projects / thirdparty / glibc.git / blame
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1 | .file "atanl.s" |
| 2 | ||
| 3 | ||
| 4 | // Copyright (c) 2000 - 2005, Intel Corporation | |
| 5 | // All rights reserved. | |
| 6 | // | |
| 7 | // Contributed 2000 by the Intel Numerics Group, Intel Corporation | |
| 8 | // | |
| 9 | // Redistribution and use in source and binary forms, with or without | |
| 10 | // modification, are permitted provided that the following conditions are | |
| 11 | // met: | |
| 12 | // | |
| 13 | // * Redistributions of source code must retain the above copyright | |
| 14 | // notice, this list of conditions and the following disclaimer. | |
| 15 | // | |
| 16 | // * Redistributions in binary form must reproduce the above copyright | |
| 17 | // notice, this list of conditions and the following disclaimer in the | |
| 18 | // documentation and/or other materials provided with the distribution. | |
| 19 | // | |
| 20 | // * The name of Intel Corporation may not be used to endorse or promote | |
| 21 | // products derived from this software without specific prior written | |
| 22 | // permission. | |
| 23 | ||
| 0347518d MF |
24 | // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| 25 | // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | |
| d5efd131 | 26 | // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| 0347518d | 27 | // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS |
| d5efd131 | 28 | // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
| 0347518d MF |
29 | // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, |
| 30 | // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR | |
| 31 | // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY | |
| d5efd131 | 32 | // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING |
| 0347518d MF |
33 | // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| 34 | // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | |
| 35 | // | |
| d5efd131 | 36 | // Intel Corporation is the author of this code, and requests that all |
| 0347518d | 37 | // problem reports or change requests be submitted to it directly at |
| d5efd131 MF |
38 | // http://www.intel.com/software/products/opensource/libraries/num.htm. |
| 39 | // | |
| 40 | // | |
| 41 | //********************************************************************* | |
| 42 | // | |
| 43 | // History | |
| 44 | // 02/02/00 (hand-optimized) | |
| 45 | // 04/04/00 Unwind support added | |
| 46 | // 08/15/00 Bundle added after call to __libm_error_support to properly | |
| 47 | // set [the previously overwritten] GR_Parameter_RESULT. | |
| 48 | // 03/13/01 Fixed flags when denormal raised on intermediate result | |
| 49 | // 01/08/02 Improved speed. | |
| 50 | // 02/06/02 Corrected .section statement | |
| 51 | // 05/20/02 Cleaned up namespace and sf0 syntax | |
| 52 | // 02/10/03 Reordered header: .section, .global, .proc, .align; | |
| 53 | // used data8 for long double table values | |
| 54 | // 03/31/05 Reformatted delimiters between data tables | |
| 55 | // | |
| 56 | //********************************************************************* | |
| 57 | // | |
| 58 | // Function: atanl(x) = inverse tangent(x), for double extended x values | |
| 59 | // Function: atan2l(y,x) = atan(y/x), for double extended y, x values | |
| 60 | // | |
| 61 | // API | |
| 62 | // | |
| 63 | // long double atanl (long double x) | |
| 64 | // long double atan2l (long double y, long double x) | |
| 65 | // | |
| 66 | //********************************************************************* | |
| 67 | // | |
| 68 | // Resources Used: | |
| 69 | // | |
| 70 | // Floating-Point Registers: f8 (Input and Return Value) | |
| 71 | // f9 (Input for atan2l) | |
| 72 | // f10-f15, f32-f83 | |
| 73 | // | |
| 74 | // General Purpose Registers: | |
| 75 | // r32-r51 | |
| 76 | // r49-r52 (Arguments to error support for 0,0 case) | |
| 77 | // | |
| 78 | // Predicate Registers: p6-p15 | |
| 79 | // | |
| 80 | //********************************************************************* | |
| 81 | // | |
| 82 | // IEEE Special Conditions: | |
| 83 | // | |
| 84 | // Denormal fault raised on denormal inputs | |
| 0347518d | 85 | // Underflow exceptions may occur |
| d5efd131 MF |
86 | // Special error handling for the y=0 and x=0 case |
| 87 | // Inexact raised when appropriate by algorithm | |
| 88 | // | |
| 89 | // atanl(SNaN) = QNaN | |
| 90 | // atanl(QNaN) = QNaN | |
| 91 | // atanl(+/-0) = +/- 0 | |
| 0347518d | 92 | // atanl(+/-Inf) = +/-pi/2 |
| d5efd131 MF |
93 | // |
| 94 | // atan2l(Any NaN for x or y) = QNaN | |
| 0347518d MF |
95 | // atan2l(+/-0,x) = +/-0 for x > 0 |
| 96 | // atan2l(+/-0,x) = +/-pi for x < 0 | |
| 97 | // atan2l(+/-0,+0) = +/-0 | |
| 98 | // atan2l(+/-0,-0) = +/-pi | |
| d5efd131 MF |
99 | // atan2l(y,+/-0) = pi/2 y > 0 |
| 100 | // atan2l(y,+/-0) = -pi/2 y < 0 | |
| 101 | // atan2l(+/-y, Inf) = +/-0 for finite y > 0 | |
| 0347518d MF |
102 | // atan2l(+/-Inf, x) = +/-pi/2 for finite x |
| 103 | // atan2l(+/-y, -Inf) = +/-pi for finite y > 0 | |
| d5efd131 MF |
104 | // atan2l(+/-Inf, Inf) = +/-pi/4 |
| 105 | // atan2l(+/-Inf, -Inf) = +/-3pi/4 | |
| 106 | // | |
| 107 | //********************************************************************* | |
| 108 | // | |
| 109 | // Mathematical Description | |
| 110 | // --------------------------- | |
| 111 | // | |
| 112 | // The function ATANL( Arg_Y, Arg_X ) returns the "argument" | |
| 113 | // or the "phase" of the complex number | |
| 114 | // | |
| 115 | // Arg_X + i Arg_Y | |
| 116 | // | |
| 117 | // or equivalently, the angle in radians from the positive | |
| 118 | // x-axis to the line joining the origin and the point | |
| 119 | // (Arg_X,Arg_Y) | |
| 120 | // | |
| 121 | // | |
| 122 | // (Arg_X, Arg_Y) x | |
| 123 | // \ | |
| 124 | // \ | |
| 125 | // \ | |
| 126 | // \ | |
| 127 | // \ angle between is ATANL(Arg_Y,Arg_X) | |
| 128 | ||
| 129 | ||
| 130 | ||
| 131 | ||
| 132 | // \ | |
| 133 | // ------------------> X-axis | |
| 134 | ||
| 135 | // Origin | |
| 136 | // | |
| 137 | // Moreover, this angle is reported in the range [-pi,pi] thus | |
| 138 | // | |
| 139 | // -pi <= ATANL( Arg_Y, Arg_X ) <= pi. | |
| 140 | // | |
| 141 | // From the geometry, it is easy to define ATANL when one of | |
| 142 | // Arg_X or Arg_Y is +-0 or +-inf: | |
| 143 | // | |
| 144 | // | |
| 145 | // \ Y | | |
| 146 | // X \ | +0 | -0 | +inf | -inf | finite non-zero | |
| 147 | // \ | | | | | | |
| 148 | // ______________________________________________________ | |
| 149 | // | | | | | |
| 150 | // +-0 | Invalid/ | pi/2 | -pi/2 | sign(Y)*pi/2 | |
| 151 | // | qNaN | | | | |
| 152 | // -------------------------------------------------------- | |
| 153 | // | | | | | | |
| 154 | // +inf | +0 | -0 | pi/4 | -pi/4 | sign(Y)*0 | |
| 155 | // -------------------------------------------------------- | |
| 156 | // | | | | | | |
| 157 | // -inf | +pi | -pi | 3pi/4 | -3pi/4 | sign(Y)*pi | |
| 158 | // -------------------------------------------------------- | |
| 159 | // finite | X>0? | pi/2 | -pi/2 | normal case | |
| 160 | // non-zero| sign(Y)*0: | | | | |
| 161 | // | sign(Y)*pi | | | | |
| 162 | // | |
| 163 | // | |
| 164 | // One must take note that ATANL is NOT the arctangent of the | |
| 165 | // value Arg_Y/Arg_X; but rather ATANL and arctan are related | |
| 166 | // in a slightly more complicated way as follows: | |
| 167 | // | |
| 168 | // Let U := max(|Arg_X|, |Arg_Y|); V := min(|Arg_X|, |Arg_Y|); | |
| 169 | // sign_X be the sign bit of Arg_X, i.e., sign_X is 0 or 1; | |
| 170 | // s_X be the sign of Arg_X, i.e., s_X = (-1)^sign_X; | |
| 171 | // | |
| 172 | // sign_Y be the sign bit of Arg_Y, i.e., sign_Y is 0 or 1; | |
| 173 | // s_Y be the sign of Arg_Y, i.e., s_Y = (-1)^sign_Y; | |
| 174 | // | |
| 175 | // swap be 0 if |Arg_X| >= |Arg_Y| and 1 otherwise. | |
| 176 | // | |
| 177 | // Then, ATANL(Arg_Y, Arg_X) = | |
| 178 | // | |
| 179 | // / arctan(V/U) \ sign_X = 0 & swap = 0 | |
| 180 | // | pi/2 - arctan(V/U) | sign_X = 0 & swap = 1 | |
| 181 | // s_Y * | | | |
| 182 | // | pi - arctan(V/U) | sign_X = 1 & swap = 0 | |
| 183 | // \ pi/2 + arctan(V/U) / sign_X = 1 & swap = 1 | |
| 184 | // | |
| 185 | // | |
| 186 | // This relationship also suggest that the algorithm's major | |
| 187 | // task is to calculate arctan(V/U) for 0 < V <= U; and the | |
| 188 | // final Result is given by | |
| 189 | // | |
| 190 | // s_Y * { (P_hi + P_lo) + sigma * arctan(V/U) } | |
| 191 | // | |
| 192 | // where | |
| 193 | // | |
| 194 | // (P_hi,P_lo) represents M(sign_X,swap)*(pi/2) accurately | |
| 195 | // | |
| 196 | // M(sign_X,swap) = 0 for sign_X = 0 and swap = 0 | |
| 197 | // 1 for swap = 1 | |
| 198 | // 2 for sign_X = 1 and swap = 0 | |
| 199 | // | |
| 200 | // and | |
| 201 | // | |
| 202 | // sigma = { (sign_X XOR swap) : -1.0 : 1.0 } | |
| 203 | // | |
| 204 | // = (-1) ^ ( sign_X XOR swap ) | |
| 205 | // | |
| 206 | // Both (P_hi,P_lo) and sigma can be stored in a table and fetched | |
| 207 | // using (sign_X,swap) as an index. (P_hi, P_lo) can be stored as a | |
| 208 | // double-precision, and single-precision pair; and sigma can | |
| 209 | // obviously be just a single-precision number. | |
| 210 | // | |
| 211 | // In the algorithm we propose, arctan(V/U) is calculated to high accuracy | |
| 212 | // as A_hi + A_lo. Consequently, the Result ATANL( Arg_Y, Arg_X ) is | |
| 213 | // given by | |
| 214 | // | |
| 215 | // s_Y*P_hi + s_Y*sigma*A_hi + s_Y*(sigma*A_lo + P_lo) | |
| 216 | // | |
| 217 | // We now discuss the calculation of arctan(V/U) for 0 < V <= U. | |
| 218 | // | |
| 219 | // For (V/U) < 2^(-3), we use a simple polynomial of the form | |
| 220 | // | |
| 221 | // z + z^3*(P_1 + z^2*(P_2 + z^2*(P_3 + ... + P_8))) | |
| 222 | // | |
| 223 | // where z = V/U. | |
| 224 | // | |
| 225 | // For the sake of accuracy, the first term "z" must approximate V/U to | |
| 226 | // extra precision. For z^3 and higher power, a working precision | |
| 227 | // approximation to V/U suffices. Thus, we obtain: | |
| 228 | // | |
| 229 | // z_hi + z_lo = V/U to extra precision and | |
| 230 | // z = V/U to working precision | |
| 231 | // | |
| 232 | // The value arctan(V/U) is delivered as two pieces (A_hi, A_lo) | |
| 233 | // | |
| 234 | // (A_hi,A_lo) = (z_hi, z^3*(P_1 + ... + P_8) + z_lo). | |
| 235 | // | |
| 236 | // | |
| 237 | // For 2^(-3) <= (V/U) <= 1, we use a table-driven approach. | |
| 238 | // Consider | |
| 239 | // | |
| 240 | // (V/U) = 2^k * 1.b_1 b_2 .... b_63 b_64 b_65 .... | |
| 241 | // | |
| 242 | // Define | |
| 243 | // | |
| 244 | // z_hi = 2^k * 1.b_1 b_2 b_3 b_4 1 | |
| 245 | // | |
| 246 | // then | |
| 247 | // / \ | |
| 248 | // | (V/U) - z_hi | | |
| 249 | ||
| 250 | // arctan(V/U) = arctan(z_hi) + acrtan| -------------- | | |
| 251 | // | 1 + (V/U)*z_hi | | |
| 252 | // \ / | |
| 253 | // | |
| 254 | // / \ | |
| 255 | // | V - z_hi*U | | |
| 256 | ||
| 257 | // = arctan(z_hi) + acrtan| -------------- | | |
| 258 | // | U + V*z_hi | | |
| 259 | // \ / | |
| 260 | // | |
| 261 | // = arctan(z_hi) + acrtan( V' / U' ) | |
| 262 | // | |
| 263 | // | |
| 264 | // where | |
| 265 | // | |
| 266 | // V' = V - U*z_hi; U' = U + V*z_hi. | |
| 267 | // | |
| 268 | // Let | |
| 269 | // | |
| 270 | // w_hi + w_lo = V'/U' to extra precision and | |
| 271 | // w = V'/U' to working precision | |
| 272 | // | |
| 273 | // then we can approximate arctan(V'/U') by | |
| 274 | // | |
| 275 | // arctan(V'/U') = w_hi + w_lo | |
| 276 | // + w^3*(Q_1 + w^2*(Q_2 + w^2*(Q_3 + w^2*Q_4))) | |
| 277 | // | |
| 278 | // = w_hi + w_lo + poly | |
| 279 | // | |
| 280 | // Finally, arctan(z_hi) is calculated beforehand and stored in a table | |
| 281 | // as Tbl_hi, Tbl_lo. Thus, | |
| 282 | // | |
| 283 | // (A_hi, A_lo) = (Tbl_hi, w_hi+(poly+(w_lo+Tbl_lo))) | |
| 284 | // | |
| 285 | // This completes the mathematical description. | |
| 286 | // | |
| 287 | // | |
| 288 | // Algorithm | |
| 289 | // ------------- | |
| 290 | // | |
| 291 | // Step 0. Check for unsupported format. | |
| 292 | // | |
| 293 | // If | |
| 294 | // ( expo(Arg_X) not zero AND msb(Arg_X) = 0 ) OR | |
| 295 | // ( expo(Arg_Y) not zero AND msb(Arg_Y) = 0 ) | |
| 296 | // | |
| 297 | // then one of the arguments is unsupported. Generate an | |
| 298 | // invalid and return qNaN. | |
| 299 | // | |
| 300 | // Step 1. Initialize | |
| 301 | // | |
| 302 | // Normalize Arg_X and Arg_Y and set the following | |
| 303 | // | |
| 304 | // sign_X := sign_bit(Arg_X) | |
| 305 | // s_Y := (sign_bit(Arg_Y)==0? 1.0 : -1.0) | |
| 306 | // swap := (|Arg_X| >= |Arg_Y|? 0 : 1 ) | |
| 307 | // U := max( |Arg_X|, |Arg_Y| ) | |
| 308 | // V := min( |Arg_X|, |Arg_Y| ) | |
| 309 | // | |
| 310 | // execute: frcpa E, pred, V, U | |
| 311 | // If pred is 0, go to Step 5 for special cases handling. | |
| 312 | // | |
| 313 | // Step 2. Decide on branch. | |
| 314 | // | |
| 315 | // Q := E * V | |
| 316 | // If Q < 2^(-3) go to Step 4 for simple polynomial case. | |
| 317 | // | |
| 318 | // Step 3. Table-driven algorithm. | |
| 319 | // | |
| 320 | // Q is represented as | |
| 321 | // | |
| 322 | // 2^(-k) * 1.b_1 b_2 b_3 ... b_63; k = 0,-1,-2,-3 | |
| 323 | // | |
| 324 | // and that if k = 0, b_1 = b_2 = b_3 = b_4 = 0. | |
| 325 | // | |
| 326 | // Define | |
| 327 | // | |
| 328 | // z_hi := 2^(-k) * 1.b_1 b_2 b_3 b_4 1 | |
| 329 | // | |
| 330 | // (note that there are 49 possible values of z_hi). | |
| 331 | // | |
| 332 | // ...We now calculate V' and U'. While V' is representable | |
| 333 | // ...as a 64-bit number because of cancellation, U' is | |
| 334 | // ...not in general a 64-bit number. Obtaining U' accurately | |
| 335 | // ...requires two working precision numbers | |
| 336 | // | |
| 337 | // U_prime_hi := U + V * z_hi ...WP approx. to U' | |
| 338 | // U_prime_lo := ( U - U_prime_hi ) + V*z_hi ...observe order | |
| 339 | // V_prime := V - U * z_hi ...this is exact | |
| 340 | // | |
| 341 | // C_hi := frcpa (1.0, U_prime_hi) ...C_hi approx 1/U'_hi | |
| 342 | // | |
| 343 | // loop 3 times | |
| 344 | // C_hi := C_hi + C_hi*(1.0 - C_hi*U_prime_hi) | |
| 345 | // | |
| 346 | // ...at this point C_hi is (1/U_prime_hi) to roughly 64 bits | |
| 347 | // | |
| 348 | // w_hi := V_prime * C_hi ...w_hi is V_prime/U_prime to | |
| 349 | // ...roughly working precision | |
| 350 | // | |
| 351 | // ...note that we want w_hi + w_lo to approximate | |
| 352 | // ...V_prime/(U_prime_hi + U_prime_lo) to extra precision | |
| 353 | // ...but for now, w_hi is good enough for the polynomial | |
| 354 | // ...calculation. | |
| 355 | // | |
| 356 | // wsq := w_hi*w_hi | |
| 357 | // poly := w_hi*wsq*(Q_1 + wsq*(Q_2 + wsq*(Q_3 + wsq*Q_4))) | |
| 358 | // | |
| 359 | // Fetch | |
| 360 | // (Tbl_hi, Tbl_lo) = atan(z_hi) indexed by (k,b_1,b_2,b_3,b_4) | |
| 361 | // ...Tbl_hi is a double-precision number | |
| 362 | // ...Tbl_lo is a single-precision number | |
| 363 | // | |
| 364 | // (P_hi, P_lo) := M(sign_X,swap)*(Pi_by_2_hi, Pi_by_2_lo) | |
| 365 | // ...as discussed previous. Again; the implementation can | |
| 366 | // ...chose to fetch P_hi and P_lo from a table indexed by | |
| 367 | // ...(sign_X, swap). | |
| 368 | // ...P_hi is a double-precision number; | |
| 369 | // ...P_lo is a single-precision number. | |
| 370 | // | |
| 371 | // ...calculate w_lo so that w_hi + w_lo is V'/U' accurately | |
| 372 | // w_lo := ((V_prime - w_hi*U_prime_hi) - | |
| 373 | // w_hi*U_prime_lo) * C_hi ...observe order | |
| 374 | // | |
| 375 | // | |
| 376 | // ...Ready to deliver arctan(V'/U') as A_hi, A_lo | |
| 377 | // A_hi := Tbl_hi | |
| 378 | // A_lo := w_hi + (poly + (Tbl_lo + w_lo)) ...observe order | |
| 379 | // | |
| 380 | // ...Deliver final Result | |
| 381 | // ...s_Y*P_hi + s_Y*sigma*A_hi + s_Y*(sigma*A_lo + P_lo) | |
| 382 | // | |
| 383 | // sigma := ( (sign_X XOR swap) ? -1.0 : 1.0 ) | |
| 384 | // ...sigma can be obtained by a table lookup using | |
| 385 | // ...(sign_X,swap) as index and stored as single precision | |
| 386 | // ...sigma should be calculated earlier | |
| 387 | // | |
| 388 | // P_hi := s_Y*P_hi | |
| 389 | // A_hi := s_Y*A_hi | |
| 390 | // | |
| 391 | // Res_hi := P_hi + sigma*A_hi ...this is exact because | |
| 392 | // ...both P_hi and Tbl_hi | |
| 393 | // ...are double-precision | |
| 394 | // ...and |Tbl_hi| > 2^(-4) | |
| 395 | // ...P_hi is either 0 or | |
| 396 | // ...between (1,4) | |
| 397 | // | |
| 398 | // Res_lo := sigma*A_lo + P_lo | |
| 399 | // | |
| 400 | // Return Res_hi + s_Y*Res_lo in user-defined rounding control | |
| 401 | // | |
| 402 | // Step 4. Simple polynomial case. | |
| 403 | // | |
| 404 | // ...E and Q are inherited from Step 2. | |
| 405 | // | |
| 406 | // A_hi := Q ...Q is inherited from Step 2 Q approx V/U | |
| 407 | // | |
| 408 | // loop 3 times | |
| 409 | // E := E + E2(1.0 - E*U1 | |
| 410 | // ...at this point E approximates 1/U to roughly working precision | |
| 411 | // | |
| 412 | // z := V * E ...z approximates V/U to roughly working precision | |
| 413 | // zsq := z * z | |
| 414 | // z4 := zsq * zsq; z8 := z4 * z4 | |
| 415 | // | |
| 416 | // poly1 := P_4 + zsq*(P_5 + zsq*(P_6 + zsq*(P_7 + zsq*P_8))) | |
| 417 | // poly2 := zsq*(P_1 + zsq*(P_2 + zsq*P_3)) | |
| 418 | // | |
| 419 | // poly := poly1 + z8*poly2 | |
| 420 | // | |
| 421 | // z_lo := (V - A_hi*U)*E | |
| 422 | // | |
| 423 | // A_lo := z*poly + z_lo | |
| 424 | // ...A_hi, A_lo approximate arctan(V/U) accurately | |
| 425 | // | |
| 426 | // (P_hi, P_lo) := M(sign_X,swap)*(Pi_by_2_hi, Pi_by_2_lo) | |
| 427 | // ...one can store the M(sign_X,swap) as single precision | |
| 428 | // ...values | |
| 429 | // | |
| 430 | // ...Deliver final Result | |
| 431 | // ...s_Y*P_hi + s_Y*sigma*A_hi + s_Y*(sigma*A_lo + P_lo) | |
| 432 | // | |
| 433 | // sigma := ( (sign_X XOR swap) ? -1.0 : 1.0 ) | |
| 434 | // ...sigma can be obtained by a table lookup using | |
| 435 | // ...(sign_X,swap) as index and stored as single precision | |
| 436 | // ...sigma should be calculated earlier | |
| 437 | // | |
| 438 | // P_hi := s_Y*P_hi | |
| 439 | // A_hi := s_Y*A_hi | |
| 440 | // | |
| 441 | // Res_hi := P_hi + sigma*A_hi ...need to compute | |
| 442 | // ...P_hi + sigma*A_hi | |
| 443 | // ...exactly | |
| 444 | // | |
| 445 | // tmp := (P_hi - Res_hi) + sigma*A_hi | |
| 446 | // | |
| 447 | // Res_lo := s_Y*(sigma*A_lo + P_lo) + tmp | |
| 448 | // | |
| 449 | // Return Res_hi + Res_lo in user-defined rounding control | |
| 450 | // | |
| 451 | // Step 5. Special Cases | |
| 452 | // | |
| 453 | // These are detected early in the function by fclass instructions. | |
| 454 | // | |
| 455 | // We are in one of those special cases when X or Y is 0,+-inf or NaN | |
| 456 | // | |
| 457 | // If one of X and Y is NaN, return X+Y (which will generate | |
| 458 | // invalid in case one is a signaling NaN). Otherwise, | |
| 459 | // return the Result as described in the table | |
| 460 | // | |
| 461 | // | |
| 462 | // | |
| 463 | // \ Y | | |
| 464 | // X \ | +0 | -0 | +inf | -inf | finite non-zero | |
| 465 | // \ | | | | | | |
| 466 | // ______________________________________________________ | |
| 467 | // | | | | | |
| 468 | // +-0 | Invalid/ | pi/2 | -pi/2 | sign(Y)*pi/2 | |
| 469 | // | qNaN | | | | |
| 470 | // -------------------------------------------------------- | |
| 471 | // | | | | | | |
| 472 | // +inf | +0 | -0 | pi/4 | -pi/4 | sign(Y)*0 | |
| 473 | // -------------------------------------------------------- | |
| 474 | // | | | | | | |
| 475 | // -inf | +pi | -pi | 3pi/4 | -3pi/4 | sign(Y)*pi | |
| 476 | // -------------------------------------------------------- | |
| 477 | // finite | X>0? | pi/2 | -pi/2 | | |
| 478 | // non-zero| sign(Y)*0: | | | N/A | |
| 479 | // | sign(Y)*pi | | | | |
| 480 | // | |
| 481 | // | |
| 482 | ||
| 483 | ArgY_orig = f8 | |
| 484 | Result = f8 | |
| 485 | FR_RESULT = f8 | |
| 486 | ArgX_orig = f9 | |
| 487 | ArgX = f10 | |
| 488 | FR_X = f10 | |
| 489 | ArgY = f11 | |
| 490 | FR_Y = f11 | |
| 491 | s_Y = f12 | |
| 492 | U = f13 | |
| 493 | V = f14 | |
| 494 | E = f15 | |
| 495 | Q = f32 | |
| 496 | z_hi = f33 | |
| 497 | U_prime_hi = f34 | |
| 498 | U_prime_lo = f35 | |
| 499 | V_prime = f36 | |
| 500 | C_hi = f37 | |
| 501 | w_hi = f38 | |
| 502 | w_lo = f39 | |
| 503 | wsq = f40 | |
| 504 | poly = f41 | |
| 505 | Tbl_hi = f42 | |
| 506 | Tbl_lo = f43 | |
| 507 | P_hi = f44 | |
| 508 | P_lo = f45 | |
| 509 | A_hi = f46 | |
| 510 | A_lo = f47 | |
| 511 | sigma = f48 | |
| 512 | Res_hi = f49 | |
| 513 | Res_lo = f50 | |
| 514 | Z = f52 | |
| 515 | zsq = f53 | |
| 516 | z4 = f54 | |
| 517 | z8 = f54 | |
| 518 | poly1 = f55 | |
| 519 | poly2 = f56 | |
| 520 | z_lo = f57 | |
| 521 | tmp = f58 | |
| 522 | P_1 = f59 | |
| 523 | Q_1 = f60 | |
| 524 | P_2 = f61 | |
| 525 | Q_2 = f62 | |
| 526 | P_3 = f63 | |
| 527 | Q_3 = f64 | |
| 528 | P_4 = f65 | |
| 529 | Q_4 = f66 | |
| 530 | P_5 = f67 | |
| 531 | P_6 = f68 | |
| 532 | P_7 = f69 | |
| 533 | P_8 = f70 | |
| 534 | U_hold = f71 | |
| 535 | TWO_TO_NEG3 = f72 | |
| 536 | C_hi_hold = f73 | |
| 537 | E_hold = f74 | |
| 538 | M = f75 | |
| 539 | ArgX_abs = f76 | |
| 540 | ArgY_abs = f77 | |
| 541 | Result_lo = f78 | |
| 542 | A_temp = f79 | |
| 543 | FR_temp = f80 | |
| 544 | Xsq = f81 | |
| 545 | Ysq = f82 | |
| 546 | tmp_small = f83 | |
| 547 | ||
| 548 | GR_SAVE_PFS = r33 | |
| 549 | GR_SAVE_B0 = r34 | |
| 550 | GR_SAVE_GP = r35 | |
| 551 | sign_X = r36 | |
| 0347518d MF |
552 | sign_Y = r37 |
| 553 | swap = r38 | |
| 554 | table_ptr1 = r39 | |
| 555 | table_ptr2 = r40 | |
| 556 | k = r41 | |
| 557 | lookup = r42 | |
| 558 | exp_ArgX = r43 | |
| 559 | exp_ArgY = r44 | |
| 560 | exponent_Q = r45 | |
| 561 | significand_Q = r46 | |
| 562 | special = r47 | |
| 563 | sp_exp_Q = r48 | |
| 564 | sp_exp_4sig_Q = r49 | |
| 565 | table_base = r50 | |
| d5efd131 MF |
566 | int_temp = r51 |
| 567 | ||
| 568 | GR_Parameter_X = r49 | |
| 569 | GR_Parameter_Y = r50 | |
| 570 | GR_Parameter_RESULT = r51 | |
| 571 | GR_Parameter_TAG = r52 | |
| 572 | GR_temp = r52 | |
| 573 | ||
| 574 | RODATA | |
| 0347518d | 575 | .align 16 |
| d5efd131 MF |
576 | |
| 577 | LOCAL_OBJECT_START(Constants_atan) | |
| 578 | // double pi/2 | |
| 579 | data8 0x3FF921FB54442D18 | |
| 580 | // single lo_pi/2, two**(-3) | |
| 581 | data4 0x248D3132, 0x3E000000 | |
| 582 | data8 0xAAAAAAAAAAAAAAA3, 0xBFFD // P_1 | |
| 583 | data8 0xCCCCCCCCCCCC54B2, 0x3FFC // P_2 | |
| 584 | data8 0x9249249247E4D0C2, 0xBFFC // P_3 | |
| 585 | data8 0xE38E38E058870889, 0x3FFB // P_4 | |
| 586 | data8 0xBA2E895B290149F8, 0xBFFB // P_5 | |
| 587 | data8 0x9D88E6D4250F733D, 0x3FFB // P_6 | |
| 588 | data8 0x884E51FFFB8745A0, 0xBFFB // P_7 | |
| 589 | data8 0xE1C7412B394396BD, 0x3FFA // P_8 | |
| 590 | data8 0xAAAAAAAAAAAAA52F, 0xBFFD // Q_1 | |
| 591 | data8 0xCCCCCCCCC75B60D3, 0x3FFC // Q_2 | |
| 592 | data8 0x924923AD011F1940, 0xBFFC // Q_3 | |
| 593 | data8 0xE36F716D2A5F89BD, 0x3FFB // Q_4 | |
| 594 | // | |
| 595 | // Entries Tbl_hi (double precision) | |
| 596 | // B = 1+Index/16+1/32 Index = 0 | |
| 597 | // Entries Tbl_lo (single precision) | |
| 598 | // B = 1+Index/16+1/32 Index = 0 | |
| 599 | // | |
| 0347518d | 600 | data8 0x3FE9A000A935BD8E |
| d5efd131 MF |
601 | data4 0x23ACA08F, 0x00000000 |
| 602 | // | |
| 603 | // Entries Tbl_hi (double precision) Index = 0,1,...,15 | |
| 604 | // B = 2^(-1)*(1+Index/16+1/32) | |
| 605 | // Entries Tbl_lo (single precision) | |
| 606 | // Index = 0,1,...,15 B = 2^(-1)*(1+Index/16+1/32) | |
| 607 | // | |
| 0347518d | 608 | data8 0x3FDE77EB7F175A34 |
| d5efd131 | 609 | data4 0x238729EE, 0x00000000 |
| 0347518d | 610 | data8 0x3FE0039C73C1A40B |
| d5efd131 | 611 | data4 0x249334DB, 0x00000000 |
| 0347518d | 612 | data8 0x3FE0C6145B5B43DA |
| d5efd131 | 613 | data4 0x22CBA7D1, 0x00000000 |
| 0347518d | 614 | data8 0x3FE1835A88BE7C13 |
| d5efd131 | 615 | data4 0x246310E7, 0x00000000 |
| 0347518d | 616 | data8 0x3FE23B71E2CC9E6A |
| d5efd131 | 617 | data4 0x236210E5, 0x00000000 |
| 0347518d | 618 | data8 0x3FE2EE628406CBCA |
| d5efd131 | 619 | data4 0x2462EAF5, 0x00000000 |
| 0347518d | 620 | data8 0x3FE39C391CD41719 |
| d5efd131 | 621 | data4 0x24B73EF3, 0x00000000 |
| 0347518d | 622 | data8 0x3FE445065B795B55 |
| d5efd131 | 623 | data4 0x24C11260, 0x00000000 |
| 0347518d | 624 | data8 0x3FE4E8DE5BB6EC04 |
| d5efd131 | 625 | data4 0x242519EE, 0x00000000 |
| 0347518d | 626 | data8 0x3FE587D81F732FBA |
| d5efd131 | 627 | data4 0x24D4346C, 0x00000000 |
| 0347518d | 628 | data8 0x3FE6220D115D7B8D |
| d5efd131 | 629 | data4 0x24ED487B, 0x00000000 |
| 0347518d | 630 | data8 0x3FE6B798920B3D98 |
| d5efd131 | 631 | data4 0x2495FF1E, 0x00000000 |
| 0347518d | 632 | data8 0x3FE748978FBA8E0F |
| d5efd131 | 633 | data4 0x223D9531, 0x00000000 |
| 0347518d | 634 | data8 0x3FE7D528289FA093 |
| d5efd131 | 635 | data4 0x242B0411, 0x00000000 |
| 0347518d | 636 | data8 0x3FE85D69576CC2C5 |
| d5efd131 | 637 | data4 0x2335B374, 0x00000000 |
| 0347518d | 638 | data8 0x3FE8E17AA99CC05D |
| d5efd131 MF |
639 | data4 0x24C27CFB, 0x00000000 |
| 640 | // | |
| 641 | // Entries Tbl_hi (double precision) Index = 0,1,...,15 | |
| 642 | // B = 2^(-2)*(1+Index/16+1/32) | |
| 643 | // Entries Tbl_lo (single precision) | |
| 644 | // Index = 0,1,...,15 B = 2^(-2)*(1+Index/16+1/32) | |
| 645 | // | |
| 0347518d | 646 | data8 0x3FD025FA510665B5 |
| d5efd131 MF |
647 | data4 0x24263482, 0x00000000 |
| 648 | data8 0x3FD1151A362431C9 | |
| 649 | data4 0x242C8DC9, 0x00000000 | |
| 650 | data8 0x3FD2025567E47C95 | |
| 651 | data4 0x245CF9BA, 0x00000000 | |
| 652 | data8 0x3FD2ED987A823CFE | |
| 653 | data4 0x235C892C, 0x00000000 | |
| 654 | data8 0x3FD3D6D129271134 | |
| 655 | data4 0x2389BE52, 0x00000000 | |
| 656 | data8 0x3FD4BDEE586890E6 | |
| 657 | data4 0x24436471, 0x00000000 | |
| 658 | data8 0x3FD5A2E0175E0F4E | |
| 659 | data4 0x2389DBD4, 0x00000000 | |
| 660 | data8 0x3FD685979F5FA6FD | |
| 661 | data4 0x2476D43F, 0x00000000 | |
| 662 | data8 0x3FD7660752817501 | |
| 663 | data4 0x24711774, 0x00000000 | |
| 664 | data8 0x3FD84422B8DF95D7 | |
| 665 | data4 0x23EBB501, 0x00000000 | |
| 666 | data8 0x3FD91FDE7CD0C662 | |
| 667 | data4 0x23883A0C, 0x00000000 | |
| 668 | data8 0x3FD9F93066168001 | |
| 669 | data4 0x240DF63F, 0x00000000 | |
| 670 | data8 0x3FDAD00F5422058B | |
| 671 | data4 0x23FE261A, 0x00000000 | |
| 672 | data8 0x3FDBA473378624A5 | |
| 673 | data4 0x23A8CD0E, 0x00000000 | |
| 674 | data8 0x3FDC76550AAD71F8 | |
| 675 | data4 0x2422D1D0, 0x00000000 | |
| 676 | data8 0x3FDD45AEC9EC862B | |
| 677 | data4 0x2344A109, 0x00000000 | |
| 678 | // | |
| 679 | // Entries Tbl_hi (double precision) Index = 0,1,...,15 | |
| 680 | // B = 2^(-3)*(1+Index/16+1/32) | |
| 681 | // Entries Tbl_lo (single precision) | |
| 682 | // Index = 0,1,...,15 B = 2^(-3)*(1+Index/16+1/32) | |
| 683 | // | |
| 684 | data8 0x3FC068D584212B3D | |
| 685 | data4 0x239874B6, 0x00000000 | |
| 686 | data8 0x3FC1646541060850 | |
| 687 | data4 0x2335E774, 0x00000000 | |
| 688 | data8 0x3FC25F6E171A535C | |
| 689 | data4 0x233E36BE, 0x00000000 | |
| 690 | data8 0x3FC359E8EDEB99A3 | |
| 691 | data4 0x239680A3, 0x00000000 | |
| 692 | data8 0x3FC453CEC6092A9E | |
| 693 | data4 0x230FB29E, 0x00000000 | |
| 694 | data8 0x3FC54D18BA11570A | |
| 695 | data4 0x230C1418, 0x00000000 | |
| 696 | data8 0x3FC645BFFFB3AA73 | |
| 697 | data4 0x23F0564A, 0x00000000 | |
| 698 | data8 0x3FC73DBDE8A7D201 | |
| 699 | data4 0x23D4A5E1, 0x00000000 | |
| 700 | data8 0x3FC8350BE398EBC7 | |
| 701 | data4 0x23D4ADDA, 0x00000000 | |
| 702 | data8 0x3FC92BA37D050271 | |
| 703 | data4 0x23BCB085, 0x00000000 | |
| 704 | data8 0x3FCA217E601081A5 | |
| 705 | data4 0x23BC841D, 0x00000000 | |
| 706 | data8 0x3FCB1696574D780B | |
| 707 | data4 0x23CF4A8E, 0x00000000 | |
| 708 | data8 0x3FCC0AE54D768466 | |
| 709 | data4 0x23BECC90, 0x00000000 | |
| 710 | data8 0x3FCCFE654E1D5395 | |
| 711 | data4 0x2323DCD2, 0x00000000 | |
| 712 | data8 0x3FCDF110864C9D9D | |
| 713 | data4 0x23F53F3A, 0x00000000 | |
| 714 | data8 0x3FCEE2E1451D980C | |
| 715 | data4 0x23CCB11F, 0x00000000 | |
| 716 | // | |
| 717 | data8 0x400921FB54442D18, 0x3CA1A62633145C07 // PI two doubles | |
| 718 | data8 0x3FF921FB54442D18, 0x3C91A62633145C07 // PI_by_2 two dbles | |
| 719 | data8 0x3FE921FB54442D18, 0x3C81A62633145C07 // PI_by_4 two dbles | |
| 720 | data8 0x4002D97C7F3321D2, 0x3C9A79394C9E8A0A // 3PI_by_4 two dbles | |
| 721 | LOCAL_OBJECT_END(Constants_atan) | |
| 722 | ||
| 723 | ||
| 724 | .section .text | |
| 725 | GLOBAL_IEEE754_ENTRY(atanl) | |
| 726 | ||
| 727 | // Use common code with atan2l after setting x=1.0 | |
| 728 | { .mfi | |
| 729 | alloc r32 = ar.pfs, 0, 17, 4, 0 | |
| 730 | fma.s1 Ysq = ArgY_orig, ArgY_orig, f0 // Form y*y | |
| 731 | nop.i 999 | |
| 732 | } | |
| 733 | { .mfi | |
| 734 | addl table_ptr1 = @ltoff(Constants_atan#), gp // Address of table pointer | |
| 735 | fma.s1 Xsq = f1, f1, f0 // Form x*x | |
| 736 | nop.i 999 | |
| 737 | } | |
| 738 | ;; | |
| 739 | ||
| 740 | { .mfi | |
| 741 | ld8 table_ptr1 = [table_ptr1] // Get table pointer | |
| 742 | fnorm.s1 ArgY = ArgY_orig | |
| 743 | nop.i 999 | |
| 744 | } | |
| 745 | { .mfi | |
| 746 | nop.m 999 | |
| 747 | fnorm.s1 ArgX = f1 | |
| 748 | nop.i 999 | |
| 749 | } | |
| 750 | ;; | |
| 751 | ||
| 752 | { .mfi | |
| 753 | getf.exp sign_X = f1 // Get signexp of x | |
| 754 | fmerge.s ArgX_abs = f0, f1 // Form |x| | |
| 755 | nop.i 999 | |
| 756 | } | |
| 757 | { .mfi | |
| 758 | nop.m 999 | |
| 759 | fnorm.s1 ArgX_orig = f1 | |
| 760 | nop.i 999 | |
| 761 | } | |
| 762 | ;; | |
| 763 | ||
| 764 | { .mfi | |
| 765 | getf.exp sign_Y = ArgY_orig // Get signexp of y | |
| 766 | fmerge.s ArgY_abs = f0, ArgY_orig // Form |y| | |
| 767 | mov table_base = table_ptr1 // Save base pointer to tables | |
| 768 | } | |
| 769 | ;; | |
| 770 | ||
| 771 | { .mfi | |
| 772 | ldfd P_hi = [table_ptr1],8 // Load double precision hi part of pi | |
| 773 | fclass.m p8,p0 = ArgY_orig, 0x1e7 // Test y natval, nan, inf, zero | |
| 0347518d | 774 | nop.i 999 |
| d5efd131 MF |
775 | } |
| 776 | ;; | |
| 777 | ||
| 778 | { .mfi | |
| 779 | ldfps P_lo, TWO_TO_NEG3 = [table_ptr1], 8 // Load P_lo and constant 2^-3 | |
| 0347518d MF |
780 | nop.f 999 |
| 781 | nop.i 999 | |
| d5efd131 MF |
782 | } |
| 783 | { .mfi | |
| 784 | nop.m 999 | |
| 785 | fma.s1 M = f1, f1, f0 // Set M = 1.0 | |
| 0347518d | 786 | nop.i 999 |
| d5efd131 MF |
787 | } |
| 788 | ;; | |
| 789 | ||
| 790 | // | |
| 791 | // Check for everything - if false, then must be pseudo-zero | |
| 792 | // or pseudo-nan (IA unsupporteds). | |
| 793 | // | |
| 794 | { .mfb | |
| 795 | nop.m 999 | |
| 796 | fclass.m p0,p12 = f1, 0x1FF // Test x unsupported | |
| 797 | (p8) br.cond.spnt ATANL_Y_SPECIAL // Branch if y natval, nan, inf, zero | |
| 798 | } | |
| 799 | ;; | |
| 800 | ||
| 801 | // U = max(ArgX_abs,ArgY_abs) | |
| 802 | // V = min(ArgX_abs,ArgY_abs) | |
| 803 | { .mfi | |
| 804 | nop.m 999 | |
| 805 | fcmp.ge.s1 p6,p7 = Xsq, Ysq // Test for |x| >= |y| using squares | |
| 0347518d | 806 | nop.i 999 |
| d5efd131 MF |
807 | } |
| 808 | { .mfb | |
| 809 | nop.m 999 | |
| 810 | fma.s1 V = ArgX_abs, f1, f0 // Set V assuming |x| < |y| | |
| 811 | br.cond.sptk ATANL_COMMON // Branch to common code | |
| 812 | } | |
| 813 | ;; | |
| 814 | ||
| 815 | GLOBAL_IEEE754_END(atanl) | |
| 816 | ||
| 817 | GLOBAL_IEEE754_ENTRY(atan2l) | |
| 818 | ||
| 819 | { .mfi | |
| 820 | alloc r32 = ar.pfs, 0, 17, 4, 0 | |
| 821 | fma.s1 Ysq = ArgY_orig, ArgY_orig, f0 // Form y*y | |
| 822 | nop.i 999 | |
| 823 | } | |
| 824 | { .mfi | |
| 825 | addl table_ptr1 = @ltoff(Constants_atan#), gp // Address of table pointer | |
| 826 | fma.s1 Xsq = ArgX_orig, ArgX_orig, f0 // Form x*x | |
| 827 | nop.i 999 | |
| 828 | } | |
| 829 | ;; | |
| 830 | ||
| 831 | { .mfi | |
| 832 | ld8 table_ptr1 = [table_ptr1] // Get table pointer | |
| 833 | fnorm.s1 ArgY = ArgY_orig | |
| 834 | nop.i 999 | |
| 835 | } | |
| 836 | { .mfi | |
| 837 | nop.m 999 | |
| 838 | fnorm.s1 ArgX = ArgX_orig | |
| 839 | nop.i 999 | |
| 840 | } | |
| 841 | ;; | |
| 842 | ||
| 843 | { .mfi | |
| 844 | getf.exp sign_X = ArgX_orig // Get signexp of x | |
| 845 | fmerge.s ArgX_abs = f0, ArgX_orig // Form |x| | |
| 846 | nop.i 999 | |
| 847 | } | |
| 848 | ;; | |
| 849 | ||
| 850 | { .mfi | |
| 851 | getf.exp sign_Y = ArgY_orig // Get signexp of y | |
| 852 | fmerge.s ArgY_abs = f0, ArgY_orig // Form |y| | |
| 853 | mov table_base = table_ptr1 // Save base pointer to tables | |
| 854 | } | |
| 855 | ;; | |
| 856 | ||
| 857 | { .mfi | |
| 858 | ldfd P_hi = [table_ptr1],8 // Load double precision hi part of pi | |
| 859 | fclass.m p8,p0 = ArgY_orig, 0x1e7 // Test y natval, nan, inf, zero | |
| 0347518d | 860 | nop.i 999 |
| d5efd131 MF |
861 | } |
| 862 | ;; | |
| 863 | ||
| 864 | { .mfi | |
| 865 | ldfps P_lo, TWO_TO_NEG3 = [table_ptr1], 8 // Load P_lo and constant 2^-3 | |
| 866 | fclass.m p9,p0 = ArgX_orig, 0x1e7 // Test x natval, nan, inf, zero | |
| 0347518d | 867 | nop.i 999 |
| d5efd131 MF |
868 | } |
| 869 | { .mfi | |
| 870 | nop.m 999 | |
| 871 | fma.s1 M = f1, f1, f0 // Set M = 1.0 | |
| 0347518d | 872 | nop.i 999 |
| d5efd131 MF |
873 | } |
| 874 | ;; | |
| 875 | ||
| 876 | // | |
| 877 | // Check for everything - if false, then must be pseudo-zero | |
| 878 | // or pseudo-nan (IA unsupporteds). | |
| 879 | // | |
| 880 | { .mfb | |
| 881 | nop.m 999 | |
| 882 | fclass.m p0,p12 = ArgX_orig, 0x1FF // Test x unsupported | |
| 883 | (p8) br.cond.spnt ATANL_Y_SPECIAL // Branch if y natval, nan, inf, zero | |
| 884 | } | |
| 885 | ;; | |
| 886 | ||
| 887 | // U = max(ArgX_abs,ArgY_abs) | |
| 888 | // V = min(ArgX_abs,ArgY_abs) | |
| 889 | { .mfi | |
| 890 | nop.m 999 | |
| 891 | fcmp.ge.s1 p6,p7 = Xsq, Ysq // Test for |x| >= |y| using squares | |
| 0347518d | 892 | nop.i 999 |
| d5efd131 MF |
893 | } |
| 894 | { .mfb | |
| 895 | nop.m 999 | |
| 896 | fma.s1 V = ArgX_abs, f1, f0 // Set V assuming |x| < |y| | |
| 897 | (p9) br.cond.spnt ATANL_X_SPECIAL // Branch if x natval, nan, inf, zero | |
| 898 | } | |
| 899 | ;; | |
| 900 | ||
| 901 | // Now common code for atanl and atan2l | |
| 902 | ATANL_COMMON: | |
| 903 | { .mfi | |
| 904 | nop.m 999 | |
| 905 | fclass.m p0,p13 = ArgY_orig, 0x1FF // Test y unsupported | |
| 906 | shr sign_X = sign_X, 17 // Get sign bit of x | |
| 907 | } | |
| 908 | { .mfi | |
| 909 | nop.m 999 | |
| 910 | fma.s1 U = ArgY_abs, f1, f0 // Set U assuming |x| < |y| | |
| 911 | adds table_ptr1 = 176, table_ptr1 // Point to Q4 | |
| 912 | } | |
| 913 | ;; | |
| 914 | ||
| 915 | { .mfi | |
| 916 | (p6) add swap = r0, r0 // Set swap=0 if |x| >= |y| | |
| 917 | (p6) frcpa.s1 E, p0 = ArgY_abs, ArgX_abs // Compute E if |x| >= |y| | |
| 918 | shr sign_Y = sign_Y, 17 // Get sign bit of y | |
| 919 | } | |
| 920 | { .mfb | |
| 921 | nop.m 999 | |
| 922 | (p6) fma.s1 V = ArgY_abs, f1, f0 // Set V if |x| >= |y| | |
| 923 | (p12) br.cond.spnt ATANL_UNSUPPORTED // Branch if x unsupported | |
| 924 | } | |
| 925 | ;; | |
| 926 | ||
| 927 | // Set p8 if y >=0 | |
| 928 | // Set p9 if y < 0 | |
| 929 | // Set p10 if |x| >= |y| and x >=0 | |
| 930 | // Set p11 if |x| >= |y| and x < 0 | |
| 931 | { .mfi | |
| 932 | cmp.eq p8, p9 = 0, sign_Y // Test for y >= 0 | |
| 933 | (p7) frcpa.s1 E, p0 = ArgX_abs, ArgY_abs // Compute E if |x| < |y| | |
| 934 | (p7) add swap = 1, r0 // Set swap=1 if |x| < |y| | |
| 935 | } | |
| 936 | { .mfb | |
| 937 | (p6) cmp.eq.unc p10, p11 = 0, sign_X // If |x| >= |y|, test for x >= 0 | |
| 938 | (p6) fma.s1 U = ArgX_abs, f1, f0 // Set U if |x| >= |y| | |
| 939 | (p13) br.cond.spnt ATANL_UNSUPPORTED // Branch if y unsupported | |
| 940 | } | |
| 941 | ;; | |
| 942 | ||
| 943 | // | |
| 944 | // if p8, s_Y = 1.0 | |
| 945 | // if p9, s_Y = -1.0 | |
| 946 | // | |
| 947 | .pred.rel "mutex",p8,p9 | |
| 948 | { .mfi | |
| 949 | nop.m 999 | |
| 950 | (p8) fadd.s1 s_Y = f0, f1 // If y >= 0 set s_Y = 1.0 | |
| 951 | nop.i 999 | |
| 952 | } | |
| 953 | { .mfi | |
| 954 | nop.m 999 | |
| 955 | (p9) fsub.s1 s_Y = f0, f1 // If y < 0 set s_Y = -1.0 | |
| 956 | nop.i 999 | |
| 957 | } | |
| 958 | ;; | |
| 959 | ||
| 960 | .pred.rel "mutex",p10,p11 | |
| 961 | { .mfi | |
| 962 | nop.m 999 | |
| 963 | (p10) fsub.s1 M = M, f1 // If |x| >= |y| and x >=0, set M=0 | |
| 964 | nop.i 999 | |
| 965 | } | |
| 966 | { .mfi | |
| 967 | nop.m 999 | |
| 968 | (p11) fadd.s1 M = M, f1 // If |x| >= |y| and x < 0, set M=2.0 | |
| 969 | nop.i 999 | |
| 970 | } | |
| 971 | ;; | |
| 972 | ||
| 973 | { .mfi | |
| 974 | nop.m 999 | |
| 975 | fcmp.eq.s0 p0, p9 = ArgX_orig, ArgY_orig // Dummy to set denormal flag | |
| 976 | nop.i 999 | |
| 977 | } | |
| 978 | // ************************************************* | |
| 979 | // ********************* STEP2 ********************* | |
| 980 | // ************************************************* | |
| 981 | // | |
| 982 | // Q = E * V | |
| 983 | // | |
| 984 | { .mfi | |
| 985 | nop.m 999 | |
| 986 | fmpy.s1 Q = E, V | |
| 987 | nop.i 999 | |
| 988 | } | |
| 989 | ;; | |
| 990 | ||
| 991 | { .mfi | |
| 992 | nop.m 999 | |
| 993 | fnma.s1 E_hold = E, U, f1 // E_hold = 1.0 - E*U (1) if POLY path | |
| 994 | nop.i 999 | |
| 995 | } | |
| 996 | ;; | |
| 997 | ||
| 0347518d | 998 | // Create a single precision representation of the signexp of Q with the |
| d5efd131 MF |
999 | // 4 most significant bits of the significand followed by a 1 and then 18 0's |
| 1000 | { .mfi | |
| 1001 | nop.m 999 | |
| 1002 | fmpy.s1 P_hi = M, P_hi | |
| 1003 | dep.z special = 0x1, 18, 1 // Form 0x0000000000040000 | |
| 1004 | } | |
| 1005 | { .mfi | |
| 1006 | nop.m 999 | |
| 1007 | fmpy.s1 P_lo = M, P_lo | |
| 1008 | add table_ptr2 = 32, table_ptr1 | |
| 1009 | } | |
| 1010 | ;; | |
| 1011 | ||
| 1012 | { .mfi | |
| 1013 | nop.m 999 | |
| 1014 | fma.s1 A_temp = Q, f1, f0 // Set A_temp if POLY path | |
| 1015 | nop.i 999 | |
| 1016 | } | |
| 1017 | { .mfi | |
| 1018 | nop.m 999 | |
| 1019 | fma.s1 E = E, E_hold, E // E = E + E*E_hold (1) if POLY path | |
| 1020 | nop.i 999 | |
| 1021 | } | |
| 1022 | ;; | |
| 1023 | ||
| 1024 | // | |
| 1025 | // Is Q < 2**(-3)? | |
| 1026 | // swap = xor(swap,sign_X) | |
| 1027 | // | |
| 1028 | { .mfi | |
| 1029 | nop.m 999 | |
| 1030 | fcmp.lt.s1 p9, p0 = Q, TWO_TO_NEG3 // Test Q < 2^-3 | |
| 1031 | xor swap = sign_X, swap | |
| 1032 | } | |
| 1033 | ;; | |
| 1034 | ||
| 1035 | // P_hi = s_Y * P_hi | |
| 1036 | { .mmf | |
| 1037 | getf.exp exponent_Q = Q // Get signexp of Q | |
| 1038 | cmp.eq.unc p7, p6 = 0x00000, swap | |
| 1039 | fmpy.s1 P_hi = s_Y, P_hi | |
| 1040 | } | |
| 1041 | ;; | |
| 1042 | ||
| 1043 | // | |
| 1044 | // if (PR_1) sigma = -1.0 | |
| 1045 | // if (PR_2) sigma = 1.0 | |
| 1046 | // | |
| 1047 | { .mfi | |
| 1048 | getf.sig significand_Q = Q // Get significand of Q | |
| 1049 | (p6) fsub.s1 sigma = f0, f1 | |
| 1050 | nop.i 999 | |
| 1051 | } | |
| 1052 | { .mfb | |
| 1053 | (p9) add table_ptr1 = 128, table_base // Point to P8 if POLY path | |
| 1054 | (p7) fadd.s1 sigma = f0, f1 | |
| 1055 | (p9) br.cond.spnt ATANL_POLY // Branch to POLY if 0 < Q < 2^-3 | |
| 1056 | } | |
| 1057 | ;; | |
| 1058 | ||
| 1059 | // | |
| 1060 | // ************************************************* | |
| 1061 | // ******************** STEP3 ********************** | |
| 1062 | // ************************************************* | |
| 1063 | // | |
| 1064 | // lookup = b_1 b_2 b_3 B_4 | |
| 1065 | // | |
| 1066 | { .mmi | |
| 1067 | nop.m 999 | |
| 1068 | nop.m 999 | |
| 1069 | andcm k = 0x0003, exponent_Q // k=0,1,2,3 for exp_Q=0,-1,-2,-3 | |
| 1070 | } | |
| 1071 | ;; | |
| 1072 | ||
| 1073 | // | |
| 0347518d | 1074 | // Generate sign_exp_Q b_1 b_2 b_3 b_4 1 0 0 0 ... 0 in single precision |
| d5efd131 MF |
1075 | // representation. Note sign of Q is always 0. |
| 1076 | // | |
| 1077 | { .mfi | |
| 1078 | cmp.eq p8, p9 = 0x0000, k // Test k=0 | |
| 1079 | nop.f 999 | |
| 1080 | extr.u lookup = significand_Q, 59, 4 // Extract b_1 b_2 b_3 b_4 for index | |
| 1081 | } | |
| 1082 | { .mfi | |
| 1083 | sub sp_exp_Q = 0x7f, k // Form single prec biased exp of Q | |
| 1084 | nop.f 999 | |
| 1085 | sub k = k, r0, 1 // Decrement k | |
| 1086 | } | |
| 1087 | ;; | |
| 1088 | ||
| 1089 | // Form pointer to B index table | |
| 1090 | { .mfi | |
| 1091 | ldfe Q_4 = [table_ptr1], -16 // Load Q_4 | |
| 1092 | nop.f 999 | |
| 1093 | (p9) shl k = k, 8 // k = 0, 256, or 512 | |
| 1094 | } | |
| 1095 | { .mfi | |
| 1096 | (p9) shladd table_ptr2 = lookup, 4, table_ptr2 | |
| 1097 | nop.f 999 | |
| 1098 | shladd sp_exp_4sig_Q = sp_exp_Q, 4, lookup // Shift and add in 4 high bits | |
| 1099 | } | |
| 1100 | ;; | |
| 1101 | ||
| 1102 | { .mmi | |
| 1103 | (p8) add table_ptr2 = -16, table_ptr2 // Pointer if original k was 0 | |
| 1104 | (p9) add table_ptr2 = k, table_ptr2 // Pointer if k was 1, 2, 3 | |
| 1105 | dep special = sp_exp_4sig_Q, special, 19, 13 // Form z_hi as single prec | |
| 1106 | } | |
| 1107 | ;; | |
| 1108 | ||
| 1109 | // z_hi = s exp 1.b_1 b_2 b_3 b_4 1 0 0 0 ... 0 | |
| 1110 | { .mmi | |
| 1111 | ldfd Tbl_hi = [table_ptr2], 8 // Load Tbl_hi from index table | |
| 1112 | ;; | |
| 1113 | setf.s z_hi = special // Form z_hi | |
| 1114 | nop.i 999 | |
| 1115 | } | |
| 1116 | { .mmi | |
| 1117 | ldfs Tbl_lo = [table_ptr2], 8 // Load Tbl_lo from index table | |
| 1118 | ;; | |
| 1119 | ldfe Q_3 = [table_ptr1], -16 // Load Q_3 | |
| 1120 | nop.i 999 | |
| 1121 | } | |
| 1122 | ;; | |
| 1123 | ||
| 1124 | { .mmi | |
| 1125 | ldfe Q_2 = [table_ptr1], -16 // Load Q_2 | |
| 1126 | nop.m 999 | |
| 1127 | nop.i 999 | |
| 1128 | } | |
| 1129 | ;; | |
| 1130 | ||
| 1131 | { .mmf | |
| 1132 | ldfe Q_1 = [table_ptr1], -16 // Load Q_1 | |
| 1133 | nop.m 999 | |
| 1134 | nop.f 999 | |
| 1135 | } | |
| 1136 | ;; | |
| 1137 | ||
| 1138 | { .mfi | |
| 1139 | nop.m 999 | |
| 1140 | fma.s1 U_prime_hi = V, z_hi, U // U_prime_hi = U + V * z_hi | |
| 1141 | nop.i 999 | |
| 1142 | } | |
| 1143 | { .mfi | |
| 1144 | nop.m 999 | |
| 1145 | fnma.s1 V_prime = U, z_hi, V // V_prime = V - U * z_hi | |
| 1146 | nop.i 999 | |
| 1147 | } | |
| 1148 | ;; | |
| 1149 | ||
| 1150 | { .mfi | |
| 1151 | nop.m 999 | |
| 1152 | mov A_hi = Tbl_hi // Start with A_hi = Tbl_hi | |
| 1153 | nop.i 999 | |
| 1154 | } | |
| 1155 | ;; | |
| 1156 | ||
| 1157 | { .mfi | |
| 1158 | nop.m 999 | |
| 1159 | fsub.s1 U_hold = U, U_prime_hi // U_hold = U - U_prime_hi | |
| 1160 | nop.i 999 | |
| 1161 | } | |
| 1162 | ;; | |
| 1163 | ||
| 1164 | { .mfi | |
| 1165 | nop.m 999 | |
| 1166 | frcpa.s1 C_hi, p0 = f1, U_prime_hi // C_hi = frcpa(1,U_prime_hi) | |
| 1167 | nop.i 999 | |
| 1168 | } | |
| 1169 | ;; | |
| 1170 | ||
| 1171 | { .mfi | |
| 1172 | nop.m 999 | |
| 1173 | fmpy.s1 A_hi = s_Y, A_hi // A_hi = s_Y * A_hi | |
| 1174 | nop.i 999 | |
| 1175 | } | |
| 1176 | ;; | |
| 1177 | ||
| 1178 | { .mfi | |
| 1179 | nop.m 999 | |
| 1180 | fma.s1 U_prime_lo = z_hi, V, U_hold // U_prime_lo = U_hold + V * z_hi | |
| 1181 | nop.i 999 | |
| 1182 | } | |
| 1183 | ;; | |
| 1184 | ||
| 1185 | // C_hi_hold = 1 - C_hi * U_prime_hi (1) | |
| 1186 | { .mfi | |
| 1187 | nop.m 999 | |
| 0347518d | 1188 | fnma.s1 C_hi_hold = C_hi, U_prime_hi, f1 |
| d5efd131 MF |
1189 | nop.i 999 |
| 1190 | } | |
| 1191 | ;; | |
| 1192 | ||
| 1193 | { .mfi | |
| 1194 | nop.m 999 | |
| 1195 | fma.s1 Res_hi = sigma, A_hi, P_hi // Res_hi = P_hi + sigma * A_hi | |
| 1196 | nop.i 999 | |
| 1197 | } | |
| 1198 | ;; | |
| 1199 | ||
| 1200 | { .mfi | |
| 1201 | nop.m 999 | |
| 1202 | fma.s1 C_hi = C_hi_hold, C_hi, C_hi // C_hi = C_hi + C_hi * C_hi_hold (1) | |
| 1203 | nop.i 999 | |
| 1204 | } | |
| 1205 | ;; | |
| 1206 | ||
| 1207 | // C_hi_hold = 1 - C_hi * U_prime_hi (2) | |
| 1208 | { .mfi | |
| 1209 | nop.m 999 | |
| 1210 | fnma.s1 C_hi_hold = C_hi, U_prime_hi, f1 | |
| 1211 | nop.i 999 | |
| 1212 | } | |
| 1213 | ;; | |
| 1214 | ||
| 1215 | { .mfi | |
| 1216 | nop.m 999 | |
| 1217 | fma.s1 C_hi = C_hi_hold, C_hi, C_hi // C_hi = C_hi + C_hi * C_hi_hold (2) | |
| 1218 | nop.i 999 | |
| 1219 | } | |
| 1220 | ;; | |
| 1221 | ||
| 1222 | // C_hi_hold = 1 - C_hi * U_prime_hi (3) | |
| 1223 | { .mfi | |
| 1224 | nop.m 999 | |
| 0347518d | 1225 | fnma.s1 C_hi_hold = C_hi, U_prime_hi, f1 |
| d5efd131 MF |
1226 | nop.i 999 |
| 1227 | } | |
| 1228 | ;; | |
| 1229 | ||
| 1230 | { .mfi | |
| 1231 | nop.m 999 | |
| 1232 | fma.s1 C_hi = C_hi_hold, C_hi, C_hi // C_hi = C_hi + C_hi * C_hi_hold (3) | |
| 1233 | nop.i 999 | |
| 1234 | } | |
| 1235 | ;; | |
| 1236 | ||
| 1237 | { .mfi | |
| 1238 | nop.m 999 | |
| 1239 | fmpy.s1 w_hi = V_prime, C_hi // w_hi = V_prime * C_hi | |
| 1240 | nop.i 999 | |
| 1241 | } | |
| 1242 | ;; | |
| 1243 | ||
| 1244 | { .mfi | |
| 1245 | nop.m 999 | |
| 1246 | fmpy.s1 wsq = w_hi, w_hi // wsq = w_hi * w_hi | |
| 1247 | nop.i 999 | |
| 1248 | } | |
| 1249 | { .mfi | |
| 1250 | nop.m 999 | |
| 1251 | fnma.s1 w_lo = w_hi, U_prime_hi, V_prime // w_lo = V_prime-w_hi*U_prime_hi | |
| 1252 | nop.i 999 | |
| 1253 | } | |
| 1254 | ;; | |
| 1255 | ||
| 1256 | { .mfi | |
| 1257 | nop.m 999 | |
| 1258 | fma.s1 poly = wsq, Q_4, Q_3 // poly = Q_3 + wsq * Q_4 | |
| 1259 | nop.i 999 | |
| 1260 | } | |
| 1261 | { .mfi | |
| 1262 | nop.m 999 | |
| 1263 | fnma.s1 w_lo = w_hi, U_prime_lo, w_lo // w_lo = w_lo - w_hi * U_prime_lo | |
| 1264 | nop.i 999 | |
| 1265 | } | |
| 1266 | ;; | |
| 1267 | ||
| 1268 | { .mfi | |
| 1269 | nop.m 999 | |
| 1270 | fma.s1 poly = wsq, poly, Q_2 // poly = Q_2 + wsq * poly | |
| 1271 | nop.i 999 | |
| 1272 | } | |
| 1273 | { .mfi | |
| 1274 | nop.m 999 | |
| 1275 | fmpy.s1 w_lo = C_hi, w_lo // w_lo = = w_lo * C_hi | |
| 1276 | nop.i 999 | |
| 1277 | } | |
| 1278 | ;; | |
| 1279 | ||
| 1280 | { .mfi | |
| 1281 | nop.m 999 | |
| 1282 | fma.s1 poly = wsq, poly, Q_1 // poly = Q_1 + wsq * poly | |
| 1283 | nop.i 999 | |
| 1284 | } | |
| 1285 | { .mfi | |
| 1286 | nop.m 999 | |
| 1287 | fadd.s1 A_lo = Tbl_lo, w_lo // A_lo = Tbl_lo + w_lo | |
| 1288 | nop.i 999 | |
| 1289 | } | |
| 1290 | ;; | |
| 1291 | ||
| 1292 | { .mfi | |
| 1293 | nop.m 999 | |
| 1294 | fmpy.s0 Q_1 = Q_1, Q_1 // Dummy operation to raise inexact | |
| 1295 | nop.i 999 | |
| 1296 | } | |
| 1297 | ;; | |
| 1298 | ||
| 1299 | { .mfi | |
| 1300 | nop.m 999 | |
| 1301 | fmpy.s1 poly = wsq, poly // poly = wsq * poly | |
| 1302 | nop.i 999 | |
| 1303 | } | |
| 1304 | ;; | |
| 1305 | ||
| 1306 | { .mfi | |
| 1307 | nop.m 999 | |
| 1308 | fmpy.s1 poly = w_hi, poly // poly = w_hi * poly | |
| 1309 | nop.i 999 | |
| 1310 | } | |
| 1311 | ;; | |
| 1312 | ||
| 1313 | { .mfi | |
| 1314 | nop.m 999 | |
| 1315 | fadd.s1 A_lo = A_lo, poly // A_lo = A_lo + poly | |
| 1316 | nop.i 999 | |
| 1317 | } | |
| 1318 | ;; | |
| 1319 | ||
| 1320 | { .mfi | |
| 1321 | nop.m 999 | |
| 1322 | fadd.s1 A_lo = A_lo, w_hi // A_lo = A_lo + w_hi | |
| 1323 | nop.i 999 | |
| 1324 | } | |
| 1325 | ;; | |
| 1326 | ||
| 1327 | { .mfi | |
| 1328 | nop.m 999 | |
| 1329 | fma.s1 Res_lo = sigma, A_lo, P_lo // Res_lo = P_lo + sigma * A_lo | |
| 1330 | nop.i 999 | |
| 1331 | } | |
| 1332 | ;; | |
| 1333 | ||
| 1334 | // | |
| 1335 | // Result = Res_hi + Res_lo * s_Y (User Supplied Rounding Mode) | |
| 1336 | // | |
| 1337 | { .mfb | |
| 1338 | nop.m 999 | |
| 1339 | fma.s0 Result = Res_lo, s_Y, Res_hi | |
| 1340 | br.ret.sptk b0 // Exit table path 2^-3 <= V/U < 1 | |
| 1341 | } | |
| 1342 | ;; | |
| 1343 | ||
| 1344 | ||
| 0347518d | 1345 | ATANL_POLY: |
| d5efd131 MF |
1346 | // Here if 0 < V/U < 2^-3 |
| 1347 | // | |
| 1348 | // *********************************************** | |
| 1349 | // ******************** STEP4 ******************** | |
| 1350 | // *********************************************** | |
| 1351 | ||
| 1352 | // | |
| 1353 | // Following: | |
| 1354 | // Iterate 3 times E = E + E*(1.0 - E*U) | |
| 1355 | // Also load P_8, P_7, P_6, P_5, P_4 | |
| 1356 | // | |
| 1357 | { .mfi | |
| 1358 | ldfe P_8 = [table_ptr1], -16 // Load P_8 | |
| 1359 | fnma.s1 z_lo = A_temp, U, V // z_lo = V - A_temp * U | |
| 1360 | nop.i 999 | |
| 1361 | } | |
| 1362 | { .mfi | |
| 1363 | nop.m 999 | |
| 1364 | fnma.s1 E_hold = E, U, f1 // E_hold = 1.0 - E*U (2) | |
| 1365 | nop.i 999 | |
| 1366 | } | |
| 1367 | ;; | |
| 1368 | ||
| 1369 | { .mmi | |
| 1370 | ldfe P_7 = [table_ptr1], -16 // Load P_7 | |
| 1371 | ;; | |
| 1372 | ldfe P_6 = [table_ptr1], -16 // Load P_6 | |
| 1373 | nop.i 999 | |
| 1374 | } | |
| 1375 | ;; | |
| 1376 | ||
| 1377 | { .mfi | |
| 1378 | ldfe P_5 = [table_ptr1], -16 // Load P_5 | |
| 1379 | fma.s1 E = E, E_hold, E // E = E + E_hold*E (2) | |
| 1380 | nop.i 999 | |
| 1381 | } | |
| 1382 | ;; | |
| 1383 | ||
| 1384 | { .mmi | |
| 1385 | ldfe P_4 = [table_ptr1], -16 // Load P_4 | |
| 1386 | ;; | |
| 1387 | ldfe P_3 = [table_ptr1], -16 // Load P_3 | |
| 1388 | nop.i 999 | |
| 1389 | } | |
| 1390 | ;; | |
| 1391 | ||
| 1392 | { .mfi | |
| 1393 | ldfe P_2 = [table_ptr1], -16 // Load P_2 | |
| 1394 | fnma.s1 E_hold = E, U, f1 // E_hold = 1.0 - E*U (3) | |
| 1395 | nop.i 999 | |
| 1396 | } | |
| 1397 | { .mlx | |
| 1398 | nop.m 999 | |
| 1399 | movl int_temp = 0x24005 // Signexp for small neg number | |
| 1400 | } | |
| 1401 | ;; | |
| 1402 | ||
| 1403 | { .mmf | |
| 1404 | ldfe P_1 = [table_ptr1], -16 // Load P_1 | |
| 1405 | setf.exp tmp_small = int_temp // Form small neg number | |
| 1406 | fma.s1 E = E, E_hold, E // E = E + E_hold*E (3) | |
| 1407 | } | |
| 1408 | ;; | |
| 1409 | ||
| 1410 | // | |
| 1411 | // | |
| 1412 | // At this point E approximates 1/U to roughly working precision | |
| 1413 | // Z = V*E approximates V/U | |
| 1414 | // | |
| 1415 | { .mfi | |
| 1416 | nop.m 999 | |
| 1417 | fmpy.s1 Z = V, E // Z = V * E | |
| 1418 | nop.i 999 | |
| 1419 | } | |
| 1420 | { .mfi | |
| 1421 | nop.m 999 | |
| 1422 | fmpy.s1 z_lo = z_lo, E // z_lo = z_lo * E | |
| 1423 | nop.i 999 | |
| 1424 | } | |
| 1425 | ;; | |
| 1426 | ||
| 1427 | // | |
| 1428 | // Now what we want to do is | |
| 1429 | // poly1 = P_4 + zsq*(P_5 + zsq*(P_6 + zsq*(P_7 + zsq*P_8))) | |
| 1430 | // poly2 = zsq*(P_1 + zsq*(P_2 + zsq*P_3)) | |
| 1431 | // | |
| 1432 | // | |
| 1433 | // Fixup added to force inexact later - | |
| 1434 | // A_hi = A_temp + z_lo | |
| 1435 | // z_lo = (A_temp - A_hi) + z_lo | |
| 1436 | // | |
| 1437 | { .mfi | |
| 1438 | nop.m 999 | |
| 1439 | fmpy.s1 zsq = Z, Z // zsq = Z * Z | |
| 1440 | nop.i 999 | |
| 1441 | } | |
| 1442 | { .mfi | |
| 1443 | nop.m 999 | |
| 1444 | fadd.s1 A_hi = A_temp, z_lo // A_hi = A_temp + z_lo | |
| 1445 | nop.i 999 | |
| 1446 | } | |
| 1447 | ;; | |
| 1448 | ||
| 1449 | { .mfi | |
| 1450 | nop.m 999 | |
| 1451 | fma.s1 poly1 = zsq, P_8, P_7 // poly1 = P_7 + zsq * P_8 | |
| 1452 | nop.i 999 | |
| 1453 | } | |
| 1454 | { .mfi | |
| 1455 | nop.m 999 | |
| 1456 | fma.s1 poly2 = zsq, P_3, P_2 // poly2 = P_2 + zsq * P_3 | |
| 1457 | nop.i 999 | |
| 1458 | } | |
| 1459 | ;; | |
| 1460 | ||
| 1461 | { .mfi | |
| 1462 | nop.m 999 | |
| 1463 | fmpy.s1 z4 = zsq, zsq // z4 = zsq * zsq | |
| 1464 | nop.i 999 | |
| 1465 | } | |
| 1466 | { .mfi | |
| 1467 | nop.m 999 | |
| 1468 | fsub.s1 A_temp = A_temp, A_hi // A_temp = A_temp - A_hi | |
| 1469 | nop.i 999 | |
| 1470 | } | |
| 1471 | ;; | |
| 1472 | ||
| 1473 | { .mfi | |
| 1474 | nop.m 999 | |
| 1475 | fmerge.s tmp = A_hi, A_hi // Copy tmp = A_hi | |
| 1476 | nop.i 999 | |
| 1477 | } | |
| 1478 | ;; | |
| 1479 | ||
| 1480 | { .mfi | |
| 1481 | nop.m 999 | |
| 1482 | fma.s1 poly1 = zsq, poly1, P_6 // poly1 = P_6 + zsq * poly1 | |
| 1483 | nop.i 999 | |
| 1484 | } | |
| 1485 | { .mfi | |
| 1486 | nop.m 999 | |
| 1487 | fma.s1 poly2 = zsq, poly2, P_1 // poly2 = P_2 + zsq * poly2 | |
| 1488 | nop.i 999 | |
| 1489 | } | |
| 1490 | ;; | |
| 1491 | ||
| 1492 | { .mfi | |
| 1493 | nop.m 999 | |
| 1494 | fmpy.s1 z8 = z4, z4 // z8 = z4 * z4 | |
| 1495 | nop.i 999 | |
| 1496 | } | |
| 1497 | { .mfi | |
| 1498 | nop.m 999 | |
| 1499 | fadd.s1 z_lo = A_temp, z_lo // z_lo = (A_temp - A_hi) + z_lo | |
| 1500 | nop.i 999 | |
| 1501 | } | |
| 1502 | ;; | |
| 1503 | ||
| 1504 | { .mfi | |
| 1505 | nop.m 999 | |
| 1506 | fma.s1 poly1 = zsq, poly1, P_5 // poly1 = P_5 + zsq * poly1 | |
| 1507 | nop.i 999 | |
| 1508 | } | |
| 1509 | { .mfi | |
| 1510 | nop.m 999 | |
| 1511 | fmpy.s1 poly2 = poly2, zsq // poly2 = zsq * poly2 | |
| 1512 | nop.i 999 | |
| 1513 | } | |
| 1514 | ;; | |
| 1515 | ||
| 1516 | // Create small GR double in case need to raise underflow | |
| 1517 | { .mfi | |
| 1518 | nop.m 999 | |
| 1519 | fma.s1 poly1 = zsq, poly1, P_4 // poly1 = P_4 + zsq * poly1 | |
| 1520 | dep GR_temp = -1,r0,0,53 | |
| 1521 | } | |
| 1522 | ;; | |
| 1523 | ||
| 1524 | // Create small double in case need to raise underflow | |
| 1525 | { .mfi | |
| 0347518d | 1526 | setf.d FR_temp = GR_temp |
| d5efd131 MF |
1527 | fma.s1 poly = z8, poly1, poly2 // poly = poly2 + z8 * poly1 |
| 1528 | nop.i 999 | |
| 1529 | } | |
| 1530 | ;; | |
| 1531 | ||
| 1532 | { .mfi | |
| 1533 | nop.m 999 | |
| 1534 | fma.s1 A_lo = Z, poly, z_lo // A_lo = z_lo + Z * poly | |
| 1535 | nop.i 999 | |
| 1536 | } | |
| 1537 | ;; | |
| 1538 | ||
| 1539 | { .mfi | |
| 1540 | nop.m 999 | |
| 1541 | fadd.s1 A_hi = tmp, A_lo // A_hi = tmp + A_lo | |
| 1542 | nop.i 999 | |
| 1543 | } | |
| 1544 | ;; | |
| 1545 | ||
| 1546 | { .mfi | |
| 1547 | nop.m 999 | |
| 1548 | fsub.s1 tmp = tmp, A_hi // tmp = tmp - A_hi | |
| 1549 | nop.i 999 | |
| 1550 | } | |
| 1551 | { .mfi | |
| 1552 | nop.m 999 | |
| 1553 | fmpy.s1 A_hi = s_Y, A_hi // A_hi = s_Y * A_hi | |
| 1554 | nop.i 999 | |
| 1555 | } | |
| 1556 | ;; | |
| 1557 | ||
| 1558 | { .mfi | |
| 1559 | nop.m 999 | |
| 1560 | fadd.s1 A_lo = tmp, A_lo // A_lo = tmp + A_lo | |
| 1561 | nop.i 999 | |
| 1562 | } | |
| 1563 | { .mfi | |
| 1564 | nop.m 999 | |
| 1565 | fma.s1 Res_hi = sigma, A_hi, P_hi // Res_hi = P_hi + sigma * A_hi | |
| 1566 | nop.i 999 | |
| 1567 | } | |
| 1568 | ;; | |
| 1569 | ||
| 1570 | { .mfi | |
| 1571 | nop.m 999 | |
| 1572 | fsub.s1 tmp = P_hi, Res_hi // tmp = P_hi - Res_hi | |
| 1573 | nop.i 999 | |
| 1574 | } | |
| 1575 | ;; | |
| 1576 | ||
| 1577 | // | |
| 1578 | // Test if A_lo is zero | |
| 1579 | // | |
| 1580 | { .mfi | |
| 1581 | nop.m 999 | |
| 1582 | fclass.m p6,p0 = A_lo, 0x007 // Test A_lo = 0 | |
| 1583 | nop.i 999 | |
| 1584 | } | |
| 1585 | ;; | |
| 1586 | ||
| 1587 | { .mfi | |
| 1588 | nop.m 999 | |
| 1589 | (p6) mov A_lo = tmp_small // If A_lo zero, make very small | |
| 1590 | nop.i 999 | |
| 1591 | } | |
| 1592 | ;; | |
| 1593 | ||
| 1594 | { .mfi | |
| 1595 | nop.m 999 | |
| 1596 | fma.s1 tmp = A_hi, sigma, tmp // tmp = sigma * A_hi + tmp | |
| 1597 | nop.i 999 | |
| 1598 | } | |
| 1599 | { .mfi | |
| 1600 | nop.m 999 | |
| 1601 | fma.s1 sigma = A_lo, sigma, P_lo // sigma = A_lo * sigma + P_lo | |
| 1602 | nop.i 999 | |
| 1603 | } | |
| 1604 | ;; | |
| 1605 | ||
| 1606 | { .mfi | |
| 1607 | nop.m 999 | |
| 1608 | fma.s1 Res_lo = s_Y, sigma, tmp // Res_lo = s_Y * sigma + tmp | |
| 1609 | nop.i 999 | |
| 1610 | } | |
| 1611 | ;; | |
| 1612 | ||
| 1613 | // | |
| 1614 | // Test if Res_lo is denormal | |
| 1615 | // | |
| 1616 | { .mfi | |
| 1617 | nop.m 999 | |
| 1618 | fclass.m p14, p15 = Res_lo, 0x0b | |
| 1619 | nop.i 999 | |
| 1620 | } | |
| 1621 | ;; | |
| 1622 | ||
| 1623 | // | |
| 1624 | // Compute Result = Res_lo + Res_hi. Use s3 if Res_lo is denormal. | |
| 1625 | // | |
| 1626 | { .mfi | |
| 1627 | nop.m 999 | |
| 1628 | (p14) fadd.s3 Result = Res_lo, Res_hi // Result for Res_lo denormal | |
| 1629 | nop.i 999 | |
| 1630 | } | |
| 1631 | { .mfi | |
| 1632 | nop.m 999 | |
| 1633 | (p15) fadd.s0 Result = Res_lo, Res_hi // Result for Res_lo normal | |
| 1634 | nop.i 999 | |
| 1635 | } | |
| 1636 | ;; | |
| 1637 | ||
| 0347518d | 1638 | // |
| d5efd131 | 1639 | // If Res_lo is denormal test if Result equals zero |
| 0347518d | 1640 | // |
| d5efd131 MF |
1641 | { .mfi |
| 1642 | nop.m 999 | |
| 1643 | (p14) fclass.m.unc p14, p0 = Result, 0x07 | |
| 1644 | nop.i 999 | |
| 1645 | } | |
| 1646 | ;; | |
| 1647 | ||
| 1648 | // | |
| 1649 | // If Res_lo is denormal and Result equals zero, raise inexact, underflow | |
| 1650 | // by squaring small double | |
| 1651 | // | |
| 1652 | { .mfb | |
| 1653 | nop.m 999 | |
| 1654 | (p14) fmpy.d.s0 FR_temp = FR_temp, FR_temp | |
| 1655 | br.ret.sptk b0 // Exit POLY path, 0 < Q < 2^-3 | |
| 1656 | } | |
| 1657 | ;; | |
| 1658 | ||
| 1659 | ||
| 0347518d | 1660 | ATANL_UNSUPPORTED: |
| d5efd131 MF |
1661 | { .mfb |
| 1662 | nop.m 999 | |
| 0347518d | 1663 | fmpy.s0 Result = ArgX,ArgY |
| d5efd131 MF |
1664 | br.ret.sptk b0 |
| 1665 | } | |
| 1666 | ;; | |
| 1667 | ||
| 1668 | // Here if y natval, nan, inf, zero | |
| 1669 | ATANL_Y_SPECIAL: | |
| 1670 | // Here if x natval, nan, inf, zero | |
| 1671 | ATANL_X_SPECIAL: | |
| 1672 | { .mfi | |
| 1673 | nop.m 999 | |
| 1674 | fclass.m p13,p12 = ArgY_orig, 0x0c3 // Test y nan | |
| 1675 | nop.i 999 | |
| 1676 | } | |
| 1677 | ;; | |
| 1678 | ||
| 1679 | { .mfi | |
| 1680 | nop.m 999 | |
| 1681 | fclass.m p15,p14 = ArgY_orig, 0x103 // Test y natval | |
| 1682 | nop.i 999 | |
| 1683 | } | |
| 1684 | ;; | |
| 1685 | ||
| 1686 | { .mfi | |
| 1687 | nop.m 999 | |
| 1688 | (p12) fclass.m p13,p0 = ArgX_orig, 0x0c3 // Test x nan | |
| 1689 | nop.i 999 | |
| 1690 | } | |
| 1691 | ;; | |
| 1692 | ||
| 1693 | { .mfi | |
| 1694 | nop.m 999 | |
| 1695 | (p14) fclass.m p15,p0 = ArgX_orig, 0x103 // Test x natval | |
| 1696 | nop.i 999 | |
| 1697 | } | |
| 1698 | ;; | |
| 1699 | ||
| 1700 | { .mfb | |
| 1701 | nop.m 999 | |
| 1702 | (p13) fmpy.s0 Result = ArgX_orig, ArgY_orig // Result nan if x or y nan | |
| 1703 | (p13) br.ret.spnt b0 // Exit if x or y nan | |
| 1704 | } | |
| 1705 | ;; | |
| 1706 | ||
| 1707 | { .mfb | |
| 1708 | nop.m 999 | |
| 1709 | (p15) fmpy.s0 Result = ArgX_orig, ArgY_orig // Result natval if x or y natval | |
| 1710 | (p15) br.ret.spnt b0 // Exit if x or y natval | |
| 1711 | } | |
| 1712 | ;; | |
| 1713 | ||
| 1714 | ||
| 1715 | // Here if x or y inf or zero | |
| 0347518d | 1716 | ATANL_SPECIAL_HANDLING: |
| d5efd131 MF |
1717 | { .mfi |
| 1718 | nop.m 999 | |
| 1719 | fclass.m p6, p7 = ArgY_orig, 0x007 // Test y zero | |
| 1720 | mov special = 992 // Offset to table | |
| 1721 | } | |
| 1722 | ;; | |
| 1723 | ||
| 1724 | { .mfb | |
| 1725 | add table_ptr1 = table_base, special // Point to 3pi/4 | |
| 1726 | fcmp.eq.s0 p0, p9 = ArgX_orig, ArgY_orig // Dummy to set denormal flag | |
| 1727 | (p7) br.cond.spnt ATANL_ArgY_Not_ZERO // Branch if y not zero | |
| 1728 | } | |
| 1729 | ;; | |
| 1730 | ||
| 1731 | // Here if y zero | |
| 1732 | { .mmf | |
| 1733 | ldfd Result = [table_ptr1], 8 // Get pi high | |
| 1734 | nop.m 999 | |
| 1735 | fclass.m p14, p0 = ArgX, 0x035 // Test for x>=+0 | |
| 1736 | } | |
| 1737 | ;; | |
| 1738 | ||
| 1739 | { .mmf | |
| 1740 | nop.m 999 | |
| 1741 | ldfd Result_lo = [table_ptr1], -8 // Get pi lo | |
| 1742 | fclass.m p15, p0 = ArgX, 0x036 // Test for x<=-0 | |
| 1743 | } | |
| 1744 | ;; | |
| 1745 | ||
| 1746 | // | |
| 1747 | // Return sign_Y * 0 when ArgX > +0 | |
| 1748 | // | |
| 1749 | { .mfi | |
| 1750 | nop.m 999 | |
| 1751 | (p14) fmerge.s Result = ArgY, f0 // If x>=+0, y=0, hi sgn(y)*0 | |
| 1752 | nop.i 999 | |
| 1753 | } | |
| 1754 | ;; | |
| 1755 | ||
| 1756 | { .mfi | |
| 1757 | nop.m 999 | |
| 1758 | fclass.m p13, p0 = ArgX, 0x007 // Test for x=0 | |
| 1759 | nop.i 999 | |
| 1760 | } | |
| 1761 | ;; | |
| 1762 | ||
| 1763 | { .mfi | |
| 1764 | nop.m 999 | |
| 1765 | (p14) fmerge.s Result_lo = ArgY, f0 // If x>=+0, y=0, lo sgn(y)*0 | |
| 1766 | nop.i 999 | |
| 1767 | } | |
| 1768 | ;; | |
| 1769 | ||
| 1770 | { .mfi | |
| 1771 | (p13) mov GR_Parameter_TAG = 36 // Error tag for x=0, y=0 | |
| 1772 | nop.f 999 | |
| 1773 | nop.i 999 | |
| 1774 | } | |
| 1775 | ;; | |
| 1776 | ||
| 1777 | // | |
| 1778 | // Return sign_Y * pi when ArgX < -0 | |
| 1779 | // | |
| 1780 | { .mfi | |
| 1781 | nop.m 999 | |
| 1782 | (p15) fmerge.s Result = ArgY, Result // If x<0, y=0, hi=sgn(y)*pi | |
| 1783 | nop.i 999 | |
| 1784 | } | |
| 1785 | ;; | |
| 1786 | ||
| 1787 | { .mfi | |
| 1788 | nop.m 999 | |
| 1789 | (p15) fmerge.s Result_lo = ArgY, Result_lo // If x<0, y=0, lo=sgn(y)*pi | |
| 1790 | nop.i 999 | |
| 1791 | } | |
| 1792 | ;; | |
| 1793 | ||
| 1794 | // | |
| 1795 | // Call error support function for atan(0,0) | |
| 1796 | // | |
| 1797 | { .mfb | |
| 1798 | nop.m 999 | |
| 1799 | fadd.s0 Result = Result, Result_lo | |
| 1800 | (p13) br.cond.spnt __libm_error_region // Branch if atan(0,0) | |
| 1801 | } | |
| 1802 | ;; | |
| 1803 | ||
| 1804 | { .mib | |
| 1805 | nop.m 999 | |
| 1806 | nop.i 999 | |
| 1807 | br.ret.sptk b0 // Exit for y=0, x not 0 | |
| 1808 | } | |
| 1809 | ;; | |
| 1810 | ||
| 1811 | // Here if y not zero | |
| 0347518d | 1812 | ATANL_ArgY_Not_ZERO: |
| d5efd131 MF |
1813 | { .mfi |
| 1814 | nop.m 999 | |
| 1815 | fclass.m p0, p10 = ArgY, 0x023 // Test y inf | |
| 1816 | nop.i 999 | |
| 1817 | } | |
| 1818 | ;; | |
| 1819 | ||
| 1820 | { .mfb | |
| 1821 | nop.m 999 | |
| 1822 | fclass.m p6, p0 = ArgX, 0x017 // Test for 0 <= |x| < inf | |
| 1823 | (p10) br.cond.spnt ATANL_ArgY_Not_INF // Branch if 0 < |y| < inf | |
| 1824 | } | |
| 1825 | ;; | |
| 1826 | ||
| 1827 | // Here if y=inf | |
| 1828 | // | |
| 1829 | // Return +PI/2 when ArgY = +Inf and ArgX = +/-0 or normal | |
| 1830 | // Return -PI/2 when ArgY = -Inf and ArgX = +/-0 or normal | |
| 1831 | // Return +PI/4 when ArgY = +Inf and ArgX = +Inf | |
| 1832 | // Return -PI/4 when ArgY = -Inf and ArgX = +Inf | |
| 1833 | // Return +3PI/4 when ArgY = +Inf and ArgX = -Inf | |
| 1834 | // Return -3PI/4 when ArgY = -Inf and ArgX = -Inf | |
| 1835 | // | |
| 1836 | { .mfi | |
| 1837 | nop.m 999 | |
| 1838 | fclass.m p7, p0 = ArgX, 0x021 // Test for x=+inf | |
| 1839 | nop.i 999 | |
| 1840 | } | |
| 1841 | ;; | |
| 1842 | ||
| 1843 | { .mfi | |
| 0347518d | 1844 | (p6) add table_ptr1 = 16, table_ptr1 // Point to pi/2, if x finite |
| d5efd131 MF |
1845 | fclass.m p8, p0 = ArgX, 0x022 // Test for x=-inf |
| 1846 | nop.i 999 | |
| 1847 | } | |
| 1848 | ;; | |
| 1849 | ||
| 1850 | { .mmi | |
| 1851 | (p7) add table_ptr1 = 32, table_ptr1 // Point to pi/4 if x=+inf | |
| 1852 | ;; | |
| 1853 | (p8) add table_ptr1 = 48, table_ptr1 // Point to 3pi/4 if x=-inf | |
| 1854 | ||
| 1855 | nop.i 999 | |
| 1856 | } | |
| 1857 | ;; | |
| 1858 | ||
| 1859 | { .mmi | |
| 1860 | ldfd Result = [table_ptr1], 8 // Load pi/2, pi/4, or 3pi/4 hi | |
| 1861 | ;; | |
| 1862 | ldfd Result_lo = [table_ptr1], -8 // Load pi/2, pi/4, or 3pi/4 lo | |
| 1863 | nop.i 999 | |
| 1864 | } | |
| 1865 | ;; | |
| 1866 | ||
| 1867 | { .mfi | |
| 1868 | nop.m 999 | |
| 1869 | fmerge.s Result = ArgY, Result // Merge sgn(y) in hi | |
| 1870 | nop.i 999 | |
| 1871 | } | |
| 1872 | ;; | |
| 1873 | ||
| 1874 | { .mfi | |
| 1875 | nop.m 999 | |
| 1876 | fmerge.s Result_lo = ArgY, Result_lo // Merge sgn(y) in lo | |
| 1877 | nop.i 999 | |
| 1878 | } | |
| 1879 | ;; | |
| 1880 | ||
| 1881 | { .mfb | |
| 1882 | nop.m 999 | |
| 1883 | fadd.s0 Result = Result, Result_lo // Compute complete result | |
| 1884 | br.ret.sptk b0 // Exit for y=inf | |
| 1885 | } | |
| 1886 | ;; | |
| 1887 | ||
| 1888 | // Here if y not INF, and x=0 or INF | |
| 0347518d | 1889 | ATANL_ArgY_Not_INF: |
| d5efd131 MF |
1890 | // |
| 1891 | // Return +PI/2 when ArgY NOT Inf, ArgY > 0 and ArgX = +/-0 | |
| 1892 | // Return -PI/2 when ArgY NOT Inf, ArgY < 0 and ArgX = +/-0 | |
| 1893 | // Return +0 when ArgY NOT Inf, ArgY > 0 and ArgX = +Inf | |
| 1894 | // Return -0 when ArgY NOT Inf, ArgY > 0 and ArgX = +Inf | |
| 1895 | // Return +PI when ArgY NOT Inf, ArgY > 0 and ArgX = -Inf | |
| 1896 | // Return -PI when ArgY NOT Inf, ArgY > 0 and ArgX = -Inf | |
| 1897 | // | |
| 1898 | { .mfi | |
| 1899 | nop.m 999 | |
| 1900 | fclass.m p7, p9 = ArgX, 0x021 // Test for x=+inf | |
| 1901 | nop.i 999 | |
| 1902 | } | |
| 1903 | ;; | |
| 1904 | ||
| 1905 | { .mfi | |
| 1906 | nop.m 999 | |
| 1907 | fclass.m p6, p0 = ArgX, 0x007 // Test for x=0 | |
| 1908 | nop.i 999 | |
| 1909 | } | |
| 1910 | ;; | |
| 1911 | ||
| 1912 | { .mfi | |
| 1913 | (p6) add table_ptr1 = 16, table_ptr1 // Point to pi/2 | |
| 1914 | fclass.m p8, p0 = ArgX, 0x022 // Test for x=-inf | |
| 1915 | nop.i 999 | |
| 1916 | } | |
| 1917 | ;; | |
| 1918 | ||
| 1919 | .pred.rel "mutex",p7,p9 | |
| 1920 | { .mfi | |
| 1921 | (p9) ldfd Result = [table_ptr1], 8 // Load pi or pi/2 hi | |
| 1922 | (p7) fmerge.s Result = ArgY, f0 // If y not inf, x=+inf, sgn(y)*0 | |
| 1923 | nop.i 999 | |
| 1924 | } | |
| 1925 | ;; | |
| 1926 | ||
| 1927 | { .mfi | |
| 1928 | (p9) ldfd Result_lo = [table_ptr1], -8 // Load pi or pi/2 lo | |
| 1929 | (p7) fnorm.s0 Result = Result // If y not inf, x=+inf normalize | |
| 1930 | nop.i 999 | |
| 1931 | } | |
| 1932 | ;; | |
| 1933 | ||
| 1934 | { .mfi | |
| 1935 | nop.m 999 | |
| 1936 | (p9) fmerge.s Result = ArgY, Result // Merge sgn(y) in hi | |
| 1937 | nop.i 999 | |
| 1938 | } | |
| 1939 | ;; | |
| 1940 | ||
| 1941 | { .mfi | |
| 1942 | nop.m 999 | |
| 1943 | (p9) fmerge.s Result_lo = ArgY, Result_lo // Merge sgn(y) in lo | |
| 1944 | nop.i 999 | |
| 1945 | } | |
| 1946 | ;; | |
| 1947 | ||
| 1948 | { .mfb | |
| 1949 | nop.m 999 | |
| 1950 | (p9) fadd.s0 Result = Result, Result_lo // Compute complete result | |
| 1951 | br.ret.spnt b0 // Exit for y not inf, x=0,inf | |
| 1952 | } | |
| 1953 | ;; | |
| 1954 | ||
| 1955 | GLOBAL_IEEE754_END(atan2l) | |
| 0347518d | 1956 | |
| d5efd131 MF |
1957 | LOCAL_LIBM_ENTRY(__libm_error_region) |
| 1958 | .prologue | |
| 1959 | { .mfi | |
| 1960 | add GR_Parameter_Y=-32,sp // Parameter 2 value | |
| 1961 | nop.f 0 | |
| 1962 | .save ar.pfs,GR_SAVE_PFS | |
| 1963 | mov GR_SAVE_PFS=ar.pfs // Save ar.pfs | |
| 1964 | } | |
| 1965 | { .mfi | |
| 1966 | .fframe 64 | |
| 1967 | add sp=-64,sp // Create new stack | |
| 1968 | nop.f 0 | |
| 1969 | mov GR_SAVE_GP=gp // Save gp | |
| 1970 | };; | |
| 1971 | { .mmi | |
| 1972 | stfe [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack | |
| 1973 | add GR_Parameter_X = 16,sp // Parameter 1 address | |
| 1974 | .save b0, GR_SAVE_B0 | |
| 1975 | mov GR_SAVE_B0=b0 // Save b0 | |
| 1976 | };; | |
| 1977 | .body | |
| 1978 | { .mib | |
| 1979 | stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack | |
| 1980 | add GR_Parameter_RESULT = 0,GR_Parameter_Y | |
| 1981 | nop.b 0 // Parameter 3 address | |
| 1982 | } | |
| 1983 | { .mib | |
| 1984 | stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack | |
| 1985 | add GR_Parameter_Y = -16,GR_Parameter_Y | |
| 1986 | br.call.sptk b0=__libm_error_support# // Call error handling function | |
| 1987 | };; | |
| 1988 | { .mmi | |
| 1989 | nop.m 0 | |
| 1990 | nop.m 0 | |
| 1991 | add GR_Parameter_RESULT = 48,sp | |
| 1992 | };; | |
| 1993 | { .mmi | |
| 1994 | ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack | |
| 1995 | .restore sp | |
| 1996 | add sp = 64,sp // Restore stack pointer | |
| 1997 | mov b0 = GR_SAVE_B0 // Restore return address | |
| 1998 | };; | |
| 1999 | { .mib | |
| 2000 | mov gp = GR_SAVE_GP // Restore gp | |
| 2001 | mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs | |
| 2002 | br.ret.sptk b0 // Return | |
| 2003 | };; | |
| 2004 | ||
| 2005 | LOCAL_LIBM_END(__libm_error_region#) | |
| 2006 | .type __libm_error_support#,@function | |
| 2007 | .global __libm_error_support# |