# Numerical Calculation

This chapter lists code examples of performing numerical calculations, including Null value judgment, Random values, Constants of various data types, Signs of numbers, Involution and evolution, Decimal truncation and rounding, Continued multiplication & factorial, Accumulated sum, Greatest common divisor & least common multiple, Permutation & combination, Pi, Trigonometric functions, Logarithmic functions, Compute expressions with different conditions, Use temp variable in expressions and Logic operations.

## Null value judgment

 A 1 =null 2 =0 0 3 =if(A1==null,"null","not null") null 4 =if(!A1,"null","not null") null 5 =if(A2!=null,"not null","null") not null 6 =[,1,2,3].ifn() 1 7 =["",,,0,3].nvl() 0

## Random values

 A 1 =rand() Get a random value between 0 and 1 2 =rand(1000) Get random integer values between 0 and 1,000 inclusive

## Constants of various data types

 A 1 time String type "time" 2 -3415 32-bit integer -3415 3 3.1415927 Floating point number 3.1415927 4 1101022000L 64-bit long integer 1101022000 5 12345678901 An integer exceeding the value range of a 32-bit integer will be automatically parsed into the 64-bit long integer 12345678901 6 35% 0.35, which is floating point number represented by a percentage 7 0x33 The value is 51, a hexadecimal long integer headed by 0x 8 '345+6 The value is string "345+6"; the sign ' marks a string type constant

## Signs of numbers

 A 1 =sign(45) Return 1 for a positive number 2 =sign(-100.34) Return -1 for a negative number 3 =sign(0) Return 0 for zero 4 =abs(-4.6) Return the absolute value 4.6

## Involution and evolution

 A 1 =power(2,3) Cube 2 =power(-2,3) Cube 3 =power(4,0.5) Square root 4 =sqrt(8,2) Square root 5 =power(27,1/3) Cube root 6 =sqrt(8,3) Cube root

## Decimal truncation and rounding

 A 1 =round(3451251.274,1) Round down to 1 decimal place 2 =round(3451251.274,2) Round down to 2 decimal places 3 =ceil(3450001.003,-2) Carry the remaining figures to the column of hundreds 4 =ceil(3450001.003,2) Carry the remaining figures and round off to 2 decimal places 5 =floor(3451291.234,-2) Round to the column of hundreds and discard all the remaining figures 6 =floor(3451281.238,2) Round off to 2 decimal places and discard the remaining figure

## Continued multiplication & factorial

 A 1 =product(2, 3, 5, 7) 210, the value of calculating 2*3*5*7 2 =product([7, 4, 4]) 112, the value of continual multiplication of the numbers in the given sequence 3 =fact(5) 120, the value of factorial 5 4 =fact(0) 1

## Accumulated sum

 A 1 =[1,2,3,4].(cum(~)) [1,3,6,10], iterative sum

## Greatest common divisor & Least common multiple

 A 1 =gcd(2000, 875, 325) 25, gcd of the 3 numbers 2 =gcd([1001, 28]) 7, gcd of the members of the sequence 3 =gcd(20005, 1234) 1; the two numbers are coprime 4 =lcm(10, 35, 28) 140, lcm of the 3 numbers 5 =lcm([1001, 111]) 111111, lcm of the members of the sequence，

## Permutation & combination

 A 1 =combin(10, 3) 120, the number of combinations of selecting 3 from 10 elements 2 =combin(5, 4) 5, the number of combinations of selecting 4 from 5 elements 3 =permut(10, 3) 720, the number of permutations of selecting 3 from 10 elements 4 =permut(5, 4) 120, the number of permutations of selecting 4 from 5 elements

## Pi

 A 1 =pi() π 2 =pi(4) 4*π

## Infinity

 A 1 =inf() Positive infinity 2 =-inf() Negative infinity

## Trigonometric functions

 A 1 =sin(pi(30/180)) Sine 2 =cos(pi()/2) Cosine 3 =tan(pi()/4) Tangent 4 =asin(0.5) Arc sine 5 =acos(-0.5) Arc cosine 6 =atan(1) Arc tangent 7 =sinh(1) Hyperbolic sine 8 =cosh(4) Hyperbolic cosine 9 =tanh(0.5) Hyperbolic tangent 10 =asinh(10) Inverse hyperbolic sine 11 =acosh(10) Inverse hyperbolic cosine 12 =atanh(0.5) Inverse hyperbolic tangent

## Logarithmic functions

 A 1 =lg(10000) Logarithm to base 10 2 =lg(8,2) Logarithm to base 2 3 =ln(1000) Natural logarithm 4 =exp(A2) e to the nth power

## Compute expressions with different conditions

 A 1 3000 2 =if(A1>10000, A1*0.45+450, A1>5000, A1*0.15+150, A1*0.05) 150.0 3 manager 4 =case(A3,"president":500,"manager":300,"employee":150) 300

## Use temp variables in expressions

 A 1 =(a=1,b=a*3,b+4) 7 2 =a 1 3 =b 3

## Logic operations

 A 1 =and(6,10) 2, bitwise AND 2 =or(3,5) 7, bitwise OR 3 =not(6) -7, bitwise NOT 4 =xor(6,11) 13, bitwise XOR 5 =shift(13,2) 3, Shift right two bit positions 6 =shift(13,-2) 52, Shift left two bit positions