/* * This file is part of the MicroPython project, http://micropython.org/ * * This file is adapted from from newlib-nano-2, the newlib/libm/common/fdlib.h, * available from https://github.com/32bitmicro/newlib-nano-2. The main change * is removal of anything to do with double precision. * * Appropriate copyright headers are reproduced below. */ /* @(#)fdlibm.h 5.1 93/09/24 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #include /* Default to XOPEN_MODE. */ #define _XOPEN_MODE /* Most routines need to check whether a float is finite, infinite, or not a number, and many need to know whether the result of an operation will overflow. These conditions depend on whether the largest exponent is used for NaNs & infinities, or whether it's used for finite numbers. The macros below wrap up that kind of information: FLT_UWORD_IS_FINITE(X) True if a positive float with bitmask X is finite. FLT_UWORD_IS_NAN(X) True if a positive float with bitmask X is not a number. FLT_UWORD_IS_INFINITE(X) True if a positive float with bitmask X is +infinity. FLT_UWORD_MAX The bitmask of FLT_MAX. FLT_UWORD_HALF_MAX The bitmask of FLT_MAX/2. FLT_UWORD_EXP_MAX The bitmask of the largest finite exponent (129 if the largest exponent is used for finite numbers, 128 otherwise). FLT_UWORD_LOG_MAX The bitmask of log(FLT_MAX), rounded down. This value is the largest input that can be passed to exp() without producing overflow. FLT_UWORD_LOG_2MAX The bitmask of log(2*FLT_MAX), rounded down. This value is the largest input than can be passed to cosh() without producing overflow. FLT_LARGEST_EXP The largest biased exponent that can be used for finite numbers (255 if the largest exponent is used for finite numbers, 254 otherwise) */ #ifdef _FLT_LARGEST_EXPONENT_IS_NORMAL #define FLT_UWORD_IS_FINITE(x) 1 #define FLT_UWORD_IS_NAN(x) 0 #define FLT_UWORD_IS_INFINITE(x) 0 #define FLT_UWORD_MAX 0x7fffffff #define FLT_UWORD_EXP_MAX 0x43010000 #define FLT_UWORD_LOG_MAX 0x42b2d4fc #define FLT_UWORD_LOG_2MAX 0x42b437e0 #define HUGE ((float)0X1.FFFFFEP128) #else #define FLT_UWORD_IS_FINITE(x) ((x)<0x7f800000L) #define FLT_UWORD_IS_NAN(x) ((x)>0x7f800000L) #define FLT_UWORD_IS_INFINITE(x) ((x)==0x7f800000L) #define FLT_UWORD_MAX 0x7f7fffffL #define FLT_UWORD_EXP_MAX 0x43000000 #define FLT_UWORD_LOG_MAX 0x42b17217 #define FLT_UWORD_LOG_2MAX 0x42b2d4fc #define HUGE ((float)3.40282346638528860e+38) #endif #define FLT_UWORD_HALF_MAX (FLT_UWORD_MAX-(1L<<23)) #define FLT_LARGEST_EXP (FLT_UWORD_MAX>>23) /* Many routines check for zero and subnormal numbers. Such things depend on whether the target supports denormals or not: FLT_UWORD_IS_ZERO(X) True if a positive float with bitmask X is +0. Without denormals, any float with a zero exponent is a +0 representation. With denormals, the only +0 representation is a 0 bitmask. FLT_UWORD_IS_SUBNORMAL(X) True if a non-zero positive float with bitmask X is subnormal. (Routines should check for zeros first.) FLT_UWORD_MIN The bitmask of the smallest float above +0. Call this number REAL_FLT_MIN... FLT_UWORD_EXP_MIN The bitmask of the float representation of REAL_FLT_MIN's exponent. FLT_UWORD_LOG_MIN The bitmask of |log(REAL_FLT_MIN)|, rounding down. FLT_SMALLEST_EXP REAL_FLT_MIN's exponent - EXP_BIAS (1 if denormals are not supported, -22 if they are). */ #ifdef _FLT_NO_DENORMALS #define FLT_UWORD_IS_ZERO(x) ((x)<0x00800000L) #define FLT_UWORD_IS_SUBNORMAL(x) 0 #define FLT_UWORD_MIN 0x00800000 #define FLT_UWORD_EXP_MIN 0x42fc0000 #define FLT_UWORD_LOG_MIN 0x42aeac50 #define FLT_SMALLEST_EXP 1 #else #define FLT_UWORD_IS_ZERO(x) ((x)==0) #define FLT_UWORD_IS_SUBNORMAL(x) ((x)<0x00800000L) #define FLT_UWORD_MIN 0x00000001 #define FLT_UWORD_EXP_MIN 0x43160000 #define FLT_UWORD_LOG_MIN 0x42cff1b5 #define FLT_SMALLEST_EXP -22 #endif #ifdef __STDC__ #undef __P #define __P(p) p #else #define __P(p) () #endif /* * set X_TLOSS = pi*2**52, which is possibly defined in * (one may replace the following line by "#include ") */ #define X_TLOSS 1.41484755040568800000e+16 /* Functions that are not documented, and are not in . */ /* Undocumented float functions. */ #ifdef _SCALB_INT extern float scalbf __P((float, int)); #else extern float scalbf __P((float, float)); #endif extern float significandf __P((float)); /* ieee style elementary float functions */ extern float __ieee754_sqrtf __P((float)); extern float __ieee754_acosf __P((float)); extern float __ieee754_acoshf __P((float)); extern float __ieee754_logf __P((float)); extern float __ieee754_atanhf __P((float)); extern float __ieee754_asinf __P((float)); extern float __ieee754_atan2f __P((float,float)); extern float __ieee754_expf __P((float)); extern float __ieee754_coshf __P((float)); extern float __ieee754_fmodf __P((float,float)); extern float __ieee754_powf __P((float,float)); extern float __ieee754_lgammaf_r __P((float,int *)); extern float __ieee754_gammaf_r __P((float,int *)); extern float __ieee754_log10f __P((float)); extern float __ieee754_sinhf __P((float)); extern float __ieee754_hypotf __P((float,float)); extern float __ieee754_j0f __P((float)); extern float __ieee754_j1f __P((float)); extern float __ieee754_y0f __P((float)); extern float __ieee754_y1f __P((float)); extern float __ieee754_jnf __P((int,float)); extern float __ieee754_ynf __P((int,float)); extern float __ieee754_remainderf __P((float,float)); extern __int32_t __ieee754_rem_pio2f __P((float,float*)); #ifdef _SCALB_INT extern float __ieee754_scalbf __P((float,int)); #else extern float __ieee754_scalbf __P((float,float)); #endif /* float versions of fdlibm kernel functions */ extern float __kernel_sinf __P((float,float,int)); extern float __kernel_cosf __P((float,float)); extern float __kernel_tanf __P((float,float,int)); extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const __uint8_t*)); /* A union which permits us to convert between a float and a 32 bit int. */ typedef union { float value; __uint32_t word; } ieee_float_shape_type; /* Get a 32 bit int from a float. */ #define GET_FLOAT_WORD(i,d) \ do { \ ieee_float_shape_type gf_u; \ gf_u.value = (d); \ (i) = gf_u.word; \ } while (0) /* Set a float from a 32 bit int. */ #define SET_FLOAT_WORD(d,i) \ do { \ ieee_float_shape_type sf_u; \ sf_u.word = (i); \ (d) = sf_u.value; \ } while (0) /* Macros to avoid undefined behaviour that can arise if the amount of a shift is exactly equal to the size of the shifted operand. */ #define SAFE_LEFT_SHIFT(op,amt) \ (((amt) < 8 * sizeof(op)) ? ((op) << (amt)) : 0) #define SAFE_RIGHT_SHIFT(op,amt) \ (((amt) < 8 * sizeof(op)) ? ((op) >> (amt)) : 0)