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redo and clean up math.

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R=r
DELTA=243  (60 added, 72 deleted, 111 changed)
OCL=22909
CL=22912
This commit is contained in:
Russ Cox 2009-01-15 19:11:32 -08:00
parent 293c8f8c65
commit 2c8d9a5619
12 changed files with 170 additions and 182 deletions
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53
src/lib/math/log.go
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@ -37,11 +37,11 @@ import "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) ~ L1*s +L2*s +L3*s +L4*s +L5*s +L6*s +L7*s
// (the values of L1 to L7 are listed in the program)
// and
// | 2 14 | -58.45
// | lg1*s +...+lg7*s - R(z) | <= 2
// | L1*s +...+L7*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
@ -49,11 +49,11 @@ import "math"
// log(1+f) = f - s*(f - R) (if f is not too large)
// log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
//
// 3. Finally, log(x) = k*ln2 + log(1+f).
// = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
// Here ln2 is split into two floating point number:
// ln2_hi + ln2_lo,
// where n*ln2_hi is always exact for |n| < 2000.
// 3. Finally, log(x) = k*Ln2 + log(1+f).
// = k*Ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*Ln2_lo)))
// Here Ln2 is split into two floating point number:
// Ln2_hi + Ln2_lo,
// where n*Ln2_hi is always exact for |n| < 2000.
//
// Special cases:
// log(x) is NaN with signal if x < 0 (including -INF) ;
@ -70,19 +70,19 @@ import "math"
// compiler will convert from decimal to binary accurately enough
// 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 */
)
export func Log(x float64) float64 {
const (
Ln2Hi = 6.93147180369123816490e-01; /* 3fe62e42 fee00000 */
Ln2Lo = 1.90821492927058770002e-10; /* 3dea39ef 35793c76 */
L1 = 6.666666666666735130e-01; /* 3FE55555 55555593 */
L2 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */
L3 = 2.857142874366239149e-01; /* 3FD24924 94229359 */
L4 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */
L5 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */
L6 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */
L7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
)
// special cases
switch {
case sys.isNaN(x) || sys.isInf(x, 1):
@ -106,23 +106,18 @@ 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*(L1 + s4*(L3 + s4*(L5 + s4*L7)));
t2 := s4*(L2 + s4*(L4 + s4*L6));
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
(
ln10u1 = .4342944819032518276511;
)
export func Log10(arg float64) float64 {
if arg <= 0 {
return sys.NaN();
}
return Log(arg) * ln10u1;
return Log(arg) * (1/Ln10);
}