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math: clean up inverse trigonometric functions

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modifications:
* avoid unsigned->signed conversions
* removed various volatile hacks
* use FORCE_EVAL when evaluating only for side-effects
* factor out R() rational approximation instead of manual inline
* __invtrigl.h now only provides __invtrigl_R, __pio2_hi and __pio2_lo
* use 2*pio2_hi, 2*pio2_lo instead of pi_hi, pi_lo

otherwise the logic is not changed, long double versions will
need a revisit when a genaral long double cleanup happens
This commit is contained in:
Szabolcs Nagy
2012-12-11 23:56:59 +01:00
parent 482ccd2f74
commit b12a73d5bf
12 changed files with 261 additions and 380 deletions
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src/math/atan2l.c
+19 -21
View File
@@ -24,8 +24,6 @@ long double atan2l(long double y, long double x)
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#include "__invtrigl.h"
// FIXME:
static const volatile long double tiny = 1.0e-300;
long double atan2l(long double y, long double x)
{
@@ -40,12 +38,12 @@ long double atan2l(long double y, long double x)
ux.e = x;
expsignx = ux.xbits.expsign;
exptx = expsignx & 0x7fff;
if ((exptx==BIAS+LDBL_MAX_EXP &&
if ((exptx==0x7fff &&
((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */
(expty==BIAS+LDBL_MAX_EXP &&
(expty==0x7fff &&
((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* y is NaN */
return x+y;
if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) /* x=1.0 */
if (expsignx==0x3fff && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) /* x=1.0 */
return atanl(y);
m = ((expsigny>>15)&1) | ((expsignx>>14)&2); /* 2*sign(x)+sign(y) */
@@ -54,39 +52,39 @@ long double atan2l(long double y, long double x)
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 2: return pi_hi+tiny; /* atan(+0,-anything) = pi */
case 3: return -pi_hi-tiny; /* atan(-0,-anything) =-pi */
case 2: return 2*pio2_hi+0x1p-1000; /* atan(+0,-anything) = pi */
case 3: return -2*pio2_hi-0x1p-1000; /* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if (exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
return expsigny < 0 ? -pio2_hi-tiny : pio2_hi+tiny;
return expsigny < 0 ? -pio2_hi-0x1p-1000 : pio2_hi+0x1p-1000;
/* when x is INF */
if (exptx == BIAS+LDBL_MAX_EXP) {
if (expty == BIAS+LDBL_MAX_EXP) {
if (exptx == 0x7fff) {
if (expty == 0x7fff) {
switch(m) {
case 0: return pio2_hi*0.5+tiny; /* atan(+INF,+INF) */
case 1: return -pio2_hi*0.5-tiny; /* atan(-INF,+INF) */
case 2: return 1.5*pio2_hi+tiny; /* atan(+INF,-INF) */
case 3: return -1.5*pio2_hi-tiny; /* atan(-INF,-INF) */
case 0: return pio2_hi*0.5+0x1p-1000; /* atan(+INF,+INF) */
case 1: return -pio2_hi*0.5-0x1p-1000; /* atan(-INF,+INF) */
case 2: return 1.5*pio2_hi+0x1p-1000; /* atan(+INF,-INF) */
case 3: return -1.5*pio2_hi-0x1p-1000; /* atan(-INF,-INF) */
}
} else {
switch(m) {
case 0: return 0.0; /* atan(+...,+INF) */
case 1: return -0.0; /* atan(-...,+INF) */
case 2: return pi_hi+tiny; /* atan(+...,-INF) */
case 3: return -pi_hi-tiny; /* atan(-...,-INF) */
case 2: return 2*pio2_hi+0x1p-1000; /* atan(+...,-INF) */
case 3: return -2*pio2_hi-0x1p-1000; /* atan(-...,-INF) */
}
}
}
/* when y is INF */
if (expty == BIAS+LDBL_MAX_EXP)
return expsigny < 0 ? -pio2_hi-tiny : pio2_hi+tiny;
if (expty == 0x7fff)
return expsigny < 0 ? -pio2_hi-0x1p-1000 : pio2_hi+0x1p-1000;
/* compute y/x */
k = expty-exptx;
if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */
z = pio2_hi+pio2_lo;
z = pio2_hi+0x1p-1000;
m &= 1;
} else if (expsignx < 0 && k < -LDBL_MANT_DIG-2) /* |y/x| tiny, x<0 */
z = 0.0;
@@ -95,9 +93,9 @@ long double atan2l(long double y, long double x)
switch (m) {
case 0: return z; /* atan(+,+) */
case 1: return -z; /* atan(-,+) */
case 2: return pi_hi-(z-pi_lo); /* atan(+,-) */
case 2: return 2*pio2_hi-(z-2*pio2_lo); /* atan(+,-) */
default: /* case 3 */
return (z-pi_lo)-pi_hi; /* atan(-,-) */
return (z-2*pio2_lo)-2*pio2_hi; /* atan(-,-) */
}
}
#endif