#define FLOAT_ROUND_UP 3
#define FLOAT_ROUNDING_MODE FLOAT_ROUND_NEAREST_EVEN
+/* Relax propagation of NaN. Binary operations with a NaN source will still
+ * produce a NaN result, but it won't follow strict IEEE rules.
+ */
+#define RELAXED_NAN_PROPAGATION
+
/* Absolute value of a Float64 :
* Clear the sign bit
*/
__fneg64(uint64_t __a)
{
uvec2 a = unpackUint2x32(__a);
- uint t = a.y;
-
- t ^= (1u << 31);
- a.y = mix(t, a.y, __is_nan(__a));
+ a.y ^= (1u << 31);
return packUint2x32(a);
}
uint
__extractFloat64Sign(uint64_t a)
{
- return unpackUint2x32(a).y >> 31;
+ return unpackUint2x32(a).y & 0x80000000u;
}
-/* Returns true if the 64-bit value formed by concatenating `a0' and `a1' is less
- * than the 64-bit value formed by concatenating `b0' and `b1'. Otherwise,
- * returns false.
+/* Returns true if the signed 64-bit value formed by concatenating `a0' and
+ * `a1' is less than the signed 64-bit value formed by concatenating `b0' and
+ * `b1'. Otherwise, returns false.
*/
bool
-lt64(uint a0, uint a1, uint b0, uint b1)
+ilt64(uint a0, uint a1, uint b0, uint b1)
{
- return (a0 < b0) || ((a0 == b0) && (a1 < b1));
+ return (int(a0) < int(b0)) || ((a0 == b0) && (a1 < b1));
}
bool
{
uvec2 a = unpackUint2x32(__a);
uvec2 b = unpackUint2x32(__b);
- uint aSign = __extractFloat64Sign(__a);
- uint bSign = __extractFloat64Sign(__b);
- if (aSign != bSign)
- return (aSign != 0u) && ((((a.y | b.y)<<1) | a.x | b.x) != 0u);
- return mix(lt64(a.y, a.x, b.y, b.x), lt64(b.y, b.x, a.y, a.x), aSign != 0u);
+ /* IEEE 754 floating point numbers are specifically designed so that, with
+ * two exceptions, values can be compared by bit-casting to signed integers
+ * with the same number of bits.
+ *
+ * From https://en.wikipedia.org/wiki/IEEE_754-1985#Comparing_floating-point_numbers:
+ *
+ * When comparing as 2's-complement integers: If the sign bits differ,
+ * the negative number precedes the positive number, so 2's complement
+ * gives the correct result (except that negative zero and positive zero
+ * should be considered equal). If both values are positive, the 2's
+ * complement comparison again gives the correct result. Otherwise (two
+ * negative numbers), the correct FP ordering is the opposite of the 2's
+ * complement ordering.
+ *
+ * The logic implied by the above quotation is:
+ *
+ * !both_are_zero(a, b) && (both_negative(a, b) ? a > b : a < b)
+ *
+ * This is equivalent to
+ *
+ * fne(a, b) && (both_negative(a, b) ? a >= b : a < b)
+ *
+ * fne(a, b) && (both_negative(a, b) ? !(a < b) : a < b)
+ *
+ * fne(a, b) && ((both_negative(a, b) && !(a < b)) ||
+ * (!both_negative(a, b) && (a < b)))
+ *
+ * (A!|B)&(A|!B) is (A xor B) which is implemented here using !=.
+ *
+ * fne(a, b) && (both_negative(a, b) != (a < b))
+ */
+ bool lt = ilt64(a.y, a.x, b.y, b.x);
+ bool both_negative = (a.y & b.y & 0x80000000u) != 0;
+
+ return !__feq64_nonnan(__a, __b) && (lt != both_negative);
}
/* Returns true if the double-precision floating-point value `a' is less than
bool
__flt64(uint64_t a, uint64_t b)
{
- if (__is_nan(a) || __is_nan(b))
- return false;
+ /* This weird layout matters. Doing the "obvious" thing results in extra
+ * flow control being inserted to implement the short-circuit evaluation
+ * rules. Flow control is bad!
+ */
+ bool x = !__is_nan(a);
+ bool y = !__is_nan(b);
+ bool z = __flt64_nonnan(a, b);
- return __flt64_nonnan(a, b);
+ return (x && y && z);
}
/* Returns true if the double-precision floating-point value `a' is greater
bool
__fge64(uint64_t a, uint64_t b)
{
- if (__is_nan(a) || __is_nan(b))
- return false;
+ /* This weird layout matters. Doing the "obvious" thing results in extra
+ * flow control being inserted to implement the short-circuit evaluation
+ * rules. Flow control is bad!
+ */
+ bool x = !__is_nan(a);
+ bool y = !__is_nan(b);
+ bool z = !__flt64_nonnan(a, b);
- return !__flt64_nonnan(a, b);
+ return (x && y && z);
}
uint64_t
__fsat64(uint64_t __a)
{
- if (__flt64(__a, 0ul))
+ uvec2 a = unpackUint2x32(__a);
+
+ /* fsat(NaN) should be zero. */
+ if (__is_nan(__a) || int(a.y) < 0)
return 0ul;
- if (__fge64(__a, 0x3FF0000000000000ul /* 1.0 */))
+ /* IEEE 754 floating point numbers are specifically designed so that, with
+ * two exceptions, values can be compared by bit-casting to signed integers
+ * with the same number of bits.
+ *
+ * From https://en.wikipedia.org/wiki/IEEE_754-1985#Comparing_floating-point_numbers:
+ *
+ * When comparing as 2's-complement integers: If the sign bits differ,
+ * the negative number precedes the positive number, so 2's complement
+ * gives the correct result (except that negative zero and positive zero
+ * should be considered equal). If both values are positive, the 2's
+ * complement comparison again gives the correct result. Otherwise (two
+ * negative numbers), the correct FP ordering is the opposite of the 2's
+ * complement ordering.
+ *
+ * We know that both values are not negative, and we know that at least one
+ * value is not zero. Therefore, we can just use the 2's complement
+ * comparison ordering.
+ */
+ if (ilt64(0x3FF00000, 0x00000000, a.y, a.x))
return 0x3FF0000000000000ul;
return __a;
{
uvec2 z;
- z.y = (zSign << 31) + (uint(zExp) << 20) + zFrac0;
+ z.y = zSign + (uint(zExp) << 20) + zFrac0;
z.x = zFrac1;
return packUint2x32(z);
}
zFrac1 &= ~(1u) + uint(zFrac2 == 0u) & uint(roundNearestEven);
}
return mix(packUint2x32(uvec2(zFrac1, zFrac0)), default_nan,
- (zSign !=0u && (zFrac0 | zFrac1) != 0u));
+ (zSign != 0u && (zFrac0 | zFrac1) != 0u));
}
int64_t
int64_t absZ = mix(int64_t(packUint2x32(uvec2(zFrac1, zFrac0))),
-int64_t(packUint2x32(uvec2(zFrac1, zFrac0))),
- (zSign != 0u));
- int64_t nan = mix(default_PosNaN, default_NegNaN, bool(zSign));
- return mix(absZ, nan, bool(zSign ^ uint(absZ < 0)) && bool(absZ));
+ zSign != 0u);
+ int64_t nan = mix(default_PosNaN, default_NegNaN, zSign != 0u);
+ return mix(absZ, nan, ((zSign != 0u) != (absZ < 0)) && bool(absZ));
}
/* Returns the number of leading 0 bits before the most-significant 1 bit of
uint64_t
__propagateFloat64NaN(uint64_t __a, uint64_t __b)
{
+#if defined RELAXED_NAN_PROPAGATION
+ uvec2 a = unpackUint2x32(__a);
+ uvec2 b = unpackUint2x32(__b);
+
+ return packUint2x32(uvec2(a.x | b.x, a.y | b.y));
+#else
bool aIsNaN = __is_nan(__a);
bool bIsNaN = __is_nan(__b);
uvec2 a = unpackUint2x32(__a);
b.y |= 0x00080000u;
return packUint2x32(mix(b, mix(a, b, bvec2(bIsNaN, bIsNaN)), bvec2(aIsNaN, aIsNaN)));
+#endif
}
+/* If a shader is in the soft-fp64 path, it almost certainly has register
+ * pressure problems. Choose a method to exchange two values that does not
+ * require a temporary.
+ */
+#define EXCHANGE(a, b) \
+ do { \
+ a ^= b; \
+ b ^= a; \
+ a ^= b; \
+ } while (false)
+
/* Returns the result of adding the double-precision floating-point values
* `a' and `b'. The operation is performed according to the IEEE Standard for
* Floating-Point Arithmetic.
uint bFracHi = __extractFloat64FracHi(b);
int aExp = __extractFloat64Exp(a);
int bExp = __extractFloat64Exp(b);
- uint zFrac0 = 0u;
- uint zFrac1 = 0u;
int expDiff = aExp - bExp;
if (aSign == bSign) {
- uint zFrac2 = 0u;
+ uint zFrac0;
+ uint zFrac1;
+ uint zFrac2;
int zExp;
- bool orig_exp_diff_is_zero = (expDiff == 0);
- if (orig_exp_diff_is_zero) {
+ if (expDiff == 0) {
if (aExp == 0x7FF) {
- bool propagate = (aFracHi | aFracLo | bFracHi | bFracLo) != 0u;
+ bool propagate = ((aFracHi | bFracHi) | (aFracLo| bFracLo)) != 0u;
return mix(a, __propagateFloat64NaN(a, b), propagate);
}
__add64(aFracHi, aFracLo, bFracHi, bFracLo, zFrac0, zFrac1);
zExp = aExp;
__shift64ExtraRightJamming(
zFrac0, zFrac1, zFrac2, 1, zFrac0, zFrac1, zFrac2);
- } else if (0 < expDiff) {
- if (aExp == 0x7FF) {
- bool propagate = (aFracHi | aFracLo) != 0u;
- return mix(a, __propagateFloat64NaN(a, b), propagate);
- }
+ } else {
+ if (0 < expDiff) {
+ if (aExp == 0x7FF) {
+ bool propagate = (aFracHi | aFracLo) != 0u;
+ return mix(a, __propagateFloat64NaN(a, b), propagate);
+ }
- expDiff = mix(expDiff, expDiff - 1, bExp == 0);
- bFracHi = mix(bFracHi | 0x00100000u, bFracHi, bExp == 0);
- __shift64ExtraRightJamming(
- bFracHi, bFracLo, 0u, expDiff, bFracHi, bFracLo, zFrac2);
- zExp = aExp;
- } else if (expDiff < 0) {
- if (bExp == 0x7FF) {
- bool propagate = (bFracHi | bFracLo) != 0u;
- return mix(__packFloat64(aSign, 0x7ff, 0u, 0u), __propagateFloat64NaN(a, b), propagate);
+ expDiff = mix(expDiff, expDiff - 1, bExp == 0);
+ bFracHi = mix(bFracHi | 0x00100000u, bFracHi, bExp == 0);
+ __shift64ExtraRightJamming(
+ bFracHi, bFracLo, 0u, expDiff, bFracHi, bFracLo, zFrac2);
+ zExp = aExp;
+ } else {
+ EXCHANGE(aFracHi, bFracHi);
+ EXCHANGE(aFracLo, bFracLo);
+ EXCHANGE(aExp, bExp);
+
+ if (aExp == 0x7FF) {
+ bool propagate = (aFracHi | aFracLo) != 0u;
+ return mix(__packFloat64(aSign, 0x7ff, 0u, 0u), __propagateFloat64NaN(a, b), propagate);
+ }
+ expDiff = mix(expDiff, expDiff + 1, bExp == 0);
+ bFracHi = mix(bFracHi | 0x00100000u, bFracHi, bExp == 0);
+ __shift64ExtraRightJamming(
+ bFracHi, bFracLo, 0u, - expDiff, bFracHi, bFracLo, zFrac2);
+ zExp = aExp;
}
- expDiff = mix(expDiff, expDiff + 1, aExp == 0);
- aFracHi = mix(aFracHi | 0x00100000u, aFracHi, aExp == 0);
- __shift64ExtraRightJamming(
- aFracHi, aFracLo, 0u, - expDiff, aFracHi, aFracLo, zFrac2);
- zExp = bExp;
- }
- if (!orig_exp_diff_is_zero) {
+
aFracHi |= 0x00100000u;
__add64(aFracHi, aFracLo, bFracHi, bFracLo, zFrac0, zFrac1);
--zExp;
__shortShift64Left(aFracHi, aFracLo, 10, aFracHi, aFracLo);
__shortShift64Left(bFracHi, bFracLo, 10, bFracHi, bFracLo);
if (0 < expDiff) {
+ uint zFrac0;
+ uint zFrac1;
+
if (aExp == 0x7FF) {
bool propagate = (aFracHi | aFracLo) != 0u;
return mix(a, __propagateFloat64NaN(a, b), propagate);
return __normalizeRoundAndPackFloat64(aSign, zExp - 10, zFrac0, zFrac1);
}
if (expDiff < 0) {
+ uint zFrac0;
+ uint zFrac1;
+
if (bExp == 0x7FF) {
bool propagate = (bFracHi | bFracLo) != 0u;
- return mix(__packFloat64(aSign ^ 1u, 0x7ff, 0u, 0u), __propagateFloat64NaN(a, b), propagate);
+ return mix(__packFloat64(aSign ^ 0x80000000u, 0x7ff, 0u, 0u), __propagateFloat64NaN(a, b), propagate);
}
expDiff = mix(expDiff, expDiff + 1, aExp == 0);
aFracHi = mix(aFracHi | 0x40000000u, aFracHi, aExp == 0);
bFracHi |= 0x40000000u;
__sub64(bFracHi, bFracLo, aFracHi, aFracLo, zFrac0, zFrac1);
zExp = bExp;
- aSign ^= 1u;
+ aSign ^= 0x80000000u;
--zExp;
return __normalizeRoundAndPackFloat64(aSign, zExp - 10, zFrac0, zFrac1);
}
if (aExp == 0x7FF) {
- bool propagate = (aFracHi | aFracLo | bFracHi | bFracLo) != 0u;
+ bool propagate = ((aFracHi | bFracHi) | (aFracLo | bFracLo)) != 0u;
return mix(0xFFFFFFFFFFFFFFFFUL, __propagateFloat64NaN(a, b), propagate);
}
bExp = mix(bExp, 1, aExp == 0);
aExp = mix(aExp, 1, aExp == 0);
- bool zexp_normal = false;
- bool blta = true;
+
+ uint zFrac0;
+ uint zFrac1;
+ uint sign_of_difference = 0;
if (bFracHi < aFracHi) {
__sub64(aFracHi, aFracLo, bFracHi, bFracLo, zFrac0, zFrac1);
- zexp_normal = true;
}
else if (aFracHi < bFracHi) {
__sub64(bFracHi, bFracLo, aFracHi, aFracLo, zFrac0, zFrac1);
- blta = false;
- zexp_normal = true;
+ sign_of_difference = 0x80000000;
}
- else if (bFracLo < aFracLo) {
+ else if (bFracLo <= aFracLo) {
+ /* It is possible that zFrac0 and zFrac1 may be zero after this. */
__sub64(aFracHi, aFracLo, bFracHi, bFracLo, zFrac0, zFrac1);
- zexp_normal = true;
}
- else if (aFracLo < bFracLo) {
+ else {
__sub64(bFracHi, bFracLo, aFracHi, aFracLo, zFrac0, zFrac1);
- blta = false;
- zexp_normal = true;
+ sign_of_difference = 0x80000000;
}
- zExp = mix(bExp, aExp, blta);
- aSign = mix(aSign ^ 1u, aSign, blta);
- uint64_t retval_0 = __packFloat64(uint(FLOAT_ROUNDING_MODE == FLOAT_ROUND_DOWN), 0, 0u, 0u);
+ zExp = mix(bExp, aExp, sign_of_difference == 0u);
+ aSign ^= sign_of_difference;
+ uint64_t retval_0 = __packFloat64(uint(FLOAT_ROUNDING_MODE == FLOAT_ROUND_DOWN) << 31, 0, 0u, 0u);
uint64_t retval_1 = __normalizeRoundAndPackFloat64(aSign, zExp - 11, zFrac0, zFrac1);
- return mix(retval_0, retval_1, zexp_normal);
+ return mix(retval_0, retval_1, zFrac0 != 0u || zFrac1 != 0u);
}
}
return __packFloat64(zSign, 0x7FF, 0u, 0u);
}
if (bExp == 0x7FF) {
+ /* a cannot be NaN, but is b NaN? */
if ((bFracHi | bFracLo) != 0u)
+#if defined RELAXED_NAN_PROPAGATION
+ return b;
+#else
return __propagateFloat64NaN(a, b);
+#endif
if ((uint(aExp) | aFracHi | aFracLo) == 0u)
return 0xFFFFFFFFFFFFFFFFUL;
return __packFloat64(zSign, 0x7FF, 0u, 0u);
__shift64RightJamming(aFracHi, aFracLo, shiftDist, aFracHi, aFracLo);
if ((aFracHi & 0xFFFFF000u) != 0u)
- return mix(~0u, 0u, (aSign != 0u));
+ return mix(~0u, 0u, aSign != 0u);
uint z = 0u;
uint zero = 0u;
__shift64Right(aFracHi, aFracLo, 12, zero, z);
- uint expt = mix(~0u, 0u, (aSign != 0u));
+ uint expt = mix(~0u, 0u, aSign != 0u);
return mix(z, expt, (aSign != 0u) && (z != 0u));
}
uint a = floatBitsToUint(f);
uint aFrac = a & 0x007FFFFFu;
int aExp = int((a>>23) & 0xFFu);
- uint aSign = a>>31;
+ uint aSign = a & 0x80000000u;
uint zFrac0 = 0u;
uint zFrac1 = 0u;
uint zFrac2 = 0u;
uint a = floatBitsToUint(f);
uint aFrac = a & 0x007FFFFFu;
int aExp = int((a>>23) & 0xFFu);
- uint aSign = a>>31;
+ uint aSign = a & 0x80000000u;
uint zFrac0 = 0u;
uint zFrac1 = 0u;
uint zFrac2 = 0u;
uint64_t absA = mix(uint64_t(a), uint64_t(-a), a < 0);
uint aFracHi = __extractFloat64FracHi(absA);
uvec2 aFrac = unpackUint2x32(absA);
- uint zSign = uint(a < 0);
+ uint zSign = uint(unpackInt2x32(a).y) & 0x80000000u;
if ((aFracHi & 0x80000000u) != 0u) {
- return mix(0ul, __packFloat64(1, 0x434, 0u, 0u), a < 0);
+ return mix(0ul, __packFloat64(0x80000000u, 0x434, 0u, 0u), a < 0);
}
return __normalizeRoundAndPackFloat64(zSign, 0x432, aFrac.y, aFrac.x);
if (0x41E < aExp) {
if ((aExp == 0x7FF) && bool(aFracHi | aFracLo))
aSign = 0u;
- return mix(0x7FFFFFFF, 0x80000000, bool(aSign));
+ return mix(0x7FFFFFFF, 0x80000000, aSign != 0u);
}
__shortShift64Left(aFracHi | 0x00100000u, aFracLo, shiftCount, absZ, aFracExtra);
} else {
absZ = aFracHi >> (- shiftCount);
}
- int z = mix(int(absZ), -int(absZ), (aSign != 0u));
- int nan = mix(0x7FFFFFFF, 0x80000000, bool(aSign));
- return mix(z, nan, bool(aSign ^ uint(z < 0)) && bool(z));
+ int z = mix(int(absZ), -int(absZ), aSign != 0u);
+ int nan = mix(0x7FFFFFFF, 0x80000000, aSign != 0u);
+ return mix(z, nan, ((aSign != 0u) != (z < 0)) && bool(z));
}
/* Returns the result of converting the 32-bit two's complement integer `a'
uint zFrac1 = 0u;
if (a==0)
return __packFloat64(0u, 0, 0u, 0u);
- uint zSign = uint(a < 0);
+ uint zSign = uint(a) & 0x80000000u;
uint absA = mix(uint(a), uint(-a), a < 0);
int shiftCount = __countLeadingZeros32(absA) - 11;
if (0 <= shiftCount) {
float
__packFloat32(uint zSign, int zExp, uint zFrac)
{
- return uintBitsToFloat((zSign<<31) + (uint(zExp)<<23) + zFrac);
+ return uintBitsToFloat(zSign + (uint(zExp)<<23) + zFrac);
}
/* Takes an abstract floating-point value having sign `zSign', exponent `zExp',
uint aSign = __extractFloat64Sign(__a);
if (aExp == 0x7FF) {
__shortShift64Left(a.y, a.x, 12, a.y, a.x);
- float rval = uintBitsToFloat((aSign<<31) | 0x7FC00000u | (a.y>>9));
+ float rval = uintBitsToFloat(aSign | 0x7FC00000u | (a.y>>9));
rval = mix(__packFloat32(aSign, 0xFF, 0u), rval, (aFracHi | aFracLo) != 0u);
return rval;
}
float
__int64_to_fp32(int64_t __a)
{
- uint aSign = uint(__a < 0);
+ uint aSign = uint(unpackInt2x32(__a).y) & 0x80000000u;
uint64_t absA = mix(uint64_t(__a), uint64_t(-__a), __a < 0);
uvec2 aFrac = unpackUint2x32(absA);
int shiftCount = mix(__countLeadingZeros32(aFrac.y) - 33,
uint a = floatBitsToUint(f);
uint aFrac = a & 0x007FFFFFu;
int aExp = int((a>>23) & 0xFFu);
- uint aSign = a>>31;
+ uint aSign = a & 0x80000000u;
uint zFrac0 = 0u;
uint zFrac1 = 0u;
uint nanLo = 0u;
uint nanHi = a<<9;
__shift64Right(nanHi, nanLo, 12, nanHi, nanLo);
- nanHi |= ((aSign<<31) | 0x7FF80000u);
+ nanHi |= aSign | 0x7FF80000u;
return packUint2x32(uvec2(nanLo, nanHi));
}
return __packFloat64(aSign, 0x7FF, 0u, 0u);
uint64_t
__ffloor64(uint64_t a)
{
- bool is_positive = __fge64(a, 0ul);
+ /* The big assumtion is that when 'a' is NaN, __ftrunc(a) returns a. Based
+ * on that assumption, NaN values that don't have the sign bit will safely
+ * return NaN (identity). This is guarded by RELAXED_NAN_PROPAGATION
+ * because otherwise the NaN should have the "signal" bit set. The
+ * __fadd64 will ensure that occurs.
+ */
+ bool is_positive =
+#if defined RELAXED_NAN_PROPAGATION
+ int(unpackUint2x32(a).y) >= 0
+#else
+ __fge64(a, 0ul)
+#endif
+ ;
uint64_t tr = __ftrunc64(a);
if (is_positive || __feq64(tr, a)) {
uint64_t
__fmin64(uint64_t a, uint64_t b)
{
- if (__is_nan(a)) return b;
- if (__is_nan(b)) return a;
+ /* This weird layout matters. Doing the "obvious" thing results in extra
+ * flow control being inserted to implement the short-circuit evaluation
+ * rules. Flow control is bad!
+ */
+ bool b_nan = __is_nan(b);
+ bool a_lt_b = __flt64_nonnan(a, b);
+ bool a_nan = __is_nan(a);
- if (__flt64_nonnan(a, b)) return a;
- return b;
+ return (b_nan || a_lt_b) && !a_nan ? a : b;
}
uint64_t
__fmax64(uint64_t a, uint64_t b)
{
- if (__is_nan(a)) return b;
- if (__is_nan(b)) return a;
+ /* This weird layout matters. Doing the "obvious" thing results in extra
+ * flow control being inserted to implement the short-circuit evaluation
+ * rules. Flow control is bad!
+ */
+ bool b_nan = __is_nan(b);
+ bool a_lt_b = __flt64_nonnan(a, b);
+ bool a_nan = __is_nan(a);
- if (__flt64_nonnan(a, b)) return b;
- return a;
+ return (b_nan || a_lt_b) && !a_nan ? b : a;
}
uint64_t
projects / mesa.git / blobdiff