test: add float example from the Madrid workshop

Author: jodavies

check/features.frm

@@ -595,6 +595,82 @@ assert result("F", 3) =~ expr("
      & x1**2*x2 + x1**3
 ")
 *--#] Format_noreset_linelen :
+*--#[ Float_1 :
+#-
+* Example from the FORM Workshop (Madrid 2023) slides, also in the manual.
+
+#StartFloat 500,15
+
+Local F1 =
+	-mzv_(8,1,1,5)
+	+29056868/39414375*mzv_(2)^6*mzv_(3)
+	-47576/40425*mzv_(2)^5*mzv_(5)
+	-163291/18375*mzv_(2)^4*mzv_(7)
+	-4/105*mzv_(2)^3*mzv_(3)^3
+	-450797/11025*mzv_(2)^3*mzv_(9)
+	+7/5*mzv_(2)^2*mzv_(3)^2*mzv_(5)
+	+16/25*mzv_(2)^2*mzv_(3)*mzv_(5,3)
+	+454049/1400*mzv_(2)^2*mzv_(11)
+	-16/25*mzv_(2)^2*mzv_(5,3,3)
+	+3*mzv_(2)*mzv_(3)^2*mzv_(7)
+	+61/14*mzv_(2)*mzv_(3)*mzv_(5)^2
+	+2/7*mzv_(2)*mzv_(3)*mzv_(7,3)
+	+2172853/420*mzv_(2)*mzv_(13)
+	-2/7*mzv_(2)*mzv_(7,3,3)
+	+1/7*mzv_(2)*mzv_(5,5,3)
+	-33/4*mzv_(3)^2*mzv_(9)
+	-133/6*mzv_(3)*mzv_(5)*mzv_(7)
+	-25/9*mzv_(3)*mzv_(9,3)
+	-244/105*mzv_(5)^3
+	-359/105*mzv_(5)*mzv_(7,3)
+	+3/10*mzv_(7)*mzv_(5,3)
+	+89/18*mzv_(9,3,3)
+	+569/105*mzv_(7,3,5);
+L F2 = mzv_(15);
+Evaluate mzv_;
+Print;
+.sort
+
+Skip F1,F2;
+Local X = F1/F2;
+ToRational;
+Print;
+.sort
+
+#EndFloat
+Local G1 = F1;
+Local G2 = F2;
+
+Print G1,G2;
+.end
+#pend_if wordsize == 2
+assert succeeded?
+assert result("X") =~ expr("229903169/25200")
+assert stdout =~ exact_pattern(<<'EOF')
+   F1 =
+      9.1234206877960755900164875575406726239325002222490534540605137258846994\
+      916348297032751308227224952419629422497720599224543719959652966613231560\
+      6913926e+03;
+EOF
+assert stdout =~ exact_pattern(<<'EOF')
+   F2 =
+      1.0000305882363070204935517285106450625876279487068581775065699328933322\
+      671563422795730723343470175484943669684442492832530297757588781904321794\
+      40477e+00;
+EOF
+assert stdout =~ exact_pattern(<<'EOF')
+   G1 =
+      float_(10,10,1,225649930152063087544280124519603661924016376904153173222\
+      961313295752588365049496190204609112667217257624737508104376810254484309\
+      3830597279756558899541412580219255737022507716035);
+EOF
+assert stdout =~ exact_pattern(<<'EOF')
+   G2 =
+      float_(10,10,1,247337966873870703631573653423368526098272821023387457752\
+      643030990710929556575503489173572446024607642191456056189912528713904095\
+      704444384800390830056125051605311704862654126);
+EOF
+*--#] Float_1 :
 *--#[ evaluate_symbol :
 #-
 #StartFloat 64

doc/manual/float.tex

@@ -97,14 +97,14 @@ \chapter{Floating point}
     .sort
 
    F1 =
-      9.1234206877960755900164875575406726239325002222490534540605137258846994\
-      916348297032751308227224952419629422497720599224543719959652966613231560\
-      6913925597e+0;
+       9.1234206877960755900164875575406726239325002222490534540605137258846994\
+       916348297032751308227224952419629422497720599224543719959652966613231560\
+       6913926e+03;
 
    F2 =
-      1.0000305882363070204935517285106450625876279487068581775065699328933322\
-      671563422795730723343470175484943669684442492832530297757588781904321794\
-      4047700034253;
+       1.0000305882363070204935517285106450625876279487068581775065699328933322\
+       671563422795730723343470175484943669684442492832530297757588781904321794\
+       40477e+00;
 
     Skip F1,F2;
     L	X = F1/F2;
@@ -122,10 +122,10 @@ \chapter{Floating point}
 maximum weight for MZVs and Euler sums. The functions are only evaluated 
 when the proper command is given. In the second module we divide the 
 numbers and convert the result to a rational. It is a good idea to try this 
-with various precisions to see whether this is stable. With 100 bits the 
+with various precisions to see whether this is stable. With 60 bits the 
 final answer would be
 \begin{verbatim}
-    24136499874427167202968388241342/2645634679509635700210944273;
+    145537942402475031/15952490572234;
 \end{verbatim}
 while at 150 bits we have already the same answer as with 500 bits. The 
 fraction that is obtained by this program can be proven to be correct.