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 #include <sys/cdefs.h> 13 //__FBSDID("$FreeBSD: src/lib/msun/src/e_log2f.c,v 1.5 2011/10/15 05:23:28 das Exp $"); 14 15 /* 16 * Float version of e_log2.c. See the latter for most comments. 17 */ 18 19 #include "openlibm.h" 20 #include "math_private.h" 21 #include "k_logf.h" 22 23 // VBS 24 #define float_t float 25 26 static const float 27 two25 = 3.3554432000e+07, /* 0x4c000000 */ 28 ivln2hi = 1.4428710938e+00, /* 0x3fb8b000 */ 29 ivln2lo = -1.7605285393e-04; /* 0xb9389ad4 */ 30 31 static const float zero = 0.0; 32 33 float 34 __ieee754_log2f(float x) 35 { 36 float f,hfsq,hi,lo,r,y; 37 int32_t i,k,hx; 38 39 GET_FLOAT_WORD(hx,x); 40 41 k=0; 42 if (hx < 0x00800000) { /* x < 2**-126 */ 43 if ((hx&0x7fffffff)==0) 44 return -two25/zero; /* log(+-0)=-inf */ 45 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 46 k -= 25; x *= two25; /* subnormal number, scale up x */ 47 GET_FLOAT_WORD(hx,x); 48 } 49 if (hx >= 0x7f800000) return x+x; 50 if (hx == 0x3f800000) 51 return zero; /* log(1) = +0 */ 52 k += (hx>>23)-127; 53 hx &= 0x007fffff; 54 i = (hx+(0x4afb0d))&0x800000; 55 SET_FLOAT_WORD(x,hx|(i^0x3f800000)); /* normalize x or x/2 */ 56 k += (i>>23); 57 y = (float)k; 58 f = x - (float)1.0; 59 hfsq = (float)0.5*f*f; 60 r = k_log1pf(f); 61 62 /* 63 * We no longer need to avoid falling into the multi-precision 64 * calculations due to compiler bugs breaking Dekker's theorem. 65 * Keep avoiding this as an optimization. See e_log2.c for more 66 * details (some details are here only because the optimization 67 * is not yet available in double precision). 68 * 69 * Another compiler bug turned up. With gcc on i386, 70 * (ivln2lo + ivln2hi) would be evaluated in float precision 71 * despite runtime evaluations using double precision. So we 72 * must cast one of its terms to float_t. This makes the whole 73 * expression have type float_t, so return is forced to waste 74 * time clobbering its extra precision. 75 */ 76 if (sizeof(float_t) > sizeof(float)) 77 return (r - hfsq + f) * ((float_t)ivln2lo + ivln2hi) + y; 78 79 hi = f - hfsq; 80 GET_FLOAT_WORD(hx,hi); 81 SET_FLOAT_WORD(hi,hx&0xfffff000); 82 lo = (f - hi) - hfsq + r; 83 return (lo+hi)*ivln2lo + lo*ivln2hi + hi*ivln2hi + y; 84 } 85