Evaluating a string of simple mathematical expressions
Challenge
Here is the challenge (of my own invention, though I wouldn't be surprised if it has previously appeared elsewhere on the web).
Write a function that takes a single argument that is a string representation of a simple mathematical expression and evaluates it as a floating point value. A "simple expression" may include any of the following: positive or negative decimal numbers, +, -, *, /, (, ). Expressions use (normal) infix notation. Operators should be evaluated in the order they appear, i.e. not as in BODMAS, though brackets should be correctly observed, of course. The function should return the correct result for any possible expression of this form. However, the function does not have to handle malformed expressions (i.e. ones with bad syntax).
Examples of expressions:
1 + 3 / -8 = -0.5 (No BODMAS) 2*3*4*5+99 = 219 4 * (9 - 4) / (2 * 6 - 2) + 8 = 10 1 + ((123 * 3 - 69) / 100) = 4 2.45/8.5*9.27+(5*0.0023) = 2.68...
Rules
I anticipate some form of "cheating"/craftiness here, so please let me forewarn against it! By cheating, I refer to the use of the eval or equivalent function in dynamic languages such as JavaScript or PHP, or equally compiling and executing code on the fly. (I think my specification of "no BODMAS" has pretty much guaranteed this however.) Apart from that, there are no restrictions. I anticipate a few Regex solutions here, but it would be nice to see more than just that.
Now, I'm mainly interested in a C#/.NET solution here, but any other language would be perfectly acceptable too (in particular, F# and Python for the functional/mixed approaches). I haven't yet decided whether I'm going to accept the shortest or most ingenious solution (at least for the language) as the answer, but I would welcome any form of solution in any language, except what I've just prohibited above!
My Solution
I've now posted my C# solution here (403 chars). Update: My new solution has beaten the old one significantly at 294 chars, with the help of a bit of lovely regex! I suspected that this will get easily beaten by some of the languages out there with lighter syntax (particularly the funcional/dynamic ones), and have been proved right, but I'd be curious if someone could beat this in C# still.
Update
I've seen some very crafty solutions already. Thanks to everyone who has posted one. Although I haven't tested any of them yet, I'm going to trust people and assume they at least work with all of the given examples.
Just for the note, re-entrancy (i.e. thread-safety) is not a requirement for the function, though it is a bonus.
Format
Please post all answers in the following format for the purpose of easy comparison:
Language
Number of characters: ???
Fully obfuscated function:
(code here)Clear/semi-obfuscated function:
(code here)Any notes on the algorithm/clever shortcuts it takes.
Answer
Assembler
427 bytes
Obfuscated, assembled with the excellent A86 into a .com executable:
dd 0db9b1f89h, 081bee3h, 0e8af789h, 0d9080080h, 0bdac7674h, 013b40286h
dd 07400463ah, 0ccfe4508h, 08ce9f675h, 02fc8000h, 013b0057eh, 0feaac42ah
dd 0bedf75c9h, 0ba680081h, 04de801h, 04874f73bh, 04474103ch, 0e8e8b60fh
dd 08e8a003fh, 0e880290h, 0de0153h, 08b57e6ebh, 0d902a93eh, 046d891dh
dd 08906c783h, 05f02a93eh, 03cffcee8h, 057197510h, 02a93e8bh, 08b06ef83h
dd 05d9046dh, 02a93e89h, 03bc9d95fh, 0ac0174f7h, 074f73bc3h, 0f3cac24h
dd 0eed9c474h, 0197f0b3ch, 07cc4940fh, 074f73b09h, 0103cac09h, 0a3ce274h
dd 0e40a537eh, 0e0d90274h, 02a3bac3h, 021cd09b4h, 03e8b20cdh, 0ff8102a9h
dd 0ed7502abh, 0474103ch, 0e57d0b3ch, 0be02a3bfh, 014d903a3h, 0800344f6h
dd 02db00574h, 0d9e0d9aah, 0d9029f2eh, 0bb34dfc0h, 08a0009h, 01c75f0a8h
dd 020750fa8h, 0b0f3794bh, 021e9aa30h, 0de607400h, 08802990eh, 0de07df07h
dd 0c392ebc1h, 0e8c0008ah, 0aa300404h, 0f24008ah, 04baa3004h, 02eb0ee79h
dd 03005c6aah, 0c0d90ab1h, 0e9defcd9h, 02a116deh, 0e480e0dfh, 040fc8045h
dd 0ede1274h, 0c0d90299h, 015dffcd9h, 047300580h, 0de75c9feh, 0303d804fh
dd 03d80fa74h, 04f01752eh, 0240145c6h, 0dfff52e9h, 0d9029906h, 0f73b025fh
dd 03caca174h, 07fed740ah, 0df07889ah, 0277d807h, 047d9c1deh, 0990ede02h
dd 025fd902h, 03130e0ebh, 035343332h, 039383736h, 02f2b2d2eh, 02029282ah
dd 0e9000a09h, 07fc9f9c1h, 04500000fh, 0726f7272h
db 024h, 0abh, 02h
EDIT: Unobfuscated source:
mov [bx],bx
finit
mov si,81h
mov di,si
mov cl,[80h]
or cl,bl
jz ret
l1:
lodsb
mov bp,d1
mov ah,19
l2:
cmp al,[bp]
je l3
inc bp
dec ah
jne l2
jmp exit
l3:
cmp ah,2
jle l4
mov al,19
sub al,ah
stosb
l4:
dec cl
jnz l1
mov si,81h
push done
decode:
l5:
call l7
l50:
cmp si,di
je ret
cmp al,16
je ret
db 0fh, 0b6h, 0e8h ; movzx bp,al
call l7
mov cl,[bp+op-11]
mov byte ptr [sm1],cl
db 0deh
sm1:db ?
jmp l50
open:
push di
mov di,word ptr [s]
fstp dword ptr [di]
mov [di+4],bp
add di,6
mov word ptr [s],di
pop di
call decode
cmp al,16
jne ret
push di
mov di,word ptr [s]
sub di,6
mov bp,[di+4]
fld dword ptr [di]
mov word ptr [s],di
pop di
fxch st(1)
cmp si,di
je ret
lodsb
ret
l7: cmp si,di
je exit
lodsb
cmp al,15
je open
fldz
cmp al,11
jg exit
db 0fh, 94h, 0c4h ; sete ah
jl l10
l9:
cmp si,di
je l12
lodsb
cmp al,16
je ret
l10:
cmp al,10
jle l12i
l12:
or ah,ah
je l13
fchs
l13:
ret
exit:
mov dx,offset res
mov ah,9
int 21h
int 20h
done:
mov di,word ptr [s]
cmp di,(offset s)+2
jne exit
cmp al,16
je ok
cmp al,11
jge exit
ok:
mov di,res
mov si,res+100h
fst dword ptr [si]
test byte ptr [si+3],80h
jz pos
mov al,'-'
stosb
fchs
pos:
fldcw word ptr [cw]
fld st(0)
fbstp [si]
mov bx,9
l1000:
mov al,[si+bx]
test al,0f0h
jne startu
test al,0fh
jne startl
dec bx
jns l1000
mov al,'0'
stosb
jmp frac
l12i:
je l11
fimul word ptr [d3]
mov [bx],al
fild word ptr [bx]
faddp
jmp l9
ret
startu:
mov al,[si+bx]
shr al,4
add al,'0'
stosb
startl:
mov al,[si+bx]
and al,0fh
add al,'0'
stosb
dec bx
jns startu
frac:
mov al,'.'
stosb
mov byte ptr [di],'0'
mov cl,10
fld st(0)
frndint
frac1:
fsubp st(1)
ficom word ptr [zero]
fstsw ax
and ah,045h
cmp ah,040h
je finished
fimul word ptr [d3]
fld st(0)
frndint
fist word ptr [di]
add byte ptr [di],'0'
inc di
dec cl
jnz frac1
finished:
dec di
cmp byte ptr [di],'0'
je finished
cmp byte ptr [di],'.'
jne f2
dec di
f2:
mov byte ptr [di+1],'$'
exit2:
jmp exit
l11:
fild word ptr [d3]
fstp dword ptr [bx+2]
l111:
cmp si,di
je ret
lodsb
cmp al,10
je exit2
jg ret
mov [bx],al
fild word ptr [bx]
fdiv dword ptr [bx+2]
faddp
fld dword ptr [bx+2]
fimul word ptr [d3]
fstp dword ptr [bx+2]
jmp l111
d1: db '0123456789.-+/*()', 32, 9
d3: dw 10
op: db 0e9h, 0c1h, 0f9h, 0c9h
cw: dw 0f7fh
zero: dw 0
res:db 'Error$'
s: dw (offset s)+2