| 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;
|
| }
|
|
|