I4LIB
A Single Precision Integer Arithmetic Utility Library

I4LIB is a Python 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 FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

C4LIB, a Python library which contains many utility routines, using "C4" or "single precision complex" arithmetic.

C8LIB, a Python library which contains many utility routines, using "C8" or "double precision complex" arithmetic.

R4LIB, a Python library which contains many utility routines using single precision real (R4) arithmetic.

R8LIB, a Python library which contains many utility routines using double precision real (R8) arithmetic.

UNIFORM, a Python library which contains uniform random number generators (RNG's) for several arithmetic types.

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:

• gamma_log_values.py, returns selected values of the logarithm of the gamma function.
• i4_abs.py, returns the absolute value of an I4.
• i4_and.py, returns the AND of two I4's.
• i4_bclr.py, sets a given bit of an I4 to 0.
• i4_bit_hi1.py, returns the position of the high 1 bit base 2 in an I4.
• i4_bit_lo0.py, returns the position of the low 0 bit base 2 in an I4.
• i4_bit_lo1.py, returns the position of the low 1 bit base 2 in an I4.
• i4_bit_reverse.py, reverses the bits in an I4.
• i4_bset.py, sets a given bit of an I4 to 1.
• i4_btest.py, is true if bit POS of I is a 1.
• i4_ceiling.py, rounds an R8 up to an I4.
• i4_characteristic.py, computes the characteristic of an I4.
• i4_choose.py, computes the binomial coefficient C(N,K) as an I4.
• i4_choose_check.py, determines whether the binomial coefficient C(N,K) can be computed as an I4.
• i4_choose_log.py, computes the logarithm of the binomial coefficient C(N,K) as an I4.
• i4_division.py, returns the result of division of one I4 by another.
• i4_divp.py, returns the smallest multiple of J greater than or equal to I.
• i4_factorial.py, evaluates the factorial function as an I4.
• i4_factorial_log.py, evaluates the logarithm of the factorial function as an I4.
• i4_factorial_values.py, returns selected values of the factorial function.
• i4_factorial2.py, evaluates the double factorial function as an I4.
• i4_fall.py, evaluates the falling factorial function.
• i4_fall_values.py, returns selected values of the falling factorial function.
• i4_floor.py, rounds an R8 down to an I4.
• i4_fraction.py, computes a ratio and returns an I4 result.
• i4_gcd.py, returns the greatest common divisor of two I4's;
• i4_gcdb.py, returns the greatest common divisor of the form K^N of two I4's.
• i4_huge.py, returns a huge I4;
• i4_huge_normalizer.py, returns the normalizer for i4_huge();
• i4_is_even.py, is true if an I4 is even.
• i4_is_odd.py, is true if an I4 is odd.
• i4_is_power_of_2.py, is true if an I4 is a power of 2.
• i4_is_power_of_10.py, is true if an I4 is a power of 10.
• i4_is_prime.py, is true if I4 is prime.
• i4_lcm.py, returns the lowest common multiple of two I4's;
• i4_lcm_12n.py, returns the lowest common multiple of 1 through N;
• i4_log_2.py, returns the integer part of the logarithm base 2 of ABS(X);
• i4_log_10.py, returns the integer part of the logarithm base 10 of ABS(X);
• i4_log_i4.py, returns the integer part of the logarithm of ABS(X) to an I4 base.
• i4_log_r8.py, returns the integer part of the logarithm of ABS(X) to an R8 base.
• i4_mant.py, returns the mantissa of an R8.
• i4_max.py, returns the maximum of two I4's.
• i4_min.py, returns the minimum of two I4's.
• i4_mod_inv.py, calculates the inverse of B mod N.
• i4_moddiv.py, breaks a number into a multiple of a divisor and remainder.
• i4_modp.py, returns the nonnegative remainder of I4 division.
• i4_mop.py, returns the I-th power of -1 as an I4.
• i4_not.py, returns the NOT of an I4 with respect to a value J.
• i4_or.py, returns the inclusive OR of two I4's.
• i4_power.py, returns I to the power J.
• i4_rise.py, evaluates the rising factorial function as an I4.
• i4_rise_values.py, returns selected values of the rising factorial function.
• i4_sign.py, returns the sign of an I4 as an I4.
• i4_sign3.py, returns the three-way sign of an I4 as an I4.
• i4_swap.py, swaps two I4's.
• i4_swap3.py, swaps three I4's.
• i4_to_angle.py, maps integers to points on a circle.
• i4_to_halton.py, computes an element of a multidimensional Halton sequence.
• i4_to_isbn.py, converts an I4 to an ISBN digit.
• i4_to_l4.py, converts an I4 to an L4.
• i4_to_pascal.py, converts an I4 to a pair of indices in Pascal's triangle;
• i4_to_pascal_degree.py, converts an I4 to the degree (sum) of the corresponding pair of indices in Pascal's triangle;
• i4_to_triangle_lower.py, converts an I4 to a pair of indices in a lower triangle;
• i4_to_triangle_upper.py, converts an I4 to a pair of indices in an upper triangle;
• i4_uniform_ab.py, returns a scaled uniform I4 between A and B.
• i4_unswap3.py, unswaps three I4's.
• i4_walsh_1d.py, evaluates the Walsh function.
• i4_width.py, returns the "width" of an I4.
• i4_wrap.py, forces an I4 to lie between given limits by wrapping.
• i4_xor.py, returns the exclusive OR of two I4's.
• i4mat_flip_cols.py, reverses the order of the columns of an I4MAT.
• i4mat_flip_rows.py, reverses the order of the rows of an I4MAT.
• i4mat_indicator.py, returns an indicator I4MAT.
• i4mat_is_binary.py, is true if the I4MAT has only 0 and 1 entries.
• i4mat_is_integer.py, is TRUE if all entries of an I4MAT are actually integers;
• i4mat_max.py, returns the maximum entry in an I4MAT.
• i4mat_min.py, returns the minimum entry in an I4MAT.
• i4mat_mm.py, returns the product of two I4MAT's.
• i4mat_print.py, prints an I4MAT.
• i4mat_print_some.py, prints some of an I4MAT.
• i4mat_product_elementwise.py, computes the elementwise product of two I4MAT's.
• i4mat_ref.py, returns the integer row echelon form (IREF) of an I4MAT.
• i4mat_row_reduce.py, divides a common factor from a row of an I4MAT.
• i4mat_row_swap.py, swaps two rows of an I4MAT.
• i4mat_rref.m, returns the integer reduced row echelon form (IRREF) of an I4MAT.
• i4mat_rref_solve_binary.py, seeks binary solutions (if any) of an integer row reduced echelon form (IRREF) linear system.
• i4mat_rref_solve_binary_nz.py, seeks binary solutions (if any) of an integer row reduced echelon form (IRREF) linear system, but only consider solutions with exactly NZ nonzeros.
• i4mat_sum.py, returns the sum of the entries in an I4MAT.
• i4mat_transpose.py, transposes an I4MAT.
• i4mat_transpose_print.py, prints an I4MAT, transposed.
• i4mat_transpose_print_some.py, prints some of an I4MAT, transposed.
• i4mat_u_solve.py, solves an upper triangular linear system involving only integer values.
• i4mat_u1_inverse.py, returns the inverse of a unit upper triangular I4MAT.
• i4mat_uniform_ab.py, returns an I4MAT whose entries are uniformly random between A and B.
• i4mat_width.py, returns the printing width of an I4MAT.
• i4row_max.py, returns the row maximums of an I4ROW.
• i4row_mean.py, returns the row means of an I4ROW.
• i4row_min.py, returns the minimums of an I4ROW.
• i4row_variance.py, returns the variances of an I4ROW.
• i4rows_to_i4mat.py, copies data from a rowwise vector to a columnwise doubly indexed array.
• i4vec_add.py, adds two I4VEC's.
• i4vec_amax.py, returns the largest of the magnitudes of the entries of an I4VEC.
• i4vec_amin.py, returns the smallest of the magnitudes of the entries of an I4VEC.
• i4vec_binary_next.py, returns the next binary vector as an I4VEC.
• i4vec_choose.py, evaluates the generalized binomial coefficient.
• i4vec_concatenate.py, concatenates two I4VEC's.
• i4vec_copy.py, copies an I4VEC.
• i4vec_decrement.py, decrements an I4VEC.
• i4vec_dot_product.py, computes the dot product of two I4VEC's.
• i4vec_frac.py, searches for the K-th smallest entry in an I4VEC.
• i4vec_heap_d.py, sets an I4VEC to a descending heap;
• i4vec_identity_row.py, returns a row of the identity matrix as an I4VEC.
• i4vec_increment.py, increments an I4VEC.
• i4vec_index.py, returns the location of the first occurrence of a given value in an I4VEC.
• i4vec_indicator0.py, returns an indicator vector as an I4VEC.
• i4vec_indicator1.py, returns an indicator vector as an I4VEC.
• i4vec_is_ascending.py, is true if the I4VEC is ascending.
• i4vec_is_binary.py, is true if the I4VEC has only 0 and 1 entries.
• i4vec_is_descending.py, is true if the I4VEC is descending.
• i4vec_is_distinct.py, is true if the entries of an I4VEC are distinct.
• i4vec_is_equal.py, is true if two I4VEC's are equal.
• i4vec_is_even_all.py, is true if the entries of an I4VEC are all even.
• i4vec_is_even_any.py, is true if any entry of an I4VEC is even.
• i4vec_is_lt_any.py, is true if any entry of an I4VEC X is less than the corresponding entry of an I4VEC Y.
• i4vec_is_negative_any.py, is true if any entry of an I4VEC is negative.
• i4vec_is_nonpositive_all.py, is true if the entries of an I4VEC are all nonpositive.
• i4vec_is_odd_all.py, is true if the entries of an I4VEC are all odd.
• i4vec_is_odd_any.py, is true if any entry of an I4VEC is odd.
• i4vec_is_one.py, is true if the entries of an I4VEC are all 1.
• i4vec_is_pairwise_prime.py, is true if the elements of an I4VEC are pairwise prime.
• i4vec_is_zero.py, is true if the entries of an I4VEC are all 0.
• i4vec_max.py, returns the maximum entry in an I4VEC.
• i4vec_max_index_last.py, returns the index of the last maximal element of an I4VEC.
• i4vec_mean.py, returns the mean of an I4VEC.
• i4vec_mean_i4.py, returns the I4 mean of an I4VEC.
• i4vec_min.py, returns the minimum entry in an I4VEC.
• i4vec_permute.py, applies a 0-based permutation to an I4VEC.
• i4vec_permute_uniform.py, randomly permutes an I4VEC.
• i4vec_print.py, prints an I4VEC.
• i4vec_print_mask.py, prints the masked elements of an I4VEC.
• i4vec_product.py, computes the product of the entries of an I4VEC.
• i4vec_red.py, divides out common factors in an I4VEC;
• i4vec_reverse.py, reverses the order of the entries of an I4VEC.
• i4vec_run_count.py, counts the number of runs in an I4VEC.
• i4vec_search_binary_a.py, searches the ascending sorted I4VEC for a value.
• i4vec_search_binary_d.py, searches the descending sorted I4VEC for a value.
• i4vec_sort_bubble_a.py, ascending sorts an I4VEC using bubble sort;
• i4vec_sort_heap_a.py, ascending sorts an I4VEC using heap sort;
• i4vec_sort_heap_index_a.py, returns an index vector to ascending sort an I4VEC.
• i4vec_sort_heap_index_d.py, returns an index vector to descending sort an I4VEC.
• i4vec_sort_insert_a.py, ascending sorts an I4VEC using insertion sort;
• i4vec_sort_insert_d.py, descending sorts an I4VEC using insertion sort;
• i4vec_sorted_unique.py, returns the unique elements in a sorted I4VEC;
• i4vec_sorted_unique_count.py, counts the number of unique elements in a sorted I4VEC;
• i4vec_sorted_unique_hist.py, creates a histogram of the unique elements in a sorted I4VEC;
• i4vec_sum.py, sums the entries of an I4VEC.
• i4vec_sum_vec.py, returns the pairwise sum of two I4VEC's.
• i4vec_transpose_print.py, prints an I4VEC "transposed", that is, 5 entries to a line.
• i4vec_uniform_ab.py, returns an I4VEC whose entries are uniformly random between A and B.
• i4vec_unique_count.py, counts the unique elements in an I4VEC.
• i4vec_variance.py, returns the variance of an I4VEC.
• i4vec_width.py, returns the printing width of an I4VEC.
• i4vec2_print.py, prints a pair of I4VECs.
• ksub_next4.py, selects the next subset of size K from a set of size N.
• l4_to_i4.py, converts an L4 to an I4.
• pascal_to_i4.py, converts a pair of indices in Pascal's triangle to a linear index;
• perm0_check.py, checks a permutation of (0,...,N-1).
• perm0_uniform.py, randomly selects a permutation of (0,...,N-1).
• perm1_check.py, checks a permutation of (1,...,N).
• perm1_uniform.py, randomly selects a permutation of (1,...,N).
• permutation_symbol.py, evaluates the Levi-Civita permutation symbol.
• prime.py, returns a prime number from a stored table.
• r8_gamma_log.py, computes the logarithm of the gamma function;
• r8_uniform_ab.py, returns a random R8 between given limits;
• r8vec_print.py, prints an R8VEC.
• timestamp.py, prints the current YMDHMS date as a timestamp;
• triangle_lower_to_i4.py, converts a pair of indices in a lower triangle to an I4.
• triangle_upper_to_i4.py, converts a pair of indices in an upper triangle to an I4.

Examples and Tests:

• i4lib_test.py, calls all the tests;
• i4lib_test.sh, runs all the tests;
• i4lib_test.txt, the output file;

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