//
// This confidential and proprietary software may be used only as
// authorised by a licensing agreement from ARM Limited
// (C) COPYRIGHT 2023 ARM Limited
// ALL RIGHTS RESERVED
// The entire notice above must be reproduced on all authorised
// copies and copies may only be made to the extent permitted
// by a licensing agreement from ARM Limited.

== Appendix A

NOTE: This appendix is at an early stage of development at this point in time

=== Random data generation

The following function generates a pseudo-random floating-point value in the range -1.0 to +1.0 for use as test data.
It uses a modulo (1<<32) recurrent sequence with multiplier derived from "TOSASETS" and the set number.

[source,c++]
----
float set_data(uint32_t set, uint32_t index)
{
    uint32_t m = (8*set + 1) * 0x705A5E75;   // mod (1<<32) calculation
    uint32_t r = m + 1;                      // mod (1<<32) calculation
    for (uint32_t i = 0; i < index; i++) {
        r = r * m + 1;                       // mod (1<<32) calculation
    }
    float  sign = (r>>31)==0 ? +1 : -1;
    return sign * (float)(r & 0x7FFFFFFF) / (float)(0x7FFFFFFF);
}
----

=== Dot product floating-point test data sets

Each test set is indexed by a pair (S, N) where:

* S is the test set number
* N is the number of elements in a single test vector

Each test set (S, N) contains multiple tests that statistics are calculated over.
The parameter T is the number of tests in a given set.
In the table below, t is the test number within a set in the range 0 to T-1.

[cols="1,1,1,5,5"]
|===
| Set S | N range | T | x[k] formula for k < N | w[k] formula for k < N

| 0
| 2-25,50,100,1000
| 10
| x[k]=set_data(S, 2*t*N+2*k) < 0 ? 0.0 : set_data(S, 2*t*N+2*k+1)
| w[k]=set_data(S, 2*t*N+2*k) < 0 ? set_data(S, 2*t*N+2*k+1) : 0.0

| 1
| 2-25,50,100,1000
| 1000
| x[k]=2.0*set_data(S,  2*t*N + k)
| w[k]=2.0*set_data(S, (2*t+1)*N + k)

| 2
| 2-25,50,100,1000
| 1000
| x[0]=1.0, x[k]=set_data(S, 2*t*N + k)/sqrt(N) for k>0
| w[0]=1.0, w[k]=set_data(S, (2*t+1)*N + k)/sqrt(N) for k>0

|===