RNG doc (#1892)

* RNG doc

* Add some missing note qualifiers in comments

* code_800FD970 -> rand in Makefile and disasm CSVs

Makefile

@@ -238,7 +238,7 @@ $(BUILD_DIR)/src/boot/stackcheck.o: OPTFLAGS := -O2
 $(BUILD_DIR)/src/code/__osMalloc.o: OPTFLAGS := -O2
 $(BUILD_DIR)/src/code/code_800FC620.o: OPTFLAGS := -O2
 $(BUILD_DIR)/src/code/code_800FCE80.o: OPTFLAGS := -O2
-$(BUILD_DIR)/src/code/code_800FD970.o: OPTFLAGS := -O2
+$(BUILD_DIR)/src/code/rand.o: OPTFLAGS := -O2
 $(BUILD_DIR)/src/code/gfxprint.o: OPTFLAGS := -O2
 $(BUILD_DIR)/src/code/jpegutils.o: OPTFLAGS := -O2
 $(BUILD_DIR)/src/code/jpegdecoder.o: OPTFLAGS := -O2

spec

@@ -482,7 +482,7 @@ beginseg
     include "$(BUILD_DIR)/src/code/code_800FCE80.o"
     include "$(BUILD_DIR)/src/code/fp.o"
     include "$(BUILD_DIR)/src/code/system_malloc.o"
-    include "$(BUILD_DIR)/src/code/code_800FD970.o"
+    include "$(BUILD_DIR)/src/code/rand.o"
     include "$(BUILD_DIR)/src/code/__osMalloc.o"
 #if !OOT_DEBUG
     include "$(BUILD_DIR)/src/libultra/libc/sprintf.o"

src/code/code_800FD970.c

@@ -1,79 +0,0 @@
-#include "global.h"
-
-// The latest generated random number, used to generate the next number in the sequence.
-static u32 sRandInt = 1;
-
-// Space to store a value to be re-interpreted as a float.
-static u32 sRandFloat;
-
-/**
- * Gets the next integer in the sequence of pseudo-random numbers.
- */
-u32 Rand_Next(void) {
-    return sRandInt = (sRandInt * 1664525) + 1013904223;
-}
-
-/**
- * Seeds the pseudo-random number generator by providing a starting value.
- */
-void Rand_Seed(u32 seed) {
-    sRandInt = seed;
-}
-
-/**
- * Returns a pseudo-random floating-point number between 0.0f and 1.0f, by generating
- * the next integer and masking it to an IEEE-754 compliant floating-point number
- * between 1.0f and 2.0f, returning the result subtract 1.0f.
- */
-f32 Rand_ZeroOne(void) {
-    sRandInt = (sRandInt * 1664525) + 1013904223;
-    sRandFloat = ((sRandInt >> 9) | 0x3F800000);
-    return *((f32*)&sRandFloat) - 1.0f;
-}
-
-/**
- * Returns a pseudo-random floating-point number between -0.5f and 0.5f by the same
- * manner in which Rand_ZeroOne generates its result.
- */
-f32 Rand_Centered(void) {
-    sRandInt = (sRandInt * 1664525) + 1013904223;
-    sRandFloat = ((sRandInt >> 9) | 0x3F800000);
-    return *((f32*)&sRandFloat) - 1.5f;
-}
-
-/**
- * Seeds a pseudo-random number at rndNum with a provided seed.
- */
-void Rand_Seed_Variable(u32* rndNum, u32 seed) {
-    *rndNum = seed;
-}
-
-/**
- * Generates the next pseudo-random integer from the provided rndNum.
- */
-u32 Rand_Next_Variable(u32* rndNum) {
-    return *rndNum = (*rndNum * 1664525) + 1013904223;
-}
-
-/**
- * Generates the next pseudo-random floating-point number between 0.0f and
- * 1.0f from the provided rndNum.
- */
-f32 Rand_ZeroOne_Variable(u32* rndNum) {
-    u32 next = (*rndNum * 1664525) + 1013904223;
-
-    sRandFloat = ((*rndNum = next) >> 9) | 0x3F800000;
-    return *((f32*)&sRandFloat) - 1.0f;
-}
-
-/**
- * Generates the next pseudo-random floating-point number between -0.5f and
- * 0.5f from the provided rndNum.
- */
-f32 Rand_Centered_Variable(u32* rndNum) {
-    u32 next = (*rndNum * 1664525) + 1013904223;
-
-    *rndNum = next;
-    sRandFloat = (next >> 9) | 0x3F800000;
-    return *((f32*)&sRandFloat) - 1.5f;
-}

src/code/rand.c

@@ -0,0 +1,162 @@
+/**
+ * @file rand.c
+ *
+ * This file implements the primary random number generator the game relies on. The generator is pseudo-random and
+ * implemented as a Linear Congruential Generator (LCG).
+ *
+ * A LCG computes random numbers sequentially via the relation
+ *      X(n+1) = (a * X(n) + c) mod m
+ * where m is the modulus, a is the multiplier and c is the increment.
+ *
+ * These three parameters (a,c,m) completely specify the LCG and should be chosen such that
+ *  - m > 0
+ *  - 0 < a < m
+ *  - 0 <= c < m
+ *
+ * The period of the LCG (a, c, m) is the smallest period p such that X(n + p) = X(n), past n=p the sequence will repeat
+ * itself in its outputs.
+ * A good LCG should have the maximum possible period, which will be equal to m as there are at most m possible values
+ * for X. This occurs when (Hull, T.E., & Dobell, A.R. (1962). Random Number Generators. Siam Review, 4, 230-254.):
+ *  - m,c are relatively prime, that is the only integer that divides both m and c with no remainder is 1.
+ *  - a - 1 is divisible by all prime factors of m.
+ *  - a - 1 is divisible by 4 if m is divisible by 4.
+ *
+ * Ideally m is chosen to be a large power of 2 so that the modulo operation is inexpensive to compute. In this case the
+ * prime factors of m = 2^k are just k copies of 2. For k > 1 m is divisible by 4, so a - 1 must be divisible by 4. 2^k
+ * and c can easily be made relatively prime by making c an odd number.
+ * If we let k=32 to match the size of an integer, the modulo operation is made implicit by the width of the data type
+ * and becomes free to compute.
+ *
+ * The parameter a should be selected such that a-1 is divisible by 4 (and hence divisible by 2) and c should be any odd
+ * number. The precise values should fare well against the spectral test, a measure of "how random" a particular LCG is.
+ * A pair (a,c) that satisfies these requirements is (1664525, 1013904223), recommended by "Numerical Recipes in C: The
+ * Art of Scientific Computing" (p. 284).
+ *
+ * Therefore, the LCG with parameters (1664525, 1013904223, 2^32) that is implemented in this file has a maximal period
+ * of 2^32 and produces high-quality pseudo-random numbers.
+ *
+ * @note If sampling the LCG for a n-bit number it is important to use the upper n bits instead of the lower n bits of
+ * the LCG output. The lower n bits only have a period of 2^n which may significantly worsen the quality of the
+ * resulting random numbers compared to the quality of the full 32-bit result.
+ *
+ * @note Original name: qrand.c
+ */
+#include "ultra64.h"
+
+#define RAND_MULTIPLIER 1664525
+#define RAND_INCREMENT 1013904223
+
+/**
+ * The latest generated random number, used to generate the next number in the sequence.
+ *
+ * @note Original name: __qrand_idum
+ */
+static u32 sRandInt = 1;
+
+/**
+ * Space to store a value to be re-interpreted as a float.
+ *
+ * @note Orignal name: __qrand_itemp
+ */
+static fu sRandFloat;
+
+/**
+ * Gets the next integer in the sequence of pseudo-random numbers.
+ *
+ * @note Original name: qrand
+ */
+u32 Rand_Next(void) {
+    return sRandInt = sRandInt * RAND_MULTIPLIER + RAND_INCREMENT;
+}
+
+/**
+ * Seeds the pseudo-random number generator by providing a starting value.
+ *
+ * @note Original name: sqrand
+ */
+void Rand_Seed(u32 seed) {
+    sRandInt = seed;
+}
+
+/**
+ * Returns a pseudo-random floating-point number between 0.0f and 1.0f, by generating the next integer and masking it
+ * to an IEEE-754 compliant floating-point number between 1.0f and 2.0f, returning the result subtract 1.0f.
+ *
+ * @note This technique for generating pseudo-random floats is recommended as a particularly fast but potentially
+ *       non-portable generator in "Numerical Recipes in C: The Art of Scientic Computing", pp. 284-5.
+ *
+ * @note Original name: fqrand
+ */
+f32 Rand_ZeroOne(void) {
+    sRandInt = sRandInt * RAND_MULTIPLIER + RAND_INCREMENT;
+    // Samples the upper 23 bits to avoid effectively reducing the LCG period.
+    sRandFloat.i = (sRandInt >> 9) | 0x3F800000;
+    return sRandFloat.f - 1.0f;
+}
+
+/**
+ * Returns a pseudo-random floating-point number between -0.5f and 0.5f by the same manner in which Rand_ZeroOne
+ * generates its result.
+ *
+ * @see Rand_ZeroOne
+ *
+ * @note Original name: fqrand2
+ */
+f32 Rand_Centered(void) {
+    sRandInt = sRandInt * RAND_MULTIPLIER + RAND_INCREMENT;
+    sRandFloat.i = (sRandInt >> 9) | 0x3F800000;
+    return sRandFloat.f - 1.5f;
+}
+
+//! All functions below are unused variants of the above four, that use a provided random number variable instead of the
+//! internal `sRandInt`
+
+/**
+ * Seeds a pseudo-random number at rndNum with a provided starting value.
+ *
+ * @see Rand_Seed
+ *
+ * @note Original name: sqrand_r
+ */
+void Rand_Seed_Variable(u32* rndNum, u32 seed) {
+    *rndNum = seed;
+}
+
+/**
+ * Generates the next pseudo-random integer from the provided rndNum.
+ *
+ * @see Rand_Next
+ *
+ * @note Original name: qrand_r
+ */
+u32 Rand_Next_Variable(u32* rndNum) {
+    return *rndNum = (*rndNum) * RAND_MULTIPLIER + RAND_INCREMENT;
+}
+
+/**
+ * Generates the next pseudo-random floating-point number between 0.0f and 1.0f from the provided rndNum.
+ *
+ * @see Rand_ZeroOne
+ *
+ * @note Original name: fqrand_r
+ */
+f32 Rand_ZeroOne_Variable(u32* rndNum) {
+    u32 next = (*rndNum) * RAND_MULTIPLIER + RAND_INCREMENT;
+
+    sRandFloat.i = ((*rndNum = next) >> 9) | 0x3F800000;
+    return sRandFloat.f - 1.0f;
+}
+
+/**
+ * Generates the next pseudo-random floating-point number between -0.5f and 0.5f from the provided rndNum.
+ *
+ * @see Rand_ZeroOne, Rand_Centered
+ *
+ * @note Original name: fqrand2_r
+ */
+f32 Rand_Centered_Variable(u32* rndNum) {
+    u32 next = (*rndNum) * RAND_MULTIPLIER + RAND_INCREMENT;
+
+    sRandFloat.i = ((*rndNum = next) >> 9) | 0x3F800000;
+    return sRandFloat.f - 1.5f;
+}

tools/disasm/gc-eu-mq/files_code.csv

@@ -132,7 +132,7 @@ BCBE0,800CDAE0,src/code/padsetup
 BCD20,800CDC20,src/code/code_800FCE80
 BD230,800CE130,src/code/fp
 BD390,800CE290,src/code/system_malloc
-BD560,800CE460,src/code/code_800FD970
+BD560,800CE460,src/code/rand
 BD720,800CE620,src/code/__osMalloc
 BE4D0,800CF3D0,src/libultra/libc/sprintf
 BE5A0,800CF4A0,src/code/printutils
@@ -295,7 +295,7 @@ F0640,80101540,src/code/logseverity
 F0650,80101550,src/code/gfxprint
 F0F00,80101E00,src/code/code_800FC620
 F0F20,80101E20,src/code/fp
-F0F30,80101E30,src/code/code_800FD970
+F0F30,80101E30,src/code/rand
 F0F40,80101E40,src/code/__osMalloc
 F0F50,80101E50,src/libultra/gu/sins
 F1750,80102650,src/libultra/io/siacs
@@ -451,7 +451,7 @@ offset,vram,.bss
 119530,8012A430,src/code/gfxprint
 119540,8012A440,src/code/code_800FCE80
 119550,8012A450,src/code/system_malloc
-119580,8012A480,src/code/code_800FD970
+119580,8012A480,src/code/rand
 119590,8012A490,src/code/__osMalloc
 1195A0,8012A4A0,src/code/jpegdecoder
 1195B0,8012A4B0,src/libultra/io/sptask