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# Binary search

Binary search
You are encouraged to solve this task according to the task description, using any language you may know.

A binary search divides a range of values into halves, and continues to narrow down the field of search until the unknown value is found. It is the classic example of a "divide and conquer" algorithm.

As an analogy, consider the children's game "guess a number." The scorer has a secret number, and will only tell the player if their guessed number is higher than, lower than, or equal to the secret number. The player then uses this information to guess a new number.

As the player, an optimal strategy for the general case is to start by choosing the range's midpoint as the guess, and then asking whether the guess was higher, lower, or equal to the secret number. If the guess was too high, one would select the point exactly between the range midpoint and the beginning of the range. If the original guess was too low, one would ask about the point exactly between the range midpoint and the end of the range. This process repeats until one has reached the secret number.

Given the starting point of a range, the ending point of a range, and the "secret value", implement a binary search through a sorted integer array for a certain number. Implementations can be recursive or iterative (both if you can). Print out whether or not the number was in the array afterwards. If it was, print the index also.

There are several binary search algorithms commonly seen. They differ by how they treat multiple values equal to the given value, and whether they indicate whether the element was found or not. For completeness we will present pseudocode for all of them.

All of the following code examples use an "inclusive" upper bound (i.e. `high = N-1` initially). Any of the examples can be converted into an equivalent example using "exclusive" upper bound (i.e. `high = N` initially) by making the following simple changes (which simply increase `high` by 1):

• change `high = N-1` to `high = N`
• change `high = mid-1` to `high = mid`
• (for recursive algorithm) change `if (high < low)` to `if (high <= low)`
• (for iterative algorithm) change `while (low <= high)` to `while (low < high)`

The algorithms are as follows (from Wikipedia). The algorithms return the index of some element that equals the given value (if there are multiple such elements, it returns some arbitrary one). It is also possible, when the element is not found, to return the "insertion point" for it (the index that the value would have if it were inserted into the array).

Recursive Pseudocode:

```  // initially called with low = 0, high = N-1
BinarySearch(A[0..N-1], value, low, high) {
// invariants: value > A[i] for all i < low
value < A[i] for all i > high
if (high < low)
return not_found // value would be inserted at index "low"
mid = (low + high) / 2
if (A[mid] > value)
return BinarySearch(A, value, low, mid-1)
else if (A[mid] < value)
return BinarySearch(A, value, mid+1, high)
else
return mid
}
```

Iterative Pseudocode:

```  BinarySearch(A[0..N-1], value) {
low = 0
high = N - 1
while (low <= high) {
// invariants: value > A[i] for all i < low
value < A[i] for all i > high
mid = (low + high) / 2
if (A[mid] > value)
high = mid - 1
else if (A[mid] < value)
low = mid + 1
else
return mid
}
return not_found // value would be inserted at index "low"
}
```
Leftmost insertion point

The following algorithms return the leftmost place where the given element can be correctly inserted (and still maintain the sorted order). This is the lower (inclusive) bound of the range of elements that are equal to the given value (if any). Equivalently, this is the lowest index where the element is greater than or equal to the given value (since if it were any lower, it would violate the ordering), or 1 past the last index if such an element does not exist. This algorithm does not determine if the element is actually found. This algorithm only requires one comparison per level.

Recursive Pseudocode:

```  // initially called with low = 0, high = N - 1
BinarySearch_Left(A[0..N-1], value, low, high) {
// invariants: value > A[i] for all i < low
value <= A[i] for all i > high
if (high < low)
return low
mid = (low + high) / 2
if (A[mid] >= value)
return BinarySearch_Left(A, value, low, mid-1)
else
return BinarySearch_Left(A, value, mid+1, high)
}
```

Iterative Pseudocode:

```  BinarySearch_Left(A[0..N-1], value) {
low = 0
high = N - 1
while (low <= high) {
// invariants: value > A[i] for all i < low
value <= A[i] for all i > high
mid = (low + high) / 2
if (A[mid] >= value)
high = mid - 1
else
low = mid + 1
}
return low
}
```
Rightmost insertion point

The following algorithms return the rightmost place where the given element can be correctly inserted (and still maintain the sorted order). This is the upper (exclusive) bound of the range of elements that are equal to the given value (if any). Equivalently, this is the lowest index where the element is greater than the given value, or 1 past the last index if such an element does not exist. This algorithm does not determine if the element is actually found. This algorithm only requires one comparison per level. Note that these algorithms are almost exactly the same as the leftmost-insertion-point algorithms, except for how the inequality treats equal values.

Recursive Pseudocode:

```  // initially called with low = 0, high = N - 1
BinarySearch_Right(A[0..N-1], value, low, high) {
// invariants: value >= A[i] for all i < low
value < A[i] for all i > high
if (high < low)
return low
mid = (low + high) / 2
if (A[mid] > value)
return BinarySearch_Right(A, value, low, mid-1)
else
return BinarySearch_Right(A, value, mid+1, high)
}
```

Iterative Pseudocode:

```  BinarySearch_Right(A[0..N-1], value) {
low = 0
high = N - 1
while (low <= high) {
// invariants: value >= A[i] for all i < low
value < A[i] for all i > high
mid = (low + high) / 2
if (A[mid] > value)
high = mid - 1
else
low = mid + 1
}
return low
}
```
Extra credit

Make sure it does not have overflow bugs.

The line in the pseudo-code above to calculate the mean of two integers:

`mid = (low + high) / 2`

could produce the wrong result in some programming languages when used with a bounded integer type, if the addition causes an overflow. (This can occur if the array size is greater than half the maximum integer value.) If signed integers are used, and `low + high` overflows, it becomes a negative number, and dividing by 2 will still result in a negative number. Indexing an array with a negative number could produce an out-of-bounds exception, or other undefined behavior. If unsigned integers are used, an overflow will result in losing the largest bit, which will produce the wrong result.

One way to fix it is to manually add half the range to the low number:

`mid = low + (high - low) / 2`

Even though this is mathematically equivalent to the above, it is not susceptible to overflow.

Another way for signed integers, possibly faster, is the following:

`mid = (low + high) >>> 1`

where ` >>> ` is the logical right shift operator. The reason why this works is that, for signed integers, even though it overflows, when viewed as an unsigned number, the value is still the correct sum. To divide an unsigned number by 2, simply do a logical right shift.

## 11l

`F binary_search(l, value)   V low = 0   V high = l.len - 1   L low <= high      V mid = (low + high) I/ 2      I l[mid] > value         high = mid - 1      E I l[mid] < value         low = mid + 1      E         R mid   R -1`

## 360 Assembly

`*        Binary search             05/03/2017BINSEAR  CSECT         USING  BINSEAR,R13        base register         B      72(R15)            skip savearea         DC     17F'0'             savearea         STM    R14,R12,12(R13)    save previous context         ST     R13,4(R15)         link backward         ST     R15,8(R13)         link forward         LR     R13,R15            set addressability         MVC    LOW,=H'1'          low=1         MVC    HIGH,=AL2((XVAL-T)/2)  high=hbound(t)         SR     R6,R6              i=0         MVI    F,X'00'            f=false         LH     R4,LOW             low       DO WHILE=(CH,R4,LE,HIGH)    do while low<=high         LA     R6,1(R6)             i=i+1         LH     R1,LOW               low         AH     R1,HIGH              +high         SRA    R1,1                 /2  {by right shift}         STH    R1,MID               mid=(low+high)/2         SLA    R1,1                 *2         LH     R7,T-2(R1)           y=t(mid)       IF CH,R7,EQ,XVAL THEN         if xval=y then         MVI    F,X'01'                f=true         B      EXITDO                 leave       ENDIF    ,                    endif       IF CH,R7,GT,XVAL THEN         if y>xval then         LH     R2,MID                 mid         BCTR   R2,0                   -1         STH    R2,HIGH                high=mid-1       ELSE     ,                    else         LH     R2,MID                 mid         LA     R2,1(R2)               +1         STH    R2,LOW                low=mid+1       ENDIF    ,                    endif         LH     R4,LOW               low       ENDDO    ,                  enddoEXITDO   EQU    *                exitdo:         XDECO  R6,XDEC            edit i         MVC    PG(4),XDEC+8       output i         MVC    PG+4(6),=C' loops'         XPRNT  PG,L'PG            print buffer         LH     R1,XVAL            xval         XDECO  R1,XDEC            edit xval         MVC    PG(4),XDEC+8       output xval       IF CLI,F,EQ,X'01' THEN      if f then         MVC    PG+4(10),=C' found at '         LH     R1,MID               mid         XDECO  R1,XDEC              edit mid         MVC    PG+14(4),XDEC+8      output mid       ELSE     ,                  else         MVC    PG+4(20),=C' is not in the list.'       ENDIF    ,                  endif         XPRNT  PG,L'PG            print buffer         L      R13,4(0,R13)       restore previous savearea pointer         LM     R14,R12,12(R13)    restore previous context         XR     R15,R15            rc=0         BR     R14                exitT        DC     H'3',H'7',H'13',H'19',H'23',H'31',H'43',H'47'         DC     H'61',H'73',H'83',H'89',H'103',H'109',H'113',H'131'         DC     H'139',H'151',H'167',H'181',H'193',H'199',H'229',H'233'         DC     H'241',H'271',H'283',H'293',H'313',H'317',H'337',H'349'XVAL     DC     H'229'             <= search valueLOW      DS     HHIGH     DS     HMID      DS     HF        DS     X                  flagPG       DC     CL80' '            bufferXDEC     DS     CL12               temp         YREGS         END    BINSEAR`
Output:
```   5 loops
229 found at   23
```

## 8080 Assembly

This is the iterative version of the 'leftmost insertion point' algorithm. (On a processor like the 8080, you would not want to use recursion if you can avoid it. A subroutine call alone takes two bytes of stack space, meaning the needed stack space would be bigger than the array that's being searched.) For simplicity, it operates on an array of unsigned 8-bit integers, as this is the 8080's native datatype, and this task is about binary search, not about implementing operations on other datatypes in terms of 8-bit integers.

On entry, the subroutine `binsrch` takes the lookup value in the `B` register, a pointer to the start of the array in the `HL` registers, and a pointer to the end of the array in the `DE` registers. On exit, `HL` will contain the location of the value in the array, if it was found, and the leftmost insertion point, if it was not.

Test code is included, which will loop through the values [0..255] and report for each number whether it was in the array or not.

`		org	100h	; Entry for test code		jmp	test  		;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;		;; Binary search in array of unsigned 8-bit integers		;; B = value to look for		;; HL = begin of array (low)		;; DE = end of array, inclusive (high)		;; The entry point is 'binsrch'		;; On return, HL = location of value (if contained		;; in array), or insertion point (if not) binsrch_lo:	inx	h	; low = mid + 1		inx	sp	; throw away 'low'		inx	sp binsrch:	mov	a,d	; low > high? (are we there yet?)		cmp	h	; test high byte		rc		mov	a,e	; test low byte		cmp	l		rc 		push	h	; store 'low' 		dad	d	; mid = (low+high)>>1		mov	a,h	; rotate the carry flag back in		rar		; to take care of any overflow		mov	h,a		mov	a,l		rar		mov	l,a 		mov	a,m	; A[mid] >= value?		cmp	b		jc	binsrch_lo 		xchg		; high = mid - 1		dcx	d		pop	h	; restore 'low'		jmp	binsrch 		;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;		;; Test data primes:		db	2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37		db	41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83		db	89, 97, 101, 103, 107, 109, 113, 127, 131		db	137, 139, 149, 151, 157, 163, 167, 173, 179		db	181, 191, 193, 197, 199, 211, 223, 227, 229		db	233, 239, 241, 251primes_last:	equ	\$ - 1 		;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;		;; Test code (CP/M compatible) yep:		db	": yes", 13, 10, "\$"nope:		db	": no", 13, 10, "\$" num_out:	mov	a,b		;; Output number in B as decimal		mvi	c,100		call	dgt_out		mvi	c,10		call	dgt_out		mvi	c,1dgt_out:	mvi	e,'0' - 1	;; Output 100s, 10s or 1sdgt_out_loop:	inr	e		;; (depending on C)		sub	c				jnc	dgt_out_loop		add	ce_out:		push	psw		;; Output character in E		push	b		;; preserving working registers		mvi	c,2		call	5		pop	b		pop	psw		ret 		;; Main test codetest:		mvi	b,0		; Test value test_loop:	call	num_out		; Output current number to test 		lxi	h,primes	; Set up input for binary search		lxi	d,primes_last		call	binsrch		; Search for B in array 		lxi	d,nope		; Location of "no" string		mov	a,b		; Check if location binsrch returned		cmp	m		; contains the value we were looking for		jnz	str_out		; If not, print the "no" string		lxi	d,yep		; But if so, use location of "yes" stringstr_out:	push	b		; Preserve B across CP/M call		mvi	c,9		; Print the string		call	5		pop	b		; Restore B				 		inr	b		; Test next value		jnz	test_loop			 		rst	0 `

## AArch64 Assembly

Works with: as version Raspberry Pi 3B version Buster 64 bits
` /* ARM assembly AARCH64 Raspberry PI 3B *//*  program binSearch64.s   */ /*******************************************//* Constantes file                         *//*******************************************//* for this file see task include a file in language AArch64 assembly*/.include "../includeConstantesARM64.inc" /*********************************//* Initialized data              *//*********************************/.datasMessResult:        .asciz "Value find at index : @ \n"szCarriageReturn:   .asciz "\n"sMessRecursif:      .asciz "Recursive search : \n"sMessNotFound:      .asciz "Value not found. \n" TableNumber:        .quad   4,6,7,10,11,15,22,30,35                    .equ NBELEMENTS,  (. - TableNumber) / 8/*********************************//* UnInitialized data            *//*********************************/.bsssZoneConv:          .skip 24/*********************************//*  code section                 *//*********************************/.text.global main main:                                           // entry of program     mov x0,4                                    // search first value    ldr x1,qAdrTableNumber                      // address number table    mov x2,NBELEMENTS                           // number of élements     bl bSearch    ldr x1,qAdrsZoneConv    bl conversion10                             // décimal conversion     ldr x0,qAdrsMessResult    ldr x1,qAdrsZoneConv    bl strInsertAtCharInc                       // insert result at @ character    bl affichageMess                            // display message     mov x0,#11                                  // search median value    ldr x1,qAdrTableNumber    mov x2,#NBELEMENTS    bl bSearch    ldr x1,qAdrsZoneConv    bl conversion10                             // decimal conversion     ldr x0,qAdrsMessResult    ldr x1,qAdrsZoneConv    bl strInsertAtCharInc                       // insert result at @ character    bl affichageMess                            // display message     mov x0,#12                                  //value not found    ldr x1,qAdrTableNumber    mov x2,#NBELEMENTS    bl bSearch    cmp x0,#-1    bne 2f    ldr x0,qAdrsMessNotFound    bl affichageMess     b 3f2:    ldr x1,qAdrsZoneConv    bl conversion10                             // décimal conversion     ldr x0,qAdrsMessResult    ldr x1,qAdrsZoneConv    bl strInsertAtCharInc                       // insert result at @ character    bl affichageMess                            // display message3:    mov x0,#35                                  // search last value    ldr x1,qAdrTableNumber    mov x2,#NBELEMENTS    bl bSearch    ldr x1,qAdrsZoneConv    bl conversion10                             // décimal conversion     ldr x0,qAdrsMessResult    ldr x1,qAdrsZoneConv    bl strInsertAtCharInc                       // insert result at @ character    bl affichageMess                            // display message /****************************************//*       recursive                      *//****************************************/    ldr x0,qAdrsMessRecursif    bl affichageMess                            // display message     mov x0,#4                                   // search first value    ldr x1,qAdrTableNumber    mov x2,#0                                   // low index of elements    mov x3,#NBELEMENTS - 1                      // high index of elements    bl bSearchR    ldr x1,qAdrsZoneConv    bl conversion10                             // décimal conversion     ldr x0,qAdrsMessResult    ldr x1,qAdrsZoneConv    bl strInsertAtCharInc                       // insert result at @ character    bl affichageMess                            // display message     mov x0,#11    ldr x1,qAdrTableNumber    mov x2,#0    mov x3,#NBELEMENTS - 1    bl bSearchR    ldr x1,qAdrsZoneConv    bl conversion10                             // décimal conversion     ldr x0,qAdrsMessResult    ldr x1,qAdrsZoneConv    bl strInsertAtCharInc                       // insert result at @ character    bl affichageMess                            // display message     mov x0,#12    ldr x1,qAdrTableNumber    mov x2,#0    mov x3,#NBELEMENTS - 1    bl bSearchR    cmp x0,#-1    bne 4f    ldr x0,qAdrsMessNotFound    bl affichageMess     b 5f4:    ldr x1,qAdrsZoneConv    bl conversion10                             // décimal conversion     ldr x0,qAdrsMessResult    ldr x1,qAdrsZoneConv    bl strInsertAtCharInc                       // insert result at @ character    bl affichageMess                            // display message 5:    mov x0,#35    ldr x1,qAdrTableNumber    mov x2,#0    mov x3,#NBELEMENTS - 1    bl bSearchR    ldr x1,qAdrsZoneConv    bl conversion10                             // décimal conversion     ldr x0,qAdrsMessResult    ldr x1,qAdrsZoneConv    bl strInsertAtCharInc                       // insert result at @ character    bl affichageMess                            // display message  100:                                            // standard end of the program     mov x0, #0                                  // return code    mov x8, #EXIT                               // request to exit program    svc #0                                      // perform the system call //qAdrsMessValeur:          .quad sMessValeurqAdrsZoneConv:            .quad sZoneConvqAdrszCarriageReturn:     .quad szCarriageReturnqAdrsMessResult:          .quad sMessResultqAdrsMessRecursif:        .quad sMessRecursifqAdrsMessNotFound:        .quad sMessNotFoundqAdrTableNumber:          .quad TableNumber /******************************************************************//*     binary search   iterative                                  */ /******************************************************************//* x0 contains the value to search *//* x1 contains the adress of table *//* x2 contains the number of elements *//* x0 return index or -1 if not find */bSearch:    stp x1,lr,[sp,-16]!              // save  registers    stp x2,x3,[sp,-16]!              // save  registers    stp x4,x5,[sp,-16]!              // save  registers    mov x3,#0                        // low index    sub x4,x2,#1                     // high index = number of elements - 11:    cmp x3,x4    bgt 99f    add x2,x3,x4                     // compute (low + high) /2    lsr x2,x2,#1    ldr x5,[x1,x2,lsl #3]            // load value of table at index x2    cmp x5,x0    beq 98f    bgt 2f    add x3,x2,#1                     // lower -> index low = index + 1    b 1b                             // and loop2:    sub x4,x2,#1                     // bigger -> index high = index - 1    b 1b                             // and loop98:    mov x0,x2                        // find !!!    b 100f99:    mov x0,#-1                       //not found100:    ldp x4,x5,[sp],16                // restaur  2 registers    ldp x2,x3,[sp],16                // restaur  2 registers    ldp x1,lr,[sp],16                // restaur  2 registers    ret                              // return to address lr x30/******************************************************************//*     binary search   recursif                                  */ /******************************************************************//* x0 contains the value to search *//* x1 contains the adress of table *//* x2 contains the low index of elements *//* x3 contains the high index of elements *//* x0 return index or -1 if not find */bSearchR:    stp x2,lr,[sp,-16]!              // save  registers    stp x3,x4,[sp,-16]!              // save  registers    stp x5,x6,[sp,-16]!              // save  registers    cmp x3,x2                        // index high < low ?    bge 1f    mov x0,#-1                       // yes -> not found    b 100f1:    add x4,x2,x3                                     // compute (low + high) /2    lsr x4,x4,#1    ldr x5,[x1,x4,lsl #3]                            // load value of table at index x4    cmp x5,x0    beq 99f     bgt 2f                                           // bigger ?    add x2,x4,#1                                     // no new search with low = index + 1    bl bSearchR    b 100f2:                                                   // bigger    sub x3,x4,#1                                     // new search with high = index - 1    bl bSearchR    b 100f99:    mov x0,x4                                      // find !!!    b 100f 100:    ldp x5,x6,[sp],16                // restaur  2 registers    ldp x3,x4,[sp],16                // restaur  2 registers    ldp x2,lr,[sp],16                // restaur  2 registers    ret                              // return to address lr x30/********************************************************//*        File Include fonctions                        *//********************************************************//* for this file see task include a file in language AArch64 assembly */.include "../includeARM64.inc" `
```Value find at index : 0
Value find at index : 4
Value find at index : 8
Recursive search :
Value find at index : 0
Value find at index : 4
Value find at index : 8
```

## ACL2

`(defun defarray (name size initial-element)   (cons name         (compress1 name                    (cons (list :HEADER                                :DIMENSIONS (list size)                                :MAXIMUM-LENGTH (1+ size)                                :DEFAULT initial-element                                :NAME name)                                nil)))) (defconst *dim* 100000) (defun array-name (array)   (first array)) (defun set-at (array i val)   (cons (array-name array)         (aset1 (array-name array)                (cdr array)                i                val))) (defun populate-array-ordered (array n)   (if (zp n)       array       (populate-array-ordered (set-at array                                       (- *dim* n)                                       (- *dim* n))                               (1- n))))(include-book "arithmetic-3/top" :dir :system) (defun binary-search-r (needle haystack low high)   (declare (xargs :measure (nfix (1+ (- high low)))))   (let* ((mid (floor (+ low high) 2))          (current (aref1 (array-name haystack)                          (cdr haystack)                          mid)))         (cond ((not (and (natp low) (natp high))) nil)               ((= current needle)                mid)               ((zp (1+ (- high low))) nil)               ((> current needle)                (binary-search-r needle                                 haystack                                 low                                 (1- mid)))               (t (binary-search-r needle                                   haystack                                   (1+ mid)                                   high))))) (defun binary-search (needle haystack)   (binary-search-r needle haystack 0                    (maximum-length (array-name haystack)                                    (cdr haystack)))) (defun test-bsearch (needle)   (binary-search needle                  (populate-array-ordered                   (defarray 'haystack *dim* 0)                   *dim*)))`

Both solutions are generic. The element can be of any comparable type (such that the operation < is visible in the instantiation scope of the function Search). Note that the completion condition is different from one given in the pseudocode example above. The example assumes that the array index type does not overflow when mid is incremented or decremented beyond the corresponding array bound. This is a wrong assumption for Ada, where array bounds can start or end at the very first or last value of the index type. To deal with this, the exit condition is rather directly expressed as crossing the corresponding array bound by the coming interval middle.

Recursive
`with Ada.Text_IO;  use Ada.Text_IO; procedure Test_Recursive_Binary_Search is   Not_Found : exception;    generic      type Index is range <>;      type Element is private;      type Array_Of_Elements is array (Index range <>) of Element;      with function "<" (L, R : Element) return Boolean is <>;   function Search (Container : Array_Of_Elements; Value : Element) return Index;    function Search (Container : Array_Of_Elements; Value : Element) return Index is      Mid : Index;   begin      if Container'Length > 0 then         Mid := (Container'First + Container'Last) / 2;         if Value < Container (Mid) then            if Container'First /= Mid then               return Search (Container (Container'First..Mid - 1), Value);            end if;         elsif Container (Mid) < Value then            if Container'Last /= Mid then               return Search (Container (Mid + 1..Container'Last), Value);            end if;         else            return Mid;         end if;      end if;      raise Not_Found;   end Search;    type Integer_Array is array (Positive range <>) of Integer;   function Find is new Search (Positive, Integer, Integer_Array);    procedure Test (X : Integer_Array; E : Integer) is   begin      New_Line;      for I in X'Range loop         Put (Integer'Image (X (I)));      end loop;      Put (" contains" & Integer'Image (E) & " at" & Integer'Image (Find (X, E)));   exception      when Not_Found =>         Put (" does not contain" & Integer'Image (E));   end Test;begin   Test ((2, 4, 6, 8, 9), 2);   Test ((2, 4, 6, 8, 9), 1);   Test ((2, 4, 6, 8, 9), 8);   Test ((2, 4, 6, 8, 9), 10);   Test ((2, 4, 6, 8, 9), 9);   Test ((2, 4, 6, 8, 9), 5);end Test_Recursive_Binary_Search;`
Iterative
`with Ada.Text_IO;  use Ada.Text_IO; procedure Test_Binary_Search is   Not_Found : exception;    generic      type Index is range <>;      type Element is private;      type Array_Of_Elements is array (Index range <>) of Element;      with function "<" (L, R : Element) return Boolean is <>;   function Search (Container : Array_Of_Elements; Value : Element) return Index;    function Search (Container : Array_Of_Elements; Value : Element) return Index is      Low  : Index := Container'First;      High : Index := Container'Last;      Mid  : Index;   begin      if Container'Length > 0 then         loop            Mid := (Low + High) / 2;            if Value < Container (Mid) then               exit when Low = Mid;               High := Mid - 1;            elsif Container (Mid) < Value then               exit when High = Mid;               Low := Mid + 1;            else               return Mid;            end if;         end loop;      end if;      raise Not_Found;   end Search;    type Integer_Array is array (Positive range <>) of Integer;   function Find is new Search (Positive, Integer, Integer_Array);    procedure Test (X : Integer_Array; E : Integer) is   begin      New_Line;      for I in X'Range loop         Put (Integer'Image (X (I)));      end loop;      Put (" contains" & Integer'Image (E) & " at" & Integer'Image (Find (X, E)));   exception      when Not_Found =>         Put (" does not contain" & Integer'Image (E));   end Test;begin   Test ((2, 4, 6, 8, 9), 2);   Test ((2, 4, 6, 8, 9), 1);   Test ((2, 4, 6, 8, 9), 8);   Test ((2, 4, 6, 8, 9), 10);   Test ((2, 4, 6, 8, 9), 9);   Test ((2, 4, 6, 8, 9), 5);end Test_Binary_Search;`

Sample output:

``` 2 4 6 8 9 contains 2 at 1
2 4 6 8 9 does not contain 1
2 4 6 8 9 contains 8 at 4
2 4 6 8 9 does not contain 10
2 4 6 8 9 contains 9 at 5
2 4 6 8 9 does not contain 5
```

## ALGOL 68

`BEGINMODE ELEMENT = STRING; # Iterative: #PROC iterative binary search = ([]ELEMENT hay stack, ELEMENT needle)INT: (    INT out,        low := LWB hay stack,        high := UPB hay stack;    WHILE low < high DO        INT mid := (low+high) OVER 2;        IF hay stack[mid] > needle THEN high := mid-1        ELIF hay stack[mid] < needle THEN low := mid+1        ELSE out:= mid; stop iteration FI    OD;        low EXIT    stop iteration:        out);# Recursive: #PROC recursive binary search = ([]ELEMENT hay stack, ELEMENT needle)INT: (    IF LWB hay stack > UPB hay stack THEN        LWB hay stack    ELIF LWB hay stack = UPB hay stack THEN        IF hay stack[LWB hay stack] = needle THEN LWB hay stack        ELSE LWB hay stack FI    ELSE        INT mid := (LWB hay stack+UPB hay stack) OVER 2;        IF hay stack[mid] > needle THEN recursive binary search(hay stack[:mid-1], needle)        ELIF hay stack[mid] < needle THEN mid + recursive binary search(hay stack[mid+1:], needle)        ELSE mid FI   FI);# Test cases: #test:(  ELEMENT needle = "mister";  []ELEMENT hay stack = ("AA","Maestro","Mario","Master","Mattress","Mister","Mistress","ZZ"),          test cases = ("A","Master","Monk","ZZZ");   PROC test search = (PROC([]ELEMENT, ELEMENT)INT search, []ELEMENT test cases)VOID:    FOR case TO UPB test cases DO        ELEMENT needle = test cases[case];        INT index = search(hay stack, needle);        BOOL found = ( index <= 0 | FALSE | hay stack[index]=needle);        print(("""", needle, """ ", (found|"FOUND at"|"near"), " index ", whole(index, 0), newline))    OD;  test search(iterative binary search, test cases);  test search(recursive binary search, test cases))END`
Output:

Shows iterative search output - recursive search output is the same.

```"A" near index 1
"Master" FOUND at index 4
"Monk" near index 8
"ZZZ" near index 8
```

## ALGOL W

Ieterative and recursive binary search procedures, from the pseudo code. Finds the left most occurance/insertion point.

`begin % binary search %    % recursive binary search, left most insertion point %    integer procedure binarySearchLR ( integer array A ( * )                                     ; integer value find, Low, high                                     ) ;        if high < low then low        else begin            integer mid;            mid := ( low + high ) div 2;            if A( mid ) >= find then binarySearchLR( A, find, low,     mid - 1 )            else                     binarySearchLR( A, find, mid + 1, high    )        end binarySearchR ;    % iteratve binary search leftmost insertion point %    integer procedure binarySearchLI ( integer array A ( * )                                     ; integer value find, lowInit, highInit                                     ) ;        begin            integer low, high;            low  := lowInit;            high := highInit;            while low <= high do begin                integer mid;                mid := ( low + high ) div 2;                if A( mid ) >= find then high := mid - 1                else                     low  := mid + 1            end while_low_le_high ;            low        end binarySearchLI ;    % tests %    begin        integer array t ( 1 :: 10 );        integer tPos;        tPos := 1;        for tValue := 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 do begin            t( tPos ) := tValue;            tPos      := tPOs + 1        end for_tValue ;        for s := 0 step 8 until 24 do begin            integer pos;            pos := binarySearchLR( t, s, 1, 10 );            if t( pos ) = s then write( I_W := 3, S_W := 0, "recursive search finds           ", s, " at ", pos )            else                 write( I_W := 3, S_W := 0, "recursive search suggests insert ", s, " at ", pos )            ;            pos := binarySearchLI( t, s, 1, 10 );            if t( pos ) = s then write( I_W := 3, S_W := 0, "iterative search finds           ", s, " at ", pos )            else                 write( I_W := 3, S_W := 0, "iterative search suggests insert ", s, " at ", pos )        end for_s    endend.`
Output:
```recursive search suggests insert   0 at   1
iterative search suggests insert   0 at   1
recursive search suggests insert   8 at   3
iterative search suggests insert   8 at   3
recursive search finds            16 at   4
iterative search finds            16 at   4
recursive search suggests insert  24 at   5
iterative search suggests insert  24 at   5
```

## APL

Works with: Dyalog APL
`binsrch←{   ⎕IO(⍺{                       ⍝ first lower bound is start of array       ⍵<⍺:⍬                    ⍝ if high < low, we didn't find it       mid←⌊(⍺+⍵)÷2             ⍝ calculate mid point       ⍺⍺[mid]>⍵⍵:⍺∇mid-1       ⍝ if too high, search from ⍺ to mid-1       ⍺⍺[mid]<⍵⍵:(mid+1)∇⍵     ⍝ if too low, search from mid+1 to ⍵       mid                      ⍝ otherwise, we did find it   }⍵)⎕IO+(≢⍺)-1                ⍝ first higher bound is top of array} `

## AppleScript

`on binarySearch(n, theList, l, r)    repeat until (l = r)        set m to (l + r) div 2        if (item m of theList < n) then            set l to m + 1        else            set r to m        end if    end repeat     if (item l of theList is n) then return l    return missing valueend binarySearch on test(n, theList, l, r)    set |result| to binarySearch(n, theList, l, r)    if (|result| is missing value) then        return (n as text) & " is not in range " & l & " thru " & r & " of the list"    else        return "The first occurrence of " & n & " in range " & l & " thru " & r & " of the list is at index " & |result|    end ifend test set theList to {1, 2, 3, 3, 5, 7, 7, 8, 9, 10, 11, 12}return test(7, theList, 4, 11) & linefeed & test(7, theList, 7, 12) & linefeed & test(7, theList, 1, 5)`
Output:

(AppleScript indices are 1-based)

```"The first occurrence of 7 in range 4 thru 11 of the list is at index 6
The first occurrence of 7 in range 7 thru 12 of the list is at index 7
7 is not in range 1 thru 5 of the list"```

## ARM Assembly

Works with: as version Raspberry Pi
`  /* ARM assembly Raspberry PI  *//*  program binsearch.s   */ /************************************//* Constantes                       *//************************************/.equ STDOUT, 1     @ Linux output console.equ EXIT,   1     @ Linux syscall.equ WRITE,  4     @ Linux syscall/*********************************//* Initialized data              *//*********************************/.datasMessResult:        .ascii "Value find at index : "sMessValeur:        .fill 11, 1, ' '            @ size => 11szCarriageReturn:   .asciz "\n"sMessRecursif:      .asciz "Recursive search : \n"sMessNotFound:      .asciz "Value not found. \n" .equ NBELEMENTS,      9TableNumber:	     .int   4,6,7,10,11,15,22,30,35 /*********************************//* UnInitialized data            *//*********************************/.bss  /*********************************//*  code section                 *//*********************************/.text.global main main:                                           @ entry of program     mov r0,#4                                   @ search first value    ldr r1,iAdrTableNumber                      @ address number table    mov r2,#NBELEMENTS                          @ number of élements     bl bSearch    ldr r1,iAdrsMessValeur                      @ display value    bl conversion10                             @ call function    ldr r0,iAdrsMessResult    bl affichageMess                            @ display message     mov r0,#11                                  @ search median value    ldr r1,iAdrTableNumber    mov r2,#NBELEMENTS    bl bSearch    ldr r1,iAdrsMessValeur                      @ display value    bl conversion10                             @ call function    ldr r0,iAdrsMessResult    bl affichageMess                            @ display message     mov r0,#12                                  @value not found    ldr r1,iAdrTableNumber    mov r2,#NBELEMENTS    bl bSearch    cmp r0,#-1    bne 2f    ldr r0,iAdrsMessNotFound    bl affichageMess     b 3f2:    ldr r1,iAdrsMessValeur                      @ display value    bl conversion10                             @ call function    ldr r0,iAdrsMessResult    bl affichageMess                            @ display message3:    mov r0,#35                                  @ search last value    ldr r1,iAdrTableNumber    mov r2,#NBELEMENTS    bl bSearch    ldr r1,iAdrsMessValeur                      @ display value    bl conversion10                             @ call function    ldr r0,iAdrsMessResult    bl affichageMess                            @ display message/****************************************//*       recursive                      *//****************************************/    ldr r0,iAdrsMessRecursif    bl affichageMess                            @ display message     mov r0,#4                                   @ search first value    ldr r1,iAdrTableNumber    mov r2,#0                                   @ low index of elements    mov r3,#NBELEMENTS - 1                      @ high index of elements    bl bSearchR    ldr r1,iAdrsMessValeur                      @ display value    bl conversion10                             @ call function    ldr r0,iAdrsMessResult    bl affichageMess                            @ display message     mov r0,#11    ldr r1,iAdrTableNumber    mov r2,#0    mov r3,#NBELEMENTS - 1    bl bSearchR    ldr r1,iAdrsMessValeur                      @ display value    bl conversion10                             @ call function    ldr r0,iAdrsMessResult    bl affichageMess                            @ display message     mov r0,#12    ldr r1,iAdrTableNumber    mov r2,#0    mov r3,#NBELEMENTS - 1    bl bSearchR    cmp r0,#-1    bne 2f    ldr r0,iAdrsMessNotFound    bl affichageMess     b 3f2:    ldr r1,iAdrsMessValeur                      @ display value    bl conversion10                             @ call function    ldr r0,iAdrsMessResult    bl affichageMess                            @ display message3:    mov r0,#35    ldr r1,iAdrTableNumber    mov r2,#0    mov r3,#NBELEMENTS - 1    bl bSearchR    ldr r1,iAdrsMessValeur                      @ display value    bl conversion10                             @ call function    ldr r0,iAdrsMessResult    bl affichageMess                            @ display message 100:                                            @ standard end of the program     mov r0, #0                                  @ return code    mov r7, #EXIT                               @ request to exit program    svc #0                                      @ perform the system call iAdrsMessValeur:          .int sMessValeuriAdrszCarriageReturn:     .int szCarriageReturniAdrsMessResult:          .int sMessResultiAdrsMessRecursif:        .int sMessRecursifiAdrsMessNotFound:        .int sMessNotFoundiAdrTableNumber:          .int TableNumber /******************************************************************//*     binary search   iterative                                  */ /******************************************************************//* r0 contains the value to search *//* r1 contains the adress of table *//* r2 contains the number of elements *//* r0 return index or -1 if not find */bSearch:    push {r2-r5,lr}                                 @ save registers    mov r3,#0                                       @ low index    sub r4,r2,#1                                    @ high index = number of elements - 11:    cmp r3,r4    movgt r0,#-1                                    @not found    bgt 100f    add r2,r3,r4                                    @ compute (low + high) /2    lsr r2,#1    ldr r5,[r1,r2,lsl #2]                           @ load value of table at index r2    cmp r5,r0    moveq r0,r2                                     @ find !!!    beq 100f    addlt r3,r2,#1                                  @ lower -> index low = index + 1    subgt r4,r2,#1                                  @ bigger -> index high = index - 1    b 1b                                            @ and loop100:    pop {r2-r5,lr}    bx lr                       @ return /******************************************************************//*     binary search   recursif                                  */ /******************************************************************//* r0 contains the value to search *//* r1 contains the adress of table *//* r2 contains the low index of elements *//* r3 contains the high index of elements *//* r0 return index or -1 if not find */bSearchR:    push {r2-r5,lr}                                  @ save registers    cmp r3,r2                                        @ index high < low ?    movlt r0,#-1                                     @ yes -> not found    blt 100f     add r4,r2,r3                                     @ compute (low + high) /2    lsr r4,#1    ldr r5,[r1,r4,lsl #2]                            @ load value of table at index r4    cmp r5,r0    moveq r0,r4                                      @ find !!!    beq 100f      bgt 1f                                           @ bigger ?    add r2,r4,#1                                     @ no new search with low = index + 1    bl bSearchR    b 100f1:                                                   @ bigger    sub r3,r4,#1                                     @ new search with high = index - 1    bl bSearchR100:    pop {r2-r5,lr}    bx lr                                            @ return /******************************************************************//*     display text with size calculation                         */ /******************************************************************//* r0 contains the address of the message */affichageMess:    push {r0,r1,r2,r7,lr}                          @ save  registres    mov r2,#0                                      @ counter length 1:                                                 @ loop length calculation     ldrb r1,[r0,r2]                                @ read octet start position + index     cmp r1,#0                                      @ if 0 its over     addne r2,r2,#1                                 @ else add 1 in the length     bne 1b                                         @ and loop                                                    @ so here r2 contains the length of the message     mov r1,r0                                      @ address message in r1     mov r0,#STDOUT                                 @ code to write to the standard output Linux     mov r7, #WRITE                                 @ code call system "write"     svc #0                                         @ call systeme     pop {r0,r1,r2,r7,lr}                           @ restaur des  2 registres    bx lr                                          @ return  /******************************************************************//*     Converting a register to a decimal unsigned                */ /******************************************************************//* r0 contains value and r1 address area   *//* r0 return size of result (no zero final in area) *//* area size => 11 bytes          */.equ LGZONECAL,   10conversion10:    push {r1-r4,lr}                                 @ save registers     mov r3,r1    mov r2,#LGZONECAL 1:	                                            @ start loop    bl divisionpar10U                               @unsigned  r0 <- dividende. quotient ->r0 reste -> r1    add r1,#48                                      @ digit    strb r1,[r3,r2]                                 @ store digit on area    cmp r0,#0                                       @ stop if quotient = 0     subne r2,#1                                     @ else previous position    bne 1b	                                    @ and loop                                                    @ and move digit from left of area    mov r4,#02:    ldrb r1,[r3,r2]    strb r1,[r3,r4]    add r2,#1    add r4,#1    cmp r2,#LGZONECAL    ble 2b                                                     @ and move spaces in end on area    mov r0,r4                                        @ result length     mov r1,#' '                                      @ space3:    strb r1,[r3,r4]                                  @ store space in area    add r4,#1                                        @ next position    cmp r4,#LGZONECAL    ble 3b                                           @ loop if r4 <= area size 100:    pop {r1-r4,lr}                                   @ restaur registres     bx lr                                            @return /***************************************************//*   division par 10   unsigned                    *//***************************************************//* r0 dividende   *//* r0 quotient */	/* r1 remainder  */divisionpar10U:    push {r2,r3,r4, lr}    mov r4,r0                                        @ save value    //mov r3,#0xCCCD                                 @ r3 <- magic_number lower  raspberry 3    //movt r3,#0xCCCC                                @ r3 <- magic_number higter raspberry 3    ldr r3,iMagicNumber                              @ r3 <- magic_number    raspberry 1 2    umull r1, r2, r3, r0                             @ r1<- Lower32Bits(r1*r0) r2<- Upper32Bits(r1*r0)     mov r0, r2, LSR #3                               @ r2 <- r2 >> shift 3    add r2,r0,r0, lsl #2                             @ r2 <- r0 * 5     sub r1,r4,r2, lsl #1                             @ r1 <- r4 - (r2 * 2)  = r4 - (r0 * 10)    pop {r2,r3,r4,lr}    bx lr                                            @ leave function iMagicNumber:  	.int 0xCCCCCCCD  `

## Arturo

`binarySearch: function [arr,val,low,high][    if high < low -> return ø    mid: shr low+high 1    case [val]        when? [< arr \ mid] -> return binarySearch arr val low mid-1        when? [> arr \ mid] -> return binarySearch arr val mid+1 high        else                -> return mid] ary: [    0 1 4 5 6 7 8 9 12 26 45 67     78 90 98 123 211 234 456 769     865 2345 3215 14345 24324] loop [0 42 45 24324 99999] 'v [    i: binarySearch ary v 0 (size ary)-1    if? not? null? i    -> print ["found" v "at index:" i]    else                -> print [v "not found"]]`
Output:
```found 0 at index: 0
found 45 at index: 10
found 24324 at index: 24

## AutoHotkey

`array := "1,2,4,6,8,9"StringSplit, A, array, `,   ; creates associative arrayMsgBox % x := BinarySearch(A, 4, 1, A0) ; RecursiveMsgBox % A%x%MsgBox % x := BinarySearchI(A, A0, 4)  ; IterativeMsgBox % A%x% BinarySearch(A, value, low, high) { ; A0 contains length of array  If (high < low)               ; A1, A2, A3...An are array elements    Return not_found  mid := Floor((low + high) / 2)  If (A%mid% > value) ; A%mid% is automatically global since no such locals are present    Return BinarySearch(A, value, low, mid - 1)  Else If (A%mid% < value)    Return BinarySearch(A, value, mid + 1, high)  Else    Return mid} BinarySearchI(A, lengthA, value) {  low := 0  high := lengthA - 1  While (low <= high) {    mid := Floor((low + high) / 2) ; round to lower integer    If (A%mid% > value)         high := mid - 1    Else If (A%mid% < value)      low := mid + 1    Else      Return mid  }  Return not_found}`

## AWK

Works with: Gawk
Works with: Mawk
Works with: Nawk

Recursive

`function binary_search(array, value, left, right,       middle) {    if (right < left) return 0    middle = int((right + left) / 2)    if (value == array[middle]) return 1    if (value <  array[middle])        return binary_search(array, value, left, middle - 1)    return binary_search(array, value, middle + 1, right)}`

Iterative

`function binary_search(array, value, left, right,       middle) {    while (left <= right) {        middle = int((right + left) / 2)        if (value == array[middle]) return 1        if (value <  array[middle]) right = middle - 1        else                        left  = middle + 1    }    return 0}`

## Axe

Iterative

BSEARCH takes 3 arguments: a pointer to the start of the data, the data to find, and the length of the array in bytes.

`Lbl BSEARCH0→Lr₃-1→HWhile L≤H (L+H)/2→M If {L+M}>r₂  M-1→H ElseIf {L+M}<r₂  M+1→L Else  M  Return EndEnd-1Return`

## BASIC

Recursive

Works with: FreeBASIC
Works with: RapidQ
`FUNCTION binary_search ( array() AS Integer, value AS Integer, lo AS Integer, hi AS Integer) AS Integer  DIM middle AS Integer   IF hi < lo THEN    binary_search = 0  ELSE    middle = (hi + lo) / 2    SELECT CASE value      CASE IS < array(middle)	binary_search = binary_search(array(), value, lo, middle-1)      CASE IS > array(middle)	binary_search = binary_search(array(), value, middle+1, hi)      CASE ELSE	binary_search = middle    END SELECT  END IFEND FUNCTION`

Iterative

Works with: FreeBASIC
Works with: RapidQ
`FUNCTION binary_search ( array() AS Integer, value AS Integer, lo AS Integer, hi AS Integer) AS Integer  DIM middle AS Integer   WHILE lo <= hi    middle = (hi + lo) / 2    SELECT CASE value      CASE IS < array(middle)	hi = middle - 1      CASE IS > array(middle)	lo = middle + 1      CASE ELSE	binary_search = middle	EXIT FUNCTION    END SELECT  WEND  binary_search = 0END FUNCTION`

Testing the function

The following program can be used to test both recursive and iterative version.

`SUB search (array() AS Integer, value AS Integer)  DIM idx AS Integer   idx = binary_search(array(), value, LBOUND(array), UBOUND(array))  PRINT "Value "; value;  IF idx < 1 THEN    PRINT " not found"  ELSE    PRINT " found at index "; idx  END IFEND SUB DIM test(1 TO 10) AS IntegerDIM i AS Integer DATA 2, 3, 5, 6, 8, 10, 11, 15, 19, 20FOR i = 1 TO 10		' Fill the test array  READ test(i)NEXT i search test(), 4search test(), 8search test(), 20`

Output:

```Value 4 not found
Value 8 found at index 5
Value 20 found at index 10
```

### BBC BASIC

`      DIM array%(9)      array%() = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70       secret% = 42      index% = FNwhere(array%(), secret%, 0, DIM(array%(),1))      IF index% >= 0 THEN        PRINT "The value "; secret% " was found at index "; index%      ELSE        PRINT "The value "; secret% " was not found"      ENDIF      END       REM Search ordered array A%() for the value S% from index B% to T%      DEF FNwhere(A%(), S%, B%, T%)      LOCAL H%      H% = 2      WHILE H%<(T%-B%) H% *= 2:ENDWHILE      H% /= 2      REPEAT        IF (B%+H%)<=T% IF S%>=A%(B%+H%) B% += H%        H% /= 2      UNTIL H%=0      IF S%=A%(B%) THEN = B% ELSE = -1`

### FreeBASIC

`function binsearch( array() as integer, target as integer ) as integer    'returns the index of the target number, or -1 if it is not in the array    dim as uinteger lo = lbound(array), hi = ubound(array), md = (lo + hi)\2    if array(lo) = target then return lo    if array(hi) = target then return hi    while lo + 1 < hi        if array(md) = target then return md        if array(md)<target then lo = md else hi = md        md = (lo + hi)\2    wend    return -1end function`

### IS-BASIC

`100 PROGRAM "Search.bas"110 RANDOMIZE120 NUMERIC ARR(1 TO 20)130 CALL FILL(ARR)140 PRINT:INPUT PROMPT "Value: ":N150 LET IDX=SEARCH(ARR,N)160 IF IDX THEN170   PRINT "The value";N;"was found the index";IDX180 ELSE190   PRINT "The value";N;"was not found."200 END IF210 DEF FILL(REF T)220   LET T(LBOUND(T))=RND(3):PRINT T(1);230   FOR I=LBOUND(T)+1 TO UBOUND(T)240     LET T(I)=T(I-1)+RND(3)+1250     PRINT T(I);260   NEXT270 END DEF280 DEF SEARCH(REF T,N)290   LET SEARCH=0:LET BO=LBOUND(T):LET UP=UBOUND(T)300   DO310     LET K=INT((BO+UP)/2)320     IF T(K)<N THEN LET BO=K+1330     IF T(K)>N THEN LET UP=K-1340   LOOP WHILE BO<=UP AND T(K)<>N350   IF BO<=UP THEN LET SEARCH=K360 END DEF`

## Batch File

` @echo off & setlocal enabledelayedexpansion :: Binary Chop Algorithm - Michael Sanders 2017:::: example output...:::: binary chop algorithm vs. standard for loop:::: number to find 941:: for loop required 941 iterations:: binchop required 10 iterations :setup    set x=1   set y=999   set /a z=(%random% * (%y% - 1) / 32768 + 1) :pseudoarray    for /l %%q in (%x%,1,%y%) do set /a array[%%q]=%%q :std4loop    for /l %%q in (%x%,1,%y%) do (      if !array[%%q]!==%z% (set f=%%q& goto :binchop)   ) :binchop    if !x! leq !y! (      set /a i+=1      set /a "p=(!x!+!y!)/2"      call set /a t=%%array[!p!]%%      if !t! equ !z! (set b=!i!& goto :done)      if !t! lss !z! (set /a x=!p!+1) else (set /a y=!p!-1)      goto :binchop   ) :done    cls   echo binary chop algorithm vs. standard for loop...   echo.   echo . number to find !z!   echo . for loop required !f! iterations   echo . binchop required !b! iterations   endlocal & exit /b 0 `

## Brat

`binary_search = { search_array, value, low, high |  true? high < low    { null }    {      mid = ((low + high) / 2).to_i       true? search_array[mid] > value        { binary_search search_array, value, low, mid - 1 }	{ true? search_array[mid] < value	  { binary_search search_array, value, mid + 1, high }	  { mid }      }   }} #Populate arraynumbers = 1000.of { random 1000 } #Sort the arraynumbers.sort! #Find a numberx = random 1000 p "Looking for #{x}" index = binary_search numbers, x, 0, numbers.length - 1 null? index	{ p "Not found" }	{ p "Found at index: #{index}" }`

## C

`#include <stdio.h> int bsearch (int *a, int n, int x) {    int i = 0, j = n - 1;    while (i <= j) {        int k = i + ((j - i) / 2);        if (a[k] == x) {            return k;        }        else if (a[k] < x) {            i = k + 1;        }        else {            j = k - 1;        }    }    return -1;} int bsearch_r (int *a, int x, int i, int j) {    if (j < i) {        return -1;    }    int k = i + ((j - i) / 2);    if (a[k] == x) {        return k;    }    else if (a[k] < x) {        return bsearch_r(a, x, k + 1, j);    }    else {        return bsearch_r(a, x, i, k - 1);    }} int main () {    int a[] = {-31, 0, 1, 2, 2, 4, 65, 83, 99, 782};    int n = sizeof a / sizeof a[0];    int x = 2;    int i = bsearch(a, n, x);    printf("%d is at index %d\n", x, i);    x = 5;    i = bsearch_r(a, x, 0, n - 1);    printf("%d is at index %d\n", x, i);    return 0;} `
Output:
```2 is at index 4
5 is at index -1
```

## C#

Recursive

`namespace Search {  using System;   public static partial class Extensions {    /// <summary>Use Binary Search to find index of GLB for value</summary>    /// <typeparam name="T">type of entries and value</typeparam>    /// <param name="entries">array of entries</param>    /// <param name="value">search value</param>    /// <remarks>entries must be in ascending order</remarks>    /// <returns>index into entries of GLB for value</returns>    public static int RecursiveBinarySearchForGLB<T>(this T[] entries, T value)      where T : IComparable {      return entries.RecursiveBinarySearchForGLB(value, 0, entries.Length - 1);    }     /// <summary>Use Binary Search to find index of GLB for value</summary>    /// <typeparam name="T">type of entries and value</typeparam>    /// <param name="entries">array of entries</param>    /// <param name="value">search value</param>    /// <param name="left">leftmost index to search</param>    /// <param name="right">rightmost index to search</param>    /// <remarks>entries must be in ascending order</remarks>    /// <returns>index into entries of GLB for value</returns>    public static int RecursiveBinarySearchForGLB<T>(this T[] entries, T value, int left, int right)      where T : IComparable {      if (left <= right) {        var middle = left + (right - left) / 2;        return entries[middle].CompareTo(value) < 0 ?          entries.RecursiveBinarySearchForGLB(value, middle + 1, right) :          entries.RecursiveBinarySearchForGLB(value, left, middle - 1);      }       //[Assert]left == right + 1      // GLB: entries[right] < value && value <= entries[right + 1]      return right;    }     /// <summary>Use Binary Search to find index of LUB for value</summary>    /// <typeparam name="T">type of entries and value</typeparam>    /// <param name="entries">array of entries</param>    /// <param name="value">search value</param>    /// <remarks>entries must be in ascending order</remarks>    /// <returns>index into entries of LUB for value</returns>    public static int RecursiveBinarySearchForLUB<T>(this T[] entries, T value)      where T : IComparable {      return entries.RecursiveBinarySearchForLUB(value, 0, entries.Length - 1);    }     /// <summary>Use Binary Search to find index of LUB for value</summary>    /// <typeparam name="T">type of entries and value</typeparam>    /// <param name="entries">array of entries</param>    /// <param name="value">search value</param>    /// <param name="left">leftmost index to search</param>    /// <param name="right">rightmost index to search</param>    /// <remarks>entries must be in ascending order</remarks>    /// <returns>index into entries of LUB for value</returns>    public static int RecursiveBinarySearchForLUB<T>(this T[] entries, T value, int left, int right)      where T : IComparable {      if (left <= right) {        var middle = left + (right - left) / 2;        return entries[middle].CompareTo(value) <= 0 ?          entries.RecursiveBinarySearchForLUB(value, middle + 1, right) :          entries.RecursiveBinarySearchForLUB(value, left, middle - 1);      }       //[Assert]left == right + 1      // LUB: entries[left] > value && value >= entries[left - 1]      return left;    }  }}`

Iterative

`namespace Search {  using System;   public static partial class Extensions {    /// <summary>Use Binary Search to find index of GLB for value</summary>    /// <typeparam name="T">type of entries and value</typeparam>    /// <param name="entries">array of entries</param>    /// <param name="value">search value</param>    /// <remarks>entries must be in ascending order</remarks>    /// <returns>index into entries of GLB for value</returns>    public static int BinarySearchForGLB<T>(this T[] entries, T value)      where T : IComparable {      return entries.BinarySearchForGLB(value, 0, entries.Length - 1);    }     /// <summary>Use Binary Search to find index of GLB for value</summary>    /// <typeparam name="T">type of entries and value</typeparam>    /// <param name="entries">array of entries</param>    /// <param name="value">search value</param>    /// <param name="left">leftmost index to search</param>    /// <param name="right">rightmost index to search</param>    /// <remarks>entries must be in ascending order</remarks>    /// <returns>index into entries of GLB for value</returns>    public static int BinarySearchForGLB<T>(this T[] entries, T value, int left, int right)      where T : IComparable {      while (left <= right) {        var middle = left + (right - left) / 2;        if (entries[middle].CompareTo(value) < 0)          left = middle + 1;        else          right = middle - 1;      }       //[Assert]left == right + 1      // GLB: entries[right] < value && value <= entries[right + 1]      return right;    }     /// <summary>Use Binary Search to find index of LUB for value</summary>    /// <typeparam name="T">type of entries and value</typeparam>    /// <param name="entries">array of entries</param>    /// <param name="value">search value</param>    /// <remarks>entries must be in ascending order</remarks>    /// <returns>index into entries of LUB for value</returns>    public static int BinarySearchForLUB<T>(this T[] entries, T value)      where T : IComparable {      return entries.BinarySearchForLUB(value, 0, entries.Length - 1);    }     /// <summary>Use Binary Search to find index of LUB for value</summary>    /// <typeparam name="T">type of entries and value</typeparam>    /// <param name="entries">array of entries</param>    /// <param name="value">search value</param>    /// <param name="left">leftmost index to search</param>    /// <param name="right">rightmost index to search</param>    /// <remarks>entries must be in ascending order</remarks>    /// <returns>index into entries of LUB for value</returns>    public static int BinarySearchForLUB<T>(this T[] entries, T value, int left, int right)      where T : IComparable {      while (left <= right) {        var middle = left + (right - left) / 2;        if (entries[middle].CompareTo(value) <= 0)          left = middle + 1;        else          right = middle - 1;      }       //[Assert]left == right + 1      // LUB: entries[left] > value && value >= entries[left - 1]      return left;    }  }}`

Example

`//#define UseRecursiveSearch using System;using Search; class Program {  static readonly int[][] tests = {    new int[] { },    new int[] { 2 },    new int[] { 2, 2 },    new int[] { 2, 2, 2, 2 },    new int[] { 3, 3, 4, 4 },    new int[] { 0, 1, 3, 3, 4, 4 },    new int[] { 0, 1, 2, 2, 2, 3, 3, 4, 4},    new int[] { 0, 1, 1, 2, 2, 2, 3, 3, 4, 4 },    new int[] { 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4 },    new int[] { 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4 },    new int[] { 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4 },  };   static void Main(string[] args) {    var index = 0;    foreach (var test in tests) {      var join = String.Join(" ", test);      Console.WriteLine(\$"test[{index}]: {join}");#if UseRecursiveSearch      var glb = test.RecursiveBinarySearchForGLB(2);      var lub = test.RecursiveBinarySearchForLUB(2);#else      var glb = test.BinarySearchForGLB(2);      var lub = test.BinarySearchForLUB(2);#endif      Console.WriteLine(\$"glb = {glb}");      Console.WriteLine(\$"lub = {lub}");       index++;    }#if DEBUG    Console.Write("Press Enter");    Console.ReadLine();#endif  }}`

Output

```test[0]:
glb = -1
lub = 0
test[1]: 2
glb = -1
lub = 1
test[2]: 2 2
glb = -1
lub = 2
test[3]: 2 2 2 2
glb = -1
lub = 4
test[4]: 3 3 4 4
glb = -1
lub = 0
test[5]: 0 1 3 3 4 4
glb = 1
lub = 2
test[6]: 0 1 2 2 2 3 3 4 4
glb = 1
lub = 5
test[7]: 0 1 1 2 2 2 3 3 4 4
glb = 2
lub = 6
test[8]: 0 1 1 1 1 2 2 3 3 4 4
glb = 4
lub = 7
test[9]: 0 1 1 1 1 2 2 2 2 2 2 2 3 3 4 4
glb = 4
lub = 12
test[10]: 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 4 4
glb = 13
lub = 21```

## C++

Recursive

` template <class T> int binsearch(const T array[], int low, int high, T value) {    if (high < low) {        return -1;    }    auto mid = (low + high) / 2;    if (value < array[mid]) {        return binsearch(array, low, mid - 1, value);    } else if (value > array[mid]) {        return binsearch(array, mid + 1, high, value);    }    return mid;} #include <iostream>int main(){  int array[] = {2, 3, 5, 6, 8};  int result1 = binsearch(array, 0, sizeof(array)/sizeof(int), 4),      result2 = binsearch(array, 0, sizeof(array)/sizeof(int), 8);  if (result1 == -1) std::cout << "4 not found!" << std::endl;  else std::cout << "4 found at " << result1 << std::endl;  if (result2 == -1) std::cout << "8 not found!" << std::endl;  else std::cout << "8 found at " << result2 << std::endl;   return 0;}`

Iterative

`template <class T>int binSearch(const T arr[], int len, T what) {  int low = 0;  int high = len - 1;  while (low <= high) {    int mid = (low + high) / 2;    if (arr[mid] > what)      high = mid - 1;    else if (arr[mid] < what)      low = mid + 1;    else      return mid;  }  return -1; // indicate not found }`

Library

C++'s Standard Template Library has four functions for binary search, depending on what information you want to get. They all need
`#include <algorithm>`

The `lower_bound()` function returns an iterator to the first position where a value could be inserted without violating the order; i.e. the first element equal to the element you want, or the place where it would be inserted.

`int *ptr = std::lower_bound(array, array+len, what); // a custom comparator can be given as fourth arg`

The `upper_bound()` function returns an iterator to the last position where a value could be inserted without violating the order; i.e. one past the last element equal to the element you want, or the place where it would be inserted.

`int *ptr = std::upper_bound(array, array+len, what); // a custom comparator can be given as fourth arg`

The `equal_range()` function returns a pair of the results of `lower_bound()` and `upper_bound()`.

`std::pair<int *, int *> bounds = std::equal_range(array, array+len, what); // a custom comparator can be given as fourth arg`

Note that the difference between the bounds is the number of elements equal to the element you want.

The `binary_search()` function returns true or false for whether an element equal to the one you want exists in the array. It does not give you any information as to where it is.

`bool found = std::binary_search(array, array+len, what); // a custom comparator can be given as fourth arg`

## Chapel

iterative -- almost a direct translation of the pseudocode

`proc binsearch(A:[], value) {        var low = A.domain.dim(1).low;        var high = A.domain.dim(1).high;        while (low <= high) {                var mid = (low + high) / 2;                 if A(mid) > value then                        high = mid - 1;                else if A(mid) < value then                        low = mid + 1;                else                        return mid;        }        return 0;} writeln(binsearch([3, 4, 6, 9, 11], 9));`
Output:
```4
```

## Clojure

Recursive

`(defn bsearch  ([coll t]    (bsearch coll 0 (dec (count coll)) t))  ([coll l u t]    (if (> l u) -1      (let [m (quot (+ l u) 2) mth (nth coll m)]        (cond          ; the middle element is greater than t          ; so search the lower half          (> mth t) (recur coll l (dec m) t)          ; the middle element is less than t          ; so search the upper half          (< mth t) (recur coll (inc m) u t)          ; we've found our target          ; so return its index          (= mth t) m)))))`

## COBOL

COBOL's `SEARCH ALL` statement is implemented as a binary search on most implementations.

`        >>SOURCE FREEIDENTIFICATION DIVISION.PROGRAM-ID. binary-search. DATA DIVISION.WORKING-STORAGE SECTION.01  nums-area                           VALUE "01040612184356".    03  nums                            PIC 9(2)                                        OCCURS 7 TIMES                                        ASCENDING KEY nums                                        INDEXED BY nums-idx.PROCEDURE DIVISION.    SEARCH ALL nums        WHEN nums (nums-idx) = 4            DISPLAY "Found 4 at index " nums-idx    END-SEARCH    .END PROGRAM binary-search.`

## CoffeeScript

Recursive

`binarySearch = (xs, x) ->  do recurse = (low = 0, high = xs.length - 1) ->    mid = Math.floor (low + high) / 2    switch      when high < low then NaN      when xs[mid] > x then recurse low, mid - 1      when xs[mid] < x then recurse mid + 1, high      else mid`

Iterative

`binarySearch = (xs, x) ->  [low, high] = [0, xs.length - 1]  while low <= high    mid = Math.floor (low + high) / 2    switch      when xs[mid] > x then high = mid - 1      when xs[mid] < x then low = mid + 1      else return mid  NaN`

Test

`do (n = 12) ->  odds = (it for it in [1..n] by 2)  result = (it for it in \    (binarySearch odds, it for it in [0..n]) \    when not isNaN it)  console.assert "#{result}" is "#{[0...odds.length]}"  console.log "#{odds} are odd natural numbers"  console.log "#{it} is ordinal of #{odds[it]}" for it in result`

Output:

```1,3,5,7,9,11 are odd natural numbers"
0 is ordinal of 1
1 is ordinal of 3
2 is ordinal of 5
3 is ordinal of 7
4 is ordinal of 9
5 is ordinal of 11```

## Common Lisp

Iterative

`(defun binary-search (value array)  (let ((low 0)        (high (1- (length array))))     (do () ((< high low) nil)      (let ((middle (floor (+ low high) 2)))         (cond ((> (aref array middle) value)               (setf high (1- middle)))               ((< (aref array middle) value)               (setf low (1+ middle)))               (t (return middle)))))))`

Recursive

`(defun binary-search (value array &optional (low 0) (high (1- (length array))))  (if (< high low)      nil      (let ((middle (floor (+ low high) 2)))         (cond ((> (aref array middle) value)               (binary-search value array low (1- middle)))               ((< (aref array middle) value)               (binary-search value array (1+ middle) high))               (t middle)))))`

## Crystal

Recursive

`class Array  def binary_search(val, low = 0, high = (size - 1))    return nil if high < low    #mid = (low + high) >> 1    mid = low + ((high - low) >> 1)    case val <=> self[mid]      when -1        binary_search(val, low, mid - 1)      when 1        binary_search(val, mid + 1, high)      else mid    end  endend ary = [0,1,4,5,6,7,8,9,12,26,45,67,78,90,98,123,211,234,456,769,865,2345,3215,14345,24324] [0, 42, 45, 24324, 99999].each do |val|  i = ary.binary_search(val)  if i    puts "found #{val} at index #{i}: #{ary[i]}"  else    puts "#{val} not found in array"  endend`

Iterative

`class Array  def binary_search_iterative(val)    low, high = 0, size - 1    while low <= high      #mid = (low + high) >> 1      mid = low + ((high - low) >> 1)      case val <=> self[mid]        when 1          low = mid + 1        when -1          high = mid - 1        else          return mid      end    end    nil  endend ary = [0,1,4,5,6,7,8,9,12,26,45,67,78,90,98,123,211,234,456,769,865,2345,3215,14345,24324] [0, 42, 45, 24324, 99999].each do |val|  i = ary.binary_search_iterative(val)  if i    puts "found #{val} at index #{i}: #{ary[i]}"  else    puts "#{val} not found in array"  endend`
Output:
```found 0 at index 0: 0
found 45 at index 10: 45
found 24324 at index 24: 24324
```

## D

`import std.stdio, std.array, std.range, std.traits; /// Recursive.bool binarySearch(R, T)(/*in*/ R data, in T x) pure nothrow @nogcif (isRandomAccessRange!R && is(Unqual!T == Unqual!(ElementType!R))) {    if (data.empty)        return false;    immutable i = data.length / 2;    immutable mid = data[i];    if (mid > x)        return data[0 .. i].binarySearch(x);    if (mid < x)        return data[i + 1 .. \$].binarySearch(x);    return true;} /// Iterative.bool binarySearchIt(R, T)(/*in*/ R data, in T x) pure nothrow @nogcif (isRandomAccessRange!R && is(Unqual!T == Unqual!(ElementType!R))) {    while (!data.empty) {        immutable i = data.length / 2;        immutable mid = data[i];        if (mid > x)            data = data[0 .. i];        else if (mid < x)            data = data[i + 1 .. \$];        else            return true;    }    return false;} void main() {    /*const*/ auto items = [2, 4, 6, 8, 9].assumeSorted;    foreach (const x; [1, 8, 10, 9, 5, 2])        writefln("%2d %5s %5s %5s", x,                 items.binarySearch(x),                 items.binarySearchIt(x),                 // Standard Binary Search:                 !items.equalRange(x).empty);}`
Output:
``` 1 false false false
8  true  true  true
10 false false false
9  true  true  true
5 false false false
2  true  true  true```

See #Pascal.

## E

`/** Returns null if the value is not found. */def binarySearch(collection, value) {    var low := 0    var high := collection.size() - 1    while (low <= high) {        def mid := (low + high) // 2        def comparison := value.op__cmp(collection[mid])        if      (comparison.belowZero()) { high := mid - 1 } \        else if (comparison.aboveZero()) { low := mid + 1 }  \        else if (comparison.isZero())    { return mid }      \        else                             { throw("You expect me to binary search with a partial order?") }    }    return null}`

## EasyLang

`func bin_search val . a[] res .  low = 0  high = len a[] - 1  res = -1  while low <= high and res = -1    mid = (low + high) div 2    if a[mid] > val      high = mid - 1    elif a[mid] < val      low = mid + 1    else      res = mid    .  ..a[] = [ 2 4 6 8 9 ]call bin_search 8 a[] rprint r`

## Eiffel

The following solution is based on the one described in: C. A. Furia, B. Meyer, and S. Velder. Loop Invariants: Analysis, Classification, and Examples. ACM Computing Surveys, 46(3), Article 34, January 2014. (Also available at http://arxiv.org/abs/1211.4470). It includes detailed loop invariants and pre- and postconditions, which make the running time linear (instead of logarithmic) when full contract checking is enabled.

`class	APPLICATION create	make feature {NONE} -- Initialization 	make		local			a: ARRAY [INTEGER]			keys: ARRAY [INTEGER]		do			a := <<0, 1, 4, 5, 6, 7, 8, 9,			       12, 26, 45, 67, 78, 90,			       98, 123, 211, 234, 456,			       769, 865, 2345, 3215,			       14345, 24324>>			keys := <<0, 42, 45, 24324, 99999>>			across keys as k loop				if has_binary (a, k.item) then					print ("The array has an element " + k.item.out)				else					print ("The array has NOT an element " + k.item.out)				end				print ("%N")			end		end feature -- Search 	has_binary (a: ARRAY [INTEGER]; key: INTEGER): BOOLEAN		-- Does `a[a.lower..a.upper]' include an element `key'?		require			is_sorted (a, a.lower, a.upper)		local			i: INTEGER		do			i := where_binary (a, key)			if a.lower <= i and i <= a.upper then				Result := True			else				Result := False			end		end 	where_binary (a: ARRAY [INTEGER]; key: INTEGER): INTEGER		-- The index of an element `key' within `a[a.lower..a.upper]' if it exists.		-- Otherwise an integer outside `[a.lower..a.upper]'		require			is_sorted (a, a.lower, a.upper)		do			Result := where_binary_range (a, key, a.lower, a.upper)		end 	where_binary_range (a: ARRAY [INTEGER]; key: INTEGER; low, high: INTEGER): INTEGER		-- The index of an element `key' within `a[low..high]' if it exists.		-- Otherwise an integer outside `[low..high]'		note			source: "http://arxiv.org/abs/1211.4470"		require			is_sorted (a, low, high)		local			i, j, mid: INTEGER		do			if low > high then				Result := low - 1			else				from					i := low					j := high					mid := low					Result := low - 1				invariant					low <= i and i <= mid + 1					low <= mid and mid <= j and j <= high					i <= j					has (a, key, i, j) = has (a, key, low, high)				until					i >= j				loop					mid := i + (j - i) // 2					if a [mid] < key then						i := mid + 1					else						j := mid					end				variant					j - i				end				if a [i] = key then					Result := i				end			end		ensure			low <= Result and Result <= high implies a [Result] = key			Result < low or Result > high implies not has (a, key, low, high)		end feature -- Implementation 	is_sorted (a: ARRAY [INTEGER]; low, high: INTEGER): BOOLEAN		-- Is `a[low..high]' sorted in nondecreasing order?		require			a.lower <= low			high <= a.upper		do			Result := across low |..| (high - 1) as i all a [i.item] <= a [i.item + 1] end		end 	has (a: ARRAY [INTEGER]; key: INTEGER; low, high: INTEGER): BOOLEAN		-- Is there an element `key' in `a[low..high]'?		require			a.lower <= low			high <= a.upper		do			Result := across low |..| high as i some a [i.item] = key end		end end`

## Elixir

`defmodule Binary do  def search(list, value), do: search(List.to_tuple(list), value, 0, length(list)-1)   def search(_tuple, _value, low, high) when high < low, do: :not_found  def search(tuple, value, low, high) do    mid = div(low + high, 2)    midval = elem(tuple, mid)    cond do      value <  midval -> search(tuple, value, low, mid-1)      value >  midval -> search(tuple, value, mid+1, high)      value == midval -> mid     end  endend list = [0,1,4,5,6,7,8,9,12,26,45,67,78,90,98,123,211,234,456,769,865,2345,3215,14345,24324]Enum.each([0,42,45,24324,99999], fn val ->  case Binary.search(list, val) do    :not_found -> IO.puts "#{val} not found in list"    index      -> IO.puts "found #{val} at index #{index}"  endend)`
Output:
```found 0 at index 0
found 45 at index 10
found 24324 at index 24
```

## Emacs Lisp

` (defun binary-search (value array)  (let ((low 0)        (high (1- (length array))))    (cl-do () ((< high low) nil)      (let ((middle (floor (+ low high) 2)))        (cond ((> (aref array middle) value)               (setf high (1- middle)))              ((< (aref array middle) value)               (setf low (1+ middle)))              (t (cl-return middle)))))))`

## Erlang

`%% Task: Binary Search algorithm%% Author: Abhay Jain -module(searching_algorithm).-export([start/0]). start() ->    List = [1,2,3],    binary_search(List, 5, 1, length(List)).  binary_search(List, Value, Low, High) ->    if Low > High ->        io:format("Number ~p not found~n", [Value]),        not_found;       true ->        Mid = (Low + High) div 2,        MidNum = lists:nth(Mid, List),        if MidNum > Value ->            binary_search(List, Value, Low, Mid-1);           MidNum < Value ->            binary_search(List, Value, Mid+1, High);           true ->            io:format("Number ~p found at index ~p", [Value, Mid]),            Mid        end    end.`

## Euphoria

### Recursive

`function binary_search(sequence s, object val, integer low, integer high)    integer mid, cmp    if high < low then        return 0 -- not found    else        mid = floor( (low + high) / 2 )        cmp = compare(s[mid], val)        if  cmp > 0 then            return binary_search(s, val, low, mid-1)        elsif cmp < 0 then            return binary_search(s, val, mid+1, high)        else            return mid        end if    end ifend function`

### Iterative

`function binary_search(sequence s, object val)    integer low, high, mid, cmp    low = 1    high = length(s)    while low <= high do        mid = floor( (low + high) / 2 )        cmp = compare(s[mid], val)        if cmp > 0 then            high = mid - 1        elsif cmp < 0 then            low = mid + 1        else            return mid        end if    end while    return 0 -- not foundend function`

## F#

Generic recursive version, using #light syntax:

`let rec binarySearch (myArray:array<IComparable>, low:int, high:int, value:IComparable) =    if (high < low) then        null    else        let mid = (low + high) / 2         if (myArray.[mid] > value) then            binarySearch (myArray, low, mid-1, value)        else if (myArray.[mid] < value) then            binarySearch (myArray, mid+1, high, value)        else            myArray.[mid]`

## Factor

Factor already includes a binary search in its standard library. The following code offers an interface compatible with the requirement of this task, and returns either the index of the element if it has been found or f otherwise.

`USING: binary-search kernel math.order ; : binary-search ( seq elt -- index/f )    [ [ <=> ] curry search ] keep = [ drop f ] unless ;`

## FBSL

FBSL has built-in QuickSort() and BSearch() functions:

`#APPTYPE CONSOLE DIM va[], sign = {1, -1}, toggle PRINT "Loading ... ";DIM gtc = GetTickCount()FOR DIM i = 0 TO 1000000	va[] = sign[toggle] * PI * i	toggle = NOT toggle		' randomize the arrayNEXTPRINT "done in ", GetTickCount() - gtc, " milliseconds" PRINT "Sorting ... ";gtc = GetTickCount()QUICKSORT(va)				' quick sort the arrayPRINT "done in ", GetTickCount() - gtc, " milliseconds" gtc = GetTickCount()PRINT 1000000 * PI, " found at index ", BSEARCH(va, 1000000 * PI), _	' binary search through the array	" in ", GetTickCount() - gtc, " milliseconds" PAUSE`
Output:
```Loading ... done in 906 milliseconds
Sorting ... done in 547 milliseconds
3141592.65358979 found at index 1000000 in 0 milliseconds

Press any key to continue...```

User-defined implementations of the same would be considerably slower. Nonetheless, here they are in order to comply with the task requirements.

Iterative:

`#APPTYPE CONSOLE DIM va[] PRINT "Loading ... ";DIM gtc = GetTickCount()FOR DIM i = 0 TO 1000000: va[] = i * PI: NEXTPRINT "done in ", GetTickCount() - gtc, " milliseconds" gtc = GetTickCount()PRINT 1000000 * PI, " found at index ", BSearchIter(va, 1000000 * PI), _	" in ", GetTickCount() - gtc, " milliseconds" PAUSE FUNCTION BSearchIter(BYVAL array, BYVAL num)	STATIC low = LBOUND(va), high = UBOUND(va)	WHILE low <= high		DIM midp = (high + low) \ 2		IF array[midp] > num THEN			high = midp - 1		ELSEIF array[midp] < num THEN			low = midp + 1		ELSE			RETURN midp		END IF	WEND	RETURN -1END FUNCTION`
Output:
```Loading ... done in 391 milliseconds
3141592.65358979 found at index 1000000 in 62 milliseconds

Press any key to continue...```

Recursive:

`#APPTYPE CONSOLE DIM va[] PRINT "Loading ... ";DIM gtc = GetTickCount()FOR DIM i = 0 TO 1000000: va[] = i * PI: NEXTPRINT "done in ", GetTickCount() - gtc, " milliseconds" gtc = GetTickCount()PRINT 1000000 * PI, " found at index ", BSearchRec(va, 1000000 * PI, LBOUND(va), UBOUND(va)), _	" in ", GetTickCount() - gtc, " milliseconds" PAUSE FUNCTION BSearchRec(BYVAL array, BYVAL num, BYVAL low, BYVAL high)	IF high < low THEN RETURN -1	DIM midp = (high + low) \ 2	IF array[midp] > num THEN		RETURN BSearchRec(array, num, low, midp - 1)	ELSEIF array[midp] < num THEN		RETURN BSearchRec(array, num, midp + 1, high)	END IF	RETURN midpEND FUNCTION`
Output:
```Loading ... done in 390 milliseconds
3141592.65358979 found at index 1000000 in 938 milliseconds

Press any key to continue...```

## Forth

This version is designed for maintaining a sorted array. If the item is not found, then then location returned is the proper insertion point for the item. This could be used in an optimized Insertion sort, for example.

`defer (compare)' - is (compare) \ default to numbers : cstr-compare ( cstr1 cstr2 -- <=> ) \ counted strings  swap count rot count compare ; : mid ( u l -- mid ) tuck - 2/ -cell and + ; : bsearch ( item upper lower -- where found? )  rot >r  begin  2dup >  while  2dup mid         dup @ [email protected] (compare)         dup  while  0<         if   nip cell+   ( upper mid+1 )         else rot drop swap ( mid lower )         then  repeat drop nip nip             true  else   max ( insertion-point ) false  then  r> drop ; create test 2 , 4 , 6 , 9 , 11 ,   99 ,: probe ( n -- ) test 5 cells bounds bsearch . @ . cr ;1 probe \ 0 22 probe \ -1 23 probe \ 0 410 probe \ 0 1111 probe \ -1 1112 probe \ 0 99`

## Fortran

Recursive In ISO Fortran 90 or later use a RECURSIVE function and ARRAY SECTION argument:

`recursive function binarySearch_R (a, value) result (bsresult)    real, intent(in) :: a(:), value    integer          :: bsresult, mid     mid = size(a)/2 + 1    if (size(a) == 0) then        bsresult = 0        ! not found    else if (a(mid) > value) then        bsresult= binarySearch_R(a(:mid-1), value)    else if (a(mid) < value) then        bsresult = binarySearch_R(a(mid+1:), value)        if (bsresult /= 0) then            bsresult = mid + bsresult        end if    else        bsresult = mid      ! SUCCESS!!    end ifend function binarySearch_R`

Iterative
In ISO Fortran 90 or later use an ARRAY SECTION POINTER:

`function binarySearch_I (a, value)    integer                  :: binarySearch_I    real, intent(in), target :: a(:)    real, intent(in)         :: value    real, pointer            :: p(:)    integer                  :: mid, offset     p => a    binarySearch_I = 0    offset = 0    do while (size(p) > 0)        mid = size(p)/2 + 1        if (p(mid) > value) then            p => p(:mid-1)        else if (p(mid) < value) then            offset = offset + mid            p => p(mid+1:)        else            binarySearch_I = offset + mid    ! SUCCESS!!            return        end if    end doend function binarySearch_I`

### Iterative, exclusive bounds, three-way test.

This has the array indexed from 1 to N, and the "not found" return code is zero or negative. Changing the search to be for A(first:last) is trivial, but the "not-found" return protocol would require adjustment, as when starting the array indexing at zero. Aside from the "not found" report, The variables used in the search must be able to hold the values first - 1 and last + 1 so for example with sixteen-bit two's complement integers the maximum value for last is 32766, not 32767.

Depending on the version of Fortran the compiler supports, the specification of the array parameter may vary, as A(1) or A(*) or A(:), and in the latter case, parameter N could be omitted because the size of an array parameter may be ascertained via the SIZE function. For the more advanced fortrans, declaring the parameters to be INTENT(IN) may help, as despite passing arrays "by reference" being the norm, the newer compilers may generate copy-in, copy-out code, vitiating the whole point of using a fast binary search instead of a slow linear search. In this case, INTENT(IN) will at least prevent the copy-back. In such a situation however, preparing in-line code may be the better move: fortunately, there is not a lot of code involved. There is no point in using an explicitly recursive version (even though the same actions may result during execution) because of the overhead of parameter passing and procedure entry/exit.

Later compilers offer features allowing the development of "generic" functions so that the same function name may be used yet the actual routine invoked will be selected according to how the parameters are integers or floating-point, and of different precisions. There would still need to be a version of the function for each type combination, each with its own name. Unfortunately, there is no three-way comparison test for character data.

The use of "exclusive" bounds simplifies the adjustment of the bounds: the appropriate bound simply receives the value of P, there is no + 1 or - 1 adjustment at every step; similarly, the determination of an empty span is easy, and avoiding the risk of integer overflow via (L + R)/2 is achieved at the same time. The "inclusive" bounds version by contrast requires two manipulations of L and R at every step - once to see if the span is empty, and a second time to locate the index to test.

`      INTEGER FUNCTION FINDI(X,A,N)	!Binary chopper. Find i such that X = A(i)Careful: it is surprisingly difficult to make this neat, due to vexations when N = 0 or 1.       REAL X,A(*)		!Where is X in array A(1:N)?       INTEGER N		!The count.       INTEGER L,R,P		!Fingers.        L = 0			!Establish outer bounds, to search A(L+1:R-1).        R = N + 1		!L = first - 1; R = last + 1.    1   P = (R - L)/2		!Probe point. Beware INTEGER overflow with (L + R)/2.        IF (P.LE.0) GO TO 5	!Aha! Nowhere!! The span is empty.        P = P + L		!Convert an offset from L to an array index.        IF (X - A(P)) 3,4,2	!Compare to the probe point.    2   L = P			!A(P) < X. Shift the left bound up: X follows A(P).        GO TO 1			!Another chop.    3   R = P			!X < A(P). Shift the right bound down: X precedes A(P).        GO TO 1			!Try again.    4   FINDI = P		!A(P) = X. So, X is found, here!       RETURN			!Done.Curse it!    5   FINDI = -L		!X is not found. Insert it at L + 1, i.e. at A(1 - FINDI).      END FUNCTION FINDI	!A's values need not be all different, merely in order. `

#### Statistics

Imagine a test array containing the even numbers: 2,4,6,8. A count could be kept of the number of probes required to find each of those four values, and likewise with a search for the odd numbers 1,3,5,7,9 that would probe all the places where a value might be not found. Plot the average number of probes for the two cases, plus the maximum number of probes for any case, and then repeat for another number of elements to search. With only one element in the array to be searched, all values are the same: one probe.

#### An alternative version

`      INTEGER FUNCTION FINDI(X,A,N)	!Binary chopper. Find i such that X = A(i)Careful: it is surprisingly difficult to make this neat, due to vexations when N = 0 or 1.       REAL X,A(*)		!Where is X in array A(1:N)?       INTEGER N		!The count.       INTEGER L,R,P		!Fingers.        L = 0			!Establish outer bounds, to search A(L+1:R-1).        R = N + 1		!L = first - 1; R = last + 1.        GO TO 1			!Hop to it.    2   L = P			!A(P) < X. Shift the left bound up: X follows A(P).    1   P = (R - L)/2		!Probe point. Beware INTEGER overflow with (L + R)/2.        IF (P.LE.0) GO TO 5	!Aha! Nowhere!! The span is empty.        P = P + L		!Convert an offset from L to an array index.        IF (X - A(P)) 3,4,2	!Compare to the probe point.    3   R = P			!X < A(P). Shift the right bound down: X precedes A(P).        GO TO 1			!Try again.    4   FINDI = P		!A(P) = X. So, X is found, here!       RETURN			!Done.Curse it!    5   FINDI = -L		!X is not found. Insert it at L + 1, i.e. at A(1 - FINDI).      END FUNCTION FINDI	!A's values need not be all different, merely in order. `

The point of this is that the IF-test is going to initiate some jumps, so why not arrange that one of the bound adjustments needs no subsequent jump to the start of the next iteration - in the first version, both bound adjustments needed such a jump, the GO TO 1 statements. This was done by shifting the code for label 2 up to precede the code for label 1 - and removing its now pointless GO TO 1 (executed each time), but adding an initial GO TO 1, executed once only. This sort of change is routine when manipulating spaghetti code...

It is because the method involves such a small amount of effort per iteration that minor changes offer a significant benefit. A lot depends on the implementation of the three-way test: the hope is that after the comparison, the computer hardware has indicators set for various outcomes, so that the necessary conditional branches can be made through successive inspection of those indicators, rather than repeating the comparison. These branch tests may in turn be made in an order that notes which option (if any) involves "falling through" to the next statement, thus it may be better to swap the order of labels 3 and 4. Further, the compiler may itself choose to re-order the various code pieces. First Fortran (in 1958) had a FREQUENCY statement whereby the programmer could indicate which paths were the more likely - for the binary search, equality is the less likely discovery. An assembler version of this routine attended to all these details.

Some compilers do not produce machine code directly, but instead translate the source code into another language which is then compiled, and a common choice for that is C. This is all very well, but C is one of the many languages that do not have a three-way test option and so cannot represent Fortran's three-way IF statement directly. Before emitting asservations of faith that pseudocode such as

``` if expression > 0 then optionP
else if expression < 0 then optionN
else optionZ;
```

will be recognised by the most excellent compiler producing only one comparison, note that the two expressions are not the same (one has <, the other >), and test what happens with pseudocode such as

``` if X > 0 then print "Positive"
else if X > 0 then print "Still positive";
```

That is, does the compiler make any remark, and does the resulting machine code contain a redundant test? However, despite all the above, the three-way IF statement has been declared deprecated in later versions of Fortran, with no alternative to repeated testing offered.

Incidentally, the exclusive-bounds version leads to a good version of the interpolation search (whereby the probe position is interpolated, not just in the middle of the span), unlike the version based on inclusive-bounds. Further, the unsourced offering in Wikipedia contains a bug - try searching an array of two equal elements for that value.

## Futhark

 This example is incorrect. Please fix the code and remove this message.Details: Futhark's syntax has changed, so this example will not compile

Straightforward translation of imperative iterative algorithm.

` fun main(as: [n]int, value: int): int =  let low = 0  let high = n-1  loop ((low,high)) = while low <= high do    -- invariants: value > as[i] for all i < low    --             value < as[i] for all i > high    let mid = (low+high) / 2    in if as[mid] > value       then (low, mid - 1)       else if as[mid] < value       then (mid + 1, high)       else (mid, mid-1) -- Force termination.  in low `

## GAP

`Find := function(v, x)  local low, high, mid;  low := 1;  high := Length(v);  while low <= high do    mid := QuoInt(low + high, 2);    if v[mid] > x then      high := mid - 1;    elif v[mid] < x then      low := mid + 1;    else      return mid;    fi;  od;  return fail;end; u := [1..10]*7;# [ 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 ]Find(u, 34);# failFind(u, 35);# 5`

## Go

Recursive:

`func binarySearch(a []float64, value float64, low int, high int) int {    if high < low {        return -1    }    mid := (low + high) / 2    if a[mid] > value {        return binarySearch(a, value, low, mid-1)    } else if a[mid] < value {        return binarySearch(a, value, mid+1, high)    }    return mid}`

Iterative:

`func binarySearch(a []float64, value float64) int {    low := 0    high := len(a) - 1    for low <= high {        mid := (low + high) / 2        if a[mid] > value {            high = mid - 1        } else if a[mid] < value {            low = mid + 1        } else {            return mid        }    }    return -1}`

Library:

`import "sort" //... sort.SearchInts([]int{0,1,4,5,6,7,8,9}, 6) // evaluates to 4`

Exploration of library source code shows that it uses the mid = low + (high - low) / 2 technique to avoid overflow.

There are also functions `sort.SearchFloat64s()`, `sort.SearchStrings()`, and a very general `sort.Search()` function that allows you to binary search a range of numbers based on any condition (not necessarily just search for an index of an element in an array).

## Groovy

Both solutions use sublists and a tracking offset in preference to "high" and "low".

#### Recursive Solution

` def binSearchR//define binSearchR closure.binSearchR = { a, key, offset=0 ->    def m = n.intdiv(2)    def n = a.size()    a.empty \        ? ["The insertion point is": offset] \        : a[m] > key \            ? binSearchR(a[0..<m],key, offset) \            : a[m] < target \                ? binSearchR(a[(m + 1)..<n],key, offset + m + 1) \                : [index: offset + m]} `

#### Iterative Solution

`def binSearchI = { aList, target ->    def a = aList    def offset = 0    while (!a.empty) {        def n = a.size()        def m = n.intdiv(2)        if(a[m] > target) {            a = a[0..<m]        } else if (a[m] < target) {            a = a[(m + 1)..<n]            offset += m + 1        } else {            return [index: offset + m]        }    }    return ["insertion point": offset]}`

Test:

`def a = [] as Setdef random = new Random()while (a.size() < 20) { a << random.nextInt(30) }def source = a.sort()source[0..-2].eachWithIndex { si, i -> assert si < source[i+1] } println "\${source}"1.upto(5) {    target = random.nextInt(10) + (it - 2) * 10    print "Trial #\${it}. Looking for: \${target}"    def answers = [binSearchR, binSearchI].collect { search ->        search(source, target)    }    assert answers[0] == answers[1]    println """    Answer: \${answers[0]}, : \${source[answers[0].values().iterator().next()]}"""}`

Output:

```[1, 2, 5, 8, 9, 10, 11, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29]
Trial #1. Looking for: -9
Trial #2. Looking for: 7
Trial #3. Looking for: 18
Trial #4. Looking for: 29
Trial #5. Looking for: 32

### Recursive algorithm

The algorithm itself, parametrized by an "interrogation" predicate p in the spirit of the explanation above:

`import Data.Array (Array, Ix, (!), listArray, bounds) -- BINARY SEARCH --------------------------------------------------------------bSearch  :: Integral a  => (a -> Ordering) -> (a, a) -> Maybe abSearch p (low, high)  | high < low = Nothing  | otherwise =    let mid = (low + high) `div` 2    in case p mid of         LT -> bSearch p (low, mid - 1)         GT -> bSearch p (mid + 1, high)         EQ -> Just mid -- Application to an array:bSearchArray  :: (Ix i, Integral i, Ord e)  => Array i e -> e -> Maybe ibSearchArray a x = bSearch (compare x . (a !)) (bounds a) -- TEST -----------------------------------------------------------------------axs  :: (Num i, Ix i)  => Array i Stringaxs =  listArray    (0, 11)    [ "alpha"    , "beta"    , "delta"    , "epsilon"    , "eta"    , "gamma"    , "iota"    , "kappa"    , "lambda"    , "mu"    , "theta"    , "zeta"    ] main :: IO ()main =  let e = "mu"      found = bSearchArray axs e  in putStrLn \$     '\'' :     e ++     case found of       Nothing -> "' Not found"       Just x -> "' found at index " ++ show x`
Output:
`'mu' found at index 9`

The algorithm uses tail recursion, so the iterative and the recursive approach are identical in Haskell (the compiler will convert recursive calls into jumps).

A common optimisation of recursion is to delegate the main computation to a helper function with simpler type signature. For the option type of the return value, we could also use an Either as an alternative to a Maybe.

`import Data.Array (Array, Ix, (!), listArray, bounds) -- BINARY SEARCH USING A HELPER FUNCTION WITH A SIMPLER TYPE SIGNATUREfindIndexBinary  :: Ord a  => (a -> Ordering) -> Array Int a -> Either String IntfindIndexBinary p axs =  let go (lo, hi)        | hi < lo = Left "not found"        | otherwise =          let mid = (lo + hi) `div` 2          in case p (axs ! mid) of               LT -> go (lo, pred mid)               GT -> go (succ mid, hi)               EQ -> Right mid  in go (bounds axs) -- TEST ---------------------------------------------------haystack :: Array Int Stringhaystack =  listArray    (0, 11)    [ "alpha"    , "beta"    , "delta"    , "epsilon"    , "eta"    , "gamma"    , "iota"    , "kappa"    , "lambda"    , "mu"    , "theta"    , "zeta"    ] main :: IO ()main =  let needle = "lambda"  in putStrLn \$     '\'' :     needle ++     either       ("' " ++)       (("' found at index " ++) . show)       (findIndexBinary (compare needle) haystack)`
Output:
`'lambda' found at index 8`

### Iterative algorithm

The iterative algorithm could be written in terms of the until function, which takes a predicate p, a function f, and a seed value x.

It returns the result of applying f until p holds.

`import Data.Array (Array, Ix, (!), listArray, bounds) -- BINARY SEARCH USING THE ITERATIVE ALGORITHMfindIndexBinary_  :: Ord a  => (a -> Ordering) -> Array Int a -> Either String IntfindIndexBinary_ p axs =  let (lo, hi) =        until          (\(lo, hi) -> lo > hi || 0 == hi)          (\(lo, hi) ->              let m = quot (lo + hi) 2              in case p (axs ! m) of                   LT -> (lo, pred m)                   GT -> (succ m, hi)                   EQ -> (m, 0))          (bounds axs) :: (Int, Int)  in if 0 /= hi       then Left "not found"       else Right lo -- TEST ---------------------------------------------------haystack :: Array Int Stringhaystack =  listArray    (0, 11)    [ "alpha"    , "beta"    , "delta"    , "epsilon"    , "eta"    , "gamma"    , "iota"    , "kappa"    , "lambda"    , "mu"    , "theta"    , "zeta"    ] main :: IO ()main =  let needle = "kappa"  in putStrLn \$     '\'' :     needle ++     either       ("' " ++)       (("' found at index " ++) . show)       (findIndexBinary_ (compare needle) haystack)`
Output:
`'kappa' found at index 7`

## HicEst

`REAL :: n=10,  array(n)    array = NINT( RAN(n) )   SORT(Vector=array, Sorted=array)   x = NINT( RAN(n) )    idx = binarySearch( array, x )   WRITE(ClipBoard) x, "has position ", idx, "in ", array END FUNCTION binarySearch(A, value)   REAL :: A(1), value    low = 1   high = LEN(A)   DO i = 1, high     IF( low > high) THEN       binarySearch = 0       RETURN     ELSE       mid = INT( (low + high) / 2 )       IF( A(mid) > value) THEN         high = mid - 1       ELSEIF( A(mid) < value ) THEN         low = mid + 1       ELSE         binarySearch = mid         RETURN       ENDIF     ENDIF   ENDDO END`
`7 has position 9 in 0 0 1 2 3 3 4 6 7 85 has position 0 in 0 0 1 2 3 3 4 6 7 8`

## Hoon

`|=  [arr=(list @ud) [email protected]]=/  [email protected]  0=/  [email protected]  (dec (lent arr))|-?>  (lte lo hi)=/  mid  (div (add lo hi) 2)=/  val  (snag mid arr)?:  (lth x val)  \$(hi (dec mid))?:  (gth x val)  \$(lo +(mid))mid`

## Icon and Unicon

Only a recursive solution is shown here.

`procedure binsearch(A, target)    if *A = 0 then fail    mid := *A/2 + 1    if target > A[mid] then {        return mid + binsearch(A[(mid+1):0], target)        }    else if target < A[mid] then {        return binsearch(A[1+:(mid-1)], target)        }    return midend`

A program to test this is:

`procedure main(args)    target := integer(!args) | 3    every put(A := [], 1 to 18 by 2)     outList("Searching", A)    write(target," is ",("at "||binsearch(A, target)) | "not found")end procedure outList(prefix, A)    writes(prefix,": ")    every writes(!A," ")    write()end`

with some sample runs:

```->bins 0
Searching: 1 3 5 7 9 11 13 15 17
->bins 1
Searching: 1 3 5 7 9 11 13 15 17
1 is at 1
->bins 2
Searching: 1 3 5 7 9 11 13 15 17
->bins 3
Searching: 1 3 5 7 9 11 13 15 17
3 is at 2
->bins 16
Searching: 1 3 5 7 9 11 13 15 17
->bins 17
Searching: 1 3 5 7 9 11 13 15 17
17 is at 9
->bins 7
Searching: 1 3 5 7 9 11 13 15 17
7 is at 4
->bins 9
Searching: 1 3 5 7 9 11 13 15 17
9 is at 5
->bins 10
Searching: 1 3 5 7 9 11 13 15 17
->
```

## J

J already includes a binary search primitive (`I.`). The following code offers an interface compatible with the requirement of this task, and returns either the index of the element if it has been found or 'Not Found' otherwise:

`bs=. i. 'Not Found'"_^:([email protected]:) I.`

Examples:

`   2 3 5 6 8 10 11 15 19 20 bs 116   2 3 5 6 8 10 11 15 19 20 bs 12Not Found`

Direct tacit iterative and recursive versions to compare to other implementations follow:

Iterative

`'X Y L H M'=. i.5                            NB. Setting mnemonics for boxesf=. &({::)                                   NB. Fetching the contents of a boxo=. @:                                       NB. Composing verbs (functions) boxes=. ; , a: \$~ 3:                         NB. Appending 3 (empty) boxes to the inputsLowHigh=. (0 ; # o (X f)) (L,H)} ]           NB. Setting the low and high bounds   midpoint=. < o (<. o (2 %~ L f + H f)) M} ]  NB. Updating the midpointcase=.     >: o * o (Y f - M f { X f)        NB. Less=0, equal=1, or greater=2 squeeze=. (< o (_1 + M f) H} ])`(< o _: L} ])`(< o (1 + M f) L} ])@.casereturn=.   (M f) o ((<@:('Not Found'"_) M} ]) ^: (_ ~: L f)) bs=. return o (squeeze o midpoint ^: (L f <: H f) ^:_) o LowHigh o boxes`

Recursive

`'X Y L H M'=. i.5                            NB. Setting mnemonics for boxesf=. &({::)                                   NB. Fetching the contents of a boxo=. @:                                       NB. Composing verbs (functions) boxes=. a: ,~ ;                              NB. Appending 1 (empty) box to the inputsmidpoint=. < o (<. o (2 %~ L f + H f)) M} ]  NB. Updating the midpointcase=.     >: o * o (Y f - M f { X f)        NB. Less=0, equal=1, or greater=2 recur=. (X f bs Y f ; L f ; (_1 + M f))`(M f)`(X f bs Y f ; (1 + M f) ; H f)@.case bs=. (recur o midpoint`('Not Found'"_) @. (H f < L f) o boxes) :: ([ bs ] ; 0 ; (<: o # o [))`

## Java

Iterative

`public class BinarySearchIterative {     public static int binarySearch(int[] nums, int check) {        int hi = nums.length - 1;        int lo = 0;        while (hi >= lo) {            int guess = (lo + hi) >>> 1;  // from OpenJDK            if (nums[guess] > check) {                hi = guess - 1;            } else if (nums[guess] < check) {                lo = guess + 1;            } else {                return guess;            }        }        return -1;    }     public static void main(String[] args) {        int[] haystack = {1, 5, 6, 7, 8, 11};        int needle = 5;        int index = binarySearch(haystack, needle);        if (index == -1) {            System.out.println(needle + " is not in the array");        } else {            System.out.println(needle + " is at index " + index);        }    }}`

Recursive

`public class BinarySearchRecursive {     public static int binarySearch(int[] haystack, int needle, int lo, int hi) {        if (hi < lo) {            return -1;        }        int guess = (hi + lo) / 2;        if (haystack[guess] > needle) {            return binarySearch(haystack, needle, lo, guess - 1);        } else if (haystack[guess] < needle) {            return binarySearch(haystack, needle, guess + 1, hi);        }        return guess;    }     public static void main(String[] args) {        int[] haystack = {1, 5, 6, 7, 8, 11};        int needle = 5;         int index = binarySearch(haystack, needle, 0, haystack.length);         if (index == -1) {            System.out.println(needle + " is not in the array");        } else {            System.out.println(needle + " is at index " + index);        }    }}`

Library When the key is not found, the following functions return `~insertionPoint` (the bitwise complement of the index where the key would be inserted, which is guaranteed to be a negative number).

For arrays:

`import java.util.Arrays; int index = Arrays.binarySearch(array, thing);int index = Arrays.binarySearch(array, startIndex, endIndex, thing); // for objects, also optionally accepts an additional comparator argument:int index = Arrays.binarySearch(array, thing, comparator);int index = Arrays.binarySearch(array, startIndex, endIndex, thing, comparator);`

For Lists:

`import java.util.Collections; int index = Collections.binarySearch(list, thing);int index = Collections.binarySearch(list, thing, comparator);`

## JavaScript

### ES5

Recursive binary search implementation

`function binary_search_recursive(a, value, lo, hi) {  if (hi < lo) { return null; }   var mid = Math.floor((lo + hi) / 2);   if (a[mid] > value) {    return binary_search_recursive(a, value, lo, mid - 1);  }  if (a[mid] < value) {    return binary_search_recursive(a, value, mid + 1, hi);  }  return mid;}`

Iterative binary search implementation

`function binary_search_iterative(a, value) {  var mid, lo = 0,      hi = a.length - 1;   while (lo <= hi) {    mid = Math.floor((lo + hi) / 2);     if (a[mid] > value) {      hi = mid - 1;    } else if (a[mid] < value) {      lo = mid + 1;    } else {      return mid;    }  }  return null;}`

### ES6

Recursive and iterative, by composition of pure functions, with tests and output:

`(() => {    'use strict';     const main = () => {         // findRecursive :: a -> [a] -> Either String Int        const findRecursive = (x, xs) => {            const go = (lo, hi) => {                if (hi < lo) {                    return Left('not found');                } else {                    const                        mid = div(lo + hi, 2),                        v = xs[mid];                    return v > x ? (                        go(lo, mid - 1)                    ) : v < x ? (                        go(mid + 1, hi)                    ) : Right(mid);                }            };            return go(0, xs.length);        };          // findRecursive :: a -> [a] -> Either String Int        const findIter = (x, xs) => {            const [m, l, h] = until(                ([mid, lo, hi]) => lo > hi || lo === mid,                ([mid, lo, hi]) => {                    const                        m = div(lo + hi, 2),                        v = xs[m];                    return v > x ? [                        m, lo, m - 1                    ] : v < x ? [                        m, m + 1, hi                    ] : [m, m, hi];                },                [div(xs.length / 2), 0, xs.length - 1]            );            return l > h ? (                Left('not found')            ) : Right(m);        };         // TESTS ------------------------------------------         const            // (pre-sorted AZ)            xs = ["alpha", "beta", "delta", "epsilon", "eta", "gamma",                "iota", "kappa", "lambda", "mu", "nu", "theta", "zeta"            ];        return JSON.stringify([            'Recursive',            map(x => either(                    l => "'" + x + "' " + l,                    r => "'" + x + "' found at index " + r,                    findRecursive(x, xs)                ),                knuthShuffle(['cape'].concat(xs).concat('cairo'))            ),            '',            'Iterative:',            map(x => either(                    l => "'" + x + "' " + l,                    r => "'" + x + "' found at index " + r,                    findIter(x, xs)                ),                knuthShuffle(['cape'].concat(xs).concat('cairo'))            )        ], null, 2);    };     // GENERIC FUNCTIONS ----------------------------------     // Left :: a -> Either a b    const Left = x => ({        type: 'Either',        Left: x    });     // Right :: b -> Either a b    const Right = x => ({        type: 'Either',        Right: x    });     // div :: Int -> Int -> Int    const div = (x, y) => Math.floor(x / y);     // either :: (a -> c) -> (b -> c) -> Either a b -> c    const either = (fl, fr, e) =>        'Either' === e.type ? (            undefined !== e.Left ? (                fl(e.Left)            ) : fr(e.Right)        ) : undefined;     // Abbreviation for quick testing     // enumFromTo :: (Int, Int) -> [Int]    const enumFromTo = (m, n) =>        Array.from({            length: 1 + n - m        }, (_, i) => m + i);     // FOR TESTS     // knuthShuffle :: [a] -> [a]    const knuthShuffle = xs => {        const swapped = (iFrom, iTo, xs) =>            xs.map(                (x, i) => iFrom !== i ? (                    iTo !== i ? x : xs[iFrom]                ) : xs[iTo]            );        return enumFromTo(0, xs.length - 1)            .reduceRight((a, i) => {                const iRand = randomRInt(0, i)();                return i !== iRand ? (                    swapped(i, iRand, a)                ) : a;            }, xs);    };     // map :: (a -> b) -> [a] -> [b]    const map = (f, xs) =>        (Array.isArray(xs) ? (            xs        ) : xs.split('')).map(f);      // FOR TESTS     // randomRInt :: Int -> Int -> IO () -> Int    const randomRInt = (low, high) => () =>        low + Math.floor(            (Math.random() * ((high - low) + 1))        );     // reverse :: [a] -> [a]    const reverse = xs =>        'string' !== typeof xs ? (            xs.slice(0).reverse()        ) : xs.split('').reverse().join('');     // until :: (a -> Bool) -> (a -> a) -> a -> a    const until = (p, f, x) => {        let v = x;        while (!p(v)) v = f(v);        return v;    };     // MAIN ---    return main();})();`
Output:
```[
"Recursive",
[
"'delta' found at index 2",
"'gamma' found at index 5",
"'eta' found at index 4",
"'kappa' found at index 7",
"'alpha' found at index 0",
"'mu' found at index 9",
"'beta' found at index 1",
"'epsilon' found at index 3",
"'nu' found at index 10",
"'iota' found at index 6",
"'theta' found at index 11",
"'lambda' found at index 8",
"'zeta' found at index 12"
],
"",
"Iterative:",
[
"'theta' found at index 11",
"'kappa' found at index 7",
"'zeta' found at index 12",
"'epsilon' found at index 3",
"'beta' found at index 1",
"'nu' found at index 10",
"'eta' found at index 4",
"'alpha' found at index 0",
"'lambda' found at index 8",
"'iota' found at index 6",
"'mu' found at index 9",
"'gamma' found at index 5",
"'delta' found at index 2",
]
]```

## jq

If the input array is sorted, then binarySearch(value) as defined here will return an index (i.e. offset) of value in the array if the array contains the value, and otherwise (-1 - ix), where ix is the insertion point, if the value cannot be found. binarySearch will always terminate.

Recursive solution:
`def binarySearch(value):  # To avoid copying the array, simply pass in the current low and high offsets  def binarySearch(low; high):      if (high < low) then (-1 - low)      else ( (low + high) / 2 | floor) as \$mid           | if (.[\$mid] > value) then binarySearch(low; \$mid-1)             elif (.[\$mid] < value) then binarySearch(\$mid+1; high)             else \$mid             end      end;   binarySearch(0; length-1);`
Example:
`[-1,-1.1,1,1,null,[null]] | binarySearch(1)`
Output:

2

## Jsish

`/**   Binary search, in Jsish, based on Javascript entry   Tectonics: jsish -u -time true -verbose true binarySearch.jsi*/function binarySearchIterative(haystack, needle) {    var mid, low = 0, high = haystack.length - 1;     while (low <= high) {        mid = Math.floor((low + high) / 2);        if (haystack[mid] > needle) {            high = mid - 1;        } else if (haystack[mid] < needle) {            low = mid + 1;        } else {            return mid;        }    }    return null;} /* recursive */function binarySearchRecursive(haystack, needle, low, high) {    if (high < low) { return null; }     var mid = Math.floor((low + high) / 2);     if (haystack[mid] > needle) {        return binarySearchRecursive(haystack, needle, low, mid - 1);    }    if (haystack[mid] < needle) {        return binarySearchRecursive(haystack, needle, mid + 1, high);    }    return mid;} /* Testing and timing */if (Interp.conf('unitTest') > 0) {    var arr = [];    for (var i = -5000; i <= 5000; i++) { arr.push(i); }     assert(arr.length == 10001);    assert(binarySearchIterative(arr, 0) == 5000);    assert(binarySearchRecursive(arr, 0, 0, arr.length - 1) == 5000);     assert(binarySearchIterative(arr, 5000) == 10000);    assert(binarySearchRecursive(arr, -5000, 0, arr.length - 1) == 0);     assert(binarySearchIterative(arr, -5001) == null);     puts('--Time 100 passes--');    puts('Iterative:', Util.times(function() { binarySearchIterative(arr, 42); }, 100), 'µs');    puts('Recursive:', Util.times(function() { binarySearchRecursive(arr, 42, 0, arr.length - 1); }, 100), 'µs');}`
Output:
```prompt\$ jsish -u -time true -verbose true binarySearch.jsi
Test binarySearch.jsi
CMD: /usr/local/bin/jsish -Iasserts true -IunitTest 1 binarySearch.jsi
OUTPUT: <--Time 100 passes--
Iterative: 25969 µs
Recursive: 40863 µs
>
[PASS] binarySearch.jsi          (165 ms)```

## Julia

Works with: Julia version 0.6

Iterative:

`function binarysearch(lst::Vector{T}, val::T) where T    low = 1    high = length(lst)    while low ≤ high        mid = (low + high) ÷ 2        if lst[mid] > val            high = mid - 1        elseif lst[mid] < val            low = mid + 1        else            return mid        end    end    return 0end`

Recursive:

`function binarysearch(lst::Vector{T}, value::T, low=1, high=length(lst)) where T    if isempty(lst) return 0 end    if low ≥ high        if low > high || lst[low] != value            return 0        else            return low        end    end    mid = (low + high) ÷ 2    if lst[mid] > value        return binarysearch(lst, value, low, mid-1)    elseif lst[mid] < value        return binarysearch(lst, value, mid+1, high)    else        return mid    endend`

## K

Recursive:

` bs:{[a;t]     if[0=#a; :_n];    m:_(#a)%2;    if[t>[email protected]        tmp:_f[(m+1) _ a;t]        :[_n~tmp; :_n; :1+m+tmp]]    if[t<[email protected]        :_f[m#a;t]]    :m}   v:8 30 35 45 49 77 79 82 87 97  {bs[v;x]}' v0 1 2 3 4 5 6 7 8 9 `

## Kotlin

`fun <T : Comparable<T>> Array<T>.iterativeBinarySearch(target: T): Int {    var hi = size - 1    var lo = 0    while (hi >= lo) {        val guess = lo + (hi - lo) / 2        if (this[guess] > target) hi = guess - 1        else if (this[guess] < target) lo = guess + 1        else return guess    }    return -1} fun <T : Comparable<T>> Array<T>.recursiveBinarySearch(target: T, lo: Int, hi: Int): Int {    if (hi < lo) return -1     val guess = (hi + lo) / 2     return if (this[guess] > target) recursiveBinarySearch(target, lo, guess - 1)    else if (this[guess] < target) recursiveBinarySearch(target, guess + 1, hi)    else guess} fun main(args: Array<String>) {    val a = arrayOf(1, 3, 4, 5, 6, 7, 8, 9, 10)    var target = 6    var r = a.iterativeBinarySearch(target)    println(if (r < 0) "\$target not found" else "\$target found at index \$r")    target = 250    r = a.iterativeBinarySearch(target)    println(if (r < 0) "\$target not found" else "\$target found at index \$r")     target = 6    r = a.recursiveBinarySearch(target, 0, a.size)    println(if (r < 0) "\$target not found" else "\$target found at index \$r")    target = 250    r = a.recursiveBinarySearch(target, 0, a.size)    println(if (r < 0) "\$target not found" else "\$target found at index \$r")}`
Output:
```6 found at index 4
6 found at index 4

## Lambdatalk

Can be tested in (http://lambdaway.free.fr)[1]

` {def BS  {def BS.r {lambda {:a :v :i0 :i1}  {let { {:a :a} {:v :v} {:i0 :i0} {:i1 :i1}         {:m {floor {* {+ :i0 :i1} 0.5}}} }   {if {<  :i1 :i0}   then :v is not found   else {if {> {array.item :a :m} :v}   then {BS.r :a :v :i0 {- :m 1} }   else {if {<  {array.item :a :m} :v}   then {BS.r :a :v {+ :m 1} :i1 }   else :v is at array[:m] }}}}} } {lambda {:a :v}  {BS.r :a :v 0 {- {array.length :a} 1}} }} -> BS {def A {array 12 14 16 18 20 22 25 27 30}}-> A = [12,14,16,18,20,22,25,27,30] {BS {A} -1}  -> -1 is not found{BS {A} 24}  -> 24 is not found{BS {A} 25}  -> 25 is at array[6]{BS {A} 123} -> 123 is not found {def B {array {serie 1 100000 2}}} -> B = [1,3,5,... 99997,99999] {BS {B} 100}   -> 100 is not found{BS {B} 12345} -> 12345 is at array[6172] `

## Liberty BASIC

` dim theArray(100)for i = 1 to 100  theArray(i) = inext i print binarySearch(80,30,90) wait FUNCTION binarySearch(val, lo, hi)  IF hi < lo THEN    binarySearch = 0  ELSE    middle = int((hi + lo) / 2):print middle    if val < theArray(middle) then binarySearch = binarySearch(val, lo, middle-1)    if val > theArray(middle) then binarySearch = binarySearch(val, middle+1, hi)    if val = theArray(middle) then binarySearch = middle  END IFEND FUNCTION `

## Logo

`to bsearch :value :a :lower :upper  if :upper < :lower [output []]  localmake "mid int (:lower + :upper) / 2  if item :mid :a > :value [output bsearch :value :a :lower :mid-1]  if item :mid :a < :value [output bsearch :value :a :mid+1 :upper]  output :midend`

## Lolcode

Iterative

` HAI 1.2  CAN HAS STDIO?   VISIBLE "HAI WORLD!!!1!"  VISIBLE "IMA GONNA SHOW U BINA POUNCE NAO"   I HAS A list ITZ A BUKKIT  list HAS A index0 ITZ 2  list HAS A index1 ITZ 3  list HAS A index2 ITZ 5  list HAS A index3 ITZ 7  list HAS A index4 ITZ 8  list HAS A index5 ITZ 9  list HAS A index6 ITZ 12  list HAS A index7 ITZ 20   BTW Method to access list by index number aka: list[index4]  HOW IZ list access YR indexNameNumber	FOUND YR list'Z SRS indexNameNumber  IF U SAY SO   BTW Method to print the array on the same line  HOW IZ list printList   I HAS A allList ITZ ""	I HAS A indexNameNumber ITZ "index0"	I HAS A index ITZ 0	IM IN YR walkingLoop UPPIN YR index TIL BOTH SAEM index AN 8		indexNameNumber R SMOOSH "index" index MKAY		allList R SMOOSH allList " " list IZ access YR indexNameNumber MKAY MKAY	IM OUTTA YR walkingLoop	FOUND YR allList  IF U SAY SO   VISIBLE "WE START WIF BUKKIT LIEK DIS: " list IZ printList MKAY   I HAS A target ITZ 12  VISIBLE "AN TARGET LIEK DIS: " target   VISIBLE "AN NAO 4 MAGI"   HOW IZ I binaPounce YR list AN YR listLength AN YR target 	I HAS A left ITZ 0	I HAS A right ITZ DIFF OF listLength AN 1	IM IN YR whileLoop		BTW exit while loop when left > right		DIFFRINT left AN SMALLR OF left AN right		O RLY?			YA RLY				GTFO 		OIC 		I HAS A mid ITZ QUOSHUNT OF SUM OF left AN right AN 2		I HAS A midIndexname ITZ SMOOSH "index" mid MKAY 		BTW if target == list[mid] return mid		BOTH SAEM target AN list IZ access YR midIndexname MKAY		O RLY?			YA RLY				FOUND YR mid		OIC 		BTW if target < list[mid] right = mid - 1		DIFFRINT target AN BIGGR OF target AN list IZ access YR midIndexname MKAY		O RLY?			YA RLY				right R DIFF OF mid AN 1		OIC 		BTW if target > list[mid] left = mid + 1		DIFFRINT target AN SMALLR OF target AN list IZ access YR midIndexname MKAY		O RLY?			YA RLY				left R SUM OF mid AN 1		OIC	IM OUTTA YR whileLoop 	FOUND YR -1  IF U SAY SO   BTW call binary search on target here and print the index  I HAS A targetIndex ITZ I IZ binaPounce YR list AN YR 8 AN YR target MKAY  VISIBLE "TARGET " target " IZ IN BUKKIT " targetIndex   VISIBLE "WE HAS TEH TARGET!!1!!"  VISIBLE "I CAN HAS UR CHEEZBURGER NAO?" KTHXBYEend`

Output

```HAI WORLD!!!1!
IMA GONNA SHOW U BINA POUNCE NAO
WE START WIF BUKKIT LIEK DIS:  2 3 5 7 8 9 12 20
AN TARGET LIEK DIS: 12
AN NAO 4 MAGI
TARGET 12 IZ IN BUKKIT 6
WE HAS TEH TARGET!!1!!
I CAN HAS UR CHEEZBURGER NAO?
```

## Lua

Iterative

`function binarySearch (list,value)    local low = 1    local high = #list    while low <= high do        local mid = math.floor((low+high)/2)        if list[mid] > value then high = mid - 1        elseif list[mid] < value then low = mid + 1        else return mid        end    end    return falseend`

Recursive

`function binarySearch (list, value)    local function search(low, high)        if low > high then return false end        local mid = math.floor((low+high)/2)        if list[mid] > value then return search(low,mid-1) end        if list[mid] < value then return search(mid+1,high) end        return mid    end    return search(1,#list)end`

## M2000 Interpreter

` \\ binary searchconst N=10Dim A(0 to N-1)A(0):=1,2,3,4,5,6,8,9,10,11Print Len(A())=10Function BinarySearch(&A(), aValue) {	def long mid, lo, hi	def boolean ok=False	let lo=0, hi=Len(A())-1	While lo<=hi		mid=(lo+hi)/2		if A(mid)>aValue Then			hi=mid-1		Else.if A(mid)<aValue Then			lo=mid+1		Else			=mid			ok=True			exit		End if	End While	if not ok then =-lo-1}For i=0 to 12Rem	Print "Search for value:";i	where= BinarySearch(&A(), i)	if where>=0 then		Print "found i at index: ";where	else		where=-where-1		if where<len(A()) then			Print "Not found, we can insert it at index: ";where			Dim A(len(A())+1)   ' redim			stock A(where)	 keep len(A())-where-1, A(where+1)  'move items up			A(where)=i  ' insert value		Else			Print "Not found, we can append to array at index: ";where			Dim A(len(A())+1)   ' redim			A(where)=i  ' insert value		End If	end ifnext iPrint Len(A())=13Print A()  `

## M4

`define(`notfound',`-1')dnldefine(`midsearch',`ifelse(defn(\$1[\$4]),\$2,\$4,`ifelse(eval(defn(\$1[\$4])>\$2),1,`binarysearch(\$1,\$2,\$3,decr(\$4))',`binarysearch(\$1,\$2,incr(\$4),\$5)')')')dnldefine(`binarysearch',`ifelse(eval(\$4<\$3),1,notfound,`midsearch(\$1,\$2,\$3,eval((\$3+\$4)/2),\$4)')')dnldnldefine(`setrange',`ifelse(`\$3',`',\$2,`define(\$1[\$2],\$3)`'setrange(\$1,incr(\$2),shift(shift(shift([email protected]))))')')dnldefine(`asize',decr(setrange(`a',1,1,3,5,7,11,13,17,19,23,29)))dnldnlbinarysearch(`a',5,1,asize)binarysearch(`a',8,1,asize)`

Output:

```3
-1
```

## Maple

The calculation of "mid" cannot overflow, since Maple uses arbitrary precision integer arithmetic, and the largest list or array is far, far smaller than the effective range of integers.

Recursive

`BinarySearch := proc( A, value, low, high )        description "recursive binary search";        if high < low then                FAIL        else                local mid := iquo( high + low, 2 );                if A[ mid ] > value then                        thisproc( A, value, low, mid - 1 )                elif A[ mid ] < value then                        thisproc( A, value, mid + 1, high )                else                        mid                end if        end ifend proc:`

Iterative

`BinarySearch := proc( A, value )        description "iterative binary search";        local low, high;         low, high := ( lowerbound, upperbound )( A );        while low <= high do                local mid := iquo( low + high, 2 );                if A[ mid ] > value then                        high := mid - 1                elif A[ mid ] < value then                        low := mid + 1                else                        return mid                end if        end do;        FAILend proc:`

We can use either lists or Arrays (or Vectors) for the first argument for these.

`> N := 10:> P := [seq]( ithprime( i ), i = 1 .. N ):> BinarySearch( P, 12, 1, N ); # recursive version                                  FAIL > BinarySearch( P, 13, 1, N ); # recursive version                                   6 > BinarySearch( Array( P ), 13, 1, N ); # make P into an array                                   6 > PP := Array( -2 .. 7, P ): # check it works if the array is not 1-based.> BinarySearch( PP, 13 ); # iterative version                                   3 > PP[ 3 ];                                   13`

## Mathematica / Wolfram Language

Recursive

`BinarySearchRecursive[x_List, val_, lo_, hi_] :=  Module[{mid = lo + [email protected]((hi - lo)/2)},  If[hi < lo, Return[-1]];  Return[    Which[x[[mid]] > val, BinarySearchRecursive[x, val, lo, mid - 1],    x[[mid]] < val, BinarySearchRecursive[x, val, mid + 1, hi],    True, mid]   ];  ]`

Iterative

`BinarySearch[x_List, val_] := Module[{lo = 1, hi = [email protected], mid},  While[lo <= hi,   mid = lo + [email protected]((hi - lo)/2);   Which[x[[mid]] > val, hi = mid - 1,    x[[mid]] < val, lo = mid + 1,    True, Return[mid]    ];   ];  Return[-1];  ]`

## MATLAB

Recursive

`function mid = binarySearchRec(list,value,low,high)     if( high < low )        mid = [];        return    end     mid = floor((low + high)/2);     if( list(mid) > value )        mid = binarySearchRec(list,value,low,mid-1);        return    elseif( list(mid) < value )        mid = binarySearchRec(list,value,mid+1,high);        return    else        return    end end`

Sample Usage:

`>> binarySearchRec([1 2 3 4 5 6 6.5 7 8 9 11 18],6.5,1,numel([1 2 3 4 5 6 6.5 7 8 9 11 18])) ans =      7`

Iterative

`function mid = binarySearchIter(list,value)     low = 1;    high = numel(list) - 1;     while( low <= high )        mid = floor((low + high)/2);         if( list(mid) > value )            high = mid - 1;        elseif( list(mid) < value )        	low = mid + 1;        else            return        end    end     mid = []; end`

Sample Usage:

`>> binarySearchIter([1 2 3 4 5 6 6.5 7 8 9 11 18],6.5) ans =      7`

## Maxima

`find(L, n) := block([i: 1, j: length(L), k, p],    if n < L[i] or n > L[j] then 0 else (        while j - i > 0 do (            k: quotient(i + j, 2),            p: L[k],            if n < p then j: k - 1 elseif n > p then i: k + 1 else i: j: k        ),        if n = L[i] then i else 0    ))\$ ".."(a, b) := if a < b then makelist(i, i, a, b) else makelist(i, i, a, b, -1)\$infix("..")\$ a: sublist(1 .. 1000, primep)\$ find(a, 27);0find(a, 421);82`

## MAXScript

Iterative

`fn binarySearchIterative arr value =(    lower = 1    upper = arr.count    while lower <= upper do    (        mid = (lower + upper) / 2        if arr[mid] > value then        (            upper = mid - 1        )        else if arr[mid] < value then        (            lower = mid + 1        )        else        (            return mid        )    )    -1) arr = #(1, 3, 4, 5, 6, 7, 8, 9, 10)result = binarySearchIterative arr 6`

Recursive

`fn binarySearchRecursive arr value lower upper =(    if lower == upper then    (        if arr[lower] == value then        (            return lower        )        else        (            return -1        )    )    mid = (lower + upper) / 2    if arr[mid] > value then    (        return binarySearchRecursive arr value lower (mid-1)    )    else if arr[mid] < value then    (        return binarySearchRecursive arr value (mid+1) upper    )    else    (        return mid    )) arr = #(1, 3, 4, 5, 6, 7, 8, 9, 10)result = binarySearchRecursive arr 6 1 arr.count`

## MiniScript

Recursive:

`binarySearch = function(A, value, low, high)    if high < low then return null    mid = floor((low + high) / 2)    if A[mid] > value then return binarySearch(A, value, low, mid-1)    if A[mid] < value then return binarySearch(A, value, mid+1, high)    return midend function`

Iterative:

`binarySearch = function(A, value)    low = 0    high = A.len - 1    while true        if high < low then return null        mid = floor((low + high) / 2)        if A[mid] > value then            high = mid - 1        else if A[mid] < value then            low = mid + 1        else            return mid        end if    end whileend function`

## N/t/roff

Works with: GNU TROFF version 1.22.2
`.de end...de array.	nr \\\$1.c 0 1.	de \\\$1.push end.		nr \\\$1..\\\\n+[\\\$1.c] \\\\\$1.	end.	de \\\$1.pushln end.		if \\\\n(.\$>0 .\\\$1.push \\\\\$1.		if \\\\n(.\$>1 \{ \.			shift.			\\\$1.pushln \\\\[email protected]\}.	end....de binarysearch.	nr min 1.	nr max \\n[\\\$1.c].	nr guess \\n[min]+\\n[max]/2.	while !\\n[\\\$1..\\n[guess]]=\\\$2 \{ \.		ie \\n[\\\$1..\\n[guess]]<\\\$2 .nr min \\n[guess]+1.		el .nr max \\n[guess]-1..		if \\n[min]>\\n[max] \{.			nr guess 0.			break.		\}.		nr guess \\n[min]+\\n[max]/2.	\}\\n[guess]...array a.a.pushln 1 4 9 16 25 36 49 64 81 100 121 144.binarysearch a 100.br.ie \n[guess]=0 The item \fBdoesn't exist\fP..el The item \fBdoes exist\fP. `

## Nim

Library

`import algorithm let s = @[2,3,4,5,6,7,8,9,10,12,14,16,18,20,22,25,27,30]echo binarySearch(s, 10)`

Iterative (from the standard library)

`proc binarySearch[T](a: openArray[T], key: T): int =  var b = len(a)  while result < b:    var mid = (result + b) div 2    if a[mid] < key: result = mid + 1    else: b = mid  if result >= len(a) or a[result] != key: result = -1`

## Niue

Library

`1 2 3 4 53 bsearch . ( => 2 )5 bsearch . ( => 0 )'sam 'tom 'kenny ( must be sorted before calling bsearch ) sort.s ( => kenny sam tom )'sam bsearch . ( => 1 )'tom bsearch . ( => 0 )'kenny bsearch . ( => 2 )'tony bsearch . ( => -1)`

## Objeck

Iterative

`use Structure; bundle Default {  class BinarySearch {    function : Main(args : String[]) ~ Nil {      values := [-1, 3, 8, 13, 22];      DoBinarySearch(values, 13)->PrintLine();      DoBinarySearch(values, 7)->PrintLine();    }     function : native : DoBinarySearch(values : Int[], value : Int) ~ Int {      low := 0;      high := values->Size() - 1;       while(low <= high) {        mid := (low + high) / 2;         if(values[mid] > value) {          high := mid - 1;        }        else if(values[mid] < value) {          low := mid + 1;        }        else {          return mid;        };      };       return -1;    }  }}`

## Objective-C

Iterative

`#import <Foundation/Foundation.h> @interface NSArray (BinarySearch)// Requires all elements of this array to implement a -compare: method which// returns a NSComparisonResult for comparison.// Returns NSNotFound when not found- (NSInteger) binarySearch:(id)key;@end @implementation NSArray (BinarySearch)- (NSInteger) binarySearch:(id)key {  NSInteger lo = 0;  NSInteger hi = [self count] - 1;  while (lo <= hi) {    NSInteger mid = lo + (hi - lo) / 2;    id midVal = self[mid];    switch ([midVal compare:key]) {    case NSOrderedAscending:      lo = mid + 1;      break;    case NSOrderedDescending:      hi = mid - 1;      break;    case NSOrderedSame:      return mid;    }  }  return NSNotFound;}@end int main(){  @autoreleasepool {     NSArray *a = @[@1, @3, @4, @5, @6, @7, @8, @9, @10];    NSLog(@"6 is at position %d", [a binarySearch:@6]); // prints 4   }  return 0;}`

Recursive

`#import <Foundation/Foundation.h> @interface NSArray (BinarySearchRecursive)// Requires all elements of this array to implement a -compare: method which// returns a NSComparisonResult for comparison.// Returns NSNotFound when not found- (NSInteger) binarySearch:(id)key inRange:(NSRange)range;@end @implementation NSArray (BinarySearchRecursive)- (NSInteger) binarySearch:(id)key inRange:(NSRange)range {  if (range.length == 0)    return NSNotFound;  NSInteger mid = range.location + range.length / 2;  id midVal = self[mid];  switch ([midVal compare:key]) {  case NSOrderedAscending:    return [self binarySearch:key                      inRange:NSMakeRange(mid + 1, NSMaxRange(range) - (mid + 1))];  case NSOrderedDescending:    return [self binarySearch:key                      inRange:NSMakeRange(range.location, mid - range.location)];  default:    return mid;  }}@end int main(){  @autoreleasepool {     NSArray *a = @[@1, @3, @4, @5, @6, @7, @8, @9, @10];    NSLog(@"6 is at position %d", [a binarySearch:@6]); // prints 4   }  return 0;}`

Library

Works with: Mac OS X version 10.6+
`#import <Foundation/Foundation.h> int main(){  @autoreleasepool {     NSArray *a = @[@1, @3, @4, @5, @6, @7, @8, @9, @10];    NSLog(@"6 is at position %lu", [a indexOfObject:@6                                      inSortedRange:NSMakeRange(0, [a count])                                            options:0                                    usingComparator:^(id x, id y){ return [x compare: y]; }]); // prints 4   }  return 0;}`

Using Core Foundation (part of Cocoa, all versions):

`#import <Foundation/Foundation.h> CFComparisonResult myComparator(const void *x, const void *y, void *context) {  return [(__bridge id)x compare:(__bridge id)y];} int main(int argc, const char *argv[]) {  @autoreleasepool {     NSArray *a = @[@1, @3, @4, @5, @6, @7, @8, @9, @10];    NSLog(@"6 is at position %ld", CFArrayBSearchValues((__bridge CFArrayRef)a,                                                        CFRangeMake(0, [a count]),                                                        (__bridge const void *)@6,                                                        myComparator,                                                        NULL)); // prints 4   }  return 0;}`

## OCaml

Recursive

`let rec binary_search a value low high =  if high = low then    if a.(low) = value then      low    else      raise Not_found  else let mid = (low + high) / 2 in    if a.(mid) > value then      binary_search a value low (mid - 1)    else if a.(mid) < value then      binary_search a value (mid + 1) high    else      mid`

Output:

```# let arr = [|1; 3; 4; 5; 6; 7; 8; 9; 10|];;
val arr : int array = [|1; 3; 4; 5; 6; 7; 8; 9; 10|]
# binary_search arr 6 0 (Array.length arr - 1);;
- : int = 4
# binary_search arr 2 0 (Array.length arr - 1);;
Exception: Not_found.
```

OCaml supports proper tail-recursion; so this is effectively the same as iteration.

## Octave

Recursive

`function i = binsearch_r(array, val, low, high)  if ( high < low )    i = 0;  else    mid = floor((low + high) / 2);    if ( array(mid) > val )      i = binsearch_r(array, val, low, mid-1);    elseif ( array(mid) < val )       i = binsearch_r(array, val, mid+1, high);    else      i = mid;    endif  endifendfunction`

Iterative

`function i = binsearch(array, value)  low = 1;  high = numel(array);  i = 0;  while ( low <= high )    mid = floor((low + high)/2);    if (array(mid) > value)       high = mid - 1;    elseif (array(mid) < value)      low = mid + 1;    else      i = mid;      return;    endif  endwhileendfunction`

Example of using

`r = sort(discrete_rnd(10, [1:10], ones(10,1)/10));disp(r);binsearch_r(r, 5, 1, numel(r))binsearch(r, 5)`

## Ol

` (define (binary-search value vector)   (let helper ((low 0)                (high (- (vector-length vector) 1)))      (unless (< high low)         (let ((middle (quotient (+ low high) 2)))            (cond               ((> (vector-ref vector middle) value)                  (helper low (- middle 1)))               ((< (vector-ref vector middle) value)                  (helper (+ middle 1) high))               (else middle)))))) (print   (binary-search 12 [1 2 3 4 5 6 7 8 9 10 11 12 13])); ==> 12 `

## ooRexx

` data = .array~of(1, 3, 5, 7, 9, 11)-- search keys with a number of edge casessearchkeys = .array~of(0, 1, 4, 7, 11, 12)say "recursive binary search"loop key over searchkeys    pos = recursiveBinarySearch(data, key)    if pos == 0 then say "Key" key "not found"    else say "Key" key "found at postion" posendsaysay "iterative binary search"loop key over searchkeys    pos = iterativeBinarySearch(data, key)    if pos == 0 then say "Key" key "not found"    else say "Key" key "found at postion" posend ::routine recursiveBinarySearch  -- NB:  Rexx arrays are 1-based  use strict arg data, value, low = 1, high = (data~items)   -- make sure we don't go beyond the bounds  high = min(high, data~items)  -- zero indicates not found  if high < low then return 0   mid = (low + high) % 2  if data[mid] > value then      return recursiveBinarySearch(data, value, low, mid - 1)  else if data[mid] < value then      return recursiveBinarySearch(data, value, mid + 1, high)  -- got it!  return mid ::routine iterativeBinarySearch  -- NB:  Rexx arrays are 1-based  use strict arg data, value, low = 1, high = (data~items)   -- make sure we don't go beyond the bounds  high = min(high, data~items)  -- zero indicates not found  if high < low then return 0  loop while low <= high      mid = (low + high) % 2      if data[mid] > value then          high = mid - 1      else if data[mid] < value then          low = mid + 1      else          return mid  end  return 0 `

Output:

```recursive binary search
Key 1 found at postion 1
Key 7 found at postion 4
Key 11 found at postion 6

iterative binary search
Key 1 found at postion 1
Key 7 found at postion 4
Key 11 found at postion 6
```

## Oz

Recursive

`declare  fun {BinarySearch Arr Val}     fun {Search Low High}        if Low > High then nil        else           Mid = (Low+High) div 2        in           if Val < Arr.Mid then {Search Low Mid-1}           elseif Val > Arr.Mid then {Search Mid+1 High}           else [Mid]           end        end     end  in     {Search {Array.low Arr} {Array.high Arr}}  end   A = {Tuple.toArray unit(2 3 5 6 8)}in  {System.printInfo "searching 4: "} {Show {BinarySearch A 4}}  {System.printInfo "searching 8: "} {Show {BinarySearch A 8}}`

Iterative

`declare  fun {BinarySearch Arr Val}     Low = {NewCell {Array.low Arr}}     High = {NewCell {Array.high Arr}}  in     for while:@Low =< @High  return:Return  default:nil do        Mid = (@Low + @High) div 2     in        if Val < Arr.Mid then High := Mid-1        elseif Val > Arr.Mid then Low := Mid+1        else {Return [Mid]}        end     end  end   A = {Tuple.toArray unit(2 3 5 6 8)}in  {System.printInfo "searching 4: "} {Show {BinarySearch A 4}}  {System.printInfo "searching 8: "} {Show {BinarySearch A 8}}`

## PARI/GP

Note that, despite the name, `setsearch` works on sorted vectors as well as sets.

`setsearch(s, n)`

The following is another implementation that takes a more manual approach. Instead of using an intrinsic function, a general binary search algorithm is implemented using the language alone.

Translation of: N/t/roff
`binarysearch(v, x) = {    local(        minm = 1,        maxm = length(v),        guess = floor(maxm/2+minm/2)    );     while(v[guess] != x,            if(v[guess] < x, minm = guess + 1, maxm = guess - 1);        if(minm > maxm,            guess = 0;            break        );        guess = floor(maxm/2+minm/2)    );     return(guess);} idx = binarysearch([1,4,9,16,25,36,49,64,81,100,121,144], 121);if(idx, \    print("Item exists on index ", idx), \    print("Item does not exist anywhere.") \)`

## Pascal

Iterative

`function binary_search(element: real; list: array of real): integer;var    l, m, h: integer;begin    l := Low(list);    h := High(list);    binary_search := -1;    while l <= h do    begin        m := (l + h) div 2;        if list[m] > element then        begin            h := m - 1;        end        else if list[m] < element then        begin            l := m + 1;        end        else        begin            binary_search := m;            break;        end;    end;end;`

Usage:

`var    list: array[0 .. 9] of real;// ...indexof := binary_search(123, list);`

## Perl

Iterative

`sub binary_search {    my (\$array_ref, \$value, \$left, \$right) = @_;    while (\$left <= \$right) {        my \$middle = int((\$right + \$left) >> 1);        if (\$value == \$array_ref->[\$middle]) {            return \$middle;        }        elsif (\$value < \$array_ref->[\$middle]) {            \$right = \$middle - 1;        }        else {            \$left = \$middle + 1;        }    }    return -1;}`

Recursive

`sub binary_search {    my (\$array_ref, \$value, \$left, \$right) = @_;    return -1 if (\$right < \$left);    my \$middle = int((\$right + \$left) >> 1);    if (\$value == \$array_ref->[\$middle]) {        return \$middle;    }    elsif (\$value < \$array_ref->[\$middle]) {        binary_search(\$array_ref, \$value, \$left, \$middle - 1);    }    else {        binary_search(\$array_ref, \$value, \$middle + 1, \$right);    }}`

## Phix

Standard autoinclude builtin/bsearch.e, reproduced here

```global function binary_search(object needle, sequence haystack)
integer lo = 1,
hi = length(haystack),
mid = lo,
c = 0

while lo<=hi do
mid = floor((lo+hi)/2)
c = compare(needle, haystack[mid])
if c<0 then
hi = mid-1
elsif c>0 then
lo = mid+1
else
return mid  -- found!
end if
end while
mid += c>0
return -mid         -- where it would go, if inserted now
end function
```

The low + (high-low)/2 trick is not needed, since interim integer results are accurate to 53 bits (on 32 bit, 64 bits on 64 bit) on Phix.

Returns a positive index if found, otherwise the negative index where it would go if inserted now. Example use

`?binary_search(0,{1,3,5})   -- -1?binary_search(1,{1,3,5})   --  1?binary_search(2,{1,3,5})   -- -2?binary_search(3,{1,3,5})   --  2?binary_search(4,{1,3,5})   -- -3?binary_search(5,{1,3,5})   --  3?binary_search(6,{1,3,5})   -- -4`

## PHP

Iterative

`function binary_search( \$array, \$secret, \$start, \$end ){        do        {                \$guess = (int)(\$start + ( ( \$end - \$start ) / 2 ));                 if ( \$array[\$guess] > \$secret )                        \$end = \$guess;                 if ( \$array[\$guess] < \$secret )                        \$start = \$guess;                 if ( \$end < \$start)                        return -1;         } while ( \$array[\$guess] != \$secret );         return \$guess;}`

Recursive

`function binary_search( \$array, \$secret, \$start, \$end ){        \$guess = (int)(\$start + ( ( \$end - \$start ) / 2 ));         if ( \$end < \$start)                return -1;         if ( \$array[\$guess] > \$secret )                return (binary_search( \$array, \$secret, \$start, \$guess ));         if ( \$array[\$guess] < \$secret )                return (binary_search( \$array, \$secret, \$guess, \$end ) );         return \$guess;}`

## PicoLisp

Recursive

`(de recursiveSearch (Val Lst Len)   (unless (=0 Len)      (let (N (inc (/ Len 2))  L (nth Lst N))         (cond            ((= Val (car L)) Val)            ((> Val (car L))               (recursiveSearch Val (cdr L) (- Len N)) )            (T (recursiveSearch Val Lst (dec N))) ) ) ) )`

Output:

```: (recursiveSearch 5 (2 3 5 8 "abc" "klm" "xyz" (7) (a b)) 9)
-> 5
: (recursiveSearch '(a b) (2 3 5 8 "abc" "klm" "xyz" (7) (a b)) 9)
-> (a b)
: (recursiveSearch (9) (2 3 5 8 "abc" "klm" "xyz" (7) (a b)) 9)
-> NIL```

Iterative

`(de iterativeSearch (Val Lst Len)   (use (N L)      (loop         (T (=0 Len))         (setq            N (inc (/ Len 2))            L (nth Lst N) )         (T (= Val (car L)) Val)         (if (> Val (car L))            (setq Lst (cdr L)  Len (- Len N))            (setq Len (dec N)) ) ) ) )`

Output:

```: (iterativeSearch 5 (2 3 5 8 "abc" "klm" "xyz" (7) (a b)) 9)
-> 5
: (iterativeSearch '(a b) (2 3 5 8 "abc" "klm" "xyz" (7) (a b)) 9)
-> (a b)
: (iterativeSearch (9) (2 3 5 8 "abc" "klm" "xyz" (7) (a b)) 9)
-> NIL```

## PL/I

`/* A binary search of list A for element M */search: procedure (A, M) returns (fixed binary);   declare (A(*), M) fixed binary;   declare (l, r, mid) fixed binary;    l = lbound(a,1)-1; r = hbound(A,1)+1;   do while (l <= r);      mid = (l+r)/2;      if A(mid) = M then return (mid);      if A(mid) < M then         L = mid+1;      else         R = mid-1;   end;   return (lbound(A,1)-1);end search;`

## Pop11

Iterative

`define BinarySearch(A, value);    lvars low = 1, high = length(A), mid;    while low <= high do        (low + high) div 2 -> mid;        if A(mid) > value then            mid - 1 -> high;        elseif A(mid) < value then            mid + 1 -> low;        else            return(mid);        endif;    endwhile;    return("not_found");enddefine; /* Tests */lvars A = {2 3 5 6 8}; BinarySearch(A, 4) =>BinarySearch(A, 5) =>BinarySearch(A, 8) =>`

Recursive

`define BinarySearch(A, value);    define do_it(low, high);        if high < low then            return("not_found");        endif;        (low + high) div 2 -> mid;        if A(mid) > value then            do_it(low, mid-1);        elseif A(mid) < value then            do_it(mid+1, high);        else            mid;        endif;    enddefine;    do_it(1, length(A));enddefine;`

## PowerShell

` function BinarySearch-Iterative ([int[]]\$Array, [int]\$Value){    [int]\$low = 0    [int]\$high = \$Array.Count - 1     while (\$low -le \$high)    {        [int]\$mid = (\$low + \$high) / 2         if (\$Array[\$mid] -gt \$Value)        {            \$high = \$mid - 1        }        elseif (\$Array[\$mid] -lt \$Value)        {            \$low = \$mid + 1        }        else        {            return \$mid        }    }     return -1} function BinarySearch-Recursive ([int[]]\$Array, [int]\$Value, [int]\$Low = 0, [int]\$High = \$Array.Count){    if (\$High -lt \$Low)    {        return -1    }     [int]\$mid = (\$Low + \$High) / 2     if (\$Array[\$mid] -gt \$Value)    {        return BinarySearch \$Array \$Value \$Low (\$mid - 1)    }    elseif (\$Array[\$mid] -lt \$Value)    {        return BinarySearch \$Array \$Value (\$mid + 1) \$High    }    else    {        return \$mid    }} function Show-SearchResult ([int[]]\$Array, [int]\$Search, [ValidateSet("Iterative", "Recursive")][string]\$Function){    switch (\$Function)    {        "Iterative" {\$index = BinarySearch-Iterative -Array \$Array -Value \$Search}        "Recursive" {\$index = BinarySearch-Recursive -Array \$Array -Value \$Search}    }     if (\$index -ge 0)    {        Write-Host ("Using BinarySearch-{0}: {1} is at index {2}" -f \$Function, \$numbers[\$index], \$index)    }    else    {        Write-Host ("Using BinarySearch-{0}: {1} not found" -f \$Function, \$Search) -ForegroundColor Red    }} `
` Show-SearchResult -Array 10, 28, 41, 46, 58, 74, 76, 86, 89, 98 -Search 41 -Function IterativeShow-SearchResult -Array 10, 28, 41, 46, 58, 74, 76, 86, 89, 98 -Search 99 -Function IterativeShow-SearchResult -Array 10, 28, 41, 46, 58, 74, 76, 86, 89, 98 -Search 86 -Function RecursiveShow-SearchResult -Array 10, 28, 41, 46, 58, 74, 76, 86, 89, 98 -Search 11 -Function Recursive `
Output:
```Using BinarySearch-Iterative: 41 is at index 2
Using BinarySearch-Recursive: 86 is at index 7
```

## Prolog

Tested with Gnu-Prolog.

`bin_search(Elt,List,Result):-  length(List,N), bin_search_inner(Elt,List,1,N,Result). bin_search_inner(Elt,List,J,J,J):-  nth(J,List,Elt).bin_search_inner(Elt,List,Begin,End,Mid):-  Begin < End,  Mid is (Begin+End) div 2,  nth(Mid,List,Elt).bin_search_inner(Elt,List,Begin,End,Result):-  Begin < End,  Mid is (Begin+End) div 2,  nth(Mid,List,MidElt),  MidElt < Elt,  NewBegin is Mid+1,  bin_search_inner(Elt,List,NewBegin,End,Result).bin_search_inner(Elt,List,Begin,End,Result):-  Begin < End,  Mid is (Begin+End) div 2,  nth(Mid,List,MidElt),  MidElt > Elt,  NewEnd is Mid-1,  bin_search_inner(Elt,List,Begin,NewEnd,Result).`
Output examples:
``` ?- bin_search(4,[1,2,4,8,16,32,64,128],Result).
Result = 3.

?- bin_search(5,[1,2,4,8],Result).
Result = -1.```

## PureBasic

Both recursive and iterative procedures are included and called in the code below.

`#Recursive = 0 ;recursive binary search method#Iterative = 1 ;iterative binary search method#NotFound = -1 ;search result if item not found ;RecursiveProcedure  R_BinarySearch(Array a(1), value, low, high)  Protected mid  If high < low    ProcedureReturn #NotFound  EndIf    mid = (low + high) / 2  If a(mid) > value    ProcedureReturn R_BinarySearch(a(), value, low, mid - 1)  ElseIf a(mid) < value    ProcedureReturn R_BinarySearch(a(), value, mid + 1, high)  Else    ProcedureReturn mid  EndIf EndProcedure ;IterativeProcedure I_BinarySearch(Array a(1), value, low, high)  Protected mid  While low <= high    mid = (low + high) / 2    If a(mid) > value                  high = mid - 1    ElseIf a(mid) < value      low = mid + 1    Else      ProcedureReturn mid    EndIf  Wend   ProcedureReturn #NotFoundEndProcedure Procedure search (Array a(1), value, method)  Protected idx   Select method    Case #Iterative      idx = I_BinarySearch(a(), value, 0, ArraySize(a()))    Default      idx = R_BinarySearch(a(), value, 0, ArraySize(a()))  EndSelect   Print("  Value " + Str(Value))  If idx < 0    PrintN(" not found")  Else    PrintN(" found at index " + Str(idx))  EndIfEndProcedure  #NumElements = 9 ;zero based countDim test(#NumElements) DataSection  Data.i 2, 3, 5, 6, 8, 10, 11, 15, 19, 20EndDataSection ;fill the test arrayFor i = 0 To #NumElements		  Read test(i)Next  If OpenConsole()   PrintN("Recursive search:")  search(test(), 4, #Recursive)  search(test(), 8, #Recursive)  search(test(), 20, #Recursive)   PrintN("")  PrintN("Iterative search:")  search(test(), 4, #Iterative)  search(test(), 8, #Iterative)  search(test(), 20, #Iterative)   Print(#CRLF\$ + #CRLF\$ + "Press ENTER to exit")  Input()  CloseConsole()EndIf`

Sample output:

```Recursive search:
Value 8 found at index 4
Value 20 found at index 9

Iterative search:
Value 8 found at index 4
Value 20 found at index 9
```

## Python

### Python: Iterative

`def binary_search(l, value):    low = 0    high = len(l)-1    while low <= high:         mid = (low+high)//2        if l[mid] > value: high = mid-1        elif l[mid] < value: low = mid+1        else: return mid    return -1`

We can also generalize this kind of binary search from direct matches to searches using a custom comparator function. In addition to a search for a particular word in an AZ-sorted list, for example, we could also perform a binary search for a word of a given length (in a word-list sorted by rising length), or for a particular value of any other comparable property of items in a suitably sorted list:

`# findIndexBinary :: (a -> Ordering) -> [a] -> Maybe Intdef findIndexBinary(p):    def isFound(bounds):        (lo, hi) = bounds        return lo > hi or 0 == hi     def half(xs):        def choice(lh):            (lo, hi) = lh            mid = (lo + hi) // 2            cmpr = p(xs[mid])            return (lo, mid - 1) if cmpr < 0 else (                (1 + mid, hi) if cmpr > 0 else (                    mid, 0                )            )        return lambda bounds: choice(bounds)     def go(xs):        (lo, hi) = until(isFound)(            half(xs)        )((0, len(xs) - 1)) if xs else None        return None if 0 != hi else lo     return lambda xs: go(xs)  # COMPARISON CONSTRUCTORS --------------------------------- # compare :: a -> a -> Orderingdef compare(a):    '''Simple comparison of x and y -> LT|EQ|GT'''    return lambda b: -1 if a < b else (1 if a > b else 0)  # byKV :: (a -> b) -> a -> a -> Orderingdef byKV(f):    '''Property accessor function -> target value -> x -> LT|EQ|GT'''    def go(v, x):        fx = f(x)        return -1 if v < fx else 1 if v > fx else 0    return lambda v: lambda x: go(v, x)  # TESTS ---------------------------------------------------def main():     # BINARY SEARCH FOR WORD IN AZ-SORTED LIST     mb1 = findIndexBinary(compare('iota'))(        # Sorted AZ        ['alpha', 'beta', 'delta', 'epsilon', 'eta', 'gamma', 'iota',         'kappa', 'lambda', 'mu', 'theta', 'zeta']    )     print (        'Not found' if None is mb1 else (            'Word found at index ' + str(mb1)        )    )     # BINARY SEARCH FOR WORD OF GIVEN LENGTH (IN WORD-LENGTH SORTED LIST)     mb2 = findIndexBinary(byKV(len)(7))(        # Sorted by rising length        ['mu', 'eta', 'beta', 'iota', 'zeta', 'alpha', 'delta', 'gamma',         'kappa', 'theta', 'lambda', 'epsilon']    )     print (        'Not found' if None is mb2 else (            'Word of given length found at index ' + str(mb2)        )    )  # GENERIC ------------------------------------------------- # until :: (a -> Bool) -> (a -> a) -> a -> adef until(p):    def go(f, x):        v = x        while not p(v):            v = f(v)        return v    return lambda f: lambda x: go(f, x)  if __name__ == '__main__':    main() `
Output:
```Word found at index 6
Word of given length found at index 11```

### Python: Recursive

`def binary_search(l, value, low = 0, high = -1):    if not l: return -1    if(high == -1): high = len(l)-1    if low >= high:        if l[low] == value: return low        else: return -1    mid = (low+high)//2    if l[mid] > value: return binary_search(l, value, low, mid-1)    elif l[mid] < value: return binary_search(l, value, mid+1, high)    else: return mid`

Generalizing again with a custom comparator function (see preamble to second iterative version above).

This time using the recursive definition:

`# findIndexBinary_ :: (a -> Ordering) -> [a] -> Maybe Intdef findIndexBinary_(p):    def go(xs):        def bin(lo, hi):            if hi < lo:                return None            else:                mid = (lo + hi) // 2                cmpr = p(xs[mid])                return bin(lo, mid - 1) if -1 == cmpr else (                    bin(mid + 1, hi) if 1 == cmpr else (                        mid                    )                )        n = len(xs)        return bin(0, n - 1) if 0 < n else None    return lambda xs: go(xs)  # COMPARISON CONSTRUCTORS --------------------------------- # compare :: a -> a -> Orderingdef compare(a):    '''Simple comparison of x and y -> LT|EQ|GT'''    return lambda b: -1 if a < b else (1 if a > b else 0)  # byKV :: (a -> b) -> a -> a -> Orderingdef byKV(f):    '''Property accessor function -> target value -> x -> LT|EQ|GT'''    def go(v, x):        fx = f(x)        return -1 if v < fx else 1 if v > fx else 0    return lambda v: lambda x: go(v, x)  # TESTS ---------------------------------------------------  if __name__ == '__main__':     # BINARY SEARCH FOR WORD IN AZ-SORTED LIST     mb1 = findIndexBinary_(compare('mu'))(        # Sorted AZ        ['alpha', 'beta', 'delta', 'epsilon', 'eta', 'gamma', 'iota',         'kappa', 'lambda', 'mu', 'theta', 'zeta']    )     print (        'Not found' if None is mb1 else (            'Word found at index ' + str(mb1)        )    )     # BINARY SEARCH FOR WORD OF GIVEN LENGTH (IN WORD-LENGTH SORTED LIST)     mb2 = findIndexBinary_(byKV(len)(6))(        # Sorted by rising length        ['mu', 'eta', 'beta', 'iota', 'zeta', 'alpha', 'delta', 'gamma',         'kappa', 'theta', 'lambda', 'epsilon']    )     print (        'Not found' if None is mb2 else (            'Word of given length found at index ' + str(mb2)        )    )`
Output:
```Word found at index 9
Word of given length found at index 10```

### Python: Library

Python's `bisect` module provides binary search functions

`index = bisect.bisect_left(list, item) # leftmost insertion pointindex = bisect.bisect_right(list, item) # rightmost insertion pointindex = bisect.bisect(list, item) # same as bisect_right # same as above but actually insert the item into the list at the given place:bisect.insort_left(list, item)bisect.insort_right(list, item)bisect.insort(list, item)`

#### Python: Alternate

Complete binary search function with python's `bisect` module:

`from bisect import bisect_left def binary_search(a, x, lo=0, hi=None):   # can't use a to specify default for hi    hi = hi if hi is not None else len(a) # hi defaults to len(a)       pos = bisect_left(a,x,lo,hi)          # find insertion position    return (pos if pos != hi and a[pos] == x else -1) # don't walk off the end`

### Python: Approximate binary search

Returns the nearest item of list l to value.

`def binary_search(l, value):    low = 0    high = len(l)-1    while low + 1 < high:        mid = (low+high)//2        if l[mid] > value:            high = mid        elif l[mid] < value:            low = mid        else:            return mid    return high if abs(l[high] - value) < abs(l[low] - value) else low`

## R

Recursive

`BinSearch <- function(A, value, low, high) {  if ( high < low ) {    return(NULL)  } else {    mid <- floor((low + high) / 2)    if ( A[mid] > value )      BinSearch(A, value, low, mid-1)    else if ( A[mid] < value )      BinSearch(A, value, mid+1, high)    else      mid  }}`

Iterative

`IterBinSearch <- function(A, value) {  low = 1  high = length(A)  i = 0  while ( low <= high ) {    mid <- floor((low + high)/2)    if ( A[mid] > value )      high <- mid - 1    else if ( A[mid] < value )      low <- mid + 1    else      return(mid)  }  NULL}`

Example

`a <- 1:100IterBinSearch(a, 50)BinSearch(a, 50, 1, length(a)) # output 50IterBinSearch(a, 101) # outputs NULL`

## Racket

` #lang racket(define (binary-search x v)  ; loop : index index -> index or #f  ;   return i s.t. l<=i<h and v[i]=x  (define (loop l h)    (cond [(>= l h) #f]          [else (define m (quotient (+ l h) 2))                (define y (vector-ref v m))                (cond                   [(> y x) (loop l (- m 1))]                  [(< y x) (loop (+ m 1) h)]                  [else m])]))  (loop 0 (vector-length v))) `

Examples:

```(binary-search 6 #(1 3 4 5 6 7 8 9 10))  ; gives 4
(binary-search 6 #(1 3 4 5 7 8 9 10))    ; gives #f
```

## Raku

(formerly Perl 6) With either of the below implementations of `binary_search`, one could write a function to search any object that does `Positional` this way:

`sub search (@a, \$x --> Int) {    binary_search { \$x cmp @a[\$^i] }, 0, @a.end}`

Iterative

Works with: Rakudo version 2015.12
`sub binary_search (&p, Int \$lo is copy, Int \$hi is copy --> Int) {    until \$lo > \$hi {        my Int \$mid = (\$lo + \$hi) div 2;        given p \$mid {            when -1 { \$hi = \$mid - 1; }             when  1 { \$lo = \$mid + 1; }            default { return \$mid;    }        }    }    fail;}`

Recursive

Works with: Rakudo version 2015.12
`sub binary_search (&p, Int \$lo, Int \$hi --> Int) {    \$lo <= \$hi or fail;    my Int \$mid = (\$lo + \$hi) div 2;    given p \$mid {        when -1 { binary_search &p, \$lo,      \$mid - 1 }         when  1 { binary_search &p, \$mid + 1, \$hi      }        default { \$mid                                 }    }}`

## REXX

### recursive version

Incidentally, REXX doesn't care if the values in the list are integers (or even numbers), as long as they're in order.

(includes the extra credit)

`/*REXX program finds a  value  in a  list of integers  using an iterative binary search.*/@=  3   7  13  19  23  31  43  47  61  73  83  89 103 109 113 131 139 151 167 181,  193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401 409 421 433,  443 449 463 467 491 503 509 523 547 571 577 601 619 643 647 661 677 683 691 709,  743 761 773 797 811 823 829 839 859 863 883 887 911 919 941 953 971 983 1013                                                 /* [↑]  a list of some low weak primes.*/parse arg ? .                                    /*get a  #  that's specified on the CL.*/if ?==''  then do;    say;       say '***error***  no argument specified.';       say                      exit                       /*stick a fork in it,  we're all done. */               end low= 1high= words(@) avg= (word(@, 1) + word(@, high)) / 2 loc= binarySearch(low, high) if loc==-1  then do;  say  ?  " wasn't found in the list."                      exit                       /*stick a fork in it,  we're all done. */                 end            else say  ?  ' is in the list, its index is: '   locsaysay  'arithmetic mean of the '   high   " values is: "       avgexit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/binarySearch:  procedure expose @ ?;     parse arg low,high               if high<low  then return -1       /*the item wasn't found in the @ list. */               mid= (low + high) % 2             /*calculate the midpoint in the list.  */               y= word(@, mid)                   /*obtain the midpoint value in the list*/               if ?=y       then return  mid               if y>?       then return  binarySearch(low,   mid-1)                                 return  binarySearch(mid+1, high)`
output   when using the input of:     499.1
```499.1  wasn't found in the list.
```
output   when using the input of:     499
```arithmetic mean of the  74  values is:  510

499  is in the list, its index is:  41
```

### iterative version

(includes the extra credit)

`/*REXX program finds a  value  in a  list of integers  using an iterative binary search.*/@=  3   7  13  19  23  31  43  47  61  73  83  89 103 109 113 131 139 151 167 181,  193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401 409 421 433,  443 449 463 467 491 503 509 523 547 571 577 601 619 643 647 661 677 683 691 709,  743 761 773 797 811 823 829 839 859 863 883 887 911 919 941 953 971 983 1013                                                 /* [↑]  a list of some low weak primes.*/parse arg ? .                                    /*get a  #  that's specified on the CL.*/if ?==''  then do;    say;       say '***error***  no argument specified.';       say                      exit 13               end low= 1high= words(@)say  'arithmetic mean of the '   high    " values is: "   (word(@, 1) + word(@, high)) / 2say               do  while  low<=high;     mid= (low + high) % 2;            y= word(@, mid)                if ?=y  then do;  say ?   ' is in the list, its index is: '    mid                                 exit            /*stick a fork in it,  we're all done. */                            end                if y>?  then high= mid - 1        /*too high?                            */                       else  low= mid + 1        /*too low?                             */               end   /*while*/ say  ?   " wasn't found in the list."            /*stick a fork in it,  we're all done. */`
output   when using the input of:     -314
```arithmetic mean of the  79  values is:  508

-314  wasn't found in the list.
```
output   when using the input of:     619
```arithmetic mean of the  79  values is:  508

619  is in the list, its index is:  53
```

## Ring

` decimals(0)array = [7, 14, 21, 28, 35, 42, 49, 56, 63, 70] find= 42index = where(array,find,0,len(array))if index >= 0    see "the value " + find+ " was found at index " + indexelse   see "the value " + find + " was not found"ok func where(a,s,b,t)     h = 2     while h<(t-b)           h *= 2     end     h /= 2     while h != 0           if (b+h)<=t              if s>=a[b+h]                 b += h              ok           ok           h /= 2     end     if s=a[b]        return b-1     else         return -1     ok `

Output:

```the value 42 was found at index 6
```

## Ruby

Recursive

`class Array  def binary_search(val, low=0, high=(length - 1))    return nil if high < low    mid = (low + high) >> 1    case val <=> self[mid]      when -1        binary_search(val, low, mid - 1)      when 1        binary_search(val, mid + 1, high)      else mid    end  endend ary = [0,1,4,5,6,7,8,9,12,26,45,67,78,90,98,123,211,234,456,769,865,2345,3215,14345,24324] [0,42,45,24324,99999].each do |val|  i = ary.binary_search(val)  if i    puts "found #{val} at index #{i}: #{ary[i]}"  else    puts "#{val} not found in array"  endend`

Iterative

`class Array  def binary_search_iterative(val)    low, high = 0, length - 1    while low <= high      mid = (low + high) >> 1      case val <=> self[mid]        when 1          low = mid + 1        when -1          high = mid - 1        else          return mid      end    end    nil  endend ary = [0,1,4,5,6,7,8,9,12,26,45,67,78,90,98,123,211,234,456,769,865,2345,3215,14345,24324] [0,42,45,24324,99999].each do |val|  i = ary.binary_search_iterative(val)  if i    puts "found #{val} at index #{i}: #{ary[i]}"  else    puts "#{val} not found in array"  endend`
Output:
```found 0 at index 0: 0
found 45 at index 10: 45
found 24324 at index 24: 24324
```

Built in Since Ruby 2.0, arrays ship with a binary search method "bsearch":

`haystack = [0,1,4,5,6,7,8,9,12,26,45,67,78,90,98,123,211,234,456,769,865,2345,3215,14345,24324]needles = [0,42,45,24324,99999] needles.select{|needle| haystack.bsearch{|hay| needle <=> hay} } # => [0, 45, 24324] `
Which is 60% faster than "needles & haystack".

## Run BASIC

Recursive

`dim theArray(100)global theArrayfor i = 1 to 100  theArray(i) = inext i print binarySearch(80,30,90) FUNCTION binarySearch(val, lo, hi)  IF hi < lo THEN    binarySearch = 0  ELSE    middle = (hi + lo) / 2    if val < theArray(middle) then binarySearch = binarySearch(val, lo, middle-1)    if val > theArray(middle) then binarySearch = binarySearch(val, middle+1, hi)    if val = theArray(middle) then binarySearch = middle  END IFEND FUNCTION`

## Rust

Iterative

`//edit to return desired value (the code has bool because usually you need to know whether the element exists or not) fn binary_search<T:PartialOrd>(v: &[T], searchvalue: T) -> bool {    let mut lower = 0 as usize;    let mut upper = v.len() - 1;     while upper >= lower {        let mid = (upper + lower) / 2;        if v[mid] == searchvalue {            return true;        } else if searchvalue < v[mid] {            upper = mid - 1;        } else {            lower = mid + 1;        }    }     return false;}`

## Scala

Recursive

`def binarySearch[A <% Ordered[A]](a: IndexedSeq[A], v: A) = {  def recurse(low: Int, high: Int): Option[Int] = (low + high) / 2 match {    case _ if high < low => None    case mid if a(mid) > v => recurse(low, mid - 1)    case mid if a(mid) < v => recurse(mid + 1, high)    case mid => Some(mid)  }  recurse(0, a.size - 1)}`

Iterative

`def binarySearch[T](xs: Seq[T], x: T)(implicit ordering: Ordering[T]): Option[Int] = {    var low: Int = 0    var high: Int = xs.size - 1     while (low <= high)      low + high >>> 1 match {        case guess if ordering.gt(xs(guess), x) => high = guess - 1 //too high        case guess if ordering.lt(xs(guess), x) => low = guess + 1 // too low        case guess => return Some(guess) //found it      }    None //not found  }`

Test

`def testBinarySearch(n: Int) = {  val odds = 1 to n by 2  val result = (0 to n).flatMap(binarySearch(odds, _))  assert(result == (0 until odds.size))  println(s"\$odds are odd natural numbers")  for (it <- result)    println(s"\$it is ordinal of \${odds(it)}")} def main() = testBinarySearch(12)`

Output:

```Range(1, 3, 5, 7, 9, 11) are odd natural numbers
0 is ordinal of 1
1 is ordinal of 3
2 is ordinal of 5
3 is ordinal of 7
4 is ordinal of 9
5 is ordinal of 11```

## Scheme

Recursive

`(define (binary-search value vector)  (let helper ((low 0)               (high (- (vector-length vector) 1)))    (if (< high low)        #f        (let ((middle (quotient (+ low high) 2)))          (cond ((> (vector-ref vector middle) value)                 (helper low (- middle 1)))                ((< (vector-ref vector middle) value)                 (helper (+ middle 1) high))                (else middle))))))`

Example:

```> (binary-search 6 '#(1 3 4 5 6 7 8 9 10))
4
> (binary-search 2 '#(1 3 4 5 6 7 8 9 10))
#f
```

The calls to helper are in tail position, so since Scheme implementations support proper tail-recursion the computation proces is iterative.

## Seed7

Iterative

`const func integer: binarySearchIterative (in array elemType: arr, in elemType: aKey) is func  result    var integer: result is 0;  local    var integer: low is 1;    var integer: high is 0;    var integer: middle is 0;  begin    high := length(arr);    while result = 0 and low <= high do      middle := low + (high - low) div 2;      if aKey < arr[middle] then        high := pred(middle);      elsif aKey > arr[middle] then        low := succ(middle);      else        result := middle;      end if;    end while;  end func;`

Recursive

`const func integer: binarySearch (in array elemType: arr, in elemType: aKey, in integer: low, in integer: high) is func  result    var integer: result is 0;  begin    if low <= high then      result := (low + high) div 2;      if aKey < arr[result] then        result := binarySearch(arr, aKey, low, pred(result)); # search left      elsif aKey > arr[result] then        result := binarySearch(arr, aKey, succ(result), high); # search right      end if;    end if;  end func; const func integer: binarySearchRecursive (in array elemType: arr, in elemType: aKey) is  return binarySearch(arr, aKey, 1, length(arr));`

## SequenceL

Recursive

`binarySearch(A(1), value(0), low(0), high(0)) :=	let		mid := low + (high - low) / 2;	in			-1 when high < low //Not Found		else			binarySearch(A, value, low, mid - 1) when A[mid] > value		else			binarySearch(A, value, mid + 1, high) when A[mid] < value		else			mid;`

## Sidef

Iterative:

`func binary_search(a, i) {     var l = 0    var h = a.end     while (l <= h) {        var mid = (h+l / 2 -> int)        a[mid] > i && (h = mid-1; next)        a[mid] < i && (l = mid+1; next)        return mid    }     return -1}`

Recursive:

`func binary_search(arr, value, low=0, high=arr.end) {    high < low && return -1    var middle = ((high+low) // 2)     given (arr[middle]) { |item|        case (value < item) {            binary_search(arr, value, low, middle-1)        }        case (value > item) {            binary_search(arr, value, middle+1, high)        }        case (value == item) {            middle        }    }}`

Usage:

`say binary_search([34, 42, 55, 778], 55);       #=> 2`

## Simula

`BEGIN      INTEGER PROCEDURE BINARYSEARCHREC(A, LVALUE);        INTEGER ARRAY A;        INTEGER LVALUE; ! VALUE IS A KEY WORD ;    BEGIN         INTEGER PROCEDURE SEARCH(LOW, HIGH);            INTEGER LOW, HIGH;        BEGIN            INTEGER MID;            ! INVARIANTS: VALUE > A[I] FOR ALL I < LOW                          VALUE < A[I] FOR ALL I > HIGH ;            MID := (LOW + HIGH) // 2;            SEARCH := IF HIGH < LOW THEN -LOW - 1                 ELSE IF A(MID) > LVALUE THEN SEARCH(LOW, MID-1)                 ELSE IF A(MID) < LVALUE THEN SEARCH(MID+1, HIGH)                 ELSE MID;        END SEARCH;         BINARYSEARCHREC := SEARCH(LOWERBOUND(A, 1), UPPERBOUND(A, 1));    END BINARYSEARCHREC;      INTEGER PROCEDURE BINARYSEARCH(A, LVALUE);        INTEGER ARRAY A;        INTEGER LVALUE; ! VALUE IS A KEY WORD ;    BEGIN        INTEGER LOW, HIGH, MID;        BOOLEAN FOUND;         LOW := LOWERBOUND(A, 1);        HIGH := UPPERBOUND(A, 1);        WHILE NOT FOUND AND LOW <= HIGH DO BEGIN            ! INVARIANTS: LVALUE > A(I) FOR ALL I < LOW                          LVALUE < A(I) FOR ALL I > HIGH ;            MID := (LOW + HIGH) // 2;            IF A(MID) > LVALUE THEN                HIGH := MID - 1            ELSE IF A(MID) < LVALUE THEN                LOW := MID + 1            ELSE                FOUND := TRUE;        END;        ! LVALUE WOULD BE INSERTED AT INDEX "LOW" ;        BINARYSEARCH := IF FOUND THEN MID ELSE -LOW - 1;    END BINARYSEARCH;      COMMENT ** CAUTION ** ONLY WORKS FOR ARRAY LOWER BOUND=0;    INTEGER ARRAY HAYSTACK(0:9);    INTEGER I, J, K, NEEDLE;     OUTTEXT("ARRAY = (");    I := LOWERBOUND(HAYSTACK, 1);    FOR J := 1, 6, 17, 29, 45, 78, 79, 87, 95, 100 DO BEGIN        HAYSTACK(I) := J;        OUTINT(HAYSTACK(I), 0);        IF I < UPPERBOUND(HAYSTACK, 1) THEN OUTTEXT(", ");        I := I + 1;    END;    OUTTEXT(")");    OUTIMAGE;    OUTIMAGE;     FOR NEEDLE:= 0, 1, 7, 17, 95, 99, 100, 101 DO BEGIN         OUTTEXT("LOOKUP RECURSIV ");        OUTINT(NEEDLE, 3);        OUTTEXT(" ... INDEX = ");        K := BINARYSEARCHREC(HAYSTACK, NEEDLE);        OUTINT(K, 3);        IF K < 0 THEN OUTTEXT(" NOT FOUND!");        OUTIMAGE;         OUTTEXT("LOOKUP ITERATIV ");        OUTINT(NEEDLE, 3);        OUTTEXT(" ... INDEX = ");        K := BINARYSEARCH(HAYSTACK, NEEDLE);        OUTINT(K, 3);        IF K < 0 THEN OUTTEXT(" NOT FOUND!");        OUTIMAGE;         OUTIMAGE;    END; END`
Output:
```ARRAY = (1, 6, 17, 29, 45, 78, 79, 87, 95, 100)

LOOKUP RECURSIV   1 ... INDEX =   0
LOOKUP ITERATIV   1 ... INDEX =   0

LOOKUP RECURSIV  17 ... INDEX =   2
LOOKUP ITERATIV  17 ... INDEX =   2

LOOKUP RECURSIV  95 ... INDEX =   8
LOOKUP ITERATIV  95 ... INDEX =   8

LOOKUP RECURSIV 100 ... INDEX =   9
LOOKUP ITERATIV 100 ... INDEX =   9

```

## SPARK

SPARK does not allow recursion, so only the iterative solution is provided. This example shows the use of a loop assertion.

All the code for this task validates with SPARK GPL 2010 and compiles and executes with GPS GPL 2010.

The Binary_Searches package is shown first. Search is a procedure, rather than a function, so that it can return a Found flag and a Position for Item, if found. This is better design than having a Position value that means 'item not found'.

There are two versions of the package provided, although the Ada code of the two versions is identical.

The first version has a postcondition that if Found is True the Position value returned is correct. This version also has a number of 'check' annotations. These are inserted to allow the Simplifier to prove all the verification conditions. See the SPARK Proof Process.

`package Binary_Searches is    subtype Item_Type is Integer; -- From specs.   subtype Index_Type is Integer range 1 .. 100;   type Array_Type is array (Index_Type range <>) of Item_Type;    procedure Search (Source   : in     Array_Type;                     Item     : in     Item_Type;                     Found    :     out Boolean;                     Position :     out Index_Type);   --# derives Found,   --#         Position from   --#            Source,   --#            Item;   --# post Found -> Source (Position) = Item;   -- If Found is False then Position is undefined. end Binary_Searches;  package body Binary_Searches is    procedure Search (Source   : in     Array_Type;                     Item     : in     Item_Type;                     Found    :     out Boolean;                     Position :     out Index_Type)   is      Lower      : Index_Type; -- Lower bound of Subrange.      Upper      : Index_Type; -- Upper bound of Subrange.      Terminated : Boolean;   begin      Found := False;      -- Default status updated on success.       Lower      := Source'First;      Upper      := Source'Last;      Position   := (Lower + Upper) / 2;      Terminated := False;       while not Terminated loop      --# assert Lower >= Source'First      --#  and   Upper <= Source'Last      --#  and   Position in Lower .. Upper      --#  and   not Found;         if Item < Source (Position) then            if Position = Lower then               -- No lower subrange.               Terminated := True;            else               --# check Position > Lower;               -- For the two following proofs.                --# check Position - 1 >= Lower;               --# check Lower + Position - 1 >= Lower * 2;               --# check (Lower + Position - 1) / 2 >= Lower;               -- For "Position >= Lower" in loop assertion.                --# check Lower < Position;               --# check Lower + Position - 1 <= (Position - 1) * 2;               --# check (Lower + Position - 1) / 2 <= (Position - 1);               -- For "Position <= Upper" in loop assertion.                -- Switch to lower half subrange.               Upper := Position - 1;               Position := (Lower + Upper) / 2;            end if;          elsif Item > Source (Position) then            if Position = Upper then               -- No upper subrange.               Terminated := True;            else               --# check Position < Upper;               -- For the two following proofs.                --# check Upper >= Position + 1;               --# check Position + 1 + Upper >= (Position + 1) * 2;               --# check (Position + 1 + Upper) / 2 >= (Position + 1);               -- For "Position >= Lower" in loop assertion.                --# check Position + 1 <= Upper;               --# check Position + 1 + Upper <= Upper * 2;               --# check (Position + 1 + Upper) / 2 <= Upper;               -- For "Position <= Upper" in loop assertion.                -- Switch to upper half subrange.               Lower := Position + 1;               Position := (Lower + Upper) / 2;            end if;         else            Found      := True;            Terminated := True;         end if;      end loop;   end Search; end Binary_Searches;`

The second version of the package has a stronger postcondition on Search, which also states that if Found is False then there is no value in Source equal to Item. This postcondition cannot be proved without a precondition that Source is ordered. This version needs four user rules (see the SPARK Proof Process) to be provided to the Simplifier so that it can prove all the verification conditions.

`package Binary_Searches is    subtype Item_Type is Integer; -- From specs.   subtype Index_Type is Integer range 1 .. 100;   type Array_Type is array (Index_Type range <>) of Item_Type;    --  Ordered_Between is a 'proof function'.  It does not have a code   --  body, but its meaning is defined by a proof rule:   --   --    Ordered_Between (Source, Low_Bound, High_Bound)   --      <->   --    for all I in Index_Type range Low_Bound .. High_Bound - 1 =>   --             (Source(I) < Source(I + 1)) ;   --   --# function Ordered_Between (Source               : Array_Type;   --#                           Range_From, Range_To : Index_Type)   --#    return Boolean;    procedure Search (Source   : in     Array_Type;                     Item     : in     Item_Type;                     Found    :     out Boolean;                     Position :     out Index_Type);   --# derives Found,   --#         Position from   --#            Source,   --#            Item;   --# pre  Ordered_Between (Source, Source'First, Source'Last);   --# post (Found -> (Source (Position) = Item))   --#  and (not Found ->   --#         (for all I in Index_Type range Source'Range   --#                                  => (Source(I) /= Item))); end Binary_Searches;  package body Binary_Searches is    procedure Search (Source   : in     Array_Type;                     Item     : in     Item_Type;                     Found    :     out Boolean;                     Position :     out Index_Type)   is      Lower      : Index_Type; -- Lower bound of Subrange.      Upper      : Index_Type; -- Upper bound of Subrange.      Terminated : Boolean;   begin      Found := False;      -- Default status updated on success.       Lower      := Source'First;      Upper      := Source'Last;      Position   := (Lower + Upper) / 2;      Terminated := False;       while not Terminated loop      --# assert not Terminated      --#   and  not Found      --#   and  Lower >= Source'First      --#   and  Upper <= Source'Last      --#   and  Position in Lower .. Upper      --#   and  (Lower = Source'First or      --#         (Lower > Source'First and Source(Lower - 1) < Item))      --#   and  (Upper = Source'Last or      --#         (Upper < Source'Last and Source(Upper + 1) > Item));         if Item < Source (Position) then            if Position = Lower then               -- No lower subrange.               Terminated := True;            else               -- Switch to lower half subrange.               Upper := Position - 1;               Position := (Lower + Upper) / 2;            end if;         elsif Item > Source (Position) then            if Position = Upper then               -- No upper subrange.               Terminated := True;            else               -- Switch to upper half subrange.               Lower := Position + 1;               Position := (Lower + Upper) / 2;            end if;         else            Found      := True;            Terminated := True;         end if;      end loop;   end Search; end Binary_Searches;`

The user rules for this version of the package (written in FDL, a language for modelling algorithms).

```binary_search_rule(1): (X + Y) div 2 >= X
may_be_deduced_from
[ X <= Y,
X >= 1,
Y >= 1] .

binary_search_rule(2): (X + Y) div 2 <= Y
may_be_deduced_from
[ X <= Y,
X >= 1,
Y >= 1] .

binary_search_rule(3): for_all(I_ : integer, First <= I_ and I_ <= Last
-> element(S, [I_]) <> X)
may_be_deduced_from
[ ordered_between(S, First, Last),
P >= First,
P <= Last,
element(S, [P]) > X,
P = First or (P > First and element(S, [P - 1]) < X) ] .

binary_search_rule(4): for_all(I_ : integer, First <= I_ and I_ <= Last
-> element(S, [I_]) <> X)
may_be_deduced_from
[ ordered_between(S, First, Last),
P >= First,
P <= Last,
element(S, [P]) < X,
P = Last or (P < Last and element(S, [P + 1]) > X) ] .
```

The test program:

`with Binary_Searches;with SPARK_IO; --# inherit  Binary_Searches,--#          SPARK_IO; --# main_program;procedure Test_Binary_Search--# global in out SPARK_IO.Outputs;--# derives SPARK_IO.Outputs from *;is    subtype Index_Type5 is Binary_Searches.Index_Type range 1 .. 5;   subtype Index_Type7 is Binary_Searches.Index_Type range 1 .. 7;   subtype Index_Type9 is Binary_Searches.Index_Type range 91 .. 99;   -- Needed to define a constrained Array_Type.    subtype Array_Type5 is Binary_Searches.Array_Type (Index_Type5);   subtype Array_Type7 is Binary_Searches.Array_Type (Index_Type7);   subtype Array_Type9 is Binary_Searches.Array_Type (Index_Type9);   -- Needed to pass an array literal to Run_Search.   -- SPARK does not allow an unconstrained type mark for that purpose.    procedure Run_Search (Source : in     Binary_Searches.Array_Type;                         Item   : in     Binary_Searches.Item_Type)   --# global in out SPARK_IO.Outputs;   --# derives SPARK_IO.Outputs from *,   --#                               Item,   --#                               Source;   is      Found    : Boolean;      Position : Binary_Searches.Index_Type;   begin      SPARK_IO.Put_String (File => SPARK_IO.Standard_Output,                           Item => "Searching for ",                           Stop => 0);      SPARK_IO.Put_Integer (File  => SPARK_IO.Standard_Output,                            Item  => Item,                            Width => 3,                            Base  => 10);      SPARK_IO.Put_String (File => SPARK_IO.Standard_Output,                           Item => " in (",                           Stop => 0);      for Source_Index in Binary_Searches.Index_Type range Source'Range loop         SPARK_IO.Put_Integer (File  => SPARK_IO.Standard_Output,                               Item  => Source (Source_Index),                               Width => 3,                               Base  => 10);      end loop;      SPARK_IO.Put_String (File => SPARK_IO.Standard_Output,                           Item => "): ",                           Stop => 0);      Binary_Searches.Search (Source   => Source,    -- in                              Item     => Item,      -- in                              Found    => Found,     -- out                              Position => Position); -- out      if Found then         SPARK_IO.Put_String (File => SPARK_IO.Standard_Output,                              Item => "found as #",                              Stop => 0);         SPARK_IO.Put_Integer (File  => SPARK_IO.Standard_Output,                               Item  => Position,                               Width => 0, -- to stick to the sibling '#' sign.                               Base  => 10);         SPARK_IO.Put_Line (File => SPARK_IO.Standard_Output,                            Item => ".",                            Stop => 0);      else         SPARK_IO.Put_Line (File => SPARK_IO.Standard_Output,                            Item => "not found.",                            Stop => 0);      end if;   end Run_Search; begin   SPARK_IO.New_Line (File => SPARK_IO.Standard_Output, Spacing => 1);   Run_Search (Source => Array_Type5'(0, 1, 2, 3, 4), Item => 3);   Run_Search (Source => Array_Type5'(2, 4, 6, 8, 10), Item => 3);   Run_Search (Source => Array_Type7'(1, 2, 3, 4, 5, 6, 7), Item => 0);   Run_Search (Source => Array_Type7'(1, 2, 3, 4, 5, 6, 7), Item => 7);   Run_Search (Source => Array_Type9'(1, 2, 3, 4, 5, 6, 7, 8, 9), Item => 10);   Run_Search (Source => Array_Type9'(1, 2, 3, 4, 5, 6, 7, 8, 9), Item => 1);   Run_Search (Source => Array_Type9'(1, 2, 3, 4, 5, 6, 7, 8, 9), Item => 6);end Test_Binary_Search; `

Test output (for the last three tests the array is indexed from 91):

```Searching for   3 in (  0  1  2  3  4): found as #4.
Searching for   3 in (  2  4  6  8 10): not found.
Searching for   0 in (  1  2  3  4  5  6  7): not found.
Searching for   7 in (  1  2  3  4  5  6  7): found as #7.
Searching for  10 in (  1  2  3  4  5  6  7  8  9): not found.
Searching for   1 in (  1  2  3  4  5  6  7  8  9): found as #91.
Searching for   6 in (  1  2  3  4  5  6  7  8  9): found as #96.
```

## Standard ML

Recursive

`fun binary_search cmp (key, arr) =  let    fun aux slice =      if ArraySlice.isEmpty slice then        NONE      else        let 	  val mid = ArraySlice.length slice div 2        in	  case cmp (ArraySlice.sub (slice, mid), key)	  of LESS    => aux (ArraySlice.subslice (slice, mid+1, NONE)) 	   | GREATER => aux (ArraySlice.subslice (slice, 0, SOME mid))	   | EQUAL   => SOME (#2 (ArraySlice.base slice) + mid)        end  in    aux (ArraySlice.full arr)  end`

Usage:

```- val a = Array.fromList [2, 3, 5, 6, 8];
val a = [|2,3,5,6,8|] : int array
- binary_search Int.compare (4, a);
val it = NONE : int option
- binary_search Int.compare (8, a);
val it = SOME 4 : int option
```

Standard ML supports proper tail-recursion; so this is effectively the same as iteration.

Library

Works with: SML/NJ

Usage:

```- structure IntArray = struct
=   open Array
=   type elem = int
=   type array = int Array.array
=   type vector = int Vector.vector
= end;
structure IntArray :
sig
[ ... rest omitted ]
- structure IntBSearch = BSearchFn (IntArray);
structure IntBSearch :
sig
structure A : <sig>
val bsearch : ('a * A.elem -> order)
-> 'a * A.array -> (int * A.elem) option
end
- val a = Array.fromList [2, 3, 5, 6, 8];
val a = [|2,3,5,6,8|] : int array
- IntBSearch.bsearch Int.compare (4, a);
val it = NONE : (int * IntArray.elem) option
- IntBSearch.bsearch Int.compare (8, a);
val it = SOME (4,8) : (int * IntArray.elem) option
```

## Swift

Recursive

`func binarySearch<T: Comparable>(xs: [T], x: T) -> Int? {  var recurse: ((Int, Int) -> Int?)!  recurse = {(low, high) in switch (low + high) / 2 {    case _ where high < low: return nil    case let mid where xs[mid] > x: return recurse(low, mid - 1)    case let mid where xs[mid] < x: return recurse(mid + 1, high)    case let mid: return mid  }}  return recurse(0, xs.count - 1)}`

Iterative

`func binarySearch<T: Comparable>(xs: [T], x: T) -> Int? {  var (low, high) = (0, xs.count - 1)  while low <= high {    switch (low + high) / 2 {      case let mid where xs[mid] > x: high = mid - 1      case let mid where xs[mid] < x: low = mid + 1      case let mid: return mid    }  }  return nil}`

Test

`func testBinarySearch(n: Int) {  let odds = Array(stride(from: 1, through: n, by: 2))  let result = flatMap(0...n) {binarySearch(odds, \$0)}  assert(result == Array(0..<odds.count))  println("\(odds) are odd natural numbers")  for it in result {    println("\(it) is ordinal of \(odds[it])")  }} testBinarySearch(12) func flatMap<T, U>(source: [T], transform: (T) -> U?) -> [U] {  return source.reduce([]) {(var xs, x) in if let x = transform(x) {xs.append(x)}; return xs}}`

Output:

```[1, 3, 5, 7, 9, 11] are odd natural numbers
0 is ordinal of 1
1 is ordinal of 3
2 is ordinal of 5
3 is ordinal of 7
4 is ordinal of 9
5 is ordinal of 11```

## Symsyn

`  a : 1 : 2 : 27 : 44 : 46 : 57 : 77 : 154 : 212 binary_search param item index size index saveindex index L (index + size - 1) H if L <= H     ((L + H) shr 1) M    if base.M > item       - 1 M H    else       if base.M < item          + 1 M L       else          - saveindex M          return M       endif    endif    goif endif return -1 start  call binary_search 77 @a #a result R  "'result = ' R" []  `

## Tcl

ref: Tcl wiki

`proc binSrch {lst x} {    set len [llength \$lst]    if {\$len == 0} {        return -1    } else {        set pivotIndex [expr {\$len / 2}]        set pivotValue [lindex \$lst \$pivotIndex]        if {\$pivotValue == \$x} {            return \$pivotIndex        } elseif {\$pivotValue < \$x} {            set recursive [binSrch [lrange \$lst \$pivotIndex+1 end] \$x]            return [expr {\$recursive > -1 ? \$recursive + \$pivotIndex + 1 : -1}]        } elseif {\$pivotValue > \$x} {            set recursive [binSrch [lrange \$lst 0 \$pivotIndex-1] \$x]            return [expr {\$recursive > -1 ? \$recursive : -1}]        }    }}proc binary_search {lst x} {    if {[set idx [binSrch \$lst \$x]] == -1} {        puts "element \$x not found in list"    } else {        puts "element \$x found at index \$idx"    }}`

Note also that, from Tcl 8.4 onwards, the lsearch command includes the -sorted option to enable binary searching of Tcl lists.

`proc binarySearch {lst x} {    set idx [lsearch -sorted -exact \$lst \$x]    if {\$idx == -1} {        puts "element \$x not found in list"    } else {        puts "element \$x found at index \$idx"    }}`

## TI-83 BASIC

`PROGRAM:BINSEARC:Disp "INPUT A LIST:":Input L1:SortA(L1):Disp "INPUT A NUMBER:":Input A:1→L:dim(L1)→H:int(L+(H-L)/2)→M:While L<H and L1(M)≠A:If A>M:Then:M+1→L:Else:M-1→H:End:int(L+(H-L)/2)→M:End:If L1(M)=A:Then:Disp A:Disp "IS AT POSITION":Disp M:Else:Disp A:Disp "IS NOT IN":Disp L1`

## uBasic/4tH

Translation of: Run BASIC

The overflow is fixed - which is a bit of overkill, since uBasic/4tH has only one array of 256 elements.

`For i = 1 To 100                       ' Fill array with some values  @(i-1) = iNext Print FUNC(_binarySearch(50,0,99))     ' Now find value '50'End                                    ' and prints its index  _binarySearch Param(3)                 ' value, start index, end index  Local(1)                             ' The middle of the array If [email protected] < [email protected] Then                        ' Ok, signal we didn't find it  Return (-1)Else  [email protected] = SHL([email protected] + [email protected], -1)                ' Prevent overflow (LOL!)  If [email protected] < @([email protected]) Then Return (FUNC(_binarySearch ([email protected], [email protected], [email protected])))  If [email protected] > @([email protected]) Then Return (FUNC(_binarySearch ([email protected], [email protected]+1, [email protected])))  If [email protected] = @([email protected]) Then Return ([email protected])       ' We found it, return index!EndIf`

## UNIX Shell

` #!/bin/ksh# This should work on any clone of Bourne Shell, ksh is the fastest. value=\$1; [ -z "\$value" ] && exitarray=()size=0 while IFS= read -r line; do	size=\$((\$size + 1))	array[\${#array[*]}]=\$linedone `

Iterative

` left=0right=\$((\$size - 1))while	[ \$left -le \$right ] ; do	mid=\$(((\$left + \$right) >> 1))#	echo "\$left	\$mid(\${array[\$mid]})	\$right"	if	[ \$value -eq \${array[\$mid]} ] ; then		echo \$mid		exit	elif	[ \$value -lt \${array[\$mid]} ]; then		right=\$((\$mid - 1))	else		left=\$((mid + 1))	fidoneecho 'ERROR 404 : NOT FOUND' `

Recursive

` No code yet `

## UnixPipes

Parallel

`splitter() {   a=\$1; s=\$2; l=\$3; r=\$4;   mid=\$(expr \${#a[*]} / 2);   echo \$s \${a[*]:0:\$mid} > \$l   echo \$((\$mid + \$s)) \${a[*]:\$mid} > \$r} bsearch() {   (to=\$1; read s arr; a=(\$arr);       test  \${#a[*]} -gt 1  && (splitter \$a \$s >(bsearch \$to) >(bsearch \$to)) || (test "\$a" -eq "\$to" && echo \$a at \$s)   )} binsearch() {   (read arr; echo "0 \$arr" | bsearch \$1)} echo "1 2 3 4 6 7 8 9"  | binsearch 6`

## VBA

Recursive version:

`Public Function BinarySearch(a, value, low, high)'search for "value" in ordered array a(low..high)'return index point if found, -1 if not found  If high < low Then    BinarySearch = -1 'not found    Exit Function  End If  midd = low + Int((high - low) / 2) ' "midd" because "Mid" is reserved in VBA  If a(midd) > value Then    BinarySearch = BinarySearch(a, value, low, midd - 1)  ElseIf a(midd) < value Then    BinarySearch = BinarySearch(a, value, midd + 1, high)  Else    BinarySearch = midd  End IfEnd Function`

Here are some test functions:

`Public Sub testBinarySearch(n)Dim a(1 To 100)'create an array with values = multiples of 10For i = 1 To 100: a(i) = i * 10: NextDebug.Print BinarySearch(a, n, LBound(a), UBound(a))End Sub Public Sub stringtestBinarySearch(w)'uses BinarySearch with a string arrayDim aa = Array("AA", "Maestro", "Mario", "Master", "Mattress", "Mister", "Mistress", "ZZ")Debug.Print BinarySearch(a, w, LBound(a), UBound(a))End Sub`

and sample output:

```stringtestBinarySearch "Master"
3
testBinarySearch "Master"
-1
testBinarySearch 170
17
stringtestBinarySearch 170
-1
stringtestBinarySearch "Moo"
-1
stringtestBinarySearch "ZZ"
7
```

Iterative version:

`Public Function BinarySearch2(a, value)'search for "value" in array a'return index point if found, -1 if not found  low = LBound(a)  high = UBound(a)  Do While low <= high    midd = low + Int((high - low) / 2)    If a(midd) = value Then      BinarySearch2 = midd      Exit Function    ElseIf a(midd) > value Then      high = midd - 1    Else      low = midd + 1    End If Loop BinarySearch2 = -1 'not foundEnd Function`

## VBScript

Translation of: BASIC

Recursive

`Function binary_search(arr,value,lo,hi)		If hi < lo Then			binary_search = 0		Else			middle=Int((hi+lo)/2)			If value < arr(middle) Then				binary_search = binary_search(arr,value,lo,middle-1)			ElseIf value > arr(middle) Then				binary_search = binary_search(arr,value,middle+1,hi)			Else				binary_search = middle				Exit Function			End If		End IfEnd Function 'Tesing the function.num_range = Array(2,3,5,6,8,10,11,15,19,20)n = CInt(WScript.Arguments(0))idx = binary_search(num_range,n,LBound(num_range),UBound(num_range))If idx > 0 Then	WScript.StdOut.Write n & " found at index " & idx	WScript.StdOut.WriteLineElse	WScript.StdOut.Write n & " not found"	WScript.StdOut.WriteLineEnd If`
Output:

Note: Array index starts at 0.

```C:\>cscript /nologo binary_search.vbs 4

C:\>cscript /nologo binary_search.vbs 8
8 found at index 4

C:\>cscript /nologo binary_search.vbs 20
20 found at index 9
```

## Vedit macro language

Iterative

For this implementation, the numbers to be searched must be stored in current edit buffer, one number per line. (Could be for example a csv table where the first column is used as key field.)

`// Main program for testing BINARY_SEARCH#3 = Get_Num("Value to search: ")EOF#2 = Cur_Line                   // hi#1 = 1                          // loCall("BINARY_SEARCH")Message("Value ") Num_Type(#3, NOCR)if (Return_Value < 1) {    Message(" not found\n")} else {    Message(" found at index ") Num_Type(Return_Value)}return :BINARY_SEARCH:while (#1 <= #2) {    #12 = (#1 + #2) / 2    Goto_Line(#12)    #11 = Num_Eval()    if (#3 == #11) {        return(#12)             // found    } else {        if (#3 < #11) {            #2 = #12-1        } else {            #1 = #12+1        }    }}return(0)                       // not found`

## Visual Basic .NET

Iterative

`Function BinarySearch(ByVal A() As Integer, ByVal value As Integer) As Integer    Dim low As Integer = 0    Dim high As Integer = A.Length - 1    Dim middle As Integer = 0     While low <= high        middle = (low + high) / 2        If A(middle) > value Then            high = middle - 1        ElseIf A(middle) < value Then            low = middle + 1        Else            Return middle        End If    End While     Return NothingEnd Function`

Recursive

`Function BinarySearch(ByVal A() As Integer, ByVal value As Integer, ByVal low As Integer, ByVal high As Integer) As Integer    Dim middle As Integer = 0     If high < low Then        Return Nothing    End If     middle = (low + high) / 2     If A(middle) > value Then        Return BinarySearch(A, value, low, middle - 1)    ElseIf A(middle) < value Then        Return BinarySearch(A, value, middle + 1, high)    Else        Return middle    End IfEnd Function`

## Wortel

Translation of: JavaScript
`; Recursive@var rec &[a v l h] [  @if < h l @return null  @var m @/ +h l 2  @? {    > `m a v @!rec[a v l -m 1]    < `m a v @!rec[a v +1 m h]    m  }] ; Iterative@var itr &[a v] [  @vars{l 0 h #-a}  @while <= l h [    @var m @/ +l h 2    @iff {      > `m a v :h -m 1      < `m a v :l +m 1      @return m    }  ]  null]`

## Wren

`class BinarySearch {    static recursive(a, value, low, high) {        if (high < low) return -1        var mid = low + ((high - low)/2).floor        if (a[mid] > value) return recursive(a, value, low, mid-1)        if (a[mid] < value) return recursive(a, value, mid+1, high)        return mid    }     static iterative(a, value) {        var low = 0        var high = a.count - 1        while (low <= high) {            var mid = low + ((high - low)/2).floor            if (a[mid] > value) {                high = mid - 1            } else if (a[mid] < value) {                low = mid + 1            } else {                return mid            }        }        return -1    }} var a = [10, 22, 45, 67, 89, 97]System.print("array = %(a)") System.print("\nUsing the recursive algorithm:")for (value in [67, 93]) {    var index = BinarySearch.recursive(a, value, 0, a.count - 1)    if (index >= 0) {        System.print("  %(value) was found at index %(index) of the array.")    } else {        System.print("  %(value) was not found in the array.")    }} System.print("\nUsing the iterative algorithm:")for (value in [22, 70]) {    var index = BinarySearch.iterative(a, value)    if (index >= 0) {        System.print("  %(value) was found at index %(index) of the array.")    } else {        System.print("  %(value) was not found in the array.")    }}`
Output:
```array = [10, 22, 45, 67, 89, 97]

Using the recursive algorithm:
67 was found at index 3 of the array.

Using the iterative algorithm:
22 was found at index 1 of the array.
```

## Yabasic

Translation of: Lua
`sub floor(n)    return int(n + .5)end sub sub binarySearch(list(), value)    local low, high, mid     low = 1 : high = arraysize(list(), 1)     while(low <= high)        mid = floor((low + high) / 2)        if list(mid) > value then            high = mid - 1        elsif list(mid) < value then            low = mid + 1        else            return mid        end if    wend    return falseend sub ITEMS = 10e6 dim list(ITEMS) for n = 1 to ITEMS    list(n) = nnext n print binarySearch(list(), 3)print peek("millisrunning")`

## z/Arch Assembler

This optimized version for z/Arch, uses six general regs and avoid branch misspredictions for high/low cases.

`*        Binary search             BINSRCH  LA    R5,TABLE            Begin of table         SR    R2,R2               low  = 0                                          LA    R3,ENTRIES-1        high = N-1LOOP     CR    R2,R3               while (low <= high)                          JH    NOTFOUND            {                                            ARK   R4,R2,R3               mid = low + high                          SRL   R4,1                   mid = mid / 2         LA    R1,1(R4)               mid + 1         AHIK  R0,R4,-1               mid - 1         MSFI  R4,ENTRYL              mid * length                              AR    R4,R5                  Table[mid]                                CLC   0(L'KEY,R4),SEARCH     Compare          JE    FOUND                  Equal? => Found                         LOCRH R3,R0                  High?  => HIGH = MID-1                    LOCRL R2,R1                  Low?   => LOW  = MID+1                    J     LOOP                }`

## zkl

This algorithm is tail recursive, which means it is both recursive and iterative (since tail recursion optimizes to a jump). Overflow is not possible because Ints (64 bit) are a lot bigger than the max length of a list.

`fcn bsearch(list,value){	// list is sorted   fcn(list,value, low,high){      if (high < low) return(Void);	// not found      mid:=(low + high) / 2;      if (list[mid] > value) return(self.fcn(list,value, low,   mid-1));      if (list[mid] < value) return(self.fcn(list,value, mid+1, high));      return(mid);			// found   }(list,value,0,list.len()-1);}`
`list:=T(1,3,5,7,9,11); println("Sorted values: ",list);foreach i in ([0..12]){   n:=bsearch(list,i);   if (Void==n) println("Not found: ",i);   else println("found ",i," at index ",n);}`
Output:
```Sorted values: L(1,3,5,7,9,11)
found 1 at index 0
found 3 at index 1
found 5 at index 2
found 7 at index 3
`10 DATA 2,3,5,6,8,10,11,15,19,2020 DIM t(10)30 FOR i=1 TO 1040 READ t(i)50 NEXT i60 LET value=4: GO SUB 10070 LET value=8: GO SUB 10080 LET value=20: GO SUB 10090 STOP 100 REM Binary search110 LET lo=1: LET hi=10120 IF lo>hi THEN LET idx=0: GO TO 170130 LET middle=INT ((hi+lo)/2)140 IF value<t(middle) THEN LET hi=middle-1: GO TO 120150 IF value>t(middle) THEN LET lo=middle+1: GO TO 120160 LET idx=middle170 PRINT "Value ";value;180 IF idx=0 THEN PRINT " not found": RETURN 190 PRINT " found at index ";idx: RETURN   `