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 FORTRAN77 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:

• i4_abs.py, returns the absolute value of an I4.
• 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_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_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_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, returns TRUE if an I4 is even.
• i4_is_odd.py, returns TRUE if an I4 is odd.
• i4_is_power_of_2.py, reports whether an I4 is a power of 2.
• i4_is_prime.py, reports whether an I4 is prime.
• i4_lcm.py, returns the lowest common multiple of two I4's;
• 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_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 a boolean value.
• 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.py, converts an I4 to a pair of indices in a 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_indicator.py, returns an indicator I4MAT.
• 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_transpose_print.py, prints an I4MAT, transposed.
• i4mat_transpose_print_some.py, prints some of an I4MAT, transposed.
• 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.
• 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_concatenate.py, concatenates two I4VEC's.
• i4vec_copy.py, copies an I4VEC.
• i4vec_decrement.py, decrements an I4VEC.
• i4vec_frac.py, searches for the K-th smallest entry in an N vector.
• i4vec_increment.py, increments an I4VEC.
• i4vec_index.py, returns the location of the first occurrence of a given value.
• i4vec_indicator0.py, returns an indicator vector as an I4VEC.
• i4vec_indicator1.py, returns an indicator vector as an I4VEC.
• i4vec_max.py, returns the maximum entry in an I4VEC.
• i4vec_max_index_last.m, returns the index of the last maximal element of an I4VEC.
• i4vec_min.py, returns the minimum entry in an I4VEC.
• i4vec_pairwise_prime.py, returns TRUE if the elements of an integer vector are pairwise prime.
• 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_product.py, computes the product of the entries of an I4VEC.
• i4vec_reverse.py, reverses the order of the entries of an I4VEC.
• 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_sum.py, sums the entries of an I4VEC.
• 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.
• 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).
• prime.py, returns a prime number from a stored table.
• r8_uniform_ab.py, returns a random R8 between given limits;
• timestamp.py, prints the current YMDHMS date as a timestamp;
• triangle_to_i4.py, converts a pair of indices in a triangle to an I4.

Examples and Tests:

• i4lib_test.py, calls all the tests;
• i4lib_test.sh, runs all the tests;
• i4lib_test_output.txt, the output file;

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