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Numerical Libraries for Urbit

Current Status

  • /lib/math is distributed via the %yard desk.

  • We are preparing a release of Lagoon %real with SoftBLAS-powered jets for release with Urbit 410K.

  • We are preparing a release of Saloon %real without jets for release with Urbit 409K.

  • We are working on an implementation of tinygrad for Maroon.

  • some notion of cursor in an array would be really helpful

We envision four libraries and associated jet code living in this repository:

  • /lib/math offers basic special function support for floating-point atoms.
  • Lagoon (Linear AlGebra in hOON) offers BLAS-like operations (like NumPy's pure matrix operations).
    • Lagoon %reals are slated to ship with 410 K.
    • SoftBLAS provides a reproducible software-defined floating-point implementation of parts of BLAS and LAPACK suitable for jetting Lagoon.
    • /lib/fixed provides operations for fixed-precision operations.
  • Saloon (Scientific ALgorithms in hOON) offers transcendental functions (like NumPy's transcendental functions, optimizers, etc.).
  • Maroon (MAchine LeaRning in hOON) offers machine learning algorithms, starting with tinygrad.

Type System

  • %real IEEE 754 float (currently supported)
  • %cplx IEEE 754 float/BLAS packed complex (planned)
  • %uint unsigned integers (currently supported)
  • %int2 signed twos-complement integers (planned)
  • %sint signed ZigZag integers (planned)
  • %unum → subdivide into one of:
    • %post posits (32-bit or 16-bit) (planned)
    • %vald valids (32-bit or 16-bit) (planned)
  • %fixp fixed-precision (planned)

Fixed-Point Library /lib/fixed

> `@ub`(add:fixed 0b100.0001.0000 [8 8] 0b101.0001.0000 [8 8])
0b1001.0010.0000

> `@ub`(sub:fixed 0b100.0001.0000 [8 8] 0b101.0001.0000 [8 8])
0b1.1111.1111.0000.0000

> `[@ub ^]`(mul:fixed 0b100.0001.0000 [8 8] 0b101.0001.0000 [8 8])
[0b1.0100.1001.0001.0000.0000 17 16]

> `[@ub ^]`(div:fixed 0b100.0001.0000 [8 8] 0b101.0001.0000 [8 8])
[0b0 17 16]

> `[@ub ^]`(div:fixed 0b1.0100.0001.0000 [8 8] 0b101.0001.0000 [8 8])
[0b11 17 16]

Lagoon 410K %real Release

The 410 K release candidate for Lagoon provides %real-valued array operations equivalent to @rh, @rs, @rd, and @rq operations in vanilla Hoon. (Other types have been removed for this release but will be re/introduced in a subsequent release.) The following arms are provided:

  • ++print
  • ++slog
  • ++to-tank
  • ++get-term
  • ++squeeze
  • ++submatrix
  • ++product
  • ++gather
  • ++get-item
  • ++set-item
  • ++get-row
  • ++set-row
  • ++get-col
  • ++set-col
  • ++get-bloq-offset
  • ++get-item-number
  • ++strides
  • ++get-dim
  • ++get-item-index
  • ++ravel
  • ++en-ray
  • ++de-ray
  • ++get-item-baum
  • ++fill
  • ++spac (helper function)
  • ++unspac (helper function)
  • ++scalar-to-ray
  • ++eye
  • ++zeros
  • ++ones
  • ++iota
  • ++magic
  • ++range
  • ++linspace
  • ++urge
  • ++scale
  • ++max
  • ++argmax
  • ++min
  • ++argmin
  • ++cumsum
  • ++prod
  • ++reshape
  • ++stack
  • ++hstack
  • ++vstack
  • ++transpose
  • ++diag
  • ++trace
  • ++dot
  • ++mmul
  • ++abs
  • ++add-scalar
  • ++sub-scalar
  • ++mul-scalar
  • ++div-scalar
  • ++mod-scalar
  • ++add
  • ++sub
  • ++mul
  • ++div
  • ++mod
  • ++pow-n
  • ++gth (note boolean)
  • ++gte (note boolean)
  • ++lth (note boolean)
  • ++lte (note boolean)
  • ++mpow-n
  • ++is-close
  • ++any (note boolean)
  • ++all (note boolean)
  • ++fun-scalar (helper function)
  • ++trans-scalar (helper function)
  • ++el-wise-op (helper function)
  • ++bin-op (helper function)

The Hoon release is available in urbit/numerics, branch sigilante/reals-only. The Hoon release consists of the following files:

  • /sur/lagoon for data types necessary to use Lagoon.
  • /lib/lagoon for operations.
  • /tests/lib/lagoon for various array operation behavior tests.

A PR is at #6971.

The Vere release is available in urbit/vere, branch sigilante/lagoon-jets. The Vere release contains jets for 28 arms. These have been tested for correctness against the reference Hoon results.

A PR is at #638.

Points for discussion:

  1. Currently we ship Lagoon as /lib/lagoon and jet into the f/hex core in tree.c. Since that generally deals with Zuse-level arms, is it advisable to introduce another level g/hep for /lib jets?
  2. /sur/lagoon still lists other types in +$kind, but these are commented out for the time being.

Nonobvious points to note:

  1. The comparison gates for Lagoon flip back to boolean rather than loobean results. Furthermore, they result in numerical ones (e.g. 0x3f80.0000 for @rs) rather than simple 0x1s. This is because we want sparse matrices to remain sparse when we eventually support them, and because we want multiplication times the result of a logical operation to set or clear fields appropriately without needing to change the kind. (No solution appears to be completely satisfactory.)
  2. ++submatrix and ++stack are not jetted yet. These are both dicey jets to get right due to multiple offsets. Fortunately, once we have them correct they should work for all kinds since they only depend on bloq size not kind.
  3. The rounding mode for %real may be set for the core using the ++lake gate. This returns a copy of the Lagoon ++la core with rounding mode changed to one of ?(%n %u %d %z).
> (cumsum:(lake:la %u) (en-ray:(lake:la %u) [~[7 1] 5 %real ~] ~[.1 .5 .-5 .2 .3 .-20 .-1]))
[meta=[shape=~[1 1] bloq=5 kind=%real fxp=~] data=0x1.c170.0000]

to make:

  • logspace
  • tensordot
  • bitwise ops
  • eq, ne
  • isnan, isinf (±)
  • pad
  • pow, exp, log, whatever not in Saloon

THREE POSSIBILITIES:

  1. Logical loobean (0 true, terrible for sparse matrices)

  2. Logical boolean (1 true, normal but out of step w/ Hoon)

  3. Numeric boolean (0x3f80.0000 for 1, etc.)

Here we follow the third option in u3qf_la_gth_real() etc.