11dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* s_log1pf.c -- float version of s_log1p.c. 21dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 31dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 41dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 51dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* 61dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 71dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 81dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 91dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Developed at SunPro, a Sun Microsystems, Inc. business. 101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Permission to use, copy, modify, and distribute this 111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * software is freely granted, provided that this notice 121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * is preserved. 131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 141dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 16a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <sys/cdefs.h> 17a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes__FBSDID("$FreeBSD$"); 18a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 19a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <float.h> 201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math.h" 221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math_private.h" 231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const float 251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectln2_hi = 6.9313812256e-01, /* 0x3f317180 */ 261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ 271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projecttwo25 = 3.355443200e+07, /* 0x4c000000 */ 281dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectLp1 = 6.6666668653e-01, /* 3F2AAAAB */ 291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectLp2 = 4.0000000596e-01, /* 3ECCCCCD */ 301dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectLp3 = 2.8571429849e-01, /* 3E924925 */ 311dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectLp4 = 2.2222198546e-01, /* 3E638E29 */ 321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectLp5 = 1.8183572590e-01, /* 3E3A3325 */ 331dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectLp6 = 1.5313838422e-01, /* 3E1CD04F */ 341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectLp7 = 1.4798198640e-01; /* 3E178897 */ 351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const float zero = 0.0; 3778419467a2f88744ae2445fca5eb442877ebb1b0Elliott Hughesstatic volatile float vzero = 0.0; 381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectfloat 401dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectlog1pf(float x) 411dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project{ 421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project float hfsq,f,c,s,z,R,u; 431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project int32_t k,hx,hu,ax; 441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 451dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_FLOAT_WORD(hx,x); 461dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project ax = hx&0x7fffffff; 471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 481dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project k = 1; 491dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if (hx < 0x3ed413d0) { /* 1+x < sqrt(2)+ */ 501dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ax>=0x3f800000) { /* x <= -1.0 */ 5178419467a2f88744ae2445fca5eb442877ebb1b0Elliott Hughes if(x==(float)-1.0) return -two25/vzero; /* log1p(-1)=+inf */ 521dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ 531dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 54a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if(ax<0x38000000) { /* |x| < 2**-15 */ 551dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(two25+x>zero /* raise inexact */ 56a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes &&ax<0x33800000) /* |x| < 2**-24 */ 571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return x; 581dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else 591dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return x - x*x*(float)0.5; 601dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 611dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hx>0||hx<=((int32_t)0xbe95f619)) { 621dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project k=0;f=x;hu=1;} /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ 631dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 641dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if (hx >= 0x7f800000) return x+x; 651dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(k!=0) { 661dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hx<0x5a000000) { 67a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes STRICT_ASSIGN(float,u,(float)1.0+x); 681dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_FLOAT_WORD(hu,u); 691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project k = (hu>>23)-127; 701dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* correction term */ 711dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0); 721dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project c /= u; 731dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } else { 741dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u = x; 751dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_FLOAT_WORD(hu,u); 761dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project k = (hu>>23)-127; 771dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project c = 0; 781dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 791dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project hu &= 0x007fffff; 801dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* 811dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * The approximation to sqrt(2) used in thresholds is not 821dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * critical. However, the ones used above must give less 831dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * strict bounds than the one here so that the k==0 case is 841dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * never reached from here, since here we have committed to 851dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * using the correction term but don't use it if k==0. 861dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 871dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hu<0x3504f4) { /* u < sqrt(2) */ 881dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */ 891dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } else { 901dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project k += 1; 911dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */ 921dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project hu = (0x00800000-hu)>>2; 931dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 941dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project f = u-(float)1.0; 951dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 961dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project hfsq=(float)0.5*f*f; 971dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hu==0) { /* |f| < 2**-20 */ 98a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if(f==zero) { 99a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if(k==0) { 100a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return zero; 101a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } else { 102a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes c += k*ln2_lo; 103a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return k*ln2_hi+c; 104a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } 105a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } 1061dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project R = hfsq*((float)1.0-(float)0.66666666666666666*f); 1071dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(k==0) return f-R; else 1081dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return k*ln2_hi-((R-(k*ln2_lo+c))-f); 1091dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s = f/((float)2.0+f); 1111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = s*s; 1121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); 1131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(k==0) return f-(hfsq-s*(hfsq+R)); else 1141dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); 1151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project} 116