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Multiplies two 256-bit Base-10 integers
Supports up to 155 digits of decimal output, 78 digits of decimal input, which is sufficient to input 256-bit binary numbers in base-10. Not yet tested on inputs larger than 115792089237316195423570985008687907853269984665640564039457584007913129639936. Maximum output is 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999. 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 | ||
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| $num_re = int-arr-zero($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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| $num = int-arr-zero($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 $num | ||
| } | ||
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| function pow2 ([int]$pow){ | ||
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| # 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,935 | ||
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| # cycles | ||
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| $num_len = 155 # maximum for 512 bit integers | ||
| $num = int-arr-zero($num_len) | ||
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| $num[0] = 1 | ||
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| for ($loops = 0; $loops -lt $pow; $loops++){ | ||
| for ($element = 0; $element -lt $num_len; $element++){ #double every int in array | ||
| if ($num[$element] -ne 0){ | ||
| $num[$element] = $num[$element] * 2 | ||
| } | ||
| } | ||
| for ($element = 0; $element -lt $num_len; $element++){ #carry every int in array | ||
| if ($num[$element] -gt 9){ | ||
| $num[$element] = $num[$element] - 10 | ||
| $num[$element + 1] = $num[$element + 1] + 1 | ||
| } | ||
| } | ||
| } | ||
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| $num_re = flip-int-arr-endian ($num) | ||
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| return $num_re -join "" -replace '^0+', '' | ||
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| } | ||
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| function add-numstr ([string]$a, [string]$b){ | ||
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| # add-numstr ("1")("1") | ||
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| $num_len = 155 # maximum for 512 bit integers | ||
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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 9){ # for addition places will be no more than 9+9+1 (carry) 19, | ||
| $num[$element] = $num[$element] - 10 # 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] $num_re -replace '^0+', '' | ||
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| } | ||
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| function multiply-by-ten-shift([string]$a, [int]$shift){ # big endian only | ||
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| $num_len = 155 | ||
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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] $num_mult -replace '^0+', '' | ||
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| } | ||
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| #incomplete | ||
| #strip commas and dots | ||
| function multiply-numstr ([string]$a, [string]$b){ | ||
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| # multiply-numstr ("1")("1") | ||
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| $num_len = 155 # maximum for 512 bit integers | ||
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| $b_len = $b.Length | ||
| $stop_b_len = $a_len + $b_len + 1 | ||
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| $num_a = $a.PadLeft($num_len,"0") # directly use string | ||
| $num_b = $b.PadLeft($num_len,"0") | ||
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| $num_a2 = add-numstr($num_a)($num_a) | ||
| $num_a3 = add-numstr($num_a)($num_a2) | ||
| $num_a4 = add-numstr($num_a2)($num_a2) | ||
| $num_a5 = add-numstr($num_a2)($num_a3) | ||
| $num_a6 = add-numstr($num_a3)($num_a3) | ||
| $num_a7 = add-numstr($num_a3)($num_a4) | ||
| $num_a8 = add-numstr($num_a4)($num_a4) | ||
| $num_a9 = add-numstr($num_a4)($num_a5) | ||
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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) -join "" | ||
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| for ($i = 0; $i -lt $stop_b_len; $i++){ | ||
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| $current_place_result = int-arr-zero($num_len) -join "" | ||
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| [int] $b_mult = $num_b_little_endian[$i] | ||
| if (!($b_mult -eq 0)){ # if position #j of $a is non-zero, | ||
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| Switch ($b_mult) { | ||
| 1 {$current_place_result = $num_a} | ||
| 2 {$current_place_result = $num_a2} | ||
| 3 {$current_place_result = $num_a3} | ||
| 4 {$current_place_result = $num_a4} | ||
| 5 {$current_place_result = $num_a5} | ||
| 6 {$current_place_result = $num_a6} | ||
| 7 {$current_place_result = $num_a7} | ||
| 8 {$current_place_result = $num_a8} | ||
| 9 {$current_place_result = $num_a9} | ||
| } | ||
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| # calculate multiples of x10 | ||
| if (!($i -eq 0)){ | ||
| $current_place_result = multiply-by-ten-shift($current_place_result)($i) | ||
| } | ||
| } | ||
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| $result = add-numstr($result)($current_place_result) | ||
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| } | ||
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| return $result -join "" -replace '^0+', '' | ||
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| } | ||
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| #$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") | ||
| [console]::Write("`n`n Welcome to the Powershell multiply-512 script.`n") | ||
| [console]::Write("`n This script multiplies up to two 78 character long integers.`n") | ||
| [console]::Write(" This means it supports the multiplication of two 256-bit numbers.`n") | ||
| [console]::Write("`n Created by KohGT in 2022`n") | ||
| [console]::Write("`n --------------------0----0----1----1----2----2----3----3----4----4----5----5----6----6----7----7--7") | ||
| [console]::Write("`n --------------------0----5----0----5----0----5----0----5----0----5----0----5----0----5----0----5--8`n") | ||
| $a = Read-Host (" Input first number ") | ||
| $a = [string] $a | ||
| $b = Read-Host (" Input second number") | ||
| $b = [string] $b | ||
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| $c = multiply-numstr($a)($b) | ||
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| cls; | ||
| #length check | ||
| $alen = $a.Length | ||
| $blen = $b.Length | ||
| $clen = $c.Length | ||
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| $offset_a = $clen - $alen | ||
| $offset_b = $clen - $blen | ||
| cursor-goto-fine(0)(0) | ||
| [console]::Write("`n`n`n") | ||
| [console]::Write(" "*(12+$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("$c`n`n") | ||
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| $a = Read-Host ("Press enter to continue") | ||
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