pseudocode/library/numeric_accuracy_helpers.tosac

//
// This confidential and proprietary software may be used only as
// authorised by a licensing agreement from ARM Limited
// (C) COPYRIGHT 2020-2024 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.

fp64_t exp2(int n) {
    if (n < -1075) {
        return 0.0; // smaller than smallest denormal
    }
    REQUIRE(n <= 1023);
    fp64_t v = 1.0;
    while (n > 0) { v = v*2.0; n--; }
    while (n < 0) { v = v/2.0; n++; }
    return v;
}

int ilog2(fp64_t v) {
    REQURE(0 < v && v < infinity);
    int n = 0;
    while (v >= 2.0) { v = v/2.0; n++; }
    while (v <  1.0) { v = v*2.0; n--; }
    return n;
}

fp64_t normal_min<in_t>() {
  switch (in_t) {
    case fp32_t: return exp2(-126);
    case bf16_t: return exp2(-126);
    case fp16_t: return exp2( -14);
    case fp8e4m3_t: return exp2(-6);
    case fp8e5m2_t: return exp2(-14);
  }
}

fp64_t normal_max<in_t>() {
  switch (in_t) {
    case fp32_t: return exp2(128) - exp2(127-23);
    case bf16_t: return exp2(128) - exp2(127- 7);
    case fp16_t: return exp2( 16) - exp2( 15-10);
    case fp8e4m3_t: return exp2( 9) - exp2( 8-2);
    case fp8e5m2_t: return exp2( 16) - exp2( 15-2);
  }
}

// Number of fractional (mantissa bits)
int normal_frac<in_t> () {
  switch (in_t) {
    case fp32_t: return 23;
    case fp16_t: return 10;
    case bf16_t: return  7;
    case fp8e4m3_t: return 3;
    case fp8e5m2_t: return 2;
  }
}