SIMD Math tracking issue

[WhiteBlackGoose]

COMMUNITY-DRIVEN WORK TRACKING ISSUE

Tracks implementation of the SIMD Math Proposal.

It is being implemented in the feature/math-simd.

Tasks

API implementation

#665 (generator)

• Create
• Load
• Add
• Subtract
• Multiply
• Divide
• Abs
• Constants
• And
• Or
• Xor
• Not
• AllBitsSet
• IsHardwareAccelerated

#670

• Equal
• NotEqual
• GreaterThan
• GreaterOrEqual
• LessThan
• LessThanOrEqual
• Min
• Max

#684

• IsFinite
• IsInfinity
• IsNaN
• IsNegative
• IsNegativeInfinity
• IsNormal
• IsPositiveInfinity
• Sign

Arithmetics

• Negate

Special

• As
• IEEERemainder

Trigonometry

• Acos
• Acosh
• Asin
• Asinh
• Atan2
• Atan
• Atanh
• Cos
• Cosh
• Sin
• Sinh
• Tan
• Tanh

Powers

• Exp
• Cbrt
• Sqrt
• Pow
• Log10
• Log
• Log of two args
• Reciprocal

Rounding

• Floor
• Ceiling
• Round
• Round of two args
• Truncate

Bit operations

• ShiftLeft
• ShiftRight
• RotateLeft
• RotateRight

Tests

For all bitnesses x for all types

#670

• 4 arithmetic operators
• Less/Greater Than (OrEqual)
• Min, Max
• (Not)Equal
• Bitwise operations

#684

• State of number

Other

• Create, Load, Store
• Regular trigonometry
• Hyperbolic trigonometry
• Inverse trigonometry
• Inverse hyperbolic trigonometry
• Power
• Rounding
• Bit operations

Benchmarks

For all bitnesses x for all types

#670

• 4 arithmetic operators
• Less/Greater Than (OrEqual)
• Min, Max
• (Not)Equal

#684

• State of number
• Bitwise operations
• Abs

Other

• Create, Load, Store
• Regular trigonometry
• Hyperbolic trigonometry
• Inverse trigonometry
• Inverse hyperbolic trigonometry
• Power
• Rounding
• Bit operations

TODOs

#670

• Make fallback to 128-bit if 256-bit is not supported
• Use naive operations for 8-byte values on simd64

#684

• The random feeder should be either static or without seed or anything, otherwise it fills both vectors with the same data

Other

• Divide for integers to be done in a more efficient way link
• Multiply for bytes to be done in a more efficient way link
• Use intrinsic ShiftRight/ShiftLeft once proposal is impl
• Remove unmanaged constraints where possible
• Relax constraints to struct where possible
• Hardware accelerated comparison operations for long and ulong

Far TODOs

• Propose & add support for Simd512 (that requires runtime support)

To discuss

#678

• AllBitsSet API for Scalar

#690

Other

• MaxValueOver2 API for Simd and Scalar
• IsHardwareAccelerated should be && IsSupported? Otherwise Simd128<MyAwesomeType>.IsHardwareAccelerated returns true on net5 on avx machine
• Math.Abs throws on Math.Abs(int.MinValue). We can keep it, or we can have a faster version without this check
• CopySign API

[WhiteBlackGoose]

Ideas

Sinh / Cosh

Those two have similar formulas:

(e^x + e^-x) / 2
(e^x - e^-x) / 2

So we can have Sinh/Cosh method

Speaking of implementation, we have

var ex = Simd.Exp(x);
var exm = Simd.Reciprocal(ex);
var multiplier = Simd.Create(0.5);
var sinh = Simd.Multiply(Simd.Subtract(ex, exm), multiplier);
var cosh = Simd.Multiply(Simd.Add(ex, exm), multiplier);
return (sinh, cosh);

Exp

• AMD's expf (fast impl of exp for regular cast in C)
• AMD's simd exp (that's what we need but in asm)
• Simd exp from SO

Min/Max for longs

var compared = LessThan(left, right);
var antiCompared = GreaterThanOrEqual(left, right);
var withOnes = And(compared, Vector.Create(1));
var antiWithOnes = And(compared, Vector.Create(1));
var res = Or(Multiply(withOnes, left), Multiply(antiWithOnes, right));

State of number

1. IsPositiveInfinity and IsNegativeInfinity can be verified on exact equality (for ints it returns zero) (though Tanner mentions some exception)
2. IsFinite is & and equality: source (for ints it returns all bits set)
3. IsInfinity is trivial too (for ints it returns zero)
4. NaN can be checked with inequality to itself
5. IsNegative/IsPositive should probably be Compare Less/Greater against 0? Or source
6. IsNormal just follows source

[HurricanKai]

Should verify that for Store (and other void returning methods) the nested method trick actually works.

[WhiteBlackGoose]

128 bit sharplab

256 bit sharplab

64 bit sharplab
(well I don't have a mobile sharplab)

@HurricanKai

And also it's probably #665 -related, not this issue

[HurricanKai]

Future: Look at checking for IsHardwareAccelerated before calling down into other methods, don't want to ie call Not(LessThen(...)) if it's not hardware accelerated, because it means two loops with non-hardware accelerated Loads/Stores

[HurricanKai]

Future: Improve IsNegative check by checking for bit instead of doing a full blown compare

[WhiteBlackGoose]

Important: Notes from working group meeting