Index: fusl/src/math/log1p.c |
diff --git a/fusl/src/math/log1p.c b/fusl/src/math/log1p.c |
index 0097134940378136f861708e6b952a8d67f76b3c..0fac0ca24503d4eb29d7e8c0d324339ba412acc7 100644 |
--- a/fusl/src/math/log1p.c |
+++ b/fusl/src/math/log1p.c |
@@ -55,68 +55,69 @@ |
#include "libm.h" |
-static const double |
-ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ |
-ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ |
-Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ |
-Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ |
-Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ |
-Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ |
-Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ |
-Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ |
-Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ |
+static const double ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ |
+ ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ |
+ Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ |
+ Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ |
+ Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ |
+ Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ |
+ Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ |
+ Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ |
+ Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ |
-double log1p(double x) |
-{ |
- union {double f; uint64_t i;} u = {x}; |
- double_t hfsq,f,c,s,z,R,w,t1,t2,dk; |
- uint32_t hx,hu; |
- int k; |
+double log1p(double x) { |
+ union { |
+ double f; |
+ uint64_t i; |
+ } u = {x}; |
+ double_t hfsq, f, c, s, z, R, w, t1, t2, dk; |
+ uint32_t hx, hu; |
+ int k; |
- hx = u.i>>32; |
- k = 1; |
- if (hx < 0x3fda827a || hx>>31) { /* 1+x < sqrt(2)+ */ |
- if (hx >= 0xbff00000) { /* x <= -1.0 */ |
- if (x == -1) |
- return x/0.0; /* log1p(-1) = -inf */ |
- return (x-x)/0.0; /* log1p(x<-1) = NaN */ |
- } |
- if (hx<<1 < 0x3ca00000<<1) { /* |x| < 2**-53 */ |
- /* underflow if subnormal */ |
- if ((hx&0x7ff00000) == 0) |
- FORCE_EVAL((float)x); |
- return x; |
- } |
- if (hx <= 0xbfd2bec4) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ |
- k = 0; |
- c = 0; |
- f = x; |
- } |
- } else if (hx >= 0x7ff00000) |
- return x; |
- if (k) { |
- u.f = 1 + x; |
- hu = u.i>>32; |
- hu += 0x3ff00000 - 0x3fe6a09e; |
- k = (int)(hu>>20) - 0x3ff; |
- /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */ |
- if (k < 54) { |
- c = k >= 2 ? 1-(u.f-x) : x-(u.f-1); |
- c /= u.f; |
- } else |
- c = 0; |
- /* reduce u into [sqrt(2)/2, sqrt(2)] */ |
- hu = (hu&0x000fffff) + 0x3fe6a09e; |
- u.i = (uint64_t)hu<<32 | (u.i&0xffffffff); |
- f = u.f - 1; |
- } |
- hfsq = 0.5*f*f; |
- s = f/(2.0+f); |
- z = s*s; |
- w = z*z; |
- t1 = w*(Lg2+w*(Lg4+w*Lg6)); |
- t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); |
- R = t2 + t1; |
- dk = k; |
- return s*(hfsq+R) + (dk*ln2_lo+c) - hfsq + f + dk*ln2_hi; |
+ hx = u.i >> 32; |
+ k = 1; |
+ if (hx < 0x3fda827a || hx >> 31) { /* 1+x < sqrt(2)+ */ |
+ if (hx >= 0xbff00000) { /* x <= -1.0 */ |
+ if (x == -1) |
+ return x / 0.0; /* log1p(-1) = -inf */ |
+ return (x - x) / 0.0; /* log1p(x<-1) = NaN */ |
+ } |
+ if (hx << 1 < 0x3ca00000 << 1) { /* |x| < 2**-53 */ |
+ /* underflow if subnormal */ |
+ if ((hx & 0x7ff00000) == 0) |
+ FORCE_EVAL((float)x); |
+ return x; |
+ } |
+ if (hx <= 0xbfd2bec4) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ |
+ k = 0; |
+ c = 0; |
+ f = x; |
+ } |
+ } else if (hx >= 0x7ff00000) |
+ return x; |
+ if (k) { |
+ u.f = 1 + x; |
+ hu = u.i >> 32; |
+ hu += 0x3ff00000 - 0x3fe6a09e; |
+ k = (int)(hu >> 20) - 0x3ff; |
+ /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */ |
+ if (k < 54) { |
+ c = k >= 2 ? 1 - (u.f - x) : x - (u.f - 1); |
+ c /= u.f; |
+ } else |
+ c = 0; |
+ /* reduce u into [sqrt(2)/2, sqrt(2)] */ |
+ hu = (hu & 0x000fffff) + 0x3fe6a09e; |
+ u.i = (uint64_t)hu << 32 | (u.i & 0xffffffff); |
+ f = u.f - 1; |
+ } |
+ hfsq = 0.5 * f * f; |
+ s = f / (2.0 + f); |
+ z = s * s; |
+ w = z * z; |
+ t1 = w * (Lg2 + w * (Lg4 + w * Lg6)); |
+ t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7))); |
+ R = t2 + t1; |
+ dk = k; |
+ return s * (hfsq + R) + (dk * ln2_lo + c) - hfsq + f + dk * ln2_hi; |
} |