regression/math.sml

   1 (* Auxiliary functions for test cases *)
   2
   3 infix 1 seq
   4 fun e1 seq e2 = e2;
   5 fun check b = if b then "OK" else "WRONG";
   6 fun check' f = (if f () then "OK" else "WRONG") handle _ => "EXN";
   7
   8 fun range (from, to) p =
   9     let open Int
  10     in
  11         (from > to) orelse (p from) andalso (range (from+1, to) p)
  12     end;
  13
  14 fun checkrange bounds = check o range bounds;
  15
  16 fun tst0 s s' = print (s ^ "    \t" ^ s' ^ "\n");
  17 fun tst  s b = tst0 s (check  b);
  18 fun tst' s f = tst0 s (check' f);
  19
  20 fun tstrange s bounds = (tst s) o range bounds
  21
  22 (* test/math.sml
  23    PS 1995-02-25, 1996-04-01, 1997-03-07
  24 *)
  25
  26 val _ = print "\nFile math.sml: Testing structure Math...\n"
  27
  28 local
  29     open Math
  30     val MAXDOUBLE = 8.98846567431157E307;
  31     val MINDOUBLE = 4.94065645841246544E~324
  32     val PI = 3.14159265358979323846;
  33     val E = 2.7182818284590452354;
  34
  35     val eps = 1E~8
  36     infix 4 ===
  37     fun x === y =
  38         abs (x - y) <= eps orelse abs(x-y) <= eps * (abs x + abs y)
  39
  40     fun check1 (opr, a, r) = if opr a === r then "OK" else "WRONG"
  41     fun check2 (opr, a1, a2, r) =
  42         if opr(a1, a2) === r then "OK" else "WRONG"
  43     fun tst1 s (opr, a, r) = tst0 s (check1 (opr, a, r))
  44     fun tst2 s (opr, a1, a2, r) = tst0 s (check2 (opr, a1, a2, r))
  45
  46 val test0a = tst "test0a" (PI === pi);
  47 val test0b = tst "test0b" (E === e);
  48
  49 val test1a = tst1 "test1a" (sqrt, 64.0, 8.0);
  50 val test1b = tst1 "test1b" (sqrt, 0.0, 0.0);
  51 val test1c = tst0 "test1c" (if Real.isNan(sqrt ~1.0) then "OK" else "WRONG")
  52
  53 val test2a = tst1 "test2a" (sin, 0.0, 0.0);
  54 val test2b = tst1 "test2b" (sin, pi/2.0, 1.0);
  55 val test2c = tst1 "test2c" (sin, pi, 0.0);
  56 val test2d = tst1 "test2d" (sin, 3.0*pi/2.0, ~1.0);
  57
  58 val test3a = tst1 "test3a" (cos, 0.0, 1.0);
  59 val test3b = tst1 "test3b" (cos, pi/2.0, 0.0);
  60 val test3c = tst1 "test3c" (cos, pi, ~1.0);
  61 val test3d = tst1 "test3d" (cos, 3.0*pi/2.0, 0.0);
  62
  63 val test4a = tst1 "test4a" (tan, 0.0, 0.0);
  64 val test4b = tst1 "test4b" (tan, pi/4.0, 1.0);
  65 val test4c = tst1 "test4c" (tan, pi, 0.0);
  66 val test4d = tst1 "test4d" (tan, 3.0*pi/4.0, ~1.0);
  67 val test4e = tst1 "test4e" (tan, ~pi/4.0, ~1.0);
  68 val test4f = tst "test4f" ((abs(tan (pi/2.0))  > 1E8) handle _ => true);
  69 val test4g = tst "test4g" ((abs(tan (~pi/2.0)) > 1E8) handle _ => true);
  70
  71 val test5a = tst1 "test5a" (asin, 0.0, 0.0);
  72 val test5b = tst1 "test5b" (asin, 1.0, pi/2.0);
  73 val test5c = tst1 "test5c" (asin, ~1.0, ~pi/2.0);
  74 val test5d = tst0 "test5d" (if Real.isNan(asin 1.1) then "OK" else "WRONG")
  75 val test5e = tst0 "test5e" (if Real.isNan(asin ~1.1) then "OK" else "WRONG")
  76
  77 val test6a = tst1 "test6a" (acos, 1.0, 0.0);
  78 val test6b = tst1 "test6b" (acos, 0.0, pi/2.0);
  79 val test6c = tst1 "test6c" (acos, ~1.0, pi);
  80 val test6d = tst0 "test6d" (if Real.isNan(acos 1.1) then "OK" else "WRONG")
  81 val test6e = tst0 "test6e" (if Real.isNan(acos ~1.1) then "OK" else "WRONG")
  82
  83 val test7a = tst1 "test7a" (atan, 0.0, 0.0);
  84 val test7b = tst1 "test7b" (atan, 1.0, pi/4.0);
  85 val test7c = tst1 "test7c" (atan, ~1.0, ~pi/4.0);
  86 val test7d = tst1 "test7d" (atan, 1E8, pi/2.0);
  87 val test7e = tst1 "test7e" (atan, ~1E8, ~pi/2.0);
  88
  89 (* atan2 -- here I am in doubt over the argument order, since the New
  90 Basis document is inconsistent with itself and with atan2 in the C
  91 libraries. *)
  92
  93 val test8a = tst2 "test8a" (atan2, 0.0, 0.0, 0.0);
  94 val test8b = tst2 "test8b" (atan2, 1.0, 0.0, pi/2.0);
  95 val test8c = tst2 "test8c" (atan2, ~1.0, 0.0, ~pi/2.0);
  96 val test8d = tst2 "test8d" (atan2, 1.0, 1.0, pi/4.0);
  97 val test8e = tst2 "test8e" (atan2, ~1.0, 1.0, ~pi/4.0);
  98 val test8f = tst2 "test8f" (atan2, ~1.0, ~1.0, ~3.0*pi/4.0);
  99 val test8g = tst2 "test8g" (atan2, 1.0, ~1.0, 3.0*pi/4.0);
 100 val test8h = tst2 "test8h" (atan2, 1E8, 1.0, pi/2.0);
 101 val test8i = tst2 "test8i" (atan2, ~1E8, 1.0, ~pi/2.0);
 102 val test8j = tst2 "test8j" (atan2, 1.0, 1E8, 0.0);
 103 val test8k = tst2 "test8k" (atan2, 1.0, ~1E8, pi);
 104 val test8l = tst2 "test8l" (atan2, ~1.0, ~1E8, ~pi);
 105
 106 val test9a = tst1 "test9a" (exp, 0.0, 1.0);
 107 val test9b = tst1 "test9b" (exp, 1.0, e);
 108 val test9c = tst1 "test9c" (exp, ~1.0, 1.0/e);
 109
 110 val test10a = tst1 "test10a" (ln, 1.0, 0.0);
 111 val test10b = tst1 "test10b" (ln, e, 1.0);
 112 val test10c = tst1 "test10c" (ln, 1.0/e, ~1.0);
 113 val test10d = tst0 "test10d" (if Real.==(ln 0.0,Real.negInf) then "OK" else "WRONG")
 114 val test10e = tst0 "test10e" (if Real.isNan(ln ~1.0) then "OK" else "WRONG")
 115 val test10f = tst0 "test10f" (if Real.==(ln Real.posInf, Real.posInf) then "OK" else "WRONG")
 116 val test10g = tst0 "test10g" (if Real.==(Real.posInf, Real.posInf) then "OK" else "WRONG")
 117
 118 val test12a = tst2 "test12a" (pow, 0.0, 0.0, 1.0); (* arbitrary, might be 0.0 *)
 119 val test12b = tst2 "test12b" (pow, 7.0, 0.0, 1.0);
 120 val test12c = tst2 "test12c" (pow, 0.0, 7.0, 0.0);
 121 val test12d = tst2 "test12d" (pow, 64.0, 0.5, 8.0);
 122 val test12e = tst2 "test12e" (pow, ~9.0, 2.0, 81.0);
 123 val test12f = tst2 "test12f" (pow, 10.0, ~2.0, 0.01);
 124 val test12g = tst2 "test12g" (pow, ~10.0, ~2.0, 0.01);
 125 val test12h = tst2 "test12h" (pow, 0.0, 0.5, 0.0);
 126 val test12i = tst2 "test12i" (pow, 0.4, ~2.0, 6.25);
 127
 128 (*we do not follow the Basis Library specification exactly here, but rather follow math.h
 129 val test12j = tst0 "test12j" (if Real.==(pow(0.0, ~1.0),Real.posInf) then "OK" else "WRONG")
 130 val test12k = tst0 "test12k" (if Real.==(pow(0.0, ~0.5),Real.posInf) then "OK" else "WRONG")
 131 *)
 132 val test12l = tst0 "test12l" (if Real.isNan(pow(~1.0, 1.1)) then "OK" else "WRONG")
 133 val test12m = tst0 "test12m" (if Real.isNan(pow(~1.0, 0.5)) then "OK" else "WRONG")
 134 (* sweeks removed 12n because it fails on FreeBSD on x86, apparently due to a
 135  * 64 bit vs 80 bit issue.
 136  *)
 137 (* val test12n = tst0 "test12n" (if Real.==(pow(3.0, 1000000.0),Real.posInf) then "OK" else "WRONG") *)   (* not in basis lib spec.*)
 138 val test13a = tst1 "test13a" (log10, 1.0, 0.0);
 139 val test13b = tst1 "test13b" (log10, 10.0, 1.0);
 140 val test13c = tst1 "test13c" (log10, 100.0, 2.0);
 141 val test13d = tst1 "test13d" (log10, 0.1, ~1.0);
 142 val test13e = tst1 "test13e" (log10, 0.01, ~2.0);
 143
 144 val check14a = tst1 "test14a" (sinh, 0.0, 0.0);
 145 val check14b = tst1 "test14b" (sinh,  1.0, 1.17520119364);
 146 val check14c = tst1 "test14c" (sinh, ~1.0, ~1.17520119364);
 147 val check14d = tst1 "test14d" (sinh,  2.0,  3.62686040785);
 148 val check14e = tst1 "test14e" (sinh, ~2.0, ~3.62686040785);
 149
 150 val check15a = tst1 "test15a" (cosh, 0.0, 1.0);
 151 val check15b = tst1 "test15b" (cosh,  1.0, 1.54308063482);
 152 val check15c = tst1 "test15c" (cosh, ~1.0, 1.54308063482);
 153 val check15d = tst1 "test15d" (cosh,  2.0, 3.76219569108);
 154 val check15e = tst1 "test15e" (cosh, ~2.0, 3.76219569108);
 155
 156 val check16a = tst1 "test16a" (tanh, 0.0, 0.0);
 157 val check16b = tst1 "test16b" (tanh,  1.0,  0.761594155956);
 158 val check16c = tst1 "test16c" (tanh, ~1.0, ~0.761594155956);
 159 val check16d = tst1 "test16d" (tanh,  2.0,  0.964027580076);
 160 val check16e = tst1 "test16e" (tanh, ~2.0, ~0.964027580076);
 161 val check16f = tst1 "test16f" (tanh,  100.0,  1.0);
 162 val check16g = tst1 "test16g" (tanh, ~100.0, ~1.0);
 163 in
 164 end