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satan.s
资源名称：vxwork_src.rar　[点击查看]
上传用户：nvosite88
上传日期：2007-01-17
资源大小：4983k
文件大小：16k
源码类别：

VxWorks

开发平台：

C/C++

satan.s：源码内容
  1. /* satan.s - Motorola 68040 FP arc-tangent routines (EXC) */
  3. /* Copyright 1991-1993 Wind River Systems, Inc. */
  4. .data
  5. .globl _copyright_wind_river
  6. .long _copyright_wind_river
  8. /*
  9. modification history
  10. --------------------
  11. 01e,21jul93,kdl  added .text (SPR #2372).
  12. 01d,23aug92,jcf  changed bxxx to jxx.
  13. 01c,26may92,rrr  the tree shuffle
  14. 01b,10jan92,kdl  added modification history; general cleanup.
  15. 01a,15aug91,kdl  original version, from Motorola FPSP v2.0.
  16. */
  18. /*
  19. DESCRIPTION
  22. __x_satansa 3.3 12/19/90
  24. The entry point __x_satan computes the arctagent of an
  25. input value. __x_satand does the same except the input value is a
  26. denormalized number.
  28. Input: Double-extended value in memory location pointed to by address
  29. register a0.
  31. Output: Arctan(X) returned in floating-point register Fp0.
  33. Accuracy and Monotonicity: The returned result is within 2 ulps in
  34. 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
  35. result is subsequently rounded to double precision. The
  36. result is provably monotonic in double precision.
  38. Speed: The program __x_satan takes approximately 160 cycles for input
  39. argument X such that 1/16 < |X| < 16. For the other arguments,
  40. the program will run no worse than 10 slower.
  42. Algorithm:
  43. Step 1. If |X| >= 16 or |X| < 1/16, go to Step 5.
  45. Step 2. Let X = sgn * 2**k * 1xxxxxxxx...x. Note that k = -4, -3,...,
  46. or 3.
  47. Define F = sgn * 2**k * 1xxxx1, i.e. the first 5 significant
  48. bits of X with a bit-1 attached at the 6-th bit position.
  49. Define u to be u = (X-F) / (1 + X*F).
  51. Step 3. Approximate arctan(u) by a polynomial poly.
  53. Step 4. Return arctan(F) + poly, arctan(F) is fetched from a table
  54. of values calculated beforehand. Exit.
  56. Step 5. If |X| >= 16, go to Step 7.
  58. Step 6. Approximate arctan(X) by an odd polynomial in X. Exit.
  60. Step 7. Define X' = -1/X. Approximate arctan(X') by an odd polynomial
  61. in X'.
  62. Arctan(X) = sign(X)*Pi/2 + arctan(X'). Exit.
  65. Copyright (C) Motorola, Inc. 1990
  66. All Rights Reserved
  68. THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
  69. The copyright notice above does not evidence any
  70. actual or intended publication of such source code.
  72. __x_satan IDNT 2,1 Motorola 040 Floating Point Software Package
  74. section 8
  76. NOMANUAL
  77. */
  79. #include "fpsp040E.h"
  81. BOUNDS1: .long 0x3FFB8000,0x4002FFFF
  83. ONE: .long 0x3F800000
  85. .long 0x00000000
  87. ATANA3: .long 0xBFF6687E,0x314987D8
  88. ATANA2: .long 0x4002AC69,0x34A26DB3
  90. ATANA1: .long 0xBFC2476F,0x4E1DA28E
  91. ATANB6: .long 0x3FB34444,0x7F876989
  93. ATANB5: .long 0xBFB744EE,0x7FAF45DB
  94. ATANB4: .long 0x3FBC71C6,0x46940220
  96. ATANB3: .long 0xBFC24924,0x921872F9
  97. ATANB2: .long 0x3FC99999,0x99998FA9
  99. ATANB1: .long 0xBFD55555,0x55555555
  100. ATANC5: .long 0xBFB70BF3,0x98539E6A
  102. ATANC4: .long 0x3FBC7187,0x962D1D7D
  103. ATANC3: .long 0xBFC24924,0x827107B8
  105. ATANC2: .long 0x3FC99999,0x9996263E
  106. ATANC1: .long 0xBFD55555,0x55555536
  108. PPIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
  109. NPIBY2: .long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x00000000
  110. PTINY: .long 0x00010000,0x80000000,0x00000000,0x00000000
  111. NTINY: .long 0x80010000,0x80000000,0x00000000,0x00000000
  113. ATANTBL:
  114. .long 0x3FFB0000,0x83D152C5,0x060B7A51,0x00000000
  115. .long 0x3FFB0000,0x8BC85445,0x65498B8B,0x00000000
  116. .long 0x3FFB0000,0x93BE4060,0x17626B0D,0x00000000
  117. .long 0x3FFB0000,0x9BB3078D,0x35AEC202,0x00000000
  118. .long 0x3FFB0000,0xA3A69A52,0x5DDCE7DE,0x00000000
  119. .long 0x3FFB0000,0xAB98E943,0x62765619,0x00000000
  120. .long 0x3FFB0000,0xB389E502,0xF9C59862,0x00000000
  121. .long 0x3FFB0000,0xBB797E43,0x6B09E6FB,0x00000000
  122. .long 0x3FFB0000,0xC367A5C7,0x39E5F446,0x00000000
  123. .long 0x3FFB0000,0xCB544C61,0xCFF7D5C6,0x00000000
  124. .long 0x3FFB0000,0xD33F62F8,0x2488533E,0x00000000
  125. .long 0x3FFB0000,0xDB28DA81,0x62404C77,0x00000000
  126. .long 0x3FFB0000,0xE310A407,0x8AD34F18,0x00000000
  127. .long 0x3FFB0000,0xEAF6B0A8,0x188EE1EB,0x00000000
  128. .long 0x3FFB0000,0xF2DAF194,0x9DBE79D5,0x00000000
  129. .long 0x3FFB0000,0xFABD5813,0x61D47E3E,0x00000000
  130. .long 0x3FFC0000,0x8346AC21,0x0959ECC4,0x00000000
  131. .long 0x3FFC0000,0x8B232A08,0x304282D8,0x00000000
  132. .long 0x3FFC0000,0x92FB70B8,0xD29AE2F9,0x00000000
  133. .long 0x3FFC0000,0x9ACF476F,0x5CCD1CB4,0x00000000
  134. .long 0x3FFC0000,0xA29E7630,0x4954F23F,0x00000000
  135. .long 0x3FFC0000,0xAA68C5D0,0x8AB85230,0x00000000
  136. .long 0x3FFC0000,0xB22DFFFD,0x9D539F83,0x00000000
  137. .long 0x3FFC0000,0xB9EDEF45,0x3E900EA5,0x00000000
  138. .long 0x3FFC0000,0xC1A85F1C,0xC75E3EA5,0x00000000
  139. .long 0x3FFC0000,0xC95D1BE8,0x28138DE6,0x00000000
  140. .long 0x3FFC0000,0xD10BF300,0x840D2DE4,0x00000000
  141. .long 0x3FFC0000,0xD8B4B2BA,0x6BC05E7A,0x00000000
  142. .long 0x3FFC0000,0xE0572A6B,0xB42335F6,0x00000000
  143. .long 0x3FFC0000,0xE7F32A70,0xEA9CAA8F,0x00000000
  144. .long 0x3FFC0000,0xEF888432,0x64ECEFAA,0x00000000
  145. .long 0x3FFC0000,0xF7170A28,0xECC06666,0x00000000
  146. .long 0x3FFD0000,0x812FD288,0x332DAD32,0x00000000
  147. .long 0x3FFD0000,0x88A8D1B1,0x218E4D64,0x00000000
  148. .long 0x3FFD0000,0x9012AB3F,0x23E4AEE8,0x00000000
  149. .long 0x3FFD0000,0x976CC3D4,0x11E7F1B9,0x00000000
  150. .long 0x3FFD0000,0x9EB68949,0x3889A227,0x00000000
  151. .long 0x3FFD0000,0xA5EF72C3,0x4487361B,0x00000000
  152. .long 0x3FFD0000,0xAD1700BA,0xF07A7227,0x00000000
  153. .long 0x3FFD0000,0xB42CBCFA,0xFD37EFB7,0x00000000
  154. .long 0x3FFD0000,0xBB303A94,0x0BA80F89,0x00000000
  155. .long 0x3FFD0000,0xC22115C6,0xFCAEBBAF,0x00000000
  156. .long 0x3FFD0000,0xC8FEF3E6,0x86331221,0x00000000
  157. .long 0x3FFD0000,0xCFC98330,0xB4000C70,0x00000000
  158. .long 0x3FFD0000,0xD6807AA1,0x102C5BF9,0x00000000
  159. .long 0x3FFD0000,0xDD2399BC,0x31252AA3,0x00000000
  160. .long 0x3FFD0000,0xE3B2A855,0x6B8FC517,0x00000000
  161. .long 0x3FFD0000,0xEA2D764F,0x64315989,0x00000000
  162. .long 0x3FFD0000,0xF3BF5BF8,0xBAD1A21D,0x00000000
  163. .long 0x3FFE0000,0x801CE39E,0x0D205C9A,0x00000000
  164. .long 0x3FFE0000,0x8630A2DA,0xDA1ED066,0x00000000
  165. .long 0x3FFE0000,0x8C1AD445,0xF3E09B8C,0x00000000
  166. .long 0x3FFE0000,0x91DB8F16,0x64F350E2,0x00000000
  167. .long 0x3FFE0000,0x97731420,0x365E538C,0x00000000
  168. .long 0x3FFE0000,0x9CE1C8E6,0xA0B8CDBA,0x00000000
  169. .long 0x3FFE0000,0xA22832DB,0xCADAAE09,0x00000000
  170. .long 0x3FFE0000,0xA746F2DD,0xB7602294,0x00000000
  171. .long 0x3FFE0000,0xAC3EC0FB,0x997DD6A2,0x00000000
  172. .long 0x3FFE0000,0xB110688A,0xEBDC6F6A,0x00000000
  173. .long 0x3FFE0000,0xB5BCC490,0x59ECC4B0,0x00000000
  174. .long 0x3FFE0000,0xBA44BC7D,0xD470782F,0x00000000
  175. .long 0x3FFE0000,0xBEA94144,0xFD049AAC,0x00000000
  176. .long 0x3FFE0000,0xC2EB4ABB,0x661628B6,0x00000000
  177. .long 0x3FFE0000,0xC70BD54C,0xE602EE14,0x00000000
  178. .long 0x3FFE0000,0xCD000549,0xADEC7159,0x00000000
  179. .long 0x3FFE0000,0xD48457D2,0xD8EA4EA3,0x00000000
  180. .long 0x3FFE0000,0xDB948DA7,0x12DECE3B,0x00000000
  181. .long 0x3FFE0000,0xE23855F9,0x69E8096A,0x00000000
  182. .long 0x3FFE0000,0xE8771129,0xC4353259,0x00000000
  183. .long 0x3FFE0000,0xEE57C16E,0x0D379C0D,0x00000000
  184. .long 0x3FFE0000,0xF3E10211,0xA87C3779,0x00000000
  185. .long 0x3FFE0000,0xF919039D,0x758B8D41,0x00000000
  186. .long 0x3FFE0000,0xFE058B8F,0x64935FB3,0x00000000
  187. .long 0x3FFF0000,0x8155FB49,0x7B685D04,0x00000000
  188. .long 0x3FFF0000,0x83889E35,0x49D108E1,0x00000000
  189. .long 0x3FFF0000,0x859CFA76,0x511D724B,0x00000000
  190. .long 0x3FFF0000,0x87952ECF,0xFF8131E7,0x00000000
  191. .long 0x3FFF0000,0x89732FD1,0x9557641B,0x00000000
  192. .long 0x3FFF0000,0x8B38CAD1,0x01932A35,0x00000000
  193. .long 0x3FFF0000,0x8CE7A8D8,0x301EE6B5,0x00000000
  194. .long 0x3FFF0000,0x8F46A39E,0x2EAE5281,0x00000000
  195. .long 0x3FFF0000,0x922DA7D7,0x91888487,0x00000000
  196. .long 0x3FFF0000,0x94D19FCB,0xDEDF5241,0x00000000
  197. .long 0x3FFF0000,0x973AB944,0x19D2A08B,0x00000000
  198. .long 0x3FFF0000,0x996FF00E,0x08E10B96,0x00000000
  199. .long 0x3FFF0000,0x9B773F95,0x12321DA7,0x00000000
  200. .long 0x3FFF0000,0x9D55CC32,0x0F935624,0x00000000
  201. .long 0x3FFF0000,0x9F100575,0x006CC571,0x00000000
  202. .long 0x3FFF0000,0xA0A9C290,0xD97CC06C,0x00000000
  203. .long 0x3FFF0000,0xA22659EB,0xEBC0630A,0x00000000
  204. .long 0x3FFF0000,0xA388B4AF,0xF6EF0EC9,0x00000000
  205. .long 0x3FFF0000,0xA4D35F10,0x61D292C4,0x00000000
  206. .long 0x3FFF0000,0xA60895DC,0xFBE3187E,0x00000000
  207. .long 0x3FFF0000,0xA72A51DC,0x7367BEAC,0x00000000
  208. .long 0x3FFF0000,0xA83A5153,0x0956168F,0x00000000
  209. .long 0x3FFF0000,0xA93A2007,0x7539546E,0x00000000
  210. .long 0x3FFF0000,0xAA9E7245,0x023B2605,0x00000000
  211. .long 0x3FFF0000,0xAC4C84BA,0x6FE4D58F,0x00000000
  212. .long 0x3FFF0000,0xADCE4A4A,0x606B9712,0x00000000
  213. .long 0x3FFF0000,0xAF2A2DCD,0x8D263C9C,0x00000000
  214. .long 0x3FFF0000,0xB0656F81,0xF22265C7,0x00000000
  215. .long 0x3FFF0000,0xB1846515,0x0F71496A,0x00000000
  216. .long 0x3FFF0000,0xB28AAA15,0x6F9ADA35,0x00000000
  217. .long 0x3FFF0000,0xB37B44FF,0x3766B895,0x00000000
  218. .long 0x3FFF0000,0xB458C3DC,0xE9630433,0x00000000
  219. .long 0x3FFF0000,0xB525529D,0x562246BD,0x00000000
  220. .long 0x3FFF0000,0xB5E2CCA9,0x5F9D88CC,0x00000000
  221. .long 0x3FFF0000,0xB692CADA,0x7ACA1ADA,0x00000000
  222. .long 0x3FFF0000,0xB736AEA7,0xA6925838,0x00000000
  223. .long 0x3FFF0000,0xB7CFAB28,0x7E9F7B36,0x00000000
  224. .long 0x3FFF0000,0xB85ECC66,0xCB219835,0x00000000
  225. .long 0x3FFF0000,0xB8E4FD5A,0x20A593DA,0x00000000
  226. .long 0x3FFF0000,0xB99F41F6,0x4AFF9BB5,0x00000000
  227. .long 0x3FFF0000,0xBA7F1E17,0x842BBE7B,0x00000000
  228. .long 0x3FFF0000,0xBB471285,0x7637E17D,0x00000000
  229. .long 0x3FFF0000,0xBBFABE8A,0x4788DF6F,0x00000000
  230. .long 0x3FFF0000,0xBC9D0FAD,0x2B689D79,0x00000000
  231. .long 0x3FFF0000,0xBD306A39,0x471ECD86,0x00000000
  232. .long 0x3FFF0000,0xBDB6C731,0x856AF18A,0x00000000
  233. .long 0x3FFF0000,0xBE31CAC5,0x02E80D70,0x00000000
  234. .long 0x3FFF0000,0xBEA2D55C,0xE33194E2,0x00000000
  235. .long 0x3FFF0000,0xBF0B10B7,0xC03128F0,0x00000000
  236. .long 0x3FFF0000,0xBF6B7A18,0xDACB778D,0x00000000
  237. .long 0x3FFF0000,0xBFC4EA46,0x63FA18F6,0x00000000
  238. .long 0x3FFF0000,0xC0181BDE,0x8B89A454,0x00000000
  239. .long 0x3FFF0000,0xC065B066,0xCFBF6439,0x00000000
  240. .long 0x3FFF0000,0xC0AE345F,0x56340AE6,0x00000000
  241. .long 0x3FFF0000,0xC0F22291,0x9CB9E6A7,0x00000000
  243. #define X FP_SCR1
  244. #define XDCARE X+2
  245. #define XFRAC X+4
  246. #define XFRACLO X+8
  248. #define ATANF FP_SCR2
  249. #define ATANFHI ATANF+4
  250. #define ATANFLO ATANF+8
  253. | xref __x_t_frcinx
  254. | xref __x_t_extdnrm
  257. .text
  259. .globl __x_satand
  260. __x_satand:
  261. |--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT
  263. jra  __x_t_extdnrm
  265. .globl __x_satan
  266. __x_satan:
  267. /* |--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S */
  269. fmovex A0@,fp0 |...lOAD INPUT
  271. movel A0@,d0
  272. movew A0@(4),d0
  273. fmovex fp0,a6@(X)
  274. andil #0x7FFFFFFF,d0
  276. cmpil #0x3FFB8000,d0 |...|X| >= 1/16?
  277. jge  ATANOK1
  278. jra  ATANSM
  280. ATANOK1:
  281. cmpil #0x4002FFFF,d0 |...|X| < 16 ?
  282. jle  ATANMAIN
  283. jra  ATANBIG
  286. |--THE MOST LIKELY CASE, |X| IN [1/16, 16). WE USE TABLE TECHNIQUE
  287. |--THE IDEA IS ATAN(X) = ATAN(F) + ATAN( [X-F] / [1+XF] ).
  288. |--SO IF F IS CHOSEN TO BE CLOSE TO X AND ATAN(F) IS STORED IN
  289. |--A TABLE, ALL WE NEED IS TO APPROXIMATE ATAN(U) WHERE
  290. |--U = (X-F)/(1+XF) IS SMALL (REMEMBER F IS CLOSE TO X). IT IS
  291. |--TRUE THAT A DIVIDE IS NOW NEEDED, BUT THE APPROXIMATION FOR
  292. |--ATAN(U) IS A VERY SHORT POLYNOMIAL AND THE INDEXING TO
  293. |--FETCH F AND SAVING OF REGISTERS CAN BE ALL HIDED UNDER THE
  294. |--DIVIDE. IN THE END THIS METHOD IS MUCH FASTER THAN A TRADITIONAL
  295. |--ONE. NOTE ALSO THAT THE TRADITIONAL SCHEME THAT APPROXIMATE
  296. |--ATAN(X) DIRECTLY WILL NEED TO USE A RATIONAL APPROXIMATION
  297. |--(DIVISION NEEDED) ANYWAY BECAUSE A POLYNOMIAL APPROXIMATION
  298. |--WILL INVOLVE A VERY LONG POLYNOMIAL.
  300. |--NOW WE SEE X AS +-2^K * 1.BBBBBBB....B <- 1. + 63 BITS
  301. |--WE CHOSE F TO BE +-2^K * 1.BBBB1
  302. |--THAT IS IT MATCHES THE EXPONENT AND FIRST 5 BITS OF X, THE
  303. |--SIXTH BITS IS SET TO BE 1. SINCE K = -4, -3, |..., 3, THERE
  304. /* |--ARE ONLY 8 TIMES 16 = 2^7 = 128 |F|'S. SINCE ATAN(-|F|) IS */
  305. |-- -ATAN(|F|), WE NEED TO STORE ONLY ATAN(|F|).
  307. ATANMAIN:
  309. movew #0x0000,a6@(XDCARE) |...CLEAN UP X JUST IN CASE
  310. andil #0xF8000000,a6@(XFRAC) |...FIRST 5 BITS
  311. oril #0x04000000,a6@(XFRAC) |...SET 6-TH BIT TO 1
  312. movel #0x00000000,a6@(XFRACLO) |...lOCATION OF X IS NOW F
  314. fmovex fp0,fp1 |...FP1 IS X
  315. fmulx a6@(X),fp1 |...FP1 IS X*F, NOTE THAT X*F > 0
  316. fsubx a6@(X),fp0 |...FP0 IS X-F
  317. .long 0xf23c44a2,0x3f800000 /*  fadds  &0x3F800000,fp1 */
  318. fdivx fp1,fp0 |...FP0 IS U = (X-F)/(1+X*F)
  320. |--WHILE THE DIVISION IS TAKING ITS TIME, WE FETCH ATAN(|F|)
  321. |--CREATE ATAN(F) AND STORE IT IN ATANF, AND
  322. |--SAVE REGISTERS FP2.
  324. movel d2,a7@- |...SAVE d2 TEMPORARILY
  325. movel d0,d2 |...THE EXPO AND 16 BITS OF X
  326. andil #0x00007800,d0 /* |...4 VARYING BITS OF F'S FRACTION */
  327. andil #0x7FFF0000,d2 |...EXPONENT OF F
  328. subil #0x3FFB0000,d2 |...K+4
  329. asrl #1,d2
  330. addl d2,d0 |...THE 7 BITS IDENTIFYING F
  331. asrl #7,d0 |...INDEX INTO TBL OF ATAN(|F|)
  332. lea ATANTBL,a1
  333. addal d0,a1 |...ADDRESS OF ATAN(|F|)
  334. movel a1@+,a6@(ATANF)
  335. movel a1@+,a6@(ATANFHI)
  336. movel a1@+,a6@(ATANFLO) |...ATANF IS NOW ATAN(|F|)
  337. movel a6@(X),d0 |...lOAD SIGN AND EXPO. AGAIN
  338. andil #0x80000000,d0 |...SIGN(F)
  339. orl d0,a6@(ATANF) |...ATANF IS NOW SIGN(F)*ATAN(|F|)
  340. movel a7@+,d2 |...RESTORE d2
  342. /* |--THAT'S ALL I HAVE TO DO FOR NOW, */
  343. |--BUT ALAS, THE DIVIDE IS STILL CRANKING!
  345. |--U IN FP0, WE ARE NOW READY TO COMPUTE ATAN(U) AS
  346. |--U + A1*U*V*(A2 + V*(A3 + V)), V = U*U
  347. |--THE POLYNOMIAL MAY LOOK STRANGE, BUT IS NEVERTHELESS CORRECT.
  348. |--THE NATURAL FORM IS U + U*V*(A1 + V*(A2 + V*A3))
  349. |--WHAT WE HAVE HERE IS MERELY A1 = A3, A2 = A1/A3, A3 = A2/A3.
  350. |--THE REASON FOR THIS REARRANGEMENT IS TO MAKE THE INDEPENDENT
  351. |--PARTS A1*U*V AND (A2 + |... STUFF) MORE LOAD-BALANCED
  354. fmovex fp0,fp1
  355. fmulx fp1,fp1
  356. fmoved ATANA3,fp2
  357. faddx fp1,fp2 |...A3+V
  358. fmulx fp1,fp2 |...V*(A3+V)
  359. fmulx fp0,fp1 |...U*V
  360. faddd ATANA2,fp2 |...A2+V*(A3+V)
  361. fmuld ATANA1,fp1 |...A1*U*V
  362. fmulx fp2,fp1 |...A1*U*V*(A2+V*(A3+V))
  364. faddx fp1,fp0 |...ATAN(U), fp1 RELEASED
  365. fmovel d1,fpcr | restore users exceptions
  366. faddx a6@(ATANF),fp0 |...ATAN(X)
  367. jra  __x_t_frcinx
  369. ATANBORS:
  370. |--|X| IS IN d0 IN COMPACT FORM. FP1, d0 SAVED.
  371. |--FP0 IS X AND |X| <= 1/16 OR |X| >= 16.
  372. cmpil #0x3FFF8000,d0
  373. jgt  ATANBIG |...I.E. |X| >= 16
  375. ATANSM:
  376. |--|X| <= 1/16
  377. |--IF |X| < 2^(-40), RETURN X AS ANSWER. OTHERWISE, APPROXIMATE
  378. |--ATAN(X) BY X + X*Y*(B1+Y*(B2+Y*(B3+Y*(B4+Y*(B5+Y*B6)))))
  379. |--WHICH IS X + X*Y*( [B1+Z*(B3+Z*B5)] + [Y*(B2+Z*(B4+Z*B6)] )
  380. |--WHERE Y = X*X, AND Z = Y*Y.
  382. cmpil #0x3FD78000,d0
  383. jlt  ATANTINY
  384. |--COMPUTE POLYNOMIAL
  385. fmulx fp0,fp0 |...FP0 IS Y = X*X
  388. movew #0x0000,a6@(XDCARE)
  390. fmovex fp0,fp1
  391. fmulx fp1,fp1 |...FP1 IS Z = Y*Y
  393. fmoved ATANB6,fp2
  394. fmoved ATANB5,fp3
  396. fmulx fp1,fp2 |...Z*B6
  397. fmulx fp1,fp3 |...Z*B5
  399. faddd ATANB4,fp2 |...B4+Z*B6
  400. faddd ATANB3,fp3 |...B3+Z*B5
  402. fmulx fp1,fp2 |...Z*(B4+Z*B6)
  403. fmulx fp3,fp1 |...Z*(B3+Z*B5)
  405. faddd ATANB2,fp2 |...B2+Z*(B4+Z*B6)
  406. faddd ATANB1,fp1 |...B1+Z*(B3+Z*B5)
  408. fmulx fp0,fp2 |...Y*(B2+Z*(B4+Z*B6))
  409. fmulx a6@(X),fp0 |...X*Y
  411. faddx fp2,fp1 |...[B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]
  414. fmulx fp1,fp0 |...X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))])
  416. fmovel d1,fpcr | restore users exceptions
  417. faddx a6@(X),fp0
  419. jra  __x_t_frcinx
  421. ATANTINY:
  422. |--|X| < 2^(-40), ATAN(X) = X
  423. movew #0x0000,a6@(XDCARE)
  425. fmovel d1,fpcr | restore users exceptions
  426. fmovex a6@(X),fp0 | last inst - possible exception set
  428. jra  __x_t_frcinx
  430. ATANBIG:
  431. |--IF |X| > 2^(100), RETURN SIGN(X)*(PI/2 - TINY). OTHERWISE,
  432. |--RETURN SIGN(X)*PI/2 + ATAN(-1/X).
  433. cmpil #0x40638000,d0
  434. jgt  ATANHUGE
  436. |--APPROXIMATE ATAN(-1/X) BY
  437. /* |--X'+X'*Y*(C1+Y*(C2+Y*(C3+Y*(C4+Y*C5)))), X' = -1/X, Y = X'*X' */
  438. |--THIS CAN BE RE-WRITTEN AS
  439. /* |--X'+X'*Y*( [C1+Z*(C3+Z*C5)] + [Y*(C2+Z*C4)] ), Z = Y*Y. */
  441. .long 0xf23c4480,0xbf800000 /*  fmoves  &0xBF800000,fp1 */
  442. fdivx fp0,fp1 |...FP1 IS -1/X
  445. |--DIVIDE IS STILL CRANKING
  447. fmovex fp1,fp0 /* |...FP0 IS X' */
  448. fmulx fp0,fp0 /* |...FP0 IS Y = X'*X' */
  449. fmovex fp1,a6@(X) /* |...X IS REALLY X' */
  451. fmovex fp0,fp1
  452. fmulx fp1,fp1 |...FP1 IS Z = Y*Y
  454. fmoved ATANC5,fp3
  455. fmoved ATANC4,fp2
  457. fmulx fp1,fp3 |...Z*C5
  458. fmulx fp1,fp2 |...Z*B4
  460. faddd ATANC3,fp3 |...C3+Z*C5
  461. faddd ATANC2,fp2 |...C2+Z*C4
  463. fmulx fp3,fp1 |...Z*(C3+Z*C5), fp3 RELEASED
  464. fmulx fp0,fp2 |...Y*(C2+Z*C4)
  466. faddd ATANC1,fp1 |...C1+Z*(C3+Z*C5)
  467. fmulx a6@(X),fp0 /* |...X'*Y */
  469. faddx fp2,fp1 |...[Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)]
  472. fmulx fp1,fp0 /* |...X'*Y*([B1+Z*(B3+Z*B5)] */
  473. | |... +[Y*(B2+Z*(B4+Z*B6))])
  474. faddx a6@(X),fp0
  476. fmovel d1,fpcr | restore users exceptions
  478. btst #7,a0@
  479. jeq  pos_big
  481. neg_big:
  482. faddx NPIBY2,fp0
  483. jra  __x_t_frcinx
  485. pos_big:
  486. faddx PPIBY2,fp0
  487. jra  __x_t_frcinx
  489. ATANHUGE:
  490. |--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY
  491. btst #7,a0@
  492. jeq  pos_huge
  494. neg_huge:
  495. fmovex NPIBY2,fp0
  496. fmovel d1,fpcr
  497. fsubx NTINY,fp0
  498. jra  __x_t_frcinx
  500. pos_huge:
  501. fmovex PPIBY2,fp0
  502. fmovel d1,fpcr
  503. fsubx PTINY,fp0
  504. jra  __x_t_frcinx
  506. | end