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Oops, the last-minute optimization in rev.1.8 wasn't a good idea. The

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17+17+24 bit pi/2 must only be used when subtraction of the first 2
terms in it from the arg is exact.  This happens iff the the arg in
bits is one of the 2**17[-1] values on each side of (float)(pi/2).

Revert to the algorithm in rev.1.7 and only fix its threshold for using
the 3-term pi/2.  Use the threshold that maximizes the number of values
for which the 3-term pi/2 is used, subject to not changing the algorithm
for comparing with the threshold.  The 3-term pi/2 ends up being used
for about half of its usable range (about 64K values on each side).
This commit is contained in:
Bruce Evans 2005-10-09 04:29:08 +00:00
parent a5b7fde722
commit a0e34da09f
Notes: svn2git 2020-12-20 02:59:44 +00:00 
svn path=/head/; revision=151147
1 changed files with 18 additions and 7 deletions
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25
lib/msun/src/e_rem_pio2f.c
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@ -98,16 +98,27 @@ pio2_3t = 6.1232342629e-17; /* 0x248d3132 */
if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */ if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */
{y[0] = x; y[1] = 0; return 0;} {y[0] = x; y[1] = 0; return 0;}
if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */ if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */
/* 17+17+24 bit pi has sufficient precision and best efficiency */
if(hx>0) { if(hx>0) {
z = (x - pio2_1) - pio2_2; z = x - pio2_1;
y[0] = z - pio2_2t; if((ix&0xfffe0000)!=0x3fc80000) { /* 17+24 bit pi OK */
y[1] = (z-y[0])-pio2_2t; y[0] = z - pio2_1t;
y[1] = (z-y[0])-pio2_1t;
} else { /* near pi/2, use 17+17+24 bit pi */
z -= pio2_2;
y[0] = z - pio2_2t;
y[1] = (z-y[0])-pio2_2t;
}
return 1; return 1;
} else { /* negative x */ } else { /* negative x */
z = (x + pio2_1) + pio2_2; z = x + pio2_1;
y[0] = z + pio2_2t; if((ix&0xfffe0000)!=0x3fc80000) { /* 17+24 bit pi OK */
y[1] = (z-y[0])+pio2_2t; y[0] = z + pio2_1t;
y[1] = (z-y[0])+pio2_1t;
} else { /* near pi/2, use 17+17+24 bit pi */
z += pio2_2;
y[0] = z + pio2_2t;
y[1] = (z-y[0])+pio2_2t;
}
return -1; return -1;
} }
} }