11dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* @(#)s_expm1.c 5.1 93/09/24 */ 21dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* 31dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 41dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 51dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 61dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Developed at SunPro, a Sun Microsystems, Inc. business. 71dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Permission to use, copy, modify, and distribute this 81dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * software is freely granted, provided that this notice 91dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * is preserved. 101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 13a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <sys/cdefs.h> 14a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes__FBSDID("$FreeBSD$"); 151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* expm1(x) 171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Returns exp(x)-1, the exponential of x minus 1. 181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Method 201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 1. Argument reduction: 211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Given x, find r and integer k such that 221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658 241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Here a correction term c will be computed to compensate 261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * the error in r when rounded to a floating-point number. 271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 281dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 2. Approximating expm1(r) by a special rational function on 291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * the interval [0,0.34658]: 301dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Since 311dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ... 321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * we define R1(r*r) by 331dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r) 341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * That is, 351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r) 361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r)) 371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ... 381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * We use a special Reme algorithm on [0,0.347] to generate 391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * a polynomial of degree 5 in r*r to approximate R1. The 401dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * maximum error of this polynomial approximation is bounded 411dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * by 2**-61. In other words, 421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5 431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * where Q1 = -1.6666666666666567384E-2, 441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Q2 = 3.9682539681370365873E-4, 451dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Q3 = -9.9206344733435987357E-6, 461dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Q4 = 2.5051361420808517002E-7, 471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Q5 = -6.2843505682382617102E-9; 48a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * z = r*r, 491dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * with error bounded by 501dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * | 5 | -61 511dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2 521dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * | | 531dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 541dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * expm1(r) = exp(r)-1 is then computed by the following 551dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * specific way which minimize the accumulation rounding error: 561dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 2 3 571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * r r [ 3 - (R1 + R1*r/2) ] 581dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * expm1(r) = r + --- + --- * [--------------------] 591dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 2 2 [ 6 - r*(3 - R1*r/2) ] 601dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 611dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * To compensate the error in the argument reduction, we use 621dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * expm1(r+c) = expm1(r) + c + expm1(r)*c 631dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ~ expm1(r) + c + r*c 641dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Thus c+r*c will be added in as the correction terms for 651dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * expm1(r+c). Now rearrange the term to avoid optimization 661dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * screw up: 671dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ( 2 2 ) 681dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r ) 691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- ) 701dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 ) 711dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ( ) 721dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 731dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * = r - E 741dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 3. Scale back to obtain expm1(x): 751dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * From step 1, we have 761dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * expm1(x) = either 2^k*[expm1(r)+1] - 1 771dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * = or 2^k*[expm1(r) + (1-2^-k)] 781dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 4. Implementation notes: 791dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * (A). To save one multiplication, we scale the coefficient Qi 801dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * to Qi*2^i, and replace z by (x^2)/2. 811dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * (B). To achieve maximum accuracy, we compute expm1(x) by 821dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf) 831dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * (ii) if k=0, return r-E 841dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * (iii) if k=-1, return 0.5*(r-E)-0.5 851dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E) 861dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * else return 1.0+2.0*(r-E); 871dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1) 881dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else 891dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * (vii) return 2^k(1-((E+2^-k)-r)) 901dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 911dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Special cases: 921dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * expm1(INF) is INF, expm1(NaN) is NaN; 931dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * expm1(-INF) is -1, and 941dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * for finite argument, only expm1(0)=0 is exact. 951dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 961dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Accuracy: 971dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * according to an error analysis, the error is always less than 981dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 1 ulp (unit in the last place). 991dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 1001dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Misc. info. 1011dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * For IEEE double 1021dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * if x > 7.09782712893383973096e+02 then expm1(x) overflow 1031dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 1041dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Constants: 1051dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * The hexadecimal values are the intended ones for the following 1061dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * constants. The decimal values may be used, provided that the 1071dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * compiler will convert from decimal to binary accurately enough 1081dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * to produce the hexadecimal values shown. 1091dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 1101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 111a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <float.h> 112a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 1131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math.h" 1141dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math_private.h" 1151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double 1171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectone = 1.0, 1181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projecttiny = 1.0e-300, 1191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projecto_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */ 1201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */ 1211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */ 1221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectinvln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */ 123a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes/* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */ 1241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectQ1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */ 1251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectQ2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */ 1261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectQ3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */ 1271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectQ4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ 1281dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectQ5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ 1291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 13078419467a2f88744ae2445fca5eb442877ebb1b0Elliott Hughesstatic volatile double huge = 1.0e+300; 13178419467a2f88744ae2445fca5eb442877ebb1b0Elliott Hughes 1321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectdouble 1331dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectexpm1(double x) 1341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project{ 135a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes double y,hi,lo,c,t,e,hxs,hfx,r1,twopk; 1361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project int32_t k,xsb; 1371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u_int32_t hx; 1381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_HIGH_WORD(hx,x); 1401dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project xsb = hx&0x80000000; /* sign bit of x */ 1411dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project hx &= 0x7fffffff; /* high word of |x| */ 1421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* filter out huge and non-finite argument */ 1441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */ 1451dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hx >= 0x40862E42) { /* if |x|>=709.78... */ 1461dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hx>=0x7ff00000) { 1471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u_int32_t low; 1481dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_LOW_WORD(low,x); 1491dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(((hx&0xfffff)|low)!=0) 1501dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return x+x; /* NaN */ 1511dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ 1521dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1531dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(x > o_threshold) return huge*huge; /* overflow */ 1541dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1551dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */ 1561dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(x+tiny<0.0) /* raise inexact */ 1571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return tiny-one; /* return -1 */ 1581dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1591dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1601dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1611dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* argument reduction */ 1621dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ 1631dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ 1641dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(xsb==0) 1651dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project {hi = x - ln2_hi; lo = ln2_lo; k = 1;} 1661dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else 1671dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} 1681dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } else { 1691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project k = invln2*x+((xsb==0)?0.5:-0.5); 1701dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t = k; 1711dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ 1721dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project lo = t*ln2_lo; 1731dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 174a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes STRICT_ASSIGN(double, x, hi - lo); 1751dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project c = (hi-x)-lo; 1761dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1771dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */ 1781dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t = huge+x; /* return x with inexact flags when x!=0 */ 1791dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return x - (t-(huge+x)); 1801dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1811dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else k = 0; 1821dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1831dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* x is now in primary range */ 1841dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project hfx = 0.5*x; 1851dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project hxs = x*hfx; 1861dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); 1871dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t = 3.0-r1*hfx; 1881dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project e = hxs*((r1-t)/(6.0 - x*t)); 1891dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(k==0) return x - (x*e-hxs); /* c is 0 */ 1901dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else { 191a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes INSERT_WORDS(twopk,0x3ff00000+(k<<20),0); /* 2^k */ 1921dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project e = (x*(e-c)-c); 1931dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project e -= hxs; 1941dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(k== -1) return 0.5*(x-e)-0.5; 195a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if(k==1) { 1961dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(x < -0.25) return -2.0*(e-(x+0.5)); 1971dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else return one+2.0*(x-e); 198a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } 1991dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ 2001dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project y = one-(e-x); 201a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if (k == 1024) y = y*2.0*0x1p1023; 202a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes else y = y*twopk; 2031dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return y-one; 2041dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 2051dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t = one; 2061dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(k<20) { 2071dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */ 2081dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project y = t-(e-x); 209a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes y = y*twopk; 2101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } else { 2111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_HIGH_WORD(t,((0x3ff-k)<<20)); /* 2^-k */ 2121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project y = x-(e+t); 2131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project y += one; 214a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes y = y*twopk; 2151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 2161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 2171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return y; 2181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project} 21978419467a2f88744ae2445fca5eb442877ebb1b0Elliott Hughes 22078419467a2f88744ae2445fca5eb442877ebb1b0Elliott Hughes#if (LDBL_MANT_DIG == 53) 22178419467a2f88744ae2445fca5eb442877ebb1b0Elliott Hughes__weak_reference(expm1, expm1l); 22278419467a2f88744ae2445fca5eb442877ebb1b0Elliott Hughes#endif 223