diff options
Diffstat (limited to 'sysdeps/ieee754/dbl-64/s_log1p.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/s_log1p.c | 167 |
1 files changed, 96 insertions, 71 deletions
diff --git a/sysdeps/ieee754/dbl-64/s_log1p.c b/sysdeps/ieee754/dbl-64/s_log1p.c index 0c6f76371a..ea1dc6ca76 100644 --- a/sysdeps/ieee754/dbl-64/s_log1p.c +++ b/sysdeps/ieee754/dbl-64/s_log1p.c @@ -11,7 +11,7 @@ */ /* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, for performance improvement on pipelined processors. -*/ + */ /* double log1p(double x) * @@ -82,87 +82,112 @@ #include <math_private.h> static const double -ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ -ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ -two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ -Lp[] = {0.0, 6.666666666666735130e-01, /* 3FE55555 55555593 */ - 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ - 2.857142874366239149e-01, /* 3FD24924 94229359 */ - 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ - 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ - 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ - 1.479819860511658591e-01}; /* 3FC2F112 DF3E5244 */ + ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ + ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ + two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ + Lp[] = { 0.0, 6.666666666666735130e-01, /* 3FE55555 55555593 */ + 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ + 2.857142874366239149e-01, /* 3FD24924 94229359 */ + 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ + 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ + 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ + 1.479819860511658591e-01 }; /* 3FC2F112 DF3E5244 */ static const double zero = 0.0; double -__log1p(double x) +__log1p (double x) { - double hfsq,f,c,s,z,R,u,z2,z4,z6,R1,R2,R3,R4; - int32_t k,hx,hu,ax; + double hfsq, f, c, s, z, R, u, z2, z4, z6, R1, R2, R3, R4; + int32_t k, hx, hu, ax; - GET_HIGH_WORD(hx,x); - ax = hx&0x7fffffff; + GET_HIGH_WORD (hx, x); + ax = hx & 0x7fffffff; - k = 1; - if (hx < 0x3FDA827A) { /* x < 0.41422 */ - if(__builtin_expect(ax>=0x3ff00000, 0)) { /* x <= -1.0 */ - if(x==-1.0) return -two54/(x-x);/* log1p(-1)=+inf */ - else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ - } - if(__builtin_expect(ax<0x3e200000, 0)) { /* |x| < 2**-29 */ - math_force_eval(two54+x); /* raise inexact */ - if (ax<0x3c900000) /* |x| < 2**-54 */ - return x; - else - return x - x*x*0.5; - } - if(hx>0||hx<=((int32_t)0xbfd2bec3)) { - k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */ + k = 1; + if (hx < 0x3FDA827A) /* x < 0.41422 */ + { + if (__builtin_expect (ax >= 0x3ff00000, 0)) /* x <= -1.0 */ + { + if (x == -1.0) + return -two54 / (x - x); /* log1p(-1)=+inf */ + else + return (x - x) / (x - x); /* log1p(x<-1)=NaN */ } - else if (__builtin_expect(hx >= 0x7ff00000, 0)) return x+x; - if(k!=0) { - if(hx<0x43400000) { - u = 1.0+x; - GET_HIGH_WORD(hu,u); - k = (hu>>20)-1023; - c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */ - c /= u; - } else { - u = x; - GET_HIGH_WORD(hu,u); - k = (hu>>20)-1023; - c = 0; - } - hu &= 0x000fffff; - if(hu<0x6a09e) { - SET_HIGH_WORD(u,hu|0x3ff00000); /* normalize u */ - } else { - k += 1; - SET_HIGH_WORD(u,hu|0x3fe00000); /* normalize u/2 */ - hu = (0x00100000-hu)>>2; - } - f = u-1.0; + if (__builtin_expect (ax < 0x3e200000, 0)) /* |x| < 2**-29 */ + { + math_force_eval (two54 + x); /* raise inexact */ + if (ax < 0x3c900000) /* |x| < 2**-54 */ + return x; + else + return x - x * x * 0.5; + } + if (hx > 0 || hx <= ((int32_t) 0xbfd2bec3)) + { + k = 0; f = x; hu = 1; + } /* -0.2929<x<0.41422 */ + } + else if (__builtin_expect (hx >= 0x7ff00000, 0)) + return x + x; + if (k != 0) + { + if (hx < 0x43400000) + { + u = 1.0 + x; + GET_HIGH_WORD (hu, u); + k = (hu >> 20) - 1023; + c = (k > 0) ? 1.0 - (u - x) : x - (u - 1.0); /* correction term */ + c /= u; + } + else + { + u = x; + GET_HIGH_WORD (hu, u); + k = (hu >> 20) - 1023; + c = 0; + } + hu &= 0x000fffff; + if (hu < 0x6a09e) + { + SET_HIGH_WORD (u, hu | 0x3ff00000); /* normalize u */ + } + else + { + k += 1; + SET_HIGH_WORD (u, hu | 0x3fe00000); /* normalize u/2 */ + hu = (0x00100000 - hu) >> 2; } - hfsq=0.5*f*f; - if(hu==0) { /* |f| < 2**-20 */ - if(f==zero) { - if(k==0) return zero; - else {c += k*ln2_lo; return k*ln2_hi+c;} + f = u - 1.0; + } + hfsq = 0.5 * f * f; + if (hu == 0) /* |f| < 2**-20 */ + { + if (f == zero) + { + if (k == 0) + return zero; + else + { + c += k * ln2_lo; return k * ln2_hi + c; } - R = hfsq*(1.0-0.66666666666666666*f); - if(k==0) return f-R; else - return k*ln2_hi-((R-(k*ln2_lo+c))-f); } - s = f/(2.0+f); - z = s*s; - R1 = z*Lp[1]; z2=z*z; - R2 = Lp[2]+z*Lp[3]; z4=z2*z2; - R3 = Lp[4]+z*Lp[5]; z6=z4*z2; - R4 = Lp[6]+z*Lp[7]; - R = R1 + z2*R2 + z4*R3 + z6*R4; - if(k==0) return f-(hfsq-s*(hfsq+R)); else - return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); + R = hfsq * (1.0 - 0.66666666666666666 * f); + if (k == 0) + return f - R; + else + return k * ln2_hi - ((R - (k * ln2_lo + c)) - f); + } + s = f / (2.0 + f); + z = s * s; + R1 = z * Lp[1]; z2 = z * z; + R2 = Lp[2] + z * Lp[3]; z4 = z2 * z2; + R3 = Lp[4] + z * Lp[5]; z6 = z4 * z2; + R4 = Lp[6] + z * Lp[7]; + R = R1 + z2 * R2 + z4 * R3 + z6 * R4; + if (k == 0) + return f - (hfsq - s * (hfsq + R)); + else + return k * ln2_hi - ((hfsq - (s * (hfsq + R) + (k * ln2_lo + c))) - f); } weak_alias (__log1p, log1p) #ifdef NO_LONG_DOUBLE |