arch/m68k/fpsp040/satan.S

   1 |
   2 |       satan.sa 3.3 12/19/90
   3 |
   4 |       The entry point satan computes the arctangent of an
   5 |       input value. satand does the same except the input value is a
   6 |       denormalized number.
   7 |
   8 |       Input: Double-extended value in memory location pointed to by address
   9 |               register a0.
  10 |
  11 |       Output: Arctan(X) returned in floating-point register Fp0.
  12 |
  13 |       Accuracy and Monotonicity: The returned result is within 2 ulps in
  14 |               64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
  15 |               result is subsequently rounded to double precision. The
  16 |               result is provably monotonic in double precision.
  17 |
  18 |       Speed: The program satan takes approximately 160 cycles for input
  19 |               argument X such that 1/16 < |X| < 16. For the other arguments,
  20 |               the program will run no worse than 10% slower.
  21 |
  22 |       Algorithm:
  23 |       Step 1. If |X| >= 16 or |X| < 1/16, go to Step 5.
  24 |
  25 |       Step 2. Let X = sgn * 2**k * 1.xxxxxxxx...x. Note that k = -4, -3,..., or 3.
  26 |               Define F = sgn * 2**k * 1.xxxx1, i.e. the first 5 significant bits
  27 |               of X with a bit-1 attached at the 6-th bit position. Define u
  28 |               to be u = (X-F) / (1 + X*F).
  29 |
  30 |       Step 3. Approximate arctan(u) by a polynomial poly.
  31 |
  32 |       Step 4. Return arctan(F) + poly, arctan(F) is fetched from a table of values
  33 |               calculated beforehand. Exit.
  34 |
  35 |       Step 5. If |X| >= 16, go to Step 7.
  36 |
  37 |       Step 6. Approximate arctan(X) by an odd polynomial in X. Exit.
  38 |
  39 |       Step 7. Define X' = -1/X. Approximate arctan(X') by an odd polynomial in X'.
  40 |               Arctan(X) = sign(X)*Pi/2 + arctan(X'). Exit.
  41 |
  42
  43 |               Copyright (C) Motorola, Inc. 1990
  44 |                       All Rights Reserved
  45 |
  46 |       For details on the license for this file, please see the
  47 |       file, README, in this same directory.
  48
  49 |satan  idnt    2,1 | Motorola 040 Floating Point Software Package
  50
  51         |section        8
  52
  53 #include "fpsp.h"
  54
  55 BOUNDS1:        .long 0x3FFB8000,0x4002FFFF
  56
  57 ONE:    .long 0x3F800000
  58
  59         .long 0x00000000
  60
  61 ATANA3: .long 0xBFF6687E,0x314987D8
  62 ATANA2: .long 0x4002AC69,0x34A26DB3
  63
  64 ATANA1: .long 0xBFC2476F,0x4E1DA28E
  65 ATANB6: .long 0x3FB34444,0x7F876989
  66
  67 ATANB5: .long 0xBFB744EE,0x7FAF45DB
  68 ATANB4: .long 0x3FBC71C6,0x46940220
  69
  70 ATANB3: .long 0xBFC24924,0x921872F9
  71 ATANB2: .long 0x3FC99999,0x99998FA9
  72
  73 ATANB1: .long 0xBFD55555,0x55555555
  74 ATANC5: .long 0xBFB70BF3,0x98539E6A
  75
  76 ATANC4: .long 0x3FBC7187,0x962D1D7D
  77 ATANC3: .long 0xBFC24924,0x827107B8
  78
  79 ATANC2: .long 0x3FC99999,0x9996263E
  80 ATANC1: .long 0xBFD55555,0x55555536
  81
  82 PPIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
  83 NPIBY2: .long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x00000000
  84 PTINY:  .long 0x00010000,0x80000000,0x00000000,0x00000000
  85 NTINY:  .long 0x80010000,0x80000000,0x00000000,0x00000000
  86
  87 ATANTBL:
  88         .long   0x3FFB0000,0x83D152C5,0x060B7A51,0x00000000
  89         .long   0x3FFB0000,0x8BC85445,0x65498B8B,0x00000000
  90         .long   0x3FFB0000,0x93BE4060,0x17626B0D,0x00000000
  91         .long   0x3FFB0000,0x9BB3078D,0x35AEC202,0x00000000
  92         .long   0x3FFB0000,0xA3A69A52,0x5DDCE7DE,0x00000000
  93         .long   0x3FFB0000,0xAB98E943,0x62765619,0x00000000
  94         .long   0x3FFB0000,0xB389E502,0xF9C59862,0x00000000
  95         .long   0x3FFB0000,0xBB797E43,0x6B09E6FB,0x00000000
  96         .long   0x3FFB0000,0xC367A5C7,0x39E5F446,0x00000000
  97         .long   0x3FFB0000,0xCB544C61,0xCFF7D5C6,0x00000000
  98         .long   0x3FFB0000,0xD33F62F8,0x2488533E,0x00000000
  99         .long   0x3FFB0000,0xDB28DA81,0x62404C77,0x00000000
 100         .long   0x3FFB0000,0xE310A407,0x8AD34F18,0x00000000
 101         .long   0x3FFB0000,0xEAF6B0A8,0x188EE1EB,0x00000000
 102         .long   0x3FFB0000,0xF2DAF194,0x9DBE79D5,0x00000000
 103         .long   0x3FFB0000,0xFABD5813,0x61D47E3E,0x00000000
 104         .long   0x3FFC0000,0x8346AC21,0x0959ECC4,0x00000000
 105         .long   0x3FFC0000,0x8B232A08,0x304282D8,0x00000000
 106         .long   0x3FFC0000,0x92FB70B8,0xD29AE2F9,0x00000000
 107         .long   0x3FFC0000,0x9ACF476F,0x5CCD1CB4,0x00000000
 108         .long   0x3FFC0000,0xA29E7630,0x4954F23F,0x00000000
 109         .long   0x3FFC0000,0xAA68C5D0,0x8AB85230,0x00000000
 110         .long   0x3FFC0000,0xB22DFFFD,0x9D539F83,0x00000000
 111         .long   0x3FFC0000,0xB9EDEF45,0x3E900EA5,0x00000000
 112         .long   0x3FFC0000,0xC1A85F1C,0xC75E3EA5,0x00000000
 113         .long   0x3FFC0000,0xC95D1BE8,0x28138DE6,0x00000000
 114         .long   0x3FFC0000,0xD10BF300,0x840D2DE4,0x00000000
 115         .long   0x3FFC0000,0xD8B4B2BA,0x6BC05E7A,0x00000000
 116         .long   0x3FFC0000,0xE0572A6B,0xB42335F6,0x00000000
 117         .long   0x3FFC0000,0xE7F32A70,0xEA9CAA8F,0x00000000
 118         .long   0x3FFC0000,0xEF888432,0x64ECEFAA,0x00000000
 119         .long   0x3FFC0000,0xF7170A28,0xECC06666,0x00000000
 120         .long   0x3FFD0000,0x812FD288,0x332DAD32,0x00000000
 121         .long   0x3FFD0000,0x88A8D1B1,0x218E4D64,0x00000000
 122         .long   0x3FFD0000,0x9012AB3F,0x23E4AEE8,0x00000000
 123         .long   0x3FFD0000,0x976CC3D4,0x11E7F1B9,0x00000000
 124         .long   0x3FFD0000,0x9EB68949,0x3889A227,0x00000000
 125         .long   0x3FFD0000,0xA5EF72C3,0x4487361B,0x00000000
 126         .long   0x3FFD0000,0xAD1700BA,0xF07A7227,0x00000000
 127         .long   0x3FFD0000,0xB42CBCFA,0xFD37EFB7,0x00000000
 128         .long   0x3FFD0000,0xBB303A94,0x0BA80F89,0x00000000
 129         .long   0x3FFD0000,0xC22115C6,0xFCAEBBAF,0x00000000
 130         .long   0x3FFD0000,0xC8FEF3E6,0x86331221,0x00000000
 131         .long   0x3FFD0000,0xCFC98330,0xB4000C70,0x00000000
 132         .long   0x3FFD0000,0xD6807AA1,0x102C5BF9,0x00000000
 133         .long   0x3FFD0000,0xDD2399BC,0x31252AA3,0x00000000
 134         .long   0x3FFD0000,0xE3B2A855,0x6B8FC517,0x00000000
 135         .long   0x3FFD0000,0xEA2D764F,0x64315989,0x00000000
 136         .long   0x3FFD0000,0xF3BF5BF8,0xBAD1A21D,0x00000000
 137         .long   0x3FFE0000,0x801CE39E,0x0D205C9A,0x00000000
 138         .long   0x3FFE0000,0x8630A2DA,0xDA1ED066,0x00000000
 139         .long   0x3FFE0000,0x8C1AD445,0xF3E09B8C,0x00000000
 140         .long   0x3FFE0000,0x91DB8F16,0x64F350E2,0x00000000
 141         .long   0x3FFE0000,0x97731420,0x365E538C,0x00000000
 142         .long   0x3FFE0000,0x9CE1C8E6,0xA0B8CDBA,0x00000000
 143         .long   0x3FFE0000,0xA22832DB,0xCADAAE09,0x00000000
 144         .long   0x3FFE0000,0xA746F2DD,0xB7602294,0x00000000
 145         .long   0x3FFE0000,0xAC3EC0FB,0x997DD6A2,0x00000000
 146         .long   0x3FFE0000,0xB110688A,0xEBDC6F6A,0x00000000
 147         .long   0x3FFE0000,0xB5BCC490,0x59ECC4B0,0x00000000
 148         .long   0x3FFE0000,0xBA44BC7D,0xD470782F,0x00000000
 149         .long   0x3FFE0000,0xBEA94144,0xFD049AAC,0x00000000
 150         .long   0x3FFE0000,0xC2EB4ABB,0x661628B6,0x00000000
 151         .long   0x3FFE0000,0xC70BD54C,0xE602EE14,0x00000000
 152         .long   0x3FFE0000,0xCD000549,0xADEC7159,0x00000000
 153         .long   0x3FFE0000,0xD48457D2,0xD8EA4EA3,0x00000000
 154         .long   0x3FFE0000,0xDB948DA7,0x12DECE3B,0x00000000
 155         .long   0x3FFE0000,0xE23855F9,0x69E8096A,0x00000000
 156         .long   0x3FFE0000,0xE8771129,0xC4353259,0x00000000
 157         .long   0x3FFE0000,0xEE57C16E,0x0D379C0D,0x00000000
 158         .long   0x3FFE0000,0xF3E10211,0xA87C3779,0x00000000
 159         .long   0x3FFE0000,0xF919039D,0x758B8D41,0x00000000
 160         .long   0x3FFE0000,0xFE058B8F,0x64935FB3,0x00000000
 161         .long   0x3FFF0000,0x8155FB49,0x7B685D04,0x00000000
 162         .long   0x3FFF0000,0x83889E35,0x49D108E1,0x00000000
 163         .long   0x3FFF0000,0x859CFA76,0x511D724B,0x00000000
 164         .long   0x3FFF0000,0x87952ECF,0xFF8131E7,0x00000000
 165         .long   0x3FFF0000,0x89732FD1,0x9557641B,0x00000000
 166         .long   0x3FFF0000,0x8B38CAD1,0x01932A35,0x00000000
 167         .long   0x3FFF0000,0x8CE7A8D8,0x301EE6B5,0x00000000
 168         .long   0x3FFF0000,0x8F46A39E,0x2EAE5281,0x00000000
 169         .long   0x3FFF0000,0x922DA7D7,0x91888487,0x00000000
 170         .long   0x3FFF0000,0x94D19FCB,0xDEDF5241,0x00000000
 171         .long   0x3FFF0000,0x973AB944,0x19D2A08B,0x00000000
 172         .long   0x3FFF0000,0x996FF00E,0x08E10B96,0x00000000
 173         .long   0x3FFF0000,0x9B773F95,0x12321DA7,0x00000000
 174         .long   0x3FFF0000,0x9D55CC32,0x0F935624,0x00000000
 175         .long   0x3FFF0000,0x9F100575,0x006CC571,0x00000000
 176         .long   0x3FFF0000,0xA0A9C290,0xD97CC06C,0x00000000
 177         .long   0x3FFF0000,0xA22659EB,0xEBC0630A,0x00000000
 178         .long   0x3FFF0000,0xA388B4AF,0xF6EF0EC9,0x00000000
 179         .long   0x3FFF0000,0xA4D35F10,0x61D292C4,0x00000000
 180         .long   0x3FFF0000,0xA60895DC,0xFBE3187E,0x00000000
 181         .long   0x3FFF0000,0xA72A51DC,0x7367BEAC,0x00000000
 182         .long   0x3FFF0000,0xA83A5153,0x0956168F,0x00000000
 183         .long   0x3FFF0000,0xA93A2007,0x7539546E,0x00000000
 184         .long   0x3FFF0000,0xAA9E7245,0x023B2605,0x00000000
 185         .long   0x3FFF0000,0xAC4C84BA,0x6FE4D58F,0x00000000
 186         .long   0x3FFF0000,0xADCE4A4A,0x606B9712,0x00000000
 187         .long   0x3FFF0000,0xAF2A2DCD,0x8D263C9C,0x00000000
 188         .long   0x3FFF0000,0xB0656F81,0xF22265C7,0x00000000
 189         .long   0x3FFF0000,0xB1846515,0x0F71496A,0x00000000
 190         .long   0x3FFF0000,0xB28AAA15,0x6F9ADA35,0x00000000
 191         .long   0x3FFF0000,0xB37B44FF,0x3766B895,0x00000000
 192         .long   0x3FFF0000,0xB458C3DC,0xE9630433,0x00000000
 193         .long   0x3FFF0000,0xB525529D,0x562246BD,0x00000000
 194         .long   0x3FFF0000,0xB5E2CCA9,0x5F9D88CC,0x00000000
 195         .long   0x3FFF0000,0xB692CADA,0x7ACA1ADA,0x00000000
 196         .long   0x3FFF0000,0xB736AEA7,0xA6925838,0x00000000
 197         .long   0x3FFF0000,0xB7CFAB28,0x7E9F7B36,0x00000000
 198         .long   0x3FFF0000,0xB85ECC66,0xCB219835,0x00000000
 199         .long   0x3FFF0000,0xB8E4FD5A,0x20A593DA,0x00000000
 200         .long   0x3FFF0000,0xB99F41F6,0x4AFF9BB5,0x00000000
 201         .long   0x3FFF0000,0xBA7F1E17,0x842BBE7B,0x00000000
 202         .long   0x3FFF0000,0xBB471285,0x7637E17D,0x00000000
 203         .long   0x3FFF0000,0xBBFABE8A,0x4788DF6F,0x00000000
 204         .long   0x3FFF0000,0xBC9D0FAD,0x2B689D79,0x00000000
 205         .long   0x3FFF0000,0xBD306A39,0x471ECD86,0x00000000
 206         .long   0x3FFF0000,0xBDB6C731,0x856AF18A,0x00000000
 207         .long   0x3FFF0000,0xBE31CAC5,0x02E80D70,0x00000000
 208         .long   0x3FFF0000,0xBEA2D55C,0xE33194E2,0x00000000
 209         .long   0x3FFF0000,0xBF0B10B7,0xC03128F0,0x00000000
 210         .long   0x3FFF0000,0xBF6B7A18,0xDACB778D,0x00000000
 211         .long   0x3FFF0000,0xBFC4EA46,0x63FA18F6,0x00000000
 212         .long   0x3FFF0000,0xC0181BDE,0x8B89A454,0x00000000
 213         .long   0x3FFF0000,0xC065B066,0xCFBF6439,0x00000000
 214         .long   0x3FFF0000,0xC0AE345F,0x56340AE6,0x00000000
 215         .long   0x3FFF0000,0xC0F22291,0x9CB9E6A7,0x00000000
 216
 217         .set    X,FP_SCR1
 218         .set    XDCARE,X+2
 219         .set    XFRAC,X+4
 220         .set    XFRACLO,X+8
 221
 222         .set    ATANF,FP_SCR2
 223         .set    ATANFHI,ATANF+4
 224         .set    ATANFLO,ATANF+8
 225
 226
 227         | xref  t_frcinx
 228         |xref   t_extdnrm
 229
 230         .global satand
 231 satand:
 232 |--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT
 233
 234         bra             t_extdnrm
 235
 236         .global satan
 237 satan:
 238 |--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
 239
 240         fmovex          (%a0),%fp0      | ...LOAD INPUT
 241
 242         movel           (%a0),%d0
 243         movew           4(%a0),%d0
 244         fmovex          %fp0,X(%a6)
 245         andil           #0x7FFFFFFF,%d0
 246
 247         cmpil           #0x3FFB8000,%d0         | ...|X| >= 1/16?
 248         bges            ATANOK1
 249         bra             ATANSM
 250
 251 ATANOK1:
 252         cmpil           #0x4002FFFF,%d0         | ...|X| < 16 ?
 253         bles            ATANMAIN
 254         bra             ATANBIG
 255
 256
 257 |--THE MOST LIKELY CASE, |X| IN [1/16, 16). WE USE TABLE TECHNIQUE
 258 |--THE IDEA IS ATAN(X) = ATAN(F) + ATAN( [X-F] / [1+XF] ).
 259 |--SO IF F IS CHOSEN TO BE CLOSE TO X AND ATAN(F) IS STORED IN
 260 |--A TABLE, ALL WE NEED IS TO APPROXIMATE ATAN(U) WHERE
 261 |--U = (X-F)/(1+XF) IS SMALL (REMEMBER F IS CLOSE TO X). IT IS
 262 |--TRUE THAT A DIVIDE IS NOW NEEDED, BUT THE APPROXIMATION FOR
 263 |--ATAN(U) IS A VERY SHORT POLYNOMIAL AND THE INDEXING TO
 264 |--FETCH F AND SAVING OF REGISTERS CAN BE ALL HIDED UNDER THE
 265 |--DIVIDE. IN THE END THIS METHOD IS MUCH FASTER THAN A TRADITIONAL
 266 |--ONE. NOTE ALSO THAT THE TRADITIONAL SCHEME THAT APPROXIMATE
 267 |--ATAN(X) DIRECTLY WILL NEED TO USE A RATIONAL APPROXIMATION
 268 |--(DIVISION NEEDED) ANYWAY BECAUSE A POLYNOMIAL APPROXIMATION
 269 |--WILL INVOLVE A VERY LONG POLYNOMIAL.
 270
 271 |--NOW WE SEE X AS +-2^K * 1.BBBBBBB....B <- 1. + 63 BITS
 272 |--WE CHOSE F TO BE +-2^K * 1.BBBB1
 273 |--THAT IS IT MATCHES THE EXPONENT AND FIRST 5 BITS OF X, THE
 274 |--SIXTH BITS IS SET TO BE 1. SINCE K = -4, -3, ..., 3, THERE
 275 |--ARE ONLY 8 TIMES 16 = 2^7 = 128 |F|'S. SINCE ATAN(-|F|) IS
 276 |-- -ATAN(|F|), WE NEED TO STORE ONLY ATAN(|F|).
 277
 278 ATANMAIN:
 279
 280         movew           #0x0000,XDCARE(%a6)     | ...CLEAN UP X JUST IN CASE
 281         andil           #0xF8000000,XFRAC(%a6)  | ...FIRST 5 BITS
 282         oril            #0x04000000,XFRAC(%a6)  | ...SET 6-TH BIT TO 1
 283         movel           #0x00000000,XFRACLO(%a6)        | ...LOCATION OF X IS NOW F
 284
 285         fmovex          %fp0,%fp1                       | ...FP1 IS X
 286         fmulx           X(%a6),%fp1             | ...FP1 IS X*F, NOTE THAT X*F > 0
 287         fsubx           X(%a6),%fp0             | ...FP0 IS X-F
 288         fadds           #0x3F800000,%fp1                | ...FP1 IS 1 + X*F
 289         fdivx           %fp1,%fp0                       | ...FP0 IS U = (X-F)/(1+X*F)
 290
 291 |--WHILE THE DIVISION IS TAKING ITS TIME, WE FETCH ATAN(|F|)
 292 |--CREATE ATAN(F) AND STORE IT IN ATANF, AND
 293 |--SAVE REGISTERS FP2.
 294
 295         movel           %d2,-(%a7)      | ...SAVE d2 TEMPORARILY
 296         movel           %d0,%d2         | ...THE EXPO AND 16 BITS OF X
 297         andil           #0x00007800,%d0 | ...4 VARYING BITS OF F'S FRACTION
 298         andil           #0x7FFF0000,%d2 | ...EXPONENT OF F
 299         subil           #0x3FFB0000,%d2 | ...K+4
 300         asrl            #1,%d2
 301         addl            %d2,%d0         | ...THE 7 BITS IDENTIFYING F
 302         asrl            #7,%d0          | ...INDEX INTO TBL OF ATAN(|F|)
 303         lea             ATANTBL,%a1
 304         addal           %d0,%a1         | ...ADDRESS OF ATAN(|F|)
 305         movel           (%a1)+,ATANF(%a6)
 306         movel           (%a1)+,ATANFHI(%a6)
 307         movel           (%a1)+,ATANFLO(%a6)     | ...ATANF IS NOW ATAN(|F|)
 308         movel           X(%a6),%d0              | ...LOAD SIGN AND EXPO. AGAIN
 309         andil           #0x80000000,%d0 | ...SIGN(F)
 310         orl             %d0,ATANF(%a6)  | ...ATANF IS NOW SIGN(F)*ATAN(|F|)
 311         movel           (%a7)+,%d2      | ...RESTORE d2
 312
 313 |--THAT'S ALL I HAVE TO DO FOR NOW,
 314 |--BUT ALAS, THE DIVIDE IS STILL CRANKING!
 315
 316 |--U IN FP0, WE ARE NOW READY TO COMPUTE ATAN(U) AS
 317 |--U + A1*U*V*(A2 + V*(A3 + V)), V = U*U
 318 |--THE POLYNOMIAL MAY LOOK STRANGE, BUT IS NEVERTHELESS CORRECT.
 319 |--THE NATURAL FORM IS U + U*V*(A1 + V*(A2 + V*A3))
 320 |--WHAT WE HAVE HERE IS MERELY  A1 = A3, A2 = A1/A3, A3 = A2/A3.
 321 |--THE REASON FOR THIS REARRANGEMENT IS TO MAKE THE INDEPENDENT
 322 |--PARTS A1*U*V AND (A2 + ... STUFF) MORE LOAD-BALANCED
 323
 324
 325         fmovex          %fp0,%fp1
 326         fmulx           %fp1,%fp1
 327         fmoved          ATANA3,%fp2
 328         faddx           %fp1,%fp2               | ...A3+V
 329         fmulx           %fp1,%fp2               | ...V*(A3+V)
 330         fmulx           %fp0,%fp1               | ...U*V
 331         faddd           ATANA2,%fp2     | ...A2+V*(A3+V)
 332         fmuld           ATANA1,%fp1     | ...A1*U*V
 333         fmulx           %fp2,%fp1               | ...A1*U*V*(A2+V*(A3+V))
 334
 335         faddx           %fp1,%fp0               | ...ATAN(U), FP1 RELEASED
 336         fmovel          %d1,%FPCR               |restore users exceptions
 337         faddx           ATANF(%a6),%fp0 | ...ATAN(X)
 338         bra             t_frcinx
 339
 340 ATANBORS:
 341 |--|X| IS IN d0 IN COMPACT FORM. FP1, d0 SAVED.
 342 |--FP0 IS X AND |X| <= 1/16 OR |X| >= 16.
 343         cmpil           #0x3FFF8000,%d0
 344         bgt             ATANBIG | ...I.E. |X| >= 16
 345
 346 ATANSM:
 347 |--|X| <= 1/16
 348 |--IF |X| < 2^(-40), RETURN X AS ANSWER. OTHERWISE, APPROXIMATE
 349 |--ATAN(X) BY X + X*Y*(B1+Y*(B2+Y*(B3+Y*(B4+Y*(B5+Y*B6)))))
 350 |--WHICH IS X + X*Y*( [B1+Z*(B3+Z*B5)] + [Y*(B2+Z*(B4+Z*B6)] )
 351 |--WHERE Y = X*X, AND Z = Y*Y.
 352
 353         cmpil           #0x3FD78000,%d0
 354         blt             ATANTINY
 355 |--COMPUTE POLYNOMIAL
 356         fmulx           %fp0,%fp0       | ...FP0 IS Y = X*X
 357
 358
 359         movew           #0x0000,XDCARE(%a6)
 360
 361         fmovex          %fp0,%fp1
 362         fmulx           %fp1,%fp1               | ...FP1 IS Z = Y*Y
 363
 364         fmoved          ATANB6,%fp2
 365         fmoved          ATANB5,%fp3
 366
 367         fmulx           %fp1,%fp2               | ...Z*B6
 368         fmulx           %fp1,%fp3               | ...Z*B5
 369
 370         faddd           ATANB4,%fp2     | ...B4+Z*B6
 371         faddd           ATANB3,%fp3     | ...B3+Z*B5
 372
 373         fmulx           %fp1,%fp2               | ...Z*(B4+Z*B6)
 374         fmulx           %fp3,%fp1               | ...Z*(B3+Z*B5)
 375
 376         faddd           ATANB2,%fp2     | ...B2+Z*(B4+Z*B6)
 377         faddd           ATANB1,%fp1     | ...B1+Z*(B3+Z*B5)
 378
 379         fmulx           %fp0,%fp2               | ...Y*(B2+Z*(B4+Z*B6))
 380         fmulx           X(%a6),%fp0             | ...X*Y
 381
 382         faddx           %fp2,%fp1               | ...[B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]
 383
 384
 385         fmulx           %fp1,%fp0       | ...X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))])
 386
 387         fmovel          %d1,%FPCR               |restore users exceptions
 388         faddx           X(%a6),%fp0
 389
 390         bra             t_frcinx
 391
 392 ATANTINY:
 393 |--|X| < 2^(-40), ATAN(X) = X
 394         movew           #0x0000,XDCARE(%a6)
 395
 396         fmovel          %d1,%FPCR               |restore users exceptions
 397         fmovex          X(%a6),%fp0     |last inst - possible exception set
 398
 399         bra             t_frcinx
 400
 401 ATANBIG:
 402 |--IF |X| > 2^(100), RETURN     SIGN(X)*(PI/2 - TINY). OTHERWISE,
 403 |--RETURN SIGN(X)*PI/2 + ATAN(-1/X).
 404         cmpil           #0x40638000,%d0
 405         bgt             ATANHUGE
 406
 407 |--APPROXIMATE ATAN(-1/X) BY
 408 |--X'+X'*Y*(C1+Y*(C2+Y*(C3+Y*(C4+Y*C5)))), X' = -1/X, Y = X'*X'
 409 |--THIS CAN BE RE-WRITTEN AS
 410 |--X'+X'*Y*( [C1+Z*(C3+Z*C5)] + [Y*(C2+Z*C4)] ), Z = Y*Y.
 411
 412         fmoves          #0xBF800000,%fp1        | ...LOAD -1
 413         fdivx           %fp0,%fp1               | ...FP1 IS -1/X
 414
 415
 416 |--DIVIDE IS STILL CRANKING
 417
 418         fmovex          %fp1,%fp0               | ...FP0 IS X'
 419         fmulx           %fp0,%fp0               | ...FP0 IS Y = X'*X'
 420         fmovex          %fp1,X(%a6)             | ...X IS REALLY X'
 421
 422         fmovex          %fp0,%fp1
 423         fmulx           %fp1,%fp1               | ...FP1 IS Z = Y*Y
 424
 425         fmoved          ATANC5,%fp3
 426         fmoved          ATANC4,%fp2
 427
 428         fmulx           %fp1,%fp3               | ...Z*C5
 429         fmulx           %fp1,%fp2               | ...Z*B4
 430
 431         faddd           ATANC3,%fp3     | ...C3+Z*C5
 432         faddd           ATANC2,%fp2     | ...C2+Z*C4
 433
 434         fmulx           %fp3,%fp1               | ...Z*(C3+Z*C5), FP3 RELEASED
 435         fmulx           %fp0,%fp2               | ...Y*(C2+Z*C4)
 436
 437         faddd           ATANC1,%fp1     | ...C1+Z*(C3+Z*C5)
 438         fmulx           X(%a6),%fp0             | ...X'*Y
 439
 440         faddx           %fp2,%fp1               | ...[Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)]
 441
 442
 443         fmulx           %fp1,%fp0               | ...X'*Y*([B1+Z*(B3+Z*B5)]
 444 |                                       ...     +[Y*(B2+Z*(B4+Z*B6))])
 445         faddx           X(%a6),%fp0
 446
 447         fmovel          %d1,%FPCR               |restore users exceptions
 448
 449         btstb           #7,(%a0)
 450         beqs            pos_big
 451
 452 neg_big:
 453         faddx           NPIBY2,%fp0
 454         bra             t_frcinx
 455
 456 pos_big:
 457         faddx           PPIBY2,%fp0
 458         bra             t_frcinx
 459
 460 ATANHUGE:
 461 |--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY
 462         btstb           #7,(%a0)
 463         beqs            pos_huge
 464
 465 neg_huge:
 466         fmovex          NPIBY2,%fp0
 467         fmovel          %d1,%fpcr
 468         fsubx           NTINY,%fp0
 469         bra             t_frcinx
 470
 471 pos_huge:
 472         fmovex          PPIBY2,%fp0
 473         fmovel          %d1,%fpcr
 474         fsubx           PTINY,%fp0
 475         bra             t_frcinx
 476
 477         |end