return mix(retval_0, retval_1, zexp_normal);
}
}
+
+/* Multiplies `a' by `b' to obtain a 64-bit product. The product is broken
+ * into two 32-bit pieces which are stored at the locations pointed to by
+ * `z0Ptr' and `z1Ptr'.
+ */
+void
+__mul32To64(uint a, uint b, out uint z0Ptr, out uint z1Ptr)
+{
+ uint aLow = a & 0x0000FFFFu;
+ uint aHigh = a>>16;
+ uint bLow = b & 0x0000FFFFu;
+ uint bHigh = b>>16;
+ uint z1 = aLow * bLow;
+ uint zMiddleA = aLow * bHigh;
+ uint zMiddleB = aHigh * bLow;
+ uint z0 = aHigh * bHigh;
+ zMiddleA += zMiddleB;
+ z0 += ((uint(zMiddleA < zMiddleB)) << 16) + (zMiddleA >> 16);
+ zMiddleA <<= 16;
+ z1 += zMiddleA;
+ z0 += uint(z1 < zMiddleA);
+ z1Ptr = z1;
+ z0Ptr = z0;
+}
+
+/* Multiplies the 64-bit value formed by concatenating `a0' and `a1' to the
+ * 64-bit value formed by concatenating `b0' and `b1' to obtain a 128-bit
+ * product. The product is broken into four 32-bit pieces which are stored at
+ * the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'.
+ */
+void
+__mul64To128(uint a0, uint a1, uint b0, uint b1,
+ out uint z0Ptr,
+ out uint z1Ptr,
+ out uint z2Ptr,
+ out uint z3Ptr)
+{
+ uint z0 = 0u;
+ uint z1 = 0u;
+ uint z2 = 0u;
+ uint z3 = 0u;
+ uint more1 = 0u;
+ uint more2 = 0u;
+
+ __mul32To64(a1, b1, z2, z3);
+ __mul32To64(a1, b0, z1, more2);
+ __add64(z1, more2, 0u, z2, z1, z2);
+ __mul32To64(a0, b0, z0, more1);
+ __add64(z0, more1, 0u, z1, z0, z1);
+ __mul32To64(a0, b1, more1, more2);
+ __add64(more1, more2, 0u, z2, more1, z2);
+ __add64(z0, z1, 0u, more1, z0, z1);
+ z3Ptr = z3;
+ z2Ptr = z2;
+ z1Ptr = z1;
+ z0Ptr = z0;
+}
+
+/* Normalizes the subnormal double-precision floating-point value represented
+ * by the denormalized significand formed by the concatenation of `aFrac0' and
+ * `aFrac1'. The normalized exponent is stored at the location pointed to by
+ * `zExpPtr'. The most significant 21 bits of the normalized significand are
+ * stored at the location pointed to by `zFrac0Ptr', and the least significant
+ * 32 bits of the normalized significand are stored at the location pointed to
+ * by `zFrac1Ptr'.
+ */
+void
+__normalizeFloat64Subnormal(uint aFrac0, uint aFrac1,
+ out int zExpPtr,
+ out uint zFrac0Ptr,
+ out uint zFrac1Ptr)
+{
+ int shiftCount;
+ uint temp_zfrac0, temp_zfrac1;
+ shiftCount = __countLeadingZeros32(mix(aFrac0, aFrac1, aFrac0 == 0u)) - 11;
+ zExpPtr = mix(1 - shiftCount, -shiftCount - 31, aFrac0 == 0u);
+
+ temp_zfrac0 = mix(aFrac1<<shiftCount, aFrac1>>(-shiftCount), shiftCount < 0);
+ temp_zfrac1 = mix(0u, aFrac1<<(shiftCount & 31), shiftCount < 0);
+
+ __shortShift64Left(aFrac0, aFrac1, shiftCount, zFrac0Ptr, zFrac1Ptr);
+
+ zFrac0Ptr = mix(zFrac0Ptr, temp_zfrac0, aFrac0 == 0);
+ zFrac1Ptr = mix(zFrac1Ptr, temp_zfrac1, aFrac0 == 0);
+}
+
+/* Returns the result of multiplying the double-precision floating-point values
+ * `a' and `b'. The operation is performed according to the IEEE Standard for
+ * Floating-Point Arithmetic.
+ */
+uint64_t
+__fmul64(uint64_t a, uint64_t b)
+{
+ uint zFrac0 = 0u;
+ uint zFrac1 = 0u;
+ uint zFrac2 = 0u;
+ uint zFrac3 = 0u;
+ int zExp;
+
+ uint aFracLo = __extractFloat64FracLo(a);
+ uint aFracHi = __extractFloat64FracHi(a);
+ uint bFracLo = __extractFloat64FracLo(b);
+ uint bFracHi = __extractFloat64FracHi(b);
+ int aExp = __extractFloat64Exp(a);
+ uint aSign = __extractFloat64Sign(a);
+ int bExp = __extractFloat64Exp(b);
+ uint bSign = __extractFloat64Sign(b);
+ uint zSign = aSign ^ bSign;
+ if (aExp == 0x7FF) {
+ if (((aFracHi | aFracLo) != 0u) ||
+ ((bExp == 0x7FF) && ((bFracHi | bFracLo) != 0u))) {
+ return __propagateFloat64NaN(a, b);
+ }
+ if ((uint(bExp) | bFracHi | bFracLo) == 0u)
+ return 0xFFFFFFFFFFFFFFFFUL;
+ return __packFloat64(zSign, 0x7FF, 0u, 0u);
+ }
+ if (bExp == 0x7FF) {
+ if ((bFracHi | bFracLo) != 0u)
+ return __propagateFloat64NaN(a, b);
+ if ((uint(aExp) | aFracHi | aFracLo) == 0u)
+ return 0xFFFFFFFFFFFFFFFFUL;
+ return __packFloat64(zSign, 0x7FF, 0u, 0u);
+ }
+ if (aExp == 0) {
+ if ((aFracHi | aFracLo) == 0u)
+ return __packFloat64(zSign, 0, 0u, 0u);
+ __normalizeFloat64Subnormal(aFracHi, aFracLo, aExp, aFracHi, aFracLo);
+ }
+ if (bExp == 0) {
+ if ((bFracHi | bFracLo) == 0u)
+ return __packFloat64(zSign, 0, 0u, 0u);
+ __normalizeFloat64Subnormal(bFracHi, bFracLo, bExp, bFracHi, bFracLo);
+ }
+ zExp = aExp + bExp - 0x400;
+ aFracHi |= 0x00100000u;
+ __shortShift64Left(bFracHi, bFracLo, 12, bFracHi, bFracLo);
+ __mul64To128(
+ aFracHi, aFracLo, bFracHi, bFracLo, zFrac0, zFrac1, zFrac2, zFrac3);
+ __add64(zFrac0, zFrac1, aFracHi, aFracLo, zFrac0, zFrac1);
+ zFrac2 |= uint(zFrac3 != 0u);
+ if (0x00200000u <= zFrac0) {
+ __shift64ExtraRightJamming(
+ zFrac0, zFrac1, zFrac2, 1, zFrac0, zFrac1, zFrac2);
+ ++zExp;
+ }
+ return __roundAndPackFloat64(zSign, zExp, zFrac0, zFrac1, zFrac2);
+}