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Multiplies two arbitrarily long Base2-10 integers.
Supports multiplication of two base-10 integer inputs of at least 310 digits which is suitable for multiplying 1024-bit numbers in base-10. You can also multiply directly in binary, or base-3, 4, 5, 6, 7, 8 and 9. (Experimental). Theoretically supports up to 2.1 billion digits of integer output, 2.1 billion digits of combined integer input, if you have a computer fast enough. Not yet tested on inputs larger than 2^1024 or outputs larger than 2^2048. Returns the exact integer result. Uses strings to carry and calculate digit by digit. Powershell only supports up to uint64, anyways. That is a mere 18446744073709551616. Base-10 as in Base Ten. Otherwise any base would be Base-10 in its own base.
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| # all this script does is multiply two large numbers to form another large number. | ||
| # KGT 2022 | ||
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| ##### | ||
| # Window UI settings | ||
| ##### | ||
| $uisettings = (get-host).UI.RawUI | ||
| $x = $uisettings.WindowPosition | ||
| $x.x = 0 | ||
| $x.y = 0 | ||
| $uisettings.WindowPosition = $x | ||
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| $bgcolour = $uisettings.BackgroundColor | ||
| $bgcolour = "Black" | ||
| $uisettings.BackgroundColor = $bgcolour | ||
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| $b = $uisettings.WindowSize | ||
| $ba = $uisettings.MaxPhysicalWindowSize | ||
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| # adjust buffer size according to max physical window size | ||
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| $bf = $uisettings.BufferSize | ||
| $bf.Height = $ba.Height * 5 | ||
| $bf.Width = $ba.Width * 5 | ||
| $uisettings.BufferSize = $bf | ||
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| [int] $heightwindow = 25 # --- minimum is 20 | ||
| [int] $widthwindow = 100 # --- minimum is 20 | ||
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| # let window size be max physical window size | ||
| $b.Height = $heightwindow + 10 # larger than printed size | ||
| if ($widthwindow * 2 -lt 52){ | ||
| $b.Width = 52 | ||
| } else { | ||
| $b.Width = $widthwindow * 2 + 1 # | ||
| } | ||
| $uisettings.WindowSize = $b # apply window size changes | ||
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| function cursor-goto-fine ([int] $x_coordinate, [int] $y_coordinate){ | ||
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| [Console]::SetCursorPosition($x_coordinate, $y_coordinate); | ||
| } | ||
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| cls | ||
| cursor-goto-fine (0)(0) | ||
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| function int-arr-zero ([int] $len){ # returns int array with length $len containing all zeroes. | ||
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| $arr = @(1..$len) | ||
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| for ($i = 0; $i -lt $len; $i++){ | ||
| $arr[$i] = 0 | ||
| } | ||
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| return $arr | ||
| } | ||
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| function flip-int-arr-endian ([int[]] $arr){ #rearrange from big-endian to little-endian | ||
| $num_len = $arr.Length | ||
| $num_re = int-arr-zero($arr.Length) | ||
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| for ($element = 0; $element -lt $num_len; $element++){ | ||
| $num_re[$element] = $arr[- $element - 1] | ||
| } | ||
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| return $num_re | ||
| } | ||
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| function to-num-array ([char[]] $arr){ #cast char value into int. or else char value will become two-digit int -> # value of ascii | ||
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| $num_len = $arr.Length | ||
| $num = int-arr-zero($arr.Length) | ||
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| for ($element = 0; $element -lt $num_len; $element++){ | ||
| $num[$element] = [int] $arr[$element] - 48 | ||
| } | ||
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| return $num | ||
| } | ||
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| function add-numstr-base ([string]$a, [string]$b, [int]$base, [int]$max_num_length){ # base must be 2 to 10 | ||
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| # add-numstr ("1")("1") | ||
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| $num_len = $max_num_length #155 # maximum for 512 bit integers | ||
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| $subtractbase = $base | ||
| $carrybase = $base - 1 | ||
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| $a_len = $a.Length | ||
| $b_len = $b.Length | ||
| if ($a_len -ge $b_len){$stop_len = $a_len + 2} else {$stop_len = $b_len + 2} | ||
| if ($stop_len -ge $num_len){$stop_len = $num_len} | ||
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| $num_a = $a.PadLeft($num_len,"0").ToCharArray() # ensure same number of digits for array later on | ||
| $num_b = $b.PadLeft($num_len,"0").ToCharArray() | ||
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| $num = int-arr-zero ($num_len) | ||
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| $num_a_re = flip-int-arr-endian (to-num-array ($num_a)) | ||
| $num_b_re = flip-int-arr-endian (to-num-array ($num_b)) | ||
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| for ($element = 0; $element -lt $stop_len; $element++){ | ||
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| $num[$element] = $num_a_re[$element] + $num_b_re[$element] | ||
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| } | ||
| for ($element = 0; $element -lt $stop_len - 1; $element++){ # carry places with more than 10 | ||
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| if ($num[$element] -gt $carrybase){ # for addition places will be no more than 9+9+1 (carry) 19, | ||
| $num[$element] = $num[$element] - $subtractbase # so repeated adding of carry (while loop) is not required | ||
| $num[$element + 1] = $num[$element + 1] + 1 | ||
| } | ||
| } | ||
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| $num_re = flip-int-arr-endian ($num) | ||
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| $num_re = $num_re -join "" | ||
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| return [string] $num_re -replace '^0+', '' | ||
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| } | ||
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| function multiply-by-base-shift([string]$a, [int]$shift, [int]$max_num_length){ # big endian only | ||
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| $num_len = $max_num_length | ||
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| $num = $a.PadLeft($num_len,"0").ToCharArray() | ||
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| $num = to-num-array ($num) | ||
| $num_mult = int-arr-zero($num_len) | ||
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| for ($element = $shift; $element -lt $num_len; $element++){ | ||
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| $num_mult[$element - $shift] = $num[$element] # already set to zero as in above for the ones place. | ||
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| } | ||
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| $num_mult = $num_mult -join "" | ||
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| return [string] $num_mult -replace '^0+', '' | ||
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| } | ||
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| function single-digit-multiply ([string]$num, [string]$one_digit, [int]$base, [int]$max_num_length){ | ||
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| $num_len = $max_num_length | ||
| $multi = [int] $one_digit # is a string not a char | ||
| Switch ($multi) { | ||
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| 2 { return add-numstr-base($num)($num)($base)($num_len) } | ||
| 3 { return add-numstr-base(add-numstr-base($num)($num)($base)($num_len))($num)($base)($num_len) } | ||
| 4 { $num2 = add-numstr-base($num)($num)($base)($num_len); return add-numstr-base($num2)($num2)($base)($num_len)} | ||
| 5 { $num2 = add-numstr-base($num)($num)($base)($num_len); $num3 = add-numstr-base($num2)($num)($base)($num_len); return add-numstr-base($num2)($num3)($base)($num_len)} | ||
| 6 { $num2 = add-numstr-base($num)($num)($base)($num_len); $num3 = add-numstr-base($num2)($num)($base)($num_len); return add-numstr-base($num3)($num3)($base)($num_len)} | ||
| 7 { $num2 = add-numstr-base($num)($num)($base)($num_len); $num3 = add-numstr-base($num2)($num)($base)($num_len); $num4 = add-numstr-base($num2)($num2)($base)($num_len); return add-numstr-base($num4)($num3)($base)($num_len)} | ||
| 8 { $num2 = add-numstr-base($num)($num)($base)($num_len); $num4 = add-numstr-base($num2)($num2)($base)($num_len); return add-numstr-base($num4)($num4)($base)($num_len)} | ||
| 9 { $num2 = add-numstr-base($num)($num)($base)($num_len); $num3 = add-numstr-base($num2)($num)($base)($num_len); $num6 = add-numstr-base($num3)($num3)($base)($num_len); return add-numstr-base($num6)($num3)($base)($num_len)} | ||
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| 1 {return $num } | ||
| 0 {return "0" } | ||
| } | ||
| } | ||
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| # single-digit-multiply ("5454")("9")(10) | ||
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| #incomplete | ||
| function multiply-numstr-base ([string]$a, [string]$b, [int]$base_system, [int]$max_num_length){ | ||
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| $base = $base_system #base | ||
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| $num_len = $max_num_length #155 # maximum for 512 bit integers | ||
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| $num_a = $a -replace '^0+', '' #.PadLeft($num_len,"0") # directly use string | ||
| $num_b = $b -replace '^0+', '' #.PadLeft($num_len,"0") | ||
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| #$num_b = $num_b.PadLeft(2,"0") | ||
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| $a_len = $num_a.Length | ||
| $b_len = $num_b.Length | ||
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| # check string length | ||
| if (($num_a -eq "") -or ($num_b -eq "")){ | ||
| [string] $reply = "0" | ||
| return $reply | ||
| } | ||
| if ($num_a -eq "1") {return $b} | ||
| if ($num_b -eq "1") {return $a} | ||
| if (($a_len -eq 1) -or ($b_len -eq 1)){ #base system | ||
| if ($a_len -eq 1){ | ||
| return single-digit-multiply($num_b)($num_a)($base)($num_len) | ||
| } | ||
| if ($b_len -eq 1){ | ||
| return single-digit-multiply($num_a)($num_b)($base)($num_len) | ||
| } | ||
| } | ||
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| #### script below only works if strings are more than 1 character long excluding trailing zeroes. | ||
| # multiply-numstr ("8")("9") wont work | ||
| # multiply-numstr ("18")("9") wont work | ||
| # multiply-numstr ("1")("29") wont work | ||
| # multiply-numstr ("18")("29") yes! | ||
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| [string[]] $num_ax = @(1..($base)) | ||
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| $num_ax[1] = $num_a | ||
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| for ($i = 2; $i -lt $base; $i++){ | ||
| $num_a_mult_temp = add-numstr-base($num_a)($num_ax[$i - 1])($base)($num_len) # pre calculate multiply | ||
| # $num_a_mult_temp = $num_a_mult_temp.PadLeft($num_len,"0") | ||
| $num_ax[$i] = $num_a_mult_temp | ||
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| } | ||
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| $num_b_little_endian = flip-int-arr-endian (to-num-array($num_b.ToCharArray())) # for multiplier index | ||
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| $result = int-arr-zero($num_len) | ||
| $result = $result -join "" | ||
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| for ($i = 0; $i -lt $b_len; $i++){ | ||
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| [int] $b_mult = $num_b_little_endian[$i] | ||
| if (!($b_mult -eq 0)){ # if position #j of $a is non-zero, add. | ||
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| $current_place_result = $num_ax[$b_mult] | ||
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| # calculate multiples of x (base) - adds a zero. by shifting to the left in big endian | ||
| if (!($i -eq 0)){ | ||
| $current_place_result = multiply-by-base-shift($current_place_result)($i)($num_len) | ||
| } | ||
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| $result = add-numstr-base($result)($current_place_result)($base)($num_len) # skipped if b_mult is zero, 0 | ||
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| } | ||
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| #$current_place_result -join "" | ||
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| } | ||
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| return $result -join "" -replace '^0+', '' | ||
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| } | ||
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| function prompt(){ | ||
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| #$pow = Read-Host ("`nInput power: ") | ||
| #$ans = pow2($pow) | ||
| #[console]::Write($ans) | ||
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| #$ans = pow2 (212) | ||
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| #$ans = add-numstr(pow2(212))(pow2(212)) | ||
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| #$ans = multiply-by-ten("47604524036730424631850294460894909302930821810983811727510334984391012367348") | ||
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| [console]::Write("`n`n Welcome to the Powershell multiply script.`n") | ||
| [console]::Write("`n This script multiplies up to two arbitrary integers. Tested up to 16384 characters.`n") | ||
| [console]::Write(" It also supports multiplication in any base from base 2-10`n") | ||
| [console]::Write("`n Created by KohGT in 2022`n") | ||
| [console]::Write("`n 1 1 1 1 1 1 1 ") | ||
| [console]::Write("`n 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 0 0 1 1 2 2 3 ") | ||
| [console]::Write("`n 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 ") | ||
| [console]::Write("`n > | | | | | | | | | | | | | | | | | | | | | | | | | | |`n") | ||
| $a = Read-Host (" Input first number") | ||
| $a = [string] $a | ||
| $b = Read-Host (" Input second number") | ||
| $b = [string] $b | ||
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| $d = Read-Host (" Input base [2-10] (Default: 10)") | ||
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| if ([string]::IsNullOrWhiteSpace($d)){ | ||
| [int] $d = 10 | ||
| [console]::Write("`nNo input detected, setting base 10.`n") | ||
| } | ||
| $d = [int] $d # convert from input string to int | ||
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| #length check | ||
| $alen = $a.Length | ||
| $blen = $b.Length | ||
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| [int] $num_len = $alen + $blen + 1 | ||
| $ans = multiply-numstr-base($a)($b)($d)($num_len) | ||
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| $clen = $ans.Length | ||
| if ($clen -gt $heightwindow +88){ | ||
| [console]::Write("`nNumber extremely large, may not fit in window. Please extend the window from the right side outwards ---------------------->>> `n") | ||
| } | ||
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| $offset_a = $clen - $alen | ||
| $offset_b = $clen - $blen | ||
| cursor-goto-fine(0)(18) | ||
| [console]::Write("`n`n`n") | ||
| [console]::Write(" "*(12+$offset_a)) | ||
| [console]::Write("$a`n") | ||
| [console]::Write(" "*7) | ||
| [console]::Write("x") | ||
| [console]::Write(" "*(4+$offset_b)) | ||
| [console]::Write("$b`n") | ||
| [console]::Write(" "*5) | ||
| [console]::Write("-"*($clen + 9)) | ||
| [console]::Write("`n") | ||
| [console]::Write(" "*12) | ||
| [console]::Write("$ans`n`n") | ||
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| while (1 -eq 1){ | ||
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| cursor-goto-fine(4)(28) | ||
| [console]::Write(" ") | ||
| cursor-goto-fine(4)(28) | ||
| $a = Read-Host ("Do you want to [r]eset, or [q]uit?") | ||
| $a = [string]$a | ||
| Switch ($a){ | ||
| r { return $true } | ||
| R { return $true } | ||
| q { return $false } | ||
| Q { return $false } | ||
| default {[console]::Write("`nInvalid response!`n")} #; [console]::Beep(1500,200)} | ||
| } | ||
| } | ||
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| } | ||
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| function main(){ | ||
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| $loop = $true | ||
| while ($loop -eq $true){ | ||
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| $loop = prompt | ||
| cls; | ||
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| } | ||
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| } | ||
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| main | ||
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| # 87943789324987777777777777777777777777777777777777777777777777777777777777779999999999999999999999999999999999999999999999999999999883 | ||
| # x22222222222222222222222222222222222333333333333333333333333333333322222222222222222222222333333333333333333333333333333222222222222222 | ||
| # 1954306429444172839506172839506172849277704986727037037037037037036059883822364333333333343104865480554197530864444444434672912297220960703849261113827160493827160494061074074074074074074074074073828460493827159999999999987000000000000000000000000000013000000000000026 |