       Bugs in Mma functions on the NeXT

• To: mathgroup at yoda.physics.unc.edu
• Subject: Bugs in Mma functions on the NeXT
• From: herrmann at siam.math.tamu.edu (joe herrmann)
• Date: Wed, 10 Feb 1993 17:07:27 -0600

```Dear Mathgroup,

I installed Mma 2.1 for the NeXT which I ran under NeXTStep OS 2.1 to
fix the bugs in Mma 2.0 that E^(-625000)= 1.40101 10^22,  E^(-670000)=
2.51105 10^56, etc.  Mma 2.1 fixed these particular values and others I
identified but I have found the values given below are still incorrect
in Mma 2.1 under NeXTStep OS 2.1.    However all exponential bugs I am
aware of are fixed in Mma 2.0 or 2.1 by upgrading to NeXTStep OS 3.0.

However, I found a bug in BesselJ in 3.0 as can be seen in the
following:  BesselJ[177.4,28.-.28I]=0. + 0. I  and
BesselJ[177.4,28.]=0.   The first is definitely wrong since all zeros
of BesselJ with order greater than -1 are real, moreover for Mma 2.0 on
NeXT OS 2.1 and for Mathematica (MIPS) I find

-121
BesselJ[177.4,28.]= 2.513042235631 10

-122                   -121
BesselJ[177.4,28.-.28I]= -4.56550333659 10     - 2.49427565746 10     I

Exponential bugs in Mma 2.1 under NeXTStep OS 2.1:

Table[{x,N[E^x]},{x,-300000,-200000,5000}]
-130289
{{-300000, 4.5230253774 10       },

-71
{-295000, 4.1807 10   },

-125946
{-290000, 3.9833462329 10       },

-102060
{-235000, 6.2625720561 10       },

-296
{-230000, 1.05042 10    },

-97717
{-225000, 5.5153333723 10      },

Sincerely,

Joe Herrmann
Texas A&M Math Dept
herrmann at siam.tamu.edu

```

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