Merge pull request #398 from TA-Lib/fix/395-cheap

perf(cci,correl): test the divisor instead of reformulating around it (#395)

Author: mario4tier

CHANGELOG.md

@@ -114,7 +114,7 @@ See [github commits](https://github.com/TA-Lib/ta-lib/commits) for complete list
 - (#253) Fix many TA_IS_ZERO vs TA_IS_ZERO_SCALED choices. Numerically better for edge cases, like very small inputs (<10e-8) or mostly flat input prices.
 - (#390) STOCH and STOCHF returned `inf` or `NaN` while reporting success, for prices near the bottom of the double range. A close sitting on the window high now comes out as exactly 100.
 - (#390) KAMA could return values outside the range of the prices it was smoothing, and ER values above 1. Both come from the same efficiency ratio exceeding its own maximum when floating-point drift left the running sum of price movement below the net move it bounds. The ratio is now clamped, making ER a hard 0..1.
-- (#395) CCI returned `+/-Inf` while reporting success, and CORREL returned `NaN` or a perfect +/-1 correlation from a window that had none, for prices near the bottom of the double range. Both now divide by the value their guard actually tests, so they stay accurate to the last bits at every price scale.
+- (#395) CCI returned `+/-Inf` while reporting success, and CORREL returned `NaN` or a perfect +/-1 correlation from a window that had none, for prices near the bottom of the double range. Both now test the divisor itself, and answer such a window with 0 like any other degenerate one. Values are unchanged everywhere the old code returned a number.
 - (#395) WILLR could return values outside its documented [-100, 0] range, and answered 0 - the value meaning a close at the period high - for a close sitting on the period low whenever the window's high-low range was very small. A close on the period low now comes out as exactly -100, the range is guaranteed even for a close outside its own bar, and a window flat to within rounding of its own prices answers 0, as STOCH and STOCHF already did.
 
 ## [0.7.1] 2026-07-03

src/ta_func/ta_CCI.c

@@ -67,9 +67,10 @@
  *  082326 MF,CC  Fix #253. Scale that flatness test to the window's own price
  *                level: the fixed band zeroed the whole output for any
  *                instrument quoted small enough to fall under it.
- *  090626 MF,CC  Fix #395. Divide by the mean deviation, scale after: the
- *                pre-scaled `0.015*tempReal2` underflowed to 0.0 on a
- *                denormal price that the guard still called "not flat".
+ *  090626 MF,CC  Fix #395. Test the divisor itself, not just the deviation it
+ *                scales: `0.015*tempReal2` underflows to 0.0 on a denormal
+ *                price the deviation's own band still calls "not flat", and
+ *                the division returned +/-Inf under TA_SUCCESS.
  */
 
 TA_LIB_API int TA_CCI_Lookback( int optInTimePeriod )
@@ -206,13 +207,14 @@ TA_LIB_API TA_RetCode TA_CCI( int    startIdx,
       tempReal2 /= optInTimePeriod;
       /* And finally, the CCI... */
       tempReal = lastValue - theAverage;
-      /* Divide by the mean deviation itself and scale after: the guard has to
-       * test the very expression the division uses, or a scaling step can
-       * carry a guarded-non-zero into a zero divisor. The band is relative and
-       * the underflow of the 0.015 product is absolute, so no band on the
-       * deviation can cover the product.
+      /* The third test is the divisor itself, and it is not implied by the
+       * second: the deviation's band is RELATIVE and the product's underflow is
+       * ABSOLUTE, so below ~1.6e-308 the band admits a deviation whose scaled
+       * copy is exactly 0.0 (issue #395). An exact test, not a band -- the
+       * flatness question is already answered above, and this one is only
+       * asking whether the value the division uses exists.
        *
-       * Both tests are relative to the window's own price level (issue #253).
+       * The first two tests are relative to the window's own price level (#253).
        * They ask "is this window flat?", and flatness is a property of the
        * prices relative to each other -- but a deviation carries the quote
        * unit, so the fixed TA_IS_ZERO band these used to be answered "flat" for
@@ -222,9 +224,9 @@ TA_LIB_API TA_RetCode TA_CCI( int    startIdx,
        * average, which is what it was widened for in the first place (#7).
        */
       tempReal3 = fabs(theAverage);
-      if( !TA_IS_ZERO_SCALED(tempReal, tempReal3) && !TA_IS_ZERO_SCALED(tempReal2, tempReal3) )
+      if( !TA_IS_ZERO_SCALED(tempReal, tempReal3) && !TA_IS_ZERO_SCALED(tempReal2, tempReal3) && 0.015 * tempReal2 != 0.0 )
       {
-         outReal[outIdx++] = tempReal / tempReal2 / 0.015;
+         outReal[outIdx++] = tempReal / (0.015 * tempReal2);
       } else 
       {
          outReal[outIdx++] = 0.0;
@@ -342,9 +344,9 @@ TA_RetCode TA_S_CCI( int    startIdx,
       tempReal2 /= optInTimePeriod;
       tempReal = lastValue - theAverage;
       tempReal3 = fabs(theAverage);
-      if( !TA_IS_ZERO_SCALED(tempReal, tempReal3) && !TA_IS_ZERO_SCALED(tempReal2, tempReal3) )
+      if( !TA_IS_ZERO_SCALED(tempReal, tempReal3) && !TA_IS_ZERO_SCALED(tempReal2, tempReal3) && 0.015 * tempReal2 != 0.0 )
       {
-         outReal[outIdx++] = tempReal / tempReal2 / 0.015;
+         outReal[outIdx++] = tempReal / (0.015 * tempReal2);
       } else 
       {
          outReal[outIdx++] = 0.0;
@@ -412,13 +414,14 @@ static void TA_CCI_StepImpl( struct TA_CCI_Stream *sp, double inHigh, double inL
    tempReal2 /= sp->optInTimePeriod;
    /* And finally, the CCI... */
    tempReal = lastValue - theAverage;
-   /* Divide by the mean deviation itself and scale after: the guard has to
-    * test the very expression the division uses, or a scaling step can
-    * carry a guarded-non-zero into a zero divisor. The band is relative and
-    * the underflow of the 0.015 product is absolute, so no band on the
-    * deviation can cover the product.
+   /* The third test is the divisor itself, and it is not implied by the
+    * second: the deviation's band is RELATIVE and the product's underflow is
+    * ABSOLUTE, so below ~1.6e-308 the band admits a deviation whose scaled
+    * copy is exactly 0.0 (issue #395). An exact test, not a band -- the
+    * flatness question is already answered above, and this one is only
+    * asking whether the value the division uses exists.
     *
-    * Both tests are relative to the window's own price level (issue #253).
+    * The first two tests are relative to the window's own price level (#253).
     * They ask "is this window flat?", and flatness is a property of the
     * prices relative to each other -- but a deviation carries the quote
     * unit, so the fixed TA_IS_ZERO band these used to be answered "flat" for
@@ -428,9 +431,9 @@ static void TA_CCI_StepImpl( struct TA_CCI_Stream *sp, double inHigh, double inL
     * average, which is what it was widened for in the first place (#7).
     */
    tempReal3 = fabs(theAverage);
-   if( !TA_IS_ZERO_SCALED(tempReal, tempReal3) && !TA_IS_ZERO_SCALED(tempReal2, tempReal3) )
+   if( !TA_IS_ZERO_SCALED(tempReal, tempReal3) && !TA_IS_ZERO_SCALED(tempReal2, tempReal3) && 0.015 * tempReal2 != 0.0 )
    {
-      *outReal= tempReal / tempReal2 / 0.015;
+      *outReal= tempReal / (0.015 * tempReal2);
    } else 
    {
       *outReal= 0.0;
@@ -562,13 +565,14 @@ static TA_RetCode TA_CCI_OpenImpl( struct TA_CCI_Stream **stream, const double i
          tempReal2 /= optInTimePeriod;
          /* And finally, the CCI... */
          tempReal = lastValue - theAverage;
-         /* Divide by the mean deviation itself and scale after: the guard has to
-          * test the very expression the division uses, or a scaling step can
-          * carry a guarded-non-zero into a zero divisor. The band is relative and
-          * the underflow of the 0.015 product is absolute, so no band on the
-          * deviation can cover the product.
+         /* The third test is the divisor itself, and it is not implied by the
+          * second: the deviation's band is RELATIVE and the product's underflow is
+          * ABSOLUTE, so below ~1.6e-308 the band admits a deviation whose scaled
+          * copy is exactly 0.0 (issue #395). An exact test, not a band -- the
+          * flatness question is already answered above, and this one is only
+          * asking whether the value the division uses exists.
           *
-          * Both tests are relative to the window's own price level (issue #253).
+          * The first two tests are relative to the window's own price level (#253).
           * They ask "is this window flat?", and flatness is a property of the
           * prices relative to each other -- but a deviation carries the quote
           * unit, so the fixed TA_IS_ZERO band these used to be answered "flat" for
@@ -578,9 +582,9 @@ static TA_RetCode TA_CCI_OpenImpl( struct TA_CCI_Stream **stream, const double i
           * average, which is what it was widened for in the first place (#7).
           */
          tempReal3 = fabs(theAverage);
-         if( !TA_IS_ZERO_SCALED(tempReal, tempReal3) && !TA_IS_ZERO_SCALED(tempReal2, tempReal3) )
+         if( !TA_IS_ZERO_SCALED(tempReal, tempReal3) && !TA_IS_ZERO_SCALED(tempReal2, tempReal3) && 0.015 * tempReal2 != 0.0 )
          {
-            outReal[outIdx++ * outStride] = tempReal / tempReal2 / 0.015;
+            outReal[outIdx++ * outStride] = tempReal / (0.015 * tempReal2);
          } else 
          {
             outReal[outIdx++ * outStride] = 0.0;
@@ -704,13 +708,14 @@ TA_LIB_API TA_RetCode TA_CCI_Peek( const TA_CCI_Stream *stream, double inHigh, d
    tempReal2 /= sp->optInTimePeriod;
    /* And finally, the CCI... */
    tempReal = lastValue - theAverage;
-   /* Divide by the mean deviation itself and scale after: the guard has to
-    * test the very expression the division uses, or a scaling step can
-    * carry a guarded-non-zero into a zero divisor. The band is relative and
-    * the underflow of the 0.015 product is absolute, so no band on the
-    * deviation can cover the product.
+   /* The third test is the divisor itself, and it is not implied by the
+    * second: the deviation's band is RELATIVE and the product's underflow is
+    * ABSOLUTE, so below ~1.6e-308 the band admits a deviation whose scaled
+    * copy is exactly 0.0 (issue #395). An exact test, not a band -- the
+    * flatness question is already answered above, and this one is only
+    * asking whether the value the division uses exists.
     *
-    * Both tests are relative to the window's own price level (issue #253).
+    * The first two tests are relative to the window's own price level (#253).
     * They ask "is this window flat?", and flatness is a property of the
     * prices relative to each other -- but a deviation carries the quote
     * unit, so the fixed TA_IS_ZERO band these used to be answered "flat" for
@@ -720,9 +725,9 @@ TA_LIB_API TA_RetCode TA_CCI_Peek( const TA_CCI_Stream *stream, double inHigh, d
     * average, which is what it was widened for in the first place (#7).
     */
    tempReal3 = fabs(theAverage);
-   if( !TA_IS_ZERO_SCALED(tempReal, tempReal3) && !TA_IS_ZERO_SCALED(tempReal2, tempReal3) )
+   if( !TA_IS_ZERO_SCALED(tempReal, tempReal3) && !TA_IS_ZERO_SCALED(tempReal2, tempReal3) && 0.015 * tempReal2 != 0.0 )
    {
-      *outReal= tempReal / tempReal2 / 0.015;
+      *outReal= tempReal / (0.015 * tempReal2);
    } else 
    {
       *outReal= 0.0;

src/ta_func/ta_CORREL.c

@@ -60,11 +60,10 @@
  *  082326 MF    Fix #242. Cancellation-free sums (shifted data + reseed, as
  *               TA_VAR does since #118), per-factor degeneracy test and a
  *               range clamp.
- *  090626 MF,CC Fix #395. A root of each guarded factor, not a root of their
- *               product: sqrt(ssX*ssY) left the double range at both ends
- *               while ssX and ssY were still ordinary normals, returning NaN
- *               under TA_SUCCESS and a perfect correlation from a degenerate
- *               window.
+ *  090626 MF,CC Fix #395. Test the product too: it underflows to 0.0 while ssX
+ *               and ssY are still ordinary normals, and the divide then
+ *               returned NaN under TA_SUCCESS -- which the range clamp cannot
+ *               catch -- or a perfect correlation from a degenerate window.
  */
 
 TA_LIB_API int TA_CORREL_Lookback( int optInTimePeriod )
@@ -301,13 +300,23 @@ TA_LIB_API TA_RetCode TA_CORREL( int    startIdx,
        * is also the cheaper test: the two fabs() cost ~7% of this function's
        * runtime, and buy a wrong answer.
        *
-       * A root of each guarded factor, never a root of their product: that
-       * product leaves the double range at BOTH ends while ssX and ssY are
-       * still ordinary normals, which no test of the factors can see (#395).
+       * sqrt(ssX*ssY) rather than sqrt(ssX)*sqrt(ssY): the guard has already
+       * established both are positive, so the product needs no protection from
+       * a negative operand, and the second square root is worth ~14% of this
+       * function's runtime (measured, #395).
+       *
+       * The product is then tested on its own, because neither factor's test
+       * implies it: at that fourth power it underflows to exactly 0.0 while ssX
+       * and ssY are still ordinary normals (#395). A zero divisor there gives
+       * NaN, which the clamp below does NOT catch -- NaN fails both comparisons
+       * -- or an infinity the clamp rewrites into a perfect correlation. Exact,
+       * not a band: an absolute band on the product is the #253 defect at a new
+       * address. At the other end the product overflows to +Inf and the quotient
+       * is 0.0, the degenerate answer anyway.
        */
-      if( ssX > 0.00000000000001 * sumX2 && ssY > 0.00000000000001 * sumY2 )
+      if( ssX > 0.00000000000001 * sumX2 && ssY > 0.00000000000001 * sumY2 && ssX * ssY > 0.0 )
       {
-         tempReal = spXY / (sqrt(ssX) * sqrt(ssY));
+         tempReal = spXY / sqrt(ssX * ssY);
          /* A correlation coefficient cannot leave [-1,1]; rounding in the
           * three sums can still put it a few ulp outside.
           */
@@ -482,9 +491,9 @@ TA_RetCode TA_S_CORREL( int    startIdx,
       trailingX = (double)inReal0[trailingIdx] - shiftX;
       trailingY = (double)inReal1[trailingIdx] - shiftY;
       trailingIdx += 1;
-      if( ssX > 0.00000000000001 * sumX2 && ssY > 0.00000000000001 * sumY2 )
+      if( ssX > 0.00000000000001 * sumX2 && ssY > 0.00000000000001 * sumY2 && ssX * ssY > 0.0 )
       {
-         tempReal = spXY / (sqrt(ssX) * sqrt(ssY));
+         tempReal = spXY / sqrt(ssX * ssY);
          if( tempReal > 1.0 )
          {
             tempReal = 1.0;
@@ -695,13 +704,23 @@ static void TA_CORREL_StepImpl( struct TA_CORREL_Stream *sp, double inReal0, dou
     * is also the cheaper test: the two fabs() cost ~7% of this function's
     * runtime, and buy a wrong answer.
     *
-    * A root of each guarded factor, never a root of their product: that
-    * product leaves the double range at BOTH ends while ssX and ssY are
-    * still ordinary normals, which no test of the factors can see (#395).
+    * sqrt(ssX*ssY) rather than sqrt(ssX)*sqrt(ssY): the guard has already
+    * established both are positive, so the product needs no protection from
+    * a negative operand, and the second square root is worth ~14% of this
+    * function's runtime (measured, #395).
+    *
+    * The product is then tested on its own, because neither factor's test
+    * implies it: at that fourth power it underflows to exactly 0.0 while ssX
+    * and ssY are still ordinary normals (#395). A zero divisor there gives
+    * NaN, which the clamp below does NOT catch -- NaN fails both comparisons
+    * -- or an infinity the clamp rewrites into a perfect correlation. Exact,
+    * not a band: an absolute band on the product is the #253 defect at a new
+    * address. At the other end the product overflows to +Inf and the quotient
+    * is 0.0, the degenerate answer anyway.
     */
-   if( ssX > 0.00000000000001 * sumX2 && ssY > 0.00000000000001 * sumY2 )
+   if( ssX > 0.00000000000001 * sumX2 && ssY > 0.00000000000001 * sumY2 && ssX * ssY > 0.0 )
    {
-      tempReal = spXY / (sqrt(ssX) * sqrt(ssY));
+      tempReal = spXY / sqrt(ssX * ssY);
       /* A correlation coefficient cannot leave [-1,1]; rounding in the
        * three sums can still put it a few ulp outside.
        */
@@ -955,13 +974,23 @@ static TA_RetCode TA_CORREL_OpenImpl( struct TA_CORREL_Stream **stream, const do
           * is also the cheaper test: the two fabs() cost ~7% of this function's
           * runtime, and buy a wrong answer.
           *
-          * A root of each guarded factor, never a root of their product: that
-          * product leaves the double range at BOTH ends while ssX and ssY are
-          * still ordinary normals, which no test of the factors can see (#395).
+          * sqrt(ssX*ssY) rather than sqrt(ssX)*sqrt(ssY): the guard has already
+          * established both are positive, so the product needs no protection from
+          * a negative operand, and the second square root is worth ~14% of this
+          * function's runtime (measured, #395).
+          *
+          * The product is then tested on its own, because neither factor's test
+          * implies it: at that fourth power it underflows to exactly 0.0 while ssX
+          * and ssY are still ordinary normals (#395). A zero divisor there gives
+          * NaN, which the clamp below does NOT catch -- NaN fails both comparisons
+          * -- or an infinity the clamp rewrites into a perfect correlation. Exact,
+          * not a band: an absolute band on the product is the #253 defect at a new
+          * address. At the other end the product overflows to +Inf and the quotient
+          * is 0.0, the degenerate answer anyway.
           */
-         if( ssX > 0.00000000000001 * sumX2 && ssY > 0.00000000000001 * sumY2 )
+         if( ssX > 0.00000000000001 * sumX2 && ssY > 0.00000000000001 * sumY2 && ssX * ssY > 0.0 )
          {
-            tempReal = spXY / (sqrt(ssX) * sqrt(ssY));
+            tempReal = spXY / sqrt(ssX * ssY);
             /* A correlation coefficient cannot leave [-1,1]; rounding in the
              * three sums can still put it a few ulp outside.
              */
@@ -1246,13 +1275,23 @@ TA_LIB_API TA_RetCode TA_CORREL_Peek( const TA_CORREL_Stream *stream, double inR
     * is also the cheaper test: the two fabs() cost ~7% of this function's
     * runtime, and buy a wrong answer.
     *
-    * A root of each guarded factor, never a root of their product: that
-    * product leaves the double range at BOTH ends while ssX and ssY are
-    * still ordinary normals, which no test of the factors can see (#395).
+    * sqrt(ssX*ssY) rather than sqrt(ssX)*sqrt(ssY): the guard has already
+    * established both are positive, so the product needs no protection from
+    * a negative operand, and the second square root is worth ~14% of this
+    * function's runtime (measured, #395).
+    *
+    * The product is then tested on its own, because neither factor's test
+    * implies it: at that fourth power it underflows to exactly 0.0 while ssX
+    * and ssY are still ordinary normals (#395). A zero divisor there gives
+    * NaN, which the clamp below does NOT catch -- NaN fails both comparisons
+    * -- or an infinity the clamp rewrites into a perfect correlation. Exact,
+    * not a band: an absolute band on the product is the #253 defect at a new
+    * address. At the other end the product overflows to +Inf and the quotient
+    * is 0.0, the degenerate answer anyway.
     */
-   if( ssX > 0.00000000000001 * sumX2 && ssY > 0.00000000000001 * sumY2 )
+   if( ssX > 0.00000000000001 * sumX2 && ssY > 0.00000000000001 * sumY2 && ssX * ssY > 0.0 )
    {
-      tempReal = spXY / (sqrt(ssX) * sqrt(ssY));
+      tempReal = spXY / sqrt(ssX * ssY);
       /* A correlation coefficient cannot leave [-1,1]; rounding in the
        * three sums can still put it a few ulp outside.
        */