Mathematical expression parsing and calculation engine library. 数学表达式解析计算引擎库

Overview

Math-Engine

Build Status Go Report Card godoc.org

使用 Go 实现的数学表达式解析计算引擎库,它小巧,无任何依赖,具有扩展性(比如可以注册自己的函数到引擎中),比较完整的完成了数学表达式解析执行,包括词法分析、语法分析、构建AST、运行。

go get -u github.com/dengsgo/math-engine

能够处理的表达式样例:

  • 1+127-21+(3-4)*6/2.5
  • (88+(1+8)*6)/2+99
  • 123_345_456 * 1.5 - 2 ^ 4
  • -4 * 6 + 2e2 - 1.6e-3
  • sin(pi/2)+cos(45-45*1)+tan(pi/4)
  • 99+abs(-1)-ceil(88.8)+floor(88.8)
  • max(min(2^3, 3^2), 10*1.5-7)
  • double(6) + 3 , double是一个自定义的函数

Demo

asciicast

Method Support

symbol explanation e.g.
+ 加,plus 1+2 = 3
- 减,sub 8-3.5 = 4.5
* 乘,multiply 2*3 = 6
/ 除,division 5/2 = 2.5
% 取余,remainder 5%2 = 1
^ 整数次方,integer power 2^3 = 8, 3^2 = 9
e 科学计数法,E-notation 1.2e3 = 1.2e+3 = 1200,1.2e-2 = 0.012
() 括号,brackets (2+3)*4 = 20
_ 数字分隔符,number separator 123_456_789 = 123456789
pi π pi = 3.141592653589793
sin(x) 正弦函数,sine sin(pi/2) = 1
cos(x) 余弦函数,cosine cos(0) = 1
tan(x) 正切函数,tangent tan(pi/4) = 1
cot(x) 余切函数,cotangent cot(pi/4) = 1
sec(x) 正割函数,secant sec(0) = 1
csc(x) 余割函数,cosecant csc(pi/2) = 1
abs(x) 绝对值,absolute value abs(-6) = 6
ceil(x) 向上取整 ceil(4.2) = 5
floor(x) 向下取整 floor(4.8) = 4
round(x) 四舍五入取整 round(4.4) = 4, round(4.5) = 5
sqrt(x) 平方根,square root sqrt(4) = 2
cbrt(x) 立方根,cube root cbrt(27) = 3
max(x, y) x, y 中的较大值 max(2, 3) = 3
min(x, y) x, y 中的较小值 min(2, 3) = 2
noerr(x) 计算 x 出错时返回 0 noerr(1 / 1) = 1, noerr( 1/ 0 ) = 0
double(x) 返回 x 的双倍值,这是一个自定义的函数示例,你可以注册任意的自定义函数到引擎中 double(6) = 12

Usage

你可以直接引用该库嵌入到自己的程序中:

go get -u github.com/dengsgo/math-engine

在代码中引入:

import "github.com/dengsgo/math-engine/engine"

e.g. 1 常规用法: 直接调用解析执行函数 :

import "github.com/dengsgo/math-engine/engine"

func main() {
  s := "1 + 2 * 6 / 4 + (456 - 8 * 9.2) - (2 + 4 ^ 5)"
  // call top level function
  r, err := engine.ParseAndExec(s)
  if err != nil {
    fmt.Println(err)
  }
  fmt.Printf("%s = %v", s, r)
}

e.g. 2 高级用法: 依次调用函数,手动执行 :

import "github.com/dengsgo/math-engine/engine"

func main() {
	s := "1 + 2 * 6 / 4 + (456 - 8 * 9.2) - (2 + 4 ^ 5)"
	exec(s)
}

// call engine
// one by one
func exec(exp string) {
	// input text -> []token
	toks, err := engine.Parse(exp)
	if err != nil {
		fmt.Println("ERROR: " + err.Error())
		return
	}
	// []token -> AST Tree
	ast := engine.NewAST(toks, exp)
	if ast.Err != nil {
		fmt.Println("ERROR: " + ast.Err.Error())
		return
	}
	// AST builder
	ar := ast.ParseExpression()
	if ast.Err != nil {
		fmt.Println("ERROR: " + ast.Err.Error())
		return
	}
	fmt.Printf("ExprAST: %+v\n", ar)
	// AST traversal -> result
	r := engine.ExprASTResult(ar)
	fmt.Println("progressing ...\t", r)
	fmt.Printf("%s = %v\n", exp, r)
}

编译运行,应该可以看到如下输出:

ExprAST: {Op:- Lhs:{Op:+ Lhs:{Op:+ Lhs:{Val:1} Rhs:{Op:/ Lhs:{Op:* Lhs:{Val:2} Rhs:{Val:6}} Rhs:{Val:4}}} Rhs:{Op:- Lhs:{Val:456} Rhs:{Op:* Lhs:{Val:8} Rhs:{Val:9.2}}}} Rhs:{Op:+ Lhs:{Val:2} Rhs:{Op:^ Lhs:{Val:4} Rhs:{Val:5}}}}
progressing ...  -639.6
1+2*6/4+(456-8*9.2)-(2+4^5) = -639.6

TrigonometricMode

三角函数的参数类型默认为弧度RadianMode,e.g. sin(pi/2) = 1.

你可以通过设置 TrigonometricMode 调整参数类型,可选 弧度RadianMode、角度AngleMode,e.g. :

import "github.com/dengsgo/math-engine/engine"

func main() {
  s := "1 + sin(90)"
  engine.TrigonometricMode = engine.AngleMode
  engine.ParseAndExec(s) // will return 2, nil
  s = "1 + sin(pi/2)"
  engine.TrigonometricMode = engine.RadianMode
  engine.ParseAndExec(s) // will return 2, nil
}

Register Function

math-engine 提供了自定义函数注册到引擎的能力。你可以把常用的函数注册到引擎中,然后就能像内置函数一样在输入的数学表达式中使用。

e.g

  // RegFunction is Top level function
  // the same function name only needs to be registered once.
  // double is register function name.
  // 1 is a number of parameter signatures.
  // func(expr ...engine.ExprAST) float64 is your function.
  engine.RegFunction("double", 1, func(expr ...engine.ExprAST) float64 {
    // you can use the index value directly according to the number of parameters
    // without worrying about crossing the boundary.
    // use ExprASTResult to get the result of the ExprAST structure.
    return engine.ExprASTResult(expr[0]) * 2
  })

然后你就可以在输入的表达式中使用这个函数 double:

//exp := "double(6) + 2"
r, err := engine.ParseAndExec("double(6) + 2")
if err != nil {
  panic(err)
}
fmt.Printf("double(6) + 2 = %f\n", r) // will print : double(6) + 2 = 14.000000

注意事项:

  • 注册的函数名只能是英文字母和数字,且必须英文字母开头(区分大小写);
  • 每一个函数名只能且只需注册一次;
  • 注册的函数逻辑中如果有 panic ,需要程序自己捕获处理;

Compile

go version 1.12

# Compile Demo
go test
go build
./math-engine

也可以直接下载已编译好的二进制文件,直接运行:

Github Releases

实现细节

请阅读我的博客文章:用 Go 实现一个完整的数学表达式计算引擎

TODO

已实现

  • +
  • -
  • *
  • /
  • 取余 %
  • 整数次方 ^
  • 科学计数法 e.g. 1.2e71.2e-7
  • 括号 ()
  • 混合运算 e.g. 1+2*6/4+(456-8*9.2)-(2+4^5)*2e3+1.2e-2
  • 友好的长数字 e.g. 123_456_789
  • 三角函数 e.g. sin, cos, tan, cot, sec, csc
  • 常量 pi
  • 辅助函数 e.g. abs, ceil, floor, sqrt, cbrt, max, min, noerr
  • 提供自定义函数注册功能,注册后可以在表达式中使用
  • 精确的数据计算
  • 友好的错误消息 e.g.
input /> 123+89-0.0.9
ERROR: strconv.ParseFloat: parsing "0.0.9": invalid syntax
want '(' or '0-9' but get '0.0.9'
------------
123+89-0.0.9
       ^
------------
Comments
  • V3.0 update: the top-level function ExprASTResult will have a panic error when a runtime error occurs

    V3.0 update: the top-level function ExprASTResult will have a panic error when a runtime error occurs

    V3.0 update: the top-level function ExprASTResult will have a panic error when a runtime error occurs .

    Most of the time you should use ParseAndExec, which automatically handles the errors that occur with ExprASTResult . Use recover to catch the panic if you really need to call ExprASTResult :

    defer func() {
    	if e := recover(); e != nil {
    		// todo
    	}
    }()
    ExprASTResult(expr)
    
    break change 
    opened by dengsgo 4
  • Proposal: Please start using Semantic Versioning

    Proposal: Please start using Semantic Versioning

    I found that this project already supports Go modules. But sadly, the [tags](https://github.com https://github.com/dengsgo/math-engine/tags) doesn't follow Semantic Versioning, which means that all tags of this project will be ignored by Go modules and replaced by pseudo-versions, go get acts weirdly when tags are not in that form. It would be great to have the tagged release be named in the format vX.X.X format so that go mod can read it.

    	github.com/dengsgo/math-engine v0.0.0-20200627074419-8918d8f8ea02
    

    Else the mod file shows something like github.com/dengsgo/math-engine v0.0.0-20200627074419-8918d8f8ea02 which is not very readable and difficult to upgrade. It’s hard to verify which version is in use. This is not conducive to version control.

    So, I propose this project to follow Semantic Versioning in future versions. For example, v1.0.1, v2.0.0, v3.1.0-alpha, v3.1.0-beta.2etc, so that other project can use tag in go.mod.

    opened by KateGo520 3
  • 0.7*  表达式无效

    0.7* 表达式无效

    package main
    
    import (
    	"fmt"
    
    	"github.com/dengsgo/math-engine/engine"
    )
    
    func main() {
    	s := "0.7*"
    	// call top level function
    	r, err := engine.ParseAndExec(s)
    	if err != nil {
    		fmt.Println(err)
    	}
    
    	fmt.Println(r)
            // 0.7
    }
    

    类似 0.7- 、0.7+ 这种表达式也是无效吧。

    bug 
    opened by jimyag 1
  • 1-- panic

    1-- panic

    input /> 1--
    runtime: goroutine stack exceeds 1000000000-byte limit
    fatal error: stack overflow
    
    runtime stack:
    runtime.throw(0x10d97b0, 0xe)
    	/usr/local/go/src/runtime/panic.go:617 +0x72
    runtime.newstack()
    	/usr/local/go/src/runtime/stack.go:1041 +0x6f0
    runtime.morestack()
    	/usr/local/go/src/runtime/asm_amd64.s:429 +0x8f
    
    goroutine 1 [running]:
    github.com/dengsgo/math-engine/engine.(*AST).parsePrimary(0xc043fffdb0, 0x0, 0x0)
    	/Users/admin/go/pkg/mod/github.com/dengsgo/[email protected]/engine/ast.go:164 +0x85c fp=0xc0240003e8 sp=0xc0240003e0 pc=0x109ef4c
    github.com/dengsgo/math-engine/engine.(*AST).parsePrimary(0xc043fffdb0, 0x0, 0x0)
    
    opened by xuanskyer 1
  • 增加注册自定义函数的能力

    增加注册自定义函数的能力

    可以把常用的函数注册到引擎中,然后就能像内置函数一样在输入的数学表达式中使用。

    e.g

      engine.RegFunction("double", 1, func(expr ...engine.ExprAST) float64 {
        return engine.ExprASTResult(expr[0]) * 2
      })
    

    然后就可以在输入的表达式中使用这个函数 double:

    exp := "double(6) + 2"
    r, err := engine.ParseAndExec("double(6) + 2")
    if err != nil {
      panic(err)
    }
    fmt.Printf("double(6) + 2 = %f\n", r) // will print : double(6) + 2 = 14.000000
    
    feature 
    opened by dengsgo 5
Releases(v3.4.0)
Owner
Deng.Liu
Back-end Engineer
Deng.Liu
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