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ca7b4bd236
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`.
110 lines
2.8 KiB
C
110 lines
2.8 KiB
C
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/* @(#)s_scalbn.c 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/*
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FUNCTION
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<<scalbn>>, <<scalbnf>>, <<scalbln>>, <<scalblnf>>---scale by power of FLT_RADIX (=2)
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INDEX
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scalbn
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INDEX
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scalbnf
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INDEX
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scalbln
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INDEX
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scalblnf
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SYNOPSIS
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#include <math.h>
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double scalbn(double <[x]>, int <[n]>);
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float scalbnf(float <[x]>, int <[n]>);
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double scalbln(double <[x]>, long int <[n]>);
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float scalblnf(float <[x]>, long int <[n]>);
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DESCRIPTION
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The <<scalbn>> and <<scalbln>> functions compute
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@ifnottex
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<[x]> times FLT_RADIX to the power <[n]>.
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@end ifnottex
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@tex
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$x \cdot FLT\_RADIX^n$.
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@end tex
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efficiently. The result is computed by manipulating the exponent, rather than
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by actually performing an exponentiation or multiplication. In this
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floating-point implementation FLT_RADIX=2, which makes the <<scalbn>>
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functions equivalent to the <<ldexp>> functions.
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RETURNS
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<[x]> times 2 to the power <[n]>. A range error may occur.
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PORTABILITY
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ANSI C, POSIX
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SEEALSO
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<<ldexp>>
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*/
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/*
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* scalbn (double x, int n)
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* scalbn(x,n) returns x* 2**n computed by exponent
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* manipulation rather than by actually performing an
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* exponentiation or a multiplication.
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*/
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#include "fdlibm.h"
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#ifndef _DOUBLE_IS_32BITS
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#ifdef __STDC__
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static const double
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#else
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static double
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#endif
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two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
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twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
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huge = 1.0e+300,
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tiny = 1.0e-300;
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#ifdef __STDC__
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double scalbn (double x, int n)
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#else
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double scalbn (x,n)
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double x; int n;
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#endif
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{
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__int32_t k,hx,lx;
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EXTRACT_WORDS(hx,lx,x);
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k = (hx&0x7ff00000)>>20; /* extract exponent */
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if (k==0) { /* 0 or subnormal x */
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if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
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x *= two54;
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GET_HIGH_WORD(hx,x);
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k = ((hx&0x7ff00000)>>20) - 54;
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if (n< -50000) return tiny*x; /*underflow*/
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}
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if (k==0x7ff) return x+x; /* NaN or Inf */
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if (n > 50000) /* in case integer overflow in n+k */
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return huge*copysign(huge,x); /*overflow*/
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k = k+n;
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if (k > 0x7fe) return huge*copysign(huge,x); /* overflow */
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if (k > 0) /* normal result */
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{SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); return x;}
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if (k <= -54)
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return tiny*copysign(tiny,x); /*underflow*/
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k += 54; /* subnormal result */
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SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20));
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return x*twom54;
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}
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#endif /* _DOUBLE_IS_32BITS */
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