From 91a60fdfa6226ff730c20423b4ee65be77f52ff8 Mon Sep 17 00:00:00 2001
From: "Timothy B. Terriberry" <tterribe@xiph.org>
Date: Thu, 11 Feb 2016 06:38:34 -0800
Subject: [PATCH] Fix some additional overflows in the 64x64 DCT.

Test #350 could overflow even with 4-point lapping.
Tests #200 and #242 could only overflow with 8-point lapping.

Again, this has exactly zero impact on measured MSE in dcttest.
There is a very small impact on the reported biases, but the first
 several significant figures of each one do not change.

Changes in metrics on ntt-short-1 seem to be mostly noise:
          RATE (%)  DSNR (dB)
    PSNR  0.00470  -0.00014
 PSNRHVS  0.00603  -0.00028
    SSIM  0.00379  -0.00009
FASTSSIM -0.06955   0.00187
---
 src/dct.c | 30 +++++++++++++++---------------
 1 file changed, 15 insertions(+), 15 deletions(-)

diff --git a/src/dct.c b/src/dct.c
index 13778216..88b8fd06 100644
--- a/src/dct.c
+++ b/src/dct.c
@@ -1369,9 +1369,9 @@ void od_bin_idct16x16(od_coeff *x, int xstride,
         0.505367194937830 */ \
     OD_DCT_OVERFLOW_CHECK(t1, 1035, 1024, 199); \
     t6 += (t1*1035 + 1024) >> 11; \
-    /* 14699/16384 ~= Sqrt[2]*Sin[7*Pi/32] ~= 0.897167586342636 */ \
-    OD_DCT_OVERFLOW_CHECK(t6, 14699, 8192, 200); \
-    t1 -= (t6*14699 + 8192) >> 14; \
+    /* 3675/4096 ~= Sqrt[2]*Sin[7*Pi/32] ~= 0.897167586342636 */ \
+    OD_DCT_OVERFLOW_CHECK(t6, 3675, 2048, 200); \
+    t1 -= (t6*3675 + 2048) >> 12; \
     /* 851/8192 ~= (Cos[7*Pi/32] - 1/Sqrt[2])/Sin[7*Pi/32] ~=
         0.103884567856159 */ \
     OD_DCT_OVERFLOW_CHECK(t1, 851, 4096, 201); \
@@ -1531,8 +1531,8 @@ void od_bin_idct16x16(od_coeff *x, int xstride,
     /* 851/8192 ~= (Cos[7*Pi/32] - 1/Sqrt[2])/Sin[7*Pi/32] ~=
         0.103884567856159 */ \
     t3 += (t4*851 + 4096) >> 13; \
-    /* 14699/16384 ~= Sqrt[2]*Sin[7*Pi/32] ~= 0.897167586342636 */ \
-    t4 += (t3*14699 + 8192) >> 14; \
+    /* 3675/4096 ~= Sqrt[2]*Sin[7*Pi/32] ~= 0.897167586342636 */ \
+    t4 += (t3*3675 + 2048) >> 12; \
     /* 1035/2048 ~= (Sqrt[2] - Cos[7*Pi/32])/(2*Sin[7*Pi/32]) ~=
         0.505367194937830 */ \
     t3 -= (t4*1035 + 1024) >> 11; \
@@ -1757,9 +1757,9 @@ void od_bin_idct16x16(od_coeff *x, int xstride,
     /* 2485/8192 ~= Tan[3*Pi/32] ~= 0.303346683607342 */ \
     OD_DCT_OVERFLOW_CHECK(s9, 2485, 4096, 241); \
     s6 += (s9*2485 + 4096) >> 13; \
-    /* 18205/32768 ~= Sin[3*Pi/16] ~= 0.555570233019602 */ \
-    OD_DCT_OVERFLOW_CHECK(s6, 18205, 16384, 242); \
-    s9 -= (s6*18205 + 16384) >> 15; \
+    /* 4551/8192 ~= Sin[3*Pi/16] ~= 0.555570233019602 */ \
+    OD_DCT_OVERFLOW_CHECK(s6, 4551, 4096, 242); \
+    s9 -= (s6*4551 + 4096) >> 13; \
     /* 2485/8192 ~= Tan[3*Pi/32] ~= 0.303346683607342 */ \
     OD_DCT_OVERFLOW_CHECK(s9, 2485, 4096, 243); \
     s6 += (s9*2485 + 4096) >> 13; \
@@ -2011,8 +2011,8 @@ void od_bin_idct16x16(od_coeff *x, int xstride,
     se -= (s1*3227 + 16384) >> 15; \
     /* 2485/8192 ~= Tan[3*Pi/32] ~= 0.303346683607342 */ \
     s6 -= (s9*2485 + 4096) >> 13; \
-    /* 18205/32768 ~= Sin[3*Pi/16] ~= 0.555570233019602 */ \
-    s9 += (s6*18205 + 16384) >> 15; \
+    /* 4551/8192 ~= Sin[3*Pi/16] ~= 0.555570233019602 */ \
+    s9 += (s6*4551 + 4096) >> 13; \
     /* 2485/8192 ~= Tan[3*Pi/32] ~= 0.303346683607342 */ \
     s6 -= (s9*2485 + 4096) >> 13; \
     /* 8757/16384 ~= Tan[5*Pi/32] ~= 0.534511135950792 */ \
@@ -3160,9 +3160,9 @@ void od_bin_idct16x16(od_coeff *x, int xstride,
         0.6685570995525147 */ \
     OD_DCT_OVERFLOW_CHECK(to, 5477, 4096, 349); \
     t7 += (to*5477 + 4096) >> 13; \
-    /* 8339/32768 ~= Sqrt[2]*Sin[15*Pi/128] ~= 0.5089684416985407 */ \
-    OD_DCT_OVERFLOW_CHECK(t7, 8339, 8192, 350); \
-    to -= (t7*8339 + 8192) >> 14; \
+    /* 4169/8192 ~= Sqrt[2]*Sin[15*Pi/128] ~= 0.5089684416985407 */ \
+    OD_DCT_OVERFLOW_CHECK(t7, 4169, 4096, 350); \
+    to -= (t7*4169 + 4096) >> 13; \
     /* -2571/4096 ~= (1/Sqrt[2] - Cos[15*Pi/128])/Sin[15*Pi/128] ~=
         -0.6276441593165217 */ \
     OD_DCT_OVERFLOW_CHECK(to, 2571, 2048, 351); \
@@ -3413,8 +3413,8 @@ void od_bin_idct16x16(od_coeff *x, int xstride,
     /* -2571/4096 ~= (1/Sqrt[2] - Cos[15*Pi/128])/Sin[15*Pi/128] ~=
         -0.6276441593165217 */ \
     ts += (t3*2571 + 2048) >> 12; \
-    /* 8339/32768 ~= Sqrt[2]*Sin[15*Pi/128] ~= 0.5089684416985407 */ \
-    t3 += (ts*8339 + 8192) >> 14; \
+    /* 4169/8192 ~= Sqrt[2]*Sin[15*Pi/128] ~= 0.5089684416985407 */ \
+    t3 += (ts*4169 + 4096) >> 13; \
     /* 5477/8192 ~= (1/Sqrt[2] - Cos[15*Pi/128]/2)/Sin[15*Pi/128] ~=
         0.6685570995525147 */ \
     ts -= (t3*5477 + 4096) >> 13; \