Do not left-shift a negative number (inducing undefined behavior in

C/C++) in exp(3), expf(3), expm1(3) and expm1f(3) during intermediate
computations that compute the IEEE-754 bit pattern for |2**k| for
integer |k|.

The implementations of exp(3), expf(3), expm1(3) and expm1f(3) need to
compute IEEE-754 bit patterns for 2**k in certain places.  (k is an
integer and 2**k is exactly representable in IEEE-754.)

Currently they do things like 0x3FF0'0000+(k<<20), which is to say they
take the bit pattern representing 1 and then add directly to the
exponent field to get the desired power of two.  This is fine when k is
non-negative.

But when k<0 (and certain classes of input trigger this), this
left-shifts a negative number -- an operation with undefined behavior in
C and C++.

The desired semantics can be achieved by instead adding the
possibly-negative k to the IEEE-754 exponent bias to get the desired
exponent field, _then_ shifting that into its proper overall position.

(Note that in case of s_expm1.c and s_expm1f.c, there are SET_HIGH_WORD
and SET_FLOAT_WORD uses further down in each of these files that perform
shift operations involving k, but by these points k's range has been
restricted to 2 < k <= 56, and the shift operations under those
circumstances can't do anything that would be UB.)

Submitted by:	Jeff Walden, https://github.com/jswalden
Obtained from:	https://github.com/freebsd/freebsd/pull/411
Obtained from:	https://github.com/freebsd/freebsd/pull/412
MFC after:	3 days

lib/msun/src/e_exp.c

@@ -145,9 +145,9 @@ __ieee754_exp(double x)	/* default IEEE double exp */
     /* x is now in primary range */
 	t  = x*x;
 	if(k >= -1021)
-	    INSERT_WORDS(twopk,0x3ff00000+(k<<20), 0);
+	    INSERT_WORDS(twopk,((u_int32_t)(0x3ff+k))<<20, 0);
 	else
-	    INSERT_WORDS(twopk,0x3ff00000+((k+1000)<<20), 0);
+	    INSERT_WORDS(twopk,((u_int32_t)(0x3ff+(k+1000)))<<20, 0);
 	c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
 	if(k==0) 	return one-((x*c)/(c-2.0)-x); 
 	else 		y = one-((lo-(x*c)/(2.0-c))-hi);

lib/msun/src/e_expf.c

@@ -83,9 +83,9 @@ __ieee754_expf(float x)
     /* x is now in primary range */
 	t  = x*x;
 	if(k >= -125)
-	    SET_FLOAT_WORD(twopk,0x3f800000+(k<<23));
+	    SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+k))<<23);
 	else
-	    SET_FLOAT_WORD(twopk,0x3f800000+((k+100)<<23));
+	    SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+(k+100)))<<23);
 	c  = x - t*(P1+t*P2);
 	if(k==0) 	return one-((x*c)/(c-(float)2.0)-x);
 	else 		y = one-((lo-(x*c)/((float)2.0-c))-hi);

lib/msun/src/s_expm1.c

@@ -188,7 +188,7 @@ expm1(double x)
 	e  = hxs*((r1-t)/(6.0 - x*t));
 	if(k==0) return x - (x*e-hxs);		/* c is 0 */
 	else {
-	    INSERT_WORDS(twopk,0x3ff00000+(k<<20),0);	/* 2^k */
+	    INSERT_WORDS(twopk,((u_int32_t)(0x3ff+k))<<20,0);	/* 2^k */
 	    e  = (x*(e-c)-c);
 	    e -= hxs;
 	    if(k== -1) return 0.5*(x-e)-0.5;

lib/msun/src/s_expm1f.c

@@ -94,7 +94,7 @@ expm1f(float x)
 	e  = hxs*((r1-t)/((float)6.0 - x*t));
 	if(k==0) return x - (x*e-hxs);		/* c is 0 */
 	else {
-	    SET_FLOAT_WORD(twopk,0x3f800000+(k<<23));	/* 2^k */
+	    SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+k))<<23);	/* 2^k */
 	    e  = (x*(e-c)-c);
 	    e -= hxs;
 	    if(k== -1) return (float)0.5*(x-e)-(float)0.5;