Replaced my trig functions with mpmath package.

Fascinatingly, I still have discrepancies between a well-tested
high-precision math package 'mpmath' and math.sin, math.cos.
This happens running on my own hardware, which makes me think
there is something wrong with my system, not GitHub's backend.

Here is output comparing mpmath.sin with math.sin,
and mpmath.cos with math.cos.

PY Trigonometry: maxdiff=3.32359e-12, worst angle = 719.9 degrees: PASS

I'm going to commit this to try it on other hardware/OS combinations.

generate/dontrig.py

@@ -21,7 +21,7 @@ def xsin(angle:float) -> float:
         prev = sum
         sum += term
         if Debug:
-            print('xsin: n={:02d}  term={:24.16e}  sum={:20.16f}  fact={:g}  diff={:24.16e}'.format(n, term, sum, fact, sum-prev))
+            print('xsin: n={:02d}  term={:24.16e}  sum={:20.16f}  diff={:24.16e}'.format(n, term, sum, sum-prev))
         if prev == sum:
             return sum
         term *= numerator / ((n+1) * (n+2))
@@ -40,7 +40,7 @@ def xcos(angle:float) -> float:
         prev = sum
         sum += term
         if Debug:
-            print('xcos: n={:02d}  term={:24.16e}  sum={:20.16f}   fact={:g}'.format(n, term, sum, fact))
+            print('xcos: n={:02d}  term={:24.16e}  sum={:20.16f}  diff={:24.16e}'.format(n, term, sum, sum-prev))
         if prev == sum:
             return sum
         term *= numerator / ((n+1) * (n+2))

generate/test.py

@@ -6,10 +6,19 @@
 from itertools import chain
 sys.path.append('../source/python')
 import astronomy
-from dontrig import xcos, xsin
+#from dontrig import xcos, xsin
+import mpmath
 
 #-----------------------------------------------------------------------------------------------------------
 
+mpmath.dps = 30
+
+def xsin(angle: float) -> float:
+    return float(mpmath.sin(angle))
+
+def xcos(angle: float) -> float:
+    return float(mpmath.cos(angle))
+
 if os.getenv('GITHUB_JOB'):
     # Super weird hack: re-define _sin and _cos to have exactly reproducible values.
     print('test.py - NOTE: Detected GitHub job. Replacing trig functions...')
@@ -3375,6 +3384,7 @@ def Trigonometry() -> int:
     tolerance = 3.5e-12     # Not very good yet!
     maxDiff = 0.0
     inFileName = 'trigonometry/trig.txt'
+    worstDeg = None
     with open(inFileName, 'rt') as infile:
         lnum = 0
         for line in infile:
@@ -3392,13 +3402,16 @@ def Trigonometry() -> int:
             sinCalc = xsin(rad)
             cosDiff = abs(cosCalc - cosCorrect)
             sinDiff = abs(sinCalc - sinCorrect)
-            maxDiff = max(maxDiff, cosDiff, sinDiff)
+            diff = max(cosDiff, sinDiff)
+            if diff > maxDiff:
+                maxDiff = diff
+                worstDeg = deg
             if (cosDiff > tolerance) or (sinDiff > tolerance):
                 return Fail(
                     'Trigonometry({:s} line {:d})'.format(inFileName, lnum),
                     'EXCESS ERROR - deg={:0.1f}, cosDiff={:g}, sinDiff={:g}'.format(deg, cosDiff, sinDiff)
                 )
-    return Pass('Trigonometry: maxdiff={:g}'.format(maxDiff))
+    return Pass('Trigonometry: maxdiff={:g}, worst angle = {:0.1f} degrees'.format(maxDiff, worstDeg))
 
 #-----------------------------------------------------------------------------------------------------------