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<html>
<head>
<title>
I4LIB - A Single Precision Integer Arithmetic Utility Library
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
I4LIB <br> A Single Precision Integer Arithmetic Utility Library
</h1>
<hr>
<p>
<b>I4LIB</b>
is a C++ library which
includes a number of utility routines for "I4" or
single precision integer arithmetic.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>I4LIB</b> is available in
<a href = "../../c_src/i4lib/i4lib.html">a C version</a> and
<a href = "../../cpp_src/i4lib/i4lib.html">a C++ version</a> and
<a href = "../../f77_src/i4lib/i4lib.html">a FORTRAN77 version</a> and
<a href = "../../f_src/i4lib/i4lib.html">a FORTRAN90 version</a> and
<a href = "../../m_src/i4lib/i4lib.html">a MATLAB version</a> and
<a href = "../../py_src/i4lib/i4lib.html">a Python version</a>.
</p>
<h3 align = "center">
Related Programs:
</h3>
<p>
<a href = "../../cpp_src/c4lib/c4lib.html">
C4LIB</a>,
a C++ library which
implements certain elementary functions for "C4" or
single precision complex variables;
</p>
<p>
<a href = "../../cpp_src/c8lib/c8lib.html">
C8LIB</a>,
a C++ library which
implements certain elementary functions for "C8" or
double precision complex variables;
</p>
<p>
<a href = "../../cpp_src/i8lib/i8lib.html">
I8LIB</a>,
a C++ library which
contains many utility routines, using "I8" or "double precision integer"
arithmetic.
</p>
<p>
<a href = "../../cpp_src/r4lib/r4lib.html">
R4LIB</a>,
a C++ library which
contains many utility routines, using "R4" or
"single precision real" arithmetic.
</p>
<p>
<a href = "../../cpp_src/r8lib/r8lib.html">
R8LIB</a>,
a C++ library which
contains many utility routines, using "R8" or
"double precision real" arithmetic.
</p>
<p>
<a href = "../../cpp_src/subpak/subpak.html">
SUBPAK</a>,
a C++ library which
contains many utility routines;
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Milton Abramowitz, Irene Stegun,<br>
Handbook of Mathematical Functions,<br>
National Bureau of Standards, 1964,<br>
ISBN: 0-486-61272-4,<br>
LC: QA47.A34.
</li>
<li>
Thomas Cormen, Charles Leiserson, Ronald Rivest,<br>
Introduction to Algorithms,<br>
MIT Press, 2001,<br>
ISBN: 0262032937,<br>
LC: QA76.C662.
</li>
<li>
Albert Nijenhuis, Herbert Wilf,<br>
Combinatorial Algorithms for Computers and Calculators,<br>
Second Edition,<br>
Academic Press, 1978,<br>
ISBN: 0-12-519260-6,<br>
LC: QA164.N54.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "i4lib.cpp">i4lib.cpp</a>, the source code;
</li>
<li>
<a href = "i4lib.hpp">i4lib.hpp</a>, the include file.
</li>
<li>
<a href = "i4lib.sh">i4lib.sh</a>,
commands to compile the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "i4lib_prb.cpp">i4lib_prb.cpp</a>, the calling program;
</li>
<li>
<a href = "i4lib_prb.sh">i4lib_prb.sh</a>,
commands to compile, link and run the calling program;
</li>
<li>
<a href = "i4lib_prb_output.txt">i4lib_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>I4_ABS</b> returns the absolute value of an I4.
</li>
<li>
<b>I4_BIT_HI1</b> returns the position of the high 1 bit base 2 in an I4.
</li>
<li>
<b>I4_BIT_LO0</b> returns the position of the low 0 bit base 2 in an I4.
</li>
<li>
<b>I4_BIT_LO1</b> returns the position of the low 1 bit base 2 in an I4.
</li>
<li>
<b>I4_BIT_REVERSE</b> reverses the bits in an I4.
</li>
<li>
<b>I4_CEILING</b> rounds an R8 up to the next I4.
</li>
<li>
<b>I4_CHARACTERISTIC</b> gives the characteristic for an I4.
</li>
<li>
<b>I4_CHOOSE</b> computes the binomial coefficient C(N,K).
</li>
<li>
<b>I4_DIV_ROUNDED</b> computes the rounded result of I4 division.
</li>
<li>
<b>I4_DIVP</b> returns the smallest multiple of J greater than or equal to an I4.
</li>
<li>
<b>I4_EVEN</b> returns TRUE if an I4 is even.
</li>
<li>
<b>I4_FACTORIAL</b> computes the factorial of N.
</li>
<li>
<b>I4_FLOOR</b> rounds an R8 down to the nearest I4.
</li>
<li>
<b>I4_FRACTION</b> computes a ratio and returns an integer result.
</li>
<li>
<b>I4_GCD</b> finds the greatest common divisor of two I4's.
</li>
<li>
<b>I4_GCDB</b> finds the greatest common divisor of the form K**N of two I4's.
</li>
<li>
<b>I4_HUGE</b> returns a "huge" I4.
</li>
<li>
<b>I4_HUGE_NORMALIZER</b> returns the "normalizer" for I4_HUGE.
</li>
<li>
<b>I4_IS_POWER_OF_2</b> reports whether an I4 is a power of 2.
</li>
<li>
<b>I4_IS_PRIME</b> reports whether an I4 is prime.
</li>
<li>
<b>I4_LCM</b> computes the least common multiple of two I4's.
</li>
<li>
<b>I4_LOG_10</b> returns the integer part of the logarithm base 10 of an I4.
</li>
<li>
<b>I4_LOG_2</b> returns the integer part of the logarithm base 2 of an I4.
</li>
<li>
<b>I4_LOG_I4</b> returns the logarithm of an I4 to an I4 base.
</li>
<li>
<b>I4_LOG_R8</b> returns the integer part of the logarithm base B of an I4.
</li>
<li>
<b>I4_MANT</b> computes the "mantissa" of an R4.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the minimum of two I4's.
</li>
<li>
<b>I4_MOD_INV</b> calculates the inverse of B mod N.
</li>
<li>
<b>I4_MODDIV</b> breaks an I4 into a multiple of a divisor and remainder.
</li>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of I4 division.
</li>
<li>
<b>I4_MOP</b> returns the I-th power of -1 as an I4 value.
</li>
<li>
<b>I4_ODD</b> returns TRUE if an I4 is odd.
</li>
<li>
<b>I4_POWER</b> returns the value of I^J.
</li>
<li>
<b>I4_REVERSE_BYTES</b> reverses the bytes in an I4.
</li>
<li>
<b>I4_SIGN</b> returns the sign of an I4.
</li>
<li>
<b>I4_SWAP</b> switches two I4's.
</li>
<li>
<b>I4_SWAP3</b> swaps three I4's.
</li>
<li>
<b>I4_TO_ANGLE</b> maps I4's to points on a circle.
</li>
<li>
<b>I4_TO_DIGITS_BINARY</b> produces the binary digits of an I4.
</li>
<li>
<b>I4_TO_DIGITS_DECIMAL</b> determines the last N decimal digits of an I4.
</li>
<li>
<b>I4_TO_FAC</b> converts an I4 into a product of prime factors.
</li>
<li>
<b>I4_TO_HALTON</b> computes one element of a leaped Halton subsequence.
</li>
<li>
<b>I4_TO_ISBN</b> converts an I4 to an ISBN digit.
</li>
<li>
<b>I4_TO_L</b> converts an I4 to a logical value.
</li>
<li>
<b>I4_UNIFORM</b> returns a scaled pseudorandom I4.
</li>
<li>
<b>I4_UNSWAP3</b> unswaps three I4's.
</li>
<li>
<b>I4_WALSH_1D</b> evaluates the Walsh function of a real scalar argument.
</li>
<li>
<b>I4_WIDTH</b> returns the "width" of an I4.
</li>
<li>
<b>I4_WRAP</b> forces an I4 to lie between given limits by wrapping.
</li>
<li>
<b>I4_XOR</b> calculates the exclusive OR of two I4's.
</li>
<li>
<b>I43MAT_FLIP_COLS</b> swaps the columns of an I43MAT.
</li>
<li>
<b>I43MAT_FLIP_ROWS</b> swaps the rows of an I43MAT.
</li>
<li>
<b>I4BLOCK_DELETE</b> frees memory associated with an I4BLOCK.
</li>
<li>
<b>I4BLOCK_NEW</b> allocates a new I4BLOCK.
</li>
<li>
<b>I4COL_COMPARE</b> compares columns I and J of an I4COL.
</li>
<li>
<b>I4COL_FIND</b> seeks a table column equal to an I4COL.
</li>
<li>
<b>I4COL_FIND_ITEM</b> searches an I4COL for a given value.
</li>
<li>
<b>I4COL_FIND_PAIR_WRAP</b> wrap searches an I4COL for a pair of items.
</li>
<li>
<b>I4COL_FIRST_INDEX</b> indexes the first occurrence of values in an I4COL.
</li>
<li>
<b>I4COL_SORT_A</b> ascending sorts the columns of an I4COL.
</li>
<li>
<b>I4COL_SORT_D</b> descending sorts the columns of an I4COL.
</li>
<li>
<b>I4COL_SORT2_A</b> ascending sorts the elements of each column of an I4COL.
</li>
<li>
<b>I4COL_SORT2_D</b> descending sorts the elements of each column of an I4COL.
</li>
<li>
<b>I4COL_SORTED_SINGLETON_COUNT</b> counts singletons in an I4COL.
</li>
<li>
<b>I4COL_SORTED_UNIQUE</b> keeps unique elements in a sorted I4COL.
</li>
<li>
<b>I4COL_SORTED_UNIQUE_COUNT</b> counts unique elements in an I4COL.
</li>
<li>
<b>I4COL_SWAP</b> swaps two columns of an I4COL.
</li>
<li>
<b>I4COL_UNIQUE_INDEX</b> indexes the unique occurrence of values in an I4COL.
</li>
<li>
<b>I4I4_SORT_A</b> ascending sorts a pair of I4's.
</li>
<li>
<b>I4I4I4_SORT_A</b> ascending sorts a triple of I4's.
</li>
<li>
<b>I4INT_TO_R4INT</b> maps an I4 interval to an R4 interval.
</li>
<li>
<b>I4INT_TO_R8INT</b> maps an I4 interval to an R8 interval.
</li>
<li>
<b>I4LIST_PRINT</b> prints an I4LIST.
</li>
<li>
<b>I4MAT_BORDER_ADD</b> adds a "border" to an I4MAT.
</li>
<li>
<b>I4MAT_BORDER_CUT</b> cuts the "border" of an I4MAT.
</li>
<li>
<b>I4MAT_COPY</b> copies one I4MAT to another.
</li>
<li>
<b>I4MAT_COPY_NEW</b> copies an I4MAT to a "new" I4MAT.
</li>
<li>
<b>I4MAT_DELETE</b> frees memory associated with an I4MAT.
</li>
<li>
<b>I4MAT_ELIM</b> carries out exact Gauss elimination on an I4MAT.
</li>
<li>
<b>I4MAT_FLIP_COLS</b> swaps the columns of an I4MAT.
</li>
<li>
<b>I4MAT_FLIP_ROWS</b> swaps the rows of an I4MAT.
</li>
<li>
<b>I4MAT_HISTOGRAM</b> computes a histogram of the elements of an I4MAT.
</li>
<li>
<b>I4MAT_INDICATOR_NEW</b> sets up an "indicator" I4MAT.
</li>
<li>
<b>I4MAT_L1_INVERSE</b> inverts a unit lower triangular I4MAT.
</li>
<li>
<b>I4MAT_MAX</b> returns the maximum of an I4MAT.
</li>
<li>
<b>I4MAT_MAX_INDEX</b> returns the location of the maximum of an I4MAT.
</li>
<li>
<b>I4MAT_MIN</b> returns the minimum of an I4MAT.
</li>
<li>
<b>I4MAT_MIN_INDEX</b> returns the location of the minimum of an I4MAT.
</li>
<li>
<b>I4MAT_MM</b> multiplies two I4MAT's.
</li>
<li>
<b>I4MAT_NEW</b> allocates a new I4MAT.
</li>
<li>
<b>I4MAT_PERM_UNIFORM</b> selects a random permutation of an I4MAT.
</li>
<li>
<b>I4MAT_PERM2_UNIFORM</b> selects a random permutation of an I4MAT.
</li>
<li>
<b>I4MAT_PRINT</b> prints an I4MAT.
</li>
<li>
<b>I4MAT_PRINT_SOME</b> prints some of an I4MAT.
</li>
<li>
<b>I4MAT_RED</b> divides out common factors in a row or column of an I4MAT.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT</b> prints an I4MAT, transposed.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of an I4MAT, transposed.
</li>
<li>
<b>I4MAT_U1_INVERSE</b> inverts a unit upper triangular I4MAT.
</li>
<li>
<b>I4MAT_UNIFORM_NEW</b> returns a scaled pseudorandom I4MAT.
</li>
<li>
<b>I4ROW_COMPARE</b> compares two rows of a integer array.
</li>
<li>
<b>I4ROW_FIND_ITEM</b> searches the rows of an I4ROW for a given value.
</li>
<li>
<b>I4ROW_MAX</b> returns the maximums of an I4ROW.
</li>
<li>
<b>I4ROW_MEAN</b> returns the means of an I4ROW.
</li>
<li>
<b>I4ROW_MIN</b> returns the minimums of an I4ROW.
</li>
<li>
<b>I4ROW_SORT_A</b> ascending sorts the rows of an I4ROW.
</li>
<li>
<b>I4ROW_SORT_D</b> descending sorts the rows of an I4ROW.
</li>
<li>
<b>I4ROW_SORT2_D</b> descending sorts the elements of each row of an I4ROW.
</li>
<li>
<b>I4ROW_SUM</b> returns the sums of the rows of an I4ROW.
</li>
<li>
<b>I4ROW_SWAP</b> swaps two rows of an I4ROW.
</li>
<li>
<b>I4ROW_VARIANCE</b> returns the variances of an I4ROW.
</li>
<li>
<b>I4VEC_ADD_NEW</b> computes C = A + B for I4VEC's.
</li>
<li>
<b>I4VEC_ALL_NONPOSITIVE:</b> ( all ( A <= 0 ) ) for I4VEC's.
</li>
<li>
<b>I4VEC_AMAX</b> returns the largest magnitude in an I4VEC.
</li>
<li>
<b>I4VEC_AMAX_INDEX</b> returns the index of the maximum absolute value in an I4VEC.
</li>
<li>
<b>I4VEC_AMIN</b> returns the smallest magnitude in an I4VEC.
</li>
<li>
<b>I4VEC_AMIN_INDEX</b> returns the index of the minimum absolute value in an I4VEC.
</li>
<li>
<b>I4VEC_AMINZ</b> returns the smallest nonzero magnitude in an I4VEC.
</li>
<li>
<b>I4VEC_AMINZ_INDEX</b> returns the smallest nonzero magnitude in an I4VEC.
</li>
<li>
<b>I4VEC_ANY_LT:</b> ( any ( A < B ) ) for I4VEC's.
</li>
<li>
<b>I4VEC_ANY_NEGATIVE:</b> ( any A < 0 ) for I4VEC's.
</li>
<li>
<b>I4VEC_ANY_NONZERO:</b> ( any A nonzero ) for I4VEC's.
</li>
<li>
<b>I4VEC_ASCEND_SUB</b> computes the longest ascending subsequence in an I4VEC.
</li>
<li>
<b>I4VEC_ASCENDS</b> determines if an I4VEC is (weakly) ascending.
</li>
<li>
<b>I4VEC_AXPY</b> adds IA times the vector IX to the vector IY.
</li>
<li>
<b>I4VEC_BRACKET</b> searches a sorted I4VEC for successive brackets of a value.
</li>
<li>
<b>I4VEC_COMPARE</b> compares two I4VEC's.
</li>
<li>
<b>I4VEC_COPY</b> copies an I4VEC.
</li>
<li>
<b>I4VEC_COPY_NEW</b> copies an I4VEC to a "new" I4VEC.
</li>
<li>
<b>I4VEC_CUM</b> computes the cumulutive sum of the entries of an I4VEC.
</li>
<li>
<b>I4VEC_CUM0</b> computes the cumulutive sum of the entries of an I4VEC.
</li>
<li>
<b>I4VEC_DESCENDS</b> determines if an I4VEC is (weakly) descending.
</li>
<li>
<b>I4VEC_DIRECT_PRODUCT</b> creates a direct product of I4VEC's.
</li>
<li>
<b>I4VEC_DIRECT_PRODUCT2</b> creates a direct product of I4VEC's.
</li>
<li>
<b>I4VEC_DOT_PRODUCT</b> computes the dot product of two I4VEC's.
</li>
<li>
<b>I4VEC_EVEN_ALL</b> is TRUE if all entries of an I4VEC are even.
</li>
<li>
<b>I4VEC_EVEN_ANY</b> is TRUE if any entry of an I4VEC is even.
</li>
<li>
<b>I4VEC_FIND</b> finds the first occurrence of a value in an I4VEC.
</li>
<li>
<b>I4VEC_FIRST_INDEX</b> indexes the first occurrence of values in an I4VEC.
</li>
<li>
<b>I4VEC_FRAC</b> searches for the K-th smallest entry in an I4VEC.
</li>
<li>
<b>I4VEC_GCD</b> returns the greatest common divisor of an I4VEC.
</li>
<li>
<b>I4VEC_HEAP_A</b> reorders an I4VEC into a ascending heap.
</li>
<li>
<b>I4VEC_HEAP_D</b> reorders an I4VEC into a descending heap.
</li>
<li>
<b>I4VEC_HEAP_D_EXTRACT</b> extracts the maximum value from a descending heap.
</li>
<li>
<b>I4VEC_HEAP_D_INSERT</b> inserts a new value into a descending heap.
</li>
<li>
<b>I4VEC_HEAP_D_MAX</b> returns the maximum value in a descending heap of integers.
</li>
<li>
<b>I4VEC_HISTOGRAM</b> computes a histogram of the elements of an I4VEC.
</li>
<li>
<b>I4VEC_INDEX</b> locates a value in an I4VEC.
</li>
<li>
<b>I4VEC_INDEX_DELETE_ALL</b> deletes all occurrences of a value from an indexed sorted list.
</li>
<li>
<b>I4VEC_INDEX_DELETE_DUPES</b> deletes duplicates from an indexed sorted I4VEC.
</li>
<li>
<b>I4VEC_INDEX_DELETE_ONE</b> deletes one copy of an I4 from an indexed sorted I4VEC.
</li>
<li>
<b>I4VEC_INDEX_INSERT</b> inserts an I4 into an indexed sorted I4VEC.
</li>
<li>
<b>I4VEC_INDEX_INSERT_UNIQUE</b> inserts a unique I4 in an indexed sorted I4VEC.
</li>
<li>
<b>I4VEC_INDEX_ORDER</b> sorts an I4VEC using an index vector.
</li>
<li>
<b>I4VEC_INDEX_SEARCH</b> searches for an I4 in an indexed sorted I4VEC.
</li>
<li>
<b>I4VEC_INDEX_SORT_UNIQUE</b> creates a sort index for an I4VEC.
</li>
<li>
<b>I4VEC_INDEXED_HEAP_D</b> creates a descending heap from an indexed I4VEC.
</li>
<li>
<b>I4VEC_INDEXED_HEAP_D_EXTRACT:</b> extract from heap descending indexed I4VEC.
</li>
<li>
<b>I4VEC_INDEXED_HEAP_D_INSERT:</b> insert value into heap descending indexed I4VEC.
</li>
<li>
<b>I4VEC_INDEXED_HEAP_D_MAX:</b> maximum value in heap descending indexed I4VEC.
</li>
<li>
<b>I4VEC_INDICATOR</b> sets an I4VEC to the indicator vector.
</li>
<li>
<b>I4VEC_INDICATOR_NEW</b> sets an I4VEC to the indicator vector.
</li>
<li>
<b>I4VEC_INSERT</b> inserts a value into an I4VEC.
</li>
<li>
<b>I4VEC_LCM</b> returns the least common multiple of an I4VEC.
</li>
<li>
<b>I4VEC_MAX</b> returns the value of the maximum element in an I4VEC.
</li>
<li>
<b>I4VEC_MAX_INDEX</b> returns the index of the maximum value in an I4VEC.
</li>
<li>
<b>I4VEC_MAX_INDEX_LAST:</b> index of the last maximum value in an I4VEC.
</li>
<li>
<b>I4VEC_MEAN</b> returns the mean of an I4VEC.
</li>
<li>
<b>I4VEC_MEDIAN</b> returns the median of an unsorted I4VEC.
</li>
<li>
<b>I4VEC_MERGE_A</b> merges two ascending sorted I4VEC's.
</li>
<li>
<b>I4VEC_MIN</b> returns the value of the minimum element in an I4VEC.
</li>
<li>
<b>I4VEC_MIN_INDEX</b> returns the index of the minimum value in an I4VEC.
</li>
<li>
<b>I4VEC_MIN_MV</b> determines U(1:N) /\ V for vectors U and a single vector V.
</li>
<li>
<b>I4VEC_NEGONE</b> sets an I4VEC to -1.
</li>
<li>
<b>I4VEC_NEGONE_NEW</b> creates an I4VEC and sets it to -1.
</li>
<li>
<b>I4VEC_NONZERO_COUNT</b> counts the nonzero entries in an I4VEC.
</li>
<li>
<b>I4VEC_NONZERO_FIRST</b> left-shifts all nonzeros in an I4VEC.
</li>
<li>
<b>I4VEC_ODD_ALL</b> is TRUE if all entries of an I4VEC are odd.
</li>
<li>
<b>I4VEC_ODD_ANY</b> is TRUE if any entry of an I4VEC is odd.
</li>
<li>
<b>I4VEC_ORDER_TYPE:</b> is an I4VEC is (non)strictly ascending/descending?
</li>
<li>
<b>I4VEC_PAIRWISE_PRIME</b> checks whether an I4VEC is pairwise prime.
</li>
<li>
<b>I4VEC_PART</b> partitions an int NVAL into N nearly equal parts.
</li>
<li>
<b>I4VEC_PART_QUICK_A</b> reorders an I4VEC as part of a quick sort.
</li>
<li>
<b>I4VEC_PERMUTE</b> permutes an I4VEC in place.
</li>
<li>
<b>I4VEC_PERMUTE_UNIFORM</b> randomly permutes an I4VEC.
</li>
<li>
<b>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>I4VEC_PRINT_PART</b> prints "part" of an I4VEC.
</li>
<li>
<b>I4VEC_PRINT_SOME</b> prints "some" of an I4VEC.
</li>
<li>
<b>I4VEC_PRODUCT</b> multiplies the entries of an I4VEC.
</li>
<li>
<b>I4VEC_RED</b> divides out common factors in an I4VEC.
</li>
<li>
<b>I4VEC_REVERSE</b> reverses the elements of an I4VEC.
</li>
<li>
<b>I4VEC_ROTATE</b> rotates an I4VEC in place.
</li>
<li>
<b>I4VEC_RUN_COUNT</b> counts runs of equal values in an I4VEC.
</li>
<li>
<b>I4VEC_SEARCH_BINARY_A</b> searches an ascending sorted I4VEC for a value.
</li>
<li>
<b>I4VEC_SEARCH_BINARY_D</b> searches a descending sorted I4VEC for a value.
</li>
<li>
<b>I4VEC_SORT_BUBBLE_A</b> ascending sorts an I4VEC using bubble sort.
</li>
<li>
<b>I4VEC_SORT_BUBBLE_D</b> descending sorts an I4VEC using bubble sort.
</li>
<li>
<b>I4VEC_SORT_HEAP_A</b> ascending sorts an I4VEC using heap sort.
</li>
<li>
<b>I4VEC_SORT_HEAP_D</b> descending sorts an I4VEC using heap sort.
</li>
<li>
<b>I4VEC_SORT_HEAP_INDEX_A</b> does an indexed heap ascending sort of an I4VEC.
</li>
<li>
<b>I4VEC_SORT_HEAP_INDEX_D</b> does an indexed heap descending sort of an I4VEC.
</li>
<li>
<b>I4VEC_SORT_INSERT_A</b> uses an ascending insertion sort on an I4VEC.
</li>
<li>
<b>I4VEC_SORT_INSERT_D</b> uses a descending insertion sort on an I4VEC.
</li>
<li>
<b>I4VEC_SORT_QUICK_A</b> ascending sorts an I4VEC using quick sort.
</li>
<li>
<b>I4VEC_SORT_SHELL_A</b> ascending sorts an I4VEC using Shell's sort.
</li>
<li>
<b>I4VEC_SORTED_UNDEX</b> returns unique sorted indexes for a sorted I4VEC.
</li>
<li>
<b>I4VEC_SORTED_UNIQUE</b> finds the unique elements in a sorted I4VEC.
</li>
<li>
<b>I4VEC_SORTED_UNIQUE_COUNT</b> counts unique elements in a sorted I4VEC.
</li>
<li>
<b>I4VEC_SORTED_UNIQUE_HIST</b> histograms the unique elements of a sorted I4VEC.
</li>
<li>
<b>I4VEC_SPLIT</b> "splits" an unsorted I4VEC based on a splitting value.
</li>
<li>
<b>I4VEC_STD</b> returns the standard deviation of an I4VEC.
</li>
<li>
<b>I4VEC_SUM</b> sums the entries of an I4VEC.
</li>
<li>
<b>I4VEC_SWAP</b> swaps two I4VEC's.
</li>
<li>
<b>I4VEC_TRANSPOSE_PRINT</b> prints an I4VEC "transposed".
</li>
<li>
<b>I4VEC_UNDEX</b> returns unique sorted indexes for an I4VEC.
</li>
<li>
<b>I4VEC_UNIFORM</b> returns a scaled pseudorandom I4VEC.
</li>
<li>
<b>I4VEC_UNIFORM_NEW</b> returns a scaled pseudorandom I4VEC.
</li>
<li>
<b>I4VEC_UNIQUE_COUNT</b> counts the unique elements in an unsorted I4VEC.
</li>
<li>
<b>I4VEC_UNIQUE_INDEX</b> indexes the unique occurrence of values in an I4VEC.
</li>
<li>
<b>I4VEC_VALUE_INDEX</b> indexes I4VEC entries equal to a given value.
</li>
<li>
<b>I4VEC_VALUE_NUM</b> counts I4VEC entries equal to a given value.
</li>
<li>
<b>I4VEC_VARIANCE</b> returns the variance of an I4VEC.
</li>
<li>
<b>I4VEC_WIDTH</b> returns the "width" of an I4VEC.
</li>
<li>
<b>I4VEC_ZERO</b> zeroes an I4VEC.
</li>
<li>
<b>I4VEC_ZERO_NEW</b> creates and zeroes an I4VEC.
</li>
<li>
<b>I4VEC2_COMPARE</b> compares pairs of integers stored in two vectors.
</li>
<li>
<b>I4VEC2_PRINT</b> prints an I4VEC2.
</li>
<li>
<b>I4VEC2_SORT_A</b> ascending sorts an I4VEC2.
</li>
<li>
<b>I4VEC2_SORT_D</b> descending sorts an I4VEC2.
</li>
<li>
<b>I4VEC2_SORTED_UNIQUE</b> keeps the unique elements in an I4VEC2.
</li>
<li>
<b>L_TO_I4</b> converts an L to an I4.
</li>
<li>
<b>PERM_CHECK</b> checks that a vector represents a permutation.
</li>
<li>
<b>PERM_CYCLE</b> analyzes a permutation.
</li>
<li>
<b>PERM_UNIFORM_NEW</b> selects a random permutation of N objects.
</li>
<li>
<b>PRIME</b> returns any of the first PRIME_MAX prime numbers.
</li>
<li>
<b>R4_NINT</b> returns the nearest integer to an R4.
</li>
<li>
<b>R8_ABS</b> returns the absolute value of an R8.
</li>
<li>
<b>R8_NINT</b> returns the nearest integer to an R8.
</li>
<li>
<b>SORT_HEAP_EXTERNAL</b> externally sorts a list of items into ascending order.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 05 March 2012.
</i>
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