sysdeps/ia64/fpu/e_atan2f.S

   1 .file "atan2f.s"
   2
   3
   4 // Copyright (c) 2000 - 2003, Intel Corporation
   5 // All rights reserved.
   6 //
   7 //
   8 // Redistribution and use in source and binary forms, with or without
   9 // modification, are permitted provided that the following conditions are
  10 // met:
  11 //
  12 // * Redistributions of source code must retain the above copyright
  13 // notice, this list of conditions and the following disclaimer.
  14 //
  15 // * Redistributions in binary form must reproduce the above copyright
  16 // notice, this list of conditions and the following disclaimer in the
  17 // documentation and/or other materials provided with the distribution.
  18 //
  19 // * The name of Intel Corporation may not be used to endorse or promote
  20 // products derived from this software without specific prior written
  21 // permission.
  22
  23 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  24 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  25 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
  26 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
  27 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
  28 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
  29 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
  30 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
  31 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
  32 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
  33 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  34 //
  35 // Intel Corporation is the author of this code, and requests that all
  36 // problem reports or change requests be submitted to it directly at
  37 // http://www.intel.com/software/products/opensource/libraries/num.htm.
  38
  39 // History
  40 //==============================================================
  41 // 06/01/00 Initial version
  42 // 08/15/00 Bundle added after call to __libm_error_support to properly
  43 //          set [the previously overwritten] GR_Parameter_RESULT.
  44 // 08/17/00 Changed predicate register macro-usage to direct predicate
  45 //          names due to an assembler bug.
  46 // 01/05/01 Fixed flag settings for denormal input.
  47 // 01/19/01 Added documentation
  48 // 01/30/01 Improved speed
  49 // 02/06/02 Corrected .section statement
  50 // 05/20/02 Cleaned up namespace and sf0 syntax
  51 // 02/06/03 Reordered header: .section, .global, .proc, .align
  52
  53 // Description
  54 //=========================================
  55 // The atan2 function computes the principle value of the arc tangent of y/x using
  56 // the signs of both arguments to determine the quadrant of the return value.
  57 // A domain error may occur if both arguments are zero.
  58
  59 // The atan2 function returns the arc tangent of y/x in the range [-pi,+pi] radians.
  60
  61 //..
  62 //..Let (v,u) = (y,x) if |y| <= |x|, and (v,u) = (x,y) otherwise. Note that
  63 //..v and u can be negative. We state the relationship between atan2(y,x) and
  64 //..atan(v/u).
  65 //..
  66 //..Let swap = false if v = y, and swap = true if v = x.
  67 //..Define C according to the matrix
  68 //..
  69 //..                   TABLE FOR C
  70 //..                              x +ve       x -ve
  71 //..   no swap (swap = false)    sgn(y)*0     sgn(y)*pi
  72 //..   swap    (swap = true )    sgn(y)*pi/2  sgn(y)*pi/2
  73 //..
  74 //..   atan2(y,x) =  C +  atan(v/u)  if no swap
  75 //..   atan2(y,x) =  C -  atan(v/u)  if  swap
  76 //..
  77 //..These relationship is more efficient to compute as we accommodate signs in v and u
  78 //..saving the need to obtain the absolute value before computation can proceed.
  79 //..
  80 //..Suppose (v,u) = (y,x), we calculate atan(v/u) as follows:
  81 //..A = y * frcpa(x)    (so A = (y/x)(1 - beta))
  82 //..atan(y/x) = atan(A) + atan( ((y/x)-A))/(1 + (y/x)A) ), the second term is
  83 //..a correction.
  84 //..atan(A) is approximated by a polynomial
  85 //..A + p1 A^3 + p2 A^5 + ... + p10 A^21,
  86 //..atan(G) is approximated as follows:
  87 //..Let G = (y - Ax)/(x + Ay), atan(G) can be approximated by G + g * p1
  88 //..where g is a limited precision approximation to G via g = (y - Ax)*frcpa(x + Ay).
  89 //..
  90 //..Suppose (v,u) = (x,y), we calculate atan(v/u) as follows:
  91 //..Z = x * frcpa(y)    (so Z = (x/y)(1 - beta))
  92 //..atan(x/y) = atan(Z) + atan( ((x/y)-Z))/(1 + (x/y)Z) ), the second term is
  93 //..a correction.
  94 //..atan(Z) is approximated by a polynomial
  95 //..Z + p1 Z^3 + p2 Z^5 + ... + p10 Z^21,
  96 //..atan(T) is approximated as follows:
  97 //..Let T = (x - Ay)/(y + Ax), atan(T) can be approximated by T + t * p1
  98 //..where t is a limited precision approximation to T via t = (x - Ay)*frcpa(y + Ax).
  99 //..
 100 //..
 101 //..A = y * frcpa(x)
 102 //..atan(A) ~=~ A + p1 A^3 + ... + P10 A^21
 103 //..
 104 //..This polynomial is computed as follows:
 105 //..Asq = A*A; Acub = A*Asq, A4 = Asq*Asq
 106 //..A5 = Asq*Acub, A6 = Asq*A4; A11 = A5 * A6
 107 //..
 108 //..poly_A1 = p9 + Asq*p10, poly_A2 = p7 + Asq*p8, poly_A3 = p5 + Asq*p6
 109 //..poly_A1 = poly_A2 + A4 * poly_A1
 110 //..poly_A1 = poly_A3 + A4 * poly_A1
 111 //..
 112 //..poly_A4 = p1 * A
 113 //,,poly_A5 = p3 + Asq * p4, poly_A4 = A + Asq*poly_A4
 114 //..poly_A5 = p2 + Asq * poly_A5
 115 //..poly_A4 = poly_A4 + A5 * poly_A5
 116 //..
 117 //..atan_A = poly_A4 + A11 * poly_A1
 118 //..
 119 //..atan(G) is approximated as follows:
 120 //..G_numer = y - A*x, G_denom = x + A*y
 121 //..H1 = frcpa(G_denom)
 122 //..H_beta = 1 - H1 * G_denom
 123 //..H2 = H1 + H1 * H_beta
 124 //..H_beta2 = H_beta*H_beta
 125 //..H3 = H2 + H2*H_beta2
 126 //..g = H1 * G_numer; gsq = g*g; atan_G = g*p1, atan_G = atan_G*gsq
 127 //..atan_G = G_numer*H3 + atan_G
 128 //..
 129 //..
 130 //..A = y * frcpa(x)
 131 //..atan(A) ~=~ A + p1 A^3 + ... + P10 A^21
 132 //..
 133 //..This polynomial is computed as follows:
 134 //..Asq = A*A; Acub = A*Asq, A4 = Asq*Asq
 135 //..A5 = Asq*Acub, A6 = Asq*A4; A11 = A5 * A6
 136 //..
 137 //..poly_A1 = p9 + Asq*p10, poly_A2 = p7 + Asq*p8, poly_A3 = p5 + Asq*p6
 138 //..poly_A1 = poly_A2 + A4 * poly_A1
 139 //..poly_A1 = poly_A3 + A4 * poly_A1
 140 //..
 141 //..poly_A4 = p1 * A
 142 //,,poly_A5 = p3 + Asq * p4, poly_A4 = A + Asq*poly_A4
 143 //..poly_A5 = p2 + Asq * poly_A5
 144 //..poly_A4 = poly_A4 + A5 * poly_A5
 145 //..
 146 //..atan_A = poly_A4 + A11 * poly_A1
 147 //..
 148 //..
 149 //..====================================================================
 150 //..    COEFFICIENTS USED IN THE COMPUTATION
 151 //..====================================================================
 152
 153 //coef_pj, j = 1,2,...,10;  atan(A) ~=~ A + p1 A^3 + p2 A^5 + ... + p10 A^21
 154 //
 155 //  coef_p1          =      -.3333332707155439167401311806315789E+00
 156 //  coef_p1   in dbl = BFD5 5555 1219 1621
 157 //
 158 //  coef_p2          =       .1999967670926658391827857030875748E+00
 159 //  coef_p2   in dbl = 3FC9 997E 7AFB FF4E
 160 //
 161 //  coef_p3          =      -.1427989384500152360161563301087296E+00
 162 //  coef_p3   in dbl = BFC2 473C 5145 EE38
 163 //
 164 //  coef_p4          =       .1105852823460720770079031213661163E+00
 165 //  coef_p4   in dbl = 3FBC 4F51 2B18 65F5
 166 //
 167 //  coef_p5          =      -.8811839915595312348625710228448363E-01
 168 //  coef_p5   in dbl = BFB6 8EED 6A8C FA32
 169 //
 170 //  coef_p6          =       .6742329836955067042153645159059714E-01
 171 //  coef_p6   in dbl = 3FB1 42A7 3D7C 54E3
 172 //
 173 //  coef_p7          =      -.4468571068774672908561591262231909E-01
 174 //  coef_p7   in dbl = BFA6 E10B A401 393F
 175 //
 176 //  coef_p8          =       .2252333246746511135532726960586493E-01
 177 //  coef_p8   in dbl = 3F97 105B 4160 F86B
 178 //
 179 //  coef_p9          =      -.7303884867007574742501716845542314E-02
 180 //  coef_p9   in dbl = BF7D EAAD AA33 6451
 181 //
 182 //  coef_p10         =       .1109686868355312093949039454619058E-02
 183 //  coef_p10  in dbl = 3F52 2E5D 33BC 9BAA
 184 //
 185
 186 // Special values
 187 //==============================================================
 188 //              Y                 x          Result
 189 //             +number           +inf        +0
 190 //             -number           +inf        -0
 191 //             +number           -inf        +pi
 192 //             -number           -inf        -pi
 193 //
 194 //             +inf              +number     +pi/2
 195 //             -inf              +number     -pi/2
 196 //             +inf              -number     +pi/2
 197 //             -inf              -number     -pi/2
 198 //
 199 //             +inf              +inf        +pi/4
 200 //             -inf              +inf        -pi/4
 201 //             +inf              -inf        +3pi/4
 202 //             -inf              -inf        -3pi/4
 203 //
 204 //             +1                +1          +pi/4
 205 //             -1                +1          -pi/4
 206 //             +1                -1          +3pi/4
 207 //             -1                -1          -3pi/4
 208 //
 209 //             +number           +0          +pi/2    // does not raise DBZ
 210 //             -number           +0          -pi/2    // does not raise DBZ
 211 //             +number           -0          +pi/2    // does not raise DBZ
 212 //             -number           -0          -pi/2    // does not raise DBZ
 213 //
 214 //             +0                +number     +0
 215 //             -0                +number     -0
 216 //             +0                -number     +pi
 217 //             -0                -number     -pi
 218 //
 219 //             +0                +0          +0      // does not raise invalid
 220 //             -0                +0          -0      // does not raise invalid
 221 //             +0                -0          +pi     // does not raise invalid
 222 //             -0                -0          -pi     // does not raise invalid
 223 //
 224 //            Nan             anything      quiet Y
 225 //            anything        NaN           quiet X
 226
 227 // atan2(+-0/+-0) sets double error tag to 37
 228 // atan2f(+-0/+-0) sets single error tag to 38
 229 // These are domain errors.
 230
 231
 232 //
 233 // Assembly macros
 234 //=========================================
 235
 236
 237 // integer registers
 238 atan2f_GR_Addr_1              = r33
 239 atan2f_GR_Addr_2              = r34
 240 GR_SAVE_B0                    = r35
 241
 242 GR_SAVE_PFS                   = r36
 243 GR_SAVE_GP                    = r37
 244
 245 GR_Parameter_X                = r38
 246 GR_Parameter_Y                = r39
 247 GR_Parameter_RESULT           = r40
 248 GR_Parameter_TAG              = r41
 249
 250 // floating point registers
 251 atan2f_coef_p1         = f32
 252 atan2f_coef_p10        = f33
 253 atan2f_coef_p7         = f34
 254 atan2f_coef_p6         = f35
 255
 256 atan2f_coef_p3         = f36
 257 atan2f_coef_p2         = f37
 258 atan2f_coef_p9         = f38
 259 atan2f_coef_p8         = f39
 260 atan2f_coef_p5         = f40
 261
 262 atan2f_coef_p4         = f41
 263 atan2f_const_piby2     = f42
 264 atan2f_const_pi        = f43
 265 atan2f_const_piby4     = f44
 266 atan2f_const_3piby4    = f45
 267
 268 atan2f_xsq             = f46
 269 atan2f_ysq             = f47
 270 atan2f_xy              = f48
 271 atan2f_const_1         = f49
 272 atan2f_sgn_Y           = f50
 273
 274 atan2f_Z0              = f51
 275 atan2f_A0              = f52
 276 atan2f_Z               = f53
 277 atan2f_A               = f54
 278 atan2f_C               = f55
 279
 280 atan2f_U               = f56
 281 atan2f_Usq             = f57
 282 atan2f_U4              = f58
 283 atan2f_U6              = f59
 284 atan2f_U8              = f60
 285
 286 atan2f_poly_u109       = f61
 287 atan2f_poly_u87        = f62
 288 atan2f_poly_u65        = f63
 289 atan2f_poly_u43        = f64
 290 atan2f_poly_u21        = f65
 291
 292 atan2f_poly_u10to7     = f66
 293 atan2f_poly_u6to3      = f67
 294 atan2f_poly_u10to3     = f68
 295 atan2f_poly_u10to0     = f69
 296 atan2f_poly_u210       = f70
 297
 298 atan2f_T_numer         = f71
 299 atan2f_T_denom         = f72
 300 atan2f_G_numer         = f73
 301 atan2f_G_denom         = f74
 302 atan2f_p1rnum          = f75
 303
 304 atan2f_R_denom         = f76
 305 atan2f_R_numer         = f77
 306 atan2f_pR              = f78
 307 atan2f_pRC             = f79
 308 atan2f_pQRC            = f80
 309
 310 atan2f_Q1              = f81
 311 atan2f_Q_beta          = f82
 312 atan2f_Q2              = f83
 313 atan2f_Q_beta2         = f84
 314 atan2f_Q3              = f85
 315
 316 atan2f_r               = f86
 317 atan2f_rsq             = f87
 318 atan2f_poly_atan_U     = f88
 319
 320
 321 // predicate registers
 322 //atan2f_Pred_Swap     = p6 // |y| >  |x|
 323 //atan2f_Pred_noSwap   = p7 // |y| <= |x|
 324 //atan2f_Pred_Xpos     = p8 //  x  >=  0
 325 //atan2f_Pred_Xneg     = p9 //  x  <   0
 326
 327
 328 RODATA
 329
 330 .align 16
 331
 332 LOCAL_OBJECT_START(atan2f_coef_table1)
 333 data8 0xBFD5555512191621 // p1
 334 data8 0x3F522E5D33BC9BAA // p10
 335 data8 0xBFA6E10BA401393F // p7
 336 data8 0x3FB142A73D7C54E3 // p6
 337 data8 0xBFC2473C5145EE38 // p3
 338 data8 0x3FC9997E7AFBFF4E // p2
 339 LOCAL_OBJECT_END(atan2f_coef_table1)
 340
 341 LOCAL_OBJECT_START(atan2f_coef_table2)
 342 data8 0xBF7DEAADAA336451 // p9
 343 data8 0x3F97105B4160F86B // p8
 344 data8 0xBFB68EED6A8CFA32 // p5
 345 data8 0x3FBC4F512B1865F5 // p4
 346 data8 0x3ff921fb54442d18 // pi/2
 347 data8 0x400921fb54442d18 // pi
 348 data8 0x3fe921fb54442d18 // pi/4
 349 data8 0x4002d97c7f3321d2 // 3pi/4
 350 LOCAL_OBJECT_END(atan2f_coef_table2)
 351
 352
 353
 354 .section .text
 355 GLOBAL_IEEE754_ENTRY(atan2f)
 356
 357 {     .mfi
 358      alloc      r32           = ar.pfs,1,5,4,0
 359      frcpa.s1  atan2f_Z0,p0     =    f1,f8   // Approx to 1/y
 360      nop.i  999
 361 }
 362 {     .mfi
 363      addl      atan2f_GR_Addr_1    =    @ltoff(atan2f_coef_table1),gp
 364      fma.s1    atan2f_xsq     =    f9,f9,f0
 365      nop.i  999 ;;
 366 }
 367
 368
 369 {     .mfi
 370      ld8       atan2f_GR_Addr_1    =    [atan2f_GR_Addr_1]
 371      frcpa.s1  atan2f_A0,p0     =    f1,f9   // Approx to 1/x
 372      nop.i  999
 373 }
 374 {     .mfi
 375      nop.m  999
 376      fma.s1    atan2f_ysq     =    f8,f8,f0
 377      nop.i  999 ;;
 378 }
 379
 380 {     .mfi
 381      nop.m  999
 382      fcmp.ge.s1     p8,p9  =    f9,f0  // Set p8 if x>=0, p9 if x<0
 383      nop.i  999
 384 }
 385 {     .mfi
 386      nop.m  999
 387      fma.s1    atan2f_xy     =    f9,f8,f0
 388      nop.i  999 ;;
 389 }
 390
 391
 392 {     .mfi
 393      add   atan2f_GR_Addr_2 = 0x30, atan2f_GR_Addr_1
 394      fmerge.s  atan2f_sgn_Y   =    f8,f1
 395      nop.i  999 ;;
 396 }
 397
 398 {     .mmf
 399      ldfpd     atan2f_coef_p1,atan2f_coef_p10 =    [atan2f_GR_Addr_1],16
 400      ldfpd     atan2f_coef_p9,atan2f_coef_p8 =    [atan2f_GR_Addr_2],16
 401      fclass.m  p10,p0 =    f9,0xe7      // Test x @inf|@snan|@qnan|@zero
 402 }
 403 ;;
 404
 405 {     .mfi
 406      ldfpd     atan2f_coef_p7,atan2f_coef_p6 =    [atan2f_GR_Addr_1],16
 407      fma.s1    atan2f_T_denom =    atan2f_Z0,atan2f_xsq,f8
 408      nop.i  999
 409 }
 410 {     .mfi
 411      ldfpd     atan2f_coef_p5,atan2f_coef_p4     =    [atan2f_GR_Addr_2],16
 412      fma.s1    atan2f_Z                      =    atan2f_Z0,f9,f0
 413      nop.i  999 ;;
 414 }
 415
 416
 417 {     .mfi
 418      ldfpd     atan2f_coef_p3,atan2f_coef_p2 =    [atan2f_GR_Addr_1],16
 419      fma.s1    atan2f_G_denom =    atan2f_A0,atan2f_ysq,f9
 420      nop.i  999
 421 }
 422 {     .mfi
 423      ldfpd     atan2f_const_piby2,atan2f_const_pi =    [atan2f_GR_Addr_2],16
 424      fma.s1    atan2f_A                           =    atan2f_A0,f8,f0
 425      nop.i  999 ;;
 426 }
 427
 428 {     .mfi
 429      ldfpd     atan2f_const_piby4,atan2f_const_3piby4 = [atan2f_GR_Addr_2]
 430      fclass.m  p11,p0 = f8,0xe7 // Test y @inf|@snan|@qnan|@zero
 431      nop.i  999
 432 }
 433 {     .mfb
 434      nop.m  999
 435      fnma.s1   atan2f_T_numer =    atan2f_Z0,atan2f_xy,f9
 436 (p10) br.cond.spnt ATAN2F_XY_INF_NAN_ZERO ;;   // Branch on x nan,inf,zero
 437 }
 438
 439
 440 // p6 if |y|>|x|, p7 if |x|>=|y| , use xsq and ysq for test
 441 {     .mfi
 442      nop.m  999
 443      fcmp.gt.s1 p6,p7 = atan2f_ysq,atan2f_xsq
 444      nop.i  999
 445 }
 446 {     .mfb
 447      nop.m  999
 448      fnma.s1   atan2f_G_numer =    atan2f_A0,atan2f_xy,f8
 449 (p11) br.cond.spnt ATAN2F_XY_INF_NAN_ZERO ;;  // Branch on y nan,inf,zero
 450 }
 451
 452
 453 {     .mfi
 454      nop.m  999
 455 (p8) fma.s1    atan2f_const_1 =    atan2f_sgn_Y,f0,f0
 456      nop.i  999
 457 }
 458 {     .mfi
 459      nop.m  999
 460 (p9) fma.s1    atan2f_const_1 =    atan2f_sgn_Y,f1,f0
 461      nop.i  999 ;;
 462 }
 463
 464
 465 {     .mfi
 466      nop.m  999
 467 (p6) fnma.s1    atan2f_U       =    atan2f_Z,f1,f0
 468      nop.i  999
 469 }
 470 {     .mfi
 471      nop.m  999
 472 (p6) fma.s1    atan2f_Usq     =    atan2f_Z,atan2f_Z,f0
 473      nop.i  999 ;;
 474 }
 475
 476
 477 {     .mfi
 478      nop.m  999
 479 (p7) fma.s1    atan2f_U       =    atan2f_A,f1,f0
 480      nop.i  999
 481 }
 482 {     .mfi
 483      nop.m  999
 484 (p7) fma.s1    atan2f_Usq     =    atan2f_A,atan2f_A,f0
 485      nop.i  999 ;;
 486 }
 487
 488
 489 {     .mfi
 490      nop.m  999
 491 (p6) frcpa.s1  atan2f_Q1,p0    =    f1,atan2f_T_denom
 492      nop.i  999
 493 }
 494 {     .mfi
 495      nop.m  999
 496 (p6) fma.s1    atan2f_R_denom =   atan2f_T_denom,f1,f0
 497      nop.i  999 ;;
 498 }
 499
 500
 501 {     .mfi
 502      nop.m  999
 503 (p7) frcpa.s1  atan2f_Q1,p0    =    f1,atan2f_G_denom
 504      nop.i  999
 505 }
 506 {     .mfi
 507      nop.m  999
 508 (p7) fma.s1    atan2f_R_denom =   atan2f_G_denom,f1,f0
 509      nop.i  999 ;;
 510 }
 511
 512
 513 {     .mfi
 514      nop.m  999
 515 (p6) fnma.s1    atan2f_R_numer =   atan2f_T_numer,f1,f0
 516      nop.i  999
 517 }
 518 {     .mfi
 519      nop.m  999
 520 (p7) fma.s1    atan2f_R_numer =   atan2f_G_numer,f1,f0
 521      nop.i  999 ;;
 522 }
 523
 524
 525 {     .mfi
 526      nop.m  999
 527 (p6) fnma.s1    atan2f_p1rnum =   atan2f_T_numer,atan2f_coef_p1,f0
 528      nop.i  999 ;;
 529 }
 530 {     .mfi
 531      nop.m  999
 532 (p7) fma.s1    atan2f_p1rnum =   atan2f_G_numer,atan2f_coef_p1,f0
 533      nop.i  999 ;;
 534 }
 535
 536
 537 {     .mfi
 538      nop.m  999
 539      fma.s1    atan2f_U4 =    atan2f_Usq,atan2f_Usq,f0
 540      nop.i  999
 541 }
 542 {     .mfi
 543      nop.m  999
 544      fma.s1    atan2f_poly_u109 = atan2f_Usq,atan2f_coef_p10,atan2f_coef_p9
 545      nop.i  999 ;;
 546 }
 547
 548 {     .mfi
 549      nop.m  999
 550      fma.s1    atan2f_poly_u87 =    atan2f_Usq,atan2f_coef_p8,atan2f_coef_p7
 551      nop.i  999
 552 }
 553 {     .mfi
 554      nop.m  999
 555      fma.s1    atan2f_poly_u65 =    atan2f_Usq,atan2f_coef_p6,atan2f_coef_p5
 556      nop.i  999 ;;
 557 }
 558
 559
 560 {     .mfi
 561      nop.m  999
 562      fma.s1    atan2f_poly_u43 =    atan2f_Usq,atan2f_coef_p4,atan2f_coef_p3
 563      nop.i  999
 564 }
 565 {     .mfi
 566      nop.m  999
 567      fnma.s1   atan2f_Q_beta  =    atan2f_Q1,atan2f_R_denom,f1
 568      nop.i  999 ;;
 569 }
 570
 571
 572 {     .mfi
 573      nop.m  999
 574      fma.s1    atan2f_poly_u21 =    atan2f_Usq,atan2f_coef_p2,atan2f_coef_p1
 575      nop.i  999
 576 }
 577 {     .mfi
 578      nop.m  999
 579      fma.s1    atan2f_r  =    atan2f_Q1,atan2f_R_numer,f0
 580      nop.i  999 ;;
 581 }
 582
 583 {     .mfi
 584      nop.m  999
 585 (p6) fma.s1    atan2f_C  =    atan2f_sgn_Y,atan2f_const_piby2,f0
 586      nop.i  999
 587 }
 588 {     .mfi
 589      nop.m  999
 590 (p7) fma.s1    atan2f_C  =    atan2f_const_1,atan2f_const_pi,f0
 591      nop.i  999 ;;
 592 }
 593
 594 {     .mfi
 595      nop.m  999
 596      fma.s1    atan2f_U6 =    atan2f_U4,atan2f_Usq,f0
 597      nop.i  999
 598 }
 599 {     .mfi
 600      nop.m  999
 601      fma.s1    atan2f_U8 =    atan2f_U4,atan2f_U4,f0
 602      nop.i  999 ;;
 603 }
 604
 605 {     .mfi
 606      nop.m  999
 607      fma.s1    atan2f_poly_u10to7 = atan2f_U4,atan2f_poly_u109,atan2f_poly_u87
 608      nop.i  999
 609 }
 610 {     .mfi
 611      nop.m  999
 612      fma.s1    atan2f_pR = atan2f_p1rnum,atan2f_Q1,f0
 613      nop.i  999 ;;
 614 }
 615
 616 {     .mfi
 617      nop.m  999
 618      fma.s1    atan2f_poly_u6to3 = atan2f_U4,atan2f_poly_u65,atan2f_poly_u43
 619      nop.i  999
 620 }
 621 {     .mfi
 622      nop.m  999
 623      fma.s1    atan2f_Q2 =    atan2f_Q1,atan2f_Q_beta,atan2f_Q1
 624      nop.i  999 ;;
 625 }
 626
 627 {     .mfi
 628      nop.m  999
 629      fma.s1    atan2f_Q_beta2 =    atan2f_Q_beta,atan2f_Q_beta,f0
 630      nop.i  999
 631 }
 632 {     .mfi
 633      nop.m  999
 634      fma.s1    atan2f_rsq     =    atan2f_r,atan2f_r,f0
 635      nop.i  999 ;;
 636 }
 637
 638 {     .mfi
 639      nop.m  999
 640      fma.s1    atan2f_poly_u210 = atan2f_Usq,atan2f_poly_u21,f1
 641      nop.i  999 ;;
 642 }
 643
 644 {     .mfi
 645      nop.m 999
 646      fcmp.eq.s0 p8,p0 = f8,f9      // Dummy op to set flag on denormal inputs
 647      nop.i 999
 648 }
 649 {     .mfi
 650      nop.m  999
 651      fma.s1 atan2f_poly_u10to3 = atan2f_U8,atan2f_poly_u10to7,atan2f_poly_u6to3
 652      nop.i  999 ;;
 653 }
 654
 655 {     .mfi
 656      nop.m                 999
 657      fma.s1    atan2f_Q3 =    atan2f_Q2,atan2f_Q_beta2,atan2f_Q2
 658      nop.i                 999
 659 }
 660 {     .mfi
 661      nop.m  999
 662      fma.s1    atan2f_pRC = atan2f_rsq,atan2f_pR,atan2f_C
 663      nop.i  999 ;;
 664 }
 665
 666 {     .mfi
 667      nop.m  999
 668      fma.s1 atan2f_poly_u10to0 = atan2f_U6,atan2f_poly_u10to3,atan2f_poly_u210
 669      nop.i  999 ;;
 670 }
 671
 672 {     .mfi
 673      nop.m  999
 674      fma.s1    atan2f_pQRC = atan2f_R_numer,atan2f_Q3,atan2f_pRC
 675      nop.i  999 ;;
 676 }
 677
 678 {     .mfb
 679      nop.m  999
 680      fma.s.s0    f8 = atan2f_U,atan2f_poly_u10to0,atan2f_pQRC
 681      br.ret.sptk b0 ;;
 682 }
 683
 684
 685
 686 ATAN2F_XY_INF_NAN_ZERO:
 687
 688 { .mfi
 689       nop.m 999
 690       fclass.m   p10,p0 = f8,0xc3       // Is y nan
 691       nop.i 999
 692 }
 693 ;;
 694
 695 { .mfi
 696       nop.m 999
 697       fclass.m   p12,p0 = f9,0xc3       // Is x nan
 698       nop.i 999
 699 }
 700 ;;
 701
 702 { .mfi
 703       nop.m 999
 704       fclass.m   p6,p0 = f9,0x21        // Is x +inf
 705       nop.i 999
 706 }
 707 { .mfb
 708       nop.m 999
 709 (p10) fma.s.s0 f8  = f9,f8,f0          // Result quietized y if y is nan
 710 (p10) br.ret.spnt b0                // Exit if y is nan
 711 }
 712 ;;
 713
 714
 715 { .mfi
 716       nop.m 999
 717 (p6)  fclass.m.unc   p7,p8 = f8,0x23    // x +inf, is y inf
 718       nop.i 999
 719 }
 720 { .mfb
 721       nop.m 999
 722 (p12) fnorm.s.s0 f8 = f9               // Result quietized x if x is nan, y not nan
 723 (p12) br.ret.spnt b0                // Exit if x is nan, y not nan
 724 }
 725 ;;
 726
 727 // Here if x or y inf, or x or y zero
 728 { .mfi
 729       nop.m 999
 730       fcmp.eq.s0 p15,p0 = f8,f9     // Dummy op to set flag on denormal inputs
 731       nop.i 999
 732 }
 733 ;;
 734
 735 { .mfi
 736       nop.m 999
 737       fclass.m   p11,p12 = f9,0x22      // Is x -inf
 738       nop.i 999
 739 }
 740 { .mfb
 741       nop.m 999
 742 (p7)  fma.s.s0 f8 = atan2f_sgn_Y, atan2f_const_piby4,f0 // Result +-pi/4
 743 (p7)  br.ret.spnt b0            // Exit if x +inf and y inf
 744 }
 745 ;;
 746
 747 { .mfb
 748       nop.m 999
 749 (p8)  fmerge.s   f8 = f8,f0     // If x +inf and y not inf, result +-0
 750 (p8)  br.ret.spnt b0            // Exit if x +inf and y not inf
 751 }
 752 ;;
 753
 754 { .mfi
 755       nop.m 999
 756 (p12) fclass.m.unc   p13,p0 = f8,0x23   // x not -inf, is y inf
 757       nop.i 999
 758 }
 759 ;;
 760
 761 { .mfi
 762       nop.m 999
 763 (p11) fclass.m.unc   p14,p15 = f8,0x23  // x -inf, is y inf
 764       nop.i 999
 765 }
 766 ;;
 767
 768 { .mfi
 769       nop.m 999
 770       fclass.m  p6,p7 = f9,0x7  // Is x zero
 771       nop.i 999
 772 }
 773 { .mfb
 774       nop.m 999
 775 (p13) fma.s.s0   f8 = atan2f_sgn_Y, atan2f_const_piby2,f0 // Result +-pi/2
 776 (p13) br.ret.spnt b0           // Exit if x not -inf and y inf
 777 }
 778 ;;
 779
 780 { .mfi
 781       nop.m 999
 782 (p14) fma.s.s0   f8 = atan2f_sgn_Y, atan2f_const_3piby4,f0 // Result +-3pi/4
 783       nop.i 999
 784 }
 785 { .mfb
 786       nop.m 999
 787 (p15) fma.s.s0   f8 = atan2f_sgn_Y, atan2f_const_pi,f0 // Result +-pi
 788 (p11) br.ret.spnt b0           // Exit if x -inf
 789 }
 790 ;;
 791
 792 // Here if x or y zero
 793 { .mfi
 794       nop.m 999
 795 (p7)  fclass.m.unc   p8,p9 = f9,0x19    // x not zero, y zero, is x > zero
 796       nop.i 999
 797 }
 798 ;;
 799
 800 { .mfi
 801       nop.m 999
 802 (p6)  fclass.m.unc   p10,p11 = f8,0x7   // x zero, is y zero
 803       nop.i 999
 804 }
 805 ;;
 806
 807 { .mfi
 808       nop.m 999
 809 (p8)  fmerge.s  f8 = f8, f0  // x > zero and y zero, result is +-zero
 810       nop.i 999
 811 }
 812 { .mfb
 813       nop.m 999
 814 (p9)  fma.s.s0  f8 = atan2f_sgn_Y, atan2f_const_pi,f0 // x < 0, y 0, result +-pi
 815 (p10) br.cond.spnt   __libm_error_region // Branch if x zero and y zero
 816 }
 817 ;;
 818
 819 { .mfb
 820       nop.m 999
 821 (p11) fma.s.s0  f8 = atan2f_sgn_Y, atan2f_const_piby2,f0 // x zero, y not zero
 822       br.ret.sptk b0         // Final special case exit
 823 }
 824 ;;
 825
 826
 827 GLOBAL_IEEE754_END(atan2f)
 828 libm_alias_float_other (__atan2, atan2)
 829
 830
 831 LOCAL_LIBM_ENTRY(__libm_error_region)
 832 .prologue
 833          mov            GR_Parameter_TAG      = 38
 834          fclass.m       p10,p11               = f9,0x5  // @zero | @pos
 835 ;;
 836 (p10)    fmerge.s       f10                   = f8, f0
 837 (p11)    fma.s.s0          f10                   = atan2f_sgn_Y, atan2f_const_pi,f0
 838 ;;
 839
 840 { .mfi
 841         add   GR_Parameter_Y=-32,sp             // Parameter 2 value
 842         nop.f 999
 843 .save   ar.pfs,GR_SAVE_PFS
 844         mov  GR_SAVE_PFS=ar.pfs                 // Save ar.pfs
 845 }
 846
 847 { .mfi
 848 .fframe 64
 849         add sp=-64,sp                           // Create new stack
 850         nop.f 0
 851         mov GR_SAVE_GP=gp                       // Save gp
 852 }
 853 ;;
 854
 855 { .mmi
 856         stfs [GR_Parameter_Y] = f9,16         // Store Parameter 2 on stack
 857         add GR_Parameter_X = 16,sp              // Parameter 1 address
 858 .save   b0, GR_SAVE_B0
 859         mov GR_SAVE_B0=b0                       // Save b0
 860 }
 861 ;;
 862
 863
 864 .body
 865 { .mib
 866         stfs [GR_Parameter_X] = f8            // Store Parameter 1 on stack
 867         add   GR_Parameter_RESULT = 0,GR_Parameter_Y
 868         nop.b 0                                 // Parameter 3 address
 869 }
 870 { .mib
 871         stfs [GR_Parameter_Y] = f10       // Store Parameter 3 on stack
 872         add   GR_Parameter_Y = -16,GR_Parameter_Y
 873         br.call.sptk b0=__libm_error_support#   // Call error handling function
 874 }
 875 ;;
 876 { .mmi
 877         nop.m 0
 878         nop.m 0
 879         add   GR_Parameter_RESULT = 48,sp
 880 };;
 881
 882 { .mmi
 883         ldfs  f8 = [GR_Parameter_RESULT]       // Get return result off stack
 884 .restore sp
 885         add   sp = 64,sp                       // Restore stack pointer
 886         mov   b0 = GR_SAVE_B0                  // Restore return address
 887 }
 888 ;;
 889
 890 { .mib
 891         mov   gp = GR_SAVE_GP                  // Restore gp
 892         mov   ar.pfs = GR_SAVE_PFS             // Restore ar.pfs
 893         br.ret.sptk     b0                     // Return
 894 }
 895 ;;
 896
 897 LOCAL_LIBM_END(__libm_error_region)
 898
 899 .type   __libm_error_support#,@function
 900 .global __libm_error_support#