test_gaulegf1D.c running 
calling gaulegf(-1.000000, 2.000000, x, w, n) 
n=1, equivalent h=3.000000 
x[1]=0.500000, w[1]=3.000000 

calling gaulegf(-1.000000, 2.000000, x, w, n) 
n=2, equivalent h=1.500000 
x[1]=-0.366025, w[1]=1.500000 
x[2]=1.366025, w[2]=1.500000 

calling gaulegf(-1.000000, 2.000000, x, w, n) 
n=3, equivalent h=1.000000 
x[1]=-0.661895, w[1]=0.833333 
x[2]=0.500000, w[2]=1.333333 
x[3]=1.661895, w[3]=0.833333 

calling gaulegf(-1.000000, 2.000000, x, w, n) 
n=4, equivalent h=0.750000 
x[1]=-0.791704, w[1]=0.521782 
x[2]=-0.009972, w[2]=0.978218 
x[3]=1.009972, w[3]=0.978218 
x[4]=1.791704, w[4]=0.521782 

calling gaulegf(-1.000000, 2.000000, x, w, n) 
n=5, equivalent h=0.600000 
x[1]=-0.859270, w[1]=0.355390 
x[2]=-0.307704, w[2]=0.717943 
x[3]=0.500000, w[3]=0.853333 
x[4]=1.307704, w[4]=0.717943 
x[5]=1.859270, w[5]=0.355390 

f11(x)=x+2.0 
n=1, area=7.500000, exact=7.500000, error=0 
n=2, area=7.500000, exact=7.500000, error=-3.55271e-15 
n=3, area=7.500000, exact=7.500000, error=-2.22045e-14 
n=4, area=7.500000, exact=7.500000, error=-4.52971e-14 
n=5, area=7.500000, exact=7.500000, error=-5.50671e-14 

f21(x)=x*x+2.0*x+3.0 
n=1, area=12.750000, exact=15.000000, error=-2.25 
n=2, area=15.000000, exact=15.000000, error=-7.10543e-15 
n=3, area=15.000000, exact=15.000000, error=-4.9738e-14 
n=4, area=15.000000, exact=15.000000, error=-1.08358e-13 
n=5, area=15.000000, exact=15.000000, error=-1.35003e-13 

f31(x)=x*x*x+2.0*x*x+3.0*x+4.0 
n=1, area=18.375000, exact=26.250000, error=-7.875 
n=2, area=26.250000, exact=26.250000, error=-1.42109e-14 
n=3, area=26.250000, exact=26.250000, error=-9.59233e-14 
n=4, area=26.250000, exact=26.250000, error=-2.20268e-13 
n=5, area=26.250000, exact=26.250000, error=-2.77112e-13 

f41(x)=x*x*x*x+2.0*x*x*x+3.0*x*x+4.0*x+5.0 
n=1, area=24.187500, exact=44.100000, error=-19.9125 
n=2, area=42.750000, exact=44.100000, error=-1.35 
n=3, area=44.100000, exact=44.100000, error=-1.77636e-13 
n=4, area=44.100000, exact=44.100000, error=-4.33431e-13 
n=5, area=44.100000, exact=44.100000, error=-5.61329e-13 

fe1(x)=exp(x) 
n=1, area=4.946164, exact=7.021177, error=-2.07501 
n=2, area=6.919838, exact=7.021177, error=-0.101338 
n=3, area=7.019261, exact=7.021177, error=-0.00191535 
n=4, area=7.021157, exact=7.021177, error=-1.92899e-05 
n=5, area=7.021177, exact=7.021177, error=-1.2069e-07 

phi(x,2,3,xg) 
n=1, area=1.687500, exact=1.125000, error=0.5625 
n=2, area=1.125000, exact=1.125000, error=-4.44089e-16 
n=3, area=1.125000, exact=1.125000, error=-1.9984e-15 
n=4, area=1.125000, exact=1.125000, error=-2.44249e-15 
n=5, area=1.125000, exact=1.125000, error=-2.22045e-15 
n=6, area=1.125000, exact=1.125000, error=-4.21885e-15 
n=7, area=1.125000, exact=1.125000, error=-1.33227e-15 

phi(x,2,3,xg)*f11=x+2.0 
n=1, area=4.218750, exact=3.825000, error=0.39375 
n=2, area=4.500000, exact=3.825000, error=0.675 
n=3, area=3.825000, exact=3.825000, error=-1.02141e-14 
n=4, area=3.825000, exact=3.825000, error=-1.5099e-14 
n=5, area=3.825000, exact=3.825000, error=-1.37668e-14 
n=6, area=3.825000, exact=3.825000, error=-1.77636e-14 
n=7, area=3.825000, exact=3.825000, error=-8.43769e-15 

phi(x,2,3,xg)*f21=x*x+2.0*x+3.0 
n=1, area=7.171875, exact=8.325000, error=-1.15312 
n=2, area=10.687500, exact=8.325000, error=2.3625 
n=3, area=8.325000, exact=8.325000, error=-2.66454e-14 
n=4, area=8.325000, exact=8.325000, error=-4.08562e-14 
n=5, area=8.325000, exact=8.325000, error=-3.73035e-14 
n=6, area=8.325000, exact=8.325000, error=-4.26326e-14 
n=7, area=8.325000, exact=8.325000, error=-2.13163e-14 

phi(x,2,3,xg)*f31=x*x*x+2.0*x*x+3.0*x+4.0 
n=1, area=10.335938, exact=15.460714, error=-5.12478 
n=2, area=20.812500, exact=15.460714, error=5.35179 
n=3, area=15.851250, exact=15.460714, error=0.390536 
n=4, area=15.460714, exact=15.460714, error=2.85714e-07 
n=5, area=15.460714, exact=15.460714, error=2.85714e-07 
n=6, area=15.460714, exact=15.460714, error=2.85714e-07 
n=7, area=15.460714, exact=15.460714, error=2.85714e-07 

phi(x,2,3,xg)*f41=x*x*x*x+2.0*x*x*x+3.0*x*x+4.0*x+5.0 
n=1, area=13.605469, exact=26.373214, error=-12.7677 
n=2, area=36.281250, exact=26.373214, error=9.90804 
n=3, area=28.130625, exact=26.373214, error=1.75741 
n=4, area=26.373214, exact=26.373214, error=2.85714e-07 
n=5, area=26.373214, exact=26.373214, error=2.85714e-07 
n=6, area=26.373214, exact=26.373214, error=2.85714e-07 
n=7, area=26.373214, exact=26.373214, error=2.85714e-07 

phi(x,2,3,xg)*fe1=exp(x) 
n=1, area=2.782217, exact=4.262081, error=-1.47986 
n=2, area=5.738211, exact=4.262081, error=1.47613 
n=3, area=4.392371, exact=4.262081, error=0.13029 
n=4, area=4.265621, exact=4.262081, error=0.00354036 
n=5, area=4.262127, exact=4.262081, error=4.63262e-05 
n=6, area=4.262081, exact=4.262081, error=2.07438e-07 
n=7, area=4.262081, exact=4.262081, error=-1.4921e-07 

end of 'exact' being correct 

phi(x,3,5,xg) 
n=1, area=1.757813, exact=1.125000, error=0.632813 
n=2, area=0.086806, exact=1.125000, error=-1.03819 
n=3, area=0.520833, exact=1.125000, error=-0.604167 
n=4, area=0.520833, exact=1.125000, error=-0.604167 
n=5, area=0.520833, exact=1.125000, error=-0.604167 
n=6, area=0.520833, exact=1.125000, error=-0.604167 
n=7, area=0.520833, exact=1.125000, error=-0.604167 

phi(x,3,5,xg)*f11=x+2.0 
n=1, area=4.394531, exact=3.825000, error=0.569531 
n=2, area=0.434028, exact=3.825000, error=-3.39097 
n=3, area=0.130208, exact=3.825000, error=-3.69479 
n=4, area=0.967262, exact=3.825000, error=-2.85774 
n=5, area=0.967262, exact=3.825000, error=-2.85774 
n=6, area=0.967262, exact=3.825000, error=-2.85774 
n=7, area=0.967262, exact=3.825000, error=-2.85774 

phi(x,3,5,xg)*f21=x*x+2.0*x+3.0 
n=1, area=7.470703, exact=8.325000, error=-0.854297 
n=2, area=1.085069, exact=8.325000, error=-7.23993 
n=3, area=-1.653646, exact=8.325000, error=-9.97865 
n=4, area=1.108631, exact=8.325000, error=-7.21637 
n=5, area=1.108631, exact=8.325000, error=-7.21637 
n=6, area=1.108631, exact=8.325000, error=-7.21637 
n=7, area=1.108631, exact=8.325000, error=-7.21637 

phi(x,3,5,xg)*f31=x*x*x+2.0*x*x+3.0*x+4.0 
n=1, area=10.766602, exact=15.460714, error=-4.69411 
n=2, area=2.170139, exact=15.460714, error=-13.2906 
n=3, area=-6.360677, exact=15.460714, error=-21.8214 
n=4, area=-0.485757, exact=15.460714, error=-15.9465 
n=5, area=-0.007440, exact=15.460714, error=-15.4682 
n=6, area=-0.007440, exact=15.460714, error=-15.4682 
n=7, area=-0.007440, exact=15.460714, error=-15.4682 

phi(x,3,5,xg)*f41=x*x*x*x+2.0*x*x*x+3.0*x*x+4.0*x+5.0 
n=1, area=14.172363, exact=26.373214, error=-12.2009 
n=2, area=3.841146, exact=26.373214, error=-22.5321 
n=3, area=-15.787109, exact=26.373214, error=-42.1603 
n=4, area=-5.583546, exact=26.373214, error=-31.9568 
n=5, area=-3.526786, exact=26.373214, error=-29.9 
n=6, area=-3.526786, exact=26.373214, error=-29.9 
n=7, area=-3.526786, exact=26.373214, error=-29.9 

phi(x,3,5,xg)*fe1=exp(x) 
n=1, area=2.898143, exact=4.262081, error=-1.36394 
n=2, area=0.604454, exact=4.262081, error=-3.65763 
n=3, area=-1.862334, exact=4.262081, error=-6.12441 
n=4, area=-0.227732, exact=4.262081, error=-4.48981 
n=5, area=-0.076763, exact=4.262081, error=-4.33884 
n=6, area=-0.072605, exact=4.262081, error=-4.33469 
n=7, area=-0.072550, exact=4.262081, error=-4.33463 

phi(x,0,5,xg)*fe1=exp(x) 
n=1, area=0.057963, exact=0.000000, error=0.0579629 
n=2, area=-0.026264, exact=0.000000, error=-0.0262639 
n=3, area=0.217457, exact=0.000000, error=0.217457 
n=4, area=0.144382, exact=0.000000, error=0.144382 
n=5, area=0.134307, exact=0.000000, error=0.134307 
n=6, area=0.133992, exact=0.000000, error=0.133992 
n=7, area=0.133987, exact=0.000000, error=0.133987 

phi(x,5,5,xg)*fe1=exp(x) 
n=1, area=0.057963, exact=0.000000, error=0.0579629 
n=2, area=-0.061836, exact=0.000000, error=-0.0618359 
n=3, area=0.888651, exact=0.000000, error=0.888651 
n=4, area=1.212645, exact=0.000000, error=1.21265 
n=5, area=1.233793, exact=0.000000, error=1.23379 
n=6, area=1.234311, exact=0.000000, error=1.23431 
n=7, area=1.234318, exact=0.000000, error=1.23432 

phip(x,0,5,xg)*fe1=exp(x) 
n=1, area=-0.038642, exact=0.000000, error=-0.0386419 
n=2, area=0.170398, exact=0.000000, error=0.170398 
n=3, area=-0.216155, exact=0.000000, error=-0.216155 
n=4, area=-0.487245, exact=0.000000, error=-0.487245 
n=5, area=-0.501581, exact=0.000000, error=-0.501581 
n=6, area=-0.501864, exact=0.000000, error=-0.501864 
n=7, area=-0.501867, exact=0.000000, error=-0.501867 

phip(x,5,5,xg)*fe1=exp(x) 
n=1, area=0.038642, exact=0.000000, error=0.0386419 
n=2, area=1.446511, exact=0.000000, error=1.44651 
n=3, area=5.543091, exact=0.000000, error=5.54309 
n=4, area=6.131338, exact=0.000000, error=6.13134 
n=5, area=6.154337, exact=0.000000, error=6.15434 
n=6, area=6.154734, exact=0.000000, error=6.15473 
n=7, area=6.154738, exact=0.000000, error=6.15474