lib/libm/src/math_private.h

   1 /*
   2  * ====================================================
   3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   4  *
   5  * Developed at SunPro, a Sun Microsystems, Inc. business.
   6  * Permission to use, copy, modify, and distribute this
   7  * software is freely granted, provided that this notice
   8  * is preserved.
   9  * ====================================================
  10  */
  11
  12 /*
  13  * from: @(#)fdlibm.h 5.1 93/09/24
  14  * $NetBSD: math_private.h,v 1.22 2015/03/26 11:59:38 justin Exp $
  15  */
  16
  17 #ifndef _MATH_PRIVATE_H_
  18 #define _MATH_PRIVATE_H_
  19
  20 #include <sys/types.h>
  21
  22 /* The original fdlibm code used statements like:
  23         n0 = ((*(int*)&one)>>29)^1;             * index of high word *
  24         ix0 = *(n0+(int*)&x);                   * high word of x *
  25         ix1 = *((1-n0)+(int*)&x);               * low word of x *
  26    to dig two 32 bit words out of the 64 bit IEEE floating point
  27    value.  That is non-ANSI, and, moreover, the gcc instruction
  28    scheduler gets it wrong.  We instead use the following macros.
  29    Unlike the original code, we determine the endianness at compile
  30    time, not at run time; I don't see much benefit to selecting
  31    endianness at run time.  */
  32
  33 /* A union which permits us to convert between a double and two 32 bit
  34    ints.  */
  35
  36 /*
  37  * The ARM ports are little endian except for the FPA word order which is
  38  * big endian.
  39  */
  40
  41 #if (BYTE_ORDER == BIG_ENDIAN) || (defined(__arm__) && !defined(__VFP_FP__))
  42
  43 typedef union
  44 {
  45   double value;
  46   struct
  47   {
  48     u_int32_t msw;
  49     u_int32_t lsw;
  50   } parts;
  51   struct {
  52     u_int64_t w;
  53   } xparts;
  54 } ieee_double_shape_type;
  55
  56 #endif
  57
  58 #if (BYTE_ORDER == LITTLE_ENDIAN) && \
  59     !(defined(__arm__) && !defined(__VFP_FP__))
  60
  61 typedef union
  62 {
  63   double value;
  64   struct
  65   {
  66     u_int32_t lsw;
  67     u_int32_t msw;
  68   } parts;
  69   struct {
  70     u_int64_t w;
  71   } xparts;
  72 } ieee_double_shape_type;
  73
  74 #endif
  75
  76 /* Get two 32 bit ints from a double.  */
  77
  78 #define EXTRACT_WORDS(ix0,ix1,d)                                \
  79 do {                                                            \
  80   ieee_double_shape_type ew_u;                                  \
  81   ew_u.value = (d);                                             \
  82   (ix0) = ew_u.parts.msw;                                       \
  83   (ix1) = ew_u.parts.lsw;                                       \
  84 } while (/*CONSTCOND*/0)
  85
  86 /* Get a 64-bit int from a double. */
  87 #define EXTRACT_WORD64(ix,d)                                    \
  88 do {                                                            \
  89   ieee_double_shape_type ew_u;                                  \
  90   ew_u.value = (d);                                             \
  91   (ix) = ew_u.xparts.w;                                         \
  92 } while (/*CONSTCOND*/0)
  93
  94
  95 /* Get the more significant 32 bit int from a double.  */
  96
  97 #define GET_HIGH_WORD(i,d)                                      \
  98 do {                                                            \
  99   ieee_double_shape_type gh_u;                                  \
 100   gh_u.value = (d);                                             \
 101   (i) = gh_u.parts.msw;                                         \
 102 } while (/*CONSTCOND*/0)
 103
 104 /* Get the less significant 32 bit int from a double.  */
 105
 106 #define GET_LOW_WORD(i,d)                                       \
 107 do {                                                            \
 108   ieee_double_shape_type gl_u;                                  \
 109   gl_u.value = (d);                                             \
 110   (i) = gl_u.parts.lsw;                                         \
 111 } while (/*CONSTCOND*/0)
 112
 113 /* Set a double from two 32 bit ints.  */
 114
 115 #define INSERT_WORDS(d,ix0,ix1)                                 \
 116 do {                                                            \
 117   ieee_double_shape_type iw_u;                                  \
 118   iw_u.parts.msw = (ix0);                                       \
 119   iw_u.parts.lsw = (ix1);                                       \
 120   (d) = iw_u.value;                                             \
 121 } while (/*CONSTCOND*/0)
 122
 123 /* Set a double from a 64-bit int. */
 124 #define INSERT_WORD64(d,ix)                                     \
 125 do {                                                            \
 126   ieee_double_shape_type iw_u;                                  \
 127   iw_u.xparts.w = (ix);                                         \
 128   (d) = iw_u.value;                                             \
 129 } while (/*CONSTCOND*/0)
 130
 131
 132 /* Set the more significant 32 bits of a double from an int.  */
 133
 134 #define SET_HIGH_WORD(d,v)                                      \
 135 do {                                                            \
 136   ieee_double_shape_type sh_u;                                  \
 137   sh_u.value = (d);                                             \
 138   sh_u.parts.msw = (v);                                         \
 139   (d) = sh_u.value;                                             \
 140 } while (/*CONSTCOND*/0)
 141
 142 /* Set the less significant 32 bits of a double from an int.  */
 143
 144 #define SET_LOW_WORD(d,v)                                       \
 145 do {                                                            \
 146   ieee_double_shape_type sl_u;                                  \
 147   sl_u.value = (d);                                             \
 148   sl_u.parts.lsw = (v);                                         \
 149   (d) = sl_u.value;                                             \
 150 } while (/*CONSTCOND*/0)
 151
 152 /* A union which permits us to convert between a float and a 32 bit
 153    int.  */
 154
 155 typedef union
 156 {
 157   float value;
 158   u_int32_t word;
 159 } ieee_float_shape_type;
 160
 161 /* Get a 32 bit int from a float.  */
 162
 163 #define GET_FLOAT_WORD(i,d)                                     \
 164 do {                                                            \
 165   ieee_float_shape_type gf_u;                                   \
 166   gf_u.value = (d);                                             \
 167   (i) = gf_u.word;                                              \
 168 } while (/*CONSTCOND*/0)
 169
 170 /* Set a float from a 32 bit int.  */
 171
 172 #define SET_FLOAT_WORD(d,i)                                     \
 173 do {                                                            \
 174   ieee_float_shape_type sf_u;                                   \
 175   sf_u.word = (i);                                              \
 176   (d) = sf_u.value;                                             \
 177 } while (/*CONSTCOND*/0)
 178
 179 /*
 180  * Attempt to get strict C99 semantics for assignment with non-C99 compilers.
 181  */
 182 #if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
 183 #define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval))
 184 #else
 185 #define STRICT_ASSIGN(type, lval, rval) do {    \
 186         volatile type __lval;                   \
 187                                                 \
 188         if (sizeof(type) >= sizeof(long double))        \
 189                 (lval) = (rval);                \
 190         else {                                  \
 191                 __lval = (rval);                \
 192                 (lval) = __lval;                \
 193         }                                       \
 194 } while (/*CONSTCOND*/0)
 195 #endif
 196
 197 #ifdef  _COMPLEX_H
 198
 199 /*
 200  * Quoting from ISO/IEC 9899:TC2:
 201  *
 202  * 6.2.5.13 Types
 203  * Each complex type has the same representation and alignment requirements as
 204  * an array type containing exactly two elements of the corresponding real type;
 205  * the first element is equal to the real part, and the second element to the
 206  * imaginary part, of the complex number.
 207  */
 208 typedef union {
 209         float complex z;
 210         float parts[2];
 211 } float_complex;
 212
 213 typedef union {
 214         double complex z;
 215         double parts[2];
 216 } double_complex;
 217
 218 typedef union {
 219         long double complex z;
 220         long double parts[2];
 221 } long_double_complex;
 222
 223 #define REAL_PART(z)    ((z).parts[0])
 224 #define IMAG_PART(z)    ((z).parts[1])
 225
 226 #endif  /* _COMPLEX_H */
 227
 228 /* ieee style elementary functions */
 229 extern double __ieee754_sqrt __P((double));
 230 extern double __ieee754_acos __P((double));
 231 extern double __ieee754_acosh __P((double));
 232 extern double __ieee754_log __P((double));
 233 extern double __ieee754_atanh __P((double));
 234 extern double __ieee754_asin __P((double));
 235 extern double __ieee754_atan2 __P((double,double));
 236 extern double __ieee754_exp __P((double));
 237 extern double __ieee754_cosh __P((double));
 238 extern double __ieee754_fmod __P((double,double));
 239 extern double __ieee754_pow __P((double,double));
 240 extern double __ieee754_lgamma_r __P((double,int *));
 241 extern double __ieee754_gamma_r __P((double,int *));
 242 extern double __ieee754_lgamma __P((double));
 243 extern double __ieee754_gamma __P((double));
 244 extern double __ieee754_log10 __P((double));
 245 extern double __ieee754_log2 __P((double));
 246 extern double __ieee754_sinh __P((double));
 247 extern double __ieee754_hypot __P((double,double));
 248 extern double __ieee754_j0 __P((double));
 249 extern double __ieee754_j1 __P((double));
 250 extern double __ieee754_y0 __P((double));
 251 extern double __ieee754_y1 __P((double));
 252 extern double __ieee754_jn __P((int,double));
 253 extern double __ieee754_yn __P((int,double));
 254 extern double __ieee754_remainder __P((double,double));
 255 extern int32_t __ieee754_rem_pio2 __P((double,double*));
 256 extern double __ieee754_scalb __P((double,double));
 257
 258 /* fdlibm kernel function */
 259 extern double __kernel_standard __P((double,double,int));
 260 extern double __kernel_sin __P((double,double,int));
 261 extern double __kernel_cos __P((double,double));
 262 extern double __kernel_tan __P((double,double,int));
 263 extern int    __kernel_rem_pio2 __P((double*,double*,int,int,int,const int32_t*));
 264
 265
 266 /* ieee style elementary float functions */
 267 extern float __ieee754_sqrtf __P((float));
 268 extern float __ieee754_acosf __P((float));
 269 extern float __ieee754_acoshf __P((float));
 270 extern float __ieee754_logf __P((float));
 271 extern float __ieee754_atanhf __P((float));
 272 extern float __ieee754_asinf __P((float));
 273 extern float __ieee754_atan2f __P((float,float));
 274 extern float __ieee754_expf __P((float));
 275 extern float __ieee754_coshf __P((float));
 276 extern float __ieee754_fmodf __P((float,float));
 277 extern float __ieee754_powf __P((float,float));
 278 extern float __ieee754_lgammaf_r __P((float,int *));
 279 extern float __ieee754_gammaf_r __P((float,int *));
 280 extern float __ieee754_lgammaf __P((float));
 281 extern float __ieee754_gammaf __P((float));
 282 extern float __ieee754_log10f __P((float));
 283 extern float __ieee754_log2f __P((float));
 284 extern float __ieee754_sinhf __P((float));
 285 extern float __ieee754_hypotf __P((float,float));
 286 extern float __ieee754_j0f __P((float));
 287 extern float __ieee754_j1f __P((float));
 288 extern float __ieee754_y0f __P((float));
 289 extern float __ieee754_y1f __P((float));
 290 extern float __ieee754_jnf __P((int,float));
 291 extern float __ieee754_ynf __P((int,float));
 292 extern float __ieee754_remainderf __P((float,float));
 293 extern int32_t __ieee754_rem_pio2f __P((float,float*));
 294 extern float __ieee754_scalbf __P((float,float));
 295
 296 /* float versions of fdlibm kernel functions */
 297 extern float __kernel_sinf __P((float,float,int));
 298 extern float __kernel_cosf __P((float,float));
 299 extern float __kernel_tanf __P((float,float,int));
 300 extern int   __kernel_rem_pio2f __P((float*,float*,int,int,int,const int32_t*));
 301
 302 /* ieee style elementary long double functions */
 303 extern long double __ieee754_fmodl(long double, long double);
 304 extern long double __ieee754_sqrtl(long double);
 305
 306 /*
 307  * TRUNC() is a macro that sets the trailing 27 bits in the mantissa of an
 308  * IEEE double variable to zero.  It must be expression-like for syntactic
 309  * reasons, and we implement this expression using an inline function
 310  * instead of a pure macro to avoid depending on the gcc feature of
 311  * statement-expressions.
 312  */
 313 #define TRUNC(d)        (_b_trunc(&(d)))
 314
 315 static __inline void
 316 _b_trunc(volatile double *_dp)
 317 {
 318         uint32_t _lw;
 319
 320         GET_LOW_WORD(_lw, *_dp);
 321         SET_LOW_WORD(*_dp, _lw & 0xf8000000);
 322 }
 323
 324 struct Double {
 325         double  a;
 326         double  b;
 327 };
 328
 329 /*
 330  * Functions internal to the math package, yet not static.
 331  */
 332 double  __exp__D(double, double);
 333 struct Double __log__D(double);
 334
 335 #endif /* _MATH_PRIVATE_H_ */