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|
/* Safe-but-slow arithmetic that can handle larger numbers without
overflowing. */
#define DEFINE_SAFE_1(STYPE) \
\
STYPE##2 _CL_OVERLOADABLE safe_normalize (STYPE##2 const a) \
{ \
STYPE const halfbits = 4 * sizeof (STYPE); \
STYPE const halfmax = (STYPE)1 << halfbits; \
STYPE const halfmask = halfmax - (STYPE)1; \
STYPE##2 b; \
b.s0 = a.s0 & halfmask; \
b.s1 = a.s1 + (STYPE) (a.s0 >> halfbits); \
return b; \
} \
\
STYPE##4 _CL_OVERLOADABLE safe_normalize (STYPE##4 const a) \
{ \
STYPE const halfbits = 4 * sizeof (STYPE); \
STYPE const halfmax = (STYPE)1 << halfbits; \
STYPE const halfmask = halfmax - (STYPE)1; \
STYPE tmp; \
STYPE##4 b; \
tmp = a.s0; \
b.s0 = tmp & halfmask; \
tmp = (STYPE) (tmp >> halfbits) + a.s1; \
b.s1 = tmp & halfmask; \
tmp = (STYPE) (tmp >> halfbits) + a.s2; \
b.s2 = tmp & halfmask; \
tmp = (STYPE) (tmp >> halfbits) + a.s3; \
b.s3 = tmp; \
return b; \
} \
\
STYPE _CL_OVERLOADABLE safe_extract (STYPE##2 const a) \
{ \
STYPE const halfbits = 4 * sizeof (STYPE); \
STYPE const halfmax = (STYPE)1 << halfbits; \
STYPE const halfmask = halfmax - (STYPE)1; \
STYPE b; \
b = a.s0 | (STYPE) (a.s1 << halfbits); \
return b; \
} \
\
STYPE _CL_OVERLOADABLE safe_extract (STYPE##4 const a) \
{ \
STYPE const halfbits = 4 * sizeof (STYPE); \
STYPE const halfmax = (STYPE)1 << halfbits; \
STYPE const halfmask = halfmax - (STYPE)1; \
STYPE b; \
if (safe_extract (a.hi) != 0 && safe_extract (a.hi) != -1) \
{ \
printf ("FAIL: safe_extract [%d,%d,%d,%d]\n", (int)a.s0, (int)a.s1, \
(int)a.s2, (int)a.s3); \
} \
return safe_extract (a.lo); \
} \
\
bool _CL_OVERLOADABLE safe_isneg (STYPE##2 a) { return a.s1 < (STYPE)0; } \
\
bool _CL_OVERLOADABLE safe_isneg (STYPE##4 a) { return a.s3 < (STYPE)0; } \
\
STYPE##2 _CL_OVERLOADABLE safe_neg (STYPE##2 a) \
{ \
STYPE##2 b; \
b.s0 = -a.s0; \
b.s1 = -a.s1; \
return safe_normalize (b); \
} \
\
STYPE##4 _CL_OVERLOADABLE safe_neg (STYPE##4 a) \
{ \
STYPE##4 b; \
b.s0 = -a.s0; \
b.s1 = -a.s1; \
b.s2 = -a.s2; \
b.s3 = -a.s3; \
return safe_normalize (b); \
} \
\
STYPE##2 _CL_OVERLOADABLE safe_abs (STYPE##2 const a) \
{ \
STYPE##2 b; \
b = a; \
if (safe_isneg (b)) \
{ \
b = safe_neg (b); \
} \
return b; \
} \
\
STYPE##4 _CL_OVERLOADABLE safe_abs (STYPE##4 const a) \
{ \
STYPE##4 b; \
b = a; \
if (safe_isneg (b)) \
{ \
b = safe_neg (b); \
} \
return b; \
} \
\
STYPE##2 _CL_OVERLOADABLE safe_add (STYPE##2 const a, STYPE##2 const b) \
{ \
STYPE##2 c; \
c.s0 = a.s0 + b.s0; \
c.s1 = a.s1 + b.s1; \
return safe_normalize (c); \
} \
\
STYPE##4 _CL_OVERLOADABLE safe_add (STYPE##4 const a, STYPE##4 const b) \
{ \
STYPE##4 c; \
c.s0 = a.s0 + b.s0; \
c.s1 = a.s1 + b.s1; \
c.s2 = a.s2 + b.s2; \
c.s3 = a.s3 + b.s3; \
return safe_normalize (c); \
} \
\
STYPE##2 _CL_OVERLOADABLE safe_sub (STYPE##2 const a, STYPE##2 const b) \
{ \
STYPE##2 c; \
c.s0 = a.s0 - b.s0; \
c.s1 = a.s1 - b.s1; \
return safe_normalize (c); \
} \
\
STYPE##4 _CL_OVERLOADABLE safe_sub (STYPE##4 const a, STYPE##4 const b) \
{ \
STYPE##4 c; \
c.s0 = a.s0 - b.s0; \
c.s1 = a.s1 - b.s1; \
c.s2 = a.s2 - b.s2; \
c.s3 = a.s3 - b.s3; \
return safe_normalize (c); \
} \
\
STYPE##2 _CL_OVERLOADABLE safe_create (STYPE const a); \
STYPE##2 _CL_OVERLOADABLE safe_minimul (STYPE const a, STYPE const b) \
{ \
STYPE##2 tmp1 = safe_create ((STYPE) (a * (STYPE) (b & (STYPE)1))); \
STYPE##2 tmp2 = safe_create ((STYPE) (a * (STYPE) (b >> (STYPE)1))); \
STYPE##2 res; \
res = safe_add (tmp1, safe_add (tmp2, tmp2)); \
return res; \
} \
\
STYPE##4 _CL_OVERLOADABLE safe_mul (STYPE##2 a, STYPE##2 b) \
{ \
bool a_neg = safe_isneg (a); \
bool b_neg = safe_isneg (b); \
a = safe_abs (a); \
b = safe_abs (b); \
STYPE##4 c00, c01, c10, c11; \
c00 = 0; \
c00.s01 = safe_minimul (a.s0, b.s0); \
c00 = safe_normalize (c00); \
c01 = 0; \
c01.s12 = safe_minimul (a.s0, b.s1); \
c01 = safe_normalize (c01); \
c10 = 0; \
c10.s12 = safe_minimul (a.s1, b.s0); \
c10 = safe_normalize (c10); \
c11 = 0; \
c11.s23 = safe_minimul (a.s1, b.s1); \
c11 = safe_normalize (c11); \
STYPE##4 c; \
c = safe_add (safe_add (c00, c01), safe_add (c10, c11)); \
if (a_neg ^ b_neg) \
c = safe_neg (c); \
return c; \
} \
\
STYPE##2 _CL_OVERLOADABLE safe_max (STYPE##2 const a, STYPE##2 const b) \
{ \
STYPE##2 c; \
if (safe_isneg (safe_sub (a, b))) \
{ \
c = b; \
} \
else \
{ \
c = a; \
} \
return c; \
} \
\
STYPE##4 _CL_OVERLOADABLE safe_max (STYPE##4 const a, STYPE##4 const b) \
{ \
STYPE##4 c; \
if (safe_isneg (safe_sub (a, b))) \
{ \
c = b; \
} \
else \
{ \
c = a; \
} \
return c; \
} \
\
STYPE##2 _CL_OVERLOADABLE safe_min (STYPE##2 const a, STYPE##2 const b) \
{ \
STYPE##2 c; \
if (safe_isneg (safe_sub (a, b))) \
{ \
c = a; \
} \
else \
{ \
c = b; \
} \
return c; \
} \
\
STYPE##4 _CL_OVERLOADABLE safe_min (STYPE##4 const a, STYPE##4 const b) \
{ \
STYPE##4 c; \
if (safe_isneg (safe_sub (a, b))) \
{ \
c = a; \
} \
else \
{ \
c = b; \
} \
return c; \
} \
\
STYPE##2 _CL_OVERLOADABLE safe_clamp (STYPE##2 const a, STYPE##2 const alo, \
STYPE##2 const ahi) \
{ \
return safe_max (alo, safe_min (ahi, a)); \
} \
\
STYPE##4 _CL_OVERLOADABLE safe_clamp (STYPE##4 const a, STYPE##4 const alo, \
STYPE##4 const ahi) \
{ \
return safe_max (alo, safe_min (ahi, a)); \
} \
\
STYPE##2 _CL_OVERLOADABLE safe_rshift (STYPE##2 a) \
{ \
STYPE const halfbits = 4 * sizeof (STYPE); \
STYPE const halfmax = (STYPE)1 << halfbits; \
STYPE const halfmask = halfmax - (STYPE)1; \
STYPE##2 b; \
b.s0 = a.s0 | ((a.s1 & (STYPE)1) << halfbits); \
b.s1 = a.s1 & ~(STYPE)1; \
b.s0 >>= (STYPE)1; \
b.s1 >>= (STYPE)1; \
return safe_normalize (b); \
} \
\
STYPE##2 _CL_OVERLOADABLE safe_lo (STYPE##2 a) \
{ \
STYPE const halfbits = 4 * sizeof (STYPE); \
STYPE const halfmax = (STYPE)1 << halfbits; \
STYPE const halfmask = halfmax - (STYPE)1; \
bool a_neg = a.s1 < (STYPE)0; \
a = safe_abs (a); \
if (a.s1 >= halfmax) \
a.s1 &= halfmask; \
if (a_neg) \
a = safe_neg (a); \
return a; \
} \
\
STYPE##2 _CL_OVERLOADABLE safe_lo (STYPE##4 a) \
{ \
bool a_neg = a.s3 < (STYPE)0; \
a = safe_abs (a); \
STYPE##2 res = safe_normalize (a.lo); \
if (a_neg) \
res = safe_neg (res); \
return res; \
} \
\
STYPE##2 _CL_OVERLOADABLE safe_hi (STYPE##4 a) \
{ \
return safe_normalize (a.hi); \
}
#define DEFINE_SAFE_2(TYPE, STYPE) \
\
STYPE##2 _CL_OVERLOADABLE safe_create (TYPE const a) \
{ \
STYPE const halfbits = 4 * sizeof (STYPE); \
STYPE const halfmax = (STYPE)1 << halfbits; \
STYPE const halfmask = halfmax - (STYPE)1; \
STYPE##2 b; \
/* input may be unsigned */ \
b.s0 = a & (TYPE)halfmask; \
b.s1 = a >> (TYPE)halfbits; \
b = safe_normalize (b); \
if ((TYPE)safe_extract (b) != a) \
{ \
printf ("FAIL: safe_create %d (got %d)\n", (int)a, \
(int)(TYPE)safe_extract (b)); \
} \
return b; \
} \
\
STYPE##4 _CL_OVERLOADABLE safe_create4 (TYPE const a) \
{ \
STYPE const halfbits = 4 * sizeof (STYPE); \
STYPE const halfmax = (STYPE)1 << halfbits; \
STYPE const halfmask = halfmax - (STYPE)1; \
STYPE##4 b; \
/* input may be unsigned */ \
TYPE tmp = a; \
b.s0 = tmp & (TYPE)halfmask; \
tmp >>= halfbits; \
b.s1 = tmp & (TYPE)halfmask; \
tmp >>= halfbits; \
b.s2 = tmp & (TYPE)halfmask; \
tmp >>= halfbits; \
b.s3 = tmp; \
b = safe_normalize (b); \
if ((TYPE)safe_extract (b) != a) \
{ \
printf ("FAIL: safe_create4 sz=%d sg=%d %d (got %d) [%d,%d,%d,%d]\n", \
(int)sizeof (TYPE), (int)((TYPE)-1 < (TYPE)0), (int)a, \
(int)(TYPE)safe_extract (b), (int)b.s0, (int)b.s1, (int)b.s2, \
(int)b.s3); \
} \
return b; \
}
DEFINE_SAFE_1 (char)
DEFINE_SAFE_1 (short)
DEFINE_SAFE_1 (int)
__IF_INT64 (DEFINE_SAFE_1 (long))
DEFINE_SAFE_2 (char, char)
DEFINE_SAFE_2 (uchar, char)
DEFINE_SAFE_2 (short, short)
DEFINE_SAFE_2 (ushort, short)
DEFINE_SAFE_2 (int, int)
DEFINE_SAFE_2 (uint, int)
__IF_INT64 (DEFINE_SAFE_2 (long, long))
__IF_INT64 (DEFINE_SAFE_2 (ulong, long))
#define IMPLEMENT_BODY_G_HADD(NAME, BODY, SIZE, GTYPE, SGTYPE, UGTYPE, \
SUGTYPE) \
void NAME##_##GTYPE () \
{ \
typedef GTYPE gtype; \
typedef SGTYPE sgtype; \
typedef UGTYPE ugtype; \
typedef SUGTYPE sugtype; \
string const typename = #GTYPE; \
const int vecsize = SIZE; \
int const bits = count_bits (sgtype); \
sgtype const tmin = is_signed (sgtype) \
? (sgtype) ((sugtype)1 << (sugtype) (bits - 1)) \
: (sgtype)0; \
sgtype const tmax = (sgtype) ((sugtype)tmin - (sugtype)1); \
for (int iter = 0; iter < nrandoms; ++iter) \
{ \
typedef union \
{ \
gtype v; \
ugtype u; \
sgtype s[16]; \
} Tvec; \
Tvec x, y, z; \
Tvec good_abs; \
Tvec good_abs_diff, good_add_sat, good_mad_sat, good_sub_sat; \
Tvec good_hadd, good_mad_hi, good_mul_hi, good_rhadd; \
for (int n = 0; n < vecsize; ++n) \
{ \
x.s[n] = randoms[(iter + n) % nrandoms]; \
y.s[n] = randoms[(iter + n + 20) % nrandoms]; \
z.s[n] = randoms[(iter + n + 40) % nrandoms]; \
if (bits > 32) \
{ \
x.s[n] = (x.s[n] << (bits / 2)) \
| randoms[(iter + n + 100) % nrandoms]; \
y.s[n] = (y.s[n] << (bits / 2)) \
| randoms[(iter + n + 120) % nrandoms]; \
z.s[n] = (z.s[n] << (bits / 2)) \
| randoms[(iter + n + 140) % nrandoms]; \
} \
good_abs.s[n] = safe_extract (safe_abs (safe_create (x.s[n]))); \
good_abs_diff.s[n] = safe_extract (safe_abs ( \
safe_sub (safe_create (x.s[n]), safe_create (y.s[n])))); \
good_add_sat.s[n] = safe_extract (safe_clamp ( \
safe_add (safe_create (x.s[n]), safe_create (y.s[n])), \
safe_create (tmin), safe_create (tmax))); \
good_mad_sat.s[n] = safe_extract ( \
safe_clamp (safe_add (safe_mul (safe_create (x.s[n]), \
safe_create (y.s[n])), \
safe_create4 (z.s[n])), \
safe_create4 (tmin), safe_create4 (tmax))); \
good_sub_sat.s[n] = safe_extract (safe_clamp ( \
safe_sub (safe_create (x.s[n]), safe_create (y.s[n])), \
safe_create (tmin), safe_create (tmax))); \
good_hadd.s[n] = safe_extract (safe_rshift ( \
safe_add (safe_create (x.s[n]), safe_create (y.s[n])))); \
good_mad_hi.s[n] = safe_extract ( \
safe_lo (safe_add (safe_hi (safe_mul (safe_create (x.s[n]), \
safe_create (y.s[n]))), \
safe_create (z.s[n])))); \
good_mul_hi.s[n] = safe_extract (safe_hi ( \
safe_mul (safe_create (x.s[n]), safe_create (y.s[n])))); \
good_rhadd.s[n] = safe_extract (safe_rshift (safe_add ( \
safe_add (safe_create (x.s[n]), safe_create (y.s[n])), \
safe_create ((sgtype)1)))); \
} \
Tvec res_abs; \
Tvec res_abs_diff, res_add_sat, res_mad_sat, res_sub_sat; \
Tvec res_hadd, res_mad_hi, res_mul_hi, res_rhadd; \
res_abs.u = abs (x.v); \
res_abs_diff.u = abs_diff (x.v, y.v); \
res_add_sat.v = add_sat (x.v, y.v); \
res_mad_sat.v = mad_sat (x.v, y.v, z.v); \
res_sub_sat.v = sub_sat (x.v, y.v); \
res_hadd.v = hadd (x.v, y.v); \
res_mad_hi.v = mad_hi (x.v, y.v, z.v); \
res_mul_hi.v = mul_hi (x.v, y.v); \
res_rhadd.v = rhadd (x.v, y.v); \
bool error = false; \
bool equal; \
BODY; \
} \
}
#define DEFINE_BODY_G_HADD(NAME, EXPR) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 1, char, char, uchar, uchar) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 2, char2, char, uchar2, uchar) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 3, char3, char, uchar3, uchar) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 4, char4, char, uchar4, uchar) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 8, char8, char, uchar8, uchar) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 16, char16, char, uchar16, uchar) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 1, uchar, uchar, uchar, uchar) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 2, uchar2, uchar, uchar2, uchar) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 3, uchar3, uchar, uchar3, uchar) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 4, uchar4, uchar, uchar4, uchar) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 8, uchar8, uchar, uchar8, uchar) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 16, uchar16, uchar, uchar16, uchar) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 1, short, short, ushort, ushort) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 2, short2, short, ushort2, ushort) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 3, short3, short, ushort3, ushort) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 4, short4, short, ushort4, ushort) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 8, short8, short, ushort8, ushort) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 16, short16, short, ushort16, ushort) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 1, ushort, ushort, ushort, ushort) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 2, ushort2, ushort, ushort2, ushort) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 3, ushort3, ushort, ushort3, ushort) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 4, ushort4, ushort, ushort4, ushort) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 8, ushort8, ushort, ushort8, ushort) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 16, ushort16, ushort, ushort16, ushort) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 1, int, int, uint, uint) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 2, int2, int, uint2, uint) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 3, int3, int, uint3, uint) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 4, int4, int, uint4, uint) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 8, int8, int, uint8, uint) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 16, int16, int, uint16, uint) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 1, uint, uint, uint, uint) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 2, uint2, uint, uint2, uint) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 3, uint3, uint, uint3, uint) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 4, uint4, uint, uint4, uint) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 8, uint8, uint, uint8, uint) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 16, uint16, uint, uint16, uint) \
__IF_INT64 ( \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 1, long, long, ulong, ulong) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 2, long2, long, ulong2, ulong) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 3, long3, long, ulong3, ulong) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 4, long4, long, ulong4, ulong) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 8, long8, long, ulong8, ulong) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 16, long16, long, ulong16, ulong) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 1, ulong, ulong, ulong, ulong) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 2, ulong2, ulong, ulong2, ulong) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 3, ulong3, ulong, ulong3, ulong) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 4, ulong4, ulong, ulong4, ulong) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 8, ulong8, ulong, ulong8, ulong) \
IMPLEMENT_BODY_G_HADD (NAME, EXPR, 16, ulong16, ulong, ulong16, ulong))
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