diff options
Diffstat (limited to 'src/lib/math/log.go')
| -rw-r--r-- | src/lib/math/log.go | 37 |
1 files changed, 17 insertions, 20 deletions
diff --git a/src/lib/math/log.go b/src/lib/math/log.go index c0cfebf8b..9c54858b4 100644 --- a/src/lib/math/log.go +++ b/src/lib/math/log.go @@ -4,6 +4,8 @@ package math +import "math" + // The original C code, the long comment, and the constants // below are from FreeBSD's /usr/src/lib/msun/src/e_log.c // and came with this notice. The go code is a simpler @@ -35,11 +37,11 @@ package math // of this polynomial approximation is bounded by 2**-58.45. In // other words, // 2 4 6 8 10 12 14 -// R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s -// (the values of Lg1 to Lg7 are listed in the program) +// R(z) ~ lg1*s +lg2*s +lg3*s +lg4*s +lg5*s +lg6*s +lg7*s +// (the values of lg1 to lg7 are listed in the program) // and // | 2 14 | -58.45 -// | Lg1*s +...+Lg7*s - R(z) | <= 2 +// | lg1*s +...+lg7*s - R(z) | <= 2 // | | // Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. // In order to guarantee error in log below 1ulp, we compute log @@ -69,20 +71,15 @@ package math // to produce the hexadecimal values shown. const ( - Ln2Hi = 6.93147180369123816490e-01; /* 3fe62e42 fee00000 */ - Ln2Lo = 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 */ - - Two54 = 1<<54; // 2^54 - TwoM20 = 1.0/(1<<20); // 2^-20 - TwoM1022 = 2.2250738585072014e-308; // 2^-1022 - Sqrt2 = 1.41421356237309504880168872420969808; + ln2Hi = 6.93147180369123816490e-01; /* 3fe62e42 fee00000 */ + ln2Lo = 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 */ ) export func Log(x float64) float64 { @@ -109,11 +106,11 @@ export func Log(x float64) float64 { s := f/(2+f); s2 := s*s; s4 := s2*s2; - t1 := s2*(Lg1 + s4*(Lg3 + s4*(Lg5 + s4*Lg7))); - t2 := s4*(Lg2 + s4*(Lg4 + s4*Lg6)); + t1 := s2*(lg1 + s4*(lg3 + s4*(lg5 + s4*lg7))); + t2 := s4*(lg2 + s4*(lg4 + s4*lg6)); R := t1 + t2; hfsq := 0.5*f*f; - return k*Ln2Hi - ((hfsq-(s*(hfsq+R)+k*Ln2Lo)) - f); + return k*ln2Hi - ((hfsq-(s*(hfsq+R)+k*ln2Lo)) - f); } const |