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>

include/fixed_point.h

@@ -0,0 +1,34 @@
+#ifndef FIXED_POINT_H
+#define FIXED_POINT_H
+#include "ultra64.h"
+
+extern f32 qNaN0x3FFFFF;
+extern f32 qNaN0x10000;
+extern f32 sNaN0x3FFFFF;
+
+f32 floorf(f32 x);
+f64 floor(f64 x);
+s32 lfloorf(f32 x);
+s32 lfloor(f64 x);
+
+f32 ceilf(f32 x);
+f64 ceil(f64 x);
+s32 lceilf(f32 x);
+s32 lceil(f64 x);
+
+f32 truncf(f32 x);
+f64 trunc(f64 x);
+s32 ltruncf(f32 x);
+s32 ltrunc(f64 x);
+
+f32 nearbyintf(f32 x);
+f64 nearbyint(f64 x);
+s32 lnearbyintf(f32 x);
+s32 lnearbyint(f64 x);
+
+f32 roundf(f32 x);
+f64 round(f64 x);
+s32 lroundf(f32 x);
+s32 lround(f64 x);
+
+#endif

spec

@@ -43,8 +43,8 @@ beginseg
     include "build/data/boot/boot_800862E0.data.o"
     include "build/src/boot_O2/padsetup.o"
     include "build/src/boot_O2/boot_80086760.o"
-    include "build/data/boot/boot_80086760.bss.o"
     include "build/asm/boot/fp.text.o"
+    include "build/data/boot/fp.data.o"
     include "build/src/boot_O2/system_malloc.o"
     include "build/src/boot_O2/rand.o"
     include "build/src/boot_O2/__osMalloc.o"

src/boot_O2/boot_80086760.c

@@ -1,27 +1,210 @@
+/**
+ * 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"
 
-#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086760.s")
+extern f32 func_80086C70(f32 x);
+extern f32 func_80086CA8(f32 x);
+extern f32 func_80086D50(f32 x);
+extern f32 func_80086CE0(f32 x);
+extern f32 func_80086D18(f32 x);
 
-#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086794.s")
+s32 gUseAtanContFrac;
 
-#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_800867B4.s")
+/**
+ * Tangent function computed using libultra __sinf and __cosf
+ */
+// Math_FTanF
+f32 func_80086760(f32 x) {
+    return __sinf(x) / __cosf(x);
+}
 
-#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_800867D4.s")
+// Unused
+// Math_FFloorF
+f32 func_80086794(f32 x) {
+    func_80086C70(x);
+}
 
-#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_800867F4.s")
+// Unused
+// Math_FCeilF
+f32 func_800867B4(f32 x) {
+    func_80086CA8(x);
+}
 
-#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086814.s")
+// Unused
+// Math_FRoundF
+f32 func_800867D4(f32 x) {
+    func_80086D50(x);
+}
 
-#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086834.s")
+// Unused
+// Math_FTruncF
+f32 func_800867F4(f32 x) {
+    func_80086CE0(x);
+}
 
-#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086880.s")
+// Math_FNearbyIntF
+f32 func_80086814(f32 x) {
+    func_80086D18(x);
+}
 
-#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_800869A4.s")
+/**
+ * Arctangent approximation using a Maclaurin series [https://mathworld.wolfram.com/MaclaurinSeries.html]
+ * (one quadrant, i.e. |x| < 1)
+ */
+// Math_FAtanTaylorQF
+f32 func_80086834(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,
+    };
 
-#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086AF0.s")
+    f32 poly = x;
+    f32 sq = SQ(x);
+    f32 exp = x * sq;
+    const f32* c = coeffs;
+    f32 term;
 
-#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086B30.s")
+    // 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;
+    }
 
-#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086C18.s")
+    return poly;
+}
 
-#pragma GLOBAL_ASM("asm/non_matchings/boot/boot_80086760/func_80086C48.s")
+/**
+ * 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 func_80086834 is a good approximation
+ */
+// Math_FAtanTaylorF
+f32 func_80086880(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 func_80086834(x);
+    }
+
+    if (t >= M_SQRT2 + 1.0f) {
+        q = M_PI / 2 - func_80086834(1.0f / t);
+    } else { // in the interval (\sqrt{2} - 1, \sqrt{2} + 1)
+        q = M_PI / 4 - func_80086834((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
+ */
+// Math_FAtanContFracF
+f32 func_800869A4(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;
+    }
+}
+
+// Math_FAtanF
+/**
+ * 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 func_80086AF0(f32 x) {
+    if (!gUseAtanContFrac) {
+        return func_80086880(x);
+    } else {
+        return func_800869A4(x);
+    }
+}
+
+// Math_FAtan2F
+/**
+ * Main two-argument arctangent function
+ */
+f32 func_80086B30(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 func_80086AF0(y / x);
+    } else if (y < 0.0f) {
+        return func_80086AF0(y / x) - M_PI;
+    } else {
+        return M_PI - func_80086AF0(-(y / x));
+    }
+}
+
+// Math_FAsinF
+f32 func_80086C18(f32 x) {
+    return func_80086B30(x, sqrtf(1.0f - SQ(x)));
+}
+
+// Math_FAcosF
+f32 func_80086C48(f32 x) {
+    return M_PI / 2 - func_80086C18(x);
+}

tools/disasm/files.txt

@@ -257,6 +257,7 @@
             0x80096C40 : "stackcheck",
             0x80096C50 : "gfxprint",
             0x80097500 : "boot_800862E0",
+            0x80097520 : "fp",
             0x80097530 : "rand",
             0x80097540 : "vimodeHpf",
             0x800975E0 : "sins",

tools/disasm/variables.txt

@@ -36,7 +36,9 @@
     0x80096CF0:("sGfxPrintUnkData","u8","[8]",0x8),
     0x80096CF8:("sGfxPrintFontData","u8","[0x800]",0x800),
     0x80097500:("D_80097500","UNK_TYPE4","",0x4),
-    0x80097524:("D_80097524","UNK_TYPE4","",0x4),
+    0x80097520:("qNaN0x3FFFFF","f32","",0x4),
+    0x80097524:("qNaN0x10000","f32","",0x4),
+    0x80097528:("sNaN0x3FFFFF","f32","",0x4),
     0x80097530:("sRandInt","u32","",0x4),
     0x80097540:("osViModeNtscHpf1","OSViMode","",0x50),
     0x80097590:("osViModePalLan1","OSViMode","",0x50),