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sysdeps: Simplify sin Taylor Series calculation

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The macro TAYLOR_SIN adds the term `-0.5*da*a^2 + da` in hopes
of regaining some precision as a function of da. However the
comment says we add the term `-0.5*da*a^2 + 0.5*da` which is
different. This fix updates the comment to reflect the
code and also simplifies the calculation by replacing `a` with `x`
because they always have the same value.

Signed-off-by: Akila Welihinda <akilawelihinda@ucla.edu>
Reviewed-by: Paul Zimmermann <Paul.Zimmermann@inria.fr>
This commit is contained in:
Akila Welihinda 2021-12-12 10:35:03 -08:00 committed by Paul Zimmermann
parent 104d2005d5
commit 3b1402b3fc
1 changed files with 5 additions and 5 deletions
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10
sysdeps/ieee754/dbl-64/s_sin.c
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@ -51,16 +51,16 @@
#define POLYNOMIAL(xx) (POLYNOMIAL2 (xx) + s1)
/* The computed polynomial is a variation of the Taylor series expansion for
sin(a):
sin(x):
a - a^3/3! + a^5/5! - a^7/7! + a^9/9! + (1 - a^2) * da / 2
x - x^3/3! + x^5/5! - x^7/7! + x^9/9! - dx*x^2/2 + dx
The constants s1, s2, s3, etc. are pre-computed values of 1/3!, 1/5! and so
on. The result is returned to LHS. */
#define TAYLOR_SIN(xx, a, da) \
#define TAYLOR_SIN(xx, x, dx) \
({ \
double t = ((POLYNOMIAL (xx) * (a) - 0.5 * (da)) * (xx) + (da)); \
double res = (a) + t; \
double t = ((POLYNOMIAL (xx) * (x) - 0.5 * (dx)) * (xx) + (dx)); \
double res = (x) + t; \
res; \
})