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author | bde <bde@FreeBSD.org> | 2005-11-23 14:27:56 +0000 |
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committer | bde <bde@FreeBSD.org> | 2005-11-23 14:27:56 +0000 |
commit | 1e3150891d464e1facd589ec96a72f6450139305 (patch) | |
tree | 6e4fe2726792c217377ba4d1b066f47a4ac7fc1a /lib | |
parent | 11e07dda3098d413b7052b24dbcb7d51fc6dcfa6 (diff) | |
download | FreeBSD-src-1e3150891d464e1facd589ec96a72f6450139305.zip FreeBSD-src-1e3150891d464e1facd589ec96a72f6450139305.tar.gz |
Use only double precision for "kernel" tanf (except for returning float).
This is a minor interface change. The function is renamed from
__kernel_tanf() to __kernel_tandf() so that misues of it will cause
link errors and not crashes.
This version is a routine translation with no special optimizations
for accuracy or efficiency. It gives an unimportant increase in
accuracy, from ~0.9 ulps to 0.5285 ulps. Almost all of the error is
from the minimax polynomial (~0.03 ulps and the final rounding step
(< 0.5 ulps). It gives strange differences in efficiency in the -5
to +10% range, with -O1 fairly consistently becoming faster and -O2
slower on AXP and A64 with gcc-3.3 and gcc-3.4.
Diffstat (limited to 'lib')
-rw-r--r-- | lib/msun/src/k_tanf.c | 37 | ||||
-rw-r--r-- | lib/msun/src/math_private.h | 2 | ||||
-rw-r--r-- | lib/msun/src/s_tanf.c | 10 |
3 files changed, 20 insertions, 29 deletions
diff --git a/lib/msun/src/k_tanf.c b/lib/msun/src/k_tanf.c index cc498d5..77bc7b71 100644 --- a/lib/msun/src/k_tanf.c +++ b/lib/msun/src/k_tanf.c @@ -21,35 +21,32 @@ static char rcsid[] = "$FreeBSD$"; #include "math.h" #include "math_private.h" -static const float -pio4 = 7.8539812565e-01, /* 0x3f490fda */ -pio4lo= 3.7748947079e-08, /* 0x33222168 */ -/* |tan(x)/x - t(x)| < 2**-29.2 (~[-1.73e-09, 1.724e-09]). */ +static const double +pio4 = M_PI_4, +/* |tan(x)/x - t(x)| < 2**-29.1 (~[-1.72e-09, 1.719e-09]). */ T[] = { - 0xaaaaa3.0p-25, /* 0.33333310485 */ - 0x888b06.0p-26, /* 0.13334283238 */ - 0xdc84c8.0p-28, /* 0.053837567568 */ - 0xb9d8f1.0p-29, /* 0.022686453536 */ - 0xcfe632.0p-31, /* 0.0063445800915 */ - 0xeaf97e.0p-31, /* 0.0071708550677 */ + 0x1555545f8b54d0.0p-54, /* 0.333333104424423432022 */ + 0x111160cdc2c9af.0p-55, /* 0.133342838734802765499 */ + 0x1b9097e5693cd0.0p-57, /* 0.0538375346701457369036 */ + 0x173b2333895b6f.0p-58, /* 0.0226865291791357691353 */ + 0x19fcb197e825ab.0p-60, /* 0.00634450313965243938713 */ + 0x1d5f3701b44a27.0p-60, /* 0.00717088210082520490646 */ }; #ifdef INLINE_KERNEL_TANF extern inline #endif float -__kernel_tanf(float x, float y, int iy) +__kernel_tandf(double x, int iy) { - float z,r,v,w,s; + double z,r,v,w,s; int32_t ix,hx; GET_FLOAT_WORD(hx,x); ix = hx&0x7fffffff; if(ix>=0x3f2ca140) { /* |x|>=0.67434 */ - if(hx<0) {x = -x; y = -y;} - z = pio4-x; - w = pio4lo-y; - x = z+w; y = 0.0; + if(hx<0) {x = -x;} + x = pio4-x; } z = x*x; w = z*z; @@ -60,13 +57,13 @@ __kernel_tanf(float x, float y, int iy) r = T[1]+w*(T[3]+w*T[5]); v = z*(T[2]+w*T[4]); s = z*x; - r = y + z*(s*(r+v)+y); + r = z*s*(r+v); r += T[0]*s; w = x+r; if(ix>=0x3f2ca140) { - v = (float)iy; - return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r))); + v = (double)iy; + return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r))); } if(iy==1) return w; - else return -1.0/((double)x+r); + else return -1.0/w; } diff --git a/lib/msun/src/math_private.h b/lib/msun/src/math_private.h index 27337a9..257ff63 100644 --- a/lib/msun/src/math_private.h +++ b/lib/msun/src/math_private.h @@ -266,7 +266,7 @@ int __kernel_rem_pio2(double*,double*,int,int,int,const int*); int __ieee754_rem_pio2f(float,float*); float __kernel_sinf(float,float,int); float __kernel_cosf(float,float); -float __kernel_tanf(float,float,int); +float __kernel_tandf(double,int); int __kernel_rem_pio2f(float*,float*,int,int,int,const int*); #endif /* !_MATH_PRIVATE_H_ */ diff --git a/lib/msun/src/s_tanf.c b/lib/msun/src/s_tanf.c index 470b336..a78957f 100644 --- a/lib/msun/src/s_tanf.c +++ b/lib/msun/src/s_tanf.c @@ -29,12 +29,6 @@ t2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */ t3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */ t4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ -static inline float -__kernel_tandf(double x, int iy) -{ - return __kernel_tanf((float)x, x - (float)x, iy); -} - float tanf(float x) { @@ -47,7 +41,7 @@ tanf(float x) if(ix <= 0x3f490fda) { /* |x| ~<= pi/4 */ if(ix<0x39800000) /* |x| < 2**-12 */ if(((int)x)==0) return x; /* x with inexact if x != 0 */ - return __kernel_tanf(x,0.0,1); + return __kernel_tandf(x,1); } if(ix<=0x407b53d1) { /* |x| ~<= 5*pi/4 */ if(ix<=0x4016cbe3) /* |x| ~<= 3pi/4 */ @@ -69,6 +63,6 @@ tanf(float x) else { n = __ieee754_rem_pio2f(x,y); /* integer parameter: 1 -- n even; -1 -- n odd */ - return __kernel_tanf(y[0],y[1],1-((n&1)<<1)); + return __kernel_tandf((double)y[0]+y[1],1-((n&1)<<1)); } } |