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//
// 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;
}
}
double calcAbsErrorBound<in_t>(double bound_magnitude, double bounds_value,
double lower_bound, double normal_divisor) {
double error_bound = 0.0;
// Avoid cases where we generate an error_bound of NaN by multiplying inf * 0
if (is_finite(bounds_value) || abs(bound_magnitude) != 0.0) {
double value_bound = abs(bound_magnitude) * bounds_value;
if (lower_bound > 0) {
value_bound = max(lower_bound, value_bound);
}
error_bound = exp2(-normal_frac<in_t> / normal_divisor) * value_bound;
}
return error_bound;
}
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