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// https://github.com/artyom-beilis/float16/blob/master/c_src/float16.c
#include "float16.h"
#include <stdint-gcc.h>
#define SIGN_MASK 0x8000
#define EXP_MASK 0x7C00
#define NAN_VALUE 0x7FFF
#define IS_ZERO(x) (((x) & 0x7FFF) == 0)
#define IS_INVALID(x) (((x) & EXP_MASK) == EXP_MASK)
#define IS_NAN(x) (((x) & 0x7FFF) > 0x7C00)
#define IS_INF(x) ( ((x) & 0x7FFF) == 0x7C00)
#define MANTISSA(x) (((x) & 1023) | (((x) & 0x7C00) == 0 ? 0 : 1024))
#define EXPONENT(x) (((x) & 0x7C00) >> 10)
#define SIGNED_INF_VALUE(x) ((x & SIGN_MASK) | 0x7C00)
short f16_sub(short ain,short bin)
{
unsigned short a=ain;
unsigned short b=bin;
if(((a ^ b) & 0x8000) != 0)
return f16_add(a,b ^ 0x8000);
unsigned short sign = a & 0x8000;
a = a << 1;
b = b << 1;
if(a < b) {
unsigned short x=a;
a=b;
b=x;
sign ^= 0x8000;
}
unsigned short ax = a & 0xF800;
unsigned short bx = b & 0xF800;
if(a >=0xf800 || b>=0xf800) {
if(a > 0xF800 || b > 0xF800 || a==b)
return 0x7FFF;
unsigned short res = sign | 0x7C00;
if(a == 0xf800)
return res;
else
return res ^ 0x8000;
}
int exp_diff = ax - bx;
unsigned short exp_part = ax;
if(exp_diff != 0) {
int shift = exp_diff >> 11;
if(bx != 0)
b = ((b & 2047) | 2048) >> shift;
else
b >>= (shift - 1);
}
else {
if(bx == 0) {
unsigned short res = (a-b) >> 1;
if(res == 0)
return res;
return res | sign;
}
else {
b=(b & 2047) | 2048;
}
}
unsigned short r=a - b;
if((r & 0xF800) == exp_part) {
return (r>>1) | sign;
}
unsigned short am = (a & 2047) | 2048;
unsigned short new_m = am - b;
if(new_m == 0)
return 0;
while(exp_part !=0 && !(new_m & (2048))) {
exp_part-=0x800;
if(exp_part!=0)
new_m<<=1;
}
return (((new_m & 2047) | exp_part) >> 1) | sign;
}
short f16_add(short a,short b)
{
if (((a ^ b) & 0x8000) != 0)
return f16_sub(a,b ^ 0x8000);
short sign = a & 0x8000;
a &= 0x7FFF;
b &= 0x7FFF;
if(a<b) {
short x=a;
a=b;
b=x;
}
if(a >= 0x7C00 || b>=0x7C00) {
if(a>0x7C00 || b>0x7C00)
return 0x7FFF;
return 0x7C00 | sign;
}
short ax = (a & 0x7C00);
short bx = (b & 0x7C00);
short exp_diff = ax - bx;
short exp_part = ax;
if(exp_diff != 0) {
int shift = exp_diff >> 10;
if(bx != 0)
b = ((b & 1023) | 1024) >> shift;
else
b >>= (shift - 1);
}
else {
if(bx == 0) {
return (a + b) | sign;
}
else {
b=(b & 1023) | 1024;
}
}
short r=a+b;
if ((r & 0x7C00) != exp_part) {
unsigned short am = (a & 1023) | 1024;
unsigned short new_m = (am + b) >> 1;
r =( exp_part + 0x400) | (1023 & new_m);
}
if((unsigned short)r >= 0x7C00u) {
return sign | 0x7C00;
}
return r | sign;
}
short f16_mul(short a,short b)
{
int sign = (a ^ b) & SIGN_MASK;
if(IS_INVALID(a) || IS_INVALID(b)) {
if(IS_NAN(a) || IS_NAN(b) || IS_ZERO(a) || IS_ZERO(b))
return NAN_VALUE;
return sign | 0x7C00;
}
if(IS_ZERO(a) || IS_ZERO(b))
return 0;
unsigned short m1 = MANTISSA(a);
unsigned short m2 = MANTISSA(b);
uint32_t v=m1;
v*=m2;
int ax = EXPONENT(a);
int bx = EXPONENT(b);
ax += (ax==0);
bx += (bx==0);
int new_exp = ax + bx - 15;
if(v & ((uint32_t)1<<21)) {
v >>= 11;
new_exp++;
}
else if(v & ((uint32_t)1<<20)) {
v >>= 10;
}
else { // denormal
new_exp -= 10;
while(v >= 2048) {
v>>=1;
new_exp++;
}
}
if(new_exp <= 0) {
v>>=(-new_exp + 1);
new_exp = 0;
}
else if(new_exp >= 31) {
return SIGNED_INF_VALUE(sign);
}
return (sign) | (new_exp << 10) | (v & 1023);
}
short f16_div(short a,short b)
{
short sign = (a ^ b) & SIGN_MASK;
if(IS_NAN(a) || IS_NAN(b) || (IS_INVALID(a) && IS_INVALID(b)) || (IS_ZERO(a) && IS_ZERO(b)))
return 0x7FFF;
if(IS_INVALID(a) || IS_ZERO(b))
return sign | 0x7C00;
if(IS_INVALID(b))
return 0;
if(IS_ZERO(a))
return 0;
unsigned short m1 = MANTISSA(a);
unsigned short m2 = MANTISSA(b);
uint32_t m1_shifted = m1;
m1_shifted <<= 10;
uint32_t v= m1_shifted / m2;
unsigned short rem = m1_shifted % m2;
int ax = EXPONENT(a);
int bx = EXPONENT(b);
ax += (ax==0);
bx += (bx==0);
int new_exp = ax - bx + 15 ;
if(v == 0 && rem==0)
return 0;
while(v < 1024 && new_exp > 0) {
v<<=1;
rem<<=1;
if(rem >= m2) {
v++;
rem -= m2;
}
new_exp--;
}
while(v >= 2048) {
v>>=1;
new_exp++;
}
if(new_exp <= 0) {
v>>=(-new_exp + 1);
new_exp = 0;
}
else if(new_exp >= 31) {
return SIGNED_INF_VALUE(sign);
}
return sign | (v & 1023) | (new_exp << 10);
}
short f16_neg(short v)
{
return SIGN_MASK ^ v;
}
short f16_from_int(int32_t sv)
{
uint32_t v;
int sig = 0;
if(sv < 0) {
v=-sv;
sig=1;
}
else
v=sv;
if(v==0)
return 0;
int e=25;
while(v >= 2048) {
v>>=1;
e++;
}
while(v<1024) {
v<<=1;
e--;
}
if(e>=31)
return SIGNED_INF_VALUE(sig << 15);
return (sig << 15) | (e << 10) | (v & 1023);
}
int32_t f16_int(short a)
{
unsigned short value = MANTISSA(a);
short shift = EXPONENT(a) - 25;
if(shift > 0)
value <<= shift;
else if(shift < 0)
value >>= -shift;
if(a & SIGN_MASK)
return -(int32_t)(value);
return value;
}
int f16_gte(short a,short b)
{
if(IS_ZERO(a) && IS_ZERO(b))
return 1;
if(IS_NAN(a) || IS_NAN(b))
return 0;
if((a & SIGN_MASK) == 0) {
if((b & SIGN_MASK) == SIGN_MASK)
return 1;
return a >= b;
}
else {
if((b & SIGN_MASK) == 0)
return 0;
return (a & 0x7FFF) <= (b & 0x7FFF);
}
}
int f16_gt(short a,short b)
{
if(IS_NAN(a) || IS_NAN(b))
return 0;
if(IS_ZERO(a) && IS_ZERO(b))
return 0;
if((a & SIGN_MASK) == 0) {
if((b & SIGN_MASK) == SIGN_MASK)
return 1;
return a > b;
}
else {
if((b & SIGN_MASK) == 0)
return 0;
return (a & 0x7FFF) < (b & 0x7FFF);
}
}
int f16_eq(short a,short b)
{
if(IS_NAN(a) || IS_NAN(b))
return 0;
if(IS_ZERO(a) && IS_ZERO(b))
return 1;
return a==b;
}
int f16_lte(short a,short b)
{
if(IS_NAN(a) || IS_NAN(b))
return 0;
return f16_gte(b,a);
}
int f16_lt(short a,short b)
{
if(IS_NAN(a) || IS_NAN(b))
return 0;
return f16_gt(b,a);
}
int f16_neq(short a,short b)
{
return !f16_eq(a,b);
}
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