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LibF7: sinh: Fix loss of precision due to cancellation for small values.

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libgcc/config/avr/libf7/
	* libf7-const.def [F7MOD_sinh_]: Add MiniMax polynomial.
	* libf7.c (f7_sinh): Use it instead of (exp(x) - exp(-x)) / 2
	when |x| < 0.5 to avoid loss of precision due to cancellation.
This commit is contained in:
Georg-Johann Lay 2023-11-14 12:05:19 +01:00
parent e47e836f31
commit 3232e73c44
2 changed files with 27 additions and 0 deletions
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10
libgcc/config/avr/libf7/libf7-const.def
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@ -194,5 +194,15 @@ F7_CONST_DEF (X, 1, 0xc7,0xb5,0x6a,0xf8,0x0e,0x32,0x07, -37)
F7_CONST_DEF (pi_low,0, 0xd3,0x13,0x19,0x8a,0x2e,0x03,0x70, 1 - F7_MANT_BITS-2)
#endif
#elif defined (F7MOD_sinh_)
// MiniMax for sinh(q)/q, q = sqrt(x) for q in [0, 0.2505]. Quality pQ10 > 70.
// 0.99999999999999998094379 + 0.16666666666667217765428 x + 0.0083333333330755574996361 x^2 + 1.9841270281701916844502e-4 x^3 + 2.7556979384534689658282e-6 x^4 + 2.5172859336028750964929e-8 x^5
F7_CONST_DEF (X, 0, 0xff,0xff,0xff,0xff,0xff,0xff,0xff, -1)
F7_CONST_DEF (X, 0, 0xaa,0xaa,0xaa,0xaa,0xaa,0xb0,0xdf, -3)
F7_CONST_DEF (X, 0, 0x88,0x88,0x88,0x88,0x76,0x64,0xdb, -7)
F7_CONST_DEF (X, 0, 0xd0,0x0d,0x01,0x1d,0x88,0x4c,0xed, -13)
F7_CONST_DEF (X, 0, 0xb8,0xee,0x87,0xb4,0x30,0xf0,0xa1, -19)
F7_CONST_DEF (X, 0, 0xd8,0x3b,0xb3,0xfd,0x9e,0x6c,0xcf, -26)
#endif
#endif /* ! IN_LIBF7_H && ! F7MOD_const_ */

17
libgcc/config/avr/libf7/libf7.c
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@ -2022,9 +2022,26 @@ void f7_sinhcosh (f7_t *cc, const f7_t *aa, bool do_sinh)
#ifdef F7MOD_sinh_
#define ARRAY_NAME coeff_sinh
#include "libf7-array.def"
#undef ARRAY_NAME
F7_WEAK
void f7_sinh (f7_t *cc, const f7_t *aa)
{
if (aa->expo <= -2)
{
// For small values, exp(A) - exp(-A) suffers from cancellation, hence
// use a MiniMax polynomial for |A| < 0.5.
f7_t xx7, *xx = &xx7;
f7_t hh7, *hh = &hh7;
f7_square (xx, aa);
f7_horner (hh, xx, n_coeff_sinh, coeff_sinh, NULL);
f7_mul (cc, aa, hh);
return;
}
f7_sinhcosh (cc, aa, true);
}
#endif // F7MOD_sinh_