newlib/libm/common/math_config.h

   1 /* Configuration for math routines.
   2    Copyright (c) 2017-2018 Arm Ltd.  All rights reserved.
   3
   4    SPDX-License-Identifier: BSD-3-Clause
   5
   6    Redistribution and use in source and binary forms, with or without
   7    modification, are permitted provided that the following conditions
   8    are met:
   9    1. Redistributions of source code must retain the above copyright
  10       notice, this list of conditions and the following disclaimer.
  11    2. Redistributions in binary form must reproduce the above copyright
  12       notice, this list of conditions and the following disclaimer in the
  13       documentation and/or other materials provided with the distribution.
  14    3. The name of the company may not be used to endorse or promote
  15       products derived from this software without specific prior written
  16       permission.
  17
  18    THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS'' AND ANY EXPRESS OR IMPLIED
  19    WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
  20    MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
  21    IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  22    SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
  23    TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
  24    PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
  25    LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
  26    NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
  27    SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
  28
  29 #ifndef _MATH_CONFIG_H
  30 #define _MATH_CONFIG_H
  31
  32 #include <math.h>
  33 #include <stdint.h>
  34
  35 #ifndef WANT_ROUNDING
  36 /* Correct special case results in non-nearest rounding modes.  */
  37 # define WANT_ROUNDING 1
  38 #endif
  39 #ifdef _IEEE_LIBM
  40 # define WANT_ERRNO 0
  41 # define _LIB_VERSION _IEEE_
  42 #else
  43 /* Set errno according to ISO C with (math_errhandling & MATH_ERRNO) != 0.  */
  44 # define WANT_ERRNO 1
  45 # define _LIB_VERSION _POSIX_
  46 #endif
  47 #ifndef WANT_ERRNO_UFLOW
  48 /* Set errno to ERANGE if result underflows to 0 (in all rounding modes).  */
  49 # define WANT_ERRNO_UFLOW (WANT_ROUNDING && WANT_ERRNO)
  50 #endif
  51
  52 #define _IEEE_  -1
  53 #define _POSIX_ 0
  54
  55 /* Compiler can inline round as a single instruction.  */
  56 #ifndef HAVE_FAST_ROUND
  57 # if __aarch64__
  58 #   define HAVE_FAST_ROUND 1
  59 # else
  60 #   define HAVE_FAST_ROUND 0
  61 # endif
  62 #endif
  63
  64 /* Compiler can inline lround, but not (long)round(x).  */
  65 #ifndef HAVE_FAST_LROUND
  66 # if __aarch64__ && (100*__GNUC__ + __GNUC_MINOR__) >= 408 && __NO_MATH_ERRNO__
  67 #   define HAVE_FAST_LROUND 1
  68 # else
  69 #   define HAVE_FAST_LROUND 0
  70 # endif
  71 #endif
  72
  73 /* Compiler can inline fma as a single instruction.  */
  74 #ifndef HAVE_FAST_FMA
  75 # if __aarch64__ || (__ARM_FEATURE_FMA && (__ARM_FP & 8)) \
  76      || __riscv_flen >= 64 || defined (__riscv_zdinx)
  77 #   define HAVE_FAST_FMA 1
  78 # else
  79 #   define HAVE_FAST_FMA 0
  80 # endif
  81 #endif
  82
  83 #ifndef HAVE_FAST_FMAF
  84 # if HAVE_FAST_FMA || (__ARM_FEATURE_FMA && (__ARM_FP & 4)) \
  85      || __riscv_flen >= 32 || defined (__riscv_zfinx)
  86 #  define HAVE_FAST_FMAF 1
  87 # else
  88 #  define HAVE_FAST_FMAF 0
  89 # endif
  90 #endif
  91
  92 #if HAVE_FAST_ROUND
  93 /* When set, the roundtoint and converttoint functions are provided with
  94    the semantics documented below.  */
  95 # define TOINT_INTRINSICS 1
  96
  97 /* Round x to nearest int in all rounding modes, ties have to be rounded
  98    consistently with converttoint so the results match.  If the result
  99    would be outside of [-2^31, 2^31-1] then the semantics is unspecified.  */
 100 static inline double_t
 101 roundtoint (double_t x)
 102 {
 103   return round (x);
 104 }
 105
 106 /* Convert x to nearest int in all rounding modes, ties have to be rounded
 107    consistently with roundtoint.  If the result is not representible in an
 108    int32_t then the semantics is unspecified.  */
 109 static inline int32_t
 110 converttoint (double_t x)
 111 {
 112 # if HAVE_FAST_LROUND
 113   return lround (x);
 114 # else
 115   return (long) round (x);
 116 # endif
 117 }
 118 #endif
 119
 120 #ifndef TOINT_INTRINSICS
 121 # define TOINT_INTRINSICS 0
 122 #endif
 123
 124 static inline uint32_t
 125 asuint (float f)
 126 {
 127   union
 128   {
 129     float f;
 130     uint32_t i;
 131   } u = {f};
 132   return u.i;
 133 }
 134
 135 static inline float
 136 asfloat (uint32_t i)
 137 {
 138   union
 139   {
 140     uint32_t i;
 141     float f;
 142   } u = {i};
 143   return u.f;
 144 }
 145
 146 static inline uint64_t
 147 asuint64 (double f)
 148 {
 149   union
 150   {
 151     double f;
 152     uint64_t i;
 153   } u = {f};
 154   return u.i;
 155 }
 156
 157 static inline double
 158 asdouble (uint64_t i)
 159 {
 160   union
 161   {
 162     uint64_t i;
 163     double f;
 164   } u = {i};
 165   return u.f;
 166 }
 167
 168 #ifndef IEEE_754_2008_SNAN
 169 # define IEEE_754_2008_SNAN 1
 170 #endif
 171 static inline int
 172 issignalingf_inline (float x)
 173 {
 174   uint32_t ix = asuint (x);
 175   if (!IEEE_754_2008_SNAN)
 176     return (ix & 0x7fc00000) == 0x7fc00000;
 177   return 2 * (ix ^ 0x00400000) > 0xFF800000u;
 178 }
 179
 180 static inline int
 181 issignaling_inline (double x)
 182 {
 183   uint64_t ix = asuint64 (x);
 184   if (!IEEE_754_2008_SNAN)
 185     return (ix & 0x7ff8000000000000) == 0x7ff8000000000000;
 186   return 2 * (ix ^ 0x0008000000000000) > 2 * 0x7ff8000000000000ULL;
 187 }
 188
 189 #if __aarch64__ && __GNUC__
 190 /* Prevent the optimization of a floating-point expression.  */
 191 static inline float
 192 opt_barrier_float (float x)
 193 {
 194   __asm__ __volatile__ ("" : "+w" (x));
 195   return x;
 196 }
 197 static inline double
 198 opt_barrier_double (double x)
 199 {
 200   __asm__ __volatile__ ("" : "+w" (x));
 201   return x;
 202 }
 203 /* Force the evaluation of a floating-point expression for its side-effect.  */
 204 static inline void
 205 force_eval_float (float x)
 206 {
 207   __asm__ __volatile__ ("" : "+w" (x));
 208 }
 209 static inline void
 210 force_eval_double (double x)
 211 {
 212   __asm__ __volatile__ ("" : "+w" (x));
 213 }
 214 #else
 215 static inline float
 216 opt_barrier_float (float x)
 217 {
 218   volatile float y = x;
 219   return y;
 220 }
 221 static inline double
 222 opt_barrier_double (double x)
 223 {
 224   volatile double y = x;
 225   return y;
 226 }
 227 #pragma GCC diagnostic ignored "-Wunused-variable"
 228 static inline void
 229 force_eval_float (float x)
 230 {
 231   volatile float y = x;
 232 }
 233 static inline void
 234 force_eval_double (double x)
 235 {
 236   volatile double y = x;
 237 }
 238 #pragma GCC diagnostic pop
 239 #endif
 240
 241 /* Evaluate an expression as the specified type, normally a type
 242    cast should be enough, but compilers implement non-standard
 243    excess-precision handling, so when FLT_EVAL_METHOD != 0 then
 244    these functions may need to be customized.  */
 245 static inline float
 246 eval_as_float (float x)
 247 {
 248   return x;
 249 }
 250 static inline double
 251 eval_as_double (double x)
 252 {
 253   return x;
 254 }
 255
 256 #ifdef __GNUC__
 257 # define NOINLINE __attribute__ ((noinline))
 258 # define likely(x) __builtin_expect (!!(x), 1)
 259 # define unlikely(x) __builtin_expect (x, 0)
 260 #else
 261 # define NOINLINE
 262 # define likely(x) (x)
 263 # define unlikely(x) (x)
 264 #endif
 265
 266 /* gcc emitting PE/COFF doesn't support visibility */
 267 #if defined (__GNUC__) && !defined (__CYGWIN__)
 268 # define HIDDEN __attribute__ ((__visibility__ ("hidden")))
 269 #else
 270 # define HIDDEN
 271 #endif
 272
 273 /* Error handling tail calls for special cases, with a sign argument.
 274    The sign of the return value is set if the argument is non-zero.  */
 275
 276 /* The result overflows.  */
 277 HIDDEN float __math_oflowf (uint32_t);
 278 /* The result underflows to 0 in nearest rounding mode.  */
 279 HIDDEN float __math_uflowf (uint32_t);
 280 /* The result underflows to 0 in some directed rounding mode only.  */
 281 HIDDEN float __math_may_uflowf (uint32_t);
 282 /* Division by zero.  */
 283 HIDDEN float __math_divzerof (uint32_t);
 284 /* The result overflows.  */
 285 HIDDEN double __math_oflow (uint32_t);
 286 /* The result underflows to 0 in nearest rounding mode.  */
 287 HIDDEN double __math_uflow (uint32_t);
 288 /* The result underflows to 0 in some directed rounding mode only.  */
 289 HIDDEN double __math_may_uflow (uint32_t);
 290 /* Division by zero.  */
 291 HIDDEN double __math_divzero (uint32_t);
 292
 293 /* Error handling using input checking.  */
 294
 295 /* Invalid input unless it is a quiet NaN.  */
 296 HIDDEN float __math_invalidf (float);
 297 /* Invalid input unless it is a quiet NaN.  */
 298 HIDDEN double __math_invalid (double);
 299
 300 /* Error handling using output checking, only for errno setting.  */
 301
 302 /* Check if the result overflowed to infinity.  */
 303 HIDDEN double __math_check_oflow (double);
 304 /* Check if the result underflowed to 0.  */
 305 HIDDEN double __math_check_uflow (double);
 306
 307 /* Check if the result overflowed to infinity.  */
 308 static inline double
 309 check_oflow (double x)
 310 {
 311   return WANT_ERRNO ? __math_check_oflow (x) : x;
 312 }
 313
 314 /* Check if the result underflowed to 0.  */
 315 static inline double
 316 check_uflow (double x)
 317 {
 318   return WANT_ERRNO ? __math_check_uflow (x) : x;
 319 }
 320
 321 /* Shared between expf, exp2f and powf.  */
 322 #define EXP2F_TABLE_BITS 5
 323 #define EXP2F_POLY_ORDER 3
 324 extern const struct exp2f_data
 325 {
 326   uint64_t tab[1 << EXP2F_TABLE_BITS];
 327   double shift_scaled;
 328   double poly[EXP2F_POLY_ORDER];
 329   double shift;
 330   double invln2_scaled;
 331   double poly_scaled[EXP2F_POLY_ORDER];
 332 } __exp2f_data HIDDEN;
 333
 334 #define LOGF_TABLE_BITS 4
 335 #define LOGF_POLY_ORDER 4
 336 extern const struct logf_data
 337 {
 338   struct
 339   {
 340     double invc, logc;
 341   } tab[1 << LOGF_TABLE_BITS];
 342   double ln2;
 343   double poly[LOGF_POLY_ORDER - 1]; /* First order coefficient is 1.  */
 344 } __logf_data HIDDEN;
 345
 346 #define LOG2F_TABLE_BITS 4
 347 #define LOG2F_POLY_ORDER 4
 348 extern const struct log2f_data
 349 {
 350   struct
 351   {
 352     double invc, logc;
 353   } tab[1 << LOG2F_TABLE_BITS];
 354   double poly[LOG2F_POLY_ORDER];
 355 } __log2f_data HIDDEN;
 356
 357 #define POWF_LOG2_TABLE_BITS 4
 358 #define POWF_LOG2_POLY_ORDER 5
 359 #if TOINT_INTRINSICS
 360 # define POWF_SCALE_BITS EXP2F_TABLE_BITS
 361 #else
 362 # define POWF_SCALE_BITS 0
 363 #endif
 364 #define POWF_SCALE ((double) (1 << POWF_SCALE_BITS))
 365 extern const struct powf_log2_data
 366 {
 367   struct
 368   {
 369     double invc, logc;
 370   } tab[1 << POWF_LOG2_TABLE_BITS];
 371   double poly[POWF_LOG2_POLY_ORDER];
 372 } __powf_log2_data HIDDEN;
 373
 374 #define EXP_TABLE_BITS 7
 375 #define EXP_POLY_ORDER 5
 376 /* Use polynomial that is optimized for a wider input range.  This may be
 377    needed for good precision in non-nearest rounding and !TOINT_INTRINSICS.  */
 378 #define EXP_POLY_WIDE 0
 379 /* Use close to nearest rounding toint when !TOINT_INTRINSICS.  This may be
 380    needed for good precision in non-nearest rouning and !EXP_POLY_WIDE.  */
 381 #define EXP_USE_TOINT_NARROW 0
 382 #define EXP2_POLY_ORDER 5
 383 #define EXP2_POLY_WIDE 0
 384 extern const struct exp_data
 385 {
 386   double invln2N;
 387   double shift;
 388   double negln2hiN;
 389   double negln2loN;
 390   double poly[4]; /* Last four coefficients.  */
 391   double exp2_shift;
 392   double exp2_poly[EXP2_POLY_ORDER];
 393   uint64_t tab[2*(1 << EXP_TABLE_BITS)];
 394 } __exp_data HIDDEN;
 395
 396 #define LOG_TABLE_BITS 7
 397 #define LOG_POLY_ORDER 6
 398 #define LOG_POLY1_ORDER 12
 399 extern const struct log_data
 400 {
 401   double ln2hi;
 402   double ln2lo;
 403   double poly[LOG_POLY_ORDER - 1]; /* First coefficient is 1.  */
 404   double poly1[LOG_POLY1_ORDER - 1];
 405   struct {double invc, logc;} tab[1 << LOG_TABLE_BITS];
 406 #if !HAVE_FAST_FMA
 407   struct {double chi, clo;} tab2[1 << LOG_TABLE_BITS];
 408 #endif
 409 } __log_data HIDDEN;
 410
 411 #define LOG2_TABLE_BITS 6
 412 #define LOG2_POLY_ORDER 7
 413 #define LOG2_POLY1_ORDER 11
 414 extern const struct log2_data
 415 {
 416   double invln2hi;
 417   double invln2lo;
 418   double poly[LOG2_POLY_ORDER - 1];
 419   double poly1[LOG2_POLY1_ORDER - 1];
 420   struct {double invc, logc;} tab[1 << LOG2_TABLE_BITS];
 421 #if !HAVE_FAST_FMA
 422   struct {double chi, clo;} tab2[1 << LOG2_TABLE_BITS];
 423 #endif
 424 } __log2_data HIDDEN;
 425
 426 #define POW_LOG_TABLE_BITS 7
 427 #define POW_LOG_POLY_ORDER 8
 428 extern const struct pow_log_data
 429 {
 430   double ln2hi;
 431   double ln2lo;
 432   double poly[POW_LOG_POLY_ORDER - 1]; /* First coefficient is 1.  */
 433   /* Note: the pad field is unused, but allows slightly faster indexing.  */
 434   struct {double invc, pad, logc, logctail;} tab[1 << POW_LOG_TABLE_BITS];
 435 } __pow_log_data HIDDEN;
 436
 437 #endif