Decode/Encode Integers, Words, and IEE754 Floats
On Hackage: http://hackage.haskell.org/package/crackNum
Example: Encode a decimal number as a single-precision IEEE754 number
$ crackNum -fsp -- -2.3e6
Satisfiable. Model:
ENCODED = -2300000.0 :: Float
3 2 1 0
1 09876543 21098765432109876543210
S ---E8--- ----------S23----------
Binary layout: 1 10010100 00011000110000110000000
Hex layout: CA0C 6180
Precision: Single
Sign: Negative
Exponent: 21 (Stored: 148, Bias: 127)
Classification: FP_NORMAL
Binary: -0b1.0001100011000011p+21
Octal: -0o1.061414p+21
Decimal: -2300000.0
Hex: -0x2.3186p+20
Rounding mode: RNE: Round nearest ties to even.
Note: Conversion from "-2.3e6" was exact. No rounding happened.
Example: Decode a single-precision IEEE754 number float from memory-layout
$ crackNum -fsp 0xfc00 abc1
Satisfiable. Model:
DECODED = -2.6723903e36 :: Float
3 2 1 0
1 09876543 21098765432109876543210
S ---E8--- ----------S23----------
Binary layout: 1 11111000 00000001010101111000001
Hex layout: FC00 ABC1
Precision: Single
Sign: Negative
Exponent: 121 (Stored: 248, Bias: 127)
Classification: FP_NORMAL
Binary: -0b1.00000001010101111000001p+121
Octal: -0o2.00527404p+120
Decimal: -2.6723903e36
Hex: -0x2.02AF04p+120
$ crackNum -fdp 0xfc00 abc1 7F80 0001
Example: Decode a custom (2+3) IEEE754 float from memory-layout
$ crackNum -f2+3 0b10011
Satisfiable. Model:
DECODED = -0.75 :: FloatingPoint 2 3
4 32 10
S E2 S2
Binary layout: 1 00 11
Hex layout: 13
Precision: 2 exponent bits, 2 significand bits
Sign: Negative
Exponent: 0 (Subnormal, with fixed exponent value. Stored: 0, Bias: 1)
Classification: FP_SUBNORMAL
Binary: -0b1.1p-1
Octal: -0o6p-3
Decimal: -0.75
Hex: -0xcp-4
Example: Encode an integer as a 7-bit signed word
$ crackNum -i7 12
Satisfiable. Model:
ENCODED = 12 :: IntN 7
654 3210
Binary layout: 000 1100
Hex layout: 0C
Type: Signed 7-bit 2's complement integer
Sign: Positive
Binary: 0b1100
Octal: 0o14
Decimal: 12
Hex: 0xc
Example: Decode two half-precision floats in two lanes
$ crackNum -l2 -fhp 32\'hfdc71fc6
== Lane 1 ============================================================
Satisfiable. Model:
DECODED = NaN :: FloatingPoint 5 11
1 0
5 43210 9876543210
S -E5-- ---S10----
Binary layout: 1 11111 0111000111
Hex layout: FDC7
Precision: Half (5 exponent bits, 10 significand bits.)
Sign: Negative
Exponent: 16 (Stored: 31, Bias: 15)
Classification: FP_NAN (Signaling)
Value: NaN
Note: Representation for NaN's is not unique
== Lane 0 ============================================================
Satisfiable. Model:
DECODED = 0.0075912 :: FloatingPoint 5 11
1 0
5 43210 9876543210
S -E5-- ---S10----
Binary layout: 0 00111 1111000110
Hex layout: 1FC6
Precision: Half (5 exponent bits, 10 significand bits.)
Sign: Positive
Exponent: -8 (Stored: 7, Bias: 15)
Classification: FP_NORMAL
Binary: 0b1.111100011p-8
Octal: 0o3.706p-9
Decimal: 0.0075912
Hex: 0x1.f18p-8
Usage info
Usage: crackNum value OR binary/hex-pattern
-i N Signed integer of N-bits
-w N Unsigned integer of N-bits
-f fp Floating point format fp
-r rm Rounding mode to use. If not given, Nearest-ties-to-Even.
-l lanes Number of lanes to decode
-h, -? --help print help, with examples
-v --version print version info
-d --debug debug mode, developers only
Examples:
Encoding:
crackNum -i4 -- -2 -- encode as 4-bit signed integer
crackNum -w4 2 -- encode as 4-bit unsigned integer
crackNum -f3+4 2.5 -- encode as float with 3 bits exponent, 4 bits significand
crackNum -f3+4 2.5 -rRTZ -- encode as above, but use RTZ rounding mode.
crackNum -fbp 2.5 -- encode as a brain-precision float
crackNum -fdp 2.5 -- encode as a double-precision float
crackNum -fe4m3 2.5 -- encode as an E4M3 FP8 float
crackNum -fe5m2 2.5 -- encode as an E5M2 FP8 float
crackNum -fsp 0x3.2p5 -- encode as single-precision from hex-float
Decoding:
crackNum -i4 0b0110 -- decode as 4-bit signed integer, from binary
crackNum -w4 0xE -- decode as 4-bit unsigned integer, from hex
crackNum -f3+4 0b0111001 -- decode as float with 3 bits exponent, 4 bits significand
crackNum -fbp 0x000F -- decode as a brain-precision float
crackNum -fdp 0x8000000000000000 -- decode as a double-precision float
crackNum -fhp 0x8000000000000000 -- decode as a double-precision float
crackNum -l4 -fhp 64\'hbdffaaffdc71fc60 -- decode as half-precision float over 4 lanes using verilog notation
Notes:
- For encoding:
- Use -- to separate your argument if it's a negative number.
- For floats: You can pass in NaN, Inf, -0, -Inf etc as the argument
along with a decimal (2.3, -4.1e5) or hexadecimal float (0x2.4p3)
- For decoding:
- Use hexadecimal (0x) binary (0b), or N'h (verilog) notation as input.
Input must have one of these prefixes.
- You can use _,- or space as a digit to improve readability for the pattern to be decoded
- With -lN parameter, you can decode multiple lanes of data.
- If you use verilog input format, then we will infer the number of lanes unless you provide it.
VIM users: You can use the http://github.com/LeventErkok/crackNum/blob/master/crackNum.vim file to
use CrackNum directly from VIM. Simply locate your cursor on the text to crack, and use the
command :CrackNum options.
