mirror of https://github.com/zeldaret/mm.git
boot_0x80086760 OK and documented (#288)
* boot_80086760 OK, added fp header, resplit data * Some more documentation, data imported with unions * Sweep data under the rug * Move the fp header properly * Format * include/fp.h header guards Co-authored-by: Anghelo Carvajal <angheloalf95@gmail.com> * Engineer's review * Fix typo Co-authored-by: engineer124 <47598039+engineer124@users.noreply.github.com> * Rename header * while (true) Co-authored-by: Anghelo Carvajal <angheloalf95@gmail.com> Co-authored-by: engineer124 <47598039+engineer124@users.noreply.github.com>
This commit is contained in:
EllipticEllipsis
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@ -0,0 +1,34 @@
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#ifndef FIXED_POINT_H
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#define FIXED_POINT_H
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#include "ultra64.h"
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extern f32 qNaN0x3FFFFF;
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extern f32 qNaN0x10000;
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extern f32 sNaN0x3FFFFF;
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f32 floorf(f32 x);
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f64 floor(f64 x);
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s32 lfloorf(f32 x);
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s32 lfloor(f64 x);
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f32 ceilf(f32 x);
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f64 ceil(f64 x);
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s32 lceilf(f32 x);
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s32 lceil(f64 x);
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f32 truncf(f32 x);
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f64 trunc(f64 x);
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s32 ltruncf(f32 x);
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s32 ltrunc(f64 x);
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f32 nearbyintf(f32 x);
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f64 nearbyint(f64 x);
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s32 lnearbyintf(f32 x);
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s32 lnearbyint(f64 x);
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f32 roundf(f32 x);
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f64 round(f64 x);
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s32 lroundf(f32 x);
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s32 lround(f64 x);
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#endif
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2
spec
2
spec
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@ -43,8 +43,8 @@ beginseg
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include "build/data/boot/boot_800862E0.data.o"
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include "build/src/boot_O2/padsetup.o"
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include "build/src/boot_O2/boot_80086760.o"
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include "build/data/boot/boot_80086760.bss.o"
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include "build/asm/boot/fp.text.o"
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include "build/data/boot/fp.data.o"
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include "build/src/boot_O2/system_malloc.o"
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include "build/src/boot_O2/rand.o"
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include "build/src/boot_O2/__osMalloc.o"
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@ -1,27 +1,210 @@
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/**
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* MathF library
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* Contains tangent function, wrappers for a number of the handwritten functions in fp, and a suite of arctangents
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*/
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#include "global.h"
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#include "fixed_point.h"
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#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086760.s")
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extern f32 func_80086C70(f32 x);
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extern f32 func_80086CA8(f32 x);
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extern f32 func_80086D50(f32 x);
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extern f32 func_80086CE0(f32 x);
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extern f32 func_80086D18(f32 x);
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#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086794.s")
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s32 gUseAtanContFrac;
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#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_800867B4.s")
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/**
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* Tangent function computed using libultra __sinf and __cosf
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*/
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// Math_FTanF
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f32 func_80086760(f32 x) {
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return __sinf(x) / __cosf(x);
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}
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#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_800867D4.s")
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// Unused
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// Math_FFloorF
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f32 func_80086794(f32 x) {
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func_80086C70(x);
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}
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#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_800867F4.s")
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// Unused
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// Math_FCeilF
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f32 func_800867B4(f32 x) {
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func_80086CA8(x);
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}
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#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086814.s")
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// Unused
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// Math_FRoundF
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f32 func_800867D4(f32 x) {
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func_80086D50(x);
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}
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#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086834.s")
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// Unused
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// Math_FTruncF
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f32 func_800867F4(f32 x) {
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func_80086CE0(x);
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}
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#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086880.s")
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// Math_FNearbyIntF
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f32 func_80086814(f32 x) {
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func_80086D18(x);
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}
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#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_800869A4.s")
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/**
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* Arctangent approximation using a Maclaurin series [https://mathworld.wolfram.com/MaclaurinSeries.html]
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* (one quadrant, i.e. |x| < 1)
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*/
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// Math_FAtanTaylorQF
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f32 func_80086834(f32 x) {
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// Coefficients of Maclaurin series of arctangent
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static const f32 coeffs[] = {
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-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,
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};
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#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086AF0.s")
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f32 poly = x;
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f32 sq = SQ(x);
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f32 exp = x * sq;
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const f32* c = coeffs;
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f32 term;
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#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086B30.s")
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// Calculate the series until adding more terms does not change the float
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while (true) {
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term = *c++ * exp;
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if (poly + term == poly) {
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break;
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}
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poly += term;
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exp *= sq;
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}
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#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086C18.s")
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return poly;
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}
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#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086C48.s")
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/**
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* Extends previous arctangent function to the rest of the real numbers.
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* Uses the formulae arctan(x) = pi/2 - arctan(1/x)
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* and arctan(x) = pi/4 - arctan( (1-x)/(1+x) )
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* to extend the range in which the series computed by func_80086834 is a good approximation
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*/
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// Math_FAtanTaylorF
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f32 func_80086880(f32 x) {
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f32 t;
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f32 q;
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if (x > 0.0f) {
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t = x;
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} else if (x < 0.0f) {
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t = -x;
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} else if (x == 0.0f) {
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return 0.0f;
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} else {
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return qNaN0x10000;
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}
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if (t <= M_SQRT2 - 1.0f) {
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return func_80086834(x);
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}
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if (t >= M_SQRT2 + 1.0f) {
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q = M_PI / 2 - func_80086834(1.0f / t);
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} else { // in the interval (\sqrt{2} - 1, \sqrt{2} + 1)
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q = M_PI / 4 - func_80086834((1.0f - t) / (1.0f + t));
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}
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if (x > 0.0f) {
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return q;
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} else {
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return -q;
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}
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}
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/**
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* Arctangent approximation using a continued fraction
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* Cf. https://en.wikipedia.org/wiki/Gauss%27s_continued_fraction#The_series_2F1_2 ,
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* https://dlmf.nist.gov/4.25#E4
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*/
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// Math_FAtanContFracF
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f32 func_800869A4(f32 x) {
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s32 sector;
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f32 z;
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f32 conv;
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f32 sq;
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s32 i;
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if (x >= -1.0f && x <= 1.0f) {
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sector = 0;
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} else if (x > 1.0f) {
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sector = 1;
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x = 1.0f / x;
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} else if (x < -1.0f) {
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sector = -1;
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x = 1.0f / x;
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} else {
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return qNaN0x10000;
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}
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// Builds the continued fraction from the innermost fraction out
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sq = SQ(x);
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conv = 0.0f;
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z = 8.0f;
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for (i = 8; i != 0; i--) {
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conv = SQ(z) * sq / (2.0f * z + 1.0f + conv);
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z -= 1.0f;
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}
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conv = x / (1.0f + conv);
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if (sector == 0) {
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return conv;
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} else if (sector > 0) {
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return M_PI / 2 - conv;
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} else {
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return -M_PI / 2 - conv;
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}
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}
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// Math_FAtanF
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/**
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* Single-argument arctangent, only used by the two-argument function.
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* Nothing else sets the bss variable gUseAtanContFrac, so the Maclaurin series is always used
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*/
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f32 func_80086AF0(f32 x) {
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if (!gUseAtanContFrac) {
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return func_80086880(x);
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} else {
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return func_800869A4(x);
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}
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}
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// Math_FAtan2F
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/**
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* Main two-argument arctangent function
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*/
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f32 func_80086B30(f32 y, f32 x) {
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if (x == 0.0f) {
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if (y == 0.0f) {
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return 0.0f;
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} else if (y > 0.0f) {
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return M_PI / 2;
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} else if (y < 0.0f) {
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return -M_PI / 2;
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} else {
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return qNaN0x10000;
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}
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} else if (x >= 0.0f) {
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return func_80086AF0(y / x);
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} else if (y < 0.0f) {
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return func_80086AF0(y / x) - M_PI;
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} else {
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return M_PI - func_80086AF0(-(y / x));
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}
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}
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// Math_FAsinF
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f32 func_80086C18(f32 x) {
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return func_80086B30(x, sqrtf(1.0f - SQ(x)));
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}
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// Math_FAcosF
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f32 func_80086C48(f32 x) {
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return M_PI / 2 - func_80086C18(x);
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}
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@ -257,6 +257,7 @@
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0x80096C40 : "stackcheck",
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0x80096C50 : "gfxprint",
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0x80097500 : "boot_800862E0",
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0x80097520 : "fp",
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0x80097530 : "rand",
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0x80097540 : "vimodeHpf",
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0x800975E0 : "sins",
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0x80096CF0:("sGfxPrintUnkData","u8","[8]",0x8),
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0x80096CF8:("sGfxPrintFontData","u8","[0x800]",0x800),
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0x80097500:("D_80097500","UNK_TYPE4","",0x4),
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0x80097524:("D_80097524","UNK_TYPE4","",0x4),
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0x80097520:("qNaN0x3FFFFF","f32","",0x4),
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0x80097524:("qNaN0x10000","f32","",0x4),
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0x80097528:("sNaN0x3FFFFF","f32","",0x4),
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0x80097530:("sRandInt","u32","",0x4),
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0x80097540:("osViModeNtscHpf1","OSViMode","",0x50),
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0x80097590:("osViModePalLan1","OSViMode","",0x50),
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