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