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const.c

const.c 9.3 KB
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  1. /*							const.c
    2. 

  2.  *
    3. 

  3.  *	Globally declared constants
    4. 

  4.  *
    5. 

  5.  *
    6. 

  6.  *
    7. 

  7.  * SYNOPSIS:
    8. 

  8.  *
    9. 

  9.  * extern double nameofconstant;
    10. 

  10.  *
    11. 

  11.  *
    12. 

  12.  *
    13. 

  13.  *
    14. 

  14.  * DESCRIPTION:
    15. 

  15.  *
    16. 

  16.  * This file contains a number of mathematical constants and
    17. 

  17.  * also some needed size parameters of the computer arithmetic.
    18. 

  18.  * The values are supplied as arrays of hexadecimal integers
    19. 

  19.  * for IEEE arithmetic; arrays of octal constants for DEC
    20. 

  20.  * arithmetic; and in a normal decimal scientific notation for
    21. 

  21.  * other machines.  The particular notation used is determined
    22. 

  22.  * by a symbol (DEC, IBMPC, or UNK) defined in the include file
    23. 

  23.  * math.h.
    24. 

  24.  *
    25. 

  25.  * The default size parameters are as follows.
    26. 

  26.  *
    27. 

  27.  * For DEC and UNK modes:
    28. 

  28.  * MACHEP =  1.38777878078144567553E-17       2**-56
    29. 

  29.  * MAXLOG =  8.8029691931113054295988E1       log(2**127)
    30. 

  30.  * MINLOG = -8.872283911167299960540E1        log(2**-128)
    31. 

  31.  * MAXNUM =  1.701411834604692317316873e38    2**127
    32. 

  32.  *
    33. 

  33.  * For IEEE arithmetic (IBMPC):
    34. 

  34.  * MACHEP =  1.11022302462515654042E-16       2**-53
    35. 

  35.  * MAXLOG =  7.09782712893383996843E2         log(2**1024)
    36. 

  36.  * MINLOG = -7.08396418532264106224E2         log(2**-1022)
    37. 

  37.  * MAXNUM =  1.7976931348623158E308           2**1024
    38. 

  38.  *
    39. 

  39.  * The global symbols for mathematical constants are
    40. 

  40.  * PI     =  3.14159265358979323846           pi
    41. 

  41.  * PIO2   =  1.57079632679489661923           pi/2
    42. 

  42.  * PIO4   =  7.85398163397448309616E-1        pi/4
    43. 

  43.  * SQRT2  =  1.41421356237309504880           sqrt(2)
    44. 

  44.  * SQRTH  =  7.07106781186547524401E-1        sqrt(2)/2
    45. 

  45.  * LOG2E  =  1.4426950408889634073599         1/log(2)
    46. 

  46.  * SQ2OPI =  7.9788456080286535587989E-1      sqrt( 2/pi )
    47. 

  47.  * LOGE2  =  6.93147180559945309417E-1        log(2)
    48. 

  48.  * LOGSQ2 =  3.46573590279972654709E-1        log(2)/2
    49. 

  49.  * THPIO4 =  2.35619449019234492885           3*pi/4
    50. 

  50.  * TWOOPI =  6.36619772367581343075535E-1     2/pi
    51. 

  51.  *
    52. 

  52.  * These lists are subject to change.
    53. 

  53.  */
    54. 

  54. 
    55. 

  55. /*							const.c */
    56. 

  56. 

  57. /*
    58. 

  58. Cephes Math Library Release 2.3:  March, 1995
    59. 

  59. Copyright 1984, 1995 by Stephen L. Moshier
    60. 

  60. */
    61. 

  61. 

  62. #include <math.h>
    63. 

  63. 

  64. #ifdef UNK
    65. 

  65. #if 1
    66. 

  66. double MACHEP =  1.11022302462515654042E-16;   /* 2**-53 */
    67. 

  67. #else
    68. 

  68. double MACHEP =  1.38777878078144567553E-17;   /* 2**-56 */
    69. 

  69. #endif
    70. 

  70. double UFLOWTHRESH =  2.22507385850720138309E-308; /* 2**-1022 */
    71. 

  71. #ifdef DENORMAL
    72. 

  72. double MAXLOG =  7.09782712893383996732E2;     /* log(MAXNUM) */
    73. 

  73. /* double MINLOG = -7.44440071921381262314E2; */     /* log(2**-1074) */
    74. 

  74. double MINLOG = -7.451332191019412076235E2;     /* log(2**-1075) */
    75. 

  75. #else
    76. 

  76. double MAXLOG =  7.08396418532264106224E2;     /* log 2**1022 */
    77. 

  77. double MINLOG = -7.08396418532264106224E2;     /* log 2**-1022 */
    78. 

  78. #endif
    79. 

  79. double MAXNUM =  1.79769313486231570815E308;    /* 2**1024*(1-MACHEP) */
    80. 

  80. double PI     =  3.14159265358979323846;       /* pi */
    81. 

  81. double PIO2   =  1.57079632679489661923;       /* pi/2 */
    82. 

  82. double PIO4   =  7.85398163397448309616E-1;    /* pi/4 */
    83. 

  83. double SQRT2  =  1.41421356237309504880;       /* sqrt(2) */
    84. 

  84. double SQRTH  =  7.07106781186547524401E-1;    /* sqrt(2)/2 */
    85. 

  85. double LOG2E  =  1.4426950408889634073599;     /* 1/log(2) */
    86. 

  86. double SQ2OPI =  7.9788456080286535587989E-1;  /* sqrt( 2/pi ) */
    87. 

  87. double LOGE2  =  6.93147180559945309417E-1;    /* log(2) */
    88. 

  88. double LOGSQ2 =  3.46573590279972654709E-1;    /* log(2)/2 */
    89. 

  89. double THPIO4 =  2.35619449019234492885;       /* 3*pi/4 */
    90. 

  90. double TWOOPI =  6.36619772367581343075535E-1; /* 2/pi */
    91. 

  91. #ifdef INFINITIES
    92. 

  92. double INFINITY = 1.0/0.0;  /* 99e999; */
    93. 

  93. #else
    94. 

  94. double INFINITY =  1.79769313486231570815E308;    /* 2**1024*(1-MACHEP) */
    95. 

  95. #endif
    96. 

  96. #ifdef NANS
    97. 

  97. double NAN = 1.0/0.0 - 1.0/0.0;
    98. 

  98. #else
    99. 

  99. double NAN = 0.0;
    100. 

  100. #endif
    101. 

  101. #ifdef MINUSZERO
    102. 

  102. double NEGZERO = -0.0;
    103. 

  103. #else
    104. 

  104. double NEGZERO = 0.0;
    105. 

  105. #endif
    106. 

  106. #endif
    107. 

  107. 

  108. #ifdef IBMPC
    109. 

  109. 			/* 2**-53 =  1.11022302462515654042E-16 */
    110. 

  110. unsigned short MACHEP[4] = {0x0000,0x0000,0x0000,0x3ca0};
    111. 

  111. unsigned short UFLOWTHRESH[4] = {0x0000,0x0000,0x0000,0x0010};
    112. 

  112. #ifdef DENORMAL
    113. 

  113. 			/* log(MAXNUM) =  7.09782712893383996732224E2 */
    114. 

  114. unsigned short MAXLOG[4] = {0x39ef,0xfefa,0x2e42,0x4086};
    115. 

  115. 			/* log(2**-1074) = - -7.44440071921381262314E2 */
    116. 

  116. /*unsigned short MINLOG[4] = {0x71c3,0x446d,0x4385,0xc087};*/
    117. 

  117. unsigned short MINLOG[4] = {0x3052,0xd52d,0x4910,0xc087};
    118. 

  118. #else
    119. 

  119. 			/* log(2**1022) =   7.08396418532264106224E2 */
    120. 

  120. unsigned short MAXLOG[4] = {0xbcd2,0xdd7a,0x232b,0x4086};
    121. 

  121. 			/* log(2**-1022) = - 7.08396418532264106224E2 */
    122. 

  122. unsigned short MINLOG[4] = {0xbcd2,0xdd7a,0x232b,0xc086};
    123. 

  123. #endif
    124. 

  124. 			/* 2**1024*(1-MACHEP) =  1.7976931348623158E308 */
    125. 

  125. unsigned short MAXNUM[4] = {0xffff,0xffff,0xffff,0x7fef};
    126. 

  126. unsigned short PI[4]     = {0x2d18,0x5444,0x21fb,0x4009};
    127. 

  127. unsigned short PIO2[4]   = {0x2d18,0x5444,0x21fb,0x3ff9};
    128. 

  128. unsigned short PIO4[4]   = {0x2d18,0x5444,0x21fb,0x3fe9};
    129. 

  129. unsigned short SQRT2[4]  = {0x3bcd,0x667f,0xa09e,0x3ff6};
    130. 

  130. unsigned short SQRTH[4]  = {0x3bcd,0x667f,0xa09e,0x3fe6};
    131. 

  131. unsigned short LOG2E[4]  = {0x82fe,0x652b,0x1547,0x3ff7};
    132. 

  132. unsigned short SQ2OPI[4] = {0x3651,0x33d4,0x8845,0x3fe9};
    133. 

  133. unsigned short LOGE2[4]  = {0x39ef,0xfefa,0x2e42,0x3fe6};
    134. 

  134. unsigned short LOGSQ2[4] = {0x39ef,0xfefa,0x2e42,0x3fd6};
    135. 

  135. unsigned short THPIO4[4] = {0x21d2,0x7f33,0xd97c,0x4002};
    136. 

  136. unsigned short TWOOPI[4] = {0xc883,0x6dc9,0x5f30,0x3fe4};
    137. 

  137. #ifdef INFINITIES
    138. 

  138. unsigned short INFINITY[4] = {0x0000,0x0000,0x0000,0x7ff0};
    139. 

  139. #else
    140. 

  140. unsigned short INFINITY[4] = {0xffff,0xffff,0xffff,0x7fef};
    141. 

  141. #endif
    142. 

  142. #ifdef NANS
    143. 

  143. unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x7ffc};
    144. 

  144. #else
    145. 

  145. unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x0000};
    146. 

  146. #endif
    147. 

  147. #ifdef MINUSZERO
    148. 

  148. unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x8000};
    149. 

  149. #else
    150. 

  150. unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x0000};
    151. 

  151. #endif
    152. 

  152. #endif
    153. 

  153. 

  154. #ifdef MIEEE
    155. 

  155. 			/* 2**-53 =  1.11022302462515654042E-16 */
    156. 

  156. unsigned short MACHEP[4] = {0x3ca0,0x0000,0x0000,0x0000};
    157. 

  157. unsigned short UFLOWTHRESH[4] = {0x0010,0x0000,0x0000,0x0000};
    158. 

  158. #ifdef DENORMAL
    159. 

  159. 			/* log(2**1024) =   7.09782712893383996843E2 */
    160. 

  160. unsigned short MAXLOG[4] = {0x4086,0x2e42,0xfefa,0x39ef};
    161. 

  161. 			/* log(2**-1074) = - -7.44440071921381262314E2 */
    162. 

  162. /* unsigned short MINLOG[4] = {0xc087,0x4385,0x446d,0x71c3}; */
    163. 

  163. unsigned short MINLOG[4] = {0xc087,0x4910,0xd52d,0x3052};
    164. 

  164. #else
    165. 

  165. 			/* log(2**1022) =  7.08396418532264106224E2 */
    166. 

  166. unsigned short MAXLOG[4] = {0x4086,0x232b,0xdd7a,0xbcd2};
    167. 

  167. 			/* log(2**-1022) = - 7.08396418532264106224E2 */
    168. 

  168. unsigned short MINLOG[4] = {0xc086,0x232b,0xdd7a,0xbcd2};
    169. 

  169. #endif
    170. 

  170. 			/* 2**1024*(1-MACHEP) =  1.7976931348623158E308 */
    171. 

  171. unsigned short MAXNUM[4] = {0x7fef,0xffff,0xffff,0xffff};
    172. 

  172. unsigned short PI[4]     = {0x4009,0x21fb,0x5444,0x2d18};
    173. 

  173. unsigned short PIO2[4]   = {0x3ff9,0x21fb,0x5444,0x2d18};
    174. 

  174. unsigned short PIO4[4]   = {0x3fe9,0x21fb,0x5444,0x2d18};
    175. 

  175. unsigned short SQRT2[4]  = {0x3ff6,0xa09e,0x667f,0x3bcd};
    176. 

  176. unsigned short SQRTH[4]  = {0x3fe6,0xa09e,0x667f,0x3bcd};
    177. 

  177. unsigned short LOG2E[4]  = {0x3ff7,0x1547,0x652b,0x82fe};
    178. 

  178. unsigned short SQ2OPI[4] = {0x3fe9,0x8845,0x33d4,0x3651};
    179. 

  179. unsigned short LOGE2[4]  = {0x3fe6,0x2e42,0xfefa,0x39ef};
    180. 

  180. unsigned short LOGSQ2[4] = {0x3fd6,0x2e42,0xfefa,0x39ef};
    181. 

  181. unsigned short THPIO4[4] = {0x4002,0xd97c,0x7f33,0x21d2};
    182. 

  182. unsigned short TWOOPI[4] = {0x3fe4,0x5f30,0x6dc9,0xc883};
    183. 

  183. #ifdef INFINITIES
    184. 

  184. unsigned short INFINITY[4] = {0x7ff0,0x0000,0x0000,0x0000};
    185. 

  185. #else
    186. 

  186. unsigned short INFINITY[4] = {0x7fef,0xffff,0xffff,0xffff};
    187. 

  187. #endif
    188. 

  188. #ifdef NANS
    189. 

  189. unsigned short NAN[4] = {0x7ff8,0x0000,0x0000,0x0000};
    190. 

  190. #else
    191. 

  191. unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x0000};
    192. 

  192. #endif
    193. 

  193. #ifdef MINUSZERO
    194. 

  194. unsigned short NEGZERO[4] = {0x8000,0x0000,0x0000,0x0000};
    195. 

  195. #else
    196. 

  196. unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x0000};
    197. 

  197. #endif
    198. 

  198. #endif
    199. 

  199. 

  200. #ifdef DEC
    201. 

  201. 			/* 2**-56 =  1.38777878078144567553E-17 */
    202. 

  202. unsigned short MACHEP[4] = {0022200,0000000,0000000,0000000};
    203. 

  203. unsigned short UFLOWTHRESH[4] = {0x0080,0x0000,0x0000,0x0000};
    204. 

  204. 			/* log 2**127 = 88.029691931113054295988 */
    205. 

  205. unsigned short MAXLOG[4] = {041660,007463,0143742,025733,};
    206. 

  206. 			/* log 2**-128 = -88.72283911167299960540 */
    207. 

  207. unsigned short MINLOG[4] = {0141661,071027,0173721,0147572,};
    208. 

  208. 			/* 2**127 = 1.701411834604692317316873e38 */
    209. 

  209. unsigned short MAXNUM[4] = {077777,0177777,0177777,0177777,};
    210. 

  210. unsigned short PI[4]     = {040511,007732,0121041,064302,};
    211. 

  211. unsigned short PIO2[4]   = {040311,007732,0121041,064302,};
    212. 

  212. unsigned short PIO4[4]   = {040111,007732,0121041,064302,};
    213. 

  213. unsigned short SQRT2[4]  = {040265,002363,031771,0157145,};
    214. 

  214. unsigned short SQRTH[4]  = {040065,002363,031771,0157144,};
    215. 

  215. unsigned short LOG2E[4]  = {040270,0125073,024534,013761,};
    216. 

  216. unsigned short SQ2OPI[4] = {040114,041051,0117241,0131204,};
    217. 

  217. unsigned short LOGE2[4]  = {040061,071027,0173721,0147572,};
    218. 

  218. unsigned short LOGSQ2[4] = {037661,071027,0173721,0147572,};
    219. 

  219. unsigned short THPIO4[4] = {040426,0145743,0174631,007222,};
    220. 

  220. unsigned short TWOOPI[4] = {040042,0174603,067116,042025,};
    221. 

  221. /* Approximate infinity by MAXNUM.  */
    222. 

  222. unsigned short INFINITY[4] = {077777,0177777,0177777,0177777,};
    223. 

  223. unsigned short NAN[4] = {0000000,0000000,0000000,0000000};
    224. 

  224. #ifdef MINUSZERO
    225. 

  225. unsigned short NEGZERO[4] = {0000000,0000000,0000000,0100000};
    226. 

  226. #else
    227. 

  227. unsigned short NEGZERO[4] = {0000000,0000000,0000000,0000000};
    228. 

  228. #endif
    229. 

  229. #endif
    230. 

  230. 

  231. #ifndef UNK
    232. 

  232. extern unsigned short MACHEP[];
    233. 

  233. extern unsigned short UFLOWTHRESH[];
    234. 

  234. extern unsigned short MAXLOG[];
    235. 

  235. extern unsigned short UNDLOG[];
    236. 

  236. extern unsigned short MINLOG[];
    237. 

  237. extern unsigned short MAXNUM[];
    238. 

  238. extern unsigned short PI[];
    239. 

  239. extern unsigned short PIO2[];
    240. 

  240. extern unsigned short PIO4[];
    241. 

  241. extern unsigned short SQRT2[];
    242. 

  242. extern unsigned short SQRTH[];
    243. 

  243. extern unsigned short LOG2E[];
    244. 

  244. extern unsigned short SQ2OPI[];
    245. 

  245. extern unsigned short LOGE2[];
    246. 

  246. extern unsigned short LOGSQ2[];
    247. 

  247. extern unsigned short THPIO4[];
    248. 

  248. extern unsigned short TWOOPI[];
    249. 

  249. extern unsigned short INFINITY[];
    250. 

  250. extern unsigned short NAN[];
    251. 

  251. extern unsigned short NEGZERO[];
    252. 

  252. #endif
    253.