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Implement feqrel!(float) + fix code formatting

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Don Clugston 2012-05-22 07:34:38 +02:00
parent 28bca62304
commit a8aa8cdcd6
1 changed files with 77 additions and 53 deletions
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130
std/math.d
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@ -3487,18 +3487,27 @@ int feqrel(X)(X x, X y) @trusted pure nothrow
{ {
/* Public Domain. Author: Don Clugston, 18 Aug 2005. /* Public Domain. Author: Don Clugston, 18 Aug 2005.
*/ */
static if (X.mant_dig == 106) { // doubledouble. static if (X.mant_dig == 106) // doubledouble
if (cast(double*)(&x)[MANTISSA_MSB] == cast(double*)(&y)[MANTISSA_MSB]) { {
if (cast(double*)(&x)[MANTISSA_MSB] == cast(double*)(&y)[MANTISSA_MSB])
{
return double.mant_dig return double.mant_dig
+ feqrel(cast(double*)(&x)[MANTISSA_LSB], + feqrel(cast(double*)(&x)[MANTISSA_LSB],
cast(double*)(&y)[MANTISSA_LSB]); cast(double*)(&y)[MANTISSA_LSB]);
} else { }
else
{
return feqrel(cast(double*)(&x)[MANTISSA_MSB], return feqrel(cast(double*)(&x)[MANTISSA_MSB],
cast(double*)(&y)[MANTISSA_MSB]); cast(double*)(&y)[MANTISSA_MSB]);
} }
} else static if (X.mant_dig==64 || X.mant_dig==113 || X.mant_dig==53) { }
else
{
static assert( X.mant_dig == 64 || X.mant_dig == 113
|| X.mant_dig == double.mant_dig || X.mant_dig == float.mant_dig);
if (x == y) return X.mant_dig; // ensure diff!=0, cope with INF. if (x == y)
return X.mant_dig; // ensure diff!=0, cope with INF.
X diff = fabs(x - y); X diff = fabs(x - y);
@ -3518,16 +3527,25 @@ int feqrel(X)(X x, X y) @trusted pure nothrow
// always 1 lower than we want, except that if bitsdiff==0, // always 1 lower than we want, except that if bitsdiff==0,
// they could have 0 or 1 bits in common. // they could have 0 or 1 bits in common.
static if (X.mant_dig==64 || X.mant_dig==113) { // real80 or quadruple static if (X.mant_dig == 64 || X.mant_dig == 113)
{ // real80 or quadruple
int bitsdiff = ( ((pa[F.EXPPOS_SHORT] & F.EXPMASK) int bitsdiff = ( ((pa[F.EXPPOS_SHORT] & F.EXPMASK)
+ (pb[F.EXPPOS_SHORT] & F.EXPMASK) - 1) >> 1) + (pb[F.EXPPOS_SHORT] & F.EXPMASK) - 1) >> 1)
- pd[F.EXPPOS_SHORT]; - pd[F.EXPPOS_SHORT];
} else static if (X.mant_dig==53) { // double }
else static if (X.mant_dig == double.mant_dig)
{ // double
int bitsdiff = (( ((pa[F.EXPPOS_SHORT]&0x7FF0) int bitsdiff = (( ((pa[F.EXPPOS_SHORT]&0x7FF0)
+ (pb[F.EXPPOS_SHORT]&0x7FF0)-0x10)>>1) + (pb[F.EXPPOS_SHORT]&0x7FF0)-0x10)>>1)
- (pd[F.EXPPOS_SHORT]&0x7FF0))>>4; - (pd[F.EXPPOS_SHORT]&0x7FF0))>>4;
} }
if (pd[F.EXPPOS_SHORT] == 0) else static if (X.mant_dig == float.mant_dig)
{ // float
int bitsdiff = (( ((pa[F.EXPPOS_SHORT]&0x7F80)
+ (pb[F.EXPPOS_SHORT]&0x7F80)-0x80)>>1)
- (pd[F.EXPPOS_SHORT]&0x7F80))>>7;
}
if ( (pd[F.EXPPOS_SHORT] & F.EXPMASK) == 0)
{ // Difference is subnormal { // Difference is subnormal
// For subnormals, we need to add the number of zeros that // For subnormals, we need to add the number of zeros that
// lie at the start of diff's significand. // lie at the start of diff's significand.
@ -3540,11 +3558,15 @@ int feqrel(X)(X x, X y) @trusted pure nothrow
return bitsdiff + 1; // add the 1 we subtracted before return bitsdiff + 1; // add the 1 we subtracted before
// Avoid out-by-1 errors when factor is almost 2. // Avoid out-by-1 errors when factor is almost 2.
static if (X.mant_dig==64 || X.mant_dig==113) { // real80 or quadruple static if (X.mant_dig == 64 || X.mant_dig == 113)
{ // real80 or quadruple
return (bitsdiff == 0) ? (pa[F.EXPPOS_SHORT] == pb[F.EXPPOS_SHORT]) : 0; return (bitsdiff == 0) ? (pa[F.EXPPOS_SHORT] == pb[F.EXPPOS_SHORT]) : 0;
} else static if (X.mant_dig==53) { // double }
else static if (X.mant_dig == double.mant_dig || X.mant_dig == float.mant_dig)
{
if (bitsdiff == 0 if (bitsdiff == 0
&& !((pa[F.EXPPOS_SHORT] ^ pb[F.EXPPOS_SHORT])& F.EXPMASK)) { && !((pa[F.EXPPOS_SHORT] ^ pb[F.EXPPOS_SHORT]) & F.EXPMASK))
{
return 1; return 1;
} else return 0; } else return 0;
} }
@ -3553,53 +3575,55 @@ int feqrel(X)(X x, X y) @trusted pure nothrow
unittest unittest
{ {
// Exact equality void testFeqrel(F)()
assert(feqrel(real.max,real.max)==real.mant_dig); {
assert(feqrel(0.0L,0.0L)==real.mant_dig); // Exact equality
assert(feqrel(7.1824L,7.1824L)==real.mant_dig); assert(feqrel(F.max, F.max) == F.mant_dig);
assert(feqrel(real.infinity,real.infinity)==real.mant_dig); assert(feqrel!(F)(0.0, 0.0) == F.mant_dig);
assert(feqrel(F.infinity, F.infinity) == F.mant_dig);
// a few bits away from exact equality // a few bits away from exact equality
real w=1; F w=1;
for (int i=1; i<real.mant_dig-1; ++i) { for (int i = 1; i < F.mant_dig - 1; ++i)
assert(feqrel(1+w*real.epsilon,1.0L)==real.mant_dig-i); {
assert(feqrel(1-w*real.epsilon,1.0L)==real.mant_dig-i); assert(feqrel!(F)(1.0 + w * F.epsilon, 1.0) == F.mant_dig-i);
assert(feqrel(1.0L,1+(w-1)*real.epsilon)==real.mant_dig-i+1); assert(feqrel!(F)(1.0 - w * F.epsilon, 1.0) == F.mant_dig-i);
w*=2; assert(feqrel!(F)(1.0, 1 + (w-1) * F.epsilon) == F.mant_dig - i + 1);
} w*=2;
assert(feqrel(1.5+real.epsilon,1.5L)==real.mant_dig-1); }
assert(feqrel(1.5-real.epsilon,1.5L)==real.mant_dig-1);
assert(feqrel(1.5-real.epsilon,1.5+real.epsilon)==real.mant_dig-2);
version(X86_64) assert(feqrel!(F)(1.5+F.epsilon, 1.5) == F.mant_dig-1);
{ assert(feqrel!(F)(1.5-F.epsilon, 1.5) == F.mant_dig-1);
pragma(msg, "test disabled, see bug 5628"); assert(feqrel!(F)(1.5-F.epsilon, 1.5+F.epsilon) == F.mant_dig-2);
}
else
{
assert(feqrel(real.min_normal/8,real.min_normal/17)==3);
}
// Numbers that are close
assert(feqrel(0x1.Bp+84, 0x1.B8p+84)==5);
assert(feqrel(0x1.8p+10, 0x1.Cp+10)==2);
assert(feqrel(1.5*(1-real.epsilon), 1.0L)==2);
assert(feqrel(1.5, 1.0)==1);
assert(feqrel(2*(1-real.epsilon), 1.0L)==1);
// Factors of 2 // Numbers that are close
assert(feqrel(real.max,real.infinity)==0); assert(feqrel!(F)(0x1.Bp+84, 0x1.B8p+84) == 5);
assert(feqrel(2*(1-real.epsilon), 1.0L)==1); assert(feqrel!(F)(0x1.8p+10, 0x1.Cp+10) == 2);
assert(feqrel(1.0, 2.0)==0); assert(feqrel!(F)(1.5 * (1 - F.epsilon), 1.0L) == 2);
assert(feqrel(4.0, 1.0)==0); assert(feqrel!(F)(1.5, 1.0) == 1);
assert(feqrel!(F)(2 * (1 - F.epsilon), 1.0L) == 1);
// Extreme inequality // Factors of 2
assert(feqrel(real.nan,real.nan)==0); assert(feqrel(F.max, F.infinity) == 0);
assert(feqrel(0.0L,-real.nan)==0); assert(feqrel!(F)(2 * (1 - F.epsilon), 1.0L) == 1);
assert(feqrel(real.nan,real.infinity)==0); assert(feqrel!(F)(1.0, 2.0) == 0);
assert(feqrel(real.infinity,-real.infinity)==0); assert(feqrel!(F)(4.0, 1.0) == 0);
assert(feqrel(-real.max,real.infinity)==0);
assert(feqrel(real.max,-real.max)==0); // Extreme inequality
assert(feqrel(F.nan, F.nan) == 0);
assert(feqrel!(F)(0.0L, -F.nan) == 0);
assert(feqrel(F.nan, F.infinity) == 0);
assert(feqrel(F.infinity, -F.infinity) == 0);
assert(feqrel(F.max, -F.max) == 0);
}
assert(feqrel(7.1824L, 7.1824L) == real.mant_dig);
assert(feqrel(real.min_normal / 8, real.min_normal / 17) == 3);
testFeqrel!(real)();
testFeqrel!(double)();
testFeqrel!(float)();
} }
package: // Not public yet package: // Not public yet