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Re-style fdlibm to conform to jerry guidelines

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* First re-style was done automatically by indent to minimize the
  chance of errors during rewrite.

* Manual changes were applied to non-critical places only (comments
  and spaces):
  * Replaced all tabs with spaces.
  * Fixed tab stops in formulae in function comments.
    (Note: ASCII art for math formulae (especially for super- and
    subscripts) is a terrible idea.)
  * Unified the style of function comments.
  * Moved some in-code comments to their right places, which indent
    couldn't handle.
  * Added spaces to formulae of in-code comments to make them more
    readable.
  * Added braces mandated by jerry style guidelines.
  * Added parentheses to multiline #ifdef.

JerryScript-DCO-1.0-Signed-off-by: Akos Kiss akiss@inf.u-szeged.hu
This commit is contained in:
Akos Kiss
2016-03-17 10:42:00 +01:00
parent b39474c746
commit 8dd5186a0d
19 changed files with 2726 additions and 1887 deletions
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third-party/fdlibm/s_log.c
Vendored
+133 -89
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@@ -6,7 +6,7 @@
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
@@ -16,44 +16,44 @@
*
* Method :
* 1. Argument Reduction: find k and f such that
* x = 2^k * (1+f),
* where sqrt(2)/2 < 1+f < sqrt(2) .
* x = 2^k * (1+f),
* where sqrt(2)/2 < 1+f < sqrt(2) .
*
* 2. Approximation of log(1+f).
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
* = 2s + s*R
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
* = 2s + s*R
* We use a special Reme algorithm on [0,0.1716] to generate
* a polynomial of degree 14 to approximate R The maximum error
* 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)
* and
* | 2 14 | -58.45
* | 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
* by
* 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.
* a polynomial of degree 14 to approximate R The maximum error
* 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)
* and
* | 2 14 | -58.45
* | 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
* by
* 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.
*
* Special cases:
* log(x) is NaN with signal if x < 0 (including -INF) ;
* log(+INF) is +INF; log(0) is -INF with signal;
* log(NaN) is that NaN with no signal.
* log(x) is NaN with signal if x < 0 (including -INF) ;
* log(+INF) is +INF; log(0) is -INF with signal;
* log(NaN) is that NaN with no signal.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* Constants:
* The hexadecimal values are the intended ones for the following
@@ -65,64 +65,108 @@
#include "fdlibm.h"
#define zero 0.0
#define ln2_hi 6.93147180369123816490e-01 /* 3fe62e42 fee00000 */
#define ln2_lo 1.90821492927058770002e-10 /* 3dea39ef 35793c76 */
#define two54 1.80143985094819840000e+16 /* 43500000 00000000 */
#define Lg1 6.666666666666735130e-01 /* 3FE55555 55555593 */
#define Lg2 3.999999999940941908e-01 /* 3FD99999 9997FA04 */
#define Lg3 2.857142874366239149e-01 /* 3FD24924 94229359 */
#define Lg4 2.222219843214978396e-01 /* 3FCC71C5 1D8E78AF */
#define Lg5 1.818357216161805012e-01 /* 3FC74664 96CB03DE */
#define Lg6 1.531383769920937332e-01 /* 3FC39A09 D078C69F */
#define Lg7 1.479819860511658591e-01 /* 3FC2F112 DF3E5244 */
#define ln2_hi 6.93147180369123816490e-01 /* 3fe62e42 fee00000 */
#define ln2_lo 1.90821492927058770002e-10 /* 3dea39ef 35793c76 */
#define two54 1.80143985094819840000e+16 /* 43500000 00000000 */
#define Lg1 6.666666666666735130e-01 /* 3FE55555 55555593 */
#define Lg2 3.999999999940941908e-01 /* 3FD99999 9997FA04 */
#define Lg3 2.857142874366239149e-01 /* 3FD24924 94229359 */
#define Lg4 2.222219843214978396e-01 /* 3FCC71C5 1D8E78AF */
#define Lg5 1.818357216161805012e-01 /* 3FC74664 96CB03DE */
#define Lg6 1.531383769920937332e-01 /* 3FC39A09 D078C69F */
#define Lg7 1.479819860511658591e-01 /* 3FC2F112 DF3E5244 */
double log(double x)
double
log (double x)
{
double hfsq,f,s,z,R,w,t1,t2,dk;
int k,hx,i,j;
unsigned lx;
double hfsq, f, s, z, R, w, t1, t2, dk;
int k, hx, i, j;
unsigned lx;
hx = __HI(x); /* high word of x */
lx = __LO(x); /* low word of x */
hx = __HI (x); /* high word of x */
lx = __LO (x); /* low word of x */
k=0;
if (hx < 0x00100000) { /* x < 2**-1022 */
if (((hx&0x7fffffff)|lx)==0)
return -two54/zero; /* log(+-0)=-inf */
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
k -= 54; x *= two54; /* subnormal number, scale up x */
hx = __HI(x); /* high word of x */
}
if (hx >= 0x7ff00000) return x+x;
k += (hx>>20)-1023;
hx &= 0x000fffff;
i = (hx+0x95f64)&0x100000;
__HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */
k += (i>>20);
f = x-1.0;
if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
if(f==zero) if(k==0) return zero; else {dk=(double)k;
return dk*ln2_hi+dk*ln2_lo;}
R = f*f*(0.5-0.33333333333333333*f);
if(k==0) return f-R; else {dk=(double)k;
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
}
s = f/(2.0+f);
dk = (double)k;
z = s*s;
i = hx-0x6147a;
w = z*z;
j = 0x6b851-hx;
t1= w*(Lg2+w*(Lg4+w*Lg6));
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
i |= j;
R = t2+t1;
if(i>0) {
hfsq=0.5*f*f;
if(k==0) return f-(hfsq-s*(hfsq+R)); else
return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
} else {
if(k==0) return f-s*(f-R); else
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
}
}
k = 0;
if (hx < 0x00100000) /* x < 2**-1022 */
{
if (((hx & 0x7fffffff) | lx) == 0) /* log(+-0) = -inf */
{
return -two54 / zero;
}
if (hx < 0) /* log(-#) = NaN */
{
return (x - x) / zero;
}
k -= 54;
x *= two54; /* subnormal number, scale up x */
hx = __HI (x); /* high word of x */
}
if (hx >= 0x7ff00000)
{
return x + x;
}
k += (hx >> 20) - 1023;
hx &= 0x000fffff;
i = (hx + 0x95f64) & 0x100000;
__HI (x) = hx | (i ^ 0x3ff00000); /* normalize x or x / 2 */
k += (i >> 20);
f = x - 1.0;
if ((0x000fffff & (2 + hx)) < 3) /* |f| < 2**-20 */
{
if (f == zero)
{
if (k == 0)
{
return zero;
}
else
{
dk = (double) k;
return dk * ln2_hi + dk * ln2_lo;
}
}
R = f * f * (0.5 - 0.33333333333333333 * f);
if (k == 0)
{
return f - R;
}
else
{
dk = (double) k;
return dk * ln2_hi - ((R - dk * ln2_lo) - f);
}
}
s = f / (2.0 + f);
dk = (double) k;
z = s * s;
i = hx - 0x6147a;
w = z * z;
j = 0x6b851 - hx;
t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
i |= j;
R = t2 + t1;
if (i > 0)
{
hfsq = 0.5 * f * f;
if (k == 0)
{
return f - (hfsq - s * (hfsq + R));
}
else
{
return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) - f);
}
}
else
{
if (k == 0)
{
return f - s * (f - R);
}
else
{
return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f);
}
}
} /* log */