## Decode/Encode Integers, Words, and IEEE754 and other float formats
`crackNum` shows you exactly how a number is laid out in memory: the bit
pattern, its fields, the classification, and the value in binary, octal,
decimal, and hex. It works in both directions:
- **Encoding**: give it a value (`2.5`, `-2.3e6`, `NaN`, `0x3.2p5`), and it shows
the bit-pattern it turns into, together with the rounding that took place.
- **Decoding**: give it a bit-pattern (`0xdeadbeef`, `0b0110`, `32'hfdc71fc6`),
and it shows the value it stands for.
### Download crackNum
**→ [Ready-to-run bundles for Linux, macOS, and Windows](https://github.com/LeventErkok/crackNum/releases)**
Nothing to build, no Haskell toolchain. Each bundle carries the `crackNum`
executable, a copy of `z3`, the GUI, a LICENSE, and a `README.txt` with the
install steps for that platform.
- **Linux (x86_64)** — [`crackNum-<version>-linux-x86_64.tar.gz`](https://github.com/LeventErkok/crackNum/releases/latest).
Statically linked, so it runs as-is on any x86_64 Linux, old or new.
- **macOS (Apple Silicon)** — [`crackNum-<version>-macos-arm64.tar.gz`](https://github.com/LeventErkok/crackNum/releases/latest).
Includes `CrackNum.app`. Ad-hoc signed, so clear the quarantine flag first.
- **Windows (x86_64)** — [`crackNum-<version>-windows-x86_64.zip`](https://github.com/LeventErkok/crackNum/releases/latest).
Includes `CrackNumGUI.exe`. Unsigned, so SmartScreen warns on first run.
Unpack it, put the files on your `PATH` — `z3` included, since crackNum shells
out to it for every operation — and check with:
```
$ crackNum -fsp 3.5
$ crackNum --gui
```
### Building from source
crackNum is on [Hackage](http://hackage.haskell.org/package/crackNum):
```
$ cabal install crackNum
```
This way you also need [z3](https://github.com/Z3Prover/z3) on your `PATH`:
crackNum delegates the floating-point reasoning to it, via
[SBV](http://hackage.haskell.org/package/sbv).
### Supported formats
```
Flag Format Exponent Significand
-----------------------------------------------------------------------
-fhp Half precision (IEEE-754 binary16) 5 11
-fbp Brain float (bfloat16) 8 8
-ftf32 TensorFloat-32 8 11
-fsp Single precision (binary32) 8 24
-fdp Double precision (binary64) 11 53
-fqp Quad precision (binary128) 15 113
-fe5m2 FP8, IEEE-754 style 5 3
-fe4m3 FP8, alternate (no infinities) 4 4
-ffp4 FP4 (E2M1) 2 2
-ffp4e0m3 FP4 (E0M3), sign-magnitude 0 3
-fe8m0 E8M0 (MX scale), exponent-only 8 0
-fa+b Arbitrary IEEE-754 float a b
```
Significand sizes include the implicit bit.
Rounding mode is selected with `-r`, and defaults to `RNE` if not given:
`RNE` (nearest, ties to even), `RNA` (nearest, ties away), `RTP` (towards
positive infinity), `RTN` (towards negative infinity), and `RTZ` (towards zero).
### Example: Encode a single-precision float, rounding towards zero
```
$ crackNum -fsp 1.3 -rRTZ
Satisfiable. Model:
ENCODED = 1.3 :: Float
3 2 1 0
1 09876543 21098765432109876543210
S ---E8--- ----------S23----------
Binary layout: 0 01111111 01001100110011001100110
Hex layout: 3FA6 6666
Precision: Single
Sign: Positive
Exponent: 0 (Stored: 127, Bias: 127)
Classification: FP_NORMAL
Binary: 0b1.0100110011001100110011
Octal: 0o1.23146314
Decimal: 1.3
Hex: 0x1.4ccccc
Rounding mode: RTZ: Round towards zero.
Note: Conversion from "1.3" was not faithful. Status: Inexact.
```
### Example: Decode a single-precision bit-pattern
```
$ 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
```
### Example: Encode an E8M0 MX scale
Only powers of two are representable, so everything else rounds according to `-r`:
```
$ crackNum -fe8m0 -- 10
Satisfiable. Model:
ENCODED = 8.0 :: E8M0
76543210
---E8---
Binary layout: 10000010
Hex layout: 82
Precision: 8 exponent bits, no significand
Sign: Positive (always)
Exponent: 3 (Stored: 130, Bias: 127)
Classification: FP_NORMAL
Binary: 0b1p+3
Octal: 0o1p+3
Decimal: 8.0
Hex: 0x8
Rounding mode: RNE: Round nearest ties to even.
Note: Original value of 10.0 was rounded to 8.0.
```
### Example: Decode two half-precision 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 = 0.0075912476 :: 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: 0.0075912476
Hex: 0x1.f18p-8
```
With verilog notation (`N'h...`) the lane count is inferred from the width, so
`-l` is optional.
### Graphical interface
An optional GUI: pick a format on the left, type a value, see the result. It is a
thin front-end over the `crackNum` binary, so it supports exactly the same formats.
Launch it with `--gui`, which forwards any flags and value to the app:
```
$ crackNum --gui -- open the graphical interface
$ crackNum --gui -fsp 2.5 -- open it with single-precision selected, and 2.5 cracked
$ crackNum --gui 0xdeadbeef -- open it pre-filled with a value to decode
```
### 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
--gui launch the graphical interface
--list-formats list the formats supported by -f, one per line
Supported floating-point formats (for use with -f):
hp: Half float ( 5 + 11)
bp: Brain float ( 8 + 8)
tf32: TensorFloat-32 ( 8 + 11)
sp: Single precision ( 8 + 24)
dp: Double precision (11 + 53)
qp: Quad precision (15 + 113)
a+b: Arbitrary IEEE-754 ( a + b)
e5m2: FP8 format (IEEE-754) ( 5 + 3)
e4m3: FP8 format (Alternate) ( 4 + 4)
fp4: FP4 format (E2M1) ( 2 + 2)
fp4e0m3: FP4 format (E0M3) ( 0 + 3)
e8m0: FP8 format (MX scale) ( 8 + 0)
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 -ftf32 2.5 -- encode as a TensorFloat-32 float
crackNum -fdp 2.5 -- encode as a double-precision float
crackNum -fqp 2.5 -- encode as a quad-precision float
crackNum -fe4m3 2.5 -- encode as an E4M3 FP8 float
crackNum -fe5m2 2.5 -- encode as an E5M2 FP8 float
crackNum -ffp4 2.5 -- encode as an FP4 (E2M1) float
crackNum -ffp4e0m3 3.5 -- encode as an FP4 (E0M3) sign-magnitude integer
crackNum -fe8m0 2.5 -- encode as an E8M0 MX scale (power of two)
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 -ftf32 19\'h0000F -- decode as a TensorFloat-32 float
crackNum -fdp 0x8000000000000000 -- decode as a double-precision float
crackNum -fhp 0x8000 -- decode as a half-precision float
crackNum -ffp4 0b0111 -- decode as an FP4 (E2M1) float
crackNum -ffp4e0m3 0b1101 -- decode as an FP4 (E0M3) sign-magnitude integer
crackNum -fe8m0 0x7F -- decode as an E8M0 MX scale (power of two)
crackNum -l4 -fhp 64\'hbdffaaffdc71fc60 -- decode as half-precision float over 4 lanes using verilog notation
GUI:
crackNum --gui -- launch the graphical interface
crackNum --gui 0xdeadbeef -- launch the GUI, pre-filled with the given value
crackNum --gui -fsp 0xdeadbeef -- launch the GUI, using the given format
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)
- FP4 (E2M1) has neither NaN nor Inf, so those inputs are rejected. Finite
values outside its range of [-6, 6] saturate to the nearest end-point.
- FP4 (E0M3) is a sign-magnitude integer: a sign bit and a 3-bit magnitude,
covering -7 to 7, with both a positive and a negative zero. It has no NaN
and no Inf either, and values outside [-7, 7] saturate to the end-point.
- E8M0 (MX scale) is all exponent: no sign bit and no significand at all,
so every value is a power of two, from 2^-127 to 2^127. It has no zero
and no Inf, and 0xFF is its only NaN. Negative inputs are rejected;
values outside the range saturate to the nearest end-point.
- 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: [crackNum.vim](http://github.com/LeventErkok/crackNum/blob/master/crackNum.vim)
cracks the text under the cursor with `:CrackNum options`.