jak-project/goal_src/jak1/engine/math/math.gc

;;-*-Lisp-*-
(in-package goal)
(bundles "ENGINE.CGO" "GAME.CGO")
(require "kernel/gcommon.gc")

;; various math helpers

;; DECOMP BEGINS

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;;;; float utility
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(defun truncate ((x float))
  "Truncate a floating point number to an integer value.
  Positive values round down and negative values round up."
  (declare (inline))
  (the float (the int x)))

(defun integral? ((x float))
  "Is a float an exact integer?"
  (= (truncate x) x))

(defun fractional-part ((x float))
  "Get the fractional part of a float"
  (- x (truncate x)))

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;;;; bitfield types
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(deftype rgba (uint32)
  ((r uint8 :offset 0)
   (g uint8 :offset 8)
   (b uint8 :offset 16)
   (a uint8 :offset 24)))

(defmacro static-rgba (r g b a)
  "make a new static rgba"
  `(new 'static 'rgba :r ,r :g ,g :b ,b :a ,a))

(defmacro static-rgba-uint (col)
  "make a new static rgba"
  `(the-as rgba ,col))

;; TODO: fields
(deftype xyzw (uint128) ())

;; TODO: fields
(deftype xyzwh (uint128) ())

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;;;; utility functions
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(defun log2 ((x int))
  "Straight out of Bit Twiddling Hacks graphics.stanford.edu.
   This website is old enough that they possibly used this back
   in 1999."
  (- (sar (the-as int (the float x)) 23) 127))

(defun seek ((x float) (target float) (diff float))
  "Move x toward target by at most diff, with floats"
  (let ((err (- target x)))
    (cond
      ((>= diff (fabs err))
       ;; can get there in one go
       target)
      ((>= err 0)
       ;; increase
       (+ x diff))
      (else (- x diff)))))

(defun lerp ((minimum float) (maximum float) (amount float))
  "Interpolate between minimum and maximum.  The output is not clamped."
  (+ minimum (* amount (- maximum minimum))))

(defun lerp-scale ((min-out float) (max-out float) (in float) (min-in float) (max-in float))
  "Interpolate from [min-in, max-in] to [min-out, max-out].
   If the output is out of range, it will be clamped.
   This is not a great implementation."
  (let ((scale (fmax 0.0 (fmin 1.0 (/ (- in min-in) (- max-in min-in))))))
    (+ (* (- 1.0 scale) min-out) (* scale max-out))))

(defun lerp-clamp ((minimum float) (maximum float) (amount float))
  "Interpolate between minimum and maximum, but saturate the amount to [0, 1]"
  (cond
    ((>= 0.0 amount) minimum)
    ((>= amount 1.0) maximum)
    (else
     ;; the implementation in lerp uses fewer operations...
     (+ (* (- 1.0 amount) minimum) (* amount maximum)))))

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;;;; utility macros
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(defmacro seek! (place target rate)
  "Macro to use seek in-place. place is the base, and where the result is stored."
  `(set! ,place (seek ,place ,target ,rate)))

(defmacro seekl! (place target rate)
  "Macro to use seekl in-place. place is the base, and where the result is stored."
  `(set! ,place (seekl ,place ,target ,rate)))

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;;;; integer utility
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(defun seekl ((x int) (target int) (diff int))
  "Move x toward a target by at most diff, with integers"
  (let ((err (- target x))) (if (< (abs err) diff) (return-from #f target)) (if (>= err 0) (+ x diff) (- x diff))))

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;;;; random vu hardware
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;; in the PS2 there is a R register for generating random numbers
;; it is a "32-bit" register, but the upper bits are fixed so it always
;; represents a float in (1, 2).
;; we don't have this register on x86, so we add a special global: *_vu-reg-R_*
(define *_vu-reg-R_* 0)

(defun rand-vu-init ((seed float))
  "Initialize the VU0 random generator"
  ;; (.ctc2.i R arg0)
  ;; (.cfc2.i v0 R)
  (set! *_vu-reg-R_* (logior #x3F800000 (logand (the-as int seed) #x007FFFFF)))
  (the-as float *_vu-reg-R_*))

;; this is _almost_ sqrt(2) = 1.414
(rand-vu-init 1.418091058731079)

;; rand-vu
(defun rand-vu ()
  "Get a random number in [0, 1) and advance the random generator."
  ;; (.vrget.xyzw vf1) - get current random
  (let ((current-random *_vu-reg-R_*))
    ;; here they update the random generate with some junk
    ;; for now, we don't do this in OpenGOAL.
    ;; (.vsqrty Q vf1)
    ;; (.vaddq.x vf2 vf0 Q) ;; you're not allowed to do this!
    ;; (.vrxorw vf2)
    ;; and advance
    ;; (.vrnext.xyzw vf1)
    (let ((x (logand 1 (shr current-random 4)))
          (y (logand 1 (shr current-random 22))))
      (set! current-random (shl current-random 1))
      (set! current-random (logxor current-random (logxor x y)))
      (logxor! current-random (pc-rand))
      (set! *_vu-reg-R_* (logior #x3f800000 (logand current-random #x7fffff)))))
  ;; (.vsubw.xyzw vf1 vf1 vf0)
  ;; (.qmfc2.i v0 vf1)
  (- (the-as float *_vu-reg-R_*) 1.0))

;; rand-vu-nostep
(defun rand-vu-nostep ()
  "Get the number currently in the random generator.
   This will be equal to the last call of (rand-vu)
   This will not update the random generator"
  (- (the-as float *_vu-reg-R_*) 1.0))

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;;;; random vu utilities
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(defun rand-vu-float-range ((minimum float) (maximum float))
  "Get a random number in the given range.
  TODO: is this inclusive? I think it's [min, max)"
  (+ minimum (* (rand-vu) (- maximum minimum))))

(defun rand-vu-percent? ((prob float))
  "Get a boolean that's true with the given probability."
  (>= prob (rand-vu)))

(defun rand-vu-int-range ((first int) (second int))
  "Get an integer the given range. Inclusive of both?
   It looks like they actually did this right??"
  (local-vars (float-in-range float))
  ;; increment the larger of the range, so it is inclusive
  ;; (we should have (max - min) + 1 buckets)
  (if (< first second) (set! second (+ second 1)) (set! first (+ first 1)))
  ;; get a float in the range
  (set! float-in-range (rand-vu-float-range (the float first) (the float second)))
  ;; negatives round up and positives round down.
  ;; but we want all to round consistently, so we subtract one from negatives.
  (when (< float-in-range 0)
    (set! float-in-range (+ -1.0 float-in-range)))
  ;; and back to integer.
  (the int float-in-range))

(defun rand-vu-int-count ((maximum int))
  "Get an integer in [0, maximum)"
  (the int (* (rand-vu) (the float maximum))))

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;;;; terrible random integer generator
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(deftype random-generator (basic)
  ((seed uint32)))

(define *random-generator* (new 'global 'random-generator))

;; I wonder who wrote this code.
(set! (-> *random-generator* seed) #x666edd1e)

(defmacro sext32-64 (x)
  "Sign extend a 32-bit value to 64-bits"
  `(sar (shl ,x 32) 32))

(defun rand-uint31-gen ((gen random-generator))
  "Generate a supposedly random integer.
  Note, this might not quite be right.
  But the highest bit is always zero, like it says
  and it looks kinda random to me."
  (let* ((sd (-> gen seed))
         ;; addiu v1, r0, 16807
         ;; mult3 v0, v1, a1
         (prod (imul64 16807 sd))
         ;; mfhi v1
         (hi (shr prod 32)) ;; sign extend this?
         (lo (sar (shl prod 32) 32))
         ;; daddu v1, v1, v1
         (v1 (+ hi hi))
         ;; srl a1, v0, 31
         (a1 (logand #xffffffff (shr lo 31)))
         ;; or v1, v1, a1
         ;; daddu v0, v0 v1
         (result (+ lo (logior v1 a1))))
    (set! result (shr (logand #xffffffff (shl result 1)) 1))
    (set! (-> gen seed) result)
    (the uint result)))

(defmacro rand-float-gen (&key (gen *random-generator*))
  "Generate a float from [0, 1)"
  `(+ -1.0 (the-as float (logior #x3f800000 (/ (rand-uint31-gen ,gen) 256)))))