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Simplification of the dekkerMul2() subroutine.

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FossilOrigin-Name: bfe6432a46fd41bfadf4516a73b4e2523d9b453c3e4486fe6df7e1d25275dfb3
This commit is contained in:
drh
2023-07-05 14:42:50 +00:00
parent 6aa5a42beb
commit 1790ccb98b
3 changed files with 42 additions and 44 deletions
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72
src/util.c
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@@ -386,23 +386,19 @@ u8 sqlite3StrIHash(const char *z){
return h;
}
/* Double-Double multiplication. *(z,zz) = (x,xx) * (y,yy)
/* Double-Double multiplication. (x[0],x[1]) *= (y,yy)
**
** Reference:
** T. J. Dekker, "A Floating-Point Technique for Extending the
** Available Precision". 1971-07-26.
*/
static void dekkerMul2(
double x, double xx,
double y, double yy,
double *z, double *zz
){
static void dekkerMul2(double *x, double y, double yy){
double hx, tx, hy, ty, p, q, c, cc;
u64 m;
memcpy(&m, &x, 8);
memcpy(&m, &x[0], 8);
m &= 0xfffffffffc000000L;
memcpy(&hx, &m, 8);
tx = x - hx;
tx = x[0] - hx;
memcpy(&m, &y, 8);
m &= 0xfffffffffc000000L;
memcpy(&hy, &m, 8);
@@ -411,9 +407,9 @@ static void dekkerMul2(
q = hx*ty + tx*hy;
c = p+q;
cc = p - c + q + tx*ty;
cc = x*yy + xx*y + cc;
*z = c + cc;
*zz = c - *z + cc;
cc = x[0]*yy + x[1]*y + cc;
x[0] = c + cc;
x[1] = c - x[0] + cc;
}
/*
@@ -587,39 +583,39 @@ do_atof_calc:
}
*pResult = r;
}else{
double r, rr;
double rr[2];
u64 s2;
r = (double)s;
s2 = (u64)r;
rr = s>=s2 ? (double)(s - s2) : -(double)(s2 - s);
rr[0] = (double)s;
s2 = (u64)rr[0];
rr[1] = s>=s2 ? (double)(s - s2) : -(double)(s2 - s);
if( e>0 ){
while( e>=100 ){
e -= 100;
dekkerMul2(r, rr, 1.0e+100, -1.5902891109759918046e+83, &r, &rr);
dekkerMul2(rr, 1.0e+100, -1.5902891109759918046e+83);
}
while( e>=10 ){
e -= 10;
dekkerMul2(r, rr, 1.0e+10, 0.0, &r, &rr);
dekkerMul2(rr, 1.0e+10, 0.0);
}
while( e>=1 ){
e -= 1;
dekkerMul2(r, rr, 1.0e+01, 0.0, &r, &rr);
dekkerMul2(rr, 1.0e+01, 0.0);
}
}else{
while( e<=-100 ){
e += 100;
dekkerMul2(r, rr, 1.0e-100, -1.99918998026028836196e-117, &r, &rr);
dekkerMul2(rr, 1.0e-100, -1.99918998026028836196e-117);
}
while( e<=-10 ){
e += 10;
dekkerMul2(r,rr, 1.0e-10, -3.6432197315497741579e-27, &r, &rr);
dekkerMul2(rr, 1.0e-10, -3.6432197315497741579e-27);
}
while( e<=-1 ){
e += 1;
dekkerMul2(r,rr, 1.0e-01, -5.5511151231257827021e-18, &r, &rr);
dekkerMul2(rr, 1.0e-01, -5.5511151231257827021e-18);
}
}
*pResult = r+rr;
*pResult = rr[0]+rr[1];
if( sqlite3IsNaN(*pResult) ) *pResult = 1e300*1e300;
}
if( sign<0 ) *pResult = -*pResult;
@@ -982,35 +978,37 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
**
** SELECT decimal_sci(decimal_sub('1.0e+100',decimal(1.0e+100)));
*/
double rr = 0.0;
if( r>1.84e+19 ){
while( r>1.84e+119 ){
double rr[2];
rr[0] = r;
rr[1] = 0.0;
if( rr[0]>1.84e+19 ){
while( rr[0]>1.84e+119 ){
exp += 100;
dekkerMul2(r, rr, 1.0e-100, -1.99918998026028836196e-117, &r, &rr);
dekkerMul2(rr, 1.0e-100, -1.99918998026028836196e-117);
}
while( r>1.84e+29 ){
while( rr[0]>1.84e+29 ){
exp += 10;
dekkerMul2(r,rr, 1.0e-10, -3.6432197315497741579e-27, &r, &rr);
dekkerMul2(rr, 1.0e-10, -3.6432197315497741579e-27);
}
while( r>1.84e+19 ){
while( rr[0]>1.84e+19 ){
exp += 1;
dekkerMul2(r,rr, 1.0e-01, -5.5511151231257827021e-18, &r, &rr);
dekkerMul2(rr, 1.0e-01, -5.5511151231257827021e-18);
}
}else{
while( r<1.84e-82 ){
while( rr[0]<1.84e-82 ){
exp -= 100;
dekkerMul2(r, rr, 1.0e+100, -1.5902891109759918046e+83, &r, &rr);
dekkerMul2(rr, 1.0e+100, -1.5902891109759918046e+83);
}
while( r<1.84e+08 ){
while( rr[0]<1.84e+08 ){
exp -= 10;
dekkerMul2(r, rr, 1.0e+10, 0.0, &r, &rr);
dekkerMul2(rr, 1.0e+10, 0.0);
}
while( r<1.84e+18 ){
while( rr[0]<1.84e+18 ){
exp -= 1;
dekkerMul2(r, rr, 1.0e+01, 0.0, &r, &rr);
dekkerMul2(rr, 1.0e+01, 0.0);
}
}
v = rr<0.0 ? (u64)r-(u64)(-rr) : (u64)r+(u64)rr;
v = rr[1]<0.0 ? (u64)rr[0]-(u64)(-rr[1]) : (u64)rr[0]+(u64)rr[1];
}