
• i4lib_test77.m, tests I4VEC_SORT_HEAP_D.
• i4lib_test78.m, tests I4VEC_SORT_HEAP_INDEX_A;
• i4lib_test79.m, tests I4VEC_SORT_HEAP_INDEX_D.
• i4lib_test80.m, tests I4VEC_SORT_INSERT_A.
• i4lib_test81.m, tests I4VEC_SORT_QUICK_A.
• i4lib_test82.m, tests I4VEC_SORT_SHELL_A.
• i4lib_test83.m, tests I4VEC_SORTED_UNDEX.
• i4lib_test84.m, tests I4VEC_SORTED_UNIQUE.
• i4lib_test85.m, tests I4VEC_TRANSPOSE_PRINT;
• i4lib_test86.m, tests I4VEC_UNDEX;
• i4lib_test87.m, tests I4VEC_UNIQUE_INDEX.
• i4lib_test88.m, tests I4VEC_VALUE_INDEX.
• i4lib_test89.m, tests I4VEC_VARIANCE.
• i4lib_test90.m, tests I4VEC2_SORT_A, I4VEC2_SORT_D, and I4VEC2_SORTED_UNIQUE.

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