cc Aldy Hernandez <aldyh@redhat.com> and Andrew MacLeod <amacleod@redhat.com>,
they are author of new VRP analysis for GCC, just to make sure I didn't
mis-understanding or mis-interpreting anything on GCC site.
GCC 11 have better value range analysis, that give GCC more confidence
to perform more aggressive optimization, but it cause scalbn/scalbnf get
wrong result.
Using scalbn to demostrate what happened on GCC 11, see comments with VRP
prefix:
```c
double scalbn (double x, int n)
{
/* VRP RESULT: n = [-INF, +INF] */
__int32_t k,hx,lx;
...
k = (hx&0x7ff00000)>>20;
/* VRP RESULT: k = [0, 2047] */
if (k==0) {
/* VRP RESULT: k = 0 */
...
k = ((hx&0x7ff00000)>>20) - 54;
if (n< -50000) return tiny*x; /*underflow*/
/* VRP RESULT: k = -54 */
}
/* VRP RESULT: k = [-54, 2047] */
if (k==0x7ff) return x+x; /* NaN or Inf */
/* VRP RESULT: k = [-54, 2046] */
k = k+n;
if (k > 0x7fe) return huge*copysign(huge,x); /* overflow */
/* VRP RESULT: k = [-INF, 2046] */
/* VRP RESULT: n = [-INF, 2100],
because k + n <= 0x7fe is false, so:
1. -INF < [-54, 2046] + n <= 0x7fe(2046) < INF
2. -INF < [-54, 2046] + n <= 2046 < INF
3. -INF < n <= 2046 - [-54, 2046] < INF
4. -INF < n <= [0, 2100] < INF
5. n = [-INF, 2100] */
if (k > 0) /* normal result */
{SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); return x;}
if (k <= -54) {
/* VRP OPT: Evaluate n > 50000 as true...*/
if (n > 50000) /* in case integer overflow in n+k */
return huge*copysign(huge,x); /*overflow*/
else return tiny*copysign(tiny,x); /*underflow*/
}
k += 54; /* subnormal result */
SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20));
return x*twom54;
}
```
However give the input n = INT32_MAX, k = k+n will overflow, and then we
expect got `huge*copysign(huge,x)`, but new VRP optimization think
`n > 50000` is never be true, so optimize that into `tiny*copysign(tiny,x)`.
so the solution here is to moving the overflow handle logic before `k = k + n`.
Kito Cheng
Richard Sandiford
Jeff Johnston
Christopher Faylor