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 * Float version of e_log2.c. See the latter for most comments. 14 */ 15 16 #include "math.h" 17 #include "math_private.h" 18 #include "k_logf.h" 19 20 static const float 21 two25 = 3.3554432000e+07, /* 0x4c000000 */ 22 ivln2hi = 1.4428710938e+00, /* 0x3fb8b000 */ 23 ivln2lo = -1.7605285393e-04; /* 0xb9389ad4 */ 24 25 static const float zero = 0.0; 26 static volatile float vzero = 0.0; 27 28 float 29 log2f(float x) 30 { 31 float f,hfsq,hi,lo,r,y; 32 int32_t i,k,hx; 33 34 GET_FLOAT_WORD(hx,x); 35 36 k=0; 37 if (hx < 0x00800000) { /* x < 2**-126 */ 38 if ((hx&0x7fffffff)==0) 39 return -two25/vzero; /* log(+-0)=-inf */ 40 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 41 k -= 25; x *= two25; /* subnormal number, scale up x */ 42 GET_FLOAT_WORD(hx,x); 43 } 44 if (hx >= 0x7f800000) return x+x; 45 if (hx == 0x3f800000) 46 return zero; /* log(1) = +0 */ 47 k += (hx>>23)-127; 48 hx &= 0x007fffff; 49 i = (hx+(0x4afb0d))&0x800000; 50 SET_FLOAT_WORD(x,hx|(i^0x3f800000)); /* normalize x or x/2 */ 51 k += (i>>23); 52 y = (float)k; 53 f = x - (float)1.0; 54 hfsq = (float)0.5*f*f; 55 r = k_log1pf(f); 56 57 /* 58 * We no longer need to avoid falling into the multi-precision 59 * calculations due to compiler bugs breaking Dekker's theorem. 60 * Keep avoiding this as an optimization. See e_log2.c for more 61 * details (some details are here only because the optimization 62 * is not yet available in double precision). 63 * 64 * Another compiler bug turned up. With gcc on i386, 65 * (ivln2lo + ivln2hi) would be evaluated in float precision 66 * despite runtime evaluations using double precision. So we 67 * must cast one of its terms to float_t. This makes the whole 68 * expression have type float_t, so return is forced to waste 69 * time clobbering its extra precision. 70 */ 71 if (sizeof(float_t) > sizeof(float)) 72 return (r - hfsq + f) * ((float_t)ivln2lo + ivln2hi) + y; 73 74 hi = f - hfsq; 75 GET_FLOAT_WORD(hx,hi); 76 SET_FLOAT_WORD(hi,hx&0xfffff000); 77 lo = (f - hi) - hfsq + r; 78 return (lo+hi)*ivln2lo + lo*ivln2hi + hi*ivln2hi + y; 79 } 80