1 /* 2 * Double-precision SVE pow(x, y) function. 3 * 4 * Copyright (c) 2022-2025, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "sv_math.h" 9 #include "test_sig.h" 10 #include "test_defs.h" 11 12 /* This version share a similar algorithm as AOR scalar pow. 13 14 The core computation consists in computing pow(x, y) as 15 16 exp (y * log (x)). 17 18 The algorithms for exp and log are very similar to scalar exp and log. 19 The log relies on table lookup for 3 variables and an order 8 polynomial. 20 It returns a high and a low contribution that are then passed to the exp, 21 to minimise the loss of accuracy in both routines. 22 The exp is based on 8-bit table lookup for scale and order-4 polynomial. 23 The SVE algorithm drops the tail in the exp computation at the price of 24 a lower accuracy, slightly above 1ULP. 25 The SVE algorithm also drops the special treatement of small (< 2^-65) and 26 large (> 2^63) finite values of |y|, as they only affect non-round to 27 nearest modes. 28 29 Maximum measured error is 1.04 ULPs: 30 SV_NAME_D2 (pow) (0x1.3d2d45bc848acp+63, -0x1.a48a38b40cd43p-12) 31 got 0x1.f7116284221fcp-1 32 want 0x1.f7116284221fdp-1. */ 33 34 /* Data is defined in v_pow_log_data.c. */ 35 #define N_LOG (1 << V_POW_LOG_TABLE_BITS) 36 #define Off 0x3fe6955500000000 37 38 /* Data is defined in v_pow_exp_data.c. */ 39 #define N_EXP (1 << V_POW_EXP_TABLE_BITS) 40 #define SignBias (0x800 << V_POW_EXP_TABLE_BITS) 41 #define SmallExp 0x3c9 /* top12(0x1p-54). */ 42 #define BigExp 0x408 /* top12(512.). */ 43 #define ThresExp 0x03f /* BigExp - SmallExp. */ 44 #define HugeExp 0x409 /* top12(1024.). */ 45 46 /* Constants associated with pow. */ 47 #define SmallBoundX 0x1p-126 48 #define SmallPowX 0x001 /* top12(0x1p-126). */ 49 #define BigPowX 0x7ff /* top12(INFINITY). */ 50 #define ThresPowX 0x7fe /* BigPowX - SmallPowX. */ 51 #define SmallPowY 0x3be /* top12(0x1.e7b6p-65). */ 52 #define BigPowY 0x43e /* top12(0x1.749p62). */ 53 #define ThresPowY 0x080 /* BigPowY - SmallPowY. */ 54 55 static const struct data 56 { 57 double log_c0, log_c2, log_c4, log_c6, ln2_hi, ln2_lo; 58 double log_c1, log_c3, log_c5, off; 59 double n_over_ln2, exp_c2, ln2_over_n_hi, ln2_over_n_lo; 60 double exp_c0, exp_c1; 61 } data = { 62 .log_c0 = -0x1p-1, 63 .log_c1 = -0x1.555555555556p-1, 64 .log_c2 = 0x1.0000000000006p-1, 65 .log_c3 = 0x1.999999959554ep-1, 66 .log_c4 = -0x1.555555529a47ap-1, 67 .log_c5 = -0x1.2495b9b4845e9p0, 68 .log_c6 = 0x1.0002b8b263fc3p0, 69 .off = Off, 70 .exp_c0 = 0x1.fffffffffffd4p-2, 71 .exp_c1 = 0x1.5555571d6ef9p-3, 72 .exp_c2 = 0x1.5555576a5adcep-5, 73 .ln2_hi = 0x1.62e42fefa3800p-1, 74 .ln2_lo = 0x1.ef35793c76730p-45, 75 .n_over_ln2 = 0x1.71547652b82fep0 * N_EXP, 76 .ln2_over_n_hi = 0x1.62e42fefc0000p-9, 77 .ln2_over_n_lo = -0x1.c610ca86c3899p-45, 78 }; 79 80 /* Check if x is an integer. */ 81 static inline svbool_t 82 sv_isint (svbool_t pg, svfloat64_t x) 83 { 84 return svcmpeq (pg, svrintz_z (pg, x), x); 85 } 86 87 /* Check if x is real not integer valued. */ 88 static inline svbool_t 89 sv_isnotint (svbool_t pg, svfloat64_t x) 90 { 91 return svcmpne (pg, svrintz_z (pg, x), x); 92 } 93 94 /* Check if x is an odd integer. */ 95 static inline svbool_t 96 sv_isodd (svbool_t pg, svfloat64_t x) 97 { 98 svfloat64_t y = svmul_x (svptrue_b64 (), x, 0.5); 99 return sv_isnotint (pg, y); 100 } 101 102 /* Returns 0 if not int, 1 if odd int, 2 if even int. The argument is 103 the bit representation of a non-zero finite floating-point value. */ 104 static inline int 105 checkint (uint64_t iy) 106 { 107 int e = iy >> 52 & 0x7ff; 108 if (e < 0x3ff) 109 return 0; 110 if (e > 0x3ff + 52) 111 return 2; 112 if (iy & ((1ULL << (0x3ff + 52 - e)) - 1)) 113 return 0; 114 if (iy & (1ULL << (0x3ff + 52 - e))) 115 return 1; 116 return 2; 117 } 118 119 /* Top 12 bits (sign and exponent of each double float lane). */ 120 static inline svuint64_t 121 sv_top12 (svfloat64_t x) 122 { 123 return svlsr_x (svptrue_b64 (), svreinterpret_u64 (x), 52); 124 } 125 126 /* Returns 1 if input is the bit representation of 0, infinity or nan. */ 127 static inline int 128 zeroinfnan (uint64_t i) 129 { 130 return 2 * i - 1 >= 2 * asuint64 (INFINITY) - 1; 131 } 132 133 /* Returns 1 if input is the bit representation of 0, infinity or nan. */ 134 static inline svbool_t 135 sv_zeroinfnan (svbool_t pg, svuint64_t i) 136 { 137 return svcmpge (pg, svsub_x (pg, svadd_x (pg, i, i), 1), 138 2 * asuint64 (INFINITY) - 1); 139 } 140 141 /* Handle cases that may overflow or underflow when computing the result that 142 is scale*(1+TMP) without intermediate rounding. The bit representation of 143 scale is in SBITS, however it has a computed exponent that may have 144 overflown into the sign bit so that needs to be adjusted before using it as 145 a double. (int32_t)KI is the k used in the argument reduction and exponent 146 adjustment of scale, positive k here means the result may overflow and 147 negative k means the result may underflow. */ 148 static inline double 149 specialcase (double tmp, uint64_t sbits, uint64_t ki) 150 { 151 double scale; 152 if ((ki & 0x80000000) == 0) 153 { 154 /* k > 0, the exponent of scale might have overflowed by <= 460. */ 155 sbits -= 1009ull << 52; 156 scale = asdouble (sbits); 157 return 0x1p1009 * (scale + scale * tmp); 158 } 159 /* k < 0, need special care in the subnormal range. */ 160 sbits += 1022ull << 52; 161 /* Note: sbits is signed scale. */ 162 scale = asdouble (sbits); 163 double y = scale + scale * tmp; 164 return 0x1p-1022 * y; 165 } 166 167 /* Scalar fallback for special cases of SVE pow's exp. */ 168 static inline svfloat64_t 169 sv_call_specialcase (svfloat64_t x1, svuint64_t u1, svuint64_t u2, 170 svfloat64_t y, svbool_t cmp) 171 { 172 svbool_t p = svpfirst (cmp, svpfalse ()); 173 while (svptest_any (cmp, p)) 174 { 175 double sx1 = svclastb (p, 0, x1); 176 uint64_t su1 = svclastb (p, 0, u1); 177 uint64_t su2 = svclastb (p, 0, u2); 178 double elem = specialcase (sx1, su1, su2); 179 svfloat64_t y2 = sv_f64 (elem); 180 y = svsel (p, y2, y); 181 p = svpnext_b64 (cmp, p); 182 } 183 return y; 184 } 185 186 /* Compute y+TAIL = log(x) where the rounded result is y and TAIL has about 187 additional 15 bits precision. IX is the bit representation of x, but 188 normalized in the subnormal range using the sign bit for the exponent. */ 189 static inline svfloat64_t 190 sv_log_inline (svbool_t pg, svuint64_t ix, svfloat64_t *tail, 191 const struct data *d) 192 { 193 /* x = 2^k z; where z is in range [Off,2*Off) and exact. 194 The range is split into N subintervals. 195 The ith subinterval contains z and c is near its center. */ 196 svuint64_t tmp = svsub_x (pg, ix, d->off); 197 svuint64_t i = svand_x (pg, svlsr_x (pg, tmp, 52 - V_POW_LOG_TABLE_BITS), 198 sv_u64 (N_LOG - 1)); 199 svint64_t k = svasr_x (pg, svreinterpret_s64 (tmp), 52); 200 svuint64_t iz = svsub_x (pg, ix, svlsl_x (pg, svreinterpret_u64 (k), 52)); 201 svfloat64_t z = svreinterpret_f64 (iz); 202 svfloat64_t kd = svcvt_f64_x (pg, k); 203 204 /* log(x) = k*Ln2 + log(c) + log1p(z/c-1). */ 205 /* SVE lookup requires 3 separate lookup tables, as opposed to scalar version 206 that uses array of structures. We also do the lookup earlier in the code 207 to make sure it finishes as early as possible. */ 208 svfloat64_t invc = svld1_gather_index (pg, __v_pow_log_data.invc, i); 209 svfloat64_t logc = svld1_gather_index (pg, __v_pow_log_data.logc, i); 210 svfloat64_t logctail = svld1_gather_index (pg, __v_pow_log_data.logctail, i); 211 212 /* Note: 1/c is j/N or j/N/2 where j is an integer in [N,2N) and 213 |z/c - 1| < 1/N, so r = z/c - 1 is exactly representible. */ 214 svfloat64_t r = svmad_x (pg, z, invc, -1.0); 215 /* k*Ln2 + log(c) + r. */ 216 217 svfloat64_t ln2_hilo = svld1rq_f64 (svptrue_b64 (), &d->ln2_hi); 218 svfloat64_t t1 = svmla_lane_f64 (logc, kd, ln2_hilo, 0); 219 svfloat64_t t2 = svadd_x (pg, t1, r); 220 svfloat64_t lo1 = svmla_lane_f64 (logctail, kd, ln2_hilo, 1); 221 svfloat64_t lo2 = svadd_x (pg, svsub_x (pg, t1, t2), r); 222 223 /* Evaluation is optimized assuming superscalar pipelined execution. */ 224 225 svfloat64_t log_c02 = svld1rq_f64 (svptrue_b64 (), &d->log_c0); 226 svfloat64_t ar = svmul_lane_f64 (r, log_c02, 0); 227 svfloat64_t ar2 = svmul_x (svptrue_b64 (), r, ar); 228 svfloat64_t ar3 = svmul_x (svptrue_b64 (), r, ar2); 229 /* k*Ln2 + log(c) + r + A[0]*r*r. */ 230 svfloat64_t hi = svadd_x (pg, t2, ar2); 231 svfloat64_t lo3 = svmls_x (pg, ar2, ar, r); 232 svfloat64_t lo4 = svadd_x (pg, svsub_x (pg, t2, hi), ar2); 233 /* p = log1p(r) - r - A[0]*r*r. */ 234 /* p = (ar3 * (A[1] + r * A[2] + ar2 * (A[3] + r * A[4] + ar2 * (A[5] + r * 235 A[6])))). */ 236 237 svfloat64_t log_c46 = svld1rq_f64 (svptrue_b64 (), &d->log_c4); 238 svfloat64_t a56 = svmla_lane_f64 (sv_f64 (d->log_c5), r, log_c46, 1); 239 svfloat64_t a34 = svmla_lane_f64 (sv_f64 (d->log_c3), r, log_c46, 0); 240 svfloat64_t a12 = svmla_lane_f64 (sv_f64 (d->log_c1), r, log_c02, 1); 241 svfloat64_t p = svmla_x (pg, a34, ar2, a56); 242 p = svmla_x (pg, a12, ar2, p); 243 p = svmul_x (svptrue_b64 (), ar3, p); 244 svfloat64_t lo = svadd_x ( 245 pg, svadd_x (pg, svsub_x (pg, svadd_x (pg, lo1, lo2), lo3), lo4), p); 246 svfloat64_t y = svadd_x (pg, hi, lo); 247 *tail = svadd_x (pg, svsub_x (pg, hi, y), lo); 248 return y; 249 } 250 251 static inline svfloat64_t 252 sv_exp_core (svbool_t pg, svfloat64_t x, svfloat64_t xtail, 253 svuint64_t sign_bias, svfloat64_t *tmp, svuint64_t *sbits, 254 svuint64_t *ki, const struct data *d) 255 { 256 /* exp(x) = 2^(k/N) * exp(r), with exp(r) in [2^(-1/2N),2^(1/2N)]. */ 257 /* x = ln2/N*k + r, with int k and r in [-ln2/2N, ln2/2N]. */ 258 svfloat64_t n_over_ln2_and_c2 = svld1rq_f64 (svptrue_b64 (), &d->n_over_ln2); 259 svfloat64_t z = svmul_lane_f64 (x, n_over_ln2_and_c2, 0); 260 /* z - kd is in [-1, 1] in non-nearest rounding modes. */ 261 svfloat64_t kd = svrinta_x (pg, z); 262 *ki = svreinterpret_u64 (svcvt_s64_x (pg, kd)); 263 264 svfloat64_t ln2_over_n_hilo 265 = svld1rq_f64 (svptrue_b64 (), &d->ln2_over_n_hi); 266 svfloat64_t r = x; 267 r = svmls_lane_f64 (r, kd, ln2_over_n_hilo, 0); 268 r = svmls_lane_f64 (r, kd, ln2_over_n_hilo, 1); 269 /* The code assumes 2^-200 < |xtail| < 2^-8/N. */ 270 r = svadd_x (pg, r, xtail); 271 /* 2^(k/N) ~= scale. */ 272 svuint64_t idx = svand_x (pg, *ki, N_EXP - 1); 273 svuint64_t top 274 = svlsl_x (pg, svadd_x (pg, *ki, sign_bias), 52 - V_POW_EXP_TABLE_BITS); 275 /* This is only a valid scale when -1023*N < k < 1024*N. */ 276 *sbits = svld1_gather_index (pg, __v_pow_exp_data.sbits, idx); 277 *sbits = svadd_x (pg, *sbits, top); 278 /* exp(x) = 2^(k/N) * exp(r) ~= scale + scale * (exp(r) - 1). */ 279 svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r); 280 *tmp = svmla_lane_f64 (sv_f64 (d->exp_c1), r, n_over_ln2_and_c2, 1); 281 *tmp = svmla_x (pg, sv_f64 (d->exp_c0), r, *tmp); 282 *tmp = svmla_x (pg, r, r2, *tmp); 283 svfloat64_t scale = svreinterpret_f64 (*sbits); 284 /* Note: tmp == 0 or |tmp| > 2^-200 and scale > 2^-739, so there 285 is no spurious underflow here even without fma. */ 286 z = svmla_x (pg, scale, scale, *tmp); 287 return z; 288 } 289 290 /* Computes sign*exp(x+xtail) where |xtail| < 2^-8/N and |xtail| <= |x|. 291 The sign_bias argument is SignBias or 0 and sets the sign to -1 or 1. */ 292 static inline svfloat64_t 293 sv_exp_inline (svbool_t pg, svfloat64_t x, svfloat64_t xtail, 294 svuint64_t sign_bias, const struct data *d) 295 { 296 /* 3 types of special cases: tiny (uflow and spurious uflow), huge (oflow) 297 and other cases of large values of x (scale * (1 + TMP) oflow). */ 298 svuint64_t abstop = svand_x (pg, sv_top12 (x), 0x7ff); 299 /* |x| is large (|x| >= 512) or tiny (|x| <= 0x1p-54). */ 300 svbool_t uoflow = svcmpge (pg, svsub_x (pg, abstop, SmallExp), ThresExp); 301 302 svfloat64_t tmp; 303 svuint64_t sbits, ki; 304 if (unlikely (svptest_any (pg, uoflow))) 305 { 306 svfloat64_t z 307 = sv_exp_core (pg, x, xtail, sign_bias, &tmp, &sbits, &ki, d); 308 309 /* |x| is tiny (|x| <= 0x1p-54). */ 310 svbool_t uflow 311 = svcmpge (pg, svsub_x (pg, abstop, SmallExp), 0x80000000); 312 uflow = svand_z (pg, uoflow, uflow); 313 /* |x| is huge (|x| >= 1024). */ 314 svbool_t oflow = svcmpge (pg, abstop, HugeExp); 315 oflow = svand_z (pg, uoflow, svbic_z (pg, oflow, uflow)); 316 317 /* For large |x| values (512 < |x| < 1024) scale * (1 + TMP) can overflow 318 or underflow. */ 319 svbool_t special = svbic_z (pg, uoflow, svorr_z (pg, uflow, oflow)); 320 321 /* Update result with special and large cases. */ 322 z = sv_call_specialcase (tmp, sbits, ki, z, special); 323 324 /* Handle underflow and overflow. */ 325 svbool_t x_is_neg = svcmplt (pg, x, 0); 326 svuint64_t sign_mask 327 = svlsl_x (pg, sign_bias, 52 - V_POW_EXP_TABLE_BITS); 328 svfloat64_t res_uoflow 329 = svsel (x_is_neg, sv_f64 (0.0), sv_f64 (INFINITY)); 330 res_uoflow = svreinterpret_f64 ( 331 svorr_x (pg, svreinterpret_u64 (res_uoflow), sign_mask)); 332 /* Avoid spurious underflow for tiny x. */ 333 svfloat64_t res_spurious_uflow 334 = svreinterpret_f64 (svorr_x (pg, sign_mask, 0x3ff0000000000000)); 335 336 z = svsel (oflow, res_uoflow, z); 337 z = svsel (uflow, res_spurious_uflow, z); 338 return z; 339 } 340 341 return sv_exp_core (pg, x, xtail, sign_bias, &tmp, &sbits, &ki, d); 342 } 343 344 static inline double 345 pow_sc (double x, double y) 346 { 347 uint64_t ix = asuint64 (x); 348 uint64_t iy = asuint64 (y); 349 /* Special cases: |x| or |y| is 0, inf or nan. */ 350 if (unlikely (zeroinfnan (iy))) 351 { 352 if (2 * iy == 0) 353 return issignaling_inline (x) ? x + y : 1.0; 354 if (ix == asuint64 (1.0)) 355 return issignaling_inline (y) ? x + y : 1.0; 356 if (2 * ix > 2 * asuint64 (INFINITY) || 2 * iy > 2 * asuint64 (INFINITY)) 357 return x + y; 358 if (2 * ix == 2 * asuint64 (1.0)) 359 return 1.0; 360 if ((2 * ix < 2 * asuint64 (1.0)) == !(iy >> 63)) 361 return 0.0; /* |x|<1 && y==inf or |x|>1 && y==-inf. */ 362 return y * y; 363 } 364 if (unlikely (zeroinfnan (ix))) 365 { 366 double_t x2 = x * x; 367 if (ix >> 63 && checkint (iy) == 1) 368 x2 = -x2; 369 return (iy >> 63) ? 1 / x2 : x2; 370 } 371 return x; 372 } 373 374 svfloat64_t SV_NAME_D2 (pow) (svfloat64_t x, svfloat64_t y, const svbool_t pg) 375 { 376 const struct data *d = ptr_barrier (&data); 377 378 /* This preamble handles special case conditions used in the final scalar 379 fallbacks. It also updates ix and sign_bias, that are used in the core 380 computation too, i.e., exp( y * log (x) ). */ 381 svuint64_t vix0 = svreinterpret_u64 (x); 382 svuint64_t viy0 = svreinterpret_u64 (y); 383 384 /* Negative x cases. */ 385 svbool_t xisneg = svcmplt (pg, x, 0); 386 387 /* Set sign_bias and ix depending on sign of x and nature of y. */ 388 svbool_t yint_or_xpos = pg; 389 svuint64_t sign_bias = sv_u64 (0); 390 svuint64_t vix = vix0; 391 if (unlikely (svptest_any (pg, xisneg))) 392 { 393 /* Determine nature of y. */ 394 yint_or_xpos = sv_isint (xisneg, y); 395 svbool_t yisodd_xisneg = sv_isodd (xisneg, y); 396 /* ix set to abs(ix) if y is integer. */ 397 vix = svand_m (yint_or_xpos, vix0, 0x7fffffffffffffff); 398 /* Set to SignBias if x is negative and y is odd. */ 399 sign_bias = svsel (yisodd_xisneg, sv_u64 (SignBias), sv_u64 (0)); 400 } 401 402 /* Small cases of x: |x| < 0x1p-126. */ 403 svbool_t xsmall = svaclt (yint_or_xpos, x, SmallBoundX); 404 if (unlikely (svptest_any (yint_or_xpos, xsmall))) 405 { 406 /* Normalize subnormal x so exponent becomes negative. */ 407 svuint64_t vtopx = svlsr_x (svptrue_b64 (), vix, 52); 408 svbool_t topx_is_null = svcmpeq (xsmall, vtopx, 0); 409 410 svuint64_t vix_norm = svreinterpret_u64 (svmul_m (xsmall, x, 0x1p52)); 411 vix_norm = svand_m (xsmall, vix_norm, 0x7fffffffffffffff); 412 vix_norm = svsub_m (xsmall, vix_norm, 52ULL << 52); 413 vix = svsel (topx_is_null, vix_norm, vix); 414 } 415 416 /* y_hi = log(ix, &y_lo). */ 417 svfloat64_t vlo; 418 svfloat64_t vhi = sv_log_inline (yint_or_xpos, vix, &vlo, d); 419 420 /* z = exp(y_hi, y_lo, sign_bias). */ 421 svfloat64_t vehi = svmul_x (svptrue_b64 (), y, vhi); 422 svfloat64_t vemi = svmls_x (yint_or_xpos, vehi, y, vhi); 423 svfloat64_t velo = svnmls_x (yint_or_xpos, vemi, y, vlo); 424 svfloat64_t vz = sv_exp_inline (yint_or_xpos, vehi, velo, sign_bias, d); 425 426 /* Cases of finite y and finite negative x. */ 427 vz = svsel (yint_or_xpos, vz, sv_f64 (__builtin_nan (""))); 428 429 /* Special cases of x or y: zero, inf and nan. */ 430 svbool_t xspecial = sv_zeroinfnan (svptrue_b64 (), vix0); 431 svbool_t yspecial = sv_zeroinfnan (svptrue_b64 (), viy0); 432 svbool_t special = svorr_z (svptrue_b64 (), xspecial, yspecial); 433 434 /* Cases of zero/inf/nan x or y. */ 435 if (unlikely (svptest_any (svptrue_b64 (), special))) 436 vz = sv_call2_f64 (pow_sc, x, y, vz, special); 437 438 return vz; 439 } 440 441 TEST_SIG (SV, D, 2, pow) 442 TEST_ULP (SV_NAME_D2 (pow), 0.55) 443 TEST_DISABLE_FENV (SV_NAME_D2 (pow)) 444 /* Wide intervals spanning the whole domain but shared between x and y. */ 445 #define SV_POW_INTERVAL2(xlo, xhi, ylo, yhi, n) \ 446 TEST_INTERVAL2 (SV_NAME_D2 (pow), xlo, xhi, ylo, yhi, n) \ 447 TEST_INTERVAL2 (SV_NAME_D2 (pow), xlo, xhi, -ylo, -yhi, n) \ 448 TEST_INTERVAL2 (SV_NAME_D2 (pow), -xlo, -xhi, ylo, yhi, n) \ 449 TEST_INTERVAL2 (SV_NAME_D2 (pow), -xlo, -xhi, -ylo, -yhi, n) 450 #define EXPAND(str) str##000000000 451 #define SHL52(str) EXPAND (str) 452 SV_POW_INTERVAL2 (0, SHL52 (SmallPowX), 0, inf, 40000) 453 SV_POW_INTERVAL2 (SHL52 (SmallPowX), SHL52 (BigPowX), 0, inf, 40000) 454 SV_POW_INTERVAL2 (SHL52 (BigPowX), inf, 0, inf, 40000) 455 SV_POW_INTERVAL2 (0, inf, 0, SHL52 (SmallPowY), 40000) 456 SV_POW_INTERVAL2 (0, inf, SHL52 (SmallPowY), SHL52 (BigPowY), 40000) 457 SV_POW_INTERVAL2 (0, inf, SHL52 (BigPowY), inf, 40000) 458 SV_POW_INTERVAL2 (0, inf, 0, inf, 1000) 459 /* x~1 or y~1. */ 460 SV_POW_INTERVAL2 (0x1p-1, 0x1p1, 0x1p-10, 0x1p10, 10000) 461 SV_POW_INTERVAL2 (0x1.ep-1, 0x1.1p0, 0x1p8, 0x1p16, 10000) 462 SV_POW_INTERVAL2 (0x1p-500, 0x1p500, 0x1p-1, 0x1p1, 10000) 463 /* around estimated argmaxs of ULP error. */ 464 SV_POW_INTERVAL2 (0x1p-300, 0x1p-200, 0x1p-20, 0x1p-10, 10000) 465 SV_POW_INTERVAL2 (0x1p50, 0x1p100, 0x1p-20, 0x1p-10, 10000) 466 /* x is negative, y is odd or even integer, or y is real not integer. */ 467 TEST_INTERVAL2 (SV_NAME_D2 (pow), -0.0, -10.0, 3.0, 3.0, 10000) 468 TEST_INTERVAL2 (SV_NAME_D2 (pow), -0.0, -10.0, 4.0, 4.0, 10000) 469 TEST_INTERVAL2 (SV_NAME_D2 (pow), -0.0, -10.0, 0.0, 10.0, 10000) 470 TEST_INTERVAL2 (SV_NAME_D2 (pow), 0.0, 10.0, -0.0, -10.0, 10000) 471 /* |x| is inf, y is odd or even integer, or y is real not integer. */ 472 SV_POW_INTERVAL2 (inf, inf, 0.5, 0.5, 1) 473 SV_POW_INTERVAL2 (inf, inf, 1.0, 1.0, 1) 474 SV_POW_INTERVAL2 (inf, inf, 2.0, 2.0, 1) 475 SV_POW_INTERVAL2 (inf, inf, 3.0, 3.0, 1) 476 /* 0.0^y. */ 477 SV_POW_INTERVAL2 (0.0, 0.0, 0.0, 0x1p120, 1000) 478 /* 1.0^y. */ 479 TEST_INTERVAL2 (SV_NAME_D2 (pow), 1.0, 1.0, 0.0, 0x1p-50, 1000) 480 TEST_INTERVAL2 (SV_NAME_D2 (pow), 1.0, 1.0, 0x1p-50, 1.0, 1000) 481 TEST_INTERVAL2 (SV_NAME_D2 (pow), 1.0, 1.0, 1.0, 0x1p100, 1000) 482 TEST_INTERVAL2 (SV_NAME_D2 (pow), 1.0, 1.0, -1.0, -0x1p120, 1000) 483 CLOSE_SVE_ATTR 484