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authorSzabolcs Nagy <nsz@port70.net>2012-11-18 03:42:09 +0100
committerSzabolcs Nagy <nsz@port70.net>2012-11-18 03:42:09 +0100
commitab1772c597ba8fe0c26400256b12d7a4df23880e (patch)
treeaa9e9df0cb237e2fdf3847300b9fc6b9547fc240 /src
parent159c7655d06f04aa56a57385d633699c4c63d72c (diff)
downloadmusl-ab1772c597ba8fe0c26400256b12d7a4df23880e.tar.gz
math: expf.c cleanup
similar to exp.c cleanup: use scalbnf, don't return excess precision, drop some optimizatoins. exp.c was changed to be more consistent with expf.c code.
Diffstat (limited to 'src')
-rw-r--r--src/math/exp.c20
-rw-r--r--src/math/expf.c98
2 files changed, 55 insertions, 63 deletions
diff --git a/src/math/exp.c b/src/math/exp.c
index 5c0edee4..5ec8f8a7 100644
--- a/src/math/exp.c
+++ b/src/math/exp.c
@@ -80,7 +80,7 @@ P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
double exp(double x)
{
- double hi, lo, c, z;
+ double hi, lo, c, xx;
int k, sign;
uint32_t hx;
@@ -92,24 +92,26 @@ double exp(double x)
if (hx >= 0x40862e42) { /* if |x| >= 709.78... */
if (isnan(x))
return x;
+ if (hx == 0x7ff00000 && sign) /* -inf */
+ return 0;
if (x > 709.782712893383973096) {
/* overflow if x!=inf */
STRICT_ASSIGN(double, x, 0x1p1023 * x);
return x;
}
if (x < -745.13321910194110842) {
- /* underflow if x!=-inf */
- STRICT_ASSIGN(double, x, 0x1p-1000 / -x * 0x1p-1000);
+ /* underflow */
+ STRICT_ASSIGN(double, x, 0x1p-1000 * 0x1p-1000);
return x;
}
}
/* argument reduction */
if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
- if (hx < 0x3ff0a2b2) /* if |x| < 1.5 ln2 */
- k = 1 - sign - sign; /* optimization */
- else
+ if (hx >= 0x3ff0a2b2) /* if |x| >= 1.5 ln2 */
k = (int)(invln2*x + half[sign]);
+ else
+ k = 1 - sign - sign;
hi = x - k*ln2hi; /* k*ln2hi is exact here */
lo = k*ln2lo;
STRICT_ASSIGN(double, x, hi - lo);
@@ -124,9 +126,9 @@ double exp(double x)
}
/* x is now in primary range */
- z = x*x;
- c = x - z*(P1+z*(P2+z*(P3+z*(P4+z*P5))));
- x = 1 + ((x*c/(2-c) - lo) + hi);
+ xx = x*x;
+ c = x - xx*(P1+xx*(P2+xx*(P3+xx*(P4+xx*P5))));
+ x = 1 + (x*c/(2-c) - lo + hi);
if (k == 0)
return x;
return scalbn(x, k);
diff --git a/src/math/expf.c b/src/math/expf.c
index 3c3e2ab9..8aefc917 100644
--- a/src/math/expf.c
+++ b/src/math/expf.c
@@ -16,79 +16,69 @@
#include "libm.h"
static const float
-halF[2] = {0.5,-0.5,},
-huge = 1.0e+30,
-o_threshold = 8.8721679688e+01, /* 0x42b17180 */
-u_threshold = -1.0397208405e+02, /* 0xc2cff1b5 */
-ln2HI[2] = { 6.9314575195e-01, /* 0x3f317200 */
- -6.9314575195e-01,},/* 0xbf317200 */
-ln2LO[2] = { 1.4286067653e-06, /* 0x35bfbe8e */
- -1.4286067653e-06,},/* 0xb5bfbe8e */
-invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
+half[2] = {0.5,-0.5},
+ln2hi = 6.9314575195e-1f, /* 0x3f317200 */
+ln2lo = 1.4286067653e-6f, /* 0x35bfbe8e */
+invln2 = 1.4426950216e+0f, /* 0x3fb8aa3b */
/*
* Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
* |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
*/
-P1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */
-P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */
-
-static const volatile float twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */
+P1 = 1.6666625440e-1f, /* 0xaaaa8f.0p-26 */
+P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */
float expf(float x)
{
- float y,hi=0.0,lo=0.0,c,t,twopk;
- int32_t k=0,xsb;
+ float hi, lo, c, xx;
+ int k, sign;
uint32_t hx;
GET_FLOAT_WORD(hx, x);
- xsb = (hx>>31)&1; /* sign bit of x */
+ sign = hx >> 31; /* sign bit of x */
hx &= 0x7fffffff; /* high word of |x| */
- /* filter out non-finite argument */
- if (hx >= 0x42b17218) { /* if |x|>=88.721... */
+ /* special cases */
+ if (hx >= 0x42b17218) { /* if |x| >= 88.722839f or NaN */
if (hx > 0x7f800000) /* NaN */
- return x+x;
- if (hx == 0x7f800000) /* exp(+-inf)={inf,0} */
- return xsb==0 ? x : 0.0;
- if (x > o_threshold)
- return huge*huge; /* overflow */
- if (x < u_threshold)
- return twom100*twom100; /* underflow */
+ return x;
+ if (!sign) {
+ /* overflow if x!=inf */
+ STRICT_ASSIGN(float, x, x * 0x1p127f);
+ return x;
+ }
+ if (hx == 0x7f800000) /* -inf */
+ return 0;
+ if (hx >= 0x42cff1b5) { /* x <= -103.972084f */
+ /* underflow */
+ STRICT_ASSIGN(float, x, 0x1p-100f*0x1p-100f);
+ return x;
+ }
}
/* argument reduction */
- if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
- if (hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
- hi = x-ln2HI[xsb];
- lo = ln2LO[xsb];
- k = 1 - xsb - xsb;
- } else {
- k = invln2*x + halF[xsb];
- t = k;
- hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
- lo = t*ln2LO[0];
- }
+ if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
+ if (hx > 0x3f851592) /* if |x| > 1.5 ln2 */
+ k = invln2*x + half[sign];
+ else
+ k = 1 - sign - sign;
+ hi = x - k*ln2hi; /* k*ln2hi is exact here */
+ lo = k*ln2lo;
STRICT_ASSIGN(float, x, hi - lo);
- } else if(hx < 0x39000000) { /* |x|<2**-14 */
- /* raise inexact */
- if (huge+x > 1.0f)
- return 1.0f + x;
- } else
+ } else if (hx > 0x39000000) { /* |x| > 2**-14 */
k = 0;
+ hi = x;
+ lo = 0;
+ } else {
+ /* raise inexact */
+ FORCE_EVAL(0x1p127f + x);
+ return 1 + x;
+ }
/* x is now in primary range */
- t = x*x;
- if (k >= -125)
- SET_FLOAT_WORD(twopk, 0x3f800000+(k<<23));
- else
- SET_FLOAT_WORD(twopk, 0x3f800000+((k+100)<<23));
- c = x - t*(P1+t*P2);
+ xx = x*x;
+ c = x - xx*(P1+xx*P2);
+ x = 1 + (x*c/(2-c) - lo + hi);
if (k == 0)
- return 1.0f - ((x*c)/(c - 2.0f) - x);
- y = 1.0f - ((lo - (x*c)/(2.0f - c)) - hi);
- if (k < -125)
- return y*twopk*twom100;
- if (k == 128)
- return y*2.0f*0x1p127f;
- return y*twopk;
+ return x;
+ return scalbnf(x, k);
}