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vchuravy/half.c

Created January 20, 2021 16:02
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Half-precision
Raw
half.c
// This file is a part of Julia. License is MIT: https://julialang.org/license
// float16 intrinsics
// TODO: use LLVM's compiler-rt
#include <stdint.h>
#include <string.h> // memcpy
#include <math.h> // memcpy
static inline float half_to_float(uint16_t ival)
{
uint32_t sign = (ival & 0x8000) >> 15;
uint32_t exp = (ival & 0x7c00) >> 10;
uint32_t sig = (ival & 0x3ff) >> 0;
uint32_t ret;
if (exp == 0) {
if (sig == 0) {
sign = sign << 31;
ret = sign | exp | sig;
}
else {
int n_bit = 1;
uint16_t bit = 0x0200;
while ((bit & sig) == 0) {
n_bit = n_bit + 1;
bit = bit >> 1;
}
sign = sign << 31;
exp = ((-14 - n_bit + 127) << 23);
sig = ((sig & (~bit)) << n_bit) << (23 - 10);
ret = sign | exp | sig;
}
}
else if (exp == 0x1f) {
if (sig == 0) { // Inf
if (sign == 0)
ret = 0x7f800000;
else
ret = 0xff800000;
}
else // NaN
ret = 0x7fc00000 | (sign << 31) | (sig << (23 - 10));
}
else {
sign = sign << 31;
exp = ((exp - 15 + 127) << 23);
sig = sig << (23 - 10);
ret = sign | exp | sig;
}
float fret;
memcpy(&fret, &ret, sizeof(float));
return fret;
}
// float to half algorithm from:
// "Fast Half Float Conversion" by Jeroen van der Zijp
// ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf
//
// With adjustments for round-to-nearest, ties to even.
static uint16_t basetable[512] = {
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0400, 0x0800, 0x0c00, 0x1000, 0x1400, 0x1800, 0x1c00, 0x2000,
0x2400, 0x2800, 0x2c00, 0x3000, 0x3400, 0x3800, 0x3c00, 0x4000, 0x4400, 0x4800, 0x4c00,
0x5000, 0x5400, 0x5800, 0x5c00, 0x6000, 0x6400, 0x6800, 0x6c00, 0x7000, 0x7400, 0x7800,
0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00,
0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00,
0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00,
0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00,
0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00,
0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00,
0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00,
0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00,
0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00,
0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00, 0x7c00,
0x7c00, 0x7c00, 0x7c00, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8400, 0x8800, 0x8c00, 0x9000, 0x9400,
0x9800, 0x9c00, 0xa000, 0xa400, 0xa800, 0xac00, 0xb000, 0xb400, 0xb800, 0xbc00, 0xc000,
0xc400, 0xc800, 0xcc00, 0xd000, 0xd400, 0xd800, 0xdc00, 0xe000, 0xe400, 0xe800, 0xec00,
0xf000, 0xf400, 0xf800, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00,
0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00,
0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00,
0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00,
0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00,
0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00,
0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00,
0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00,
0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00,
0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00,
0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00, 0xfc00};
static uint8_t shifttable[512] = {
0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19,
0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19,
0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19,
0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19,
0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19,
0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19,
0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19,
0x19, 0x19, 0x19, 0x19, 0x18, 0x17, 0x16, 0x15, 0x14, 0x13, 0x12, 0x11, 0x10, 0x0f,
0x0e, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d,
0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d,
0x0d, 0x0d, 0x0d, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18,
0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18,
0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18,
0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18,
0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18,
0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18,
0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18,
0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18,
0x18, 0x18, 0x18, 0x0d, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19,
0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19,
0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19,
0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19,
0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19,
0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19,
0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19,
0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x19, 0x18, 0x17, 0x16, 0x15, 0x14, 0x13,
0x12, 0x11, 0x10, 0x0f, 0x0e, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d,
0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d,
0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x0d, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18,
0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18,
0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18,
0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18,
0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18,
0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18,
0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18,
0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18,
0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x18, 0x0d};
static inline uint16_t float_to_half(float param)
{
uint32_t f;
memcpy(&f, &param, sizeof(float));
if (isnan(param)) {
uint32_t t = 0x8000 ^ (0x8000 & ((uint16_t)(f >> 0x10)));
return t ^ ((uint16_t)(f >> 0xd));
}
int i = ((f & ~0x007fffff) >> 23);
uint8_t sh = shifttable[i];
f &= 0x007fffff;
// If `val` is subnormal, the tables are set up to force the
// result to 0, so the significand has an implicit `1` in the
// cases we care about.
f |= 0x007fffff + 0x1;
uint16_t h = (uint16_t)(basetable[i] + ((f >> sh) & 0x03ff));
// round
// NOTE: we maybe should ignore NaNs here, but the payload is
// getting truncated anyway so "rounding" it might not matter
int nextbit = (f >> (sh - 1)) & 1;
if (nextbit != 0 && (h & 0x7C00) != 0x7C00) {
// Round halfway to even or check lower bits
if ((h & 1) == 1 || (f & ((1 << (sh - 1)) - 1)) != 0)
h += UINT16_C(1);
}
return h;
}
float __gnu_h2f_ieee(uint16_t param)
{
return half_to_float(param);
}
float __extendhfsf2(uint16_t param)
{
return half_to_float(param);
}
uint16_t __gnu_f2h_ieee(float param)
{
return float_to_half(param);
}
uint16_t __truncdfhf2(double param)
{
return float_to_half((float)param);
}
Raw
main.ll
source_filename = "g"
target datalayout = "e-m:e-i64:64-n32:64"
target triple = "powerpc64le-unknown-linux-gnu"
declare i64 @llvm.ctlz.i64(i64, i1 immarg) #1
define half @julia_g_219(i64 zeroext %0, i64 signext %1, i32 signext %2) {
top:
%3 = call i64 @llvm.ctlz.i64(i64 %0, i1 false)
%4 = icmp ugt i64 %0, 65535
%5 = icmp slt i32 %2, 0
%6 = sub i32 0, %2
%7 = select i1 %5, i32 %6, i32 %2
%8 = icmp sgt i32 %7, 1
%value_phi.in = or i1 %4, %8
br i1 %value_phi.in, label %L48, label %L14
L14: ; preds = %top
%9 = sub nsw i64 52, %3
%10 = icmp ult i64 %0, 2048
%11 = lshr i64 %0, %9
%12 = icmp ugt i64 %9, 63
%13 = select i1 %12, i64 0, i64 %11
%14 = sub nsw i64 0, %9
%15 = shl i64 %0, %14
%16 = icmp ugt i64 %14, 63
%17 = select i1 %16, i64 0, i64 %15
%18 = select i1 %10, i64 %17, i64 %13
%19 = trunc i64 %18 to i16
%20 = add i16 %19, 1
%21 = lshr i16 %20, 1
%22 = icmp eq i64 %9, %1
%23 = zext i1 %22 to i16
%24 = xor i16 %23, -1
%25 = and i16 %21, %24
%26 = trunc i64 %3 to i16
%27 = shl i16 %26, 10
%28 = sub i16 13312, %27
%29 = add i16 %28, %25
%30 = bitcast i16 %29 to half
br label %L48
L48: ; preds = %L14, %top
%value_phi1 = phi half [ %30, %L14 ], [ 0xH7C00, %top ]
%31 = icmp sgt i32 %2, -1
%32 = fpext half %value_phi1 to float
%33 = fneg float %32
%34 = fptrunc float %33 to half
%35 = select i1 %31, half %value_phi1, half %34
ret half %35
}
define i32 @main() {
%val = call half @julia_g_219(i64 65520, i64 4, i32 1)
%cmp = fcmp oeq half %val, 0xH7C00
%r = zext i1 %cmp to i32
ret i32 %r
}
attributes #1 = { nounwind readnone speculatable willreturn }
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