summaryrefslogtreecommitdiff
path: root/src/math/log1pf.c
diff options
context:
space:
mode:
authorSzabolcs Nagy <nsz@port70.net>2013-10-28 01:16:14 +0000
committerSzabolcs Nagy <nsz@port70.net>2013-10-28 01:16:14 +0000
commit71d23b310383699a3101ea8bf088398796529ddd (patch)
tree812e6281a32bdc70977475abef9ee6b52b187422 /src/math/log1pf.c
parent4b15d9f46a2b260661d2e054575e617c76795578 (diff)
downloadmusl-71d23b310383699a3101ea8bf088398796529ddd.tar.gz
musl-71d23b310383699a3101ea8bf088398796529ddd.tar.bz2
musl-71d23b310383699a3101ea8bf088398796529ddd.tar.xz
musl-71d23b310383699a3101ea8bf088398796529ddd.zip
math: extensive log*.c cleanup
The log, log2 and log10 functions share a lot of code and to a lesser extent log1p too. A small part of the code was kept separately in __log1p.h, but since it did not capture much of the common code and it was inlined anyway, it did not solve the issue properly. Now the log functions have significant code duplication, which may be resolved later, until then they need to be modified together. logl, log10l, log2l, log1pl: * Fix the sign when the return value should be -inf. * Remove the volatile hack from log10l (seems unnecessary) log1p, log1pf: * Change the handling of small inputs: only |x|<2^-53 is special (then it is enough to return x with the usual subnormal handling) this fixes the sign of log1p(0) in downward rounding. * Do not handle the k==0 case specially (other than skipping the elaborate argument reduction) * Do not handle 1+x close to power-of-two specially (this code was used rarely, did not give much speed up and the precision wasn't better than the general) * Fix the correction term formula (c=1-(u-x) was used incorrectly when x<1 but (double)(x+1)==2, this was not a critical issue) * Use the exact same method for calculating log(1+f) as in log (except in log1p the c correction term is added to the result). log, logf, log10, log10f, log2, log2f: * Use double_t and float_t consistently. * Now the first part of log10 and log2 is identical to log (until the return statement, hopefully this makes maintainence easier). * Most special case formulas were removed (close to power-of-two and k==0 cases), they increase the code size without providing precision or performance benefits (and obfuscate the code). Only x==1 is handled specially so in downward rounding mode the sign of zero is correct (the general formula happens to give -0). * For x==0 instead of -1/0.0 or -two54/0.0, return -1/(x*x) to force raising the exception at runtime. * Arg reduction code is changed (slightly simplified) * The thresholds for arg reduction to [sqrt(2)/2,sqrt(2)] are now consistently the [0x3fe6a09e00000000,0x3ff6a09dffffffff] and the [0x3f3504f3,0x3fb504f2] intervals for double and float reductions respectively (the exact threshold values are not critical) * Remove the obsolete comment for the FLT_EVAL_METHOD!=0 case in log2f (The same code is used for all eval methods now, on i386 slightly simpler code could be used, but we have asm there anyway) all: * Fix signed int arithmetics (using unsigned for bitmanipulation) * Fix various comments
Diffstat (limited to 'src/math/log1pf.c')
-rw-r--r--src/math/log1pf.c125
1 files changed, 45 insertions, 80 deletions
diff --git a/src/math/log1pf.c b/src/math/log1pf.c
index e6940d29..23985c35 100644
--- a/src/math/log1pf.c
+++ b/src/math/log1pf.c
@@ -1,8 +1,5 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */
/*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
@@ -18,95 +15,63 @@
static const float
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
-two25 = 3.355443200e+07, /* 0x4c000000 */
-Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
-Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
-Lp3 = 2.8571429849e-01, /* 3E924925 */
-Lp4 = 2.2222198546e-01, /* 3E638E29 */
-Lp5 = 1.8183572590e-01, /* 3E3A3325 */
-Lp6 = 1.5313838422e-01, /* 3E1CD04F */
-Lp7 = 1.4798198640e-01; /* 3E178897 */
+/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
+Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
+Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
+Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
+Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
float log1pf(float x)
{
- float hfsq,f,c,s,z,R,u;
- int32_t k,hx,hu,ax;
-
- GET_FLOAT_WORD(hx, x);
- ax = hx & 0x7fffffff;
+ union {float f; uint32_t i;} u = {x};
+ float_t hfsq,f,c,s,z,R,w,t1,t2,dk;
+ uint32_t ix,iu;
+ int k;
+ ix = u.i;
k = 1;
- if (hx < 0x3ed413d0) { /* 1+x < sqrt(2)+ */
- if (ax >= 0x3f800000) { /* x <= -1.0 */
- if (x == -1.0f)
- return -two25/0.0f; /* log1p(-1)=+inf */
- return (x-x)/(x-x); /* log1p(x<-1)=NaN */
+ if (ix < 0x3ed413d0 || ix>>31) { /* 1+x < sqrt(2)+ */
+ if (ix >= 0xbf800000) { /* x <= -1.0 */
+ if (x == -1)
+ return x/0.0f; /* log1p(-1)=+inf */
+ return (x-x)/0.0f; /* log1p(x<-1)=NaN */
}
- if (ax < 0x38000000) { /* |x| < 2**-15 */
- /* if 0x1p-126 <= |x| < 0x1p-24, avoid raising underflow */
- if (ax < 0x33800000 && ax >= 0x00800000)
- return x;
-#if FLT_EVAL_METHOD != 0
- FORCE_EVAL(x*x);
-#endif
- return x - x*x*0.5f;
+ if (ix<<1 < 0x33800000<<1) { /* |x| < 2**-24 */
+ /* underflow if subnormal */
+ if ((ix&0x7f800000) == 0)
+ FORCE_EVAL(x*x);
+ return x;
}
- if (hx > 0 || hx <= (int32_t)0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
+ if (ix <= 0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
k = 0;
+ c = 0;
f = x;
- hu = 1;
}
- }
- if (hx >= 0x7f800000)
- return x+x;
- if (k != 0) {
- if (hx < 0x5a000000) {
- u = 1 + x;
- GET_FLOAT_WORD(hu, u);
- k = (hu>>23) - 127;
- /* correction term */
- c = k > 0 ? 1.0f-(u-x) : x-(u-1.0f);
- c /= u;
- } else {
- u = x;
- GET_FLOAT_WORD(hu,u);
- k = (hu>>23) - 127;
+ } else if (ix >= 0x7f800000)
+ return x;
+ if (k) {
+ u.f = 1 + x;
+ iu = u.i;
+ iu += 0x3f800000 - 0x3f3504f3;
+ k = (int)(iu>>23) - 0x7f;
+ /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
+ if (k < 25) {
+ c = k >= 2 ? 1-(u.f-x) : x-(u.f-1);
+ c /= u.f;
+ } else
c = 0;
- }
- hu &= 0x007fffff;
- /*
- * The approximation to sqrt(2) used in thresholds is not
- * critical. However, the ones used above must give less
- * strict bounds than the one here so that the k==0 case is
- * never reached from here, since here we have committed to
- * using the correction term but don't use it if k==0.
- */
- if (hu < 0x3504f4) { /* u < sqrt(2) */
- SET_FLOAT_WORD(u, hu|0x3f800000); /* normalize u */
- } else {
- k += 1;
- SET_FLOAT_WORD(u, hu|0x3f000000); /* normalize u/2 */
- hu = (0x00800000-hu)>>2;
- }
- f = u - 1.0f;
- }
- hfsq = 0.5f * f * f;
- if (hu == 0) { /* |f| < 2**-20 */
- if (f == 0.0f) {
- if (k == 0)
- return 0.0f;
- c += k*ln2_lo;
- return k*ln2_hi+c;
- }
- R = hfsq*(1.0f - 0.66666666666666666f * f);
- if (k == 0)
- return f - R;
- return k*ln2_hi - ((R-(k*ln2_lo+c))-f);
+ /* reduce u into [sqrt(2)/2, sqrt(2)] */
+ iu = (iu&0x007fffff) + 0x3f3504f3;
+ u.i = iu;
+ f = u.f - 1;
}
s = f/(2.0f + f);
z = s*s;
- R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
- if (k == 0)
- return f - (hfsq-s*(hfsq+R));
- return k*ln2_hi - ((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
+ w = z*z;
+ t1= w*(Lg2+w*Lg4);
+ t2= z*(Lg1+w*Lg3);
+ R = t2 + t1;
+ hfsq = 0.5f*f*f;
+ dk = k;
+ return s*(hfsq+R) + (dk*ln2_lo+c) - hfsq + f + dk*ln2_hi;
}