projects / thirdparty / glibc.git / blame
| Commit | Line | Data |
|---|---|---|
| 0ecb606c JJ |
1 | .file "logl.s" |
| 2 | ||
| 3 | ||
| 4 | // Copyright (c) 2000 - 2003, 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 | ||
| 24 | // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | |
| 25 | // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | |
| 26 | // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR | |
| 27 | // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS | |
| 28 | // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, | |
| 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 | |
| 32 | // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING | |
| 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 | // | |
| 36 | // Intel Corporation is the author of this code, and requests that all | |
| 37 | // problem reports or change requests be submitted to it directly at | |
| 38 | // http://www.intel.com/software/products/opensource/libraries/num.htm. | |
| 39 | // | |
| 40 | //********************************************************************* | |
| 41 | // | |
| 42 | // History: | |
| 43 | // 05/21/01 Extracted logl and log10l from log1pl.s file, and optimized | |
| 44 | // all paths. | |
| 45 | // 06/20/01 Fixed error tag for x=-inf. | |
| 46 | // 05/20/02 Cleaned up namespace and sf0 syntax | |
| 47 | // 02/10/03 Reordered header: .section, .global, .proc, .align; | |
| 48 | // used data8 for long double table values | |
| 49 | // | |
| 50 | //********************************************************************* | |
| 51 | // | |
| 52 | //********************************************************************* | |
| 53 | // | |
| 54 | // Function: Combined logl(x) and log10l(x) where | |
| 55 | // logl(x) = ln(x), for double-extended precision x values | |
| 56 | // log10l(x) = log (x), for double-extended precision x values | |
| 57 | // 10 | |
| 58 | // | |
| 59 | //********************************************************************* | |
| 60 | // | |
| 61 | // Resources Used: | |
| 62 | // | |
| 63 | // Floating-Point Registers: f8 (Input and Return Value) | |
| 64 | // f34-f76 | |
| 65 | // | |
| 66 | // General Purpose Registers: | |
| 67 | // r32-r56 | |
| 68 | // r53-r56 (Used to pass arguments to error handling routine) | |
| 69 | // | |
| 70 | // Predicate Registers: p6-p14 | |
| 71 | // | |
| 72 | //********************************************************************* | |
| 73 | // | |
| 74 | // IEEE Special Conditions: | |
| 75 | // | |
| 76 | // Denormal fault raised on denormal inputs | |
| 77 | // Overflow exceptions cannot occur | |
| 78 | // Underflow exceptions raised when appropriate for log1p | |
| 79 | // (Error Handling Routine called for underflow) | |
| 80 | // Inexact raised when appropriate by algorithm | |
| 81 | // | |
| 82 | // logl(inf) = inf | |
| 83 | // logl(-inf) = QNaN | |
| 84 | // logl(+/-0) = -inf | |
| 85 | // logl(SNaN) = QNaN | |
| 86 | // logl(QNaN) = QNaN | |
| 87 | // logl(EM_special Values) = QNaN | |
| 88 | // log10l(inf) = inf | |
| 89 | // log10l(-inf) = QNaN | |
| 90 | // log10l(+/-0) = -inf | |
| 91 | // log10l(SNaN) = QNaN | |
| 92 | // log10l(QNaN) = QNaN | |
| 93 | // log10l(EM_special Values) = QNaN | |
| 94 | // | |
| 95 | //********************************************************************* | |
| 96 | // | |
| 97 | // Overview | |
| 98 | // | |
| 99 | // The method consists of two cases. | |
| 100 | // | |
| 101 | // If |X-1| < 2^(-7) use case log_near1; | |
| 102 | // else use case log_regular; | |
| 103 | // | |
| 104 | // Case log_near1: | |
| 105 | // | |
| 106 | // logl( 1 + X ) can be approximated by a simple polynomial | |
| 107 | // in W = X-1. This polynomial resembles the truncated Taylor | |
| 108 | // series W - W^/2 + W^3/3 - ... | |
| 109 | // | |
| 110 | // Case log_regular: | |
| 111 | // | |
| 112 | // Here we use a table lookup method. The basic idea is that in | |
| 113 | // order to compute logl(Arg) for an argument Arg in [1,2), we | |
| 114 | // construct a value G such that G*Arg is close to 1 and that | |
| 115 | // logl(1/G) is obtainable easily from a table of values calculated | |
| 116 | // beforehand. Thus | |
| 117 | // | |
| 118 | // logl(Arg) = logl(1/G) + logl(G*Arg) | |
| 119 | // = logl(1/G) + logl(1 + (G*Arg - 1)) | |
| 120 | // | |
| 121 | // Because |G*Arg - 1| is small, the second term on the right hand | |
| 122 | // side can be approximated by a short polynomial. We elaborate | |
| 123 | // this method in four steps. | |
| 124 | // | |
| 125 | // Step 0: Initialization | |
| 126 | // | |
| 127 | // We need to calculate logl( X ). Obtain N, S_hi such that | |
| 128 | // | |
| 129 | // X = 2^N * S_hi exactly | |
| 130 | // | |
| 131 | // where S_hi in [1,2) | |
| 132 | // | |
| 133 | // Step 1: Argument Reduction | |
| 134 | // | |
| 135 | // Based on S_hi, obtain G_1, G_2, G_3 from a table and calculate | |
| 136 | // | |
| 137 | // G := G_1 * G_2 * G_3 | |
| 138 | // r := (G * S_hi - 1) | |
| 139 | // | |
| 140 | // These G_j's have the property that the product is exactly | |
| 141 | // representable and that |r| < 2^(-12) as a result. | |
| 142 | // | |
| 143 | // Step 2: Approximation | |
| 144 | // | |
| 145 | // | |
| 146 | // logl(1 + r) is approximated by a short polynomial poly(r). | |
| 147 | // | |
| 148 | // Step 3: Reconstruction | |
| 149 | // | |
| 150 | // | |
| 151 | // Finally, logl( X ) is given by | |
| 152 | // | |
| 153 | // logl( X ) = logl( 2^N * S_hi ) | |
| 154 | // ~=~ N*logl(2) + logl(1/G) + logl(1 + r) | |
| 155 | // ~=~ N*logl(2) + logl(1/G) + poly(r). | |
| 156 | // | |
| 157 | // **** Algorithm **** | |
| 158 | // | |
| 159 | // Case log_near1: | |
| 160 | // | |
| 161 | // Here we compute a simple polynomial. To exploit parallelism, we split | |
| 162 | // the polynomial into two portions. | |
| 163 | // | |
| 164 | // W := X - 1 | |
| 165 | // Wsq := W * W | |
| 166 | // W4 := Wsq*Wsq | |
| 167 | // W6 := W4*Wsq | |
| 168 | // Y_hi := W + Wsq*(P_1 + W*(P_2 + W*(P_3 + W*P_4)) | |
| 169 | // Y_lo := W6*(P_5 + W*(P_6 + W*(P_7 + W*P_8))) | |
| 170 | // | |
| 171 | // Case log_regular: | |
| 172 | // | |
| 173 | // We present the algorithm in four steps. | |
| 174 | // | |
| 175 | // Step 0. Initialization | |
| 176 | // ---------------------- | |
| 177 | // | |
| 178 | // Z := X | |
| 179 | // N := unbaised exponent of Z | |
| 180 | // S_hi := 2^(-N) * Z | |
| 181 | // | |
| 182 | // Step 1. Argument Reduction | |
| 183 | // -------------------------- | |
| 184 | // | |
| 185 | // Let | |
| 186 | // | |
| 187 | // Z = 2^N * S_hi = 2^N * 1.d_1 d_2 d_3 ... d_63 | |
| 188 | // | |
| 189 | // We obtain G_1, G_2, G_3 by the following steps. | |
| 190 | // | |
| 191 | // | |
| 192 | // Define X_0 := 1.d_1 d_2 ... d_14. This is extracted | |
| 193 | // from S_hi. | |
| 194 | // | |
| 195 | // Define A_1 := 1.d_1 d_2 d_3 d_4. This is X_0 truncated | |
| 196 | // to lsb = 2^(-4). | |
| 197 | // | |
| 198 | // Define index_1 := [ d_1 d_2 d_3 d_4 ]. | |
| 199 | // | |
| 200 | // Fetch Z_1 := (1/A_1) rounded UP in fixed point with | |
| 201 | // fixed point lsb = 2^(-15). | |
| 202 | // Z_1 looks like z_0.z_1 z_2 ... z_15 | |
| 203 | // Note that the fetching is done using index_1. | |
| 204 | // A_1 is actually not needed in the implementation | |
| 205 | // and is used here only to explain how is the value | |
| 206 | // Z_1 defined. | |
| 207 | // | |
| 208 | // Fetch G_1 := (1/A_1) truncated to 21 sig. bits. | |
| 209 | // floating pt. Again, fetching is done using index_1. A_1 | |
| 210 | // explains how G_1 is defined. | |
| 211 | // | |
| 212 | // Calculate X_1 := X_0 * Z_1 truncated to lsb = 2^(-14) | |
| 213 | // = 1.0 0 0 0 d_5 ... d_14 | |
| 214 | // This is accomplised by integer multiplication. | |
| 215 | // It is proved that X_1 indeed always begin | |
| 216 | // with 1.0000 in fixed point. | |
| 217 | // | |
| 218 | // | |
| 219 | // Define A_2 := 1.0 0 0 0 d_5 d_6 d_7 d_8. This is X_1 | |
| 220 | // truncated to lsb = 2^(-8). Similar to A_1, | |
| 221 | // A_2 is not needed in actual implementation. It | |
| 222 | // helps explain how some of the values are defined. | |
| 223 | // | |
| 224 | // Define index_2 := [ d_5 d_6 d_7 d_8 ]. | |
| 225 | // | |
| 226 | // Fetch Z_2 := (1/A_2) rounded UP in fixed point with | |
| 227 | // fixed point lsb = 2^(-15). Fetch done using index_2. | |
| 228 | // Z_2 looks like z_0.z_1 z_2 ... z_15 | |
| 229 | // | |
| 230 | // Fetch G_2 := (1/A_2) truncated to 21 sig. bits. | |
| 231 | // floating pt. | |
| 232 | // | |
| 233 | // Calculate X_2 := X_1 * Z_2 truncated to lsb = 2^(-14) | |
| 234 | // = 1.0 0 0 0 0 0 0 0 d_9 d_10 ... d_14 | |
| 235 | // This is accomplised by integer multiplication. | |
| 236 | // It is proved that X_2 indeed always begin | |
| 237 | // with 1.00000000 in fixed point. | |
| 238 | // | |
| 239 | // | |
| 240 | // Define A_3 := 1.0 0 0 0 0 0 0 0 d_9 d_10 d_11 d_12 d_13 1. | |
| 241 | // This is 2^(-14) + X_2 truncated to lsb = 2^(-13). | |
| 242 | // | |
| 243 | // Define index_3 := [ d_9 d_10 d_11 d_12 d_13 ]. | |
| 244 | // | |
| 245 | // Fetch G_3 := (1/A_3) truncated to 21 sig. bits. | |
| 246 | // floating pt. Fetch is done using index_3. | |
| 247 | // | |
| 248 | // Compute G := G_1 * G_2 * G_3. | |
| 249 | // | |
| 250 | // This is done exactly since each of G_j only has 21 sig. bits. | |
| 251 | // | |
| 252 | // Compute | |
| 253 | // | |
| 254 | // r := (G*S_hi - 1) | |
| 255 | // | |
| 256 | // | |
| 257 | // Step 2. Approximation | |
| 258 | // --------------------- | |
| 259 | // | |
| 260 | // This step computes an approximation to logl( 1 + r ) where r is the | |
| 261 | // reduced argument just obtained. It is proved that |r| <= 1.9*2^(-13); | |
| 262 | // thus logl(1+r) can be approximated by a short polynomial: | |
| 263 | // | |
| 264 | // logl(1+r) ~=~ poly = r + Q1 r^2 + ... + Q4 r^5 | |
| 265 | // | |
| 266 | // | |
| 267 | // Step 3. Reconstruction | |
| 268 | // ---------------------- | |
| 269 | // | |
| 270 | // This step computes the desired result of logl(X): | |
| 271 | // | |
| 272 | // logl(X) = logl( 2^N * S_hi ) | |
| 273 | // = N*logl(2) + logl( S_hi ) | |
| 274 | // = N*logl(2) + logl(1/G) + | |
| 275 | // logl(1 + G*S_hi - 1 ) | |
| 276 | // | |
| 277 | // logl(2), logl(1/G_j) are stored as pairs of (single,double) numbers: | |
| 278 | // log2_hi, log2_lo, log1byGj_hi, log1byGj_lo. The high parts are | |
| 279 | // single-precision numbers and the low parts are double precision | |
| 280 | // numbers. These have the property that | |
| 281 | // | |
| 282 | // N*log2_hi + SUM ( log1byGj_hi ) | |
| 283 | // | |
| 284 | // is computable exactly in double-extended precision (64 sig. bits). | |
| 285 | // Finally | |
| 286 | // | |
| 287 | // Y_hi := N*log2_hi + SUM ( log1byGj_hi ) | |
| 288 | // Y_lo := poly_hi + [ poly_lo + | |
| 289 | // ( SUM ( log1byGj_lo ) + N*log2_lo ) ] | |
| 290 | // | |
| 291 | ||
| 292 | RODATA | |
| 293 | .align 64 | |
| 294 | ||
| 295 | // ************* DO NOT CHANGE THE ORDER OF THESE TABLES ************* | |
| 296 | ||
| 297 | // P_8, P_7, P_6, P_5, P_4, P_3, P_2, and P_1 | |
| 298 | ||
| 299 | LOCAL_OBJECT_START(Constants_P) | |
| 300 | data8 0xE3936754EFD62B15,0x00003FFB | |
| 301 | data8 0x8003B271A5E56381,0x0000BFFC | |
| 302 | data8 0x9249248C73282DB0,0x00003FFC | |
| 303 | data8 0xAAAAAA9F47305052,0x0000BFFC | |
| 304 | data8 0xCCCCCCCCCCD17FC9,0x00003FFC | |
| 305 | data8 0x8000000000067ED5,0x0000BFFD | |
| 306 | data8 0xAAAAAAAAAAAAAAAA,0x00003FFD | |
| 307 | data8 0xFFFFFFFFFFFFFFFE,0x0000BFFD | |
| 308 | LOCAL_OBJECT_END(Constants_P) | |
| 309 | ||
| 310 | // log2_hi, log2_lo, Q_4, Q_3, Q_2, and Q_1 | |
| 311 | ||
| 312 | LOCAL_OBJECT_START(Constants_Q) | |
| 313 | data8 0xB172180000000000,0x00003FFE | |
| 314 | data8 0x82E308654361C4C6,0x0000BFE2 | |
| 315 | data8 0xCCCCCAF2328833CB,0x00003FFC | |
| 316 | data8 0x80000077A9D4BAFB,0x0000BFFD | |
| 317 | data8 0xAAAAAAAAAAABE3D2,0x00003FFD | |
| 318 | data8 0xFFFFFFFFFFFFDAB7,0x0000BFFD | |
| 319 | LOCAL_OBJECT_END(Constants_Q) | |
| 320 | ||
| 321 | // 1/ln10_hi, 1/ln10_lo | |
| 322 | ||
| 323 | LOCAL_OBJECT_START(Constants_1_by_LN10) | |
| 324 | data8 0xDE5BD8A937287195,0x00003FFD | |
| 325 | data8 0xD56EAABEACCF70C8,0x00003FBB | |
| 326 | LOCAL_OBJECT_END(Constants_1_by_LN10) | |
| 327 | ||
| 328 | ||
| 329 | // Z1 - 16 bit fixed | |
| 330 | ||
| 331 | LOCAL_OBJECT_START(Constants_Z_1) | |
| 332 | data4 0x00008000 | |
| 333 | data4 0x00007879 | |
| 334 | data4 0x000071C8 | |
| 335 | data4 0x00006BCB | |
| 336 | data4 0x00006667 | |
| 337 | data4 0x00006187 | |
| 338 | data4 0x00005D18 | |
| 339 | data4 0x0000590C | |
| 340 | data4 0x00005556 | |
| 341 | data4 0x000051EC | |
| 342 | data4 0x00004EC5 | |
| 343 | data4 0x00004BDB | |
| 344 | data4 0x00004925 | |
| 345 | data4 0x0000469F | |
| 346 | data4 0x00004445 | |
| 347 | data4 0x00004211 | |
| 348 | LOCAL_OBJECT_END(Constants_Z_1) | |
| 349 | ||
| 350 | // G1 and H1 - IEEE single and h1 - IEEE double | |
| 351 | ||
| 352 | LOCAL_OBJECT_START(Constants_G_H_h1) | |
| 353 | data4 0x3F800000,0x00000000 | |
| 354 | data8 0x0000000000000000 | |
| 355 | data4 0x3F70F0F0,0x3D785196 | |
| 356 | data8 0x3DA163A6617D741C | |
| 357 | data4 0x3F638E38,0x3DF13843 | |
| 358 | data8 0x3E2C55E6CBD3D5BB | |
| 359 | data4 0x3F579430,0x3E2FF9A0 | |
| 360 | data8 0xBE3EB0BFD86EA5E7 | |
| 361 | data4 0x3F4CCCC8,0x3E647FD6 | |
| 362 | data8 0x3E2E6A8C86B12760 | |
| 363 | data4 0x3F430C30,0x3E8B3AE7 | |
| 364 | data8 0x3E47574C5C0739BA | |
| 365 | data4 0x3F3A2E88,0x3EA30C68 | |
| 366 | data8 0x3E20E30F13E8AF2F | |
| 367 | data4 0x3F321640,0x3EB9CEC8 | |
| 368 | data8 0xBE42885BF2C630BD | |
| 369 | data4 0x3F2AAAA8,0x3ECF9927 | |
| 370 | data8 0x3E497F3497E577C6 | |
| 371 | data4 0x3F23D708,0x3EE47FC5 | |
| 372 | data8 0x3E3E6A6EA6B0A5AB | |
| 373 | data4 0x3F1D89D8,0x3EF8947D | |
| 374 | data8 0xBDF43E3CD328D9BE | |
| 375 | data4 0x3F17B420,0x3F05F3A1 | |
| 376 | data8 0x3E4094C30ADB090A | |
| 377 | data4 0x3F124920,0x3F0F4303 | |
| 378 | data8 0xBE28FBB2FC1FE510 | |
| 379 | data4 0x3F0D3DC8,0x3F183EBF | |
| 380 | data8 0x3E3A789510FDE3FA | |
| 381 | data4 0x3F088888,0x3F20EC80 | |
| 382 | data8 0x3E508CE57CC8C98F | |
| 383 | data4 0x3F042108,0x3F29516A | |
| 384 | data8 0xBE534874A223106C | |
| 385 | LOCAL_OBJECT_END(Constants_G_H_h1) | |
| 386 | ||
| 387 | // Z2 - 16 bit fixed | |
| 388 | ||
| 389 | LOCAL_OBJECT_START(Constants_Z_2) | |
| 390 | data4 0x00008000 | |
| 391 | data4 0x00007F81 | |
| 392 | data4 0x00007F02 | |
| 393 | data4 0x00007E85 | |
| 394 | data4 0x00007E08 | |
| 395 | data4 0x00007D8D | |
| 396 | data4 0x00007D12 | |
| 397 | data4 0x00007C98 | |
| 398 | data4 0x00007C20 | |
| 399 | data4 0x00007BA8 | |
| 400 | data4 0x00007B31 | |
| 401 | data4 0x00007ABB | |
| 402 | data4 0x00007A45 | |
| 403 | data4 0x000079D1 | |
| 404 | data4 0x0000795D | |
| 405 | data4 0x000078EB | |
| 406 | LOCAL_OBJECT_END(Constants_Z_2) | |
| 407 | ||
| 408 | // G2 and H2 - IEEE single and h2 - IEEE double | |
| 409 | ||
| 410 | LOCAL_OBJECT_START(Constants_G_H_h2) | |
| 411 | data4 0x3F800000,0x00000000 | |
| 412 | data8 0x0000000000000000 | |
| 413 | data4 0x3F7F00F8,0x3B7F875D | |
| 414 | data8 0x3DB5A11622C42273 | |
| 415 | data4 0x3F7E03F8,0x3BFF015B | |
| 416 | data8 0x3DE620CF21F86ED3 | |
| 417 | data4 0x3F7D08E0,0x3C3EE393 | |
| 418 | data8 0xBDAFA07E484F34ED | |
| 419 | data4 0x3F7C0FC0,0x3C7E0586 | |
| 420 | data8 0xBDFE07F03860BCF6 | |
| 421 | data4 0x3F7B1880,0x3C9E75D2 | |
| 422 | data8 0x3DEA370FA78093D6 | |
| 423 | data4 0x3F7A2328,0x3CBDC97A | |
| 424 | data8 0x3DFF579172A753D0 | |
| 425 | data4 0x3F792FB0,0x3CDCFE47 | |
| 426 | data8 0x3DFEBE6CA7EF896B | |
| 427 | data4 0x3F783E08,0x3CFC15D0 | |
| 428 | data8 0x3E0CF156409ECB43 | |
| 429 | data4 0x3F774E38,0x3D0D874D | |
| 430 | data8 0xBE0B6F97FFEF71DF | |
| 431 | data4 0x3F766038,0x3D1CF49B | |
| 432 | data8 0xBE0804835D59EEE8 | |
| 433 | data4 0x3F757400,0x3D2C531D | |
| 434 | data8 0x3E1F91E9A9192A74 | |
| 435 | data4 0x3F748988,0x3D3BA322 | |
| 436 | data8 0xBE139A06BF72A8CD | |
| 437 | data4 0x3F73A0D0,0x3D4AE46F | |
| 438 | data8 0x3E1D9202F8FBA6CF | |
| 439 | data4 0x3F72B9D0,0x3D5A1756 | |
| 440 | data8 0xBE1DCCC4BA796223 | |
| 441 | data4 0x3F71D488,0x3D693B9D | |
| 442 | data8 0xBE049391B6B7C239 | |
| 443 | LOCAL_OBJECT_END(Constants_G_H_h2) | |
| 444 | ||
| 445 | // G3 and H3 - IEEE single and h3 - IEEE double | |
| 446 | ||
| 447 | LOCAL_OBJECT_START(Constants_G_H_h3) | |
| 448 | data4 0x3F7FFC00,0x38800100 | |
| 449 | data8 0x3D355595562224CD | |
| 450 | data4 0x3F7FF400,0x39400480 | |
| 451 | data8 0x3D8200A206136FF6 | |
| 452 | data4 0x3F7FEC00,0x39A00640 | |
| 453 | data8 0x3DA4D68DE8DE9AF0 | |
| 454 | data4 0x3F7FE400,0x39E00C41 | |
| 455 | data8 0xBD8B4291B10238DC | |
| 456 | data4 0x3F7FDC00,0x3A100A21 | |
| 457 | data8 0xBD89CCB83B1952CA | |
| 458 | data4 0x3F7FD400,0x3A300F22 | |
| 459 | data8 0xBDB107071DC46826 | |
| 460 | data4 0x3F7FCC08,0x3A4FF51C | |
| 461 | data8 0x3DB6FCB9F43307DB | |
| 462 | data4 0x3F7FC408,0x3A6FFC1D | |
| 463 | data8 0xBD9B7C4762DC7872 | |
| 464 | data4 0x3F7FBC10,0x3A87F20B | |
| 465 | data8 0xBDC3725E3F89154A | |
| 466 | data4 0x3F7FB410,0x3A97F68B | |
| 467 | data8 0xBD93519D62B9D392 | |
| 468 | data4 0x3F7FAC18,0x3AA7EB86 | |
| 469 | data8 0x3DC184410F21BD9D | |
| 470 | data4 0x3F7FA420,0x3AB7E101 | |
| 471 | data8 0xBDA64B952245E0A6 | |
| 472 | data4 0x3F7F9C20,0x3AC7E701 | |
| 473 | data8 0x3DB4B0ECAABB34B8 | |
| 474 | data4 0x3F7F9428,0x3AD7DD7B | |
| 475 | data8 0x3D9923376DC40A7E | |
| 476 | data4 0x3F7F8C30,0x3AE7D474 | |
| 477 | data8 0x3DC6E17B4F2083D3 | |
| 478 | data4 0x3F7F8438,0x3AF7CBED | |
| 479 | data8 0x3DAE314B811D4394 | |
| 480 | data4 0x3F7F7C40,0x3B03E1F3 | |
| 481 | data8 0xBDD46F21B08F2DB1 | |
| 482 | data4 0x3F7F7448,0x3B0BDE2F | |
| 483 | data8 0xBDDC30A46D34522B | |
| 484 | data4 0x3F7F6C50,0x3B13DAAA | |
| 485 | data8 0x3DCB0070B1F473DB | |
| 486 | data4 0x3F7F6458,0x3B1BD766 | |
| 487 | data8 0xBDD65DDC6AD282FD | |
| 488 | data4 0x3F7F5C68,0x3B23CC5C | |
| 489 | data8 0xBDCDAB83F153761A | |
| 490 | data4 0x3F7F5470,0x3B2BC997 | |
| 491 | data8 0xBDDADA40341D0F8F | |
| 492 | data4 0x3F7F4C78,0x3B33C711 | |
| 493 | data8 0x3DCD1BD7EBC394E8 | |
| 494 | data4 0x3F7F4488,0x3B3BBCC6 | |
| 495 | data8 0xBDC3532B52E3E695 | |
| 496 | data4 0x3F7F3C90,0x3B43BAC0 | |
| 497 | data8 0xBDA3961EE846B3DE | |
| 498 | data4 0x3F7F34A0,0x3B4BB0F4 | |
| 499 | data8 0xBDDADF06785778D4 | |
| 500 | data4 0x3F7F2CA8,0x3B53AF6D | |
| 501 | data8 0x3DCC3ED1E55CE212 | |
| 502 | data4 0x3F7F24B8,0x3B5BA620 | |
| 503 | data8 0xBDBA31039E382C15 | |
| 504 | data4 0x3F7F1CC8,0x3B639D12 | |
| 505 | data8 0x3D635A0B5C5AF197 | |
| 506 | data4 0x3F7F14D8,0x3B6B9444 | |
| 507 | data8 0xBDDCCB1971D34EFC | |
| 508 | data4 0x3F7F0CE0,0x3B7393BC | |
| 509 | data8 0x3DC7450252CD7ADA | |
| 510 | data4 0x3F7F04F0,0x3B7B8B6D | |
| 511 | data8 0xBDB68F177D7F2A42 | |
| 512 | LOCAL_OBJECT_END(Constants_G_H_h3) | |
| 513 | ||
| 514 | ||
| 515 | // Floating Point Registers | |
| 516 | ||
| 517 | FR_Input_X = f8 | |
| 518 | ||
| 519 | FR_Y_hi = f34 | |
| 520 | FR_Y_lo = f35 | |
| 521 | ||
| 522 | FR_Scale = f36 | |
| 523 | FR_X_Prime = f37 | |
| 524 | FR_S_hi = f38 | |
| 525 | FR_W = f39 | |
| 526 | FR_G = f40 | |
| 527 | ||
| 528 | FR_H = f41 | |
| 529 | FR_wsq = f42 | |
| 530 | FR_w4 = f43 | |
| 531 | FR_h = f44 | |
| 532 | FR_w6 = f45 | |
| 533 | ||
| 534 | FR_G2 = f46 | |
| 535 | FR_H2 = f47 | |
| 536 | FR_poly_lo = f48 | |
| 537 | FR_P8 = f49 | |
| 538 | FR_poly_hi = f50 | |
| 539 | ||
| 540 | FR_P7 = f51 | |
| 541 | FR_h2 = f52 | |
| 542 | FR_rsq = f53 | |
| 543 | FR_P6 = f54 | |
| 544 | FR_r = f55 | |
| 545 | ||
| 546 | FR_log2_hi = f56 | |
| 547 | FR_log2_lo = f57 | |
| 548 | FR_p87 = f58 | |
| 549 | FR_p876 = f58 | |
| 550 | FR_p8765 = f58 | |
| 551 | FR_float_N = f59 | |
| 552 | FR_Q4 = f60 | |
| 553 | ||
| 554 | FR_p43 = f61 | |
| 555 | FR_p432 = f61 | |
| 556 | FR_p4321 = f61 | |
| 557 | FR_P4 = f62 | |
| 558 | FR_G3 = f63 | |
| 559 | FR_H3 = f64 | |
| 560 | FR_h3 = f65 | |
| 561 | ||
| 562 | FR_Q3 = f66 | |
| 563 | FR_P3 = f67 | |
| 564 | FR_Q2 = f68 | |
| 565 | FR_P2 = f69 | |
| 566 | FR_1LN10_hi = f70 | |
| 567 | ||
| 568 | FR_Q1 = f71 | |
| 569 | FR_P1 = f72 | |
| 570 | FR_1LN10_lo = f73 | |
| 571 | FR_P5 = f74 | |
| 572 | FR_rcub = f75 | |
| 573 | ||
| 574 | FR_Output_X_tmp = f76 | |
| 575 | ||
| 576 | FR_X = f8 | |
| 577 | FR_Y = f0 | |
| 578 | FR_RESULT = f76 | |
| 579 | ||
| 580 | ||
| 581 | // General Purpose Registers | |
| 582 | ||
| 583 | GR_ad_p = r33 | |
| 584 | GR_Index1 = r34 | |
| 585 | GR_Index2 = r35 | |
| 586 | GR_signif = r36 | |
| 587 | GR_X_0 = r37 | |
| 588 | GR_X_1 = r38 | |
| 589 | GR_X_2 = r39 | |
| 590 | GR_Z_1 = r40 | |
| 591 | GR_Z_2 = r41 | |
| 592 | GR_N = r42 | |
| 593 | GR_Bias = r43 | |
| 594 | GR_M = r44 | |
| 595 | GR_Index3 = r45 | |
| 596 | GR_ad_p2 = r46 | |
| 597 | GR_exp_mask = r47 | |
| 598 | GR_exp_2tom7 = r48 | |
| 599 | GR_ad_ln10 = r49 | |
| 600 | GR_ad_tbl_1 = r50 | |
| 601 | GR_ad_tbl_2 = r51 | |
| 602 | GR_ad_tbl_3 = r52 | |
| 603 | GR_ad_q = r53 | |
| 604 | GR_ad_z_1 = r54 | |
| 605 | GR_ad_z_2 = r55 | |
| 606 | GR_ad_z_3 = r56 | |
| 607 | ||
| 608 | // | |
| 609 | // Added for unwind support | |
| 610 | // | |
| 611 | ||
| 612 | GR_SAVE_PFS = r50 | |
| 613 | GR_SAVE_B0 = r51 | |
| 614 | GR_SAVE_GP = r52 | |
| 615 | GR_Parameter_X = r53 | |
| 616 | GR_Parameter_Y = r54 | |
| 617 | GR_Parameter_RESULT = r55 | |
| 618 | GR_Parameter_TAG = r56 | |
| 619 | ||
| 620 | .section .text | |
| 621 | ||
| 622 | GLOBAL_IEEE754_ENTRY(logl) | |
| 623 | { .mfi | |
| 624 | alloc r32 = ar.pfs,0,21,4,0 | |
| 625 | fclass.m p6, p0 = FR_Input_X, 0x1E3 // Test for natval, nan, inf | |
| 626 | cmp.eq p7, p14 = r0, r0 // Set p7 if logl | |
| 627 | } | |
| 628 | { .mfb | |
| 629 | addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp | |
| 630 | fnorm.s1 FR_X_Prime = FR_Input_X // Normalize x | |
| 631 | br.cond.sptk LOGL_BEGIN | |
| 632 | } | |
| 633 | ;; | |
| 634 | ||
| 635 | GLOBAL_IEEE754_END(logl) | |
| 636 | ||
| 637 | ||
| 638 | GLOBAL_IEEE754_ENTRY(log10l) | |
| 639 | { .mfi | |
| 640 | alloc r32 = ar.pfs,0,21,4,0 | |
| 641 | fclass.m p6, p0 = FR_Input_X, 0x1E3 // Test for natval, nan, inf | |
| 642 | cmp.ne p7, p14 = r0, r0 // Set p14 if log10l | |
| 643 | } | |
| 644 | { .mfb | |
| 645 | addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp | |
| 646 | fnorm.s1 FR_X_Prime = FR_Input_X // Normalize x | |
| 647 | nop.b 999 | |
| 648 | } | |
| 649 | ;; | |
| 650 | ||
| 651 | ||
| 652 | // Common code for logl and log10 | |
| 653 | LOGL_BEGIN: | |
| 654 | { .mfi | |
| 655 | ld8 GR_ad_z_1 = [GR_ad_z_1] // Get pointer to Constants_Z_1 | |
| 656 | fclass.m p10, p0 = FR_Input_X, 0x0b // Test for denormal | |
| 657 | mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7 | |
| 658 | } | |
| 659 | ;; | |
| 660 | ||
| 661 | { .mfb | |
| 662 | getf.sig GR_signif = FR_Input_X // Get significand of x | |
| 663 | fcmp.eq.s1 p9, p0 = FR_Input_X, f1 // Test for x=1.0 | |
| 664 | (p6) br.cond.spnt LOGL_64_special // Branch for nan, inf, natval | |
| 665 | } | |
| 666 | ;; | |
| 667 | ||
| 668 | { .mfi | |
| 669 | add GR_ad_tbl_1 = 0x040, GR_ad_z_1 // Point to Constants_G_H_h1 | |
| 670 | fcmp.lt.s1 p13, p0 = FR_Input_X, f0 // Test for x<0 | |
| 671 | add GR_ad_p = -0x100, GR_ad_z_1 // Point to Constants_P | |
| 672 | } | |
| 673 | { .mib | |
| 674 | add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2 | |
| 675 | add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2 | |
| 676 | (p10) br.cond.spnt LOGL_64_denormal // Branch for denormal | |
| 677 | } | |
| 678 | ;; | |
| 679 | ||
| 680 | LOGL_64_COMMON: | |
| 681 | { .mfi | |
| 682 | add GR_ad_q = 0x080, GR_ad_p // Point to Constants_Q | |
| 683 | fcmp.eq.s1 p8, p0 = FR_Input_X, f0 // Test for x=0 | |
| 684 | extr.u GR_Index1 = GR_signif, 59, 4 // Get high 4 bits of signif | |
| 685 | } | |
| 686 | { .mfb | |
| 687 | add GR_ad_tbl_3 = 0x280, GR_ad_z_1 // Point to Constants_G_H_h3 | |
| 688 | (p9) fma.s0 f8 = FR_Input_X, f0, f0 // If x=1, return +0.0 | |
| 689 | (p9) br.ret.spnt b0 // Exit if x=1 | |
| 690 | } | |
| 691 | ;; | |
| 692 | ||
| 693 | { .mfi | |
| 694 | shladd GR_ad_z_1 = GR_Index1, 2, GR_ad_z_1 // Point to Z_1 | |
| 695 | fclass.nm p10, p0 = FR_Input_X, 0x1FF // Test for unsupported | |
| 696 | extr.u GR_X_0 = GR_signif, 49, 15 // Get high 15 bits of significand | |
| 697 | } | |
| 698 | { .mfi | |
| 699 | ldfe FR_P8 = [GR_ad_p],16 // Load P_8 for near1 path | |
| 700 | fsub.s1 FR_W = FR_X_Prime, f1 // W = x - 1 | |
| 701 | add GR_ad_ln10 = 0x060, GR_ad_q // Point to Constants_1_by_LN10 | |
| 702 | } | |
| 703 | ;; | |
| 704 | ||
| 705 | { .mfi | |
| 706 | ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1 | |
| 707 | nop.f 999 | |
| 708 | mov GR_exp_mask = 0x1FFFF // Create exponent mask | |
| 709 | } | |
| 710 | { .mib | |
| 711 | shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1 // Point to G_1 | |
| 712 | mov GR_Bias = 0x0FFFF // Create exponent bias | |
| 713 | (p13) br.cond.spnt LOGL_64_negative // Branch if x<0 | |
| 714 | } | |
| 715 | ;; | |
| 716 | ||
| 717 | { .mfb | |
| 718 | ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1 | |
| 719 | fmerge.se FR_S_hi = f1,FR_X_Prime // Form |x| | |
| 720 | (p8) br.cond.spnt LOGL_64_zero // Branch if x=0 | |
| 721 | } | |
| 722 | ;; | |
| 723 | ||
| 724 | { .mmb | |
| 725 | getf.exp GR_N = FR_X_Prime // Get N = exponent of x | |
| 726 | ldfd FR_h = [GR_ad_tbl_1] // Load h_1 | |
| 727 | (p10) br.cond.spnt LOGL_64_unsupported // Branch for unsupported type | |
| 728 | } | |
| 729 | ;; | |
| 730 | ||
| 731 | { .mfi | |
| 732 | ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi | |
| 733 | fcmp.eq.s0 p8, p0 = FR_Input_X, f0 // Dummy op to flag denormals | |
| 734 | pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // Get bits 30-15 of X_0 * Z_1 | |
| 735 | } | |
| 736 | ;; | |
| 737 | ||
| 738 | // | |
| 739 | // For performance, don't use result of pmpyshr2.u for 4 cycles. | |
| 740 | // | |
| 741 | { .mmi | |
| 742 | ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo | |
| 743 | (p14) ldfe FR_1LN10_hi = [GR_ad_ln10],16 // If log10l, load 1/ln10_hi | |
| 744 | sub GR_N = GR_N, GR_Bias | |
| 745 | } | |
| 746 | ;; | |
| 747 | ||
| 748 | { .mmi | |
| 749 | ldfe FR_Q4 = [GR_ad_q],16 // Load Q4 | |
| 750 | (p14) ldfe FR_1LN10_lo = [GR_ad_ln10] // If log10l, load 1/ln10_lo | |
| 751 | nop.i 999 | |
| 752 | } | |
| 753 | ;; | |
| 754 | ||
| 755 | { .mmi | |
| 756 | ldfe FR_Q3 = [GR_ad_q],16 // Load Q3 | |
| 757 | setf.sig FR_float_N = GR_N // Put integer N into rightmost significand | |
| 758 | nop.i 999 | |
| 759 | } | |
| 760 | ;; | |
| 761 | ||
| 762 | { .mmi | |
| 763 | getf.exp GR_M = FR_W // Get signexp of w = x - 1 | |
| 764 | ldfe FR_Q2 = [GR_ad_q],16 // Load Q2 | |
| 765 | extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1 | |
| 766 | } | |
| 767 | ;; | |
| 768 | ||
| 769 | { .mmi | |
| 770 | ldfe FR_Q1 = [GR_ad_q] // Load Q1 | |
| 771 | shladd GR_ad_z_2 = GR_Index2, 2, GR_ad_z_2 // Point to Z_2 | |
| 772 | add GR_ad_p2 = 0x30,GR_ad_p // Point to P_4 | |
| 773 | } | |
| 774 | ;; | |
| 775 | ||
| 776 | { .mmi | |
| 777 | ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2 | |
| 778 | shladd GR_ad_tbl_2 = GR_Index2, 4, GR_ad_tbl_2 // Point to G_2 | |
| 779 | and GR_M = GR_exp_mask, GR_M // Get exponent of w = x - 1 | |
| 780 | } | |
| 781 | ;; | |
| 782 | ||
| 783 | { .mmi | |
| 784 | ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2 | |
| 785 | cmp.lt p8, p9 = GR_M, GR_exp_2tom7 // Test |x-1| < 2^-7 | |
| 786 | nop.i 999 | |
| 787 | } | |
| 788 | ;; | |
| 789 | ||
| 790 | // Paths are merged. | |
| 791 | // p8 is for the near1 path: |x-1| < 2^-7 | |
| 792 | // p9 is for regular path: |x-1| >= 2^-7 | |
| 793 | ||
| 794 | { .mmi | |
| 795 | ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2 | |
| 796 | nop.m 999 | |
| 797 | nop.i 999 | |
| 798 | } | |
| 799 | ;; | |
| 800 | ||
| 801 | { .mmi | |
| 802 | (p8) ldfe FR_P7 = [GR_ad_p],16 // Load P_7 for near1 path | |
| 803 | (p8) ldfe FR_P4 = [GR_ad_p2],16 // Load P_4 for near1 path | |
| 804 | (p9) pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // Get bits 30-15 of X_1 * Z_2 | |
| 805 | } | |
| 806 | ;; | |
| 807 | ||
| 808 | // | |
| 809 | // For performance, don't use result of pmpyshr2.u for 4 cycles. | |
| 810 | // | |
| 811 | { .mmi | |
| 812 | (p8) ldfe FR_P6 = [GR_ad_p],16 // Load P_6 for near1 path | |
| 813 | (p8) ldfe FR_P3 = [GR_ad_p2],16 // Load P_3 for near1 path | |
| 814 | nop.i 999 | |
| 815 | } | |
| 816 | ;; | |
| 817 | ||
| 818 | { .mmf | |
| 819 | (p8) ldfe FR_P5 = [GR_ad_p],16 // Load P_5 for near1 path | |
| 820 | (p8) ldfe FR_P2 = [GR_ad_p2],16 // Load P_2 for near1 path | |
| 821 | (p8) fmpy.s1 FR_wsq = FR_W, FR_W // wsq = w * w for near1 path | |
| 822 | } | |
| 823 | ;; | |
| 824 | ||
| 825 | { .mmi | |
| 826 | (p8) ldfe FR_P1 = [GR_ad_p2],16 ;; // Load P_1 for near1 path | |
| 827 | nop.m 999 | |
| 828 | (p9) extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2 | |
| 829 | } | |
| 830 | ;; | |
| 831 | ||
| 832 | { .mfi | |
| 833 | (p9) shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3 // Point to G_3 | |
| 834 | (p9) fcvt.xf FR_float_N = FR_float_N | |
| 835 | nop.i 999 | |
| 836 | } | |
| 837 | ;; | |
| 838 | ||
| 839 | { .mfi | |
| 840 | (p9) ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3 | |
| 841 | nop.f 999 | |
| 842 | nop.i 999 | |
| 843 | } | |
| 844 | ;; | |
| 845 | ||
| 846 | { .mfi | |
| 847 | (p9) ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3 | |
| 848 | (p9) fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2 | |
| 849 | nop.i 999 | |
| 850 | } | |
| 851 | { .mfi | |
| 852 | nop.m 999 | |
| 853 | (p9) fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2 | |
| 854 | nop.i 999 | |
| 855 | } | |
| 856 | ;; | |
| 857 | ||
| 858 | { .mmf | |
| 859 | nop.m 999 | |
| 860 | nop.m 999 | |
| 861 | (p9) fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2 | |
| 862 | } | |
| 863 | ;; | |
| 864 | ||
| 865 | { .mfi | |
| 866 | nop.m 999 | |
| 867 | (p8) fmpy.s1 FR_w4 = FR_wsq, FR_wsq // w4 = w^4 for near1 path | |
| 868 | nop.i 999 | |
| 869 | } | |
| 870 | { .mfi | |
| 871 | nop.m 999 | |
| 872 | (p8) fma.s1 FR_p87 = FR_W, FR_P8, FR_P7 // p87 = w * P8 + P7 | |
| 873 | nop.i 999 | |
| 874 | } | |
| 875 | ;; | |
| 876 | ||
| 877 | { .mfi | |
| 878 | nop.m 999 | |
| 879 | (p8) fma.s1 FR_p43 = FR_W, FR_P4, FR_P3 // p43 = w * P4 + P3 | |
| 880 | nop.i 999 | |
| 881 | } | |
| 882 | ;; | |
| 883 | ||
| 884 | { .mfi | |
| 885 | nop.m 999 | |
| 886 | (p9) fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3 | |
| 887 | nop.i 999 | |
| 888 | } | |
| 889 | { .mfi | |
| 890 | nop.m 999 | |
| 891 | (p9) fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3 | |
| 892 | nop.i 999 | |
| 893 | } | |
| 894 | ;; | |
| 895 | ||
| 896 | { .mfi | |
| 897 | nop.m 999 | |
| 898 | (p9) fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3 | |
| 899 | nop.i 999 | |
| 900 | } | |
| 901 | { .mfi | |
| 902 | nop.m 999 | |
| 903 | (p8) fmpy.s1 FR_w6 = FR_w4, FR_wsq // w6 = w^6 for near1 path | |
| 904 | nop.i 999 | |
| 905 | } | |
| 906 | ;; | |
| 907 | ||
| 908 | { .mfi | |
| 909 | nop.m 999 | |
| 910 | (p8) fma.s1 FR_p432 = FR_W, FR_p43, FR_P2 // p432 = w * p43 + P2 | |
| 911 | nop.i 999 | |
| 912 | } | |
| 913 | { .mfi | |
| 914 | nop.m 999 | |
| 915 | (p8) fma.s1 FR_p876 = FR_W, FR_p87, FR_P6 // p876 = w * p87 + P6 | |
| 916 | nop.i 999 | |
| 917 | } | |
| 918 | ;; | |
| 919 | ||
| 920 | { .mfi | |
| 921 | nop.m 999 | |
| 922 | (p9) fms.s1 FR_r = FR_G, FR_S_hi, f1 // r = G * S_hi - 1 | |
| 923 | nop.i 999 | |
| 924 | } | |
| 925 | { .mfi | |
| 926 | nop.m 999 | |
| 927 | (p9) fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi = N * log2_hi + H | |
| 928 | nop.i 999 | |
| 929 | } | |
| 930 | ;; | |
| 931 | ||
| 932 | { .mfi | |
| 933 | nop.m 999 | |
| 934 | (p9) fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h // h = N * log2_lo + h | |
| 935 | nop.i 999 | |
| 936 | } | |
| 937 | ;; | |
| 938 | ||
| 939 | { .mfi | |
| 940 | nop.m 999 | |
| 941 | (p8) fma.s1 FR_p4321 = FR_W, FR_p432, FR_P1 // p4321 = w * p432 + P1 | |
| 942 | nop.i 999 | |
| 943 | } | |
| 944 | { .mfi | |
| 945 | nop.m 999 | |
| 946 | (p8) fma.s1 FR_p8765 = FR_W, FR_p876, FR_P5 // p8765 = w * p876 + P5 | |
| 947 | nop.i 999 | |
| 948 | } | |
| 949 | ;; | |
| 950 | ||
| 951 | { .mfi | |
| 952 | nop.m 999 | |
| 953 | (p9) fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 // poly_lo = r * Q4 + Q3 | |
| 954 | nop.i 999 | |
| 955 | } | |
| 956 | { .mfi | |
| 957 | nop.m 999 | |
| 958 | (p9) fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r | |
| 959 | nop.i 999 | |
| 960 | } | |
| 961 | ;; | |
| 962 | ||
| 963 | { .mfi | |
| 964 | nop.m 999 | |
| 965 | (p8) fma.s1 FR_Y_lo = FR_wsq, FR_p4321, f0 // Y_lo = wsq * p4321 | |
| 966 | nop.i 999 | |
| 967 | } | |
| 968 | { .mfi | |
| 969 | nop.m 999 | |
| 970 | (p8) fma.s1 FR_Y_hi = FR_W, f1, f0 // Y_hi = w for near1 path | |
| 971 | nop.i 999 | |
| 972 | } | |
| 973 | ;; | |
| 974 | ||
| 975 | { .mfi | |
| 976 | nop.m 999 | |
| 977 | (p9) fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo = poly_lo * r + Q2 | |
| 978 | nop.i 999 | |
| 979 | } | |
| 980 | { .mfi | |
| 981 | nop.m 999 | |
| 982 | (p9) fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3 | |
| 983 | nop.i 999 | |
| 984 | } | |
| 985 | ;; | |
| 986 | ||
| 987 | { .mfi | |
| 988 | nop.m 999 | |
| 989 | (p8) fma.s1 FR_Y_lo = FR_w6, FR_p8765,FR_Y_lo // Y_lo = w6 * p8765 + w2 * p4321 | |
| 990 | nop.i 999 | |
| 991 | } | |
| 992 | ;; | |
| 993 | ||
| 994 | { .mfi | |
| 995 | nop.m 999 | |
| 996 | (p9) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1 * rsq + r | |
| 997 | nop.i 999 | |
| 998 | } | |
| 999 | ;; | |
| 1000 | ||
| 1001 | { .mfi | |
| 1002 | nop.m 999 | |
| 1003 | (p9) fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h // poly_lo = poly_lo*r^3 + h | |
| 1004 | nop.i 999 | |
| 1005 | } | |
| 1006 | ;; | |
| 1007 | ||
| 1008 | { .mfi | |
| 1009 | nop.m 999 | |
| 1010 | (p9) fadd.s1 FR_Y_lo = FR_poly_hi, FR_poly_lo // Y_lo = poly_hi + poly_lo | |
| 1011 | nop.i 999 | |
| 1012 | } | |
| 1013 | ;; | |
| 1014 | ||
| 1015 | // Remainder of code is common for near1 and regular paths | |
| 1016 | { .mfi | |
| 1017 | nop.m 999 | |
| 1018 | (p7) fadd.s0 f8 = FR_Y_lo,FR_Y_hi // If logl, result=Y_lo+Y_hi | |
| 1019 | nop.i 999 | |
| 1020 | } | |
| 1021 | { .mfi | |
| 1022 | nop.m 999 | |
| 1023 | (p14) fmpy.s1 FR_Output_X_tmp = FR_Y_lo,FR_1LN10_hi | |
| 1024 | nop.i 999 | |
| 1025 | } | |
| 1026 | ;; | |
| 1027 | ||
| 1028 | { .mfi | |
| 1029 | nop.m 999 | |
| 1030 | (p14) fma.s1 FR_Output_X_tmp = FR_Y_hi,FR_1LN10_lo,FR_Output_X_tmp | |
| 1031 | nop.i 999 | |
| 1032 | } | |
| 1033 | ;; | |
| 1034 | ||
| 1035 | { .mfb | |
| 1036 | nop.m 999 | |
| 1037 | (p14) fma.s0 f8 = FR_Y_hi,FR_1LN10_hi,FR_Output_X_tmp | |
| 1038 | br.ret.sptk b0 // Common exit for 0 < x < inf | |
| 1039 | } | |
| 1040 | ;; | |
| 1041 | ||
| 1042 | ||
| 1043 | // Here if x=+-0 | |
| 1044 | LOGL_64_zero: | |
| 1045 | // | |
| 1046 | // If x=+-0 raise divide by zero and return -inf | |
| 1047 | // | |
| 1048 | { .mfi | |
| 1049 | (p7) mov GR_Parameter_TAG = 0 | |
| 1050 | fsub.s1 FR_Output_X_tmp = f0, f1 | |
| 1051 | nop.i 999 | |
| 1052 | } | |
| 1053 | ;; | |
| 1054 | ||
| 1055 | { .mfb | |
| 1056 | (p14) mov GR_Parameter_TAG = 6 | |
| 1057 | frcpa.s0 FR_Output_X_tmp, p8 = FR_Output_X_tmp, f0 | |
| 1058 | br.cond.sptk __libm_error_region | |
| 1059 | } | |
| 1060 | ;; | |
| 1061 | ||
| 1062 | LOGL_64_special: | |
| 1063 | { .mfi | |
| 1064 | nop.m 999 | |
| 1065 | fclass.m.unc p8, p0 = FR_Input_X, 0x1E1 // Test for natval, nan, +inf | |
| 1066 | nop.i 999 | |
| 1067 | } | |
| 1068 | ;; | |
| 1069 | ||
| 1070 | // | |
| 1071 | // For SNaN raise invalid and return QNaN. | |
| 1072 | // For QNaN raise invalid and return QNaN. | |
| 1073 | // For +Inf return +Inf. | |
| 1074 | // | |
| 1075 | { .mfb | |
| 1076 | nop.m 999 | |
| 1077 | (p8) fmpy.s0 f8 = FR_Input_X, f1 | |
| 1078 | (p8) br.ret.sptk b0 // Return for natval, nan, +inf | |
| 1079 | } | |
| 1080 | ;; | |
| 1081 | ||
| 1082 | // | |
| 1083 | // For -Inf raise invalid and return QNaN. | |
| 1084 | // | |
| 1085 | { .mmi | |
| 1086 | (p7) mov GR_Parameter_TAG = 1 | |
| 1087 | nop.m 999 | |
| 1088 | nop.i 999 | |
| 1089 | } | |
| 1090 | ;; | |
| 1091 | ||
| 1092 | { .mfb | |
| 1093 | (p14) mov GR_Parameter_TAG = 7 | |
| 1094 | fmpy.s0 FR_Output_X_tmp = FR_Input_X, f0 | |
| 1095 | br.cond.sptk __libm_error_region | |
| 1096 | } | |
| 1097 | ;; | |
| 1098 | ||
| 1099 | // Here if x denormal or unnormal | |
| 1100 | LOGL_64_denormal: | |
| 1101 | { .mmi | |
| 1102 | getf.sig GR_signif = FR_X_Prime // Get significand of normalized input | |
| 1103 | nop.m 999 | |
| 1104 | nop.i 999 | |
| 1105 | } | |
| 1106 | ;; | |
| 1107 | ||
| 1108 | { .mmb | |
| 1109 | getf.exp GR_N = FR_X_Prime // Get exponent of normalized input | |
| 1110 | nop.m 999 | |
| 1111 | br.cond.sptk LOGL_64_COMMON // Branch back to common code | |
| 1112 | } | |
| 1113 | ;; | |
| 1114 | ||
| 1115 | LOGL_64_unsupported: | |
| 1116 | // | |
| 1117 | // Return generated NaN or other value. | |
| 1118 | // | |
| 1119 | { .mfb | |
| 1120 | nop.m 999 | |
| 1121 | fmpy.s0 f8 = FR_Input_X, f0 | |
| 1122 | br.ret.sptk b0 | |
| 1123 | } | |
| 1124 | ;; | |
| 1125 | ||
| 1126 | // Here if -inf < x < 0 | |
| 1127 | LOGL_64_negative: | |
| 1128 | // | |
| 1129 | // Deal with x < 0 in a special way - raise | |
| 1130 | // invalid and produce QNaN indefinite. | |
| 1131 | // | |
| 1132 | { .mfi | |
| 1133 | (p7) mov GR_Parameter_TAG = 1 | |
| 1134 | frcpa.s0 FR_Output_X_tmp, p8 = f0, f0 | |
| 1135 | nop.i 999 | |
| 1136 | } | |
| 1137 | ;; | |
| 1138 | ||
| 1139 | { .mib | |
| 1140 | (p14) mov GR_Parameter_TAG = 7 | |
| 1141 | nop.i 999 | |
| 1142 | br.cond.sptk __libm_error_region | |
| 1143 | } | |
| 1144 | ;; | |
| 1145 | ||
| 1146 | ||
| 1147 | GLOBAL_IEEE754_END(log10l) | |
| 1148 | ||
| 1149 | LOCAL_LIBM_ENTRY(__libm_error_region) | |
| 1150 | .prologue | |
| 1151 | { .mfi | |
| 1152 | add GR_Parameter_Y=-32,sp // Parameter 2 value | |
| 1153 | nop.f 0 | |
| 1154 | .save ar.pfs,GR_SAVE_PFS | |
| 1155 | mov GR_SAVE_PFS=ar.pfs // Save ar.pfs | |
| 1156 | } | |
| 1157 | { .mfi | |
| 1158 | .fframe 64 | |
| 1159 | add sp=-64,sp // Create new stack | |
| 1160 | nop.f 0 | |
| 1161 | mov GR_SAVE_GP=gp // Save gp | |
| 1162 | };; | |
| 1163 | { .mmi | |
| 1164 | stfe [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack | |
| 1165 | add GR_Parameter_X = 16,sp // Parameter 1 address | |
| 1166 | .save b0, GR_SAVE_B0 | |
| 1167 | mov GR_SAVE_B0=b0 // Save b0 | |
| 1168 | };; | |
| 1169 | .body | |
| 1170 | { .mib | |
| 1171 | stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack | |
| 1172 | add GR_Parameter_RESULT = 0,GR_Parameter_Y | |
| 1173 | nop.b 0 // Parameter 3 address | |
| 1174 | } | |
| 1175 | { .mib | |
| 1176 | stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack | |
| 1177 | add GR_Parameter_Y = -16,GR_Parameter_Y | |
| 1178 | br.call.sptk b0=__libm_error_support# // Call error handling function | |
| 1179 | };; | |
| 1180 | { .mmi | |
| 1181 | nop.m 999 | |
| 1182 | nop.m 999 | |
| 1183 | add GR_Parameter_RESULT = 48,sp | |
| 1184 | };; | |
| 1185 | { .mmi | |
| 1186 | ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack | |
| 1187 | .restore sp | |
| 1188 | add sp = 64,sp // Restore stack pointer | |
| 1189 | mov b0 = GR_SAVE_B0 // Restore return address | |
| 1190 | };; | |
| 1191 | { .mib | |
| 1192 | mov gp = GR_SAVE_GP // Restore gp | |
| 1193 | mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs | |
| 1194 | br.ret.sptk b0 // Return | |
| 1195 | };; | |
| 1196 | ||
| 1197 | LOCAL_LIBM_END(__libm_error_region#) | |
| 1198 | ||
| 1199 | .type __libm_error_support#,@function | |
| 1200 | .global __libm_error_support# |