| #include "SDL_internal.h" |
| /* |
| * ==================================================== |
| * 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. |
| * ==================================================== |
| */ |
| |
| #if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */ |
| /* C4723: potential divide by zero. */ |
| #pragma warning ( disable : 4723 ) |
| #endif |
| |
| /* __ieee754_log10(x) |
| * Return the base 10 logarithm of x |
| * |
| * Method : |
| * Let log10_2hi = leading 40 bits of log10(2) and |
| * log10_2lo = log10(2) - log10_2hi, |
| * ivln10 = 1/log(10) rounded. |
| * Then |
| * n = ilogb(x), |
| * if(n<0) n = n+1; |
| * x = scalbn(x,-n); |
| * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) |
| * |
| * Note 1: |
| * To guarantee log10(10**n)=n, where 10**n is normal, the rounding |
| * mode must set to Round-to-Nearest. |
| * Note 2: |
| * [1/log(10)] rounded to 53 bits has error .198 ulps; |
| * log10 is monotonic at all binary break points. |
| * |
| * Special cases: |
| * log10(x) is NaN with signal if x < 0; |
| * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; |
| * log10(NaN) is that NaN with no signal; |
| * log10(10**N) = N for N=0,1,...,22. |
| * |
| * Constants: |
| * The hexadecimal values are the intended ones for the following constants. |
| * The decimal values may be used, provided that the compiler will convert |
| * from decimal to binary accurately enough to produce the hexadecimal values |
| * shown. |
| */ |
| |
| #include "math_libm.h" |
| #include "math_private.h" |
| |
| static const double |
| two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ |
| ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ |
| log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ |
| log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ |
| |
| static const double zero = 0.0; |
| |
| double attribute_hidden __ieee754_log10(double x) |
| { |
| double y,z; |
| int32_t i,k,hx; |
| u_int32_t lx; |
| |
| EXTRACT_WORDS(hx,lx,x); |
| |
| k=0; |
| if (hx < 0x00100000) { /* x < 2**-1022 */ |
| if (((hx&0x7fffffff)|lx)==0) |
| return -two54/zero; /* log(+-0)=-inf */ |
| if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ |
| k -= 54; x *= two54; /* subnormal number, scale up x */ |
| GET_HIGH_WORD(hx,x); |
| } |
| if (hx >= 0x7ff00000) return x+x; |
| k += (hx>>20)-1023; |
| i = ((u_int32_t)k&0x80000000)>>31; |
| hx = (hx&0x000fffff)|((0x3ff-i)<<20); |
| y = (double)(k+i); |
| SET_HIGH_WORD(x,hx); |
| z = y*log10_2lo + ivln10*__ieee754_log(x); |
| return z+y*log10_2hi; |
| } |
| |
| /* |
| * wrapper log10(X) |
| */ |
| #ifndef _IEEE_LIBM |
| double log10(double x) |
| { |
| double z = __ieee754_log10(x); |
| if (_LIB_VERSION == _IEEE_ || isnan(x)) |
| return z; |
| if (x <= 0.0) { |
| if(x == 0.0) |
| return __kernel_standard(x, x, 18); /* log10(0) */ |
| return __kernel_standard(x, x, 19); /* log10(x<0) */ |
| } |
| return z; |
| } |
| #else |
| strong_alias(__ieee754_log10, log10) |
| #endif |
| libm_hidden_def(log10) |