1b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* @(#)s_expm1.c 1.5 04/04/22 */ 3b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* 4b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ==================================================== 5b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. 6b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 7b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Permission to use, copy, modify, and distribute this 8b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * software is freely granted, provided that this notice 9b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * is preserved. 10b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ==================================================== 11b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 12b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 13b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* ieee_expm1(x) 14b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Returns ieee_exp(x)-1, the exponential of x minus 1. 15b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 16b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Method 17b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 1. Argument reduction: 18b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Given x, find r and integer k such that 19b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 20b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658 21b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 22b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Here a correction term c will be computed to compensate 23b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * the error in r when rounded to a floating-point number. 24b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 25b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 2. Approximating ieee_expm1(r) by a special rational function on 26b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * the interval [0,0.34658]: 27b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Since 28b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * r*(ieee_exp(r)+1)/(ieee_exp(r)-1) = 2+ r^2/6 - r^4/360 + ... 29b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * we define R1(r*r) by 30b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * r*(ieee_exp(r)+1)/(ieee_exp(r)-1) = 2+ r^2/6 * R1(r*r) 31b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * That is, 32b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * R1(r**2) = 6/r *((ieee_exp(r)+1)/(ieee_exp(r)-1) - 2/r) 33b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * = 6/r * ( 1 + 2.0*(1/(ieee_exp(r)-1) - 1/r)) 34b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ... 35b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * We use a special Remes algorithm on [0,0.347] to generate 36b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * a polynomial of degree 5 in r*r to approximate R1. The 37b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * maximum error of this polynomial approximation is bounded 38b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * by 2**-61. In other words, 39b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5 40b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * where Q1 = -1.6666666666666567384E-2, 41b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Q2 = 3.9682539681370365873E-4, 42b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Q3 = -9.9206344733435987357E-6, 43b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Q4 = 2.5051361420808517002E-7, 44b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Q5 = -6.2843505682382617102E-9; 45b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (where z=r*r, and the values of Q1 to Q5 are listed below) 46b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * with error bounded by 47b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * | 5 | -61 48b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2 49b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * | | 50b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 51b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * expm1(r) = ieee_exp(r)-1 is then computed by the following 52b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * specific way which minimize the accumulation rounding error: 53b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 2 3 54b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * r r [ 3 - (R1 + R1*r/2) ] 55b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ieee_expm1(r) = r + --- + --- * [--------------------] 56b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 2 2 [ 6 - r*(3 - R1*r/2) ] 57b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 58b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * To compensate the error in the argument reduction, we use 59b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * expm1(r+c) = ieee_expm1(r) + c + ieee_expm1(r)*c 60b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ~ ieee_expm1(r) + c + r*c 61b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Thus c+r*c will be added in as the correction terms for 62b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * expm1(r+c). Now rearrange the term to avoid optimization 63b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * screw up: 64b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ( 2 2 ) 65b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r ) 66b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ieee_expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- ) 67b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 ) 68b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ( ) 69b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 70b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * = r - E 71b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 3. Scale back to obtain ieee_expm1(x): 72b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * From step 1, we have 73b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ieee_expm1(x) = either 2^k*[expm1(r)+1] - 1 74b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * = or 2^k*[expm1(r) + (1-2^-k)] 75b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 4. Implementation notes: 76b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (A). To save one multiplication, we scale the coefficient Qi 77b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * to Qi*2^i, and replace z by (x^2)/2. 78b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (B). To achieve maximum accuracy, we compute ieee_expm1(x) by 79b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf) 80b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (ii) if k=0, return r-E 81b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (iii) if k=-1, return 0.5*(r-E)-0.5 82b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E) 83b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * else return 1.0+2.0*(r-E); 84b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or ieee_exp(x)-1) 85b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else 86b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (vii) return 2^k(1-((E+2^-k)-r)) 87b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 88b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Special cases: 89b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * expm1(INF) is INF, ieee_expm1(NaN) is NaN; 90b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * expm1(-INF) is -1, and 91b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * for finite argument, only ieee_expm1(0)=0 is exact. 92b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 93b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Accuracy: 94b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * according to an error analysis, the error is always less than 95b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 1 ulp (unit in the last place). 96b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 97b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Misc. info. 98b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * For IEEE double 99b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * if x > 7.09782712893383973096e+02 then ieee_expm1(x) overflow 100b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 101b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Constants: 102b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * The hexadecimal values are the intended ones for the following 103b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * constants. The decimal values may be used, provided that the 104b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * compiler will convert from decimal to binary accurately enough 105b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * to produce the hexadecimal values shown. 106b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 107b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 108b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#include "fdlibm.h" 109b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 110b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 111b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double 112b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 113b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double 114b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 115b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectone = 1.0, 116b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecthuge = 1.0e+300, 117b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecttiny = 1.0e-300, 118b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecto_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */ 119b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */ 120b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */ 121b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectinvln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */ 122b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* scaled coefficients related to expm1 */ 123b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectQ1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */ 124b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectQ2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */ 125b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectQ3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */ 126b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectQ4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ 127b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectQ5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ 128b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 129b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 130b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double ieee_expm1(double x) 131b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 132b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double ieee_expm1(x) 133b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double x; 134b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 135b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project{ 136b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double y,hi,lo,c,t,e,hxs,hfx,r1; 137b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int k,xsb; 138b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project unsigned hx; 139b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 140b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project hx = __HI(x); /* high word of x */ 141b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project xsb = hx&0x80000000; /* sign bit of x */ 142b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(xsb==0) y=x; else y= -x; /* y = |x| */ 143b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project hx &= 0x7fffffff; /* high word of |x| */ 144b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 145b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* filter out huge and non-finite argument */ 146b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */ 147b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(hx >= 0x40862E42) { /* if |x|>=709.78... */ 148b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(hx>=0x7ff00000) { 149b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(((hx&0xfffff)|__LO(x))!=0) 150b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return x+x; /* NaN */ 151b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else return (xsb==0)? x:-1.0;/* ieee_exp(+-inf)={inf,-1} */ 152b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 153b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(x > o_threshold) return huge*huge; /* overflow */ 154b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 155b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */ 156b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(x+tiny<0.0) /* raise inexact */ 157b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return tiny-one; /* return -1 */ 158b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 159b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 160b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 161b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* argument reduction */ 162b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ 163b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ 164b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(xsb==0) 165b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project {hi = x - ln2_hi; lo = ln2_lo; k = 1;} 166b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else 167b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} 168b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else { 169b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project k = invln2*x+((xsb==0)?0.5:-0.5); 170b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project t = k; 171b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ 172b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project lo = t*ln2_lo; 173b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 174b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project x = hi - lo; 175b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project c = (hi-x)-lo; 176b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 177b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */ 178b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project // t = huge+x; /* return x with inexact flags when x!=0 */ 179b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project // return x - (t-(huge+x)); 180b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return x; // inexact flag is not set, but Java ignors this flag anyway 181b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 182b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else k = 0; 183b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 184b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* x is now in primary range */ 185b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project hfx = 0.5*x; 186b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project hxs = x*hfx; 187b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); 188b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project t = 3.0-r1*hfx; 189b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project e = hxs*((r1-t)/(6.0 - x*t)); 190b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(k==0) return x - (x*e-hxs); /* c is 0 */ 191b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else { 192b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project e = (x*(e-c)-c); 193b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project e -= hxs; 194b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(k== -1) return 0.5*(x-e)-0.5; 195b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(k==1) 196b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(x < -0.25) return -2.0*(e-(x+0.5)); 197b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else return one+2.0*(x-e); 198b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if (k <= -2 || k>56) { /* suffice to return ieee_exp(x)-1 */ 199b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y = one-(e-x); 200b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(y) += (k<<20); /* add k to y's exponent */ 201b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return y-one; 202b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 203b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project t = one; 204b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(k<20) { 205b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(t) = 0x3ff00000 - (0x200000>>k); /* t=1-2^-k */ 206b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y = t-(e-x); 207b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(y) += (k<<20); /* add k to y's exponent */ 208b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else { 209b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(t) = ((0x3ff-k)<<20); /* 2^-k */ 210b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y = x-(e+t); 211b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y += one; 212b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(y) += (k<<20); /* add k to y's exponent */ 213b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 214b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 215b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return y; 216b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project} 217