v2.9.0

Known Issues

• half8 == and != operators don't conform to the IEEE 754 standard (compliant with Unity.Mathematics... for now... hint)
• bool vectors generated from operations on non-(s)byte vectors do not generate the most optimal machine code possible, partly due to an LLVM performance regression, partly due to other compiler related difficulties
• float8 min() and max() functions don't handle NaNs the same way Unity.Mathematics does

Fixes

• Fixed XML documentation not showing descriptions for valid Promise flags
• Fixed cminmax documentation
• bitmask64 with numBits equal to 64 now correctly returns a bitmask with all 64 bits set if not compiling for Bmi1 i.e. AVX2
• Fixed uint8 to float8 type conversion if compiling for AVX2
• Fixed incorrect mod implementations
• (ISSUE #16) Fixed float and double (r)cbrt edge cases (+/-0, Infinity and NaN). Additionally, the scalar- and vector float implementation now returns accurate results for subnormal numbers. Performance is affected negatively yet minimally (~2 clock cycles, + ~10 instructions); new valid Promise flags allow for call-site selection of faster code paths

Additions

Divider<T>

Divider<T> is an opaque OOP-like struct which performs fast integer division and modulo operations as well as divisibility checks.
For any divisor of any scalar- or vector integer type T, a Divider<T> instance replaces division operations by multiplication-, shift- and rounding operations, utilizing the most suitable of 2 algorithms, typically used by compilers for compile time constant divisors.
Divider<T> was carefully crafted in a way that allows for complete compile-time evaluation of constant divisors of all types in Burst compiled code.
Divider<T> is NOT meant to replace divison operations; a (notable) performance gain is only to be expected in case the same divisor is used multiple times, or when multiple divisors are computed at once, utilizing SIMD (for instance, when a very predictable i is the divisor in a for-loop).
Numerous Promise flags allow for faster operations, provided that the Divider<T> instance is both initialized and used in the same block of Burst compiled code and not loaded from RAM.
The implementation is pseudo-generic and only works for integer types known to MaxMath. Furthermore, Bursts inabilty to compile-time evaluate typeof(T) often requires explicit initialization (example: new Divider<byte>((byte)42)). DEBUG only validity checks ensure correct initialization and usage.
The current Divider API consists of...:

• / and % operators:
  • LHS: scalar <> RHS: Divider(scalar): requires both scalars to be of the same type; returns a scalar of the that type
  • LHS: vector <> RHS: Divider(vector): requires both vectors to be of the same type; returns a vector of the that type
  • LHS: scalar <> RHS: Divider(vector): requires the vector type to contain integers of the scalar type; returns an instance of the vector type
  • LHS: vector <> RHS: Divider(scalar): requires the vector type to contain integers of the scalar type; returns an instance of the vector type
• DivRem member methods
• EvenlyDivides member methods
• T Divisor as a readonly property
• public const Promises within Divider<T>, documenting valid promise flags with appropriate naming, starting with "PROMISE_"
• Get/SetInnerDivider<U> methods: get or set a scalar- or vector Divider<U> within a Divider<T>
• Component shuffles: Divider<T>.wzxy swizzle "operators" as properties.

NOTE: Get/SetInnerDivider<U> methods and Divider<T>.[a][b][c][d] properties will change in the future. Due to current limitations regarding C# generics, swizzle operators only take in or return the same type the respective property is a member of, i.e. you cannot use these to get a Divider<int2> from a Divider<int4>. Get/SetInnerDivider<U> are placeholderholders both for these operations as well as for the v[a]_[b] properties for vectors with 8 or more components. C# will at some point get more complex type extension language support, at which point this API will change.

quadruple (PREVIEW)

Analogous to (U)Int128, this library now supports 128 bit floating point operations with its respective software-implemented type. It is fully IEEE754 compliant and in the typical 1 sign bit, 15 exponent bits, 112 mantissa bits format.
NOTE: quadruple is in preview for an unforseeable amount of time. This means that it is neither completely optimized, nor are all maxmath functions available for it at this time.
The following functions have been implemented: ToString and Parse (no perfect roundtrip guaranteed), All constants (example: PI_QUAD), Random128 NextQuadruple (optionally with min and max values), all type conversions except for decimal, -(unary), +(binary), -(binary), *, /, %, ==, !=, <, <=, >, >=, fmod, mad, msub, rcp, isnan, isinf, isfinite, isnormal, issubnormal, round, floor, ceil, trunc, roundtoint (and all other integer variations), fastsqrt, (r)sqrt, (r)cbrt, isinrange, approx, select, compareto, min, max, copysign, nextgreater, nextsmaller, nexttoward, radians, degrees, chgsign

Functions

• Added isnormal and issubnormal functions for floating point types
• Added hypot and inthypot functions for calculating [int]sqrt(a * a + b * b) without overflow, unless an optional Promise parameter with its NoOverflow flag set is passed as a compile time constant argument
• Added roundto(s)byte/(u)short/(u)int/(u)long/(U)Int128. These take in floating point values of any type and convert them to the respective integer scalar- or vector type while rounding towards the nearest integer
• Added cor and cxor. These reduce vectors of a given integer type to a scalar integer of that type by applying bitwise OR or XOR operations between each element
• Split approx into two overloads: one with a custom tolerance parameter (the old version) and one without, which calculates an appropriate tolerance instead
• Added roundmultiple(x, m), floormultiple(x, m), ceilmultiple(x, m) and truncmultiple(x, m) for all types, rounding x to the nearest multiple of any positive m with the selected rounding mode (for example: ceilmultiple rounds x to the nearest greater multiple of m)
• Added a whole stack of bit manipulation functions for all scalar- and vector integer types: parityodd, parityeven, countzerobits, l1cnt, t1cnt, lzmask, tzmask, l1mask, t1mask, bits_extractlowest0, bits_masktolowest, bits_masktolowest0, bits_maskfromlowest, bits_maskfromlowest0, bits_setlowest, bits_surroundlowest and bits_surroundlowest0

Global Compilation Options

• Added Global Compilation Options for OptimizeFor, FloatMode and FloatPrecision. A proposal for compile-time access to job-specific options has been forwarded to the Burst team and is on their backlog. For now, these global options are dependency-injection-style placeholders and thus hard-coded to OptimizeFor.Performance, FloatMode.Default and FloatPrecision.Standard, respectively, and can be customized within the source code itself at .../MaxMath/Runtime/Compiler Extensions/Compilation Options.cs

Improvements

Meta

• This library now fully supports ARM CPUs' SIMD instructions (huge!). It utilizes SSE2NEON and SIMDe to convert x86 SIMD instructions to ARM SIMD instructions or instruction sequences. Because of this, generated ARM code will sometimes remain slightly unoptimized, because the author is unable to verify correctness of ARM specific optimizations with unit tests in most cases.

Performance

• Implemented optimized (u)long vector to float vector type convesion operators
• Implemented the execution of two loop bodies in one for functions that use loop-based algorithms, when a vector type wider than 128 bits is used without compiling for AVX(2)
• Implemented an AssumeRangeAttribute equivalent for all vectorized functions with known return value ranges
• Implemented more optimal (U)Int128 comparison operators
• Implemented optimal (U)Int128 multiplication operations with- and division and modulo operations by compile time constants
• Implemented optimal (U)Int128 division and modulo operations by replacing a loop algorithm with straight line code. Because Burst does not expose the hardware-supported 128x64 narrowing division instruction as an intrinsic, this instruction, which is fundamentally important to the algorithm, is implemented with fallback code. A highly optimized (speed & size) native DLL written in Windows x86-64 assembly containing the most optimal implementation of any varation of 128 bit integer division was added to utilize this hardware instruction. This does mean that 128 bit integer division now results in a function call that cannot be inlined, yet the performance gain is worth it. Additionally, the C#/assembly interface was carefully crafted to avoid calling external functions partially or even entirely by utilizing Unity.Burst.CompilerServices.Constant.IsConstantExpression<T>()
• Increased valid Promise.Unsafe0 range for (u)long intcbrt from [0, 2^46} to [0, 2^48]
• Added an optional Promise parameter to gamma
• Added an optional Promise parameter to erf(c)
• Added an optional Promise parameter to gcd and lcm
• Added quarter and half scalar- and vector function overloads for min, max, minmax, clamp, saturate, isinrange, trunc, round, ceil, floor and sign
• Removed the only non-optimizing branch in vector code in the entire library within the long2/3/4 >> operator if the shift amount is not a comp...

v2.3.5

Known Issues

• half8 == and != operators don't conform to the IEEE 754 standard (compliant with Unity.Mathematics)
• (s)byte, (u)short vector and (U)Int128 multiplication, division and modulo operations by compile time constants are not optimal
• optimized (U)Int128 comparison operators didn't make it into this release
• bool vectors generated from operations on non-(s)byte vectors do not generate the most optimal machine code possible, partly due to an LLVM performance regression, partly due to other compiler related difficulties
• most vectorized function overloads don't communicate return value ranges to the compiler yet, missing out on more efficient code paths selected at compile-time-only with compile-time-only value range checks.
• AVX2 (s)byte32 all_dif lookup tables are currently way too large (kiloBytes)

Fixes

• (Issue #10) bool8/16/32 are now blittable when not used within an IJob

Additions

• added comb(n, k) for scalar- and vector integer types. This is known as the binomial coefficient or "n choose k". An optional Promise parameter can select a O(1) code path using the factorial formula, whereas the standard approach, which cannot ever overflow unless the result itself overflows (which is not true for most solutions found online that claim it), uses a O(min(k, n - k)) algorithm with respect to time
• added perm(n, k) for scalar- and vector integer types. This is known as "k-permutations of n". An optional Promise parameter can select a O(1) code path using the factorial formula, whereas the standard approach, which cannot ever overflow unless the result itself overflows, uses a O(k) algorithm with respect to time
• added nextgreater(x) for all types. For integer types, it is a wrapper function for addsaturated(x, 1). For floating point types, it returns the next greater representable floating point value(s), unless x is NaN or infinite. An optional Promise parameter allows for numerous optimizations.
• added nextsmaller(x) for all types. For integer types, it is a wrapper function for subsaturated(x, 1). For floating point types, it returns the next smaller representable floating point value(s), unless x is NaN or infinite. An optional Promise parameter allows for numerous optimizations
• added nexttoward(from, to) for all types, returning the next representable integer/floating point value(s) in a given direction, unless from is equal to to. For floating point types, from is returned if from is NaN or infinite. If to is NaN, NaN is returned. An optional Promise parameter allows for numerous optimizations.

Improvements

• improved performance of 64bit vectorized division thanks to a newly implemented and further optimized algorithm from a July 13th 2022 research paper, which replaces a vectorized loop (rather slow; up to 64 iterations; no instruction level parallelism outside the loop possible until the loop finished executing, following an almost certainly mispredicted branch) with straight line code. Due to "recent" improvements to divider circuits, this code path is inferior to hardware supported scalar division via element extraction for (u)long2, specifically, even when the quotient and/or remainder vector is in the middle of a dependency chain and even in tight loops, and is thus only implemented for (u)long3/4 types and only if compiling for AVX2
• improved performance and reduced code size of up to (s)byte8 and every (u)short vector division if not compiling with FloatMode.Fast. Reduced constants possibly read from RAM in either case.
• fixed performance regression of SIMD register <-> software abstraction conversions for types using up the entirety of a hardware register
• lcm for (s)byte vectors with 8 elements or less: decreased code size by 20 or 28 bytes; removed 2 or 4 or 8 bytes of constant data read from RAM; reduced latency by 2 or 3 clock cycles
• verified and increased the (u)long scalar- and vector intcbrt Promise.Unsafe0 range from [0, 1ul << 40] to [0, 1ul << 46], the code path of which is also possibly chosen at compile time
• implemented optimized quarter{X} IEEE-754 comparison operators (without having to cast to float{X}). Vectorized halfX comparisons are implemented in MaxMath.Intrinsics.Xse as well and used where appropriate. compareto with quarter{X} and half{X} function overloads were implemented.
• reduced latency of add/subsaturated for scalar Int128s, scalar and vector longs as well as vector ints by about a third
• replaced (U)Int128.ToString(null, null)s call to BigInteger.ToString() and thus unnecessary heap allocations with an optimized implementation
• (u)short8 / and % operators now correctly check for SSE2 support rather than AVX2
• removed aliased fixed size buffers from all types, also improving indexer operator performance if the index is a compile time constant (in some cases)

Changes

• Burst compiled code that uses a Promise argument which is not a compile time constant will throw an exception in DEBUG, as it represents significant overhead instead of an optimization. This will currently not inform users of the name of the function but rather the Burst compiled job/function that threw it.

Fixed Oversights

• added explicit type conversion operators for scalar floats and doubles to half8 and all quarter vectors (as well as scalar halfs to quarter vectors)

v2.3.0

Known Issues

• half8 == and != operators don't conform to the IEEE 754 standard (compliant with Unity.Mathematics)
• (s)byte, (u)short vector and (U)Int128 multiplication, division and modulo operations by compile time constants are not optimal
• optimized (U)Int128 comparison operators didn't make it into this release
• using bool vectors generated from 256 bit input vectors like so: long4 x = select(a, b, >>> myLong4a < myLong4b <<<) (as an example) does not generate the most efficient machine code possible
• unit tests for 64-bit bits_zerohigh functions fail 100% of the time because of a bug related to the managed debug implementation of intrinsics (reported)
• unit tests for intrinsics code paths for all functions that use "(mm256_)shuffle_ps" or "(mm256_)blendv_ps" can fail semi-randomly due to a bug which changes the bit content of ints which would be NaN if dereferenced as a float and written back to memory (reported)
• most vectorized function overloads don't communicate return value ranges to the compiler yet, missing out on more efficient code paths selected at compile-time-only with compile-time-only value range checks.
• (s)byte32 all_dif lookup tables are currently way too large (kiloBytes)

Fixes

• fixed quarter rounding behavior when casting a wider floating point type to a quarter to round towards the nearest representable value instead of truncating the mantissa

Additions

added namespace MaxMath.Intrinsics for users who want to use the math library through "high level" X86 intrinsics. Because users need to guard their intrinsics code with e.g. if (Burst.Intrinsics.X86.Sse2.IsSse2Supported) blocks and supported architectures vary (slightly) from function to function, these are considered unsafe, undocumented and unrecommended and only serve as an exposed layer of abstraction which is used internally anyway.

added flags enum Promise, with values Nothing, Everything NoOverflow, ZeroOrGreater, ZeroOrLess, NonZero and Unsafe 0 through 3 aswell as the composites Positive and Negative. This flags enum is only ever used as an optional parameter and offers faster, yet more unsafe code. Specifics vary between functions and sometimes even overloads but are documented accordingly. Optimizations are only ever to be added, not removed (= a ...promise ... of never introducing breaking changes in this regard)

Other Additions

• added factorial (for integer types) and gamma (floating point types) functions. factorial, when called without a Promise parameter, clamps the result to type.MaxValue in case of overflow
• added erf(c), the (complementary) error function for floating point types
• added (c)minmag and (c)maxmag functions, returning the (componentwise) minimum/maximum magnitude of two values or within a vector; equivalent to abs(x) > abs(y) ? x : y (maxmag) or abs(cmin(c)) > abs(cmax(c)) ? cmin(c) : cmax(c) (cmaxmag)
• added (c)minmax and (c)minmaxmag functions which return both the (componentwise/columnwise) minimum and maximum (magnitude) as out parameters
• added bitfield functions for scalar and vector integer types - small utility functions that pack several smaller integers into bigger ones
• added copysign(x, y) functions for signed types, which is equivalent to return y < 0 ? nabs(x) : abs(x)
• added (naive?) implementation for scalar- and vector float/double inverse hyberbolic functions asinh, acosh and atanh
• added intlog10 functions (integer base ten logarithm)
• added the bit test/bt family of functions for scalar and vector integer types. A testbit(POST_ACTION)((ref)x, i) function returns a boolean (vector), indicating whether the bit in x at index i is 1 and may (or may not) flip, set, or reset that bit afterwards
• added a new category of type conversion functions with the suffix "unsafe". Added to(u)longunsafe and todoubleunsafe with a Promise parameter, allowing for up to two levels of optimization (vectorized 64bit int <-> 64 bit float is not hardware supported). Details in the XML documentation. Default double <-> (u)long conversion operators - apart from having their 4-element version improved - now check whether or not a safe range for unsafe conversions can be validated at compile time
• added scalar/vectorized toquarterunsafe allowing for each type to be converted to a quarter type while specifying whether the input value will or will not overflow and/or is >= 0

Improvements

improved performance of several vector operators and function overloads for types that use up an entire hardware register while having to be up-cast to a wider type considerably - surrounding boilerplate code uses a new "in-house" faster-than-hardware algorithm with its dependency chain latency having been reduced from x [0 <= x <= 3] + (9 or 10) clock cycles down to x + (0 or 1 or 3) + (1 or 3) clock cycles

massive performance improvements for all vector types that are not a total of 128 or 256 bits wide, respectively, either through the Avx.[...]undefined[...] compiler intrinsics or through controlled undefined behaviour, by declaring an uninitialized variable and using pointer syntax to force the C# compiler into trusting that the variable has been fully initialized; this cannot lead to memory access violations, since the variable is declared and thus enough space is reserved on the stack, before it is optimized away by LLVM and assigned a hardware register instead, with undefined upper elements. This allows for upper elements of hardware registers to be ignored during compilation. Unnecessarily emitted instructions like movq xmm0, xmm0 (move the low 8 bytes from a register to the same register, zeroing out the upper 8 bytes, even though only the lower 8 bytes will be written back to memory) or far worse instruction sequences, for example when using vectors with 3 elements, are now (MOSTLY; there's still work to be done) omitted instead. Although most zero-upper-elements instruction( sequence)s only took a single clock cycle, they were always part of each dependency chain and could happen between almost each function call, including operators of course. The same improvements apply to Unity.Mathematics types when passed to maxmath functions.

improved performance throughout the library by effectively adding hundreds of thousands of Unity.Burst.CompilerServices.Constant.IsConstantExpression condition checks more to many functions within the library. Most notably, algorithms, where the total latency is dependant on the byte size of arguments, may now perform much faster. Some but not yet all of these constant checks are exposed through a Promise parameter

Other Improvements

• improved performance of scalar (u)short to (u)short2/3/4 conversion
• reduced latency of all, any first, last, count and bitmask functions for bool8/16/32 when used with an expression as the argument, such as all(x != y) - a way to force the compiler to omit unnecessary intructions was found
• reduced latency of addsaturated for scalar unsigned integer types
• reduced latency of float/double to (U)Int128 conversion
• reduced latency of shl, shrl and shra and thus all functions using those - especially for: shl for (s)byte vectors of all sizes if compiling for SSE4 and 32 byte sized vectors if compiling for AVX2; shl for (u)short vectors of 4 or more elements if compiling for at least SSE4; shra for (u)long vectors if compiling for AVX2 and the vector containing the shift amounts is a compile time constant.
• reduced long2/3/4 shra code size and latency by another 2 clock cycles if compiling for AVX2
• reduced latency of variable rol/r vector functions beyond shl/r improvements and added an optional Promise parameter, allowing the caller to promise the rotation values are in a specific range
• reduced latency of long2/3/4 "is negative checks" - mylong4 < 0/0 > mylong4 by 33% by doubling its code size. This further improves performance/adds to code size of functions in the library
• reduced latency of (u)long2/3/4 isinrange functions
• reduced latency of unsigned byte and ushort vector to float vector conversion. This also affects performance of (s)byte (u)short vector intsqrt functions, aswell as the respective % and / operators (byte2/3/4/8, all ushort vectors)
• reduced (u)long vector intcbrt latency by ~45% and reduced code size by ~20% (roughly 150 bytes). For other integer vector types, the latency has been reduced by ~8 to ~15 clock cycles
• added hidden and retroactively improved exp2 scalar and vector integer argument function overloads. These return exp2((float/double)x) or (float/double)(1 << x) in 3 instead of 6 to 7 clock cycles at best; they of course also work for negative input values i.e. reciprocals of powers of 2. The (u)int overloads convert to floats, the (u)long overloads convert to doubles; explicit integer to integer casting should (and sometimes has to) be used for optimal results. Additionally, these overloads contain an optional 'Promise' parameter, allowing for omission of clamping which is needed to ensure correct underflow/overflow behavior, as dictated by Unity's exp2 implementation. If you ever used the standard exp2 function by implicitly converting an int type to a float type, performance was improved by a factor of about 30x. This overload only "breaks" code that casts (u)long types to float types implicitly if the result is expected to be a float type. It is recommended to explicitly cast the (u)long type to a (u)int type in such a case
• added ==, !=, <, >, <= and >= operators for UInt128 and signed long/int comparisons, as the expensive float conversion and comparison was previosly used when, for instance, compar...

MaxMath v2.2.0

Known Issues

• half8 == and != operators don't conform to the IEEE 754 standard - Unity has not yet reacted to my bug-report in regards to their "half" implementation
• (s)byte, (u)short vector and (U)Int128 multiplication, division and modulo operations by compile time constants are not optimal. For (U)Int128, it requires a new Burst feature à la T Constant.ForceCompileTimeEvaluation<T, U>(Func<U, T> code)(proposed); Currently work is being done on (s)byte and (u)short vectors in this regard, which will beat any compiler. The current (tested) state of all optimizations possible is included in this version.
• pow functions with compile time constant exponents currently do not handle many decimal numbers - math.rsqrt would often be used in those cases for optimal performance but it is actually slower when the Unity.Burst.FloatMode is set to anything but FloatMode.Fast. To guarantee optimal performance, compile time access to the current FloatMode would be needed (proposed)
• double (r)cbrt functions are currently not optimized

Fixes

• linked float8 rcp and rsqrt functions to Bursts' FloatMode and FloatPrecision
• short.MinValue / -1 now correctly overflows to short.MinValue when dividing a short16 vector by another short16 vector when compiling for AVX or higher
• fixed scalar quarter to double conversion for when the quarter value is negative
• fixed scalar half to quarter conversion for when the half value is negative
• fixed vector quarter to ulong conversion for when a quarter value is negative
• fixed (u)short8 to quarter8 conversion

Additions

Added saturation arithmetic to the library for all scalar- and vector types. Saturation arithmetic clamps the result of an operation to type.MinValue and type.MaxValue if under- or overflow occurs, respectively and has single-instruction hardware support for (s)bytes and (u)shorts. The included functions are:

• addsaturated
• subsaturated
• mulsaturated
• divsaturated (only clamps division of floating point types and signed division of, for instance, sbyte.MinValue ( = -128) / -1 to sbyte.MaxValue ( =127), which would cause a hardware exception for ints and longs`)
• castsaturated (all types to all other types with a smaller range),
• csumsaturated
• cprodsaturated

(U)Int128

• added high performance (U)Int128 types with full library support, meaning: all operators and type conversions aswell as all functions support these types. Most operations of both types, in Burst code, compile down to optimal machine code. Exceptions: 1) signed 64x64 bit to 128 bit multiplication 2) *, /, % and divrem functions with a scalar compile time constant argument (See: Known Issues 2)
• added Random128 XOR-Shift pseudo random number generator for generating (U)Int128s

Cube Root

• added high performance & accuracy (r)cbrt - (reciprocal) cube root functions for scalar and vector float- and double types based on a research paper from 2021. An optional bool parameter allows the caller to decide whether or not negative input values should be handled correctly (which is not the case with math.pow(x, 1f/3f)), which is set to false by default
• added high performance intcbrt - integer cube root functions for all scalar and vector integer types. For signed integer types, an optional bool parameter allows the caller to decide whether or not negative input values should be handled correctly (which is not the case with math.pow(x, 1f/3f)), which is set to false by default

Other Additions

• added a log function to all scalar and vector float- and double types with a second parameter b, which is the logarithms' base
• added reversebytes functions for all scalar- and vector types, which convert back and forth between big endian and little endian byte order, respectively. All of them (scalar, vector) compile down to single hardware instructions
• added pow functions with scalar exponents for float and double scalars and vectors, with optimizations for selected constant exponents (not necessarily whole exponents)
• added function overloads to all functions for scalar (s)bytes and (u)shorts in order to resolve function call resolution ambiguity which was already present in Unity.Mathematics, which may also improve performance in some cases
• added a static readonly New property to RandomX XOR-Shift pseudo random generators. It calls Environment.TickCount internally (and is thus seeded somewhat randomly), makes sure it is non-zero and can be called from Burst native code
• added fastrcp functions for float scalars and vectors, faster (and substantially less accurate) than FloatPrecision.Low, FloatMode.Fast Burst implementations
• added fastrsqrt functions for float scalars and vectors, faster (and substantially less accurate) than FloatPrecision.Low, FloatMode.Fast Burst implementations

Improvements

• added AVX and AVX2 code for float8 sin, cos, tan, sincos, asin, acos, atan, atan2, sinh, cosh, tanh, pow, exp, exp2, exp10, log, log2, log10 and fmod (and the % operator)
• optimized many /, %, * and divrem operations with a scalar compile time constant argument for (s)byte vectors (see 'Known Issues 2'), which were previously not optimized (...optimally/at all) by Burst.
• added SSE2 fallback code for converting AVX vector types to SSE vector types and vice versa(for example: short16(256 bit) to byte16(128 bit))
• scalar (s)byte and (u)short rol and ror functions now compile down to single hardware instructions
• improved performance and/or reduced code size of nearly all vector comparison operations (==, > etc.)
• improved performance of - and added SSE2 fallback code for bitfield to boolean vector conversion (toboolX and thus also select(vector a, vector b, bitmask c));
• improved performance of intpow functions in general and for when the exponent is a compile time constant
• improved performance and reduced code size of compareto vector functions (especially for unsigned types)
• added more optimizations to isdivisible
• improved performance of intsqrt functions for (u)long and (s)byte scalar and vector types considerably
• reduced code size of ispow2 vector functions
• reduced code size of (s)byte vector-by-vector division
• improved performance of Random64's (u)long4 generation if compiling for AVX2
• improved performance of (s)byte matrix multiplication
• reduced code size of (u)short- and up to (s)byte8 vector by vector division and divrem functions(and improved performance if compiling for SSE2 only)
• reduced code size and improved performance of isinrange functions for (u)long vector types
• reduced code size of ushort vector >= and <= operators for SSE2 fallback code by ~75%
• improved performance and reduced code size of SSE2 down-casting fallback code

Changes

• API BREAKING CHANGE: The various boolean to integer/floating point conversion functions (touint8/tof32 etc.) are now renamed to contain C# types in their names (tobyte/tofloat etc.)
• API BREAKING CHANGE: If you use this library as intended, meaning you import it and Unity.Mathematics.math statically (using static MaxMath.maxmath;) and you use the pow functions with scalar bases and scalar exponents in those scripts, you will encounter the first ever function call resolution ambiguity. It is strongly recommended to always use the maxmath.pow function, because it optimizes any pow call enormously if the exponent is a compile time constant, which does NOT necessarily mean that such a call must declare the exponent as a literal value - the exponent may become a compile time constant due to constant propagation
• quarter is now a readonly struct
• quarter to sbyte, short, int and long coversions are now required to be declared explicitly
• removed countbits(void* ptr, ulong bytes) from the library and added it to https://github.com/MrUnbelievable92/SIMD-Algorithms with more options

Fixed Oversights

• (Issue #3) added constructor wrappers to the maxmath class analogous to Unity.Mathematics(byte4 myByte4 = (maxmath.)byte4(1, 2, 3, 4);)
• added dsub - fused divide-subtract function for scalar and vector float types
• added an optional bool fast = false parameter to dad, dsub, dadsub and dsubadd functions
• added andnot function overloads for scalar and vector bool types
• added implicit type conversions of scalar quarter values to half, float and double vectors
• added all_eq and all_dif functions for vectors of size 2
• added all_eq and all_dif functions for float and double vectors

MaxMath v2.1.2

Known Issues

• half8 "equals" and "not equals" operators don't conform to the IEEE 754 standard - Unity has not yet reacted to my bug-report in regards to their "half" implementation

Fixes

• fixed undefined behavior of "vshr" functions for vector types smaller than 128 bits
• fixed SSE2 implementations of "vrol" and "vror" functions for the (u)short16 type

Additions

• implemented Bmi1 and Bmi2 intrinsics as functions with a "bits_" prefix (except for "andn", which has already been implemented as "andnot")
• added high performance and/or SIMD "isdivisible" functions for all integer vector types and scalar value types
• added high performance and/or SIMD "intpow" - integer exponentiation - functions for (u)int, (u)long and all integer vector types
• added high performance and/or SIMD "floorpow2" functions for all integer vector types
• added "nabs" - negative absolute value functions for all non-boolean vector- and single value types
• added "indexof(vector v, value x)" functions for all non-boolean vector types

Improvements

• aggressivley optimized away global variables (shuffle masks) and thus memory access and usage where appropriate
• improved performance of 256 bit vector subvector getters
• added Sse2 fallback code for all (u)long2/3/4 operators
• improved performance of mulitplication, division and modulo operations for all (s)byte- and (u)short vector- and matrix types when dividing by a single non-compile time constant value
• added overloads for (s)byte- and (u)short vectors' "divrem" functions with a scalar value as the divisor parameter, improving performance when it is a compile time constant
• improved performance of "intsqrt" functions for most types

Changes

• bump com.unity.burst to version 1.5

Fixed Oversights

• added bitmask8 and bitmask16 functions for (s)byte and (u)short vector types, respectively

MaxMath v2.1.1

Known Issues

• half8 "equals" and "not equals" operators don't conform to the IEEE 754 standard - Unity has not yet reacted to my bug-report in regards to their "half" implementation

Fixes

• fixed triggered burst compilation error by "Sse4_1.blend_epi16" when compiling for SSE2 due to fallback code not using a constant value for "imm8"
• fixed incorrect CPU feature checks for quarter vector type-conversion code when compiling for SSE2
• fixed "tzcnt" implementations (were completely broken)
• fixed scalar (single value and C# fallback) "lzcnt" implementations for (s)byte and (u)short values and (u)long4 vectors

Additions

• added "ulong countbits(void* ptr, ulong bytes)", which counts the number of 1-bits in a given block of memory, using Wojciech Mula's SIMD population count algorithm
• added high performance and/or SIMD "gcd" a.k.a. greatest common divisor functions for (u)int, (u)long and all integer vector types, which always return unsigned types and vectors
• added high performance and/or SIMD "lcm" a.k.a. least common multiple functions for (u)int, (u)long and all integer vector types, which always return unsigned types and vectors
• added high performance and/or SIMD "intsqrt" - integer square root (floor(sqrt(x)) functions for all integer- and integer vector types, with the functions for signed integers and vectors throwing an ArgumentOutOfRangeException in case a value is negative

Improvements

• performance improvements of "avg" functions for signed integer vectors
• added SIMD implementations of the "transpose" functions for all matrix types
• added SSE4 and SSE2 fallback code for variable bitshifts ("shl", "shrl" and "shra")
• added SSE2 fallback code for (s)byte vector-by-vector division and modulo operations
• added SSE2 fallback code for "all_dif" for (s)byte16, (u)short8 and (u)int8 vectors
• added SSE2 fallback code for typecasting, propagating through the entire library
• added SSE2 fallback code for "addsub" and "subadd" functions
• bitmask32 and bitmask64 now allow for masks to be up to 32 and 64 bits wide, respectively

Changes

• renamed "BurstCompilerException" to "CPUFeatureCheckException"
• "shl", "shrl" and "shra" now have undefined behavior when bitshifting any value outside of the interval [0, 8 * sizeof(integer_type) - 1] for performance reasons and because of differences between SSE, AVX and managed C#

Fixed Oversights

• added "shl", "shrl" and "shra" (varying per element) functions for (s)byte and (u)short vectors
• added "ror" and "rol" (varying per element) functions for (s)byte and (u)short vectors
• added "compareto" functions for all vector types except half- and quarter vectors
• added "all_dif" functions for (s)byte32 vectors
• added vshr/l and vror/l functions for (s)byte32 and (u)short16 vectors

2.1.1 Hotfix

Fixes

• fixed SSE2 "shl", "shrl" and "shra" implementations
• fixed SSE2 "intsqrt" implementations

Improvements

• improved performance of (s)byte2, -3, -4, -8, -16 and (u)short2, -3, -4, -8 "gcd" functions (and thus "lcm") when compiling for Avx2
• improved performance of "tzcnt" and "lzcnt" implementations for all vector types if compiling for SSE4 or higher, propagating through a lot of the library

Fixed Oversights

Added documentation for RandomX methods

MaxMath v2.1.0

Known Issues

• half8 "equals" and "not equals" operators don't conform to the IEEE 754 standard - Unity has not yet reacted to my bug-report in regards to their "half" implementation

Fixes

• fixed triggered burst compilation error by "Sse4_1.blend_epi16" when compiling for SSE2 due to fallback code not using a constant value for "imm8"
• fixed incorrect CPU feature checks for quarter vector type-conversion code when compiling for SSE2
• fixed "tzcnt" implementations (were completely broken)
• fixed scalar (single value and C# fallback) "lzcnt" implementations for (s)byte and (u)short values and (u)long4 vectors

Additions

• added "ulong countbits(void* ptr, ulong bytes)", which counts the number of 1-bits in a given block of memory, using Wojciech Mula's SIMD population count algorithm
• added high performance and/or SIMD "gcd" a.k.a. greatest common divisor functions for (u)int, (u)long and all integer vector types, which always return unsigned types and vectors
• added high performance and/or SIMD "lcm" a.k.a. least common multiple functions for (u)int, (u)long and all integer vector types, which always return unsigned types and vectors
• added high performance and/or SIMD "intsqrt" - integer square root (floor(sqrt(x)) functions for all integer- and integer vector types, with the functions for signed integers and vectors throwing an ArgumentOutOfRangeException in case a value is negative

Improvements

• performance improvements of "avg" functions for signed integer vectors
• added SIMD implementations of the "transpose" functions for all matrix types
• added SSE4 and SSE2 fallback code for variable bitshifts ("shl", "shrl" and "shra")
• added SSE2 fallback code for (s)byte vector-by-vector division and modulo operations
• added SSE2 fallback code for "all_dif" for (s)byte16, (u)short8 and (u)int8 vectors
• added SSE2 fallback code for typecasting, propagating through the entire library
• added SSE2 fallback code for "addsub" and "subadd" functions
• bitmask32 and bitmask64 now allow for masks to be up to 32 and 64 bits wide, respectively

Changes

• renamed "BurstCompilerException" to "CPUFeatureCheckException"
• "shl", "shrl" and "shra" now have undefined behavior when bitshifting any value outside of the interval [0, 8 * sizeof(integer_type) - 1] for performance reasons and because of differences between SSE, AVX and managed C#

Fixed Oversights

• added "shl", "shrl" and "shra" (varying per element) functions for (s)byte and (u)short vectors
• added "ror" and "rol" (varying per element) functions for (s)byte and (u)short vectors
• added "compareto" functions for all vector types except half- and quarter vectors
• added "all_dif" functions for (s)byte32 vectors
• added vshr/l and vror/l functions for (s)byte32 and (u)short16 vectors

MaxMath v2.0.0

Re-Release Notes

• Version 2.0.0 adds - for the first time - fallback procedures from Avx2 to Sse4, Sse2 and platform independent instruction sets, respectively, with some major optimizations for all of them
• ARM and other instruction sets do NOT have optimized fallback procedures written for them, and there are no plans for it at this time. Burst/LLVM are good at recognizing the patterns in the code, though, and some of the code will be vectorized for other platforms (confirmed)

Known Issues

• half8 "equals" and "not equals" operators don't conform to the IEEE 754 standard - Unity has not yet reacted to my bug-report in regards to their "half" implementation

Fixes

• fixed incorrect bool4 subvector getters of the bool8 type

Improvements

• removed "fixed" vector element access to improve performance in managed C#

Additions

• added "shuffle(vector, vector, ShuffleComponent(, ShuffleComponent)(, ShuffleComponent)(, ShuffleComponent)) functions for (s)byte, (u)short, (u)long, quarter and half vectors

Changes

• Bump com.unity.burst to version 1.4.4

Fixed Oversights

• Added "addsub" function for floating point types, complementary to "subadd"

• Added "addsub" and "subadd" functions for integer types

MaxMath v1.2.0

Known Issues

• half8 "==" and "!=" operators don't conform to the IEEE 754 standard - Unity has not yet reacted to my bug-report in regards to their "half" implementation.

Fixes

• Added preliminary safety cast to a float of the half value in toboolsafe() until Unity fixes their half '==' and '!=' operators according to IEEE 754

Additions

"quarter" precision floats and vectors

• "quarter" is an 8-bit IEEE 754 1.3.4.-3 floating point value, often called a "minifloat"
• It has a very limited range of [-15.5, 15.5] with an epsilon of 0.015625. All integers, aswell as i + 0.5, within that range can be represented as a quarter
• Type conversion from - and to quarters also conforms to the IEEE 754 standard. In detail, casting to a quarter performs rounding according to a) its' precision and b) whether or not the more precise value is closer to 0 or to quarter.Epsilon. NaN and +/- zero preservation, aswell as preservation of/clamping to +/- infintiy was also implemented
• "==" and "!=" operators for vectors conforming to the IEEE 754 standard were implemented (unlike, currently, Unity's "half" type). All the other boolean- and arithmetic operators were implemented for the base type only, which will return single precision results (for arithmetic operations). For vectors, quarter vectors are to be (implicitly) cast to single precision vectors first, until/if Unity changes their "half" implementation.
• Type conversions from - and to all other single value and vector types were implemented
• Full function implementation within the library was added, including: abs(), isnan(), isinf(), isfinite(), select(), as[s]byte/asquarter(), vrol/r(), vshl/r(), toboolsafe and toquartersafe

Fixed Oversights

• Added missing type conversions from - and to half8 for (s)byte8, (u)short8 and (u)int8 vectors

• Added missing type conversions from - and to half8 for booleans and boolean vectors

• Added half "select" functions

• Improved the performance of unsafe boolean-to-half/float/double functions

• added (preliminary?) "abs", "isnan", "isinf" and "isfinite" for half and half vectors, eliminating unnecessary casting

MaxMath v1.1.0

Known Issues

• half8 "equals" and "not equals" operators don't conform to the IEEE 754 standard - Unity has not yet reacted to my bug-report in regards to their "half" implementation.

Fixes

• Fixed a bug where vshl-/vshr-ing a(n) (s)byte16 vector by 11 would return the vector itself

Changes

• Changed the return type of count(boolx) to a uint instead of an int

Additions

RNG

• Added/Modified 8, 16, 32 and 64 bit XOR-Shift pseudo random number generators:
• They use the most efficient (Avx2) SIMD instructions to generate vectors with elements of the corresponding size in bytes. When compared to Unity.Mathematics, the performance is better since a) scalar multiplication of each generated value has been replaced by a single SIMD instruction and b) doubles are generated by Random64 instead of two 32-bit RNG iterations
• Removed NextT(T max) from SIGNED integer and floating point types, since those will never generate negative numbers. One can either generate an unsigned integer and cast it to a signed value for free, or use the functions with min and max parameters, as both of these would be more clear in regards to what range the result will be in
• Unity.Mathematics.Random is implicitly convertible to Random32 and vice versa. Safe and fast explicit type conversions between Random8, 16, 32 and 64 were added

Shuffle

• Added bool8, bool16 and bool32 subvector getters

• Added setters for half8 subvectors

• Added (s)byte32 subvector getters

• Added setters for (s)byte8 and s)byte16 subvectors

• Added setters for (u)short8 subvectors

• !!! Setters for (s)byte32, (u)short16, (u)int8 and float8 subvectors are implemented, but due to Unity.Burst related bugs, they are deactivated in the code. The issue has been forwarded a month ago and should be fixed with Burst 1.5

• Slightly improved the performance of a select few (s)byte2/3/4 vector shuffle getters and setters