# Binary search

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             05/03/2017
BINSEAR  CSECT
USING  BINSEAR,R13        base register
B      72(R15)            skip savearea
DC     17F'0'             savearea
STM    R14,R12,12(R13)    save previous context
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    ,                  enddo
EXITDO   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                exit
T        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 value
LOW      DS     H
HIGH     DS     H
MID      DS     H
F        DS     X                  flag
PG       DC     CL80' '            buffer
XDEC     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, 251
primes_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,1
dgt_out:	mvi	e,'0' - 1	;; Output 100s, 10s or 1s
dgt_out_loop:	inr	e		;; (depending on C)
sub	c
jnc	dgt_out_loop
e_out:		push	psw		;; Output character in E
push	b		;; preserving working registers
mvi	c,2
call	5
pop	b
pop	psw
ret

;; Main test code
test:		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" string
str_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              */
/*********************************/
.data
sMessResult:        .asciz "Value find at index : @ \n"
szCarriageReturn:   .asciz "\n"
sMessRecursif:      .asciz "Recursive search : \n"

.equ NBELEMENTS,  (. - TableNumber) / 8
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:          .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main
main:                                           // entry of program
mov x0,4                                    // search first value
mov x2,NBELEMENTS                           // number of élements
bl bSearch
bl conversion10                             // décimal conversion
bl strInsertAtCharInc                       // insert result at @ character
bl affichageMess                            // display message

mov x0,#11                                  // search median value
mov x2,#NBELEMENTS
bl bSearch
bl conversion10                             // decimal conversion
bl strInsertAtCharInc                       // insert result at @ character
bl affichageMess                            // display message

mov x2,#NBELEMENTS
bl bSearch
cmp x0,#-1
bne 2f
bl affichageMess
b 3f
2:
bl conversion10                             // décimal conversion
bl strInsertAtCharInc                       // insert result at @ character
bl affichageMess                            // display message
3:
mov x0,#35                                  // search last value
mov x2,#NBELEMENTS
bl bSearch
bl conversion10                             // décimal conversion
bl strInsertAtCharInc                       // insert result at @ character
bl affichageMess                            // display message

/****************************************/
/*       recursive                      */
/****************************************/
bl affichageMess                            // display message

mov x0,#4                                   // search first value
mov x2,#0                                   // low index of elements
mov x3,#NBELEMENTS - 1                      // high index of elements
bl bSearchR
bl conversion10                             // décimal conversion
bl strInsertAtCharInc                       // insert result at @ character
bl affichageMess                            // display message

mov x0,#11
mov x2,#0
mov x3,#NBELEMENTS - 1
bl bSearchR
bl conversion10                             // décimal conversion
bl strInsertAtCharInc                       // insert result at @ character
bl affichageMess                            // display message

mov x0,#12
mov x2,#0
mov x3,#NBELEMENTS - 1
bl bSearchR
cmp x0,#-1
bne 4f
bl affichageMess
b 5f
4:
bl conversion10                             // décimal conversion
bl strInsertAtCharInc                       // insert result at @ character
bl affichageMess                            // display message

5:
mov x0,#35
mov x2,#0
mov x3,#NBELEMENTS - 1
bl bSearchR
bl conversion10                             // décimal conversion
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

/******************************************************************/
/*     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 - 1
1:
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 loop
2:
sub x4,x2,#1                     // bigger -> index high = index - 1
b 1b                             // and loop
98:
mov x0,x2                        // find !!!
b 100f
99:
100:
ldp x4,x5,[sp],16                // restaur  2 registers
ldp x2,x3,[sp],16                // restaur  2 registers
ldp x1,lr,[sp],16                // restaur  2 registers
/******************************************************************/
/*     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
b 100f
1:
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 100f
2:                                                   // bigger
sub x3,x4,#1                                     // new search with high = index - 1
bl bSearchR
b 100f
99:
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
/********************************************************/
/*        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
: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*)))
```

## Action!

```INT FUNC BinarySearch(INT ARRAY a INT len,value)
INT low,high,mid

low=0 high=len-1
WHILE low<=high
DO
mid=low+(high-low) RSH 1
IF a(mid)>value THEN
high=mid-1
ELSEIF a(mid)<value THEN
low=mid+1
ELSE
RETURN (mid)
FI
OD
RETURN (-1)

PROC Test(INT ARRAY a INT len,value)
INT i

Put('[)
FOR i=0 TO len-1
DO
PrintI(a(i))
IF i<len-1 THEN Put(32) FI
OD
i=BinarySearch(a,len,value)
Print("] ") PrintI(value)
IF i<0 THEN
ELSE
Print(" found at index ")
PrintIE(i)
FI
RETURN

PROC Main()
INT ARRAY a=[65530 0 1 2 5 6 8 9]

Test(a,8,6)
Test(a,8,-6)
Test(a,8,9)
Test(a,8,-10)
Test(a,8,10)
Test(a,8,7)
RETURN```
Output:
```[-6 0 1 2 5 6 8 9] 6 found at index 5
[-6 0 1 2 5 6 8 9] -6 found at index 0
[-6 0 1 2 5 6 8 9] 9 found at index 7
```

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

```BEGIN
MODE 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
end
end.```
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 value
end 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 if
end 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              */
/*********************************/
.data
sMessResult:        .ascii "Value find at index : "
sMessValeur:        .fill 11, 1, ' '            @ size => 11
szCarriageReturn:   .asciz "\n"
sMessRecursif:      .asciz "Recursive search : \n"

.equ NBELEMENTS,      9
TableNumber:	     .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
mov r2,#NBELEMENTS                          @ number of élements
bl bSearch
bl conversion10                             @ call function
bl affichageMess                            @ display message

mov r0,#11                                  @ search median value
mov r2,#NBELEMENTS
bl bSearch
bl conversion10                             @ call function
bl affichageMess                            @ display message

mov r2,#NBELEMENTS
bl bSearch
cmp r0,#-1
bne 2f
bl affichageMess
b 3f
2:
bl conversion10                             @ call function
bl affichageMess                            @ display message
3:
mov r0,#35                                  @ search last value
mov r2,#NBELEMENTS
bl bSearch
bl conversion10                             @ call function
bl affichageMess                            @ display message
/****************************************/
/*       recursive                      */
/****************************************/
bl affichageMess                            @ display message

mov r0,#4                                   @ search first value
mov r2,#0                                   @ low index of elements
mov r3,#NBELEMENTS - 1                      @ high index of elements
bl bSearchR
bl conversion10                             @ call function
bl affichageMess                            @ display message

mov r0,#11
mov r2,#0
mov r3,#NBELEMENTS - 1
bl bSearchR
bl conversion10                             @ call function
bl affichageMess                            @ display message

mov r0,#12
mov r2,#0
mov r3,#NBELEMENTS - 1
bl bSearchR
cmp r0,#-1
bne 2f
bl affichageMess
b 3f
2:
bl conversion10                             @ call function
bl affichageMess                            @ display message
3:
mov r0,#35
mov r2,#0
mov r3,#NBELEMENTS - 1
bl bSearchR
bl conversion10                             @ call function
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

/******************************************************************/
/*     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 - 1
1:
cmp r3,r4
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 loop
100:
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 ?
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 100f
1:                                                   @ bigger
sub r3,r4,#1                                     @ new search with high = index - 1
bl bSearchR
100:
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
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,   10
conversion10:
push {r1-r4,lr}                                 @ save registers
mov r3,r1
mov r2,#LGZONECAL

1:	                                            @ start loop
bl divisionpar10U                               @unsigned  r0 <- dividende. quotient ->r0 reste -> r1
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,#0
2:
ldrb r1,[r3,r2]
strb r1,[r3,r4]
cmp r2,#LGZONECAL
ble 2b
@ and move spaces in end on area
mov r0,r4                                        @ result length
mov r1,#' '                                      @ space
3:
strb r1,[r3,r4]                                  @ store space in area
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]
]
```
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 array
MsgBox % x := BinarySearch(A, 4, 1, A0) ; Recursive
MsgBox % A%x%
MsgBox % x := BinarySearchI(A, A0, 4)  ; Iterative
MsgBox % 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 BSEARCH
0→L
r₃-1→H
While L≤H
(L+H)/2→M
If {L+M}>r₂
M-1→H
ElseIf {L+M}<r₂
M+1→L
Else
M
Return
End
End
-1
Return```

## 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 IF
END 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 = 0
END 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
ELSE
PRINT " found at index "; idx
END IF
END SUB

DIM test(1 TO 10) AS Integer
DIM i AS Integer

DATA 2, 3, 5, 6, 8, 10, 11, 15, 19, 20
FOR i = 1 TO 10		' Fill the test array
NEXT i

search test(), 4
search test(), 8
search test(), 20
```

Output:

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

### ASIC

```REM Binary search
DIM A(10)
REM Sorted data
DATA -31, 0, 1, 2, 2, 4, 65, 83, 99, 782
FOR I = 0 TO 9
NEXT I
N = 10
X = 2
GOSUB DoBinarySearch:
GOSUB PrintResult:
X = 5
GOSUB DoBinarySearch:
GOSUB PrintResult:
END

PrintResult:
PRINT X;
IF IndX >= 0 THEN
PRINT " is at index ";
PRINT IndX;
PRINT "."
ELSE
ENDIF
RETURN

DoBinarySearch:
REM Binary search algorithm
REM N - number of elements
REM X - searched element
REM Result: IndX - index of X
L = 0
H = N - 1
Found = 0
Loop:
IF L > H THEN AfterLoop:
IF Found <> 0 THEN AfterLoop:
REM (L <= H) and (Found = 0)
M = H - L
M = M / 2
M = L + M
REM So, M = L + (H - L) / 2
IF A(M) < X THEN
L = M + 1
ELSE
IF A(M) > X THEN
H = M - 1
ELSE
Found = 1
ENDIF
ENDIF
GOTO Loop:
AfterLoop:
IF Found = 0 THEN
IndX = -1
ELSE
IndX = M
ENDIF
RETURN
```
Output:
```     2 is at index      4.
```

### BASIC256

#### Recursive Solution

```function binarySearchR(array, valor, lb, ub)
if ub < lb then
return false
else
mitad = floor((lb + ub) / 2)
end if
end function```

#### Iterative Solution

```function binarySearchI(array, valor)
lb = array[?,]
ub = array[?]

while lb <= ub
mitad = floor((lb + ub) / 2)
begin case
else
end case
end while
return false
end function```

Test:

```items = 10e5
dim array(items)
for n = 0 to items-1 : array[n] = n : next n

t0 = msec
print binarySearchI(array, 3)
print msec - t0; " millisec"
t1 = msec
print binarySearchR(array, 3, array[?,], array[?])
print msec - t1; " millisec"
end```
Output:
```3
839 millisec
3
50 millisec```

### 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
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
```

### Craft Basic

```'iterative binary search example

define size = 10, search = 0, flag = 0, value = 0
define middle = 0, low = 0, high = 0

dim list[2, 3, 5, 6, 8, 10, 11, 15, 19, 20]

let value = 4
gosub binarysearch

let value = 8
gosub binarysearch

let value = 20
gosub binarysearch

end

sub binarysearch

let search = 1
let middle = 0
let low = 0
let high = size

do

if low <= high then

let middle = int: ( high + low ) / 2
let flag = 1

if value < list[middle] then

let high = middle - 1
let flag = 0

endif

if value > list[middle] then

let low = middle + 1
let flag = 0

endif

if flag = 1 then

let search = 0

endif

endif

loop low <= high and search = 1

if search = 1 then

let middle = 0

endif

if middle < 1 then

endif

if middle >= 1 then

print "found at index ", middle

endif

return
```

### 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 -1
end function
```

### GW-BASIC

Translation of: ASIC
Works with: BASICA
```10 REM Binary search
20 DIM A(10)
30 N% = 10
40 FOR I% = 0 TO 9: READ A(I%): NEXT I%
50 REM Sorted data
60 DATA -31, 0, 1, 2, 2, 4, 65, 83, 99, 782
70 X = 2: GOSUB 500
80 GOSUB 200
90 X = 5: GOSUB 500
100 GOSUB 200
110 END
190 REM Print result
200 PRINT X;
210 IF INDX% >= 0 THEN PRINT "is at index"; STR\$(INDX%);"." ELSE PRINT "is not found."
220 RETURN
480 REM Binary search algorithm
490 REM N% - number of elements; X - searched element; Result: INDX% - index of X
500 L% = 0: H% = N% - 1: FOUND% = 0
520  M% = L% + (H% - L%) \ 2
530  IF A(M%) < X THEN L% = M% + 1 ELSE IF A(M%) > X THEN H% = M% - 1 ELSE FOUND% = -1
540 WEND
550 IF FOUND% = 0 THEN INDX% = -1 ELSE INDX% = M%
560 RETURN
```
Output:
```2 is at index 4.
```

### IS-BASIC

```100 PROGRAM "Search.bas"
110 RANDOMIZE
120 NUMERIC ARR(1 TO 20)
130 CALL FILL(ARR)
140 PRINT:INPUT PROMPT "Value: ":N
150 LET IDX=SEARCH(ARR,N)
160 IF IDX THEN
170   PRINT "The value";N;"was found the index";IDX
180 ELSE
200 END IF
210 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)+1
250     PRINT T(I);
260   NEXT
270 END DEF
280 DEF SEARCH(REF T,N)
290   LET SEARCH=0:LET BO=LBOUND(T):LET UP=UBOUND(T)
300   DO
310     LET K=INT((BO+UP)/2)
320     IF T(K)<N THEN LET BO=K+1
330     IF T(K)>N THEN LET UP=K-1
340   LOOP WHILE BO<=UP AND T(K)<>N
350   IF BO<=UP THEN LET SEARCH=K
360 END DEF```

### Liberty BASIC

```dim theArray(100)
for i = 1 to 100
theArray(i) = i
next 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 IF
END FUNCTION```

### Minimal BASIC

Translation of: ASIC
Works with: Commodore BASIC version 3.5
Works with: Nascom ROM BASIC version 4.7
```10 REM Binary search
20 LET N = 10
30 FOR I = 1 TO N
50 NEXT I
60 REM Sorted data
70 DATA -31, 0, 1, 2, 2, 4, 65, 83, 99, 782
80 LET X = 2
90 GOSUB 500
100 GOSUB 200
110 LET X = 5
120 GOSUB 500
130 GOSUB 200
140 END

190 REM Print result
200 PRINT X;
210 IF I1 < 0 THEN 240
220 PRINT "is at index"; I1; "."
230 RETURN
250 RETURN

460 REM Binary search algorithm
470 REM N - number of elements
480 REM X - searched element
490 REM Result: I1 - index of X
500 LET L = 0
510 LET H = N-1
520 LET F = 0
530 LET M = L
540 IF L > H THEN 650
550 IF F <> 0 THEN 650
560 LET M = L+INT((H-L)/2)
570 IF A(M) >= X THEN 600
580 LET L = M+1
590 GOTO 540
600 IF A(M) <= X THEN 630
610 LET H = M-1
620 GOTO 540
630 LET F = 1
640 GOTO 540
650 IF F = 0 THEN 680
660 LET I1 = M
670 RETURN
680 LET I1 = -1
690 RETURN
```

### Palo Alto Tiny BASIC

Translation of: ASIC
```    10 REM BINARY SEARCH
20 LET N=10
30 REM SORTED DATA
40 LET @(1)=-31,@(2)=0,@(3)=1,@(4)=2,@(5)=2
50 LET @(6)=4,@(7)=65,@(8)=83,@(9)=99,@(10)=782
60 LET X=2;GOSUB 500
70 GOSUB 200
80 LET X=5;GOSUB 500
90 GOSUB 200
100 STOP
190 REM PRINT RESULT
210 PRINT #1,X," IS AT INDEX ",J,".";RETURN
460 REM BINARY SEARCH ALGORITHM
470 REM N - NUMBER OF ELEMENTS
480 REM X - SEARCHED ELEMENT
490 REM RESULT: J - INDEX OF X
500 LET L=0,H=N-1,F=0,M=L
510 IF L>H GOTO 570
520 IF F#0 GOTO 570
530 LET M=L+(H-L)/2
540 IF @(M)<X LET L=M+1;GOTO 510
550 IF @(M)>X LET H=M-1;GOTO 510
560 LET F=1;GOTO 510
570 IF F=0 LET J=-1;RETURN
580 LET J=M;RETURN
```
Output:
``` 2 IS AT INDEX  4.
```

### 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

;Recursive
Procedure  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

;Iterative
Procedure 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 #NotFound
EndProcedure

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
Else
PrintN(" found at index " + Str(idx))
EndIf
EndProcedure

#NumElements = 9 ;zero based count
Dim test(#NumElements)

DataSection
Data.i 2, 3, 5, 6, 8, 10, 11, 15, 19, 20
EndDataSection

;fill the test array
For i = 0 To #NumElements
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
```

### Run BASIC

Recursive

```dim theArray(100)
global theArray
for i = 1 to 100
theArray(i) = i
next 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 IF
END FUNCTION```

### 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) = i
Next

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 c@ < b@ Then                        ' Ok, signal we didn't find it
Return (-1)
Else
d@ = SHL(b@ + c@, -1)                ' Prevent overflow (LOL!)
If a@ < @(d@) Then Return (FUNC(_binarySearch (a@, b@, d@-1)))
If a@ > @(d@) Then Return (FUNC(_binarySearch (a@, d@+1, c@)))
If a@ = @(d@) Then Return (d@)       ' We found it, return index!
EndIf
```

### VBA

Recursive version:

```Public Function BinarySearch(a, value, low, high)
'search for "value" in ordered array a(low..high)

If high < low Then
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 If
End Function
```

Here are some test functions:

```Public Sub testBinarySearch(n)
Dim a(1 To 100)
'create an array with values = multiples of 10
For i = 1 To 100: a(i) = i * 10: Next
Debug.Print BinarySearch(a, n, LBound(a), UBound(a))
End Sub

Public Sub stringtestBinarySearch(w)
'uses BinarySearch with a string array
Dim a
a = 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

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
End 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 If
End 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.WriteLine
Else
WScript.StdOut.WriteLine
End 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
```

### 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 Nothing
End 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 If
End Function
```

### 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 false
end sub

ITEMS = 10e6

dim list(ITEMS)

for n = 1 to ITEMS
list(n) = n
next n

print binarySearch(list(), 3)
print peek("millisrunning")```

### ZX Spectrum Basic

Translation of: FreeBASIC

Iterative method:

```10 DATA 2,3,5,6,8,10,11,15,19,20
20 DIM t(10)
30 FOR i=1 TO 10
50 NEXT i
60 LET value=4: GO SUB 100
70 LET value=8: GO SUB 100
80 LET value=20: GO SUB 100
90 STOP
100 REM Binary search
110 LET lo=1: LET hi=10
120 IF lo>hi THEN LET idx=0: GO TO 170
130 LET middle=INT ((hi+lo)/2)
140 IF value<t(middle) THEN LET hi=middle-1: GO TO 120
150 IF value>t(middle) THEN LET lo=middle+1: GO TO 120
160 LET idx=middle
170 PRINT "Value ";value;
190 PRINT " found at index ";idx: RETURN
```

## 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```

## BQN

BQN has two builtin functions for binary search: `⍋`(Bins Up) and `⍒`(Bins Down). This is a recursive method.

```BSearch ← {
BS ⟨a, value⟩:
BS ⟨a, value, 0, ¯1+≠a⟩;
BS ⟨a, value, low, high⟩:
mid ← ⌊2÷˜low+high
{
high<low ? ¯1;
(mid⊑a)>value ? BS ⟨a, value, low, mid-1⟩;
(mid⊑a)<value ? BS ⟨a, value, mid+1, high⟩;
mid
}
}

•Show BSearch ⟨8‿30‿35‿45‿49‿77‿79‿82‿87‿97, 97⟩```
```9
```

## 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 array
numbers = 1000.of { random 1000 }

#Sort the array
numbers.sort!

#Find a number
x = random 1000

p "Looking for #{x}"

index = binary_search numbers, x, 0, numbers.length - 1

null? index
{ 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;
int x = 2;
int i = bsearch(a, n, x);
if (i >= 0)
printf("%d is at index %d.\n", x, i);
else
x = 5;
i = bsearch_r(a, x, 0, n - 1);
if (i >= 0)
printf("%d is at index %d.\n", x, i);
else
return 0;
}
```
Output:
```2 is at index 4.
```

## 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");
#endif
}
}
```

Output

```test:
glb = -1
lub = 0
test: 2
glb = -1
lub = 1
test: 2 2
glb = -1
lub = 2
test: 2 2 2 2
glb = -1
lub = 4
test: 3 3 4 4
glb = -1
lub = 0
test: 0 1 3 3 4 4
glb = 1
lub = 2
test: 0 1 2 2 2 3 3 4 4
glb = 1
lub = 5
test: 0 1 1 2 2 2 3 3 4 4
glb = 2
lub = 6
test: 0 1 1 1 1 2 2 3 3 4 4
glb = 4
lub = 7
test: 0 1 1 1 1 2 2 2 2 2 2 2 3 3 4 4
glb = 4
lub = 12
test: 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);
else std::cout << "4 found at " << result1 << 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;
}
}
```

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)))))
```

## CLU

```% Binary search in an array
% If the item is found, returns `true' and the index;
% if the item is not found, returns `false' and the leftmost insertion point
% The datatype must support the < and > operators.
binary_search = proc [T: type] (a: array[T], val: T) returns (bool, int)
where T has lt: proctype (T,T) returns (bool),
T has gt: proctype (T,T) returns (bool)
low: int := array[T]\$low(a)
high: int := array[T]\$high(a)

while low <= high do
mid: int := low + (high - low) / 2
if a[mid] > val then
high := mid - 1
elseif a[mid] < val then
low := mid + 1
else
return (true, mid)
end
end
return (false, low)
end binary_search

% Test the binary search on an array
start_up = proc ()
po: stream := stream\$primary_output()

% primes up to 20 (note that arrays are 1-indexed by default)
primes: array[int] := array[int]\$[2,3,5,7,11,13,17,19]

% binary search for each number from 1 to 20
for n: int in int\$from_to(1,20) do
i: int
found: bool
found, i := binary_search[int](primes, n)

if found then
stream\$putl(po, int\$unparse(n)
|| " found at location "
|| int\$unparse(i));
else
stream\$putl(po, int\$unparse(n)
|| int\$unparse(i));
end
end
end start_up```
Output:
```1 not found, would be inserted at location 1
2 found at location 1
3 found at location 2
5 found at location 3
7 found at location 4
11 found at location 5
13 found at location 6
17 found at location 7
19 found at location 8

## COBOL

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

```        >>SOURCE FREE
IDENTIFICATION 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
end
end

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
end
end
```

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
end
end

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
end
end
```
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 @nogc
if (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 @nogc
if (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 = 1
high = len a[]
res = 0
while low <= high and res = 0
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[] r
print 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
end
end

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
index      -> IO.puts "found #{val} at index #{index}"
end
end)
```
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 ->
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
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 if
end 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
end 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

DIM gtc = GetTickCount()
FOR DIM i = 0 TO 1000000
va[] = sign[toggle] * PI * i
toggle = NOT toggle		' randomize the array
NEXT
PRINT "done in ", GetTickCount() - gtc, " milliseconds"

PRINT "Sorting ... ";
gtc = GetTickCount()
QUICKSORT(va)				' quick sort the array
PRINT "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[]

DIM gtc = GetTickCount()
FOR DIM i = 0 TO 1000000: va[] = i * PI: NEXT
PRINT "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 -1
END 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[]

DIM gtc = GetTickCount()
FOR DIM i = 0 TO 1000000: va[] = i * PI: NEXT
PRINT "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 midp
END 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 @ r@ (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 2
2 probe \ -1 2
3 probe \ 0 4
10 probe \ 0 11
11 probe \ -1 11
12 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
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 if
end 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 do
end 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);
# fail
Find(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 Set
def 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)
}
println """
}
```

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 a
bSearch 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 i
bSearchArray a x = bSearch (compare x . (a !)) (bounds a)

-- TEST -----------------------------------------------------------------------
axs
:: (Num i, Ix i)
=> Array i String
axs =
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
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 SIGNATURE
findIndexBinary
:: Ord a
=> (a -> Ordering) -> Array Int a -> Either String Int
findIndexBinary p axs =
let go (lo, hi)
| 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 String
haystack =
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 ALGORITHM
findIndexBinary_
:: Ord a
=> (a -> Ordering) -> Array Int a -> Either String Int
findIndexBinary_ 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
else Right lo

-- TEST ---------------------------------------------------
haystack :: Array Int String
haystack =
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 8
5 has position 0 in 0 0 1 2 3 3 4 6 7 8```

## Hoon

```|=  [arr=(list @ud) x=@ud]
=/  lo=@ud  0
=/  hi=@ud  (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 mid
end
```

A program to test this is:

```procedure main(args)
target := integer(!args) | 3
every put(A := [], 1 to 18 by 2)

outList("Searching", A)
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'"_^:(-.@-:) I.
```

Examples:

```   2 3 5 6 8 10 11 15 19 20 bs 11
6
2 3 5 6 8 10 11 15 19 20 bs 12
```

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

Iterative

```'X Y L H M'=. i.5                            NB. Setting mnemonics for boxes
f=. &({::)                                   NB. Fetching the contents of a box
o=. @:                                       NB. Composing verbs (functions)

boxes=. ; , a: \$~ 3:                         NB. Appending 3 (empty) boxes to the inputs
LowHigh=. (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 midpoint
case=.     >: 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} ])@.case
return=.   (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 boxes
f=. &({::)                                   NB. Fetching the contents of a box
o=. @:                                       NB. Composing verbs (functions)

boxes=. a: ,~ ;                              NB. Appending 1 (empty) box to the inputs
midpoint=. < o (<. o (2 %~ L f + H f)) M} ]  NB. Updating the midpoint
case=.     >: 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) {
} 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 ? (
) : 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 0
end
```

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
end
end
```

## K

Recursive:

```bs:{[a;t]
if[0=#a; :_n];
m:_(#a)%2;
if[t>a@m
tmp:_f[(m+1) _ a;t]
:[_n~tmp; :_n; :1+m+tmp]]
if[t<a@m
:_f[m#a;t]]
:m
}

v:8 30 35 45 49 77 79 82 87 97
{bs[v;x]}' v
0 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)

```{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}
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} 25}  -> 25 is at array

{def B {array {serie 1 100000 2}}}
-> B = [1,3,5,... 99997,99999]

{BS {B} 12345} -> 12345 is at array
```

## 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 :mid
end```

## 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
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?"

KTHXBYE
end```

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 false
end
```

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
```

## M4

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

Output:

```3
-1
```

## M2000 Interpreter

```\\ binary search
const N=10
Dim A(0 to N-1)
A(0):=1,2,3,4,5,6,8,9,10,11
Print Len(A())=10
Function 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 12
Rem	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
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
Dim A(len(A())+1)   ' redim
A(where)=i  ' insert value
End If
end if
next i
Print Len(A())=13
Print A()```

## 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 if
end 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;
FAIL
end 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 + Round@((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 = Length@x, mid},
While[lo <= hi,
mid = lo + Round@((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);
0
find(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 mid
end 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 while
end 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 \\\\\$@
\}
.	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 5
3 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)
```

## Oberon-2

Translation of: Pascal
```MODULE BS;

IMPORT Out;

VAR
List:ARRAY 10 OF REAL;

PROCEDURE Init(VAR List:ARRAY OF REAL);
BEGIN
List := -31; List := 0; List := 1; List := 2;
List := 2; List := 4; List := 65; List := 83;
List := 99; List := 782;
END Init;

PROCEDURE BinarySearch(List:ARRAY OF REAL;Element:REAL):LONGINT;
VAR
L,M,H:LONGINT;
BEGIN
L := 0;
H := LEN(List)-1;
WHILE L <= H DO
M := (L + H) DIV 2;
IF List[M] > Element THEN
H := M - 1;
ELSIF List[M] < Element THEN
L := M + 1;
ELSE
RETURN M;
END;
END;
RETURN -1;
END BinarySearch;

PROCEDURE RBinarySearch(VAR List:ARRAY OF REAL;Element:REAL;L,R:LONGINT):LONGINT;
VAR
M:LONGINT;
BEGIN
IF R < L THEN RETURN -1 END;
M := (L + R) DIV 2;
IF Element = List[M] THEN
RETURN M
ELSIF Element < List[M] THEN
RETURN RBinarySearch(List, Element, L, R-1)
ELSE
RETURN RBinarySearch(List, Element, M-1, R)
END;
END RBinarySearch;

BEGIN
Init(List);
Out.Int(BinarySearch(List, 2), 0); Out.Ln;
Out.Int(RBinarySearch(List, 65, 0, LEN(List)-1),0); Out.Ln;
END BS.
```

## 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.
- (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.
- (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
endif
endfunction
```

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
endwhile
endfunction
```

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 cases
searchkeys = .array~of(0, 1, 4, 7, 11, 12)
say "recursive binary search"
loop key over searchkeys
pos = recursiveBinarySearch(data, key)
else say "Key" key "found at postion" pos
end
say
say "iterative binary search"
loop key over searchkeys
pos = iterativeBinarySearch(data, key)
else say "Key" key "found at postion" pos
end

::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)
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)
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 (for reference only, don't copy/paste unless you plan to modify and rename it)

```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

```with javascript_semantics
?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;
}
```

## Picat

### Iterative

```go =>
A = [2, 4, 6, 8, 9],
TestValues = [2,1,8,10,9,5],

foreach(Value in TestValues)
test(binary_search,A, Value)
end,
test(binary_search,[1,20,3,4], 5),
nl.

% Test with binary search predicate Search
test(Search,A,Value) =>
Ret = apply(Search,A,Value),
printf("A: %w Value:%d Ret: %d: ", A, Value, Ret),
if Ret == -1 then
println("The array is not sorted.")
elseif Ret == 0 then
printf("The value %d is not in the array.\n", Value)
else
printf("The value %d is found at position %d.\n", Value, Ret)
end.

binary_search(A, Value) = V =>
V1 = 0,
% we want a sorted array
if not sort(A) == A then
V1 := -1
else
Low = 1,
High = A.length,
Mid = 1,
Found = 0,
while (Found == 0, Low <= High)
Mid := (Low + High) // 2,
if A[Mid] > Value then
High := Mid - 1
elseif A[Mid] < Value then
Low := Mid + 1
else
V1 := Mid,
Found := 1
end
end
end,
V = V1.```
Output:
```A: [2,4,6,8,9] Value:2 Ret: 1: The value 2 is found at position 1.
A: [2,4,6,8,9] Value:1 Ret: 0: The value 1 is not in the array.
A: [2,4,6,8,9] Value:8 Ret: 4: The value 8 is found at position 4.
A: [2,4,6,8,9] Value:10 Ret: 0: The value 10 is not in the array.
A: [2,4,6,8,9] Value:9 Ret: 5: The value 9 is found at position 5.
A: [2,4,6,8,9] Value:5 Ret: 0: The value 5 is not in the array.
A: [1,20,3,4] Value:5 Ret: -1: The array is not sorted.
```

### Recursive version

```binary_search_rec(A, Value) = Ret =>
Ret = binary_search_rec(A,Value, 1, A.length).

binary_search_rec(A, _Value, _Low, _High) = -1, sort(A) != A => true.
binary_search_rec(_A, _Value, Low, High)  =  0, High < Low   => true.
binary_search_rec(A, Value, Low, High)    = Mid =>
Mid1 = (Low + High) // 2,
if A[Mid1] > Value then
Mid1 := binary_search_rec(A, Value, Low, Mid1-1)
elseif A[Mid1] < Value then
Mid1 := binary_search_rec(A, Value, Mid1+1, High)
end,
Mid = Mid1.```

## 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
{
}
}
```
```Show-SearchResult -Array 10, 28, 41, 46, 58, 74, 76, 86, 89, 98 -Search 41 -Function Iterative
Show-SearchResult -Array 10, 28, 41, 46, 58, 74, 76, 86, 89, 98 -Search 99 -Function Iterative
Show-SearchResult -Array 10, 28, 41, 46, 58, 74, 76, 86, 89, 98 -Search 86 -Function Recursive
Show-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.```

## 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 Int
def 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 -> Ordering
def 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 -> Ordering
def 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 (
'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 (
'Word of given length found at index ' + str(mb2)
)
)

# GENERIC -------------------------------------------------

# until :: (a -> Bool) -> (a -> a) -> a -> a
def 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 Int
def 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 -> Ordering
def 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 -> Ordering
def 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 (
'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 (
'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 point
index = bisect.bisect_right(list, item) # rightmost insertion point
index = 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
```

## Quackery

Written from pseudocode for rightmost insertion point, iterative.

```  [ stack ]                   is value.bs    (         --> n   )
[ stack ]                   is nest.bs     (         --> n   )
[ stack ]                   is test.bs     (         --> n   )

[ ]'[ test.bs put
value.bs put
nest.bs put
1 - swap
[ 2dup < if done
2dup + 1 >>
nest.bs share over peek
value.bs share swap
test.bs share do iff
[ 1 - unrot nip ]
again
[ 1+ nip ] again ]
drop
nest.bs take over peek
value.bs take 2dup swap
test.bs share do
dip [ test.bs take do ]
or not
dup dip [ not + ] ]       is bsearchwith ( n n [ x --> n b )

[ dup echo
over size 0 swap 2swap
bsearchwith < iff
[ say " was identified as item " ]
else
[ say " could go into position " ]
echo
say "." cr ]              is task        (     [ n --> n   )```
Output:

Testing in the shell.

```/O>   ' [ 10 20 30 40 50 60 70 80 90 ] 30 task
...   ' [ 10 20 30 40 50 60 70 80 90 ] 66 task
...
30 was identified as item 2.
66 could go into position 6.

Stack empty.```

## 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 <- 1:100
IterBinSearch(a, 50)
BinSearch(a, 50, 1, length(a)) # output 50
IterBinSearch(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= 1
high= 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: '   loc
say
say  'arithmetic mean of the '   high   " values is: "       avg
exit                                             /*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= 1
high= words(@)
say  'arithmetic mean of the '   high    " values is: "   (word(@, 1) + word(@, high)) / 2
say
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= 42
index = where(array,find,0,len(array))
if index >= 0
see "the value " + find+ " was found at index " + index
else
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
end
end

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
end
end
```

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
end
end

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
end
end
```
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".

## Rust

Iterative

```fn binary_search<T:PartialOrd>(v: &[T], searchvalue: T) -> Option<T> {
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 Some(searchvalue);
} else if searchvalue < v[mid] {
upper = mid - 1;
} else {
lower = mid + 1;
}
}

None
}
```

## 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
}
}
```

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
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);
! 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);
OUTIMAGE;

OUTTEXT("LOOKUP ITERATIV ");
OUTINT(NEEDLE, 3);
OUTTEXT(" ... INDEX = ");
K := BINARYSEARCH(HAYSTACK, NEEDLE);
OUTINT(K, 3);
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
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))
--#         (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  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,
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`