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

;;-*-Lisp-*-
(in-package goal)

;; name: math.gc
;; name in dgo: math
;; dgos: GAME, ENGINE

;; contains various math helpers

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;;;; float macros
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;; at some point, this could be more optimized.
;; MIPS has an explicit abs.s instruction, but x86-64 doesn't.
;; modern clang on O3 does a comiss/branch and this is probably pretty close.

(defmacro fabs (x)
  `(if (< (the float ,x) 0)
       (- (the float ,x))
       (the float ,x))
  )


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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))
  )

;; todo, rgba, xyzw, xyzwh

(defun log2 ((x int))
  "Straight out of Bit Twiddling Hacks graphics.stanford.edu"
  (- (sarv (the-as integer (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)))
    ;; if we can get there all at once
    (if (<= (fabs err) diff)
      (return-from #f target)
      )

    (if (>= err 0)
      (+ x diff)
      (- 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.  Clamp output.
  For some reason, the interpolate here is done in a less efficient way than lerp."
  (if (<= amount 0.0)
    (return-from #f minimum)
    )

  (if (>= amount 1.0)
    (return-from #f maximum)
    )
  ;; lerp computes this part, but more efficiently
  (+ (* (- 1.0 amount) minimum)
     (* amount maximum)
     )
  )

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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
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;; TODO

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;;;; terrible random integer generator
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(deftype random-generator (basic)
  ((seed uint32  :offset-assert 4)
   )
  :method-count-assert 9
  :size-assert         #x8
  :flag-assert         #x900000008
  )

(define *random-generator* (new 'global 'random-generator))
;; I wonder who wrote this code.
(set! (-> *random-generator* seed) #x666EDD1E)

(defmacro sext32-64 (x)
  `(sarv (shlv ,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 (shrv prod 32)) ;; sign extend this?
         (lo (sarv (shlv prod 32) 32))
         ;; daddu v1, v1, v1
         (v1 (+ hi hi))
         ;; srl a1, v0, 31
         (a1 (logand #xffffffff (shrv lo 31)))
         ;; or v1, v1, a1
         ;; daddu v0, v0 v1
         (result (+ lo (logior v1 a1)))
        )
    (set! result (shrv (logand #xffffffff (shlv result 1)) 1))
    (set! (-> gen seed) result)
    result
    )
  )