I4LIB
A Single Precision Integer Arithmetic Utility Library

I4LIB is a FORTRAN90 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 FORTRAN90 library which implements certain elementary functions for "C4" or single precision complex variables;

C8LIB, a FORTRAN90 library which implements certain elementary functions for "C8" or double precision complex variables;

I8LIB, a FORTRAN90 library which contains many utility routines, using "I8" or "double precision integer" arithmetic.

R4LIB, a FORTRAN90 library which contains many utility routines, using "R4" or "single precision real" arithmetic.

R8LIB, a FORTRAN90 library which contains many utility routines, using "R8" or "double precision real" arithmetic.

SUBPAK, a FORTRAN90 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:

• i4lib.f90, the source code;

Examples and Tests:

• i4lib_test.f90, a sample calling program;
• i4lib_test.txt, the output file.

List of Routines:

• I4_ABS returns the absolute value of an I4.
• I4_AND calculates the AND of two I4's.
• I4_BCLR returns a copy of an I4 in which the POS-th bit is set to 0.
• I4_BIT_HI1 returns the position of the high 1 bit base 2 in an I4.
• I4_BIT_LO0 returns the position of the low 0 bit base 2 in an I4.
• I4_BIT_LO1 returns the position of the low 1 bit base 2 in an I4.
• I4_BIT_REVERSE reverses the bits in an I4.
• I4_BSET returns a copy of an I4 in which the POS-th bit is set to 1.
• I4_BTEST returns TRUE if the POS-th bit of an I4 is 1.
• I4_CEILING rounds an R8 "up" (towards +oo) to the next I4.
• I4_CHARACTERISTIC gives the characteristic for an I4.
• I4_CHOOSE computes the binomial coefficient C(N,K) as an I4.
• I4_CHOOSE_CHECK reports whether the binomial coefficient can be computed.
• I4_CHOOSE_LOG computes the logarithm of the Binomial coefficient.
• I4_DIV_ROUNDED computes the rounded result of I4 division.
• I4_DIVISION returns the result of integer division.
• I4_DIVP returns the smallest multiple of J greater than or equal to I.
• I4_FACTORIAL computes the factorial of N.
• FACTORIAL_LOG returns the logarithm of N factorial.
• I4_FACTORIAL_VALUES returns values of the factorial function.
• I4_FACTORIAL2 computes the double factorial function.
• I4_FACTORIAL2_VALUES returns values of the double factorial function.
• I4_FALL computes the falling factorial function [X]_N.
• I4_FALL_VALUES returns values of the integer falling factorial function.
• I4_FLOOR rounds an R8 "down" (towards -oo) to the nearest I4.
• I4_FRACTION computes a ratio and returns an integer result.
• I4_GCD finds the greatest common divisor of two I4's.
• I4_GCDB finds the greatest common divisor of the form K^*N of two I4's.
• I4_HUGE returns a "huge" I4.
• I4_HUGE_NORMALIZER returns the "normalizer" for I4_HUGE.
• I4_IS_EVEN returns TRUE if an I4 is even.
• I4_IS_ODD returns TRUE if an I4 is odd.
• I4_IS_POWER_OF_2 reports whether an I4 is a power of 2.
• I4_IS_POWER_OF_10 reports whether an I4 is a power of 10.
• I4_IS_PRIME reports whether an I4 is prime.
• I4_LCM computes the least common multiple of two I4's.
• I4_LOG_10 returns the integer part of the logarithm base 10 of an I4.
• I4_LOG_2 returns the integer part of the logarithm base 2 of an I4.
• I4_LOG_I4 returns the logarithm of an I4 to an I4 base.
• I4_LOG_R8 returns the logarithm of an I4 to an R8 base.
• I4_MANT computes the "mantissa" of a double precision number.
• I4_MAX returns the maximum of two I4's.
• I4_MIN returns the minimum of two I4's.
• I4_MOD_INV calculates the inverse of B mod N.
• I4_MODDIV breaks an I4 into a multiple of a divisor and remainder.
• I4_MODP returns the nonnegative remainder of I4 division.
• I4_MOP returns the I-th power of -1 as an I4.
• I4_NOT calculates the NOT of an I4 with respect to a maximum I4.
• I4_OR calculates the inclusive OR of two I4's.
• I4_POWER returns the integer power of an I4.
• I4_RISE computes the rising factorial function [X]^N.
• I4_RISE_VALUES returns values of the integer rising factorial function.
• I4_SIGN evaluates the sign of an I4.
• I4_SIGN3 evaluates the three-way sign of an I4.
• I4_SWAP swaps two I4's.
• I4_SWAP3 swaps three I4's.
• I4_TO_ANGLE maps I4's to points on a circle.
• I4_TO_DIGITS_BINARY produces the binary digits of an I4.
• I4_TO_DIGITS_DECIMAL determines the last N decimal digits of an I4.
• I4_TO_FAC converts an I4 into a product of prime factors.
• I4_TO_HALTON computes one element of a leaped Halton subsequence.
• I4_TO_ISBN converts an I4 to an ISBN digit.
• I4_TO_L4 converts an I4 to an L4.
• I4_TO_PASCAL converts a linear index to Pascal triangle coordinates.
• I4_TO_PASCAL_DEGREE converts a linear index to a Pascal triangle degree.
• I4_TO_TRIANGLE converts an integer to triangular coordinates.
• I4_UNIFORM_AB returns a scaled pseudorandom I4 between A and B.
• I4_UNSWAP3 unswaps three I4's.
• I4_WALSH_1D evaluates the Walsh function.
• I4_WIDTH returns the "width" of an I4.
• I4_WRAP forces an I4 to lie between given limits by wrapping.
• I4_XOR calculates the exclusive OR of two I4's.
• I43MAT_FLIP_COLS swaps the columns of an I43MAT.
• I43MAT_FLIP_ROWS swaps the rows of an I43MAT.
• I4BLOCK_PRINT prints an I4BLOCK.
• I4COL_COMPARE compares columns I and J of an I4COL.
• I4COL_FIND searches an I4COL for a particular column value.
• I4COL_FIND_ITEM searches an I4COL for a given scalar value.
• I4COL_FIND_PAIR_WRAP searches an I4COL for a pair of items.
• I4COL_FIRST_INDEX indexes the first occurrence of values in an I4COL.
• I4COL_SORT_A ascending sorts an I4COL.
• I4COL_SORT_D descending sorts an I4COL.
• I4COL_SORT2_A ascending sorts the elements of each column of an I4COL.
• I4COL_SORT2_D descending sorts elements of each column of an I4COL.
• I4COL_SORTED_SINGLETON_COUNT counts singletons in an I4COL.
• I4COL_SORTED_UNIQUE keeps unique elements in a sorted I4COL.
• I4COL_SORTED_UNIQUE_COUNT counts unique elements in an I4COL.
• I4COL_SWAP swaps columns J1 and J2 of an I4COL.
• I4COL_UNIQUE_INDEX indexes the unique occurrence of values in an I4COL.
• I4I4_SORT_A ascending sorts a pair of integers.
• I4I4I4_SORT_A ascending sorts a triple of integers.
• I4INT_TO_R4INT maps an I4INT to an R4INT.
• I4INT_TO_R8INT maps an I4INT to an R8INT.
• I4LIST_PRINT prints an I4LIST.
• I4MAT_BORDER_ADD adds a "border" to an I4MAT.
• I4MAT_BORDER_CUT cuts the "border" of an I4MAT.
• I4MAT_COPY copies an I4MAT.
• I4MAT_ELIM carries out exact Gauss elimination on an I4MAT.
• I4MAT_FLIP_COLS swaps the columns of an I4MAT.
• I4MAT_FLIP_ROWS swaps the rows of an I4MAT.
• I4MAT_HISTOGRAM computes a histogram of the elements of an I4MAT.
• I4MAT_INDICATOR sets up an "indicator" I4MAT.
• I4MAT_L1_INVERSE inverts a unit lower triangular I4MAT.
• I4MAT_MAX returns the maximum of an I4MAT.
• I4MAT_MAX_INDEX returns the location of the maximum of an I4MAT.
• I4MAT_MIN returns the minimum of an I4MAT.
• I4MAT_MIN_INDEX returns the location of the minimum of an I4MAT.
• I4MAT_MM multiplies two I4MAT's.
• I4MAT_PERM permutes the rows and columns of a square I4MAT.
• I4MAT_PERM_UNIFORM selects a random permutation of an I4MAT.
• I4MAT_PERM2 permutes the rows and columns of a rectangular I4MAT.
• I4MAT_PERM2_UNIFORM selects a random permutation of an I4MAT.
• I4MAT_PRINT prints an I4MAT.
• I4MAT_PRINT_SOME prints some of an I4MAT.
• I4MAT_RED divides out common factors in a row or column of an I4MAT.
• I4MAT_TRANSPOSE_PRINT prints an I4MAT, transposed.
• I4MAT_TRANSPOSE_PRINT_SOME prints some of the transpose of an I4MAT.
• I4MAT_U1_INVERSE inverts a unit upper triangular I4MAT.
• I4MAT_UNIFORM_AB returns a scaled pseudorandom I4MAT.
• I4MAT_WIDTH returns the printing width of an I4MAT.
• I4MAT_ZEROS zeroes out an I4MAT.
• I4ROW_COMPARE compares two rows of an I4ROW.
• I4ROW_FIND_ITEM searches the rows of an I4ROW for a given value.
• I4ROW_FIND_PAIR_WRAP searches rows of an I4ROW for a pair of items.
• I4ROW_MAX returns the maximums of the rows of an I4ROW.
• I4ROW_MEAN returns the means of the rows of an I4ROW.
• I4ROW_MIN returns the minimums of the rows of an I4ROW.
• I4ROW_SORT_A ascending sorts the rows of an I4ROW.
• I4ROW_SORT_D descending sorts the rows of an I4ROW.
• I4ROW_SORT2_D descending sorts the elements of each row of an I4ROW.
• I4ROW_SORTED_UNIQUE keeps unique elements in an I4ROW.
• I4ROW_SORTED_UNIQUE_COUNT counts unique elements in an I4ROW.
• I4ROW_SUM returns the sums of the rows of an I4ROW.
• I4ROW_SWAP swaps two rows of an I4ROW.
• I4ROW_VARIANCE returns the variances of an I4ROW.
• I4VEC_ADD computes C = A + B for I4VEC's.
• I4VEC_ALL_NONPOSITIVE: ( all ( A <= 0 ) ) for I4VEC's.
• I4VEC_AMAX returns the largest magnitude in an I4VEC.
• I4VEC_AMAX_INDEX returns the index of the largest magnitude in an I4VEC.
• I4VEC_AMIN returns the smallest magnitude in an I4VEC.
• I4VEC_AMIN_INDEX returns the index of the smallest magnitude in an I4VEC.
• I4VEC_AMINZ returns the smallest nonzero magnitude in an I4VEC.
• I4VEC_AMINZ_INDEX returns the smallest nonzero magnitude in an I4VEC.
• I4VEC_ANY_LT: ( any ( A < B ) ) for I4VEC's.
• I4VEC_ANY_NEGATIVE: ( any A < 0 ) for I4VEC's.
• I4VEC_ANY_NONZERO: ( any A nonzero ) for I4VEC's.
• I4VEC_ASCEND_SUB computes the longest ascending subsequence of an I4VEC.
• I4VEC_ASCENDS determines if an I4VEC is (weakly) ascending.
• I4VEC_AXPY adds a scaled multiple of one I4VEC to another.
• I4VEC_BRACKET searches a sorted I4VEC for successive brackets of a value.
• I4VEC_CHOOSE computes the generalized binomial coefficient C(M,N,K).
• I4VEC_COMPARE compares two I4VEC's.
• I4VEC_CONCATENATE concatenates two I4VEC's.
• I4VEC_COPY copies an I4VEC.
• I4VEC_CUM computes the cumulative sum of the entries of an I4VEC.
• I4VEC_CUM0 computes the cumulative sum of the entries of an I4VEC.
• I4VEC_DECREMENT decrements an I4VEC.
• I4VEC_DESCENDS determines if an I4VEC is decreasing.
• I4VEC_DIRECT_PRODUCT creates a direct product of I4VEC's.
• I4VEC_DIRECT_PRODUCT2 creates a direct product of I4VEC's.
• I4VEC_DOT_PRODUCT computes the dot product of two I4VEC's.
• I4VEC_EQ is true if two I4VECs are equal.
• I4VEC_EVEN_ALL is TRUE if all entries of an I4VEC are even.
• I4VEC_EVEN_ANY is TRUE if any entry of an I4VEC is even.
• I4VEC_FIND finds the first occurrence of a value in an I4VEC.
• I4VEC_FIRST_INDEX indexes the first occurrence of values in an I4VEC.
• I4VEC_FRAC searches for the K-th smallest element in an I4VEC.
• I4VEC_GCD returns the greatest common divisor of an I4VEC.
• I4VEC_HEAP_A reorders an I4VEC into an ascending heap.
• I4VEC_HEAP_D reorders an I4VEC into an descending heap.
• I4VEC_HEAP_D_EXTRACT extracts the maximum value from a heap descending I4VEC.
• I4VEC_HEAP_D_INSERT inserts a new I4 into a heap descending I4VEC.
• I4VEC_HEAP_D_MAX returns the maximum value in a heap descending I4VEC.
• I4VEC_HISTOGRAM computes a histogram of the elements of an I4VEC.
• I4VEC_HISTOGRAM_MASKED computes a histogram of a masked I4VEC.
• I4VEC_INCREMENT increments an I4VEC.
• I4VEC_INDEX returns the first location of a given value in an I4VEC.
• I4VEC_INDEX_DELETE_ALL deletes a value in an indexed sorted I4VEC.
• I4VEC_INDEX_DELETE_DUPES deletes duplicates from an indexed sorted I4VEC.
• I4VEC_INDEX_DELETE_ONE deletes one copy of I4 from an indexed sorted I4VEC.
• I4VEC_INDEX_INSERT inserts an I4 into an indexed sorted I4VEC.
• I4VEC_INDEX_INSERT_UNIQUE inserts a unique I4 into an indexed sorted I4VEC.
• I4VEC_INDEX_ORDER sorts an I4VEC using an index vector.
• I4VEC_INDEX_SEARCH searches for an I4 in an indexed sorted I4VEC.
• I4VEC_INDEX_SORT_UNIQUE creates a sorted unique index for an I4VEC.
• I4VEC_INDEXED_HEAP_D creates a descending heap from an indexed I4VEC.
• I4VEC_INDEXED_HEAP_D_EXTRACT: extract from heap descending indexed I4VEC.
• I4VEC_INDEXED_HEAP_D_INSERT: insert value into heap descending indexed I4VEC.
• I4VEC_INDEXED_HEAP_D_MAX: maximum value in heap descending indexed I4VEC.
• I4VEC_INDICATOR0 sets an I4VEC to the indicator vector (0,1,2,...)
• I4VEC_INDICATOR1 sets an I4VEC to the indicator vector (1,2,3,...)
• I4VEC_INSERT inserts a value into an I4VEC.
• I4VEC_LCM returns the least common multiple of an I4VEC.
• I4VEC_MASK_PRINT prints a masked I4VEC.
• I4VEC_MAX computes the maximum element of an I4VEC.
• I4VEC_MAX_INDEX computes the index of a maximum element of an I4VEC.
• I4VEC_MAX_INDEX_LAST returns the last maximal element location in an I4VEC
• I4VEC_MEAN returns the mean of an I4VEC.
• I4VEC_MEDIAN returns the median of an unsorted I4VEC.
• I4VEC_MERGE_A merges two ascending sorted I4VEC.
• I4VEC_MIN computes the minimum element of an I4VEC.
• I4VEC_MIN_INDEX computes the index of the minimum element of an I4VEC.
• I4VEC_MIN_MV determines U(1:N) /\ V for vectors U and a single vector V.
• I4VEC_NEGONE returns an I4VEC of -1's.
• I4VEC_NONZERO_COUNT counts the nonzero entries in an I4VEC.
• I4VEC_NONZERO_FIRST left-shifts all nonzeros in an I4VEC.
• I4VEC_NORM_L0 returns the l0 "norm" of an I4VEC.
• I4VEC_ODD_ALL is TRUE if all entries of an I4VEC are odd.
• I4VEC_ODD_ANY is TRUE if any entry of an I4VEC is odd.
• I4VEC_ONE returns an I4VEC of 1's.
• I4VEC_ORDER_TYPE determines if I4VEC is (non)strictly ascending/descending.
• I4VEC_PAIRWISE_PRIME checks whether an I4VEC's entries are pairwise prime.
• I4VEC_PART partitions an integer NVAL into N nearly equal parts.
• I4VEC_PART_QUICK_A reorders an I4VEC as part of a quick sort.
• I4VEC_PERMUTE permutes an I4VEC in place.
• I4VEC_PERMUTE_UNIFORM randomly permutes an I4VEC.
• I4VEC_PRINT prints an I4VEC.
• I4VEC_PRINT_PART prints "part" of an I4VEC.
• I4VEC_PRINT_SOME prints "some" of an I4VEC.
• I4VEC_PRODUCT returns the product of the entries of an I4VEC.
• I4VEC_RED divides out common factors in an I4VEC.
• I4VEC_REVERSE reverses the elements of an I4VEC.
• I4VEC_ROTATE rotates an I4VEC in place.
• I4VEC_RUN_COUNT counts runs of equal values in an I4VEC.
• I4VEC_SEARCH_BINARY_A searches an ascending sorted I4VEC for a value.
• I4VEC_SEARCH_BINARY_D searches a descending sorted I4VEC for a value.
• I4VEC_SORT_BUBBLE_A ascending sorts an I4VEC using bubble sort.
• I4VEC_SORT_BUBBLE_D descending sorts an I4VEC using bubble sort.
• I4VEC_SORT_HEAP_A ascending sorts an I4VEC using heap sort.
• I4VEC_SORT_HEAP_D descending sorts an I4VEC using heap sort.
• I4VEC_SORT_HEAP_INDEX_A does an indexed heap ascending sort of an I4VEC.
• I4VEC_SORT_HEAP_INDEX_D does an indexed heap descending sort of an I4VEC.
• I4VEC_SORT_INSERT_A uses an ascending insertion sort on an I4VEC.
• I4VEC_SORT_INSERT_D uses a descending insertion sort on an I4VEC.
• I4VEC_SORT_QUICK_A ascending sorts an I4VEC using quick sort.
• I4VEC_SORT_SHELL_A ascending sorts an I4VEC using Shell's sort.
• I4VEC_SORTED_UNDEX returns unique sorted indexes for a sorted I4VEC.
• I4VEC_SORTED_UNIQUE finds the unique elements in a sorted I4VEC.
• I4VEC_SORTED_UNIQUE_COUNT counts the unique elements in a sorted I4VEC.
• I4VEC_SORTED_UNIQUE_HIST histograms the unique elements of a sorted I4VEC.
• I4VEC_SPLIT "splits" an unsorted I4VEC based on a splitting value.
• I4VEC_STD returns the standard deviation of an I4VEC.
• I4VEC_SUM returns the sum of the entries of an I4VEC.
• I4VEC_SUM_VEC does a pairwise sum of two I4VEC's.
• I4VEC_SWAP swaps the entries of two I4VEC's.
• I4VEC_TRANSPOSE_PRINT prints an I4VEC "transposed".
• I4VEC_UNDEX returns unique sorted indexes for an I4VEC.
• I4VEC_UNIFORM_AB returns a scaled pseudorandom I4VEC.
• I4VEC_UNIQUE_COUNT counts the unique elements in an unsorted I4VEC.
• I4VEC_UNIQUE_INDEX indexes the unique occurrence of values in an I4VEC.
• I4VEC_VALUE_INDEX indexes entries equal to a given value in an I4VEC.
• I4VEC_VALUE_NUM counts entries equal to a given value in an I4VEC.
• I4VEC_VARIANCE returns the variance of an I4VEC.
• I4VEC_WIDTH returns the printing width of an I4VEC.
• I4VEC_ZEROS sets the entries of an I4VEC to 0.
• I4VEC2_COMPARE compares entries of an I4VEC2.
• I4VEC2_PRINT prints a pair of integer vectors.
• I4VEC2_SORT_A ascending sorts a vector of pairs of integers.
• I4VEC2_SORT_D descending sorts a vector of pairs of integers.
• I4VEC2_SORTED_UNIQUE keeps the unique elements in a sorted I4VEC2.
• I4VEC2_SORTED_UNIQUE_COUNT counts unique elements in a sorted I4VEC2.
• L4_TO_I4 converts an L4 to an I4.
• L4_XOR returns the exclusive OR of two L4's.
• PASCAL_TO_I4 converts Pacal triangle coordinates to a linear index.
• PERM_CYCLE analyzes a permutation.
• PERM0_CHECK checks a 0-based permutation.
• PERM0_UNIFORM selects a random permutation of 0, ..., N-1.
• PERM1_CHECK checks a 1-based permutation.
• PERM1_UNIFORM selects a random permutation of 1, ..., N.
• PRIME returns any of the first PRIME_MAX prime numbers.
• R8_GAMMA_LOG evaluates the logarithm of the gamma function.
• R8_UNIFORM_AB returns a scaled pseudorandom R8.
• R8VEC_PRINT prints an R8VEC.
• SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TRIANGLE_TO_I4 converts a triangular coordinate to an integer.

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