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-rw-r--r--lib/msun/src/e_acosf.c28
-rw-r--r--lib/msun/src/e_asinf.c53
-rw-r--r--lib/msun/src/e_atan2f.c4
-rw-r--r--lib/msun/src/s_atanf.c28
4 files changed, 42 insertions, 71 deletions
diff --git a/lib/msun/src/e_acosf.c b/lib/msun/src/e_acosf.c
index 7fbf3b2..ac0d8dd 100644
--- a/lib/msun/src/e_acosf.c
+++ b/lib/msun/src/e_acosf.c
@@ -26,16 +26,10 @@ pio2_hi = 1.5707962513e+00; /* 0x3fc90fda */
static volatile float
pio2_lo = 7.5497894159e-08; /* 0x33a22168 */
static const float
-pS0 = 1.6666667163e-01, /* 0x3e2aaaab */
-pS1 = -3.2556581497e-01, /* 0xbea6b090 */
-pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */
-pS3 = -4.0055535734e-02, /* 0xbd241146 */
-pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */
-pS5 = 3.4793309169e-05, /* 0x3811ef08 */
-qS1 = -2.4033949375e+00, /* 0xc019d139 */
-qS2 = 2.0209457874e+00, /* 0x4001572d */
-qS3 = -6.8828397989e-01, /* 0xbf303361 */
-qS4 = 7.7038154006e-02; /* 0x3d9dc62e */
+pS0 = 1.6666586697e-01,
+pS1 = -4.2743422091e-02,
+pS2 = -8.6563630030e-03,
+qS1 = -7.0662963390e-01;
float
__ieee754_acosf(float x)
@@ -51,16 +45,16 @@ __ieee754_acosf(float x)
return (x-x)/(x-x); /* acos(|x|>1) is NaN */
}
if(ix<0x3f000000) { /* |x| < 0.5 */
- if(ix<=0x23000000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
+ if(ix<=0x32800000) return pio2_hi+pio2_lo;/*if|x|<2**-26*/
z = x*x;
- p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
- q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+ p = z*(pS0+z*(pS1+z*pS2));
+ q = one+z*qS1;
r = p/q;
return pio2_hi - (x - (pio2_lo-x*r));
} else if (hx<0) { /* x < -0.5 */
z = (one+x)*(float)0.5;
- p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
- q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+ p = z*(pS0+z*(pS1+z*pS2));
+ q = one+z*qS1;
s = __ieee754_sqrtf(z);
r = p/q;
w = r*s-pio2_lo;
@@ -73,8 +67,8 @@ __ieee754_acosf(float x)
GET_FLOAT_WORD(idf,df);
SET_FLOAT_WORD(df,idf&0xfffff000);
c = (z-df*df)/(s+df);
- p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
- q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+ p = z*(pS0+z*(pS1+z*pS2));
+ q = one+z*qS1;
r = p/q;
w = r*s+c;
return (float)2.0*(df+w);
diff --git a/lib/msun/src/e_asinf.c b/lib/msun/src/e_asinf.c
index f830878..a4c3f00 100644
--- a/lib/msun/src/e_asinf.c
+++ b/lib/msun/src/e_asinf.c
@@ -22,62 +22,45 @@ __FBSDID("$FreeBSD$");
static const float
one = 1.0000000000e+00, /* 0x3F800000 */
huge = 1.000e+30,
-pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */
-pio2_lo = 7.5497894159e-08, /* 0x33a22168 */
-pio4_hi = 7.8539812565e-01, /* 0x3f490fda */
/* coefficient for R(x^2) */
-pS0 = 1.6666667163e-01, /* 0x3e2aaaab */
-pS1 = -3.2556581497e-01, /* 0xbea6b090 */
-pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */
-pS3 = -4.0055535734e-02, /* 0xbd241146 */
-pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */
-pS5 = 3.4793309169e-05, /* 0x3811ef08 */
-qS1 = -2.4033949375e+00, /* 0xc019d139 */
-qS2 = 2.0209457874e+00, /* 0x4001572d */
-qS3 = -6.8828397989e-01, /* 0xbf303361 */
-qS4 = 7.7038154006e-02; /* 0x3d9dc62e */
+pS0 = 1.6666586697e-01,
+pS1 = -4.2743422091e-02,
+pS2 = -8.6563630030e-03,
+qS1 = -7.0662963390e-01;
+
+static const double
+pio2 = 1.570796326794896558e+00;
float
__ieee754_asinf(float x)
{
- float t=0.0,w,p,q,c,r,s;
+ double s;
+ float t=0.0,w,p,q,c,r;
int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix==0x3f800000) {
/* asin(1)=+-pi/2 with inexact */
- return x*pio2_hi+x*pio2_lo;
+ return x*pio2;
} else if(ix> 0x3f800000) { /* |x|>= 1 */
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
} else if (ix<0x3f000000) { /* |x|<0.5 */
- if(ix<0x32000000) { /* if |x| < 2**-27 */
+ if(ix<0x39800000) { /* if |x| < 2**-12 */
if(huge+x>one) return x;/* return x with inexact if x!=0*/
} else
t = x*x;
- p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
- q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
+ p = t*(pS0+t*(pS1+t*pS2));
+ q = one+t*qS1;
w = p/q;
return x+x*w;
}
/* 1> |x|>= 0.5 */
w = one-fabsf(x);
t = w*(float)0.5;
- p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
- q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
- s = __ieee754_sqrtf(t);
- if(ix>=0x3F79999A) { /* if |x| > 0.975 */
- w = p/q;
- t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo);
- } else {
- int32_t iw;
- w = s;
- GET_FLOAT_WORD(iw,w);
- SET_FLOAT_WORD(w,iw&0xfffff000);
- c = (t-w*w)/(s+w);
- r = p/q;
- p = (float)2.0*s*r-(pio2_lo-(float)2.0*c);
- q = pio4_hi-(float)2.0*w;
- t = pio4_hi-(p-q);
- }
+ p = t*(pS0+t*(pS1+t*pS2));
+ q = one+t*qS1;
+ s = __ieee754_sqrt(t);
+ w = p/q;
+ t = pio2-2.0*(s+s*w);
if(hx>0) return t; else return -t;
}
diff --git a/lib/msun/src/e_atan2f.c b/lib/msun/src/e_atan2f.c
index 55435b4..a48ada1 100644
--- a/lib/msun/src/e_atan2f.c
+++ b/lib/msun/src/e_atan2f.c
@@ -80,8 +80,8 @@ __ieee754_atan2f(float y, float x)
/* compute y/x */
k = (iy-ix)>>23;
- if(k > 60) z=pi_o_2+(float)0.5*pi_lo; /* |y/x| > 2**60 */
- else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
+ if(k > 26) z=pi_o_2+(float)0.5*pi_lo; /* |y/x| > 2**26 */
+ else if(hx<0&&k<-26) z=0.0; /* |y|/x < -2**26 */
else z=atanf(fabsf(y/x)); /* safe to do y/x */
switch (m) {
case 0: return z ; /* atan(+,+) */
diff --git a/lib/msun/src/s_atanf.c b/lib/msun/src/s_atanf.c
index 8221b42..b3a371f 100644
--- a/lib/msun/src/s_atanf.c
+++ b/lib/msun/src/s_atanf.c
@@ -34,20 +34,14 @@ static const float atanlo[] = {
};
static const float aT[] = {
- 3.3333334327e-01, /* 0x3eaaaaaa */
- -2.0000000298e-01, /* 0xbe4ccccd */
- 1.4285714924e-01, /* 0x3e124925 */
- -1.1111110449e-01, /* 0xbde38e38 */
- 9.0908870101e-02, /* 0x3dba2e6e */
- -7.6918758452e-02, /* 0xbd9d8795 */
- 6.6610731184e-02, /* 0x3d886b35 */
- -5.8335702866e-02, /* 0xbd6ef16b */
- 4.9768779427e-02, /* 0x3d4bda59 */
- -3.6531571299e-02, /* 0xbd15a221 */
- 1.6285819933e-02, /* 0x3c8569d7 */
+ 3.3333328366e-01,
+ -1.9999158382e-01,
+ 1.4253635705e-01,
+ -1.0648017377e-01,
+ 6.1687607318e-02,
};
- static const float
+static const float
one = 1.0,
huge = 1.0e30;
@@ -59,13 +53,13 @@ atanf(float x)
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
- if(ix>=0x50800000) { /* if |x| >= 2^34 */
+ if(ix>=0x4c800000) { /* if |x| >= 2**26 */
if(ix>0x7f800000)
return x+x; /* NaN */
if(hx>0) return atanhi[3]+*(volatile float *)&atanlo[3];
else return -atanhi[3]-*(volatile float *)&atanlo[3];
} if (ix < 0x3ee00000) { /* |x| < 0.4375 */
- if (ix < 0x31000000) { /* |x| < 2^-29 */
+ if (ix < 0x39800000) { /* |x| < 2**-12 */
if(huge+x>one) return x; /* raise inexact */
}
id = -1;
@@ -80,7 +74,7 @@ atanf(float x)
} else {
if (ix < 0x401c0000) { /* |x| < 2.4375 */
id = 2; x = (x-(float)1.5)/(one+(float)1.5*x);
- } else { /* 2.4375 <= |x| < 2^66 */
+ } else { /* 2.4375 <= |x| < 2**26 */
id = 3; x = -(float)1.0/x;
}
}}
@@ -88,8 +82,8 @@ atanf(float x)
z = x*x;
w = z*z;
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
- s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
- s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
+ s1 = z*(aT[0]+w*(aT[2]+w*aT[4]));
+ s2 = w*(aT[1]+w*aT[3]);
if (id<0) return x - x*(s1+s2);
else {
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
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