src/internal/libm.h

   1 #ifndef _LIBM_H
   2 #define _LIBM_H
   3
   4 #include <stdint.h>
   5 #include <float.h>
   6 #include <math.h>
   7 #include <endian.h>
   8 #include "fp_arch.h"
   9
  10 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
  11 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __LITTLE_ENDIAN
  12 union ldshape {
  13         long double f;
  14         struct {
  15                 uint64_t m;
  16                 uint16_t se;
  17         } i;
  18 };
  19 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __BIG_ENDIAN
  20 /* This is the m68k variant of 80-bit long double, and this definition only works
  21  * on archs where the alignment requirement of uint64_t is <= 4. */
  22 union ldshape {
  23         long double f;
  24         struct {
  25                 uint16_t se;
  26                 uint16_t pad;
  27                 uint64_t m;
  28         } i;
  29 };
  30 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __LITTLE_ENDIAN
  31 union ldshape {
  32         long double f;
  33         struct {
  34                 uint64_t lo;
  35                 uint32_t mid;
  36                 uint16_t top;
  37                 uint16_t se;
  38         } i;
  39         struct {
  40                 uint64_t lo;
  41                 uint64_t hi;
  42         } i2;
  43 };
  44 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __BIG_ENDIAN
  45 union ldshape {
  46         long double f;
  47         struct {
  48                 uint16_t se;
  49                 uint16_t top;
  50                 uint32_t mid;
  51                 uint64_t lo;
  52         } i;
  53         struct {
  54                 uint64_t hi;
  55                 uint64_t lo;
  56         } i2;
  57 };
  58 #else
  59 #error Unsupported long double representation
  60 #endif
  61
  62 /* Support non-nearest rounding mode.  */
  63 #define WANT_ROUNDING 1
  64 /* Support signaling NaNs.  */
  65 #define WANT_SNAN 0
  66
  67 #if WANT_SNAN
  68 #error SNaN is unsupported
  69 #else
  70 #define issignalingf_inline(x) 0
  71 #define issignaling_inline(x) 0
  72 #endif
  73
  74 #ifndef TOINT_INTRINSICS
  75 #define TOINT_INTRINSICS 0
  76 #endif
  77
  78 #if TOINT_INTRINSICS
  79 /* Round x to nearest int in all rounding modes, ties have to be rounded
  80    consistently with converttoint so the results match.  If the result
  81    would be outside of [-2^31, 2^31-1] then the semantics is unspecified.  */
  82 static double_t roundtoint(double_t);
  83
  84 /* Convert x to nearest int in all rounding modes, ties have to be rounded
  85    consistently with roundtoint.  If the result is not representible in an
  86    int32_t then the semantics is unspecified.  */
  87 static int32_t converttoint(double_t);
  88 #endif
  89
  90 /* Helps static branch prediction so hot path can be better optimized.  */
  91 #ifdef __GNUC__
  92 #define predict_true(x) __builtin_expect(!!(x), 1)
  93 #define predict_false(x) __builtin_expect(x, 0)
  94 #else
  95 #define predict_true(x) (x)
  96 #define predict_false(x) (x)
  97 #endif
  98
  99 /* Evaluate an expression as the specified type. With standard excess
 100    precision handling a type cast or assignment is enough (with
 101    -ffloat-store an assignment is required, in old compilers argument
 102    passing and return statement may not drop excess precision).  */
 103
 104 static inline float eval_as_float(float x)
 105 {
 106         float y = x;
 107         return y;
 108 }
 109
 110 static inline double eval_as_double(double x)
 111 {
 112         double y = x;
 113         return y;
 114 }
 115
 116 /* fp_barrier returns its input, but limits code transformations
 117    as if it had a side-effect (e.g. observable io) and returned
 118    an arbitrary value.  */
 119
 120 #ifndef fp_barrierf
 121 #define fp_barrierf fp_barrierf
 122 static inline float fp_barrierf(float x)
 123 {
 124         volatile float y = x;
 125         return y;
 126 }
 127 #endif
 128
 129 #ifndef fp_barrier
 130 #define fp_barrier fp_barrier
 131 static inline double fp_barrier(double x)
 132 {
 133         volatile double y = x;
 134         return y;
 135 }
 136 #endif
 137
 138 #ifndef fp_barrierl
 139 #define fp_barrierl fp_barrierl
 140 static inline long double fp_barrierl(long double x)
 141 {
 142         volatile long double y = x;
 143         return y;
 144 }
 145 #endif
 146
 147 /* fp_force_eval ensures that the input value is computed when that's
 148    otherwise unused.  To prevent the constant folding of the input
 149    expression, an additional fp_barrier may be needed or a compilation
 150    mode that does so (e.g. -frounding-math in gcc). Then it can be
 151    used to evaluate an expression for its fenv side-effects only.   */
 152
 153 #ifndef fp_force_evalf
 154 #define fp_force_evalf fp_force_evalf
 155 static inline void fp_force_evalf(float x)
 156 {
 157         volatile float y;
 158         y = x;
 159 }
 160 #endif
 161
 162 #ifndef fp_force_eval
 163 #define fp_force_eval fp_force_eval
 164 static inline void fp_force_eval(double x)
 165 {
 166         volatile double y;
 167         y = x;
 168 }
 169 #endif
 170
 171 #ifndef fp_force_evall
 172 #define fp_force_evall fp_force_evall
 173 static inline void fp_force_evall(long double x)
 174 {
 175         volatile long double y;
 176         y = x;
 177 }
 178 #endif
 179
 180 #define FORCE_EVAL(x) do {                        \
 181         if (sizeof(x) == sizeof(float)) {         \
 182                 fp_force_evalf(x);                \
 183         } else if (sizeof(x) == sizeof(double)) { \
 184                 fp_force_eval(x);                 \
 185         } else {                                  \
 186                 fp_force_evall(x);                \
 187         }                                         \
 188 } while(0)
 189
 190 #define asuint(f) ((union{float _f; uint32_t _i;}){f})._i
 191 #define asfloat(i) ((union{uint32_t _i; float _f;}){i})._f
 192 #define asuint64(f) ((union{double _f; uint64_t _i;}){f})._i
 193 #define asdouble(i) ((union{uint64_t _i; double _f;}){i})._f
 194
 195 #define EXTRACT_WORDS(hi,lo,d)                    \
 196 do {                                              \
 197   uint64_t __u = asuint64(d);                     \
 198   (hi) = __u >> 32;                               \
 199   (lo) = (uint32_t)__u;                           \
 200 } while (0)
 201
 202 #define GET_HIGH_WORD(hi,d)                       \
 203 do {                                              \
 204   (hi) = asuint64(d) >> 32;                       \
 205 } while (0)
 206
 207 #define GET_LOW_WORD(lo,d)                        \
 208 do {                                              \
 209   (lo) = (uint32_t)asuint64(d);                   \
 210 } while (0)
 211
 212 #define INSERT_WORDS(d,hi,lo)                     \
 213 do {                                              \
 214   (d) = asdouble(((uint64_t)(hi)<<32) | (uint32_t)(lo)); \
 215 } while (0)
 216
 217 #define SET_HIGH_WORD(d,hi)                       \
 218   INSERT_WORDS(d, hi, (uint32_t)asuint64(d))
 219
 220 #define SET_LOW_WORD(d,lo)                        \
 221   INSERT_WORDS(d, asuint64(d)>>32, lo)
 222
 223 #define GET_FLOAT_WORD(w,d)                       \
 224 do {                                              \
 225   (w) = asuint(d);                                \
 226 } while (0)
 227
 228 #define SET_FLOAT_WORD(d,w)                       \
 229 do {                                              \
 230   (d) = asfloat(w);                               \
 231 } while (0)
 232
 233 hidden int    __rem_pio2_large(double*,double*,int,int,int);
 234
 235 hidden int    __rem_pio2(double,double*);
 236 hidden double __sin(double,double,int);
 237 hidden double __cos(double,double);
 238 hidden double __tan(double,double,int);
 239 hidden double __expo2(double,double);
 240
 241 hidden int    __rem_pio2f(float,double*);
 242 hidden float  __sindf(double);
 243 hidden float  __cosdf(double);
 244 hidden float  __tandf(double,int);
 245 hidden float  __expo2f(float,float);
 246
 247 hidden int __rem_pio2l(long double, long double *);
 248 hidden long double __sinl(long double, long double, int);
 249 hidden long double __cosl(long double, long double);
 250 hidden long double __tanl(long double, long double, int);
 251
 252 hidden long double __polevll(long double, const long double *, int);
 253 hidden long double __p1evll(long double, const long double *, int);
 254
 255 extern int __signgam;
 256 hidden double __lgamma_r(double, int *);
 257 hidden float __lgammaf_r(float, int *);
 258
 259 /* error handling functions */
 260 hidden float __math_xflowf(uint32_t, float);
 261 hidden float __math_uflowf(uint32_t);
 262 hidden float __math_oflowf(uint32_t);
 263 hidden float __math_divzerof(uint32_t);
 264 hidden float __math_invalidf(float);
 265 hidden double __math_xflow(uint32_t, double);
 266 hidden double __math_uflow(uint32_t);
 267 hidden double __math_oflow(uint32_t);
 268 hidden double __math_divzero(uint32_t);
 269 hidden double __math_invalid(double);
 270 #if LDBL_MANT_DIG != DBL_MANT_DIG
 271 hidden long double __math_invalidl(long double);
 272 #endif
 273
 274 #endif