| Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 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 | } |