algebrite/sources/scan.coffee

Computer Algebra System in Coffeescript

# This scanner uses the recursive descent method.
#
# The char pointers token_str and scan_str are pointers to the input string as
# in the following example.
#
#	| g | a | m | m | a |   | a | l | p | h | a |
#	  ^                   ^
#	  token_str           scan_str
#
# The char pointer token_buf points to a malloc buffer.
#
#	| g | a | m | m | a | \0 |
#	  ^
#	  token_buf



T_INTEGER = 1001
T_DOUBLE = 1002
T_SYMBOL = 1003
T_FUNCTION = 1004
T_NEWLINE = 1006
T_STRING = 1007
T_GTEQ = 1008
T_LTEQ = 1009
T_EQ = 1010

token = ""
newline_flag = 0
meta_mode = 0

input_str = 0
scan_str = 0
token_str = 0
token_buf = 0

# Returns number of chars scanned and expr on stack.

# Returns zero when nothing left to scan.

# takes a string

scanned = ""
scan = (s) ->
	if DEBUG then console.log "#### scanning " + s
	#if s=="y=x"
	#	debugger
	#if s=="y"
	#	debugger
	#if s=="i=sqrt(-1)"
	#	debugger
	scanned = s
	meta_mode = 0
	expanding++
	input_str = 0
	scan_str = 0
	get_next_token()
	if (token == "")
		push(symbol(NIL))
		expanding--
		return 0
	scan_stmt()
	expanding--
	return token_str - input_str

# takes a string
scan_meta = (s) ->
	scanned = s
	meta_mode = 1
	expanding++
	input_str = 0
	scan_str = 0
	get_next_token()
	if (token == "")
		push(symbol(NIL))
		expanding--
		return 0
	scan_stmt()
	expanding--
	return token_str - input_str

scan_stmt = ->
	scan_relation()
	if (token == '=')
		get_next_token()
		push_symbol(SETQ)
		swap()
		scan_relation()
		list(3)

scan_relation = ->
	scan_expression()
	switch (token)
		when T_EQ
			push_symbol(TESTEQ)
			swap()
			get_next_token()
			scan_expression()
			list(3)
		when T_LTEQ
			push_symbol(TESTLE)
			swap()
			get_next_token()
			scan_expression()
			list(3)
		when T_GTEQ
			push_symbol(TESTGE)
			swap()
			get_next_token()
			scan_expression()
			list(3)
		when '<'
			push_symbol(TESTLT)
			swap()
			get_next_token()
			scan_expression()
			list(3)
		when '>'
			push_symbol(TESTGT)
			swap()
			get_next_token()
			scan_expression()
			list(3)

scan_expression = ->
	h = tos
	switch token
		when '+'
			get_next_token()
			scan_term()
		when '-'
			get_next_token()
			scan_term()
			negate()
		else
			scan_term()

	while (newline_flag == 0 && (token == '+' || token == '-'))
		if (token == '+')
			get_next_token()
			scan_term()
		else
			get_next_token()
			scan_term()
			negate()

	if (tos - h > 1)
		list(tos - h)
		push_symbol(ADD)
		swap()
		cons()

is_factor = ->
	switch (token)
		when '*', '/'
			return 1
		when '(', T_SYMBOL, T_FUNCTION, T_INTEGER, T_DOUBLE, T_STRING
			if (newline_flag) # implicit mul can't cross line
				scan_str = token_str	# better error display
				return 0
			else
				return 1
	return 0

scan_term = ->

	h = tos

	scan_power()

	# discard integer 1

	if (tos > h && isrational(stack[tos - 1]) && equaln(stack[tos - 1], 1))
		pop()

	while (is_factor())
		if (token == '*')
			get_next_token()
			scan_power()
		else if (token == '/')
			get_next_token()
			scan_power()
			inverse()
		else
			scan_power()

		# fold constants

		if (tos > h + 1 && isnum(stack[tos - 2]) && isnum(stack[tos - 1]))
			multiply()

		# discard integer 1

		if (tos > h && isrational(stack[tos - 1]) && equaln(stack[tos - 1], 1))
			pop()

	if (h == tos)
		push_integer(1)
	else if (tos - h > 1)
		list(tos - h)
		push_symbol(MULTIPLY)
		swap()
		cons()

scan_power = ->
	scan_factor()
	if (token == '^')
		get_next_token()
		push_symbol(POWER)
		swap()
		scan_power()
		list(3)

scan_factor = ->

	h = tos

	if (token == '(')
		scan_subexpr()
	else if (token == T_SYMBOL)
		scan_symbol()
	else if (token == T_FUNCTION)
		scan_function_call()
	else if (token == T_INTEGER)
		bignum_scan_integer(token_buf)
		get_next_token()
	else if (token == T_DOUBLE)
		bignum_scan_float(token_buf)
		get_next_token()
	else if (token == T_STRING)
		scan_string()
	else
		error("syntax error")

	# index

	if (token == '[')
		get_next_token()
		push_symbol(INDEX)
		swap()
		scan_expression()
		while (token == ',')
			get_next_token()
			scan_expression()
		if (token != ']')
			error("] expected")
		get_next_token()
		list(tos - h)

	while (token == '!')
		get_next_token()
		push_symbol(FACTORIAL)
		swap()
		list(2)

scan_symbol = ->
	if (token != T_SYMBOL)
		error("symbol expected")
	if (meta_mode && token_buf.length == 1)
		switch (token_buf[0])
			when 'a'
				push(symbol(METAA))
			when 'b'
				push(symbol(METAB))
			when 'x'
				push(symbol(METAX))
			else
				push(usr_symbol(token_buf))
	else
		push(usr_symbol(token_buf))
	get_next_token()

scan_string = ->
	new_string(token_buf)
	get_next_token()

scan_function_call = ->
	n = 1
	p = new U()
	p = usr_symbol(token_buf)

	push(p)
	get_next_token()	# function name
	get_next_token()	# left paren
	if (token != ')')
		scan_stmt()
		n++
		while (token == ',')
			get_next_token()
			scan_stmt()
			n++

	if (token != ')')
		error(") expected")

	get_next_token()
	list(n)

# scan subexpression

scan_subexpr = ->
	n = 0
	if (token != '(')
		error("( expected")
	get_next_token()
	scan_stmt()
	if (token == ',')
		n = 1
		while (token == ',')
			get_next_token()
			scan_stmt()
			n++
		build_tensor(n)
	if (token != ')')
		error(") expected")
	get_next_token()

error = (errmsg) ->
	errorMessage = ""

	# try not to put question mark on orphan line

	while (input_str != scan_str)
		if ((scanned[input_str] == '\n' || scanned[input_str] == '\r') && input_str + 1 == scan_str)
			break
		errorMessage += scanned[input_str++]

	errorMessage += " ? "

	while (scanned[input_str] && (scanned[input_str] != '\n' && scanned[input_str] != '\r'))
		errorMessage +=  scanned[input_str++]

	errorMessage +=  '\n'

	stop(errmsg)

# There are n expressions on the stack, possibly tensors.
#
# This function assembles the stack expressions into a single tensor.
#
# For example, at the top level of the expression ((a,b),(c,d)), the vectors
# (a,b) and (c,d) would be on the stack.

# takes an integer
build_tensor = (n) ->
	# int i, j, k, ndim, nelem

	i = 0

	save()

	p2 = alloc_tensor(n)
	p2.tensor.ndim = 1
	p2.tensor.dim[0] = n
	for i in [0...n]
		p2.tensor.elem[i] = stack[tos-n+i]

	if p2.tensor.nelem != p2.tensor.elem.length
		console.log "something wrong in tensor dimensions"
		debugger

	tos -= n

	push(p2)

	restore()

get_next_token = ->
	newline_flag = 0
	while (1)
		get_token()
		if (token != T_NEWLINE)
			break
		newline_flag = 1
	if DEBUG then console.log "get_next_token token: " + token
	#if token == ')'
	#	debugger

get_token = ->
	# skip spaces

	while (isspace(scanned[scan_str]))
		if (scanned[scan_str] == '\n' || scanned[scan_str] == '\r')
			token = T_NEWLINE
			scan_str++
			return
		scan_str++

	token_str = scan_str

	# end of string?

	if (scan_str == scanned.length)
		token = ""
		return

	# number?

	if (isdigit(scanned[scan_str]) || scanned[scan_str] == '.')
		while (isdigit(scanned[scan_str]))
			scan_str++
		if (scanned[scan_str] == '.')
			scan_str++
			while (isdigit(scanned[scan_str]))
				scan_str++
			if (scanned[scan_str] == 'e' && (scanned[scan_str+1] == '+' || scanned[scan_str+1] == '-' || isdigit(scanned[scan_str+1])))
				scan_str += 2
				while (isdigit(scanned[scan_str]))
					scan_str++
			token = T_DOUBLE
		else
			token = T_INTEGER
		update_token_buf(token_str, scan_str)
		return

	# symbol?

	if (isalpha(scanned[scan_str]))
		while (isalnum(scanned[scan_str]))
			scan_str++
		if (scanned[scan_str] == '(')
			token = T_FUNCTION
		else
			token = T_SYMBOL
		update_token_buf(token_str, scan_str)
		return

	# string ?

	if (scanned[scan_str] == '"')
		scan_str++
		while (scanned[scan_str] != '"')
			if (scan_str == scanned.length || scanned[scan_str] == '\n' || scanned[scan_str] == '\r')
				error("runaway string")
			scan_str++
		scan_str++
		token = T_STRING
		update_token_buf(token_str + 1, scan_str - 1)
		return

	# comment?

	if (scanned[scan_str] == '#' || scanned[scan_str] == '-' && scanned[scan_str+1] == '-')
		while (scanned[scan_str] && scanned[scan_str] != '\n' && scanned[scan_str] != '\r')
			scan_str++
		if (scanned[scan_str])
			scan_str++
		token = T_NEWLINE
		return

	# relational operator?

	if (scanned[scan_str] == '=' && scanned[scan_str+1] == '=')
		scan_str += 2
		token = T_EQ
		return

	if (scanned[scan_str] == '<' && scanned[scan_str+1] == '=')
		scan_str += 2
		token = T_LTEQ
		return

	if (scanned[scan_str] == '>' && scanned[scan_str+1] == '=')
		scan_str += 2
		token = T_GTEQ
		return

	# single char token

	token = scanned[scan_str++]

# both strings
update_token_buf = (a,b) ->

	token_buf = scanned.substring(a,b)