Figure 2: Moshier Library test results

Recaps of Tests Run on Selected Double Precision and Long Double
Precision Functions in Moshier's Corresponding Function Libraries

                    Double Precision
                    ----------------

Significand: 53 Bits
Arithmetic:  Base 2

Test of exp(x) vs. xexp(x):

Test            (Log 2) Bits (Log 2) Bits Test
----              MRE   Lost  RMS E  Lost Range
                  ---   ----  -----  ---- -----
1: exp(x)        -52.43 0.57 -59.00  0.00 (-0.5*log(2),
                                           +0.5*log(2)) 
2: exp(x)        -52.23 0.77 -59.01  0.00 (-670, -0.5*log(2))
3: exp(x)        -52.55 0.45 -58.96  0.00 (10*log(2), +709)

Test of pow(x,p) vs. xpow(x,p):

Test            (Log 2) Bits (Log 2) Bits Test
----              MRE   Lost  RMS E  Lost Range
                  ---   ----  -----  ---- -----
1: pow(x,1)      -(INF) 0.00 -(INF)  0.00 (+0.5, +1)
2: pow(x*x,1.5)  -52.24 0.76 -58.74  0.00 (+0.5, +1)
3: pow(x*x,1.5)  -52.23 0.77 -58.74  0.00 (+1.0, +5.6438E+102)
4: pow(x,y)      -49.81 3.19 -57.03  0.00 x: (+0.01, +10)
                                          y: (-154.127, +154.127)

Test of sin(x) vs. xsin(x) & cos(x) vs. xcos(x):

Test            (Log 2) Bits (Log 2) Bits Test
----              MRE   Lost  RMS E  Lost Range
                  ---   ----  -----  ---- -----
1: sin(x)        -52.61 0.39 -59.22  0.00 (0.0, pi/2)
2: cos(x)        -52.29 0.71 -58.97  0.00 (0.0, pi/2)
3: sin(x)        -52.08 0.92 -58.94  0.00 (6*pi, 6.5*pi)
4: cos(x)        -52.31 0.69 -59.00  0.00 (7*pi, 7.5*pi)

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

                  Long Double Precision
                  ---------------------

Significand: 64 Bits
Arithmetic:  Base 2

Test of expl(x) vs. xexp(x):

Test            (Log 2) Bits (Log 2) Bits Test
----              MRE   Lost  RMS E  Lost Range
                  ---   ----  -----  ---- -----
1: expl(x)       -63.24 0.76 -69.96  0.00 (-0.5*log(2),
                                           +0.5*log(2))
2: expl(x)       -63.19 0.81 -69.93  0.00 (-11309, -0.5*log(2))
3: expl(x)       -63.08 0.92 -69.95  0.00 (10*log(2), +11356)

Test of powl(x,p) vs. xpow(x,p):

Test            (Log 2) Bits (Log 2) Bits Test
----              MRE   Lost  RMS E  Lost Range
                  ---   ---- -----   ---- -----
1: powl(x,1)     -63.57 0.43 -71.70  0.00 (+0.5, +1)
2: powl(x*x,1.5) -63.32 0.68 -69.74  0.00 (+0.5, +1)
3: powl(x*x,1.5) -63.30 0.70 -69.77  0.00 (+1.0, +1.0596E+1644)
4: powl(x,y)     -57.20 6.80 -64.90  0.00 x: (+0.01, +10)
                                          y: (-2466.04, +2466.04)

Test of sinl(x) vs. xsin(x) & cosl(x) vs. xcos(x):

Test            (Log 2) Bits (Log 2) Bits Test
----              MRE   Lost  RMS E  Lost Range
                  ---   ----  -----  ---- -----
1: sinl(x)       -63.21 0.79 -70.06  0.00 (0.0, pi/2)
2: cosl(x)       -63.26 0.74 -69.85  0.00 (0.0, pi/2)
3: sinl(x)       -63.15 0.85 -69.79  0.00 (6*pi, 6.5*pi)
4: cosl(x)       -63.04 0.96 -69.92  0.00 (7*pi, 7.5*pi)