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