__shift64Right(aFrac, 0u, 3, zFrac0, zFrac1);
return __packFloat64(aSign, aExp + 0x380, zFrac0, zFrac1);
}
+
+/* Adds the 96-bit value formed by concatenating `a0', `a1', and `a2' to the
+ * 96-bit value formed by concatenating `b0', `b1', and `b2'. Addition is
+ * modulo 2^96, so any carry out is lost. The result is broken into three
+ * 32-bit pieces which are stored at the locations pointed to by `z0Ptr',
+ * `z1Ptr', and `z2Ptr'.
+ */
+void
+__add96(uint a0, uint a1, uint a2,
+ uint b0, uint b1, uint b2,
+ out uint z0Ptr,
+ out uint z1Ptr,
+ out uint z2Ptr)
+{
+ uint z2 = a2 + b2;
+ uint carry1 = uint(z2 < a2);
+ uint z1 = a1 + b1;
+ uint carry0 = uint(z1 < a1);
+ uint z0 = a0 + b0;
+ z1 += carry1;
+ z0 += uint(z1 < carry1);
+ z0 += carry0;
+ z2Ptr = z2;
+ z1Ptr = z1;
+ z0Ptr = z0;
+}
+
+/* Subtracts the 96-bit value formed by concatenating `b0', `b1', and `b2' from
+ * the 96-bit value formed by concatenating `a0', `a1', and `a2'. Subtraction
+ * is modulo 2^96, so any borrow out (carry out) is lost. The result is broken
+ * into three 32-bit pieces which are stored at the locations pointed to by
+ * `z0Ptr', `z1Ptr', and `z2Ptr'.
+ */
+void
+__sub96(uint a0, uint a1, uint a2,
+ uint b0, uint b1, uint b2,
+ out uint z0Ptr,
+ out uint z1Ptr,
+ out uint z2Ptr)
+{
+ uint z2 = a2 - b2;
+ uint borrow1 = uint(a2 < b2);
+ uint z1 = a1 - b1;
+ uint borrow0 = uint(a1 < b1);
+ uint z0 = a0 - b0;
+ z0 -= uint(z1 < borrow1);
+ z1 -= borrow1;
+ z0 -= borrow0;
+ z2Ptr = z2;
+ z1Ptr = z1;
+ z0Ptr = z0;
+}
+
+/* Returns an approximation to the 32-bit integer quotient obtained by dividing
+ * `b' into the 64-bit value formed by concatenating `a0' and `a1'. The
+ * divisor `b' must be at least 2^31. If q is the exact quotient truncated
+ * toward zero, the approximation returned lies between q and q + 2 inclusive.
+ * If the exact quotient q is larger than 32 bits, the maximum positive 32-bit
+ * unsigned integer is returned.
+ */
+uint
+__estimateDiv64To32(uint a0, uint a1, uint b)
+{
+ uint b0;
+ uint b1;
+ uint rem0 = 0u;
+ uint rem1 = 0u;
+ uint term0 = 0u;
+ uint term1 = 0u;
+ uint z;
+
+ if (b <= a0)
+ return 0xFFFFFFFFu;
+ b0 = b>>16;
+ z = (b0<<16 <= a0) ? 0xFFFF0000u : (a0 / b0)<<16;
+ __mul32To64(b, z, term0, term1);
+ __sub64(a0, a1, term0, term1, rem0, rem1);
+ while (int(rem0) < 0) {
+ z -= 0x10000u;
+ b1 = b<<16;
+ __add64(rem0, rem1, b0, b1, rem0, rem1);
+ }
+ rem0 = (rem0<<16) | (rem1>>16);
+ z |= (b0<<16 <= rem0) ? 0xFFFFu : rem0 / b0;
+ return z;
+}
+
+uint
+__sqrtOddAdjustments(int index)
+{
+ uint res = 0u;
+ if (index == 0)
+ res = 0x0004u;
+ if (index == 1)
+ res = 0x0022u;
+ if (index == 2)
+ res = 0x005Du;
+ if (index == 3)
+ res = 0x00B1u;
+ if (index == 4)
+ res = 0x011Du;
+ if (index == 5)
+ res = 0x019Fu;
+ if (index == 6)
+ res = 0x0236u;
+ if (index == 7)
+ res = 0x02E0u;
+ if (index == 8)
+ res = 0x039Cu;
+ if (index == 9)
+ res = 0x0468u;
+ if (index == 10)
+ res = 0x0545u;
+ if (index == 11)
+ res = 0x631u;
+ if (index == 12)
+ res = 0x072Bu;
+ if (index == 13)
+ res = 0x0832u;
+ if (index == 14)
+ res = 0x0946u;
+ if (index == 15)
+ res = 0x0A67u;
+
+ return res;
+}
+
+uint
+__sqrtEvenAdjustments(int index)
+{
+ uint res = 0u;
+ if (index == 0)
+ res = 0x0A2Du;
+ if (index == 1)
+ res = 0x08AFu;
+ if (index == 2)
+ res = 0x075Au;
+ if (index == 3)
+ res = 0x0629u;
+ if (index == 4)
+ res = 0x051Au;
+ if (index == 5)
+ res = 0x0429u;
+ if (index == 6)
+ res = 0x0356u;
+ if (index == 7)
+ res = 0x029Eu;
+ if (index == 8)
+ res = 0x0200u;
+ if (index == 9)
+ res = 0x0179u;
+ if (index == 10)
+ res = 0x0109u;
+ if (index == 11)
+ res = 0x00AFu;
+ if (index == 12)
+ res = 0x0068u;
+ if (index == 13)
+ res = 0x0034u;
+ if (index == 14)
+ res = 0x0012u;
+ if (index == 15)
+ res = 0x0002u;
+
+ return res;
+}
+
+/* Returns an approximation to the square root of the 32-bit significand given
+ * by `a'. Considered as an integer, `a' must be at least 2^31. If bit 0 of
+ * `aExp' (the least significant bit) is 1, the integer returned approximates
+ * 2^31*sqrt(`a'/2^31), where `a' is considered an integer. If bit 0 of `aExp'
+ * is 0, the integer returned approximates 2^31*sqrt(`a'/2^30). In either
+ * case, the approximation returned lies strictly within +/-2 of the exact
+ * value.
+ */
+uint
+__estimateSqrt32(int aExp, uint a)
+{
+ uint z;
+
+ int index = int(a>>27 & 15u);
+ if ((aExp & 1) != 0) {
+ z = 0x4000u + (a>>17) - __sqrtOddAdjustments(index);
+ z = ((a / z)<<14) + (z<<15);
+ a >>= 1;
+ } else {
+ z = 0x8000u + (a>>17) - __sqrtEvenAdjustments(index);
+ z = a / z + z;
+ z = (0x20000u <= z) ? 0xFFFF8000u : (z<<15);
+ if (z <= a)
+ return uint(int(a)>>1);
+ }
+ return ((__estimateDiv64To32(a, 0u, z))>>1) + (z>>1);
+}
+
+/* Returns the square root of the double-precision floating-point value `a'.
+ * The operation is performed according to the IEEE Standard for Floating-Point
+ * Arithmetic.
+ */
+uint64_t
+__fsqrt64(uint64_t a)
+{
+ uint zFrac0 = 0u;
+ uint zFrac1 = 0u;
+ uint zFrac2 = 0u;
+ uint doubleZFrac0 = 0u;
+ uint rem0 = 0u;
+ uint rem1 = 0u;
+ uint rem2 = 0u;
+ uint rem3 = 0u;
+ uint term0 = 0u;
+ uint term1 = 0u;
+ uint term2 = 0u;
+ uint term3 = 0u;
+ uint64_t default_nan = 0xFFFFFFFFFFFFFFFFUL;
+
+ uint aFracLo = __extractFloat64FracLo(a);
+ uint aFracHi = __extractFloat64FracHi(a);
+ int aExp = __extractFloat64Exp(a);
+ uint aSign = __extractFloat64Sign(a);
+ if (aExp == 0x7FF) {
+ if ((aFracHi | aFracLo) != 0u)
+ return __propagateFloat64NaN(a, a);
+ if (aSign == 0u)
+ return a;
+ return default_nan;
+ }
+ if (aSign != 0u) {
+ if ((uint(aExp) | aFracHi | aFracLo) == 0u)
+ return a;
+ return default_nan;
+ }
+ if (aExp == 0) {
+ if ((aFracHi | aFracLo) == 0u)
+ return __packFloat64(0u, 0, 0u, 0u);
+ __normalizeFloat64Subnormal(aFracHi, aFracLo, aExp, aFracHi, aFracLo);
+ }
+ int zExp = ((aExp - 0x3FF)>>1) + 0x3FE;
+ aFracHi |= 0x00100000u;
+ __shortShift64Left(aFracHi, aFracLo, 11, term0, term1);
+ zFrac0 = (__estimateSqrt32(aExp, term0)>>1) + 1u;
+ if (zFrac0 == 0u)
+ zFrac0 = 0x7FFFFFFFu;
+ doubleZFrac0 = zFrac0 + zFrac0;
+ __shortShift64Left(aFracHi, aFracLo, 9 - (aExp & 1), aFracHi, aFracLo);
+ __mul32To64(zFrac0, zFrac0, term0, term1);
+ __sub64(aFracHi, aFracLo, term0, term1, rem0, rem1);
+ while (int(rem0) < 0) {
+ --zFrac0;
+ doubleZFrac0 -= 2u;
+ __add64(rem0, rem1, 0u, doubleZFrac0 | 1u, rem0, rem1);
+ }
+ zFrac1 = __estimateDiv64To32(rem1, 0u, doubleZFrac0);
+ if ((zFrac1 & 0x1FFu) <= 5u) {
+ if (zFrac1 == 0u)
+ zFrac1 = 1u;
+ __mul32To64(doubleZFrac0, zFrac1, term1, term2);
+ __sub64(rem1, 0u, term1, term2, rem1, rem2);
+ __mul32To64(zFrac1, zFrac1, term2, term3);
+ __sub96(rem1, rem2, 0u, 0u, term2, term3, rem1, rem2, rem3);
+ while (int(rem1) < 0) {
+ --zFrac1;
+ __shortShift64Left(0u, zFrac1, 1, term2, term3);
+ term3 |= 1u;
+ term2 |= doubleZFrac0;
+ __add96(rem1, rem2, rem3, 0u, term2, term3, rem1, rem2, rem3);
+ }
+ zFrac1 |= uint((rem1 | rem2 | rem3) != 0u);
+ }
+ __shift64ExtraRightJamming(zFrac0, zFrac1, 0u, 10, zFrac0, zFrac1, zFrac2);
+ return __roundAndPackFloat64(0u, zExp, zFrac0, zFrac1, zFrac2);
+}
projects / mesa.git / commitdiff