tests/perf_bench: Add some miscellaneous performance benchmarks.

misc_aes.py and misc_mandel.py are adapted from sources in this repository.
misc_pystone.py is the standard Python pystone test.  misc_raytrace.py is
written from scratch.

4 files changed, 724 insertions, 0 deletions

diff --git a/tests/perf_bench/misc_aes.py b/tests/perf_bench/misc_aes.py
new file mode 100644
index 0000000000..5413a06b12
--- /dev/null
+++ b/tests/perf_bench/misc_aes.py
@@ -0,0 +1,225 @@
+# Pure Python AES encryption routines.
+#
+# AES is integer based and inplace so doesn't use the heap.  It is therefore
+# a good test of raw performance and correctness of the VM/runtime.
+#
+# The AES code comes first (code originates from a C version authored by D.P.George)
+# and then the test harness at the bottom.
+#
+# MIT license; Copyright (c) 2016 Damien P. George on behalf of Pycom Ltd
+
+##################################################################
+# discrete arithmetic routines, mostly from a precomputed table
+
+# non-linear, invertible, substitution box
+aes_s_box_table = bytes((
+    0x63,0x7c,0x77,0x7b,0xf2,0x6b,0x6f,0xc5,0x30,0x01,0x67,0x2b,0xfe,0xd7,0xab,0x76,
+    0xca,0x82,0xc9,0x7d,0xfa,0x59,0x47,0xf0,0xad,0xd4,0xa2,0xaf,0x9c,0xa4,0x72,0xc0,
+    0xb7,0xfd,0x93,0x26,0x36,0x3f,0xf7,0xcc,0x34,0xa5,0xe5,0xf1,0x71,0xd8,0x31,0x15,
+    0x04,0xc7,0x23,0xc3,0x18,0x96,0x05,0x9a,0x07,0x12,0x80,0xe2,0xeb,0x27,0xb2,0x75,
+    0x09,0x83,0x2c,0x1a,0x1b,0x6e,0x5a,0xa0,0x52,0x3b,0xd6,0xb3,0x29,0xe3,0x2f,0x84,
+    0x53,0xd1,0x00,0xed,0x20,0xfc,0xb1,0x5b,0x6a,0xcb,0xbe,0x39,0x4a,0x4c,0x58,0xcf,
+    0xd0,0xef,0xaa,0xfb,0x43,0x4d,0x33,0x85,0x45,0xf9,0x02,0x7f,0x50,0x3c,0x9f,0xa8,
+    0x51,0xa3,0x40,0x8f,0x92,0x9d,0x38,0xf5,0xbc,0xb6,0xda,0x21,0x10,0xff,0xf3,0xd2,
+    0xcd,0x0c,0x13,0xec,0x5f,0x97,0x44,0x17,0xc4,0xa7,0x7e,0x3d,0x64,0x5d,0x19,0x73,
+    0x60,0x81,0x4f,0xdc,0x22,0x2a,0x90,0x88,0x46,0xee,0xb8,0x14,0xde,0x5e,0x0b,0xdb,
+    0xe0,0x32,0x3a,0x0a,0x49,0x06,0x24,0x5c,0xc2,0xd3,0xac,0x62,0x91,0x95,0xe4,0x79,
+    0xe7,0xc8,0x37,0x6d,0x8d,0xd5,0x4e,0xa9,0x6c,0x56,0xf4,0xea,0x65,0x7a,0xae,0x08,
+    0xba,0x78,0x25,0x2e,0x1c,0xa6,0xb4,0xc6,0xe8,0xdd,0x74,0x1f,0x4b,0xbd,0x8b,0x8a,
+    0x70,0x3e,0xb5,0x66,0x48,0x03,0xf6,0x0e,0x61,0x35,0x57,0xb9,0x86,0xc1,0x1d,0x9e,
+    0xe1,0xf8,0x98,0x11,0x69,0xd9,0x8e,0x94,0x9b,0x1e,0x87,0xe9,0xce,0x55,0x28,0xdf,
+    0x8c,0xa1,0x89,0x0d,0xbf,0xe6,0x42,0x68,0x41,0x99,0x2d,0x0f,0xb0,0x54,0xbb,0x16,
+))
+
+# multiplication of polynomials modulo x^8 + x^4 + x^3 + x + 1 = 0x11b
+def aes_gf8_mul_2(x):
+    if x & 0x80:
+        return (x << 1) ^ 0x11b
+    else:
+        return x << 1
+
+def aes_gf8_mul_3(x):
+    return x ^ aes_gf8_mul_2(x)
+
+# non-linear, invertible, substitution box
+def aes_s_box(a):
+    return aes_s_box_table[a & 0xff]
+
+# return 0x02^(a-1) in GF(2^8)
+def aes_r_con(a):
+    ans = 1
+    while a > 1:
+        ans <<= 1;
+        if ans & 0x100:
+            ans ^= 0x11b
+        a -= 1
+    return ans
+
+##################################################################
+# basic AES algorithm; see FIPS-197
+
+# all inputs must be size 16
+def aes_add_round_key(state, w):
+    for i in range(16):
+        state[i] ^= w[i]
+
+# combined sub_bytes, shift_rows, mix_columns, add_round_key
+# all inputs must be size 16
+def aes_sb_sr_mc_ark(state, w, w_idx, temp):
+    temp_idx = 0
+    for i in range(4):
+        x0 = aes_s_box_table[state[i * 4]]
+        x1 = aes_s_box_table[state[1 + ((i + 1) & 3) * 4]]
+        x2 = aes_s_box_table[state[2 + ((i + 2) & 3) * 4]]
+        x3 = aes_s_box_table[state[3 + ((i + 3) & 3) * 4]]
+        temp[temp_idx]     = aes_gf8_mul_2(x0) ^ aes_gf8_mul_3(x1) ^ x2 ^ x3 ^ w[w_idx]
+        temp[temp_idx + 1] = x0 ^ aes_gf8_mul_2(x1) ^ aes_gf8_mul_3(x2) ^ x3 ^ w[w_idx + 1]
+        temp[temp_idx + 2] = x0 ^ x1 ^ aes_gf8_mul_2(x2) ^ aes_gf8_mul_3(x3) ^ w[w_idx + 2]
+        temp[temp_idx + 3] = aes_gf8_mul_3(x0) ^ x1 ^ x2 ^ aes_gf8_mul_2(x3) ^ w[w_idx + 3]
+        w_idx += 4
+        temp_idx += 4
+    for i in range(16):
+        state[i] = temp[i]
+
+# combined sub_bytes, shift_rows, add_round_key
+# all inputs must be size 16
+def aes_sb_sr_ark(state, w, w_idx, temp):
+    temp_idx = 0
+    for i in range(4):
+        x0 = aes_s_box_table[state[i * 4]]
+        x1 = aes_s_box_table[state[1 + ((i + 1) & 3) * 4]]
+        x2 = aes_s_box_table[state[2 + ((i + 2) & 3) * 4]]
+        x3 = aes_s_box_table[state[3 + ((i + 3) & 3) * 4]]
+        temp[temp_idx]     = x0 ^ w[w_idx]
+        temp[temp_idx + 1] = x1 ^ w[w_idx + 1]
+        temp[temp_idx + 2] = x2 ^ w[w_idx + 2]
+        temp[temp_idx + 3] = x3 ^ w[w_idx + 3]
+        w_idx += 4
+        temp_idx += 4
+    for i in range(16):
+        state[i] = temp[i]
+
+# take state as input and change it to the next state in the sequence
+# state and temp have size 16, w has size 16 * (Nr + 1), Nr >= 1
+def aes_state(state, w, temp, nr):
+    aes_add_round_key(state, w)
+    w_idx = 16
+    for i in range(nr - 1):
+        aes_sb_sr_mc_ark(state, w, w_idx, temp)
+        w_idx += 16
+    aes_sb_sr_ark(state, w, w_idx, temp)
+
+# expand 'key' to 'w' for use with aes_state
+# key has size 4 * Nk, w has size 16 * (Nr + 1), temp has size 16
+def aes_key_expansion(key, w, temp, nk, nr):
+    for i in range(4 * nk):
+        w[i] = key[i]
+    w_idx = 4 * nk - 4
+    for i in range(nk, 4 * (nr + 1)):
+        t = temp
+        t_idx = 0
+        if i % nk == 0:
+            t[0] = aes_s_box(w[w_idx + 1]) ^ aes_r_con(i // nk)
+            for j in range(1, 4):
+                t[j] = aes_s_box(w[w_idx + (j + 1) % 4])
+        elif nk > 6 and i % nk == 4:
+            for j in range(0, 4):
+                t[j] = aes_s_box(w[w_idx + j])
+        else:
+            t = w
+            t_idx = w_idx
+        w_idx += 4
+        for j in range(4):
+            w[w_idx + j] = w[w_idx + j - 4 * nk] ^ t[t_idx + j]
+
+##################################################################
+# simple use of AES algorithm, using output feedback (OFB) mode
+
+class AES:
+    def __init__(self, keysize):
+        if keysize == 128:
+            self.nk = 4
+            self.nr = 10
+        elif keysize == 192:
+            self.nk = 6
+            self.nr = 12
+        else:
+            assert keysize == 256
+            self.nk = 8
+            self.nr = 14
+
+        self.state = bytearray(16)
+        self.w = bytearray(16 * (self.nr + 1))
+        self.temp = bytearray(16)
+        self.state_pos = 16
+
+    def set_key(self, key):
+        aes_key_expansion(key, self.w, self.temp, self.nk, self.nr)
+        self.state_pos = 16
+
+    def set_iv(self, iv):
+        for i in range(16):
+            self.state[i] = iv[i]
+        self.state_pos = 16;
+
+    def get_some_state(self, n_needed):
+        if self.state_pos >= 16:
+            aes_state(self.state, self.w, self.temp, self.nr)
+            self.state_pos = 0
+        n = 16 - self.state_pos
+        if n > n_needed:
+            n = n_needed
+        return n
+
+    def apply_to(self, data):
+        idx = 0
+        n = len(data)
+        while n > 0:
+            ln = self.get_some_state(n)
+            n -= ln
+            for i in range(ln):
+                data[idx + i] ^= self.state[self.state_pos + i]
+            idx += ln
+            self.state_pos += n
+
+###########################################################################
+# Benchmark interface
+
+bm_params = {
+    (50, 25): (1, 16),
+    (100, 100): (1, 32),
+    (1000, 1000): (4, 256),
+    (5000, 1000): (20, 256),
+}
+
+def bm_setup(params):
+    nloop, datalen = params
+
+    aes = AES(256)
+    key = bytearray(256 // 8)
+    iv = bytearray(16)
+    data = bytearray(datalen)
+    # from now on we don't use the heap
+
+    def run():
+        for loop in range(nloop):
+            # encrypt
+            aes.set_key(key)
+            aes.set_iv(iv)
+            for i in range(2):
+                aes.apply_to(data)
+
+            # decrypt
+            aes.set_key(key)
+            aes.set_iv(iv)
+            for i in range(2):
+                aes.apply_to(data)
+
+            # verify
+            for i in range(len(data)):
+                assert data[i] == 0
+
+    def result():
+        return params[0] * params[1], True
+
+    return run, result
diff --git a/tests/perf_bench/misc_mandel.py b/tests/perf_bench/misc_mandel.py
new file mode 100644
index 0000000000..a4b789136d
--- /dev/null
+++ b/tests/perf_bench/misc_mandel.py
@@ -0,0 +1,31 @@
+# Compute the Mandelbrot set, to test complex numbers
+
+def mandelbrot(w, h):
+    def in_set(c):
+        z = 0
+        for i in range(32):
+            z = z * z + c
+            if abs(z) > 100:
+                return i
+        return 0
+
+    img = bytearray(w * h)
+
+    xscale = ((w - 1) / 2.4)
+    yscale = ((h - 1) / 3.2)
+    for v in range(h):
+        line = memoryview(img)[v * w:v * w + w]
+        for u in range(w):
+            c = in_set(complex(v / yscale - 2.3, u / xscale - 1.2))
+            line[u] = c
+
+    return img
+
+bm_params = {
+    (100, 100): (20, 20),
+    (1000, 1000): (80, 80),
+    (5000, 1000): (150, 150),
+}
+
+def bm_setup(ps):
+    return lambda: mandelbrot(ps[0], ps[1]), lambda: (ps[0] * ps[1], None)
diff --git a/tests/perf_bench/misc_pystone.py b/tests/perf_bench/misc_pystone.py
new file mode 100644
index 0000000000..88626774b2
--- /dev/null
+++ b/tests/perf_bench/misc_pystone.py
@@ -0,0 +1,226 @@
+"""
+"PYSTONE" Benchmark Program
+
+Version:        Python/1.2 (corresponds to C/1.1 plus 3 Pystone fixes)
+
+Author:         Reinhold P. Weicker,  CACM Vol 27, No 10, 10/84 pg. 1013.
+
+                Translated from ADA to C by Rick Richardson.
+                Every method to preserve ADA-likeness has been used,
+                at the expense of C-ness.
+
+                Translated from C to Python by Guido van Rossum.
+"""
+
+__version__ = "1.2"
+
+[Ident1, Ident2, Ident3, Ident4, Ident5] = range(1, 6)
+
+class Record:
+
+    def __init__(self, PtrComp = None, Discr = 0, EnumComp = 0,
+                       IntComp = 0, StringComp = 0):
+        self.PtrComp = PtrComp
+        self.Discr = Discr
+        self.EnumComp = EnumComp
+        self.IntComp = IntComp
+        self.StringComp = StringComp
+
+    def copy(self):
+        return Record(self.PtrComp, self.Discr, self.EnumComp,
+                      self.IntComp, self.StringComp)
+
+TRUE = 1
+FALSE = 0
+
+def Setup():
+    global IntGlob
+    global BoolGlob
+    global Char1Glob
+    global Char2Glob
+    global Array1Glob
+    global Array2Glob
+
+    IntGlob = 0
+    BoolGlob = FALSE
+    Char1Glob = '\0'
+    Char2Glob = '\0'
+    Array1Glob = [0]*51
+    Array2Glob = [x[:] for x in [Array1Glob]*51]
+
+def Proc0(loops):
+    global IntGlob
+    global BoolGlob
+    global Char1Glob
+    global Char2Glob
+    global Array1Glob
+    global Array2Glob
+    global PtrGlb
+    global PtrGlbNext
+
+    PtrGlbNext = Record()
+    PtrGlb = Record()
+    PtrGlb.PtrComp = PtrGlbNext
+    PtrGlb.Discr = Ident1
+    PtrGlb.EnumComp = Ident3
+    PtrGlb.IntComp = 40
+    PtrGlb.StringComp = "DHRYSTONE PROGRAM, SOME STRING"
+    String1Loc = "DHRYSTONE PROGRAM, 1'ST STRING"
+    Array2Glob[8][7] = 10
+
+    for i in range(loops):
+        Proc5()
+        Proc4()
+        IntLoc1 = 2
+        IntLoc2 = 3
+        String2Loc = "DHRYSTONE PROGRAM, 2'ND STRING"
+        EnumLoc = Ident2
+        BoolGlob = not Func2(String1Loc, String2Loc)
+        while IntLoc1 < IntLoc2:
+            IntLoc3 = 5 * IntLoc1 - IntLoc2
+            IntLoc3 = Proc7(IntLoc1, IntLoc2)
+            IntLoc1 = IntLoc1 + 1
+        Proc8(Array1Glob, Array2Glob, IntLoc1, IntLoc3)
+        PtrGlb = Proc1(PtrGlb)
+        CharIndex = 'A'
+        while CharIndex <= Char2Glob:
+            if EnumLoc == Func1(CharIndex, 'C'):
+                EnumLoc = Proc6(Ident1)
+            CharIndex = chr(ord(CharIndex)+1)
+        IntLoc3 = IntLoc2 * IntLoc1
+        IntLoc2 = IntLoc3 // IntLoc1
+        IntLoc2 = 7 * (IntLoc3 - IntLoc2) - IntLoc1
+        IntLoc1 = Proc2(IntLoc1)
+
+def Proc1(PtrParIn):
+    PtrParIn.PtrComp = NextRecord = PtrGlb.copy()
+    PtrParIn.IntComp = 5
+    NextRecord.IntComp = PtrParIn.IntComp
+    NextRecord.PtrComp = PtrParIn.PtrComp
+    NextRecord.PtrComp = Proc3(NextRecord.PtrComp)
+    if NextRecord.Discr == Ident1:
+        NextRecord.IntComp = 6
+        NextRecord.EnumComp = Proc6(PtrParIn.EnumComp)
+        NextRecord.PtrComp = PtrGlb.PtrComp
+        NextRecord.IntComp = Proc7(NextRecord.IntComp, 10)
+    else:
+        PtrParIn = NextRecord.copy()
+    NextRecord.PtrComp = None
+    return PtrParIn
+
+def Proc2(IntParIO):
+    IntLoc = IntParIO + 10
+    while 1:
+        if Char1Glob == 'A':
+            IntLoc = IntLoc - 1
+            IntParIO = IntLoc - IntGlob
+            EnumLoc = Ident1
+        if EnumLoc == Ident1:
+            break
+    return IntParIO
+
+def Proc3(PtrParOut):
+    global IntGlob
+
+    if PtrGlb is not None:
+        PtrParOut = PtrGlb.PtrComp
+    else:
+        IntGlob = 100
+    PtrGlb.IntComp = Proc7(10, IntGlob)
+    return PtrParOut
+
+def Proc4():
+    global Char2Glob
+
+    BoolLoc = Char1Glob == 'A'
+    BoolLoc = BoolLoc or BoolGlob
+    Char2Glob = 'B'
+
+def Proc5():
+    global Char1Glob
+    global BoolGlob
+
+    Char1Glob = 'A'
+    BoolGlob = FALSE
+
+def Proc6(EnumParIn):
+    EnumParOut = EnumParIn
+    if not Func3(EnumParIn):
+        EnumParOut = Ident4
+    if EnumParIn == Ident1:
+        EnumParOut = Ident1
+    elif EnumParIn == Ident2:
+        if IntGlob > 100:
+            EnumParOut = Ident1
+        else:
+            EnumParOut = Ident4
+    elif EnumParIn == Ident3:
+        EnumParOut = Ident2
+    elif EnumParIn == Ident4:
+        pass
+    elif EnumParIn == Ident5:
+        EnumParOut = Ident3
+    return EnumParOut
+
+def Proc7(IntParI1, IntParI2):
+    IntLoc = IntParI1 + 2
+    IntParOut = IntParI2 + IntLoc
+    return IntParOut
+
+def Proc8(Array1Par, Array2Par, IntParI1, IntParI2):
+    global IntGlob
+
+    IntLoc = IntParI1 + 5
+    Array1Par[IntLoc] = IntParI2
+    Array1Par[IntLoc+1] = Array1Par[IntLoc]
+    Array1Par[IntLoc+30] = IntLoc
+    for IntIndex in range(IntLoc, IntLoc+2):
+        Array2Par[IntLoc][IntIndex] = IntLoc
+    Array2Par[IntLoc][IntLoc-1] = Array2Par[IntLoc][IntLoc-1] + 1
+    Array2Par[IntLoc+20][IntLoc] = Array1Par[IntLoc]
+    IntGlob = 5
+
+def Func1(CharPar1, CharPar2):
+    CharLoc1 = CharPar1
+    CharLoc2 = CharLoc1
+    if CharLoc2 != CharPar2:
+        return Ident1
+    else:
+        return Ident2
+
+def Func2(StrParI1, StrParI2):
+    IntLoc = 1
+    while IntLoc <= 1:
+        if Func1(StrParI1[IntLoc], StrParI2[IntLoc+1]) == Ident1:
+            CharLoc = 'A'
+            IntLoc = IntLoc + 1
+    if CharLoc >= 'W' and CharLoc <= 'Z':
+        IntLoc = 7
+    if CharLoc == 'X':
+        return TRUE
+    else:
+        if StrParI1 > StrParI2:
+            IntLoc = IntLoc + 7
+            return TRUE
+        else:
+            return FALSE
+
+def Func3(EnumParIn):
+    EnumLoc = EnumParIn
+    if EnumLoc == Ident3: return TRUE
+    return FALSE
+
+
+###########################################################################
+# Benchmark interface
+
+bm_params = {
+    (50, 10): (80,),
+    (100, 10): (300,),
+    (1000, 10): (4000,),
+    (5000, 10): (20000,),
+}
+
+def bm_setup(params):
+    Setup()
+    return lambda: Proc0(params[0]), lambda: (params[0], 0)
diff --git a/tests/perf_bench/misc_raytrace.py b/tests/perf_bench/misc_raytrace.py
new file mode 100644
index 0000000000..76d4194bce
--- /dev/null
+++ b/tests/perf_bench/misc_raytrace.py
@@ -0,0 +1,242 @@
+# A simple ray tracer
+# MIT license; Copyright (c) 2019 Damien P. George
+
+INF = 1e30
+EPS = 1e-6
+
+class Vec:
+    def __init__(self, x, y, z):
+        self.x, self.y, self.z = x, y, z
+
+    def __neg__(self):
+        return Vec(-self.x, -self.y, -self.z)
+
+    def __add__(self, rhs):
+        return Vec(self.x + rhs.x, self.y + rhs.y, self.z + rhs.z)
+
+    def __sub__(self, rhs):
+        return Vec(self.x - rhs.x, self.y - rhs.y, self.z - rhs.z)
+
+    def __mul__(self, rhs):
+        return Vec(self.x * rhs, self.y * rhs, self.z * rhs)
+
+    def length(self):
+        return (self.x ** 2 + self.y ** 2 + self.z ** 2) ** 0.5
+
+    def normalise(self):
+        l = self.length()
+        return Vec(self.x / l, self.y / l, self.z / l)
+
+    def dot(self, rhs):
+        return self.x * rhs.x + self.y * rhs.y + self.z * rhs.z
+
+RGB = Vec
+
+class Ray:
+    def __init__(self, p, d):
+        self.p, self.d = p, d
+
+class View:
+    def __init__(self, width, height, depth, pos, xdir, ydir, zdir):
+        self.width = width
+        self.height = height
+        self.depth = depth
+        self.pos = pos
+        self.xdir = xdir
+        self.ydir = ydir
+        self.zdir = zdir
+
+    def calc_dir(self, dx, dy):
+        return (self.xdir * dx + self.ydir * dy + self.zdir * self.depth).normalise()
+
+class Light:
+    def __init__(self, pos, colour, casts_shadows):
+        self.pos = pos
+        self.colour = colour
+        self.casts_shadows = casts_shadows
+
+class Surface:
+    def __init__(self, diffuse, specular, spec_idx, reflect, transp, colour):
+        self.diffuse = diffuse
+        self.specular = specular
+        self.spec_idx = spec_idx
+        self.reflect = reflect
+        self.transp = transp
+        self.colour = colour
+
+    @staticmethod
+    def dull(colour):
+        return Surface(0.7, 0.0, 1, 0.0, 0.0, colour * 0.6)
+
+    @staticmethod
+    def shiny(colour):
+        return Surface(0.2, 0.9, 32, 0.8, 0.0, colour * 0.3)
+
+    @staticmethod
+    def transparent(colour):
+        return Surface(0.2, 0.9, 32, 0.0, 0.8, colour * 0.3)
+
+class Sphere:
+    def __init__(self, surface, centre, radius):
+        self.surface = surface
+        self.centre = centre
+        self.radsq = radius ** 2
+
+    def intersect(self, ray):
+        v = self.centre - ray.p
+        b = v.dot(ray.d)
+        det = b ** 2 - v.dot(v) + self.radsq
+        if det > 0:
+            det **= 0.5
+            t1 = b - det
+            if t1 > EPS:
+                return t1
+            t2 = b + det
+            if t2 > EPS:
+                return t2
+        return INF
+
+    def surface_at(self, v):
+        return self.surface, (v - self.centre).normalise()
+
+class Plane:
+    def __init__(self, surface, centre, normal):
+        self.surface = surface
+        self.normal = normal.normalise()
+        self.cdotn = centre.dot(normal)
+
+    def intersect(self, ray):
+        ddotn = ray.d.dot(self.normal)
+        if abs(ddotn) > EPS:
+            t = (self.cdotn - ray.p.dot(self.normal)) / ddotn
+            if t > 0:
+                return t
+        return INF
+
+    def surface_at(self, p):
+        return self.surface, self.normal
+
+class Scene:
+    def __init__(self, ambient, light, objs):
+        self.ambient = ambient
+        self.light = light
+        self.objs = objs
+
+def trace_scene(canvas, view, scene, max_depth):
+    for v in range(canvas.height):
+        y = (-v + 0.5 * (canvas.height - 1)) * view.height / canvas.height
+        for u in range(canvas.width):
+            x = (u - 0.5 * (canvas.width - 1)) * view.width / canvas.width
+            ray = Ray(view.pos, view.calc_dir(x, y))
+            c = trace_ray(scene, ray, max_depth)
+            canvas.put_pix(u, v, c)
+
+def trace_ray(scene, ray, depth):
+    # Find closest intersecting object
+    hit_t = INF
+    hit_obj = None
+    for obj in scene.objs:
+        t = obj.intersect(ray)
+        if t < hit_t:
+            hit_t = t
+            hit_obj = obj
+
+    # Check if any objects hit
+    if hit_obj is None:
+        return RGB(0, 0, 0)
+
+    # Compute location of ray intersection
+    point = ray.p + ray.d * hit_t
+    surf, surf_norm = hit_obj.surface_at(point)
+    if ray.d.dot(surf_norm) > 0:
+        surf_norm = -surf_norm
+
+    # Compute reflected ray
+    reflected = ray.d - surf_norm * (surf_norm.dot(ray.d) * 2)
+
+    # Ambient light
+    col = surf.colour * scene.ambient
+
+    # Diffuse, specular and shadow from light source
+    light_vec = scene.light.pos - point
+    light_dist = light_vec.length()
+    light_vec = light_vec.normalise()
+    ndotl = surf_norm.dot(light_vec)
+    ldotv = light_vec.dot(reflected)
+    if ndotl > 0 or ldotv > 0:
+        light_ray = Ray(point + light_vec * EPS, light_vec)
+        light_col = trace_to_light(scene, light_ray, light_dist)
+        if ndotl > 0:
+            col += light_col * surf.diffuse * ndotl
+        if ldotv > 0:
+            col += light_col * surf.specular * ldotv ** surf.spec_idx
+
+    # Reflections
+    if depth > 0 and surf.reflect > 0:
+        col += trace_ray(scene, Ray(point + reflected * EPS, reflected), depth - 1) * surf.reflect
+
+    # Transparency
+    if depth > 0 and surf.transp > 0:
+        col += trace_ray(scene, Ray(point + ray.d * EPS, ray.d), depth - 1) * surf.transp
+
+    return col
+
+def trace_to_light(scene, ray, light_dist):
+    col = scene.light.colour
+    for obj in scene.objs:
+        t = obj.intersect(ray)
+        if t < light_dist:
+            col *= obj.surface.transp
+    return col
+
+class Canvas:
+    def __init__(self, width, height):
+        self.width = width
+        self.height = height
+        self.data = bytearray(3 * width * height)
+
+    def put_pix(self, x, y, c):
+        off = 3 * (y * self.width + x)
+        self.data[off] = min(255, max(0, int(255 * c.x)))
+        self.data[off + 1] = min(255, max(0, int(255 * c.y)))
+        self.data[off + 2] = min(255, max(0, int(255 * c.z)))
+
+    def write_ppm(self, filename):
+        with open(filename, 'wb') as f:
+            f.write(bytes('P6 %d %d 255\n' % (self.width, self.height), 'ascii'))
+            f.write(self.data)
+
+def main(w, h, d):
+    canvas = Canvas(w, h)
+    view = View(32, 32, 64, Vec(0, 0, 50), Vec(1, 0, 0), Vec(0, 1, 0), Vec(0, 0, -1))
+    scene = Scene(
+        0.5,
+        Light(Vec(0, 8, 0), RGB(1, 1, 1), True),
+        [
+            Plane(Surface.dull(RGB(1, 0, 0)), Vec(-10, 0, 0), Vec(1, 0, 0)),
+            Plane(Surface.dull(RGB(0, 1, 0)), Vec(10, 0, 0), Vec(-1, 0, 0)),
+            Plane(Surface.dull(RGB(1, 1, 1)), Vec(0, 0, -10), Vec(0, 0, 1)),
+            Plane(Surface.dull(RGB(1, 1, 1)), Vec(0, -10, 0), Vec(0, 1, 0)),
+            Plane(Surface.dull(RGB(1, 1, 1)), Vec(0, 10, 0), Vec(0, -1, 0)),
+            Sphere(Surface.shiny(RGB(1, 1, 1)), Vec(-5, -4, 3), 4),
+            Sphere(Surface.dull(RGB(0, 0, 1)), Vec(4, -5, 0), 4),
+            Sphere(Surface.transparent(RGB(0.2, 0.2, 0.2)), Vec(6, -1, 8), 4),
+        ]
+    )
+    trace_scene(canvas, view, scene, d)
+    return canvas
+
+# For testing
+#main(256, 256, 4).write_ppm('rt.ppm')
+
+###########################################################################
+# Benchmark interface
+
+bm_params = {
+    (100, 100): (5, 5, 2),
+    (1000, 100): (18, 18, 3),
+    (5000, 100): (40, 40, 3),
+}
+
+def bm_setup(params):
+    return lambda: main(*params), lambda: (params[0] * params[1] * params[2], None)