# ๐งฎ Math **#bs.math:help** The beatifull world of mathematics... **in Minecraft!** {image} /_imgs/modules/math-light.png :align: center :class: only-light  {image} /_imgs/modules/math-dark.png :align: center :class: only-dark  {epigraph} "Mathematics has very subtle inventions that can be of great service, both to satisfy the curious and to facilitate all arts and reduce the labor of men." -- Renรฉ Descartes  {button-link} https://youtu.be/Bt0HKaOosqU :color: primary :align: center :shadow: {octicon}device-camera-video Watch a demo  --- ## ๐ง Functions You can find below all functions available in this module. --- ### Combine {function} #bs.math:combine Compute the combine of 2 numbers. :Inputs: **Scores $math.combine.[n,k] bs.in**: Numbers to be combined, the smaller input will be taken from the greater input. :Outputs: **Return | Score $math.combine bs.out**: Result of the operation.  {admonition} Technical limitation :class: important The value of bs.out is incorrect if the result is greater than 2,147,483,647 or $math.combine.[n,k] bs.in are not both positive.  *Compute$combine(4,2)$:* mcfunction # Once scoreboard players set$math.combine.n bs.in 4 scoreboard players set $math.combine.k bs.in 2 function #bs.math:combine tellraw @a [{"text": "combine(4,2) = ","color":"dark_gray"},{"score":{"name":"$math.combine","objective":"bs.out"},"color":"gold"}]  > **Credits**: Ethanout --- ### Exponential ::::{tab-set} :::{tab-item} Natural {function} #bs.math:exp Compute the exponential function. :Inputs: **Storage bs:in math.exp.x**: {nbt}number Number to be exponentiated. :Outputs: **Storage bs:out math.exp**: {nbt}float Result of the operation.  *Compute $exp(3)$:* mcfunction # Once data modify storage bs:in math.exp.x set value 3.0 function #bs.math:exp data get storage bs:out math.exp  ::: :::{tab-item} Base 2 {function} #bs.math:exp2 Compute the exponential function in base 2. :Inputs: **Storage bs:in math.exp2.x**: {nbt}number Number to be exponentiated. :Outputs: **Storage bs:out math.exp2**: {nbt}float Result of the operation.  *Compute $exp2(3)$:* mcfunction # Once data modify storage bs:in math.exp2.x set value 3.0 function #bs.math:exp2 data get storage bs:out math.exp2  :::: ![](/_imgs/modules/math/exp.png) > **Credits**: Aksiome --- ### Factorial {function} #bs.math:factorial Compute the factorial of the number. :Inputs: **Score $math.factorial.n bs.in**: Number to be factorialized. :Outputs: **Return | Score $math.factorial bs.out**: Result of the operation.  {admonition} Technical limitation :class: important Due to the limit of integers that can be stored in a score, the interval of $math.factorial.n bs.in is limited to [0,12].  *Compute$3!$:* mcfunction # Once scoreboard players set$math.factorial.n bs.in 3 function #bs.math:factorial tellraw @a [{"text": "3! = ","color":"dark_gray"},{"score":{"name":"$math.factorial","objective":"bs.out"},"color":"gold"}]  ![](/_imgs/modules/math/factorial.png) > **Credits**: KubbyDev --- ### Float manipulation ::::{tab-set} :::{tab-item} Frexp {function} #bs.math:frexp Decompose a floating point number into a normalized fraction and an integral power of two. :Inputs: **Storage bs:in math.frexp.x**: {nbt}number Number to be decomposed. :Outputs: **Storage bs:out math.frexp.e**: {nbt}int Exponent for the power of 2. **Storage bs:out math.frexp.x**: {nbt}float Normalized fraction in range ]-1,-0.5] or [0.5,1[.  *Decompose 5.8 into its mantissa and exponent:* mcfunction # Once data modify storage bs:in math.frexp.x set value 5.8 function #bs.math:frexp data get storage bs:out math.frexp  ::: :::{tab-item} Ldexp {function} #bs.math:ldexp Build a floating point number from a normalized fraction and an integral power of two. :Inputs: **Storage bs:in math.ldexp.x**: {nbt}number Normalized fraction in range ]-1,-0.5] or [0.5,1[. **Storage bs:in math.ldexp.e**: {nbt}int Exponent for the power of 2. :Outputs: **Storage bs:out math.ldexp**: {nbt}float Resulting floating-point number.  *Compose a floating-point number:* mcfunction # Once data modify storage bs:in math.ldexp.e set value 3 data modify storage bs:in math.ldexp.x set value 0.75 function #bs.math:ldexp data get storage bs:out math.ldexp  ::: :::: > **Credits**: Aksiome --- ### Greatest common denominator {function} #bs.math:gcd Compute the greatest common denominator of two numbers. :Inputs: **Scores $math.gcd.[a,b] bs.in**: The two numbers. :Outputs: **Return | Score $math.gcd bs.out**: The greatest common denominator.  *Calculate the greatest common denominator between 16 and 12:* mcfunction # Once scoreboard players set$math.gcd.a bs.in 16 scoreboard players set $math.gcd.b bs.in 12 function #bs.math:gcd tellraw @a [{"text": "gcd(16,12) = ", "color": "dark_gray"},{"score":{"name":"$math.gcd", "objective": "bs.out"}, "color": "gold"}]  ![](/_imgs/modules/math/gcd.png) > **Credits**: Aksiome, Leirof --- ### Inverse trigonometry ::::{tab-set} :::{tab-item} Acos {function} #bs.math:acos Compute the arc cosine of a value between -1 and 1. :Inputs: **Score $math.acos.x bs.in**: Value you want to compute the arccosine of, shifted by 3 digits (1,2345 โ 1234) for better precision in integer scores. :Outputs: **Return | Score $math.acos bs.out**: Result of the operation in degrees, shifted by 2 digits.  *Compute and display the arccosine of 0.42:* mcfunction # Once scoreboard players set $math.acos.x bs.in 420 function #bs.math:acos tellraw @a [{"text":"acos(0.42) = ","color":"dark_gray"},{"score":{"name":"$math.acos","objective":"bs.out"},"color":"gold"}]  ![](/_imgs/modules/math/arccos.png) ::: :::{tab-item} Asin {function} #bs.math:asin Compute the arc sine of a value between -1 and 1. :Inputs: **Score $math.asin.x bs.in**: Value you want to compute the arcsine of, shifted by 3 digits (1,2345 โ 1234) for better precision in integer scores. :Outputs: **Return | Score $math.asin bs.out**: Result of the operation in degrees, shifted by 2 digits.  *Compute and display the arcsine of 0.42:* mcfunction # Once scoreboard players set $math.asin.x bs.in 420 function #bs.math:asin tellraw @a [{"text":"asin(0.42) = ","color":"dark_gray"},{"score":{"name":"$math.asin","objective":"bs.out"},"color":"gold"}]  ![](/_imgs/modules/math/arcsin.png) ::: :::{tab-item} Atan {function} #bs.math:atan Compute the arc tangent of a value between -infinite and +infinite. :Inputs: **Score $math.atan.x bs.in**: Value you want to compute the arctangent of, shifted by 3 digits (1,2345 โ 1234) for better precision in integer scores. :Outputs: **Return | Score $math.atan bs.out**: Result of the operation in degrees, shifted by 2 digits.  *Compute and display the arctan of 0.42:* mcfunction # Once scoreboard players set $math.atan.x bs.in 420 function #bs.math:atan tellraw @a [{"text":"atan(0.42) = ","color":"dark_gray"},{"score":{"name":"$math.atan","objective":"bs.out"},"color":"gold"}]  ![](/_imgs/modules/math/arctan.png) ::: :::{tab-item} Atan2 {function} #bs.math:atan2 Compute the 2-argument arctangent of y and x. :Inputs: **Scores $math.atan2.[y,x] bs.in**: Values you want to compute the arctangent of, shifted by 3 digits (1,2345 โ 1234) for better precision in integer scores. :Outputs: **Return | Score $math.atan2 bs.out**: Result of the operation in degrees, shifted by 2 digits.  *Compute and display the atan2 of (0.42, 0.8):* mcfunction # Once scoreboard players set $math.atan2.y bs.in 420 scoreboard players set$math.atan2.x bs.in 800 function #bs.math:atan2 tellraw @a [{"text":"atan2(0.42, 0.8) = ","color":"dark_gray"},{"score":{"name":"$math.atan2","objective":"bs.out"},"color":"gold"}]  ::: :::: > **Credits**: Aksiome, KubbyDev, Leirof --- ### Logarithm ::::{tab-set} :::{tab-item} Natural {function} #bs.math:log Compute the natural logarithm (base e) of a number. :Inputs: **Storage bs:in math.log.x**: {nbt}number Number to be logarithmized. :Outputs: **Storage bs:out math.log**: {nbt}float Result of the operation.  *Calculate$ln(28)$:* mcfunction # Once data modify storage bs:in math.log.x set value 28.0 function #bs.math:log data get storage bs:out math.log  ::: :::{tab-item} Base 2 {function} #bs.math:log2 Compute the logarithm in base 2 of a number. :Inputs: **Storage bs:in math.log2.x**: {nbt}number Number to be logarithmized. :Outputs: **Storage bs:out math.log2**: {nbt}float Result of the operation.  *Calculate$log_2(28)$:* mcfunction # Once data modify storage bs:in math.log2.x set value 28.0 function #bs.math:log2 data get storage bs:out math.log2  ::: :::{tab-item} Base 10 {function} #bs.math:log10 Compute the logarithm in base 10 of a number. :Inputs: **Storage bs:in math.log10.x**: {nbt}number Number to be logarithmized. :Outputs: **Storage bs:out math.log10**: {nbt}float Result of the operation.  *Calculate$log_{10}(28)$:* mcfunction # Once data modify storage bs:in math.log10.x set value 28.0 function #bs.math:log10 data get storage bs:out math.log10  ::: :::{tab-item} Base a {function} #bs.math:loga Compute the logarithm in base a of a number. :Inputs: **Storage bs:in math.loga.x**: {nbt}number Number to be logarithmized. **Storage bs:in math.loga.a**: {nbt}number Base of the logarithm. :Outputs: **Storage bs:out math.loga**: {nbt}float Result of the operation.  *Calculate$log_4(28)$:* mcfunction # Once data modify storage bs:in math.loga.a set value 4 data modify storage bs:in math.loga.x set value 28.0 function #bs.math:loga data get storage bs:out math.loga  ::: :::: > **Credits**: Aksiome --- ### Power ::::{tab-set} :::{tab-item} Integer {function} #bs.math:ipow Compute the power of integer numbers. :Inputs: **Score $math.ipow.x bs.in**: The base. **Score $math.ipow.y bs.in**: The exponent. :Outputs: **Return | Score $math.ipow bs.out**: Result of the operation.  *Compute and display $3^6$:* mcfunction # Once scoreboard players set $math.ipow.x bs.in 3 scoreboard players set$math.ipow.y bs.in 6 function #bs.math:ipow tellraw @a [{"text": "3^6 = ", "color": "dark_gray"},{"score":{"name":"$math.ipow", "objective": "bs.out"}, "color": "gold"}]  ::: :::{tab-item} Decimal {function} #bs.math:pow Compute the power of floating numbers. :Inputs: **Storage bs:in math.pow.x**: {nbt}number The base. **Storage bs:in math.pow.y**: {nbt}number The exponent. :Outputs: **Storage bs:out math.pow**: {nbt}float Result of the operation.  *Compute and display$pow(3.5, 2.25)$:* mcfunction # Once data modify storage bs:in math.pow set value {x:3.5,y:2.25} function #bs.math:pow tellraw @a [{"text": "3.5^2.25 = ", "color": "dark_gray"},{"nbt": "math.pow", "storage": "bs:out", "color": "gold"}]  ::: :::: ![](/_imgs/modules/math/power.png) > **Credits**: Aksiome, Leirof --- ### Rounded division {function} #bs.math:divide Divide a number by another then round the result to the nearest integer (Minecraft rounds down to the next integer). :Inputs: **Score $math.divide.x bs.in**: The numerator. **Score $math.divide.y bs.in**: The denominator. :Outputs: **Return | Score $math.divide bs.out**: Result of the division.  *Calculate $9/5$:* mcfunction # Once scoreboard players set $math.divide.x bs.in 9 scoreboard players set$math.divide.y bs.in 5 function #bs.math:divide tellraw @a [{"text": "9 / 5 = ", "color": "dark_gray"},{"score":{"name":"$math.divide", "objective": "bs.out"}, "color": "gold"}]  ![](/_imgs/modules/math/divide.png) > **Credits**: Aksiome, theogiraudet --- ### Square root ::::{tab-set} :::{tab-item} Integer {function} #bs.math:isqrt Compute the square root of an integer number. :Inputs: **Score $math.isqrt.x bs.in**: Number you want to calculate the square root of. :Outputs: **Return | Score $math.isqrt bs.out**: Floored result of the square root.  *Calculate and display$\sqrt{42}$:* mcfunction # Once scoreboard players set$math.isqrt.x bs.in 42 function #bs.math:isqrt tellraw @a [{"text": "sqrt(42) = ", "color": "dark_gray"},{"score":{"name":"$math.isqrt", "objective": "bs.out"}, "color": "gold"}]  ::: :::{tab-item} Decimal {function} #bs.math:sqrt Compute the square root of a floating number. :Inputs: **Storage bs:in math.sqrt.x**: {nbt}number Number you want to calculate the square root of. :Outputs: **Storage bs:out math.sqrt**: {nbt}float Result of the operation.  *Calculate and display$\sqrt{42}$:* mcfunction # Once data modify storage bs:in math.sqrt.x set value 42 function #bs.math:sqrt tellraw @a [{"text": "sqrt(42) = ", "color": "dark_gray"},{"nbt": "math.sqrt", "storage": "bs:out", "color": "gold"}]  ::: :::: ![](/_imgs/modules/math/sqrt.png) > **Credits**: Ethanout --- ### Trigonometry ::::{tab-set} :::{tab-item} Cos {function} #bs.math:cos Compute the cosine of an angle between 0 and 360. :Inputs: **Score $math.cos.x bs.in**: Angle in degrees shifted by 2 digits (ex: 90.15 โ 9015). :Outputs: **Return | Score $math.cos bs.out**: Cosine of the angle shifted by 3 digits (ex: 0.42 โ 420).  *Compute and display the cosine of 42:* mcfunction # Once scoreboard players set$math.cos.x bs.in 4200 function #bs.math:cos tellraw @a [{"text": "cos(42) = ", "color": "dark_gray"},{"score":{"name":"$math.cos", "objective": "bs.out"}, "color": "gold"}]  ![](/_imgs/modules/math/cosine.png) {admonition} How does it work? :class: dropdown This functions use the Bhaskara approximation which tell us that $$\sin(x) \approx \frac{4x(180-x)}{40500-x(180-x)} \quad \forall x \in [0, 180]$$ From this relation, and using the properties -$\sin(-x) = -\sin(x)$(antisymetry) -$\sin(x+360) = \sin(x)$(periodicity) We can compute the sine of any angle and thus the cosine. ![](/_imgs/modules/math/bhaskara.png)  ::: :::{tab-item} Sin {function} #bs.math:sin Compute the sine of an angle between 0 and 360. :Inputs: **Score $math.sin.x bs.in**: Angle in degrees shifted by 2 digits (ex: 90.15 โ 9015). :Outputs: **Return | Score $math.sin bs.out**: Sine of the angle shifted by 3 digits (ex: 0.42 โ 420).  *Compute and display the sine of 42:* mcfunction # Once scoreboard players set$math.sin.x bs.in 4200 function #bs.math:sin tellraw @a [{"text": "sin(42) = ", "color": "dark_gray"},{"score":{"name":"$math.sin", "objective": "bs.out"}, "color": "gold"}]  ![](/_imgs/modules/math/sine.png) {admonition} How does it work? :class: dropdown This functions use the Bhaskara approximation which tell us that $$\sin(x) \approx \frac{4x(180-x)}{40500-x(180-x)} \quad \forall x \in [0, 180]$$ From this relation, and using the properties -$\sin(-x) = -\sin(x)$(antisymetry) -$\sin(x+360) = \sin(x)$(periodicity) We can compute the sine of any angle. ![](/_imgs/modules/math/bhaskara.png)  ::: :::{tab-item} Tan {function} #bs.math:tan Compute the tangent of an angle between 0 and 360. :Inputs: **Score $math.tan.x bs.in**: Angle in degrees shifted by 2 digits (ex: 90.15 โ 9015). :Outputs: **Return | Score $math.tan bs.out**: Tangent of the angle shifted by 3 digits (ex: 0.42 โ 420).  *Compute and display the tangent of 42:* mcfunction # Once scoreboard players set$math.tan.x bs.in 4200 function #bs.math:tan tellraw @a [{"text": "tan(42) = ", "color": "dark_gray"},{"score":{"name":"$math.tan", "objective": "bs.out"}, "color": "gold"}]  ![](/_imgs/modules/math/tangent.png) ::: :::{tab-item} Sincos {function} #bs.math:sincos Compute both the sine and cosine of an angle between 0 and 360 in a single operation. :Inputs: **Score $math.sincos.x bs.in**: Angle in degrees shifted by 2 digits (ex: 90.15 โ 9015). :Outputs: **Score $math.sincos.cos bs.out**: Cosine of the angle shifted by 3 digits (ex: 0.42 โ 420). **Score $math.sincos.sin bs.out**: Sine of the angle shifted by 3 digits (ex: 0.42 โ 420).  *Compute and display the sine and cosine of 42:* mcfunction # Once scoreboard players set $math.sincos.x bs.in 4200 function #bs.math:sincos tellraw @a [{"text": "cos(42) = ", "color": "dark_gray"},{"score":{"name":"$math.sincos.cos", "objective": "bs.out"}, "color": "gold"}] tellraw @a [{"text": "sin(42) = ", "color": "dark_gray"},{"score":{"name":"\$math.sincos.sin", "objective": "bs.out"}, "color": "gold"}]  {admonition} How does this method differ from cos and sin? :class: dropdown This function utilizes Minecraft teleportation to calculate both the cosine and sine values. While it's slightly less efficient than calling either cos or sin individually, it allows for computing both in a single operation.  ::: :::: > **Credits**: Aksiome, Leirof ---