(********************************************************************) (* *) (* bigint.s7i Unlimited precision integer support library *) (* Copyright (C) 2006, 2008, 2010 - 2015 Thomas Mertes *) (* 2017 - 2021, 2023, 2024 Thomas Mertes *) (* *) (* This file is part of the Seed7 Runtime Library. *) (* *) (* The Seed7 Runtime Library is free software; you can *) (* redistribute it and/or modify it under the terms of the GNU *) (* Lesser General Public License as published by the Free Software *) (* Foundation; either version 2.1 of the License, or (at your *) (* option) any later version. *) (* *) (* The Seed7 Runtime Library is distributed in the hope that it *) (* will be useful, but WITHOUT ANY WARRANTY; without even the *) (* implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR *) (* PURPOSE. See the GNU Lesser General Public License for more *) (* details. *) (* *) (* You should have received a copy of the GNU Lesser General *) (* Public License along with this program; if not, write to the *) (* Free Software Foundation, Inc., 51 Franklin Street, *) (* Fifth Floor, Boston, MA 02110-1301, USA. *) (* *) (********************************************************************) include "enable_io.s7i"; (** * Signed integer numbers of unlimited size. * The literals of the type ''bigInteger'' are sequences of digits * followed by an underscore character (for example 1_ ). Although * ''bigInteger'' operations cannot overflow, it can happen that * there is not enough memory to represent a ''bigInteger'' value. * In this case the exception MEMORY_ERROR is raised. *) const type: bigInteger is subtype object; $ system "bigInteger" is bigInteger; const proc: destroy (ref bigInteger: aValue) is action "BIG_DESTR"; const proc: (ref bigInteger: dest) ::= (ref bigInteger: source) is action "BIG_CREATE"; IN_PARAM_IS_REFERENCE(bigInteger); const proc: (inout bigInteger: dest) := (in bigInteger: source) is action "BIG_CPY"; (** * Default value of ''bigInteger'' (0_). *) const bigInteger: (attr bigInteger) . value is 0_; (** * Plus sign for ''bigInteger'' numbers. * @return its operand unchanged. *) const func bigInteger: + (in bigInteger: number) is action "BIG_PLUS"; (** * Minus sign, negate a ''bigInteger'' number. * @return the negated value of the number. *) const func bigInteger: - (in bigInteger: number) is action "BIG_NEGATE"; (** * Add two ''bigInteger'' numbers. * @return the sum of the two numbers. *) const func bigInteger: (in bigInteger: summand1) + (in bigInteger: summand2) is action "BIG_ADD"; (** * Compute the subtraction of two ''bigInteger'' numbers. * @return the difference of the two numbers. *) const func bigInteger: (in bigInteger: minuend) - (in bigInteger: subtrahend) is action "BIG_SBTR"; (** * Multiply two ''bigInteger'' numbers. * @return the product of the two numbers. *) const func bigInteger: (in bigInteger: factor1) * (in bigInteger: factor2) is action "BIG_MULT"; (** * Integer division truncated towards zero. * The remainder of this division is computed with ''rem''. * For the operations ''div'' and ''rem'' holds for all A: * (A div B) * B + A rem B = A when B <> 0_ * -A div B = -(A div B) when B <> 0_ * -A rem B = -(A rem B) when B <> 0_ * A rem B >= 0_ and A rem B < abs(B) when B <> 0_ and A >= 0_ * A rem B <= 0_ and A rem B > -abs(B) when B <> 0_ and A <= 0_ * @return the quotient of the integer division. * @exception NUMERIC_ERROR If a division by zero occurs. *) const func bigInteger: (in bigInteger: dividend) div (in bigInteger: divisor) is action "BIG_DIV"; (** * Compute the remainder of the integer division ''div''. * The remainder has the same sign as the dividend. * A rem B * is equivalent to * A - (A div B) * B * @return the remainder of the integer division. * @exception NUMERIC_ERROR If a division by zero occurs. *) const func bigInteger: (in bigInteger: dividend) rem (in bigInteger: divisor) is action "BIG_REM"; (** * Integer division truncated towards negative infinity. * The modulo (remainder) of this division is computed with 'mod'. * Therefore this division is called modulo division (''mdiv''). * For the operations ''mdiv'' and ''mod'' holds for all A: * (A mdiv B) * B + A mod B = A when B <> 0_ * -A mdiv B = A mdiv -B when B <> 0_ * -A mod -B = -(A mod B) when B <> 0_ * A mod B >= 0_ and A mod B < B when B > 0_ * A mod B <= 0_ and A mod B > B when B < 0_ * @return the quotient of the integer division. * @exception NUMERIC_ERROR If a division by zero occurs. *) const func bigInteger: (in bigInteger: dividend) mdiv (in bigInteger: divisor) is action "BIG_MDIV"; (** * Compute the modulo (remainder) of the integer division ''mdiv''. * The modulo has the same sign as the divisor. * A mod B * is equivalent to * A - (A mdiv B) * B * @return the modulo of the integer division. * @exception NUMERIC_ERROR If a division by zero occurs. *) const func bigInteger: (in bigInteger: dividend) mod (in bigInteger: divisor) is action "BIG_MOD"; (** * Compute the exponentiation of a ''bigInteger'' base with an [[integer]] exponent. * A ** 0 returns 1_ for every A, even for A = 0_ * 1 ** B returns 1_ for B >= 0 * A ** B returns -(-A) ** B for A <= 0_ and B >= 0 and odd(B) * A ** B returns (-A) ** B for A <= 0_ and B >= 0 and not odd(B) * @return the result of the exponentiation. * @exception NUMERIC_ERROR If the exponent is negative. *) const func bigInteger: (in bigInteger: base) ** (in integer: exponent) is action "BIG_IPOW"; # const func bigInteger: (in bigInteger: base) ** (in bigInteger: exponent) is action "BIG_POW"; (** * Shift a ''bigInteger'' number left by lshift bits. * If lshift is negative a right shift is done instead. * A << B is equivalent to A * 2_ ** B when B >= 0 holds. * A << B is equivalent to A mdiv 2_ ** -B when B < 0 holds. * @return the left shifted number. *) const func bigInteger: (in bigInteger: number) << (in integer: lshift) is action "BIG_LSHIFT"; (** * Shift a ''bigInteger'' number right by rshift bits. * If rshift is negative a left shift is done instead. * A >> B is equivalent to A mdiv 2_ ** B when B >= 0 holds. * A >> B is equivalent to A * 2_ ** -B when B < 0 holds. * @return the right shifted number. *) const func bigInteger: (in bigInteger: number) >> (in integer: rshift) is action "BIG_RSHIFT"; (** * Increment a ''bigInteger'' variable by a delta. *) const proc: (inout bigInteger: number) +:= (in bigInteger: delta) is action "BIG_ADD_ASSIGN"; (** * Decrement a ''bigInteger'' variable by a delta. *) const proc: (inout bigInteger: number) -:= (in bigInteger: delta) is action "BIG_SBTR_ASSIGN"; (** * Multiply a ''bigInteger'' number by a factor and assign the result back to number. *) const proc: (inout bigInteger: number) *:= (in bigInteger: factor) is action "BIG_MULT_ASSIGN"; (** * Shift a number left by lshift bits and assign the result back to number. * If lshift is negative a right shift is done instead. *) const proc: (inout bigInteger: number) <<:= (in integer: lshift) is action "BIG_LSHIFT_ASSIGN"; (** * Shift a number right by rshift bits and assign the result back to number. * If rshift is negative a left shift is done instead. *) const proc: (inout bigInteger: number) >>:= (in integer: rshift) is action "BIG_RSHIFT_ASSIGN"; (** * Check if two ''bigInteger'' numbers are equal. * @return TRUE if both numbers are equal, * FALSE otherwise. *) const func boolean: (in bigInteger: number1) = (in bigInteger: number2) is action "BIG_EQ"; (** * Check if two ''bigInteger'' numbers are not equal. * @return FALSE if both numbers are equal, * TRUE otherwise. *) const func boolean: (in bigInteger: number1) <> (in bigInteger: number2) is action "BIG_NE"; (** * Check if number1 is less than number2. * @return TRUE if number1 is less than number2, * FALSE otherwise. *) const func boolean: (in bigInteger: number1) < (in bigInteger: number2) is action "BIG_LT"; (** * Check if number1 is greater than number2. * @return TRUE if number1 is greater than number2, * FALSE otherwise. *) const func boolean: (in bigInteger: number1) > (in bigInteger: number2) is action "BIG_GT"; (** * Check if number1 is less than or equal to number2. * @return TRUE if number1 is less than or equal to number2, * FALSE otherwise. *) const func boolean: (in bigInteger: number1) <= (in bigInteger: number2) is action "BIG_LE"; (** * Check if number1 is greater than or equal to number2. * @return TRUE if number1 is greater than or equal to number2, * FALSE otherwise. *) const func boolean: (in bigInteger: number1) >= (in bigInteger: number2) is action "BIG_GE"; (** * Compare two ''bigInteger'' numbers. * @return -1, 0 or 1 if the first argument is considered to be * respectively less than, equal to, or greater than the * second. *) const func integer: compare (in bigInteger: number1, in bigInteger:number2) is action "BIG_CMP"; (** * Compute the hash value of a ''bigInteger'' number. * @return the hash value. *) const func integer: hashCode (in bigInteger: number) is action "BIG_HASHCODE"; const type: quotRem is new struct var bigInteger: quotient is 0_; var bigInteger: remainder is 0_; end struct; const func quotRem: quotRem (in bigInteger: quotient, in bigInteger: remainder) is func result var quotRem: quotRemValue is quotRem.value; begin quotRemValue.quotient := quotient; quotRemValue.remainder := remainder; end func; const func boolean: (in quotRem: quotRem1) = (in quotRem: quotRem2) is return quotRem1.quotient = quotRem2.quotient and quotRem1.remainder = quotRem2.remainder; const func boolean: (in quotRem: quotRem1) <> (in quotRem: quotRem2) is return quotRem1.quotient <> quotRem2.quotient or quotRem1.remainder <> quotRem2.remainder; (** * Quotient and remainder of integer division truncated towards zero. * Compute quotient and remainder of the integer division ''div''. * @return quotRem with quotient and remainder of the integer division. * @exception NUMERIC_ERROR If a division by zero occurs. *) const func quotRem: (in bigInteger: dividend) divRem (in bigInteger: divisor) is action "BIG_DIV_REM"; (** * Successor of a ''bigInteger'' number. * succ(A) is equivalent to A+1 . * @return number + 1 . *) const func bigInteger: succ (in bigInteger: number) is action "BIG_SUCC"; (** * Predecessor of a ''bigInteger'' number. * pred(A) is equivalent to A-1 . * @return number - 1 . *) const func bigInteger: pred (in bigInteger: number) is action "BIG_PRED"; (** * Compute the absolute value of a ''bigInteger'' number. * @return the absolute value. *) const func bigInteger: abs (in bigInteger: number) is action "BIG_ABS"; (** * Compute the truncated base 10 logarithm of a ''bigInteger'' number. * The definition of ''log10'' is extended by defining log10(0_) = -1_. * log10(10_ ** A) returns A for A >= 0 * log10(pred(10_ ** A)) returns pred(A) for A >= 0 * log10(10_) returns 1 * log10(1_) returns 0 * log10(0_) returns -1 * @return the truncated base 10 logarithm. * @exception NUMERIC_ERROR The number is negative. *) const func bigInteger: log10 (in bigInteger: number) is action "BIG_LOG10"; (** * Compute the truncated base 2 logarithm of a ''bigInteger'' number. * The definition of ''log2'' is extended by defining log2(0_) = -1_. * log2(2_ ** A) returns A for A >= 0 * log2(pred(2_ ** A)) returns pred(A) for A >= 0 * log2(2_) returns 1 * log2(1_) returns 0 * log2(0_) returns -1 * @return the truncated base 2 logarithm. * @exception NUMERIC_ERROR The number is negative. *) const func bigInteger: log2 (in bigInteger: number) is action "BIG_LOG2"; (** * Determine if a ''bigInteger'' number is odd. * @return TRUE if the number is odd, * FALSE otherwise. *) const func boolean: odd (in bigInteger: number) is action "BIG_ODD"; (** * Convert a ''bigInteger'' number to [[integer]]. * @return the [[integer]] result of the conversion. * @exception RANGE_ERROR The result does not fit into an [[integer]]. *) const func integer: ord (in bigInteger: number) is action "BIG_ORD"; (** * Convert a ''bigInteger'' number to [[integer]]. * @return the [[integer]] result of the conversion. * @exception RANGE_ERROR The result does not fit into an [[integer]]. *) const func integer: integer (in bigInteger: number) is action "BIG_ORD"; (** * Compute the greatest common divisor of two ''bigInteger'' numbers. * @return the greatest common divisor of the two numbers. * The greatest common divisor is positive or zero. *) const func bigInteger: gcd (in bigInteger: number1, in bigInteger: number2) is action "BIG_GCD"; (** * Convert an [[integer]] number to ''bigInteger''. * @return the bigInteger result of the conversion. * @exception MEMORY_ERROR Not enough memory to represent the result. *) const func bigInteger: bigInteger (in integer: number) is action "BIG_ICONV1"; (** * Convert an [[integer]] number to ''bigInteger''. * @return the bigInteger result of the conversion. * @exception MEMORY_ERROR Not enough memory to represent the result. *) const func bigInteger: (attr bigInteger) conv (in integer: number) is action "BIG_ICONV3"; (** * Convert a ''bigInteger'' number to a [[string]]. * The number is converted to a string with decimal representation. * For negative numbers a minus sign is prepended. * @return the string result of the conversion. * @exception MEMORY_ERROR Not enough memory to represent the result. *) const func string: str (in bigInteger: number) is action "BIG_STR"; (** * Convert a ''bigInteger'' number to a ''bigInteger'' literal. * @return the ''bigInteger'' literal. * @exception MEMORY_ERROR Not enough memory to represent the result. *) const func string: literal (in bigInteger: number) is return str(number) & "_"; (** * Convert a ''bigInteger'' number to a [[string]] using a radix. * The conversion uses the numeral system with the given ''base''. * Digit values from 10 upward are encoded with lower case letters. * E.g.: 10 is encoded with a, 11 with b, etc. * For negative numbers a minus sign is prepended. * 3735928559_ radix 16 => "deadbeef" * -3735928559_ radix 16 => "-deadbeef" * @return the string result of the conversion. * @exception RANGE_ERROR If base < 2 or base > 36 holds. * @exception MEMORY_ERROR Not enough memory to represent the result. *) const func string: (in var bigInteger: number) radix (in integer: base) is action "BIG_radix"; (** * Convert a ''bigInteger'' number to a [[string]] using a radix. * The conversion uses the numeral system with the given ''base''. * Digit values from 10 upward are encoded with upper case letters. * E.g.: 10 is encoded with A, 11 with B, etc. * For negative numbers a minus sign is prepended. * 3735928559_ RADIX 16 => "DEADBEEF" * -3735928559_ RADIX 16 => "-DEADBEEF" * @return the string result of the conversion. * @exception RANGE_ERROR If base < 2 or base > 36 holds. * @exception MEMORY_ERROR Not enough memory to represent the result. *) const func string: (in var bigInteger: number) RADIX (in integer: base) is action "BIG_RADIX"; (** * Convert a [[string]] to a ''bigInteger'' number. * The [[string]] must contain an integer literal consisting of an * optional + or - sign, followed by a sequence of digits. Other * characters as well as leading or trailing whitespace characters * are not allowed. The sequence of digits is taken to be decimal. * @return the ''bigInteger'' result of the conversion. * @exception RANGE_ERROR If the string is empty or it does not contain * an integer literal. * @exception MEMORY_ERROR Not enough memory to represent the result. *) const func bigInteger: bigInteger (in string: stri) is action "BIG_PARSE1"; (** * Convert a [[string]] to a ''bigInteger'' number. * The [[string]] must contain an integer literal consisting of an * optional + or - sign, followed by a sequence of digits. Other * characters as well as leading or trailing whitespace characters * are not allowed. The sequence of digits is taken to be decimal. * @return the ''bigInteger'' result of the conversion. * @exception RANGE_ERROR If the string is empty or it does not contain * an integer literal. * @exception MEMORY_ERROR Not enough memory to represent the result. *) const func bigInteger: (attr bigInteger) parse (in string: stri) is return bigInteger(stri); (** * Convert a numeric [[string]], with a specified radix, to a ''bigInteger''. * The numeric [[string]] must contain the representation of an integer * in the specified radix. It consists of an optional + or - sign, * followed by a sequence of digits in the specified radix. Digit values * from 10 upward can be encoded with upper or lower case letters. * E.g.: 10 can be encoded with A or a, 11 with B or b, etc. Other * characters as well as leading or trailing whitespace characters * are not allowed. * bigInteger("deadbeef", 16) returns 3735928559_ * bigInteger("-77777777777", 8) returns -8589934591_ * bigInteger("10101010", 2) returns 170_ * bigInteger("Cafe", 16) returns 51966_ * @param base Radix of the integer in the ''stri'' parameter. * @return the ''bigInteger'' result of the conversion. * @exception RANGE_ERROR If base < 2 or base > 36 holds or * the string is empty or it does not contain an integer * literal with the specified base. * @exception MEMORY_ERROR Not enough memory to represent the result. *) const func bigInteger: bigInteger (in string: stri, in integer: base) is action "BIG_PARSE_BASED"; (** * Compute pseudo-random number in the range [low, high]. * The random values are uniform distributed. * @return a random number such that low <= rand(low, high) and * rand(low, high) <= high holds. * @exception RANGE_ERROR The range is empty (low > high holds). *) const func bigInteger: rand (in bigInteger: low, in bigInteger: high) is action "BIG_RAND"; (** * Number of bits in the minimum two's-complement representation. * The high bits equivalent to the sign bit are not part of the * minimum two's-complement representation. * bitLength(0_) returns 0 * bitLength(1_) returns 1 * bitLength(4_) returns 3 * bitLength(-1_) returns 0 * bitLength(-2_) returns 1 * bitLength(-4_) returns 2 * @return the number of bits. * @exception RANGE_ERROR The result does not fit into an integer. *) const func integer: bitLength (in bigInteger: number) is action "BIG_BIT_LENGTH"; (** * Number of lowest-order zero bits in the two's-complement representation. * This is equal to the index of the lowest-order one bit (indices start with 0). * If there are only zero bits (''number'' is 0_) the result is -1. * lowestSetBit(0_) returns -1 * lowestSetBit(1_) returns 0 * lowestSetBit(4_) returns 2 * lowestSetBit(-1_) returns 0 * lowestSetBit(-2_) returns 1 * lowestSetBit(-4_) returns 2 * @return the number of lowest-order zero bits or -1 for lowestSetBit(0_). *) const func integer: lowestSetBit (in bigInteger: number) is action "BIG_LOWEST_SET_BIT"; (** * Increment a ''bigInteger'' variable. * Increments ''number'' by 1. * This is equivalent to: * number := succ(number); *) const proc: incr (inout bigInteger: number) is action "BIG_INCR"; (** * Decrement a ''bigInteger'' variable. * Decrements ''number'' by 1. * This is equivalent to: * number := pred(number); *) const proc: decr (inout bigInteger: number) is action "BIG_DECR"; const boolean: ord (in bigInteger: number, mayRaiseRangeError) is TRUE; enable_io(bigInteger); FOR_DECLS(bigInteger); CASE_DECLS(bigInteger); (** * Convert a ''bigInteger'' number to a [[string]] in scientific notation. * Scientific notation uses a decimal significand and a decimal exponent. * The significand has an optional sign and exactly one digit before the * decimal point. The fractional part of the significand is rounded * to the specified number of digits (''precision''). Halfway cases are * rounded away from zero. The fractional part is followed by the * letter e and an exponent, which is always signed. The value zero is * never written with a negative sign. * 12345_ sci 4 returns "1.2345e+4" * 12345_ sci 3 returns "1.235e+4" * 12345_ sci 2 returns "1.23e+4" * 3141592_ sci 0 returns "3e+6" * 27182818_ sci 0 returns "3e+7" * 2_**64 sci 6 returns "1.844674e+19" * -1_ sci 3 returns "-1.000e+0" * -0_ sci 2 returns "0.00e+0" * @param precision Number of digits after the decimal point. * If the ''precision'' is zero the decimal point is omitted. * @return the string result of the conversion. * @exception RANGE_ERROR If the ''precision'' is negative. *) const func string: (in bigInteger: number) sci (in integer: precision) is func result var string: stri is ""; local var integer: exponent is 0; var bigInteger: mantissa is 0_; begin if precision < 0 then raise RANGE_ERROR; elsif number = 0_ then if precision = 0 then stri := "0e+0"; else stri := "0." & "0" mult precision & "e+0"; end if; else exponent := ord(log10(abs(number))); if precision >= exponent then stri := str(abs(number)); stri &:= "0" mult (precision - exponent); else mantissa := (abs(number) div 10_ ** pred(exponent - precision) + 5_) div 10_; stri := str(mantissa); if length(stri) > succ(precision) then # Rounding up increased the number of digits. incr(exponent); stri := stri[.. succ(precision)]; end if; end if; if precision <> 0 then stri := stri[1 fixLen 1] & "." & stri[2 .. ]; end if; stri &:= "e+" <& exponent; if number < 0_ then stri := "-" & stri; end if; end if; end func; (** * Compute the factorial of a ''bigInteger'' number. * @return the factorial of the number. * @exception NUMERIC_ERROR The number is negative. *) const func bigInteger: ! (in bigInteger: number) is func result var bigInteger: factorial is 1_; local var bigInteger: num is 0_; begin if number < 0_ then raise NUMERIC_ERROR; else for num range 2_ to number do factorial *:= num; end for; end if; end func; (** * Compute the binomial coefficient * n ! k returns 0 for k < 0, * n ! 0_ returns 1_, * n ! 1_ returns n, * n ! k returns 0 for n >= 0 and k > n, * n ! k returns !n div (!k * !(n - k)) for k >= 0 and k <= n, * n ! k returns (-1) ** k * (n + k - 1 ! k) for n < 0 and k >= 0 * @return n over k *) const func bigInteger: (in bigInteger: n) ! (in var bigInteger: k) is func result var bigInteger: binom is 0_; local var bigInteger: numerator is 0_; var bigInteger: denominator is 0_; begin if n >= 0_ and k > n >> 1 then k := n - k; end if; if k < 0_ then binom := 0_; elsif k = 0_ then binom := 1_; else binom := n; numerator := pred(n); denominator := 2_; while denominator <= k do binom *:= numerator; binom := binom div denominator; decr(numerator); incr(denominator); end while; end if; end func; (** * Compute the integer square root of a ''bigInteger'' number. * @return the integer square root. * @exception NUMERIC_ERROR If number is negative. *) const func bigInteger: sqrt (in var bigInteger: number) is func result var bigInteger: root is 0_; local var bigInteger: nextIteration is 0_; begin if number > 0_ then nextIteration := number; repeat root := nextIteration; nextIteration := (root + number div root) mdiv 2_; until root <= nextIteration; elsif number <> 0_ then raise NUMERIC_ERROR; end if; end func; (** * Compute the modular multiplicative inverse of a modulo b. * @return the modular multiplicative inverse when a and b are * coprime (gcd(a, b) = 1). * @exception RANGE_ERROR If a and b are not coprime (gcd(a, b) <> 1). *) const func bigInteger: modInverse (in var bigInteger: a, in var bigInteger: b) is func result var bigInteger: modularInverse is 0_; local var bigInteger: b_bak is 0_; var bigInteger: x is 0_; var bigInteger: y is 1_; var bigInteger: lastx is 1_; var bigInteger: lasty is 0_; var bigInteger: temp is 0_; var bigInteger: quotient is 0_; begin if b < 0_ then raise RANGE_ERROR; end if; if a < 0_ and b <> 0_ then a := a mod b; end if; b_bak := b; while b <> 0_ do temp := b; quotient := a div b; b := a rem b; a := temp; temp := x; x := lastx - quotient * x; lastx := temp; temp := y; y := lasty - quotient * y; lasty := temp; end while; if a = 1_ then modularInverse := lastx; if modularInverse < 0_ then modularInverse +:= b_bak; end if; else raise RANGE_ERROR; end if; end func; (** * Compute the modular exponentiation of base ** exponent. * @return base ** exponent mod modulus * @exception RANGE_ERROR If exponent or modulus are negative. *) const func bigInteger: modPow (in var bigInteger: base, in var bigInteger: exponent, in bigInteger: modulus) is func result var bigInteger: power is 1_; begin if exponent < 0_ or modulus < 0_ then raise RANGE_ERROR; else while exponent > 0_ do if odd(exponent) then power := (power * base) mod modulus; end if; exponent >>:= 1; base := base ** 2 mod modulus; end while; end if; end func; # Allows 'array bigInteger' everywhere without extra type definition. const type: _bigIntegerArray is array bigInteger; DECLARE_TERNARY(bigInteger); DECLARE_MIN_MAX(bigInteger);