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float8.c
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float8.c
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#include "float8.h"
/****************************
* EXPONENT_BIAS DEFINITION *
****************************/
#if EXPONENT_BITS == 1
#define EXPONENT_BIAS 0
#endif
#if EXPONENT_BITS == 2
#define EXPONENT_BIAS 1
#endif
#if EXPONENT_BITS == 3
#define EXPONENT_BIAS 3
#endif
#if EXPONENT_BITS == 4
#define EXPONENT_BIAS 7
#endif
#if EXPONENT_BITS == 5
#define EXPONENT_BIAS 15
#endif
#if EXPONENT_BITS == 6
#define EXPONENT_BIAS 31
#endif
/****************************
* FUNCTION IMPLEMENTATIONS *
****************************/
unsigned char float8_to_uchar(float8_t f8) { return *(unsigned char *)&f8; }
float8_t uchar_to_float8(unsigned char c) { return *(float8_t *)&c; }
/*
* Increase a float8_t number to the next representable value.
*
* By default the float8 numbers are rounded down to the nearest
* representable value. When needed, the number can be rounded up
* to the next representable value. Due to the format of the
* float8_t number, this can be easily done by increasing the
* unsigned char representation of the float8 number by one.
*
* @param c: unsigned char to be converted
* @return: 8-bit minifloat (float8_t) number
*/
float8_t increse_by_one(float8_t f8) {
unsigned char temp = float8_to_uchar(f8);
temp++;
return uchar_to_float8(temp);
}
float8_t float_to_float8(float f) {
float8_t result;
uint32_t *p = (uint32_t *)&f;
// Extract sign, exponent and fraction from the float
uint32_t sign = (*p >> 31) & 0x1;
uint32_t exponent = (*p >> 23) & 0xFF;
uint32_t fraction = *p & 0x7FFFFF;
// Save the sign
result.sign = sign;
#if EXPONENT_BITS == 1
if (exponent == 0x0) { // Zero case (float32 subnormal are zero in float8)
result.exponent = 0; // 0
result.fraction = 0; // 00 0000
} else if (exponent == 0xFF) { // Infinity or NaN case
result.exponent = 0x1; // 1
result.fraction = 0; // 00 0000 - Only Infinity is represented
} else {
int32_t exp_value = exponent - 127;
if (exp_value >= 1) { // Infinity case
result.exponent = 0x1;
result.fraction = 0;
} else if (exp_value <= -7) { // Zero case
result.exponent = 0;
result.fraction = 0;
} else if (exp_value == -6) { // Subnormal case
result.exponent = 0;
result.fraction = 0;
// (Rounding) Increase by one
if (((fraction >> 22) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -5) { // Subnormal case
result.exponent = 0;
result.fraction = 0b000001;
// (Rounding) Increase by one
if (((fraction >> 22) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -4) { // Subnormal case
result.exponent = 0;
result.fraction = 0b000010 | ((fraction >> 22) & 0x01);
// (Rounding) Increase by one
if (((fraction >> 21) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -3) { // Subnormal case
result.exponent = 0;
result.fraction = 0b000100 | ((fraction >> 21) & 0x03);
// (Rounding) Increase by one
if (((fraction >> 20) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -2) { // Subnormal case
result.exponent = 0;
result.fraction = 0b001000 | ((fraction >> 20) & 0x07);
// (Rounding) Increase by one
if (((fraction >> 19) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -1) { // Subnormal case
result.exponent = 0;
result.fraction = 0b010000 | ((fraction >> 19) & 0x0F);
// (Rounding) Increase by one
if (((fraction >> 18) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == 0) { // Subnormal case
result.exponent = 0;
result.fraction = 0b100000 | ((fraction >> 18) & 0x1F);
// (Rounding) Increase by one
if (((fraction >> 17) & 0x01) == 1) {
result = increse_by_one(result);
}
}
// NO normal case for 1-1-6
// The 1-1-6 float8 format DOES NOT have normal values
}
#endif
#if EXPONENT_BITS == 2
if (exponent == 0x0) { // Zero case (float32 subnormal are zero in float8)
result.exponent = 0; // 00
result.fraction = 0; // 0 0000
} else if (exponent == 0xFF) { // Infinity or NaN case
result.exponent = 0x3; // 11
result.fraction = 0; // 0 0000 - Only Infinity is represented
} else {
int32_t exp_value = exponent - 127;
if (exp_value >= 2) { // Infinity case
result.exponent = 0x3;
result.fraction = 0;
} else if (exp_value <= -7) { // Zero case
result.exponent = 0;
result.fraction = 0;
} else if (exp_value == -6) { // Subnormal case
result.exponent = 0;
result.fraction = 0;
// (Rounding) Increase by one
if (((fraction >> 22) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -5) { // Subnormal case
result.exponent = 0;
result.fraction = 0b00001;
// (Rounding) Increase by one
if (((fraction >> 22) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -4) { // Subnormal case
result.exponent = 0;
result.fraction = 0b00010 | ((fraction >> 22) & 0x01);
// (Rounding) Increase by one
if (((fraction >> 21) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -3) { // Subnormal case
result.exponent = 0;
result.fraction = 0b00100 | ((fraction >> 21) & 0x03);
// (Rounding) Increase by one
if (((fraction >> 20) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -2) { // Subnormal case
result.exponent = 0;
result.fraction = 0b01000 | ((fraction >> 20) & 0x07);
// (Rounding) Increase by one
if (((fraction >> 19) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -1) { // Subnormal case
result.exponent = 0;
result.fraction = 0b10000 | ((fraction >> 19) & 0x0F);
// (Rounding) Increase by one
if (((fraction >> 18) & 0x01) == 1) {
result = increse_by_one(result);
}
} else { // Normal case
result.exponent = exp_value + EXPONENT_BIAS;
result.fraction = fraction >> 18; // Only keep 5 bits of fraction
// (Rounding) Increase by one
if (((fraction >> 17) & 0x01) == 1) {
result = increse_by_one(result);
}
}
}
#endif
#if EXPONENT_BITS == 3
if (exponent == 0x0) { // Zero case (float32 subnormal are zero in float8)
result.exponent = 0; // 000
result.fraction = 0; // 0000
} else if (exponent == 0xFF) { // Infinity or NaN case
result.exponent = 0x7; // 111
result.fraction = 0; // 0000 - Only Infinity is represented
} else {
int32_t exp_value = exponent - 127;
if (exp_value >= 4) { // Infinity case
result.exponent = 0x7;
result.fraction = 0;
} else if (exp_value <= -8) { // Zero case
result.exponent = 0;
result.fraction = 0;
} else if (exp_value == -7) { // Subnormal case
result.exponent = 0;
result.fraction = 0;
// (Rounding) Increase by one
if (((fraction >> 22) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -6) { // Subnormal case
result.exponent = 0;
result.fraction = 0b0001;
// (Rounding) Increase by one
if (((fraction >> 22) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -5) { // Subnormal case
result.exponent = 0;
result.fraction = 0b0010 | ((fraction >> 22) & 0x01);
// (Rounding) Increase by one
if (((fraction >> 21) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -4) { // Subnormal case
result.exponent = 0;
result.fraction = 0b0100 | ((fraction >> 21) & 0x03);
// (Rounding) Increase by one
if (((fraction >> 20) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -3) { // Subnormal case
result.exponent = 0;
result.fraction = 0b1000 | ((fraction >> 20) & 0x07);
// (Rounding) Increase by one
if (((fraction >> 19) & 0x01) == 1) {
result = increse_by_one(result);
}
} else { // Normal case
result.exponent = exp_value + EXPONENT_BIAS;
result.fraction = fraction >> 19; // Only keep 4 bits of fraction
// (Rounding) Increase by one
if (((fraction >> 18) & 0x01) == 1) {
result = increse_by_one(result);
}
}
}
#endif
#if EXPONENT_BITS == 4
if (exponent == 0x0) { // Zero case (float32 subnormal are zero in float8)
result.exponent = 0; // 0000
result.fraction = 0; // 000
} else if (exponent == 0xFF) { // Infinity or NaN case
result.exponent = 0xF; // 1111
result.fraction = 0; // 000 - Only Infinity is represented
} else {
int32_t exp_value = exponent - 127;
if (exp_value >= 8) { // Infinity case
result.exponent = 0xF;
result.fraction = 0;
} else if (exp_value <= -11) { // Zero case
result.exponent = 0;
result.fraction = 0;
} else if (exp_value == -10) { // Subnormal case
result.exponent = 0;
result.fraction = 0;
// (Rounding) Increase by one
if (((fraction >> 22) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -9) { // Subnormal case
result.exponent = 0;
result.fraction = 0b001;
// (Rounding) Increase by one
if (((fraction >> 22) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -8) { // Subnormal case
result.exponent = 0;
result.fraction = 0b010 | ((fraction >> 22) & 0x01);
// (Rounding) Increase by one
if (((fraction >> 21) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -7) { // Subnormal case
result.exponent = 0;
result.fraction = 0b100 | ((fraction >> 21) & 0x03);
// (Rounding) Increase by one
if (((fraction >> 20) & 0x01) == 1) {
result = increse_by_one(result);
}
} else { // Normal case
result.exponent = exp_value + EXPONENT_BIAS;
result.fraction = fraction >> 20; // Only keep 3 bits of fraction
// (Rounding) Increase by one
if (((fraction >> 19) & 0x01) == 1) {
result = increse_by_one(result);
}
}
}
#endif
#if EXPONENT_BITS == 5
if (exponent == 0x0) { // Zero case (float32 subnormal are zero in float8)
result.exponent = 0; // 0 0000
result.fraction = 0; // 00
} else if (exponent == 0xFF) { // Infinity or NaN case
result.exponent = 0x1F; // 1 1111
result.fraction = 0; // 00 - Only Infinity is represented
} else {
int32_t exp_value = exponent - 127;
if (exp_value >= 16) { // Infinity case
result.exponent = 0x1F;
result.fraction = 0;
} else if (exp_value <= -18) { // Zero case
result.exponent = 0;
result.fraction = 0;
} else if (exp_value == -17) { // Subnormal case
result.exponent = 0;
result.fraction = 0;
// (Rounding) Increase by one
if (((fraction >> 22) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -16) { // Subnormal case
result.exponent = 0;
result.fraction = 0b01;
// (Rounding) Increase by one
if (((fraction >> 22) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -15) { // Subnormal case
result.exponent = 0;
result.fraction = 0b10 | ((fraction >> 22) & 0x01);
// (Rounding) Increase by one
if (((fraction >> 21) & 0x01) == 1) {
result = increse_by_one(result);
}
} else { // Normal case
result.exponent = exp_value + EXPONENT_BIAS;
result.fraction = fraction >> 21; // Only keep 2 bits of fraction
// (Rounding) Increase by one
if (((fraction >> 20) & 0x01) == 1) {
result = increse_by_one(result);
}
}
}
#endif
#if EXPONENT_BITS == 6
if (exponent == 0x0) { // Zero case (float32 subnormal are zero in float8)
result.exponent = 0; // 00 0000
result.fraction = 0; // 0
} else if (exponent == 0xFF) { // Infinity or NaN case
result.exponent = 0x3F; // 11 1111
result.fraction = 0; // 0 - Only Infinity is represented
} else {
int32_t exp_value = exponent - 127;
if (exp_value >= 32) { // Infinity case
result.exponent = 0x3F;
result.fraction = 0;
} else if (exp_value <= -33) { // Zero case
result.exponent = 0;
result.fraction = 0;
} else if (exp_value == -32) { // Subnormal case
result.exponent = 0;
result.fraction = 0;
// (Rounding) Increase by one
if (((fraction >> 22) & 0x01) == 1) {
result = increse_by_one(result);
}
} else if (exp_value == -31) { // Subnormal case
result.exponent = 0;
result.fraction = 0b1;
// (Rounding) Increase by one
if (((fraction >> 22) & 0x01) == 1) {
result = increse_by_one(result);
}
} else { // Normal case
result.exponent = exp_value + EXPONENT_BIAS;
result.fraction = fraction >> 22; // Only keep 1 bit (MSB) of fraction
// (Rounding) Increase by one
if (((fraction >> 21) & 0x01) == 1) {
result = increse_by_one(result);
}
}
}
#endif
return result;
}
float float8_to_float(float8_t f8) {
uint32_t sign = f8.sign;
uint32_t exponent = 0;
uint32_t fraction = 0;
#if EXPONENT_BITS == 1
if (f8.exponent == 0x0) { // Zero or subnormal case
if (f8.fraction == 0) { // Zero case
exponent = 0;
fraction = 0;
} else if (f8.fraction >> 5 == 1) { // Subnormal case
exponent = 127;
fraction = (f8.fraction & 0x1F) << 18;
} else if (f8.fraction >> 4 == 1) { // Subnormal case
exponent = 126;
fraction = (f8.fraction & 0x0F) << 19;
} else if (f8.fraction >> 3 == 1) { // Subnormal case
exponent = 125;
fraction = (f8.fraction & 0x07) << 20;
} else if (f8.fraction >> 2 == 1) { // Subnormal case
exponent = 124;
fraction = (f8.fraction & 0x03) << 21;
} else if (f8.fraction >> 1 == 1) { // Subnormal case
exponent = 123;
fraction = (f8.fraction & 0x01) << 22;
} else if (f8.fraction == 1) { // Subnormal case
exponent = 122;
fraction = 0;
}
} else if ((f8.exponent == 0x1)) { // Infinity case - No NaN implemented for float8
exponent = 0xFF; // 1111 1111
fraction = 0;
}
// NO normal case for 1-1-6
// The 1-1-6 float8 format DOES NOT have normal values
#endif
#if EXPONENT_BITS == 2
if (f8.exponent == 0x0) { // Zero or subnormal case
if (f8.fraction == 0) { // Zero case
exponent = 0;
fraction = 0;
} else if (f8.fraction >> 4 == 1) { // Subnormal case
exponent = 126;
fraction = (f8.fraction & 0x0F) << 19;
} else if (f8.fraction >> 3 == 1) { // Subnormal case
exponent = 125;
fraction = (f8.fraction & 0x07) << 20;
} else if (f8.fraction >> 2 == 1) { // Subnormal case
exponent = 124;
fraction = (f8.fraction & 0x03) << 21;
} else if (f8.fraction >> 1 == 1) { // Subnormal case
exponent = 123;
fraction = (f8.fraction & 0x01) << 22;
} else if (f8.fraction == 1) { // Subnormal case
exponent = 122;
fraction = 0;
}
} else if ((f8.exponent == 0x3)) { // Infinity case - No NaN implemented for float8
exponent = 0xFF; // 1111 1111
fraction = 0;
} else { // Normal case
exponent = (f8.exponent - EXPONENT_BIAS + 127);
fraction = f8.fraction << 18;
}
#endif
#if EXPONENT_BITS == 3
if (f8.exponent == 0x0) { // Zero or subnormal case
if (f8.fraction == 0) { // Zero case
exponent = 0;
fraction = 0;
} else if (f8.fraction >> 3 == 1) { // Subnormal case
exponent = 124;
fraction = (f8.fraction & 0x07) << 20;
} else if (f8.fraction >> 2 == 1) { // Subnormal case
exponent = 123;
fraction = (f8.fraction & 0x03) << 21;
} else if (f8.fraction >> 1 == 1) { // Subnormal case
exponent = 122;
fraction = (f8.fraction & 0x01) << 22;
} else if (f8.fraction == 1) { // Subnormal case
exponent = 121;
fraction = 0;
}
} else if (f8.exponent == 0x7) { // Infinity case - No NaN implemented for float8
exponent = 0xFF; // 1111 1111
fraction = 0;
} else { // Normal case
exponent = (f8.exponent - EXPONENT_BIAS + 127);
fraction = f8.fraction << 19;
}
#endif
#if EXPONENT_BITS == 4
if (f8.exponent == 0x0) { // Zero or subnormal case
if (f8.fraction == 0) { // Zero case
exponent = 0;
fraction = 0;
} else if (f8.fraction >> 2 == 1) { // Subnormal case
exponent = 120;
fraction = (f8.fraction & 0x03) << 21;
} else if (f8.fraction >> 1 == 1) { // Subnormal case
exponent = 119;
fraction = (f8.fraction & 0x01) << 22;
} else if (f8.fraction == 1) { // Subnormal case
exponent = 118;
fraction = 0;
}
} else if (f8.exponent == 0xF) { // Infinity case - No NaN implemented for float8
exponent = 0xFF; // 1111 1111
fraction = 0;
} else { // Normal case
exponent = (f8.exponent - EXPONENT_BIAS + 127);
fraction = f8.fraction << 20;
}
#endif
#if EXPONENT_BITS == 5
if (f8.exponent == 0x0) { // Zero or subnormal case
if (f8.fraction == 0) { // Zero case
exponent = 0;
fraction = 0;
} else if (f8.fraction >> 1 == 1) { // Subnormal case
exponent = 112;
fraction = (f8.fraction & 0x01) << 22;
} else if (f8.fraction == 1) { // Subnormal case
exponent = 111;
fraction = 0;
}
} else if (f8.exponent == 0x1F) { // Infinity case - No NaN implemented for float8
exponent = 0xFF; // 1111 1111
fraction = 0;
} else { // Normal case
exponent = (f8.exponent - EXPONENT_BIAS + 127);
fraction = f8.fraction << 21;
}
#endif
#if EXPONENT_BITS == 6
if (f8.exponent == 0x0) { // Zero or subnormal case
if (f8.fraction == 0) { // Zero case
exponent = 0;
fraction = 0;
} else if (f8.fraction == 1) { // Subnormal case
exponent = 96;
fraction = 0;
}
} else if (f8.exponent == 0x3F) { // Infinity case - No NaN implemented for float8
exponent = 0xFF; // 1111 1111
fraction = 0;
} else { // Normal case
exponent = (f8.exponent - EXPONENT_BIAS + 127);
fraction = f8.fraction << 22;
}
#endif
// Concatenate the sign, exponent and fraction to get the float
uint32_t result = (sign << 31) | (exponent << 23) | fraction;
// Cast to float to return the correct data type
return *(float *)&result;
}