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| author | Garrett Cox <garrettjcox@gmail.com> | 2024-01-05 09:58:59 -0600 |
|---|---|---|
| committer | louist103 <35883445+louist103@users.noreply.github.com> | 2024-01-05 18:00:59 -0500 |
| commit | 9be74e0026b563ba680e1dc157521eccc89fc03f (patch) | |
| tree | ad27464c5b19b239991ed369454413ea3a30c802 /src/boot/O2/math64.c | |
| parent | 7c7021f3a211a3384d25b5a4175040750d50c248 (diff) | |
Move source into subdirectory
Diffstat (limited to 'src/boot/O2/math64.c')
| -rw-r--r-- | src/boot/O2/math64.c | 191 |
1 files changed, 0 insertions, 191 deletions
diff --git a/src/boot/O2/math64.c b/src/boot/O2/math64.c deleted file mode 100644 index cb77bed50..000000000 --- a/src/boot/O2/math64.c +++ /dev/null @@ -1,191 +0,0 @@ -/** - * MathF library - * Contains tangent function, wrappers for a number of the handwritten functions in fp, and a suite of arctangents - */ -#include "global.h" -#include "fixed_point.h" - -s32 gUseAtanContFrac; - -/** - * Tangent function computed using libultra sinf and cosf - */ -f32 Math_FTanF(f32 x) { - return sinf(x) / cosf(x); -} - -// Unused -f32 Math_FFloorF(f32 x) { - return floorf(x); -} - -// Unused -f32 Math_FCeilF(f32 x) { - return ceilf(x); -} - -// Unused -f32 Math_FRoundF(f32 x) { - return roundf(x); -} - -// Unused -f32 Math_FTruncF(f32 x) { - return truncf(x); -} - -f32 Math_FNearbyIntF(f32 x) { - return nearbyintf(x); -} - -/** - * Arctangent approximation using a Maclaurin series [https://mathworld.wolfram.com/MaclaurinSeries.html] - * (one quadrant, i.e. |x| < 1) - */ -f32 Math_FAtanTaylorQF(f32 x) { - // Coefficients of Maclaurin series of arctangent - static const f32 coeffs[] = { - -1.0f / 3, +1.0f / 5, -1.0f / 7, +1.0f / 9, -1.0f / 11, +1.0f / 13, -1.0f / 15, +1.0f / 17, 0.0f, - }; - - f32 poly = x; - f32 sq = SQ(x); - f32 exp = x * sq; - const f32* c = coeffs; - f32 term; - - // Calculate the series until adding more terms does not change the float - while (true) { - term = *c++ * exp; - if (poly + term == poly) { - break; - } - poly += term; - exp *= sq; - } - - return poly; -} - -/** - * Extends previous arctangent function to the rest of the real numbers. - * Uses the formulae arctan(x) = pi/2 - arctan(1/x) - * and arctan(x) = pi/4 - arctan( (1-x)/(1+x) ) - * to extend the range in which the series computed by Math_FAtanTaylorQF is a good approximation - */ -f32 Math_FAtanTaylorF(f32 x) { - f32 t; - f32 q; - - if (x > 0.0f) { - t = x; - } else if (x < 0.0f) { - t = -x; - } else if (x == 0.0f) { - return 0.0f; - } else { - return qNaN0x10000; - } - - if (t <= M_SQRT2 - 1.0f) { - return Math_FAtanTaylorQF(x); - } - - if (t >= M_SQRT2 + 1.0f) { - q = M_PI / 2 - Math_FAtanTaylorQF(1.0f / t); - } else { // in the interval (\sqrt{2} - 1, \sqrt{2} + 1) - q = M_PI / 4 - Math_FAtanTaylorQF((1.0f - t) / (1.0f + t)); - } - - if (x > 0.0f) { - return q; - } else { - return -q; - } -} - -/** - * Arctangent approximation using a continued fraction - * Cf. https://en.wikipedia.org/wiki/Gauss%27s_continued_fraction#The_series_2F1_2 , - * https://dlmf.nist.gov/4.25#E4 - */ -f32 Math_FAtanContFracF(f32 x) { - s32 sector; - f32 z; - f32 conv; - f32 sq; - s32 i; - - if (x >= -1.0f && x <= 1.0f) { - sector = 0; - } else if (x > 1.0f) { - sector = 1; - x = 1.0f / x; - } else if (x < -1.0f) { - sector = -1; - x = 1.0f / x; - } else { - return qNaN0x10000; - } - - // Builds the continued fraction from the innermost fraction out - sq = SQ(x); - conv = 0.0f; - z = 8.0f; - for (i = 8; i != 0; i--) { - conv = SQ(z) * sq / (2.0f * z + 1.0f + conv); - z -= 1.0f; - } - conv = x / (1.0f + conv); - - if (sector == 0) { - return conv; - } else if (sector > 0) { - return M_PI / 2 - conv; - } else { - return -M_PI / 2 - conv; - } -} - -/** - * Single-argument arctangent, only used by the two-argument function. - * Nothing else sets the bss variable gUseAtanContFrac, so the Maclaurin series is always used - */ -f32 Math_FAtanF(f32 x) { - if (!gUseAtanContFrac) { - return Math_FAtanTaylorF(x); - } else { - return Math_FAtanContFracF(x); - } -} - -/** - * Main two-argument arctangent function - */ -f32 Math_FAtan2F(f32 y, f32 x) { - if (x == 0.0f) { - if (y == 0.0f) { - return 0.0f; - } else if (y > 0.0f) { - return M_PI / 2; - } else if (y < 0.0f) { - return -M_PI / 2; - } else { - return qNaN0x10000; - } - } else if (x >= 0.0f) { - return Math_FAtanF(y / x); - } else if (y < 0.0f) { - return Math_FAtanF(y / x) - M_PI; - } else { - return M_PI - Math_FAtanF(-(y / x)); - } -} - -f32 Math_FAsinF(f32 x) { - return Math_FAtan2F(x, sqrtf(1.0f - SQ(x))); -} - -f32 Math_FAcosF(f32 x) { - return M_PI / 2 - Math_FAsinF(x); -} |
