// effectively doubling its value as well as its error estimation.
residualLo = (aSignificand << (significandBits + 1)) - quotient_UQ1 * bSignificand;
writtenExponent -= 1;
+ aSignificand <<= 1;
} else {
// Highest bit is 1 (the UQ1.(SB+1) value is in [1, 2)), convert it
// to UQ1.SB by right shifting by 1. Least significant bit is omitted.
quotient_UQ1 >>= 1;
residualLo = (aSignificand << significandBits) - quotient_UQ1 * bSignificand;
}
+ // NB: residualLo is calculated above for the normal result case.
+ // It is re-computed on denormal path that is expected to be not so
+ // performance-sensitive.
+
// Now, q cannot be greater than a/b and can differ by at most 8*P * 2^-W + 2^-SB
// Each NextAfter() increments the floating point value by at least 2^-SB
// (more, if exponent was incremented).
// Now, quotient_UQ1_SB <= the correctly-rounded result
// and may need taking NextAfter() up to 3 times (see error estimates above)
// r = a - b * q
+ rep_t absResult;
+ if (writtenExponent > 0) {
+ // Clear the implicit bit
+ absResult = quotient_UQ1 & significandMask;
+ // Insert the exponent
+ absResult |= (rep_t)writtenExponent << significandBits;
+ residualLo <<= 1;
+ } else {
+ // Prevent shift amount from being negative
+ if (significandBits + writtenExponent < 0)
+ return fromRep(quotientSign);
- if (writtenExponent < 0) {
- // Result is definitely subnormal, flushing to zero
- return fromRep(quotientSign);
- }
+ absResult = quotient_UQ1 >> (-writtenExponent + 1);
- // Clear the implicit bit
- rep_t absResult = quotient_UQ1 & significandMask;
- // Insert the exponent
- absResult |= (rep_t)writtenExponent << significandBits;
+ // multiplied by two to prevent shift amount to be negative
+ residualLo = (aSignificand << (significandBits + writtenExponent)) - (absResult * bSignificand << 1);
+ }
// Round
- residualLo <<= 1;
residualLo += absResult & 1; // tie to even
// The above line conditionally turns the below LT comparison into LTE
absResult += residualLo > bSignificand;
#if defined(QUAD_PRECISION)
absResult += absResult < infRep && residualLo > (4 + 1) * bSignificand;
#endif
-
- if ((absResult & ~significandMask) == 0) {
- // Result is subnormal, flushing to zero
- return fromRep(quotientSign);
- }
- // Result is normal, insert the sign and return
return fromRep(absResult | quotientSign);
}
if (test__divdf3(0x1.0p+0, 0x1.00000001p+0, UINT64_C(0x3fefffffffe00000)))
return 1;
+ // smallest normal value divided by 2.0
+ if (test__divdf3(0x1.0p-1022, 2., UINT64_C(0x0008000000000000)))
+ return 1;
+ // smallest subnormal result
+ if (test__divdf3(0x1.0p-1022, 0x1.0p+52, UINT64_C(0x0000000000000001)))
+ return 1;
+
// some misc test cases obtained by fuzzing against h/w implementation
if (test__divdf3(0x1.fdc239dd64735p-658, -0x1.fff9364c0843fp-948, UINT64_C(0xd20fdc8fc0ceffb1)))
return 1;
return 1;
if (test__divdf3(-0x1.da7dfe6048b8bp-875, 0x1.ffc7ea3ff60a4p-610, UINT64_C(0xaf5dab1fe0269e2a)))
return 1;
+ if (test__divdf3(0x1.0p-1022, 0x1.9p+5, UINT64_C(0x000051eb851eb852)))
+ return 1;
+ if (test__divdf3(0x1.0p-1022, 0x1.0028p+41, UINT64_C(0x00000000000007ff)))
+ return 1;
+ if (test__divdf3(0x1.0p-1022, 0x1.0028p+52, UINT64_C(0x1)))
+ return 1;
return 0;
}
if (test__divsf3(0x1.0p+0F, 0x1.0001p+0F, UINT32_C(0x3f7fff00)))
return 1;
+ // smallest normal value divided by 2.0
+ if (test__divsf3(0x1.0p-126F, 2.0F, UINT32_C(0x00400000)))
+ return 1;
+ // smallest subnormal result
+ if (test__divsf3(0x1.0p-126F, 0x1p+23F, UINT32_C(0x00000001)))
+ return 1;
+
+ // some misc test cases obtained by fuzzing against h/w implementation
+ if (test__divsf3(-0x1.3e75e6p-108F, -0x1.cf372p+38F, UINT32_C(0x00000006)))
+ return 1;
+ if (test__divsf3(0x1.e77c54p+81F, -0x1.e77c52p-47F, UINT32_C(0xff800000)))
+ return 1;
+ if (test__divsf3(0x1.fffffep-126F, 2.F, UINT32_C(0x00800000)))
+ return 1;
+
return 0;
}
UINT64_C(0xfffe000000000000)))
return 1;
+ // smallest normal value divided by 2.0
+ if (test__divtf3(0x1.0p-16382L, 2.L, UINT64_C(0x0000800000000000), UINT64_C(0x0)))
+ return 1;
+ // smallest subnormal result
+ if (test__divtf3(0x1.0p-1022L, 0x1p+52L, UINT64_C(0x0), UINT64_C(0x1)))
+ return 1;
+
// any / any
if (test__divtf3(0x1.a23b45362464523375893ab4cdefp+5L,
0x1.eedcbaba3a94546558237654321fp-1L,