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 * $FreeBSD$ 15 */ 16 17 #ifndef _MATH_PRIVATE_H_ 18 #define _MATH_PRIVATE_H_ 19 20 #include <sys/types.h> 21 #include <machine/endian.h> 22 23 /* 24 * The original fdlibm code used statements like: 25 * n0 = ((*(int*)&one)>>29)^1; * index of high word * 26 * ix0 = *(n0+(int*)&x); * high word of x * 27 * ix1 = *((1-n0)+(int*)&x); * low word of x * 28 * to dig two 32 bit words out of the 64 bit IEEE floating point 29 * value. That is non-ANSI, and, moreover, the gcc instruction 30 * scheduler gets it wrong. We instead use the following macros. 31 * Unlike the original code, we determine the endianness at compile 32 * time, not at run time; I don't see much benefit to selecting 33 * endianness at run time. 34 */ 35 36 /* 37 * A union which permits us to convert between a double and two 32 bit 38 * ints. 39 */ 40 41 #ifdef __arm__ 42 #if defined(__VFP_FP__) 43 #define IEEE_WORD_ORDER BYTE_ORDER 44 #else 45 #define IEEE_WORD_ORDER BIG_ENDIAN 46 #endif 47 #else /* __arm__ */ 48 #define IEEE_WORD_ORDER BYTE_ORDER 49 #endif 50 51 #if IEEE_WORD_ORDER == BIG_ENDIAN 52 53 typedef union 54 { 55 double value; 56 struct 57 { 58 u_int32_t msw; 59 u_int32_t lsw; 60 } parts; 61 struct 62 { 63 u_int64_t w; 64 } xparts; 65 } ieee_double_shape_type; 66 67 #endif 68 69 #if IEEE_WORD_ORDER == LITTLE_ENDIAN 70 71 typedef union 72 { 73 double value; 74 struct 75 { 76 u_int32_t lsw; 77 u_int32_t msw; 78 } parts; 79 struct 80 { 81 u_int64_t w; 82 } xparts; 83 } ieee_double_shape_type; 84 85 #endif 86 87 /* Get two 32 bit ints from a double. */ 88 89 #define EXTRACT_WORDS(ix0,ix1,d) \ 90 do { \ 91 ieee_double_shape_type ew_u; \ 92 ew_u.value = (d); \ 93 (ix0) = ew_u.parts.msw; \ 94 (ix1) = ew_u.parts.lsw; \ 95 } while (0) 96 97 /* Get a 64-bit int from a double. */ 98 #define EXTRACT_WORD64(ix,d) \ 99 do { \ 100 ieee_double_shape_type ew_u; \ 101 ew_u.value = (d); \ 102 (ix) = ew_u.xparts.w; \ 103 } while (0) 104 105 /* Get the more significant 32 bit int from a double. */ 106 107 #define GET_HIGH_WORD(i,d) \ 108 do { \ 109 ieee_double_shape_type gh_u; \ 110 gh_u.value = (d); \ 111 (i) = gh_u.parts.msw; \ 112 } while (0) 113 114 /* Get the less significant 32 bit int from a double. */ 115 116 #define GET_LOW_WORD(i,d) \ 117 do { \ 118 ieee_double_shape_type gl_u; \ 119 gl_u.value = (d); \ 120 (i) = gl_u.parts.lsw; \ 121 } while (0) 122 123 /* Set a double from two 32 bit ints. */ 124 125 #define INSERT_WORDS(d,ix0,ix1) \ 126 do { \ 127 ieee_double_shape_type iw_u; \ 128 iw_u.parts.msw = (ix0); \ 129 iw_u.parts.lsw = (ix1); \ 130 (d) = iw_u.value; \ 131 } while (0) 132 133 /* Set a double from a 64-bit int. */ 134 #define INSERT_WORD64(d,ix) \ 135 do { \ 136 ieee_double_shape_type iw_u; \ 137 iw_u.xparts.w = (ix); \ 138 (d) = iw_u.value; \ 139 } while (0) 140 141 /* Set the more significant 32 bits of a double from an int. */ 142 143 #define SET_HIGH_WORD(d,v) \ 144 do { \ 145 ieee_double_shape_type sh_u; \ 146 sh_u.value = (d); \ 147 sh_u.parts.msw = (v); \ 148 (d) = sh_u.value; \ 149 } while (0) 150 151 /* Set the less significant 32 bits of a double from an int. */ 152 153 #define SET_LOW_WORD(d,v) \ 154 do { \ 155 ieee_double_shape_type sl_u; \ 156 sl_u.value = (d); \ 157 sl_u.parts.lsw = (v); \ 158 (d) = sl_u.value; \ 159 } while (0) 160 161 /* 162 * A union which permits us to convert between a float and a 32 bit 163 * int. 164 */ 165 166 typedef union 167 { 168 float value; 169 /* FIXME: Assumes 32 bit int. */ 170 unsigned int word; 171 } ieee_float_shape_type; 172 173 /* Get a 32 bit int from a float. */ 174 175 #define GET_FLOAT_WORD(i,d) \ 176 do { \ 177 ieee_float_shape_type gf_u; \ 178 gf_u.value = (d); \ 179 (i) = gf_u.word; \ 180 } while (0) 181 182 /* Set a float from a 32 bit int. */ 183 184 #define SET_FLOAT_WORD(d,i) \ 185 do { \ 186 ieee_float_shape_type sf_u; \ 187 sf_u.word = (i); \ 188 (d) = sf_u.value; \ 189 } while (0) 190 191 /* Get expsign as a 16 bit int from a long double. */ 192 193 #define GET_LDBL_EXPSIGN(i,d) \ 194 do { \ 195 union IEEEl2bits ge_u; \ 196 ge_u.e = (d); \ 197 (i) = ge_u.xbits.expsign; \ 198 } while (0) 199 200 /* Set expsign of a long double from a 16 bit int. */ 201 202 #define SET_LDBL_EXPSIGN(d,v) \ 203 do { \ 204 union IEEEl2bits se_u; \ 205 se_u.e = (d); \ 206 se_u.xbits.expsign = (v); \ 207 (d) = se_u.e; \ 208 } while (0) 209 210 #ifdef FLT_EVAL_METHOD 211 /* 212 * Attempt to get strict C99 semantics for assignment with non-C99 compilers. 213 */ 214 #if FLT_EVAL_METHOD == 0 || __GNUC__ == 0 215 #define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval)) 216 #else 217 #define STRICT_ASSIGN(type, lval, rval) do { \ 218 volatile type __lval; \ 219 \ 220 if (sizeof(type) >= sizeof(double)) \ 221 (lval) = (rval); \ 222 else { \ 223 __lval = (rval); \ 224 (lval) = __lval; \ 225 } \ 226 } while (0) 227 #endif 228 #endif 229 230 /* 231 * Common routine to process the arguments to nan(), nanf(), and nanl(). 232 */ 233 void _scan_nan(uint32_t *__words, int __num_words, const char *__s); 234 235 #ifdef _COMPLEX_H 236 237 /* 238 * C99 specifies that complex numbers have the same representation as 239 * an array of two elements, where the first element is the real part 240 * and the second element is the imaginary part. 241 */ 242 typedef union { 243 float complex f; 244 float a[2]; 245 } float_complex; 246 typedef union { 247 double complex f; 248 double a[2]; 249 } double_complex; 250 typedef union { 251 long double complex f; 252 long double a[2]; 253 } long_double_complex; 254 #define REALPART(z) ((z).a[0]) 255 #define IMAGPART(z) ((z).a[1]) 256 257 /* 258 * Inline functions that can be used to construct complex values. 259 * 260 * The C99 standard intends x+I*y to be used for this, but x+I*y is 261 * currently unusable in general since gcc introduces many overflow, 262 * underflow, sign and efficiency bugs by rewriting I*y as 263 * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product. 264 * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted 265 * to -0.0+I*0.0. 266 */ 267 static __inline float complex 268 cpackf(float x, float y) 269 { 270 float_complex z; 271 272 REALPART(z) = x; 273 IMAGPART(z) = y; 274 return (z.f); 275 } 276 277 static __inline double complex 278 cpack(double x, double y) 279 { 280 double_complex z; 281 282 REALPART(z) = x; 283 IMAGPART(z) = y; 284 return (z.f); 285 } 286 287 static __inline long double complex 288 cpackl(long double x, long double y) 289 { 290 long_double_complex z; 291 292 REALPART(z) = x; 293 IMAGPART(z) = y; 294 return (z.f); 295 } 296 #endif /* _COMPLEX_H */ 297 298 #ifdef __GNUCLIKE_ASM 299 300 /* Asm versions of some functions. */ 301 302 #ifdef __amd64__ 303 static __inline int 304 irint(double x) 305 { 306 int n; 307 308 asm("cvtsd2si %1,%0" : "=r" (n) : "x" (x)); 309 return (n); 310 } 311 #define HAVE_EFFICIENT_IRINT 312 #endif 313 314 #ifdef __i386__ 315 static __inline int 316 irint(double x) 317 { 318 int n; 319 320 asm("fistl %0" : "=m" (n) : "t" (x)); 321 return (n); 322 } 323 #define HAVE_EFFICIENT_IRINT 324 #endif 325 326 #endif /* __GNUCLIKE_ASM */ 327 328 /* 329 * ieee style elementary functions 330 * 331 * We rename functions here to improve other sources' diffability 332 * against fdlibm. 333 */ 334 #define __ieee754_sqrt sqrt 335 #define __ieee754_acos acos 336 #define __ieee754_acosh acosh 337 #define __ieee754_log log 338 #define __ieee754_log2 log2 339 #define __ieee754_atanh atanh 340 #define __ieee754_asin asin 341 #define __ieee754_atan2 atan2 342 #define __ieee754_exp exp 343 #define __ieee754_cosh cosh 344 #define __ieee754_fmod fmod 345 #define __ieee754_pow pow 346 #define __ieee754_lgamma lgamma 347 #define __ieee754_gamma gamma 348 #define __ieee754_lgamma_r lgamma_r 349 #define __ieee754_gamma_r gamma_r 350 #define __ieee754_log10 log10 351 #define __ieee754_sinh sinh 352 #define __ieee754_hypot hypot 353 #define __ieee754_j0 j0 354 #define __ieee754_j1 j1 355 #define __ieee754_y0 y0 356 #define __ieee754_y1 y1 357 #define __ieee754_jn jn 358 #define __ieee754_yn yn 359 #define __ieee754_remainder remainder 360 #define __ieee754_scalb scalb 361 #define __ieee754_sqrtf sqrtf 362 #define __ieee754_acosf acosf 363 #define __ieee754_acoshf acoshf 364 #define __ieee754_logf logf 365 #define __ieee754_atanhf atanhf 366 #define __ieee754_asinf asinf 367 #define __ieee754_atan2f atan2f 368 #define __ieee754_expf expf 369 #define __ieee754_coshf coshf 370 #define __ieee754_fmodf fmodf 371 #define __ieee754_powf powf 372 #define __ieee754_lgammaf lgammaf 373 #define __ieee754_gammaf gammaf 374 #define __ieee754_lgammaf_r lgammaf_r 375 #define __ieee754_gammaf_r gammaf_r 376 #define __ieee754_log10f log10f 377 #define __ieee754_log2f log2f 378 #define __ieee754_sinhf sinhf 379 #define __ieee754_hypotf hypotf 380 #define __ieee754_j0f j0f 381 #define __ieee754_j1f j1f 382 #define __ieee754_y0f y0f 383 #define __ieee754_y1f y1f 384 #define __ieee754_jnf jnf 385 #define __ieee754_ynf ynf 386 #define __ieee754_remainderf remainderf 387 #define __ieee754_scalbf scalbf 388 389 /* fdlibm kernel function */ 390 int __kernel_rem_pio2(double*,double*,int,int,int); 391 392 /* double precision kernel functions */ 393 #ifdef INLINE_REM_PIO2 394 __inline 395 #endif 396 int __ieee754_rem_pio2(double,double*); 397 double __kernel_sin(double,double,int); 398 double __kernel_cos(double,double); 399 double __kernel_tan(double,double,int); 400 double __ldexp_exp(double,int); 401 #ifdef _COMPLEX_H 402 double complex __ldexp_cexp(double complex,int); 403 #endif 404 405 /* float precision kernel functions */ 406 #ifdef INLINE_REM_PIO2F 407 __inline 408 #endif 409 int __ieee754_rem_pio2f(float,double*); 410 #ifdef INLINE_KERNEL_SINDF 411 __inline 412 #endif 413 float __kernel_sindf(double); 414 #ifdef INLINE_KERNEL_COSDF 415 __inline 416 #endif 417 float __kernel_cosdf(double); 418 #ifdef INLINE_KERNEL_TANDF 419 __inline 420 #endif 421 float __kernel_tandf(double,int); 422 float __ldexp_expf(float,int); 423 #ifdef _COMPLEX_H 424 float complex __ldexp_cexpf(float complex,int); 425 #endif 426 427 /* long double precision kernel functions */ 428 long double __kernel_sinl(long double, long double, int); 429 long double __kernel_cosl(long double, long double); 430 long double __kernel_tanl(long double, long double, int); 431 432 #endif /* !_MATH_PRIVATE_H_ */ 433