1 /* 2 * This file is part of the MicroPython project, http://micropython.org/ 3 * 4 * This file is adapted from from newlib-nano-2, the newlib/libm/common/fdlib.h, 5 * available from https://github.com/32bitmicro/newlib-nano-2. The main change 6 * is removal of anything to do with double precision. 7 * 8 * Appropriate copyright headers are reproduced below. 9 */ 10 11 /* @(#)fdlibm.h 5.1 93/09/24 */ 12 /* 13 * ==================================================== 14 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 15 * 16 * Developed at SunPro, a Sun Microsystems, Inc. business. 17 * Permission to use, copy, modify, and distribute this 18 * software is freely granted, provided that this notice 19 * is preserved. 20 * ==================================================== 21 */ 22 23 #include <math.h> 24 25 /* Default to XOPEN_MODE. */ 26 #define _XOPEN_MODE 27 28 /* Most routines need to check whether a float is finite, infinite, or not a 29 number, and many need to know whether the result of an operation will 30 overflow. These conditions depend on whether the largest exponent is 31 used for NaNs & infinities, or whether it's used for finite numbers. The 32 macros below wrap up that kind of information: 33 34 FLT_UWORD_IS_FINITE(X) 35 True if a positive float with bitmask X is finite. 36 37 FLT_UWORD_IS_NAN(X) 38 True if a positive float with bitmask X is not a number. 39 40 FLT_UWORD_IS_INFINITE(X) 41 True if a positive float with bitmask X is +infinity. 42 43 FLT_UWORD_MAX 44 The bitmask of FLT_MAX. 45 46 FLT_UWORD_HALF_MAX 47 The bitmask of FLT_MAX/2. 48 49 FLT_UWORD_EXP_MAX 50 The bitmask of the largest finite exponent (129 if the largest 51 exponent is used for finite numbers, 128 otherwise). 52 53 FLT_UWORD_LOG_MAX 54 The bitmask of log(FLT_MAX), rounded down. This value is the largest 55 input that can be passed to exp() without producing overflow. 56 57 FLT_UWORD_LOG_2MAX 58 The bitmask of log(2*FLT_MAX), rounded down. This value is the 59 largest input than can be passed to cosh() without producing 60 overflow. 61 62 FLT_LARGEST_EXP 63 The largest biased exponent that can be used for finite numbers 64 (255 if the largest exponent is used for finite numbers, 254 65 otherwise) */ 66 67 #ifdef _FLT_LARGEST_EXPONENT_IS_NORMAL 68 #define FLT_UWORD_IS_FINITE(x) 1 69 #define FLT_UWORD_IS_NAN(x) 0 70 #define FLT_UWORD_IS_INFINITE(x) 0 71 #define FLT_UWORD_MAX 0x7fffffff 72 #define FLT_UWORD_EXP_MAX 0x43010000 73 #define FLT_UWORD_LOG_MAX 0x42b2d4fc 74 #define FLT_UWORD_LOG_2MAX 0x42b437e0 75 #define HUGE ((float)0X1.FFFFFEP128) 76 #else 77 #define FLT_UWORD_IS_FINITE(x) ((x)<0x7f800000L) 78 #define FLT_UWORD_IS_NAN(x) ((x)>0x7f800000L) 79 #define FLT_UWORD_IS_INFINITE(x) ((x)==0x7f800000L) 80 #define FLT_UWORD_MAX 0x7f7fffffL 81 #define FLT_UWORD_EXP_MAX 0x43000000 82 #define FLT_UWORD_LOG_MAX 0x42b17217 83 #define FLT_UWORD_LOG_2MAX 0x42b2d4fc 84 #define HUGE ((float)3.40282346638528860e+38) 85 #endif 86 #define FLT_UWORD_HALF_MAX (FLT_UWORD_MAX-(1L<<23)) 87 #define FLT_LARGEST_EXP (FLT_UWORD_MAX>>23) 88 89 /* Many routines check for zero and subnormal numbers. Such things depend 90 on whether the target supports denormals or not: 91 92 FLT_UWORD_IS_ZERO(X) 93 True if a positive float with bitmask X is +0. Without denormals, 94 any float with a zero exponent is a +0 representation. With 95 denormals, the only +0 representation is a 0 bitmask. 96 97 FLT_UWORD_IS_SUBNORMAL(X) 98 True if a non-zero positive float with bitmask X is subnormal. 99 (Routines should check for zeros first.) 100 101 FLT_UWORD_MIN 102 The bitmask of the smallest float above +0. Call this number 103 REAL_FLT_MIN... 104 105 FLT_UWORD_EXP_MIN 106 The bitmask of the float representation of REAL_FLT_MIN's exponent. 107 108 FLT_UWORD_LOG_MIN 109 The bitmask of |log(REAL_FLT_MIN)|, rounding down. 110 111 FLT_SMALLEST_EXP 112 REAL_FLT_MIN's exponent - EXP_BIAS (1 if denormals are not supported, 113 -22 if they are). 114 */ 115 116 #ifdef _FLT_NO_DENORMALS 117 #define FLT_UWORD_IS_ZERO(x) ((x)<0x00800000L) 118 #define FLT_UWORD_IS_SUBNORMAL(x) 0 119 #define FLT_UWORD_MIN 0x00800000 120 #define FLT_UWORD_EXP_MIN 0x42fc0000 121 #define FLT_UWORD_LOG_MIN 0x42aeac50 122 #define FLT_SMALLEST_EXP 1 123 #else 124 #define FLT_UWORD_IS_ZERO(x) ((x)==0) 125 #define FLT_UWORD_IS_SUBNORMAL(x) ((x)<0x00800000L) 126 #define FLT_UWORD_MIN 0x00000001 127 #define FLT_UWORD_EXP_MIN 0x43160000 128 #define FLT_UWORD_LOG_MIN 0x42cff1b5 129 #define FLT_SMALLEST_EXP -22 130 #endif 131 132 #ifdef __STDC__ 133 #undef __P 134 #define __P(p) p 135 #else 136 #define __P(p) () 137 #endif 138 139 /* 140 * set X_TLOSS = pi*2**52, which is possibly defined in <values.h> 141 * (one may replace the following line by "#include <values.h>") 142 */ 143 144 #define X_TLOSS 1.41484755040568800000e+16 145 146 /* Functions that are not documented, and are not in <math.h>. */ 147 148 /* Undocumented float functions. */ 149 #ifdef _SCALB_INT 150 extern float scalbf __P((float, int)); 151 #else 152 extern float scalbf __P((float, float)); 153 #endif 154 extern float significandf __P((float)); 155 156 /* ieee style elementary float functions */ 157 extern float __ieee754_sqrtf __P((float)); 158 extern float __ieee754_acosf __P((float)); 159 extern float __ieee754_acoshf __P((float)); 160 extern float __ieee754_logf __P((float)); 161 extern float __ieee754_atanhf __P((float)); 162 extern float __ieee754_asinf __P((float)); 163 extern float __ieee754_atan2f __P((float,float)); 164 extern float __ieee754_expf __P((float)); 165 extern float __ieee754_coshf __P((float)); 166 extern float __ieee754_fmodf __P((float,float)); 167 extern float __ieee754_powf __P((float,float)); 168 extern float __ieee754_lgammaf_r __P((float,int *)); 169 extern float __ieee754_gammaf_r __P((float,int *)); 170 extern float __ieee754_log10f __P((float)); 171 extern float __ieee754_sinhf __P((float)); 172 extern float __ieee754_hypotf __P((float,float)); 173 extern float __ieee754_j0f __P((float)); 174 extern float __ieee754_j1f __P((float)); 175 extern float __ieee754_y0f __P((float)); 176 extern float __ieee754_y1f __P((float)); 177 extern float __ieee754_jnf __P((int,float)); 178 extern float __ieee754_ynf __P((int,float)); 179 extern float __ieee754_remainderf __P((float,float)); 180 extern __int32_t __ieee754_rem_pio2f __P((float,float*)); 181 #ifdef _SCALB_INT 182 extern float __ieee754_scalbf __P((float,int)); 183 #else 184 extern float __ieee754_scalbf __P((float,float)); 185 #endif 186 187 /* float versions of fdlibm kernel functions */ 188 extern float __kernel_sinf __P((float,float,int)); 189 extern float __kernel_cosf __P((float,float)); 190 extern float __kernel_tanf __P((float,float,int)); 191 extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const __uint8_t*)); 192 193 /* A union which permits us to convert between a float and a 32 bit 194 int. */ 195 196 typedef union 197 { 198 float value; 199 __uint32_t word; 200 } ieee_float_shape_type; 201 202 /* Get a 32 bit int from a float. */ 203 204 #define GET_FLOAT_WORD(i,d) \ 205 do { \ 206 ieee_float_shape_type gf_u; \ 207 gf_u.value = (d); \ 208 (i) = gf_u.word; \ 209 } while (0) 210 211 /* Set a float from a 32 bit int. */ 212 213 #define SET_FLOAT_WORD(d,i) \ 214 do { \ 215 ieee_float_shape_type sf_u; \ 216 sf_u.word = (i); \ 217 (d) = sf_u.value; \ 218 } while (0) 219 220 /* Macros to avoid undefined behaviour that can arise if the amount 221 of a shift is exactly equal to the size of the shifted operand. */ 222 223 #define SAFE_LEFT_SHIFT(op,amt) \ 224 (((amt) < 8 * sizeof(op)) ? ((op) << (amt)) : 0) 225 226 #define SAFE_RIGHT_SHIFT(op,amt) \ 227 (((amt) < 8 * sizeof(op)) ? ((op) >> (amt)) : 0) 228