src/cmd/goyacc/units.y - go - Git at Google

 // Derived from Plan 9's /sys/src/cmd/units.y
 // http://plan9.bell-labs.com/sources/plan9/sys/src/cmd/units.y
 //
 // Copyright (C) 2003, Lucent Technologies Inc. and others. All Rights Reserved.
 // Portions Copyright 2009 The Go Authors.  All Rights Reserved.
 // Distributed under the terms of the Lucent Public License Version 1.02
 // See http://plan9.bell-labs.com/plan9/license.html

 %{

 // units.y
 // example of a goyacc program
 // usage is
 //	goyacc units.y (produces y.go)
 //	6g y.go
 //	6l y.6
 //	./6.out $GOROOT/src/cmd/goyacc/units
 //	you have: c
 //	you want: furlongs/fortnight
 //		* 1.8026178e+12
 //		/ 5.5474878e-13
 //	you have:

 package main

 import (
 	"flag"
 	"fmt"
 	"bufio"
 	"os"
 	"math"
 	"strconv"
 	"utf8"
 )

 const (
 	Ndim = 15  // number of dimensions
 	Maxe = 695 // log of largest number
 )

 type Node struct {
 	vval float64
 	dim  [Ndim]int8
 }

 type Var struct {
 	name string
 	node Node
 }

 var fi *bufio.Reader // input
 var fund [Ndim]*Var  // names of fundamental units
 var line string      // current input line
 var lineno int       // current input line number
 var linep int        // index to next rune in unput
 var nerrors int      // error count
 var one Node         // constant one
 var peekrune int     // backup runt from input
 var retnode1 Node
 var retnode2 Node
 var retnode Node
 var sym string
 var vflag bool

 %}

 %union
 {
 	node	Node;
 	vvar	*Var;
 	numb	int;
 	vval	float64;
 }

 %type	<node>	prog expr expr0 expr1 expr2 expr3 expr4

 %token	<vval>	VAL
 %token	<vvar>	VAR
 %token	<numb>	SUP
 %%
 prog:
 	':' VAR expr
 	{
 		var f int;

 		f = int($2.node.dim[0]);
 		$2.node = $3;
 		$2.node.dim[0] = 1;
 		if f != 0 {
 			Error("redefinition of %v", $2.name);
 		} else
 		if vflag {
 			fmt.Printf("%v\t%v\n", $2.name, &$2.node);
 		}
 	}
 |	':' VAR '#'
 	{
 		var f, i int;

 		for i=1; i<Ndim; i++ {
 			if fund[i] == nil {
 				break;
 			}
 		}
 		if i >= Ndim {
 			Error("too many dimensions");
 			i = Ndim-1;
 		}
 		fund[i] = $2;

 		f = int($2.node.dim[0]);
 		$2.node = one;
 		$2.node.dim[0] = 1;
 		$2.node.dim[i] = 1;
 		if f != 0 {
 			Error("redefinition of %v", $2.name);
 		} else
 		if vflag {
 			fmt.Printf("%v\t#\n", $2.name);
 		}
 	}
 |	':'
 	{
 	}
 |	'?' expr
 	{
 		retnode1 = $2;
 	}
 |	'?'
 	{
 		retnode1 = one;
 	}

 expr:
 	expr4
 |	expr '+' expr4
 	{
 		add(&$$, &$1, &$3);
 	}
 |	expr '-' expr4
 	{
 		sub(&$$, &$1, &$3);
 	}

 expr4:
 	expr3
 |	expr4 '*' expr3
 	{
 		mul(&$$, &$1, &$3);
 	}
 |	expr4 '/' expr3
 	{
 		div(&$$, &$1, &$3);
 	}

 expr3:
 	expr2
 |	expr3 expr2
 	{
 		mul(&$$, &$1, &$2);
 	}

 expr2:
 	expr1
 |	expr2 SUP
 	{
 		xpn(&$$, &$1, $2);
 	}
 |	expr2 '^' expr1
 	{
 		var i int;

 		for i=1; i<Ndim; i++ {
 			if $3.dim[i] != 0 {
 				Error("exponent has units");
 				$$ = $1;
 				break;
 			}
 		}
 		if i >= Ndim {
 			i = int($3.vval);
 			if float64(i) != $3.vval {
 				Error("exponent not integral");
 			}
 			xpn(&$$, &$1, i);
 		}
 	}

 expr1:
 	expr0
 |	expr1 '|' expr0
 	{
 		div(&$$, &$1, &$3);
 	}

 expr0:
 	VAR
 	{
 		if $1.node.dim[0] == 0 {
 			Error("undefined %v", $1.name);
 			$$ = one;
 		} else
 			$$ = $1.node;
 	}
 |	VAL
 	{
 		$$ = one;
 		$$.vval = $1;
 	}
 |	'(' expr ')'
 	{
 		$$ = $2;
 	}
 %%

 type UnitsLex int

 func (_ UnitsLex) Lex(yylval *yySymType) int {
 	var c, i int

 	c = peekrune
 	peekrune = ' '

 loop:
 	if (c >= '0' && c <= '9') || c == '.' {
 		goto numb
 	}
 	if ralpha(c) {
 		goto alpha
 	}
 	switch c {
 	case ' ', '\t':
 		c = getrune()
 		goto loop
 	case '×':
 		return '*'
 	case '÷':
 		return '/'
 	case '¹', 'ⁱ':
 		yylval.numb = 1
 		return SUP
 	case '²', '⁲':
 		yylval.numb = 2
 		return SUP
 	case '³', '⁳':
 		yylval.numb = 3
 		return SUP
 	}
 	return c

 alpha:
 	sym = ""
 	for i = 0; ; i++ {
 		sym += string(c)
 		c = getrune()
 		if !ralpha(c) {
 			break
 		}
 	}
 	peekrune = c
 	yylval.vvar = lookup(0)
 	return VAR

 numb:
 	sym = ""
 	for i = 0; ; i++ {
 		sym += string(c)
 		c = getrune()
 		if !rdigit(c) {
 			break
 		}
 	}
 	peekrune = c
 	f, err := strconv.Atof64(sym)
 	if err != nil {
 		fmt.Printf("error converting %v\n", sym)
 		f = 0
 	}
 	yylval.vval = f
 	return VAL
 }

 func (_ UnitsLex) Error(s string) {
 	Error("syntax error, last name: %v", sym)
 }

 func main() {
 	var file string

 	flag.BoolVar(&vflag, "v", false, "verbose")

 	flag.Parse()

 	file = os.Getenv("GOROOT") + "/src/cmd/goyacc/units.txt"
 	if flag.NArg() > 0 {
 		file = flag.Arg(0)
 	}

 	f, err := os.Open(file, os.O_RDONLY, 0)
 	if err != nil {
 		fmt.Printf("error opening %v: %v\n", file, err)
 		os.Exit(1)
 	}
 	fi = bufio.NewReader(f)

 	one.vval = 1

 	/*
 	 * read the 'units' file to
 	 * develope a database
 	 */
 	lineno = 0
 	for {
 		lineno++
 		if readline() {
 			break
 		}
 		if len(line) == 0 || line[0] == '/' {
 			continue
 		}
 		peekrune = ':'
 		yyParse(UnitsLex(0))
 	}

 	/*
 	 * read the console to
 	 * print ratio of pairs
 	 */
 	fi = bufio.NewReader(os.NewFile(0, "stdin"))

 	lineno = 0
 	for {
 		if (lineno & 1) != 0 {
 			fmt.Printf("you want: ")
 		} else {
 			fmt.Printf("you have: ")
 		}
 		if readline() {
 			break
 		}
 		peekrune = '?'
 		nerrors = 0
 		yyParse(UnitsLex(0))
 		if nerrors != 0 {
 			continue
 		}
 		if (lineno & 1) != 0 {
 			if specialcase(&retnode, &retnode2, &retnode1) {
 				fmt.Printf("\tis %v\n", &retnode)
 			} else {
 				div(&retnode, &retnode2, &retnode1)
 				fmt.Printf("\t* %v\n", &retnode)
 				div(&retnode, &retnode1, &retnode2)
 				fmt.Printf("\t/ %v\n", &retnode)
 			}
 		} else {
 			retnode2 = retnode1
 		}
 		lineno++
 	}
 	fmt.Printf("\n")
 	os.Exit(0)
 }

 /*
  * all characters that have some
  * meaning. rest are usable as names
  */
 func ralpha(c int) bool {
 	switch c {
 	case 0, '+', '-', '*', '/', '[', ']', '(', ')',
 		'^', ':', '?', ' ', '\t', '.', '|', '#',
 		'×', '÷', '¹', 'ⁱ', '²', '⁲', '³', '⁳':
 		return false
 	}
 	return true
 }

 /*
  * number forming character
  */
 func rdigit(c int) bool {
 	switch c {
 	case '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 		'.', 'e', '+', '-':
 		return true
 	}
 	return false
 }

 func Error(s string, v ...interface{}) {
 	fmt.Printf("%v: %v\n\t", lineno, line)
 	fmt.Printf(s, v)
 	fmt.Printf("\n")

 	nerrors++
 	if nerrors > 5 {
 		fmt.Printf("too many errors\n")
 		os.Exit(1)
 	}
 }

 func add(c, a, b *Node) {
 	var i int
 	var d int8

 	for i = 0; i < Ndim; i++ {
 		d = a.dim[i]
 		c.dim[i] = d
 		if d != b.dim[i] {
 			Error("add must be like units")
 		}
 	}
 	c.vval = fadd(a.vval, b.vval)
 }

 func sub(c, a, b *Node) {
 	var i int
 	var d int8

 	for i = 0; i < Ndim; i++ {
 		d = a.dim[i]
 		c.dim[i] = d
 		if d != b.dim[i] {
 			Error("sub must be like units")
 		}
 	}
 	c.vval = fadd(a.vval, -b.vval)
 }

 func mul(c, a, b *Node) {
 	var i int

 	for i = 0; i < Ndim; i++ {
 		c.dim[i] = a.dim[i] + b.dim[i]
 	}
 	c.vval = fmul(a.vval, b.vval)
 }

 func div(c, a, b *Node) {
 	var i int

 	for i = 0; i < Ndim; i++ {
 		c.dim[i] = a.dim[i] - b.dim[i]
 	}
 	c.vval = fdiv(a.vval, b.vval)
 }

 func xpn(c, a *Node, b int) {
 	var i int

 	*c = one
 	if b < 0 {
 		b = -b
 		for i = 0; i < b; i++ {
 			div(c, c, a)
 		}
 	} else {
 		for i = 0; i < b; i++ {
 			mul(c, c, a)
 		}
 	}
 }

 func specialcase(c, a, b *Node) bool {
 	var i int
 	var d, d1, d2 int8

 	d1 = 0
 	d2 = 0
 	for i = 1; i < Ndim; i++ {
 		d = a.dim[i]
 		if d != 0 {
 			if d != 1 || d1 != 0 {
 				return false
 			}
 			d1 = int8(i)
 		}
 		d = b.dim[i]
 		if d != 0 {
 			if d != 1 || d2 != 0 {
 				return false
 			}
 			d2 = int8(i)
 		}
 	}
 	if d1 == 0 || d2 == 0 {
 		return false
 	}

 	if fund[d1].name == "°C" && fund[d2].name == "°F" &&
 		b.vval == 1 {
 		for ll := 0; ll < len(c.dim); ll++ {
 			c.dim[ll] = b.dim[ll]
 		}
 		c.vval = a.vval*9./5. + 32.
 		return true
 	}

 	if fund[d1].name == "°F" && fund[d2].name == "°C" &&
 		b.vval == 1 {
 		for ll := 0; ll < len(c.dim); ll++ {
 			c.dim[ll] = b.dim[ll]
 		}
 		c.vval = (a.vval - 32.) * 5. / 9.
 		return true
 	}
 	return false
 }

 func printdim(str string, d, n int) string {
 	var v *Var

 	if n != 0 {
 		v = fund[d]
 		if v != nil {
 			str += fmt.Sprintf("%v", v.name)
 		} else {
 			str += fmt.Sprintf("[%d]", d)
 		}
 		switch n {
 		case 1:
 			break
 		case 2:
 			str += "²"
 		case 3:
 			str += "³"
 		default:
 			str += fmt.Sprintf("^%d", n)
 		}
 	}
 	return str
 }

 func (n Node) String() string {
 	var str string
 	var f, i, d int

 	str = fmt.Sprintf("%.7e ", n.vval)

 	f = 0
 	for i = 1; i < Ndim; i++ {
 		d = int(n.dim[i])
 		if d > 0 {
 			str = printdim(str, i, d)
 		} else if d < 0 {
 			f = 1
 		}
 	}

 	if f != 0 {
 		str += " /"
 		for i = 1; i < Ndim; i++ {
 			d = int(n.dim[i])
 			if d < 0 {
 				str = printdim(str, i, -d)
 			}
 		}
 	}

 	return str
 }

 func (v *Var) String() string {
 	var str string
 	str = fmt.Sprintf("%v %v", v.name, v.node)
 	return str
 }

 func readline() bool {
 	s, err := fi.ReadString('\n')
 	if err != nil {
 		return true
 	}
 	line = s
 	linep = 0
 	return false
 }

 func getrune() int {
 	var c, n int

 	if linep >= len(line) {
 		return 0
 	}
 	c, n = utf8.DecodeRuneInString(line[linep:len(line)])
 	linep += n
 	if c == '\n' {
 		c = 0
 	}
 	return c
 }

 var symmap = make(map[string]*Var) // symbol table

 func lookup(f int) *Var {
 	var p float64
 	var w *Var

 	v, ok := symmap[sym]
 	if ok {
 		return v
 	}
 	if f != 0 {
 		return nil
 	}
 	v = new(Var)
 	v.name = sym
 	symmap[sym] = v

 	p = 1
 	for {
 		p = fmul(p, pname())
 		if p == 0 {
 			break
 		}
 		w = lookup(1)
 		if w != nil {
 			v.node = w.node
 			v.node.vval = fmul(v.node.vval, p)
 			break
 		}
 	}
 	return v
 }

 type Prefix struct {
 	vval float64
 	name string
 }

 var prefix = []Prefix{ // prefix table
 	Prefix{1e-24, "yocto"},
 	Prefix{1e-21, "zepto"},
 	Prefix{1e-18, "atto"},
 	Prefix{1e-15, "femto"},
 	Prefix{1e-12, "pico"},
 	Prefix{1e-9, "nano"},
 	Prefix{1e-6, "micro"},
 	Prefix{1e-6, "μ"},
 	Prefix{1e-3, "milli"},
 	Prefix{1e-2, "centi"},
 	Prefix{1e-1, "deci"},
 	Prefix{1e1, "deka"},
 	Prefix{1e2, "hecta"},
 	Prefix{1e2, "hecto"},
 	Prefix{1e3, "kilo"},
 	Prefix{1e6, "mega"},
 	Prefix{1e6, "meg"},
 	Prefix{1e9, "giga"},
 	Prefix{1e12, "tera"},
 	Prefix{1e15, "peta"},
 	Prefix{1e18, "exa"},
 	Prefix{1e21, "zetta"},
 	Prefix{1e24, "yotta"},
 }

 func pname() float64 {
 	var i, j, n int
 	var s string

 	/*
 	 * rip off normal prefixs
 	 */
 	n = len(sym)
 	for i = 0; i < len(prefix); i++ {
 		s = prefix[i].name
 		j = len(s)
 		if j < n && sym[0:j] == s {
 			sym = sym[j:n]
 			return prefix[i].vval
 		}
 	}

 	/*
 	 * rip off 's' suffixes
 	 */
 	if n > 2 && sym[n-1] == 's' {
 		sym = sym[0 : n-1]
 		return 1
 	}

 	return 0
 }


 // careful multiplication
 // exponents (log) are checked before multiply
 func fmul(a, b float64) float64 {
 	var l float64

 	if b <= 0 {
 		if b == 0 {
 			return 0
 		}
 		l = math.Log(-b)
 	} else {
 		l = math.Log(b)
 	}

 	if a <= 0 {
 		if a == 0 {
 			return 0
 		}
 		l += math.Log(-a)
 	} else {
 		l += math.Log(a)
 	}

 	if l > Maxe {
 		Error("overflow in multiply")
 		return 1
 	}
 	if l < -Maxe {
 		Error("underflow in multiply")
 		return 0
 	}
 	return a * b
 }

 // careful division
 // exponents (log) are checked before divide
 func fdiv(a, b float64) float64 {
 	var l float64

 	if b <= 0 {
 		if b == 0 {
 			Error("division by zero: %v %v", a, b)
 			return 1
 		}
 		l = math.Log(-b)
 	} else {
 		l = math.Log(b)
 	}

 	if a <= 0 {
 		if a == 0 {
 			return 0
 		}
 		l -= math.Log(-a)
 	} else {
 		l -= math.Log(a)
 	}

 	if l < -Maxe {
 		Error("overflow in divide")
 		return 1
 	}
 	if l > Maxe {
 		Error("underflow in divide")
 		return 0
 	}
 	return a / b
 }

 func fadd(a, b float64) float64 {
 	return a + b
 }
	// Derived from Plan 9's /sys/src/cmd/units.y
	// http://plan9.bell-labs.com/sources/plan9/sys/src/cmd/units.y
	//
	// Copyright (C) 2003, Lucent Technologies Inc. and others. All Rights Reserved.
	// Portions Copyright 2009 The Go Authors. All Rights Reserved.
	// Distributed under the terms of the Lucent Public License Version 1.02
	// See http://plan9.bell-labs.com/plan9/license.html

	%{

	// units.y
	// example of a goyacc program
	// usage is
	// goyacc units.y (produces y.go)
	// 6g y.go
	// 6l y.6
	// ./6.out $GOROOT/src/cmd/goyacc/units
	// you have: c
	// you want: furlongs/fortnight
	// * 1.8026178e+12
	// / 5.5474878e-13
	// you have:

	package main

	import (
	"flag"
	"fmt"
	"bufio"
	"os"
	"math"
	"strconv"
	"utf8"
	)

	const (
	Ndim = 15 // number of dimensions
	Maxe = 695 // log of largest number
	)

	type Node struct {
	vval float64
	dim [Ndim]int8
	}

	type Var struct {
	name string
	node Node
	}

	var fi *bufio.Reader // input
	var fund [Ndim]*Var // names of fundamental units
	var line string // current input line
	var lineno int // current input line number
	var linep int // index to next rune in unput
	var nerrors int // error count
	var one Node // constant one
	var peekrune int // backup runt from input
	var retnode1 Node
	var retnode2 Node
	var retnode Node
	var sym string
	var vflag bool

	%}

	%union
	{
	node Node;
	vvar *Var;
	numb int;
	vval float64;
	}

	%type <node> prog expr expr0 expr1 expr2 expr3 expr4

	%token <vval> VAL
	%token <vvar> VAR
	%token <numb> SUP
	%%
	prog:
	':' VAR expr
	{
	var f int;

	f = int($2.node.dim[0]);
	$2.node = $3;
	$2.node.dim[0] = 1;
	if f != 0 {
	Error("redefinition of %v", $2.name);
	} else
	if vflag {
	fmt.Printf("%v\t%v\n", $2.name, &$2.node);
	}
	}
	\| ':' VAR '#'
	{
	var f, i int;

	for i=1; i<Ndim; i++ {
	if fund[i] == nil {
	break;
	}
	}
	if i >= Ndim {
	Error("too many dimensions");
	i = Ndim-1;
	}
	fund[i] = $2;

	f = int($2.node.dim[0]);
	$2.node = one;
	$2.node.dim[0] = 1;
	$2.node.dim[i] = 1;
	if f != 0 {
	Error("redefinition of %v", $2.name);
	} else
	if vflag {
	fmt.Printf("%v\t#\n", $2.name);
	}
	}
	\| ':'
	{
	}
	\| '?' expr
	{
	retnode1 = $2;
	}
	\| '?'
	{
	retnode1 = one;
	}

	expr:
	expr4
	\| expr '+' expr4
	{
	add(&$$, &$1, &$3);
	}
	\| expr '-' expr4
	{
	sub(&$$, &$1, &$3);
	}

	expr4:
	expr3
	\| expr4 '*' expr3
	{
	mul(&$$, &$1, &$3);
	}
	\| expr4 '/' expr3
	{
	div(&$$, &$1, &$3);
	}

	expr3:
	expr2
	\| expr3 expr2
	{
	mul(&$$, &$1, &$2);
	}

	expr2:
	expr1
	\| expr2 SUP
	{
	xpn(&$$, &$1, $2);
	}
	\| expr2 '^' expr1
	{
	var i int;

	for i=1; i<Ndim; i++ {
	if $3.dim[i] != 0 {
	Error("exponent has units");
	$$ = $1;
	break;
	}
	}
	if i >= Ndim {
	i = int($3.vval);
	if float64(i) != $3.vval {
	Error("exponent not integral");
	}
	xpn(&$$, &$1, i);
	}
	}

	expr1:
	expr0
	\| expr1 '\|' expr0
	{
	div(&$$, &$1, &$3);
	}

	expr0:
	VAR
	{
	if $1.node.dim[0] == 0 {
	Error("undefined %v", $1.name);
	$$ = one;
	} else
	$$ = $1.node;
	}
	\| VAL
	{
	$$ = one;
	$$.vval = $1;
	}
	\| '(' expr ')'
	{
	$$ = $2;
	}
	%%

	type UnitsLex int

	func (_ UnitsLex) Lex(yylval *yySymType) int {
	var c, i int

	c = peekrune
	peekrune = ' '

	loop:
	if (c >= '0' && c <= '9') \|\| c == '.' {
	goto numb
	}
	if ralpha(c) {
	goto alpha
	}
	switch c {
	case ' ', '\t':
	c = getrune()
	goto loop
	case '×':
	return '*'
	case '÷':
	return '/'
	case '¹', 'ⁱ':
	yylval.numb = 1
	return SUP
	case '²', '⁲':
	yylval.numb = 2
	return SUP
	case '³', '⁳':
	yylval.numb = 3
	return SUP
	}
	return c

	alpha:
	sym = ""
	for i = 0; ; i++ {
	sym += string(c)
	c = getrune()
	if !ralpha(c) {
	break
	}
	}
	peekrune = c
	yylval.vvar = lookup(0)
	return VAR

	numb:
	sym = ""
	for i = 0; ; i++ {
	sym += string(c)
	c = getrune()
	if !rdigit(c) {
	break
	}
	}
	peekrune = c
	f, err := strconv.Atof64(sym)
	if err != nil {
	fmt.Printf("error converting %v\n", sym)
	f = 0
	}
	yylval.vval = f
	return VAL
	}

	func (_ UnitsLex) Error(s string) {
	Error("syntax error, last name: %v", sym)
	}

	func main() {
	var file string

	flag.BoolVar(&vflag, "v", false, "verbose")

	flag.Parse()

	file = os.Getenv("GOROOT") + "/src/cmd/goyacc/units.txt"
	if flag.NArg() > 0 {
	file = flag.Arg(0)
	}

	f, err := os.Open(file, os.O_RDONLY, 0)
	if err != nil {
	fmt.Printf("error opening %v: %v\n", file, err)
	os.Exit(1)
	}
	fi = bufio.NewReader(f)

	one.vval = 1

	/*
	* read the 'units' file to
	* develope a database
	*/
	lineno = 0
	for {
	lineno++
	if readline() {
	break
	}
	if len(line) == 0 \|\| line[0] == '/' {
	continue
	}
	peekrune = ':'
	yyParse(UnitsLex(0))
	}

	/*
	* read the console to
	* print ratio of pairs
	*/
	fi = bufio.NewReader(os.NewFile(0, "stdin"))

	lineno = 0
	for {
	if (lineno & 1) != 0 {
	fmt.Printf("you want: ")
	} else {
	fmt.Printf("you have: ")
	}
	if readline() {
	break
	}
	peekrune = '?'
	nerrors = 0
	yyParse(UnitsLex(0))
	if nerrors != 0 {
	continue
	}
	if (lineno & 1) != 0 {
	if specialcase(&retnode, &retnode2, &retnode1) {
	fmt.Printf("\tis %v\n", &retnode)
	} else {
	div(&retnode, &retnode2, &retnode1)
	fmt.Printf("\t* %v\n", &retnode)
	div(&retnode, &retnode1, &retnode2)
	fmt.Printf("\t/ %v\n", &retnode)
	}
	} else {
	retnode2 = retnode1
	}
	lineno++
	}
	fmt.Printf("\n")
	os.Exit(0)
	}

	/*
	* all characters that have some
	* meaning. rest are usable as names
	*/
	func ralpha(c int) bool {
	switch c {
	case 0, '+', '-', '*', '/', '[', ']', '(', ')',
	'^', ':', '?', ' ', '\t', '.', '\|', '#',
	'×', '÷', '¹', 'ⁱ', '²', '⁲', '³', '⁳':
	return false
	}
	return true
	}

	/*
	* number forming character
	*/
	func rdigit(c int) bool {
	switch c {
	case '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
	'.', 'e', '+', '-':
	return true
	}
	return false
	}

	func Error(s string, v ...interface{}) {
	fmt.Printf("%v: %v\n\t", lineno, line)
	fmt.Printf(s, v)
	fmt.Printf("\n")

	nerrors++
	if nerrors > 5 {
	fmt.Printf("too many errors\n")
	os.Exit(1)
	}
	}

	func add(c, a, b *Node) {
	var i int
	var d int8

	for i = 0; i < Ndim; i++ {
	d = a.dim[i]
	c.dim[i] = d
	if d != b.dim[i] {
	Error("add must be like units")
	}
	}
	c.vval = fadd(a.vval, b.vval)
	}

	func sub(c, a, b *Node) {
	var i int
	var d int8

	for i = 0; i < Ndim; i++ {
	d = a.dim[i]
	c.dim[i] = d
	if d != b.dim[i] {
	Error("sub must be like units")
	}
	}
	c.vval = fadd(a.vval, -b.vval)
	}

	func mul(c, a, b *Node) {
	var i int

	for i = 0; i < Ndim; i++ {
	c.dim[i] = a.dim[i] + b.dim[i]
	}
	c.vval = fmul(a.vval, b.vval)
	}

	func div(c, a, b *Node) {
	var i int

	for i = 0; i < Ndim; i++ {
	c.dim[i] = a.dim[i] - b.dim[i]
	}
	c.vval = fdiv(a.vval, b.vval)
	}

	func xpn(c, a *Node, b int) {
	var i int

	*c = one
	if b < 0 {
	b = -b
	for i = 0; i < b; i++ {
	div(c, c, a)
	}
	} else {
	for i = 0; i < b; i++ {
	mul(c, c, a)
	}
	}
	}

	func specialcase(c, a, b *Node) bool {
	var i int
	var d, d1, d2 int8

	d1 = 0
	d2 = 0
	for i = 1; i < Ndim; i++ {
	d = a.dim[i]
	if d != 0 {
	if d != 1 \|\| d1 != 0 {
	return false
	}
	d1 = int8(i)
	}
	d = b.dim[i]
	if d != 0 {
	if d != 1 \|\| d2 != 0 {
	return false
	}
	d2 = int8(i)
	}
	}
	if d1 == 0 \|\| d2 == 0 {
	return false
	}

	if fund[d1].name == "°C" && fund[d2].name == "°F" &&
	b.vval == 1 {
	for ll := 0; ll < len(c.dim); ll++ {
	c.dim[ll] = b.dim[ll]
	}
	c.vval = a.vval*9./5. + 32.
	return true
	}

	if fund[d1].name == "°F" && fund[d2].name == "°C" &&
	b.vval == 1 {
	for ll := 0; ll < len(c.dim); ll++ {
	c.dim[ll] = b.dim[ll]
	}
	c.vval = (a.vval - 32.) * 5. / 9.
	return true
	}
	return false
	}

	func printdim(str string, d, n int) string {
	var v *Var

	if n != 0 {
	v = fund[d]
	if v != nil {
	str += fmt.Sprintf("%v", v.name)
	} else {
	str += fmt.Sprintf("[%d]", d)
	}
	switch n {
	case 1:
	break
	case 2:
	str += "²"
	case 3:
	str += "³"
	default:
	str += fmt.Sprintf("^%d", n)
	}
	}
	return str
	}

	func (n Node) String() string {
	var str string
	var f, i, d int

	str = fmt.Sprintf("%.7e ", n.vval)

	f = 0
	for i = 1; i < Ndim; i++ {
	d = int(n.dim[i])
	if d > 0 {
	str = printdim(str, i, d)
	} else if d < 0 {
	f = 1
	}
	}

	if f != 0 {
	str += " /"
	for i = 1; i < Ndim; i++ {
	d = int(n.dim[i])
	if d < 0 {
	str = printdim(str, i, -d)
	}
	}
	}

	return str
	}

	func (v *Var) String() string {
	var str string
	str = fmt.Sprintf("%v %v", v.name, v.node)
	return str
	}

	func readline() bool {
	s, err := fi.ReadString('\n')
	if err != nil {
	return true
	}
	line = s
	linep = 0
	return false
	}

	func getrune() int {
	var c, n int

	if linep >= len(line) {
	return 0
	}
	c, n = utf8.DecodeRuneInString(line[linep:len(line)])
	linep += n
	if c == '\n' {
	c = 0
	}
	return c
	}

	var symmap = make(map[string]*Var) // symbol table

	func lookup(f int) *Var {
	var p float64
	var w *Var

	v, ok := symmap[sym]
	if ok {
	return v
	}
	if f != 0 {
	return nil
	}
	v = new(Var)
	v.name = sym
	symmap[sym] = v

	p = 1
	for {
	p = fmul(p, pname())
	if p == 0 {
	break
	}
	w = lookup(1)
	if w != nil {
	v.node = w.node
	v.node.vval = fmul(v.node.vval, p)
	break
	}
	}
	return v
	}

	type Prefix struct {
	vval float64
	name string
	}

	var prefix = []Prefix{ // prefix table
	Prefix{1e-24, "yocto"},
	Prefix{1e-21, "zepto"},
	Prefix{1e-18, "atto"},
	Prefix{1e-15, "femto"},
	Prefix{1e-12, "pico"},
	Prefix{1e-9, "nano"},
	Prefix{1e-6, "micro"},
	Prefix{1e-6, "μ"},
	Prefix{1e-3, "milli"},
	Prefix{1e-2, "centi"},
	Prefix{1e-1, "deci"},
	Prefix{1e1, "deka"},
	Prefix{1e2, "hecta"},
	Prefix{1e2, "hecto"},
	Prefix{1e3, "kilo"},
	Prefix{1e6, "mega"},
	Prefix{1e6, "meg"},
	Prefix{1e9, "giga"},
	Prefix{1e12, "tera"},
	Prefix{1e15, "peta"},
	Prefix{1e18, "exa"},
	Prefix{1e21, "zetta"},
	Prefix{1e24, "yotta"},
	}

	func pname() float64 {
	var i, j, n int
	var s string

	/*
	* rip off normal prefixs
	*/
	n = len(sym)
	for i = 0; i < len(prefix); i++ {
	s = prefix[i].name
	j = len(s)
	if j < n && sym[0:j] == s {
	sym = sym[j:n]
	return prefix[i].vval
	}
	}

	/*
	* rip off 's' suffixes
	*/
	if n > 2 && sym[n-1] == 's' {
	sym = sym[0 : n-1]
	return 1
	}

	return 0
	}


	// careful multiplication
	// exponents (log) are checked before multiply
	func fmul(a, b float64) float64 {
	var l float64

	if b <= 0 {
	if b == 0 {
	return 0
	}
	l = math.Log(-b)
	} else {
	l = math.Log(b)
	}

	if a <= 0 {
	if a == 0 {
	return 0
	}
	l += math.Log(-a)
	} else {
	l += math.Log(a)
	}

	if l > Maxe {
	Error("overflow in multiply")
	return 1
	}
	if l < -Maxe {
	Error("underflow in multiply")
	return 0
	}
	return a * b
	}

	// careful division
	// exponents (log) are checked before divide
	func fdiv(a, b float64) float64 {
	var l float64

	if b <= 0 {
	if b == 0 {
	Error("division by zero: %v %v", a, b)
	return 1
	}
	l = math.Log(-b)
	} else {
	l = math.Log(b)
	}

	if a <= 0 {
	if a == 0 {
	return 0
	}
	l -= math.Log(-a)
	} else {
	l -= math.Log(a)
	}

	if l < -Maxe {
	Error("overflow in divide")
	return 1
	}
	if l > Maxe {
	Error("underflow in divide")
	return 0
	}
	return a / b
	}

	func fadd(a, b float64) float64 {
	return a + b
	}