Szabolcs Nagy
482ccd2f74
modifications:
* avoid unsigned->signed integer conversion
* do not handle special cases when they work correctly anyway
* more strict threshold values (0x1p26 instead of 0x1p28 etc)
* smaller code, cleaner branching logic
* same precision as the old code:
acosh(x) has up to 2ulp error in [1,1.125]
asinh(x) has up to 1.6ulp error in [0.125,0.5], [-0.5,-0.125]
atanh(x) has up to 1.7ulp error in [0.125,0.5], [-0.5,-0.125]
32 lines
647 B
C
32 lines
647 B
C
#include "libm.h"
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#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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long double atanhl(long double x)
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{
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return atanh(x);
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}
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#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
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/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
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long double atanhl(long double x)
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{
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union {
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long double f;
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struct{uint64_t m; uint16_t se; uint16_t pad;} i;
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} u = {.f = x};
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unsigned e = u.i.se & 0x7fff;
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unsigned s = u.i.se >> 15;
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/* |x| */
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u.i.se = e;
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x = u.f;
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if (e < 0x3fff - 1) {
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/* |x| < 0.5, up to 1.7ulp error */
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x = 0.5*log1pl(2*x + 2*x*x/(1-x));
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} else {
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x = 0.5*log1pl(2*x/(1-x));
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}
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return s ? -x : x;
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}
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#endif
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