[builtins] Make divXf3 handle denormal results

[atrosinenko]

Summary

This is the last patch from the patchset introducing proper support for subnormal results to div[sdt]f3.

[atrosinenko]

Re-upload after amending previous commit

[atrosinenko]

Re-upload after D85731: [NFC][builtins] Make softfloat-related errors less noisy to get rid of "error: unknown type name 'fp_t'" and similar clang-tidy diagnostics for fp_div_impl.inc.

[atrosinenko]

Ping.

[atrosinenko]

Rebase the entire patch stack against the up-to-date master and re-upload.

[atrosinenko]

Re-upload after parent commits were changed.

[atrosinenko]

No-change re-upload: rebase onto current master branch.

[atrosinenko]

Re-upload after changing parent diff.

[atrosinenko]

Re-upload after amending parent diff.

[sepavloff]

LGTM.

[atrosinenko]

Re-upload after amending parent diff + add minor clarification.

compiler-rt/lib/builtins/fp_div_impl.inc

#endif
   // quotient_UQ1 is in [0.5, 2.0) as UQ1.(SB+1),
   // adjust it to be in [1.0, 2.0) as UQ1.SB.
   rep_t residualLo;
   if (quotient_UQ1 < (implicitBit << 1)) {
     // Highest bit is 0, so just reinterpret quotient_UQ1 as UQ1.SB,
     // 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).
   // Different cases (<---> is of 2^-SB length, * = a/b that is shown as a midpoint):
   //   q
   //   |   | * |   |   |       |       |
   //       <--->      2^t
   //   |   |   |   |   |   *   |       |
#endif
 
   // If we have overflowed the exponent, return infinity
   if (writtenExponent >= maxExponent)
     return fromRep(infRep | quotientSign);
 
   // 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
-
-  if (writtenExponent < 0) {
-    // Result is definitely subnormal, flushing to zero
-    return fromRep(quotientSign);
-  }
-
+  rep_t absResult;
+  if (writtenExponent > 0) {
     // Clear the implicit bit
-  rep_t absResult = quotient_UQ1 & significandMask;
+    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);
+
+    absResult = quotient_UQ1 >> (-writtenExponent + 1);
+
+    // 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) || (defined(SINGLE_PRECISION) && NUMBER_OF_HALF_ITERATIONS > 0)
   // Do not round Infinity to NaN
   absResult += absResult < infRep && residualLo > (2 + 1) * bSignificand;
 #endif
 #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);
 }

compiler-rt/test/builtins/Unit/divdf3_test.c

int main()
 
     // divisor is exactly 1.0
     if (test__divdf3(0x1.0p+0, 0x1.0p+0, UINT64_C(0x3ff0000000000000)))
       return 1;
     // divisor is truncated to exactly 1.0 in UQ1.31
     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;
     if (test__divdf3(-0x1.78abb261d47c8p+794, 0x1.fb01d537cc5aep+266, UINT64_C(0xe0e7c6148ffc23e3)))
       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;
 }

compiler-rt/test/builtins/Unit/divsf3_test.c

int main()
 
     // divisor is exactly 1.0
     if (test__divsf3(0x1.0p+0F, 0x1.0p+0F, UINT32_C(0x3f800000)))
       return 1;
     // divisor is truncated to exactly 1.0 in UQ1.15
     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;
 }

compiler-rt/test/builtins/Unit/divtf3_test.c

if (test__divtf3(0x1.0p+0L,
         return 1;
     // divisor is truncated to exactly 1.0 in UQ1.63
     if (test__divtf3(0x1.0p+0L,
                      0x1.0000000000000001p+0L,
                      UINT64_C(0x3ffeffffffffffff),
                      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,
                      UINT64_C(0x4004b0b72924d407),
                      UINT64_C(0x0717e84356c6eba2)))
         return 1;
     if (test__divtf3(0x1.a2b34c56d745382f9abf2c3dfeffp-50L,
                      0x1.ed2c3ba15935332532287654321fp-9L,