av1/common/daala_tx.c

#include "av1/common/daala_tx.h"
#include "av1/common/odintrin.h"

/* clang-format off */

# define OD_DCT_RSHIFT(_a, _b) OD_UNBIASED_RSHIFT32(_a, _b)

/* TODO: Daala DCT overflow checks need to be ported as a later test */
# if defined(OD_DCT_CHECK_OVERFLOW)
# else
#  define OD_DCT_OVERFLOW_CHECK(val, scale, offset, idx)
# endif

#define OD_FDCT_2(p0, p1) \
  /* Embedded 2-point orthonormal Type-II fDCT. */ \
  do { \
    /* 13573/32768 ~= Tan[pi/8] ~= 0.414213562373095 */ \
    OD_DCT_OVERFLOW_CHECK(p1, 13573, 16384, 100); \
    p0 -= (p1*13573 + 16384) >> 15; \
    /* 5793/8192 ~= Sin[pi/4] ~= 0.707106781186547 */ \
    OD_DCT_OVERFLOW_CHECK(p0, 5793, 4096, 101); \
    p1 += (p0*5793 + 4096) >> 13; \
    /* 3393/8192 ~= Tan[pi/8] ~= 0.414213562373095 */ \
    OD_DCT_OVERFLOW_CHECK(p1, 3393, 4096, 102); \
    p0 -= (p1*3393 + 4096) >> 13; \
  } \
  while (0)

#define OD_IDCT_2(p0, p1) \
  /* Embedded 2-point orthonormal Type-II iDCT. */ \
  do { \
    /* 3393/8192 ~= Tan[pi/8] ~= 0.414213562373095 */ \
    p0 += (p1*3393 + 4096) >> 13; \
    /* 5793/8192 ~= Sin[pi/4] ~= 0.707106781186547 */ \
    p1 -= (p0*5793 + 4096) >> 13; \
    /* 13573/32768 ~= Tan[pi/8] ~= 0.414213562373095 */ \
    p0 += (p1*13573 + 16384) >> 15; \
  } \
  while (0)

#define OD_FDCT_2_ASYM(p0, p1, p1h) \
  /* Embedded 2-point asymmetric Type-II fDCT. */ \
  do { \
    p0 += p1h; \
    p1 = p0 - p1; \
  } \
  while (0)

#define OD_IDCT_2_ASYM(p0, p1, p1h) \
  /* Embedded 2-point asymmetric Type-II iDCT. */ \
  do { \
    p1 = p0 - p1; \
    p1h = OD_DCT_RSHIFT(p1, 1); \
    p0 -= p1h; \
  } \
  while (0)

#define OD_FDST_2(p0, p1) \
  /* Embedded 2-point orthonormal Type-IV fDST. */ \
  do { \
    /* 10947/16384 ~= Tan[3*Pi/16] ~= 0.668178637919299 */ \
    OD_DCT_OVERFLOW_CHECK(p1, 10947, 8192, 103); \
    p0 -= (p1*10947 + 8192) >> 14; \
    /* 473/512 ~= Sin[3*Pi/8] ~= 0.923879532511287 */ \
    OD_DCT_OVERFLOW_CHECK(p0, 473, 256, 104); \
    p1 += (p0*473 + 256) >> 9; \
    /* 10947/16384 ~= Tan[3*Pi/16] ~= 0.668178637919299 */ \
    OD_DCT_OVERFLOW_CHECK(p1, 10947, 8192, 105); \
    p0 -= (p1*10947 + 8192) >> 14; \
  } \
  while (0)

#define OD_IDST_2(p0, p1) \
  /* Embedded 2-point orthonormal Type-IV iDST. */ \
  do { \
    /* 10947/16384 ~= Tan[3*Pi/16]) ~= 0.668178637919299 */ \
    p0 += (p1*10947 + 8192) >> 14; \
    /* 473/512 ~= Sin[3*Pi/8] ~= 0.923879532511287 */ \
    p1 -= (p0*473 + 256) >> 9; \
    /* 10947/16384 ~= Tan[3*Pi/16] ~= 0.668178637919299 */ \
    p0 += (p1*10947 + 8192) >> 14; \
  } \
  while (0)

#define OD_FDST_2_ASYM(p0, p1) \
  /* Embedded 2-point asymmetric Type-IV fDST. */ \
  do { \
    /* 11507/16384 ~= 4*Sin[Pi/8] - 2*Tan[Pi/8] ~= 0.702306604714169 */ \
    OD_DCT_OVERFLOW_CHECK(p1, 11507, 8192, 187); \
    p0 -= (p1*11507 + 8192) >> 14; \
    /* 669/1024 ~= Cos[Pi/8]/Sqrt[2] ~= 0.653281482438188 */ \
    OD_DCT_OVERFLOW_CHECK(p0, 669, 512, 188); \
    p1 += (p0*669 + 512) >> 10; \
    /* 4573/4096 ~= 4*Sin[Pi/8] - Tan[Pi/8] ~= 1.11652016708726 */ \
    OD_DCT_OVERFLOW_CHECK(p1, 4573, 2048, 189); \
    p0 -= (p1*4573 + 2048) >> 12; \
  } \
  while (0)

#define OD_IDST_2_ASYM(p0, p1) \
  /* Embedded 2-point asymmetric Type-IV iDST. */ \
  do { \
    /* 4573/4096 ~= 4*Sin[Pi/8] - Tan[Pi/8] ~= 1.11652016708726 */ \
    p0 += (p1*4573 + 2048) >> 12; \
    /* 669/1024 ~= Cos[Pi/8]/Sqrt[2] ~= 0.653281482438188 */ \
    p1 -= (p0*669 + 512) >> 10; \
    /* 11507/16384 ~= 4*Sin[Pi/8] - 2*Tan[Pi/8] ~= 0.702306604714169 */ \
    p0 += (p1*11507 + 8192) >> 14; \
  } \
  while (0)

#define OD_FDCT_4(q0, q2, q1, q3) \
  /* Embedded 4-point orthonormal Type-II fDCT. */ \
  do { \
    int q2h; \
    int q3h; \
    q3 = q0 - q3; \
    q3h = OD_DCT_RSHIFT(q3, 1); \
    q0 -= q3h; \
    q2 += q1; \
    q2h = OD_DCT_RSHIFT(q2, 1); \
    q1 = q2h - q1; \
    OD_FDCT_2_ASYM(q0, q2, q2h); \
    OD_FDST_2_ASYM(q3, q1); \
  } \
  while (0)

#define OD_IDCT_4(q0, q2, q1, q3) \
  /* Embedded 4-point orthonormal Type-II iDCT. */ \
  do { \
    int q1h; \
    int q3h; \
    OD_IDST_2_ASYM(q3, q2); \
    OD_IDCT_2_ASYM(q0, q1, q1h); \
    q3h = OD_DCT_RSHIFT(q3, 1); \
    q0 += q3h; \
    q3 = q0 - q3; \
    q2 = q1h - q2; \
    q1 -= q2; \
  } \
  while (0)

#define OD_FDCT_4_ASYM(q0, q2, q2h, q1, q3, q3h) \
  /* Embedded 4-point asymmetric Type-II fDCT. */ \
  do { \
    q0 += q3h; \
    q3 = q0 - q3; \
    q1 = q2h - q1; \
    q2 = q1 - q2; \
    OD_FDCT_2(q0, q2); \
    OD_FDST_2(q3, q1); \
  } \
  while (0)

#define OD_IDCT_4_ASYM(q0, q2, q1, q1h, q3, q3h) \
  /* Embedded 4-point asymmetric Type-II iDCT. */ \
  do { \
    OD_IDST_2(q3, q2); \
    OD_IDCT_2(q0, q1); \
    q1 = q2 - q1; \
    q1h = OD_DCT_RSHIFT(q1, 1); \
    q2 = q1h - q2; \
    q3 = q0 - q3; \
    q3h = OD_DCT_RSHIFT(q3, 1); \
    q0 -= q3h; \
  } \
  while (0)

#define OD_FDST_4(q0, q2, q1, q3) \
  /* Embedded 4-point orthonormal Type-IV fDST. */ \
  do { \
    int q0h; \
    int q1h; \
    /* 13573/32768 ~= Tan[Pi/8] ~= 0.414213562373095 */ \
    OD_DCT_OVERFLOW_CHECK(q1, 13573, 16384, 190); \
    q2 += (q1*13573 + 16384) >> 15; \
    /* 5793/8192 ~= Sin[Pi/4] ~= 0.707106781186547 */ \
    OD_DCT_OVERFLOW_CHECK(q2, 5793, 4096, 191); \
    q1 -= (q2*5793 + 4096) >> 13; \
    /* 3393/8192 ~= Tan[Pi/8] ~= 0.414213562373095 */ \
    OD_DCT_OVERFLOW_CHECK(q1, 3393, 4096, 192); \
    q2 += (q1*3393 + 4096) >> 13; \
    q0 += q2; \
    q0h = OD_DCT_RSHIFT(q0, 1); \
    q2 = q0h - q2; \
    q1 += q3; \
    q1h = OD_DCT_RSHIFT(q1, 1); \
    q3 -= q1h; \
    /* 537/1024 ~= (1/Sqrt[2] - Cos[3*Pi/16]/2)/Sin[3*Pi/16] ~=
        0.524455699240090 */ \
    OD_DCT_OVERFLOW_CHECK(q1, 537, 512, 193); \
    q2 -= (q1*537 + 512) >> 10; \
    /* 1609/2048 ~= Sqrt[2]*Sin[3*Pi/16] ~= 0.785694958387102 */ \
    OD_DCT_OVERFLOW_CHECK(q2, 1609, 1024, 194); \
    q1 += (q2*1609 + 1024) >> 11; \
    /* 7335/32768 ~= (1/Sqrt[2] - Cos[3*Pi/16])/Sin[3*Pi/16] ~=
        0.223847182092655 */ \
    OD_DCT_OVERFLOW_CHECK(q1, 7335, 16384, 195); \
    q2 += (q1*7335 + 16384) >> 15; \
    /* 5091/8192 ~= (1/Sqrt[2] - Cos[7*Pi/16]/2)/Sin[7*Pi/16] ~=
        0.6215036383171189 */ \
    OD_DCT_OVERFLOW_CHECK(q0, 5091, 4096, 196); \
    q3 += (q0*5091 + 4096) >> 13; \
    /* 5681/4096 ~= Sqrt[2]*Sin[7*Pi/16] ~= 1.38703984532215 */ \
    OD_DCT_OVERFLOW_CHECK(q3, 5681, 2048, 197); \
    q0 -= (q3*5681 + 2048) >> 12; \
    /* 4277/8192 ~= (1/Sqrt[2] - Cos[7*Pi/16])/Sin[7*Pi/16] ~=
        0.52204745462729 */ \
    OD_DCT_OVERFLOW_CHECK(q0, 4277, 4096, 198); \
    q3 += (q0*4277 + 4096) >> 13; \
  } \
  while (0)

#define OD_IDST_4(q0, q2, q1, q3) \
  /* Embedded 4-point orthonormal Type-IV iDST. */ \
  do { \
    int q0h; \
    int q2h; \
    /* 4277/8192 ~= (1/Sqrt[2] - Cos[7*Pi/16])/Sin[7*Pi/16] ~=
        0.52204745462729 */ \
    q3 -= (q0*4277 + 4096) >> 13; \
    /* 5681/4096 ~= Sqrt[2]*Sin[7*Pi/16] ~= 1.38703984532215 */ \
    q0 += (q3*5681 + 2048) >> 12; \
    /* 5091/8192 ~= (1/Sqrt[2] - Cos[7*Pi/16]/2)/Sin[7*Pi/16] ~=
        0.6215036383171189 */ \
    q3 -= (q0*5091 + 4096) >> 13; \
    /* 7335/32768 ~= (1/Sqrt[2] - Cos[3*Pi/16])/Sin[3*Pi/16] ~=
        0.223847182092655 */ \
    q1 -= (q2*7335 + 16384) >> 15; \
    /* 1609/2048 ~= Sqrt[2]*Sin[3*Pi/16] ~= 0.785694958387102 */ \
    q2 -= (q1*1609 + 1024) >> 11; \
    /* 537/1024 ~= (1/Sqrt[2] - Cos[3*Pi/16]/2)/Sin[3*Pi/16] ~=
        0.524455699240090 */ \
    q1 += (q2*537 + 512) >> 10; \
    q2h = OD_DCT_RSHIFT(q2, 1); \
    q3 += q2h; \
    q2 -= q3; \
    q0h = OD_DCT_RSHIFT(q0, 1); \
    q1 = q0h - q1; \
    q0 -= q1; \
    /* 3393/8192 ~= Tan[Pi/8] ~= 0.414213562373095 */ \
    q1 -= (q2*3393 + 4096) >> 13; \
    /* 5793/8192 ~= Sin[Pi/4] ~= 0.707106781186547 */ \
    q2 += (q1*5793 + 4096) >> 13; \
    /* 13573/32768 ~= Tan[Pi/8] ~= 0.414213562373095 */ \
    q1 -= (q2*13573 + 16384) >> 15; \
  } \
  while (0)

#define OD_FDST_4_ASYM(t0, t0h, t2, t1, t3) \
  /* Embedded 4-point asymmetric Type-IV fDST. */ \
  do { \
    /* 7489/8192 ~= Tan[Pi/8] + Tan[Pi/4]/2 ~= 0.914213562373095 */ \
    OD_DCT_OVERFLOW_CHECK(t1, 7489, 4096, 106); \
    t2 -= (t1*7489 + 4096) >> 13; \
    /* 11585/16384 ~= Sin[Pi/4] ~= 0.707106781186548 */ \
    OD_DCT_OVERFLOW_CHECK(t1, 11585, 8192, 107); \
    t1 += (t2*11585 + 8192) >> 14; \
    /* -19195/32768 ~= Tan[Pi/8] - Tan[Pi/4] ~= -0.585786437626905 */ \
    OD_DCT_OVERFLOW_CHECK(t1, 19195, 16384, 108); \
    t2 += (t1*19195 + 16384) >> 15; \
    t3 += OD_DCT_RSHIFT(t2, 1); \
    t2 -= t3; \
    t1 = t0h - t1; \
    t0 -= t1; \
    /* 6723/8192 ~= Tan[7*Pi/32] ~= 0.820678790828660 */ \
    OD_DCT_OVERFLOW_CHECK(t0, 6723, 4096, 109); \
    t3 += (t0*6723 + 4096) >> 13; \
    /* 8035/8192 ~= Sin[7*Pi/16] ~= 0.980785280403230 */ \
    OD_DCT_OVERFLOW_CHECK(t3, 8035, 4096, 110); \
    t0 -= (t3*8035 + 4096) >> 13; \
    /* 6723/8192 ~= Tan[7*Pi/32] ~= 0.820678790828660 */ \
    OD_DCT_OVERFLOW_CHECK(t0, 6723, 4096, 111); \
    t3 += (t0*6723 + 4096) >> 13; \
    /* 8757/16384 ~= Tan[5*Pi/32] ~= 0.534511135950792 */ \
    OD_DCT_OVERFLOW_CHECK(t1, 8757, 8192, 112); \
    t2 += (t1*8757 + 8192) >> 14; \
    /* 6811/8192 ~= Sin[5*Pi/16] ~= 0.831469612302545 */ \
    OD_DCT_OVERFLOW_CHECK(t2, 6811, 4096, 113); \
    t1 -= (t2*6811 + 4096) >> 13; \
    /* 8757/16384 ~= Tan[5*Pi/32] ~= 0.534511135950792 */ \
    OD_DCT_OVERFLOW_CHECK(t1, 8757, 8192, 114); \
    t2 += (t1*8757 + 8192) >> 14; \
  } \
  while (0)

#define OD_IDST_4_ASYM(t0, t0h, t2, t1, t3) \
  /* Embedded 4-point asymmetric Type-IV iDST. */ \
  do { \
    /* 8757/16384 ~= Tan[5*Pi/32] ~= 0.534511135950792 */ \
    t1 -= (t2*8757 + 8192) >> 14; \
    /* 6811/8192 ~= Sin[5*Pi/16] ~= 0.831469612302545 */ \
    t2 += (t1*6811 + 4096) >> 13; \
    /* 8757/16384 ~= Tan[5*Pi/32] ~= 0.534511135950792 */ \
    t1 -= (t2*8757 + 8192) >> 14; \
    /* 6723/8192 ~= Tan[7*Pi/32] ~= 0.820678790828660 */ \
    t3 -= (t0*6723 + 4096) >> 13; \
    /* 8035/8192 ~= Sin[7*Pi/16] ~= 0.980785280403230 */ \
    t0 += (t3*8035 + 4096) >> 13; \
    /* 6723/8192 ~= Tan[7*Pi/32] ~= 0.820678790828660 */ \
    t3 -= (t0*6723 + 4096) >> 13; \
    t0 += t2; \
    t0h = OD_DCT_RSHIFT(t0, 1); \
    t2 = t0h - t2; \
    t1 += t3; \
    t3 -= OD_DCT_RSHIFT(t1, 1); \
    /* -19195/32768 ~= Tan[Pi/8] - Tan[Pi/4] ~= -0.585786437626905 */ \
    t1 -= (t2*19195 + 16384) >> 15; \
    /* 11585/16384 ~= Sin[Pi/4] ~= 0.707106781186548 */ \
    t2 -= (t1*11585 + 8192) >> 14; \
    /* 7489/8192 ~= Tan[Pi/8] + Tan[Pi/4]/2 ~= 0.914213562373095 */ \
    t1 += (t2*7489 + 4096) >> 13; \
  } \
  while (0)

#define OD_FDCT_8(r0, r4, r2, r6, r1, r5, r3, r7) \
  /* Embedded 8-point orthonormal Type-II fDCT. */ \
  do { \
    int r4h; \
    int r5h; \
    int r6h; \
    int r7h; \
    r7 = r0 - r7; \
    r7h = OD_DCT_RSHIFT(r7, 1); \
    r0 -= r7h; \
    r6 += r1; \
    r6h = OD_DCT_RSHIFT(r6, 1); \
    r1 = r6h - r1; \
    r5 = r2 - r5; \
    r5h = OD_DCT_RSHIFT(r5, 1); \
    r2 -= r5h; \
    r4 += r3; \
    r4h = OD_DCT_RSHIFT(r4, 1); \
    r3 = r4h - r3; \
    OD_FDCT_4_ASYM(r0, r4, r4h, r2, r6, r6h); \
    OD_FDST_4_ASYM(r7, r7h, r3, r5, r1); \
  } \
  while (0)

#define OD_IDCT_8(r0, r4, r2, r6, r1, r5, r3, r7) \
  /* Embedded 8-point orthonormal Type-II iDCT. */ \
  do { \
    int r1h; \
    int r3h; \
    int r5h; \
    int r7h; \
    OD_IDST_4_ASYM(r7, r7h, r5, r6, r4); \
    OD_IDCT_4_ASYM(r0, r2, r1, r1h, r3, r3h); \
    r0 += r7h; \
    r7 = r0 - r7; \
    r6 = r1h - r6; \
    r1 -= r6; \
    r5h = OD_DCT_RSHIFT(r5, 1); \
    r2 += r5h; \
    r5 = r2 - r5; \
    r4 = r3h - r4; \
    r3 -= r4; \
  } \
  while (0)

#define OD_FDCT_8_ASYM(r0, r4, r4h, r2, r6, r6h, r1, r5, r5h, r3, r7, r7h) \
  /* Embedded 8-point asymmetric Type-II fDCT. */ \
  do { \
    r0 += r7h; \
    r7 = r0 - r7; \
    r1 = r6h - r1; \
    r6 -= r1; \
    r2 += r5h; \
    r5 = r2 - r5; \
    r3 = r4h - r3; \
    r4 -= r3; \
    OD_FDCT_4(r0, r4, r2, r6); \
    OD_FDST_4(r7, r3, r5, r1); \
  } \
  while (0)

#define OD_IDCT_8_ASYM(r0, r4, r2, r6, r1, r1h, r5, r5h, r3, r3h, r7, r7h) \
  /* Embedded 8-point asymmetric Type-II iDCT. */ \
  do { \
    OD_IDST_4(r7, r5, r6, r4); \
    OD_IDCT_4(r0, r2, r1, r3); \
    r7 = r0 - r7; \
    r7h = OD_DCT_RSHIFT(r7, 1); \
    r0 -= r7h; \
    r1 += r6; \
    r1h = OD_DCT_RSHIFT(r1, 1); \
    r6 = r1h - r6; \
    r5 = r2 - r5; \
    r5h = OD_DCT_RSHIFT(r5, 1); \
    r2 -= r5h; \
    r3 += r4; \
    r3h = OD_DCT_RSHIFT(r3, 1); \
    r4 = r3h - r4; \
  } \
  while (0)

#define OD_FDST_8(t0, t4, t2, t6, t1, t5, t3, t7)  \
  /* Embedded 8-point orthonormal Type-IV fDST. */ \
  do { \
    int t0h; \
    int t2h; \
    int t5h; \
    int t7h; \
    /* 13573/32768 ~= Tan[Pi/8] ~= 0.414213562373095 */ \
    OD_DCT_OVERFLOW_CHECK(t1, 13573, 16384, 115); \
    t6 -= (t1*13573 + 16384) >> 15; \
    /* 11585/16384 ~= Sin[Pi/4] ~= 0.707106781186547 */ \
    OD_DCT_OVERFLOW_CHECK(t6, 11585, 8192, 116); \
    t1 += (t6*11585 + 8192) >> 14; \
    /* 13573/32768 ~= Tan[Pi/8] ~= 0.414213562373095 */ \
    OD_DCT_OVERFLOW_CHECK(t1, 13573, 16384, 117); \
    t6 -= (t1*13573 + 16384) >> 15; \
    /* 21895/32768 ~= Tan[3*Pi/16] ~= 0.668178637919299 */ \
    OD_DCT_OVERFLOW_CHECK(t2, 21895, 16384, 118); \
    t5 -= (t2*21895 + 16384) >> 15; \
    /* 15137/16384 ~= Sin[3*Pi/8] ~= 0.923879532511287 */ \
    OD_DCT_OVERFLOW_CHECK(t5, 15137, 8192, 119); \
    t2 += (t5*15137 + 8192) >> 14; \
    /* 10947/16384 ~= Tan[3*Pi/16] ~= 0.668178637919299 */ \
    OD_DCT_OVERFLOW_CHECK(t2, 10947, 8192, 120); \
    t5 -= (t2*10947 + 8192) >> 14; \
    /* 3259/16384 ~= Tan[Pi/16] ~= 0.198912367379658 */ \
    OD_DCT_OVERFLOW_CHECK(t3, 3259, 8192, 121); \
    t4 -= (t3*3259 + 8192) >> 14; \
    /* 3135/8192 ~= Sin[Pi/8] ~= 0.382683432365090 */ \
    OD_DCT_OVERFLOW_CHECK(t4, 3135, 4096, 122); \
    t3 += (t4*3135 + 4096) >> 13; \
    /* 3259/16384 ~= Tan[Pi/16] ~= 0.198912367379658 */ \
    OD_DCT_OVERFLOW_CHECK(t3, 3259, 8192, 123); \
    t4 -= (t3*3259 + 8192) >> 14; \
    t7 += t1; \
    t7h = OD_DCT_RSHIFT(t7, 1); \
    t1 -= t7h; \
    t2 = t3 - t2; \
    t2h = OD_DCT_RSHIFT(t2, 1); \
    t3 -= t2h; \
    t0 -= t6; \
    t0h = OD_DCT_RSHIFT(t0, 1); \
    t6 += t0h; \
    t5 = t4 - t5; \
    t5h = OD_DCT_RSHIFT(t5, 1); \
    t4 -= t5h; \
    t1 += t5h; \
    t5 = t1 - t5; \
    t4 += t0h; \
    t0 -= t4; \
    t6 -= t2h; \
    t2 += t6; \
    t3 -= t7h; \
    t7 += t3; \
    /* TODO: Can we move this into another operation */ \
    t7 = -t7; \
    /* 7425/8192 ~= Tan[15*Pi/64] ~= 0.906347169019147 */ \
    OD_DCT_OVERFLOW_CHECK(t7, 7425, 4096, 124); \
    t0 -= (t7*7425 + 4096) >> 13; \
    /* 8153/8192 ~= Sin[15*Pi/32] ~= 0.995184726672197 */ \
    OD_DCT_OVERFLOW_CHECK(t0, 8153, 4096, 125); \
    t7 += (t0*8153 + 4096) >> 13; \
    /* 7425/8192 ~= Tan[15*Pi/64] ~= 0.906347169019147 */ \
    OD_DCT_OVERFLOW_CHECK(t7, 7425, 4096, 126); \
    t0 -= (t7*7425 + 4096) >> 13; \
    /* 4861/32768 ~= Tan[3*Pi/64] ~= 0.148335987538347 */ \
    OD_DCT_OVERFLOW_CHECK(t1, 4861, 16384, 127); \
    t6 -= (t1*4861 + 16384) >> 15; \
    /* 1189/4096 ~= Sin[3*Pi/32] ~= 0.290284677254462 */ \
    OD_DCT_OVERFLOW_CHECK(t6, 1189, 2048, 128); \
    t1 += (t6*1189 + 2048) >> 12; \
    /* 4861/32768 ~= Tan[3*Pi/64] ~= 0.148335987538347 */ \
    OD_DCT_OVERFLOW_CHECK(t1, 4861, 16384, 129); \
    t6 -= (t1*4861 + 16384) >> 15; \
    /* 2455/4096 ~= Tan[11*Pi/64] ~= 0.599376933681924 */ \
    OD_DCT_OVERFLOW_CHECK(t5, 2455, 2048, 130); \
    t2 -= (t5*2455 + 2048) >> 12; \
    /* 7225/8192 ~= Sin[11*Pi/32] ~= 0.881921264348355 */ \
    OD_DCT_OVERFLOW_CHECK(t2, 7225, 4096, 131); \
    t5 += (t2*7225 + 4096) >> 13; \
    /* 2455/4096 ~= Tan[11*Pi/64] ~= 0.599376933681924 */ \
    OD_DCT_OVERFLOW_CHECK(t5, 2455, 2048, 132); \
    t2 -= (t5*2455 + 2048) >> 12; \
    /* 11725/32768 ~= Tan[7*Pi/64] ~= 0.357805721314524 */ \
    OD_DCT_OVERFLOW_CHECK(t3, 11725, 16384, 133); \
    t4 -= (t3*11725 + 16384) >> 15; \
    /* 5197/8192 ~= Sin[7*Pi/32] ~= 0.634393284163645 */ \
    OD_DCT_OVERFLOW_CHECK(t4, 5197, 4096, 134); \
    t3 += (t4*5197 + 4096) >> 13; \
    /* 11725/32768 ~= Tan[7*Pi/64] ~= 0.357805721314524 */ \
    OD_DCT_OVERFLOW_CHECK(t3, 11725, 16384, 135); \
    t4 -= (t3*11725 + 16384) >> 15; \
  } \
  while (0)

#define OD_IDST_8(t0, t4, t2, t6, t1, t5, t3, t7) \
  /* Embedded 8-point orthonormal Type-IV iDST. */ \
  do { \
    int t0h; \
    int t2h; \
    int t5h_; \
    int t7h_; \
    /* 11725/32768 ~= Tan[7*Pi/64] ~= 0.357805721314524 */ \
    t1 += (t6*11725 + 16384) >> 15; \
    /* 5197/8192 ~= Sin[7*Pi/32] ~= 0.634393284163645 */ \
    t6 -= (t1*5197 + 4096) >> 13; \
    /* 11725/32768 ~= Tan[7*Pi/64] ~= 0.357805721314524 */ \
    t1 += (t6*11725 + 16384) >> 15; \
    /* 2455/4096 ~= Tan[11*Pi/64] ~= 0.599376933681924 */ \
    t2 += (t5*2455 + 2048) >> 12; \
    /* 7225/8192 ~= Sin[11*Pi/32] ~= 0.881921264348355 */ \
    t5 -= (t2*7225 + 4096) >> 13; \
    /* 2455/4096 ~= Tan[11*Pi/64] ~= 0.599376933681924 */ \
    t2 += (t5*2455 + 2048) >> 12; \
    /* 4861/32768 ~= Tan[3*Pi/64] ~= 0.148335987538347 */ \
    t3 += (t4*4861 + 16384) >> 15; \
    /* 1189/4096 ~= Sin[3*Pi/32] ~= 0.290284677254462 */ \
    t4 -= (t3*1189 + 2048) >> 12; \
    /* 4861/32768 ~= Tan[3*Pi/64] ~= 0.148335987538347 */ \
    t3 += (t4*4861 + 16384) >> 15; \
    /* 7425/8192 ~= Tan[15*Pi/64] ~= 0.906347169019147 */ \
    t0 += (t7*7425 + 4096) >> 13; \
    /* 8153/8192 ~= Sin[15*Pi/32] ~= 0.995184726672197 */ \
    t7 -= (t0*8153 + 4096) >> 13; \
    /* 7425/8192 ~= Tan[15*Pi/64] ~= 0.906347169019147 */ \
    t0 += (t7*7425 + 4096) >> 13; \
    /* TODO: Can we move this into another operation */ \
    t7 = -t7; \
    t7 -= t6; \
    t7h_ = OD_DCT_RSHIFT(t7, 1); \
    t6 += t7h_; \
    t2 -= t3; \
    t2h = OD_DCT_RSHIFT(t2, 1); \
    t3 += t2h; \
    t0 += t1; \
    t0h = OD_DCT_RSHIFT(t0, 1); \
    t1 -= t0h; \
    t5 = t4 - t5; \
    t5h_ = OD_DCT_RSHIFT(t5, 1); \
    t4 -= t5h_; \
    t1 += t5h_; \
    t5 = t1 - t5; \
    t3 -= t0h; \
    t0 += t3; \
    t6 += t2h; \
    t2 = t6 - t2; \
    t4 += t7h_; \
    t7 -= t4; \
    /* 3259/16384 ~= Tan[Pi/16] ~= 0.198912367379658 */ \
    t1 += (t6*3259 + 8192) >> 14; \
    /* 3135/8192 ~= Sin[Pi/8] ~= 0.382683432365090 */ \
    t6 -= (t1*3135 + 4096) >> 13; \
    /* 3259/16384 ~= Tan[Pi/16] ~= 0.198912367379658 */ \
    t1 += (t6*3259 + 8192) >> 14; \
    /* 10947/16384 ~= Tan[3*Pi/16] ~= 0.668178637919299 */ \
    t5 += (t2*10947 + 8192) >> 14; \
    /* 15137/16384 ~= Sin[3*Pi/8] ~= 0.923879532511287 */ \
    t2 -= (t5*15137 + 8192) >> 14; \
    /* 21895/32768 ~= Tan[3*Pi/16] ~= 0.668178637919299 */ \
    t5 += (t2*21895 + 16384) >> 15; \
    /* 13573/32768 ~= Tan[Pi/8] ~= 0.414213562373095 */ \
    t3 += (t4*13573 + 16384) >> 15; \
    /* 11585/16384 ~= Sin[Pi/4] ~= 0.707106781186547 */ \
    t4 -= (t3*11585 + 8192) >> 14; \
    /* 13573/32768 ~= Tan[Pi/8] ~= 0.414213562373095 */ \
    t3 += (t4*13573 + 16384) >> 15; \
  } \
  while (0)

/* Rewrite this so that t0h can be passed in. */
#define OD_FDST_8_ASYM(t0, t4, t2, t6, t1, t5, t3, t7) \
  /* Embedded 8-point asymmetric Type-IV fDST. */ \
  do { \
    int t0h; \
    int t2h; \
    int t5h; \
    int t7h; \
    /* 1035/2048 ~= (Sqrt[2] - Cos[7*Pi/32])/(2*Sin[7*Pi/32]) */ \
    OD_DCT_OVERFLOW_CHECK(t1, 1035, 1024, 199); \
    t6 += (t1*1035 + 1024) >> 11; \
    /* 3675/4096 ~= Sqrt[2]*Sin[7*Pi/32] */ \
    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] */ \
    OD_DCT_OVERFLOW_CHECK(t1, 851, 4096, 201); \
    t6 -= (t1*851 + 4096) >> 13; \
    /* 4379/8192 ~= (Sqrt[2] - Sin[5*Pi/32])/(2*Cos[5*Pi/32]) */ \
    OD_DCT_OVERFLOW_CHECK(t2, 4379, 4096, 202); \
    t5 += (t2*4379 + 4096) >> 13; \
    /* 10217/8192 ~= Sqrt[2]*Cos[5*Pi/32] */ \
    OD_DCT_OVERFLOW_CHECK(t5, 10217, 4096, 203); \
    t2 -= (t5*10217 + 4096) >> 13; \
    /* 4379/16384 ~= (1/Sqrt[2] - Sin[5*Pi/32])/Cos[5*Pi/32] */ \
    OD_DCT_OVERFLOW_CHECK(t2, 4379, 8192, 204); \
    t5 += (t2*4379 + 8192) >> 14; \
    /* 12905/16384 ~= (Sqrt[2] - Cos[3*Pi/32])/(2*Sin[3*Pi/32]) */ \
    OD_DCT_OVERFLOW_CHECK(t3, 12905, 8192, 205); \
    t4 += (t3*12905 + 8192) >> 14; \
    /* 3363/8192 ~= Sqrt[2]*Sin[3*Pi/32] */ \
    OD_DCT_OVERFLOW_CHECK(t4, 3363, 4096, 206); \
    t3 -= (t4*3363 + 4096) >> 13; \
    /* 3525/4096 ~= (Cos[3*Pi/32] - 1/Sqrt[2])/Sin[3*Pi/32] */ \
    OD_DCT_OVERFLOW_CHECK(t3, 3525, 2048, 207); \
    t4 -= (t3*3525 + 2048) >> 12; \
    /* 5417/8192 ~= (Sqrt[2] - Sin[Pi/32])/(2*Cos[Pi/32]) */ \
    OD_DCT_OVERFLOW_CHECK(t0, 5417, 4096, 208); \
    t7 += (t0*5417 + 4096) >> 13; \
    /* 5765/4096 ~= Sqrt[2]*Cos[Pi/32] */ \
    OD_DCT_OVERFLOW_CHECK(t7, 5765, 2048, 209); \
    t0 -= (t7*5765 + 2048) >> 12; \
    /* 2507/4096 ~= (1/Sqrt[2] - Sin[Pi/32])/Cos[Pi/32] */ \
    OD_DCT_OVERFLOW_CHECK(t0, 2507, 2048, 210); \
    t7 += (t0*2507 + 2048) >> 12; \
    t0 += t1; \
    t0h = OD_DCT_RSHIFT(t0, 1); \
    t1 -= t0h; \
    t2 -= t3; \
    t2h = OD_DCT_RSHIFT(t2, 1); \
    t3 += t2h; \
    t5 -= t4; \
    t5h = OD_DCT_RSHIFT(t5, 1); \
    t4 += t5h; \
    t7 += t6; \
    t7h = OD_DCT_RSHIFT(t7, 1); \
    t6 = t7h - t6; \
    t4 = t7h - t4; \
    t7 -= t4; \
    t1 += t5h; \
    t5 = t1 - t5; \
    t6 += t2h; \
    t2 = t6 - t2; \
    t3 -= t0h; \
    t0 += t3; \
    /* 3259/16384 ~= Tan[Pi/16] ~= 0.198912367379658 */ \
    OD_DCT_OVERFLOW_CHECK(t6, 3259, 8192, 211); \
    t1 += (t6*3259 + 8192) >> 14; \
    /* 3135/8192 ~= Sin[Pi/8] ~= 0.382683432365090 */ \
    OD_DCT_OVERFLOW_CHECK(t1, 3135, 4096, 212); \
    t6 -= (t1*3135 + 4096) >> 13; \
    /* 3259/16384 ~= Tan[Pi/16] ~= 0.198912367379658 */ \
    OD_DCT_OVERFLOW_CHECK(t6, 3259, 8192, 213); \
    t1 += (t6*3259 + 8192) >> 14; \
    /* 2737/4096 ~= Tan[3*Pi/16] ~= 0.668178637919299 */ \
    OD_DCT_OVERFLOW_CHECK(t2, 2737, 2048, 214); \
    t5 += (t2*2737 + 2048) >> 12; \
    /* 473/512 ~= Sin[3*Pi/8] ~= 0.923879532511287 */ \
    OD_DCT_OVERFLOW_CHECK(t5, 473, 256, 215); \
    t2 -= (t5*473 + 256) >> 9; \
    /* 2737/4096 ~= Tan[3*Pi/16] ~= 0.668178637919299 */ \
    OD_DCT_OVERFLOW_CHECK(t2, 2737, 2048, 216); \
    t5 += (t2*2737 + 2048) >> 12; \
    /* 3393/8192 ~= Tan[Pi/8] ~= 0.414213562373095 */ \
    OD_DCT_OVERFLOW_CHECK(t4, 3393, 4096, 217); \
    t3 += (t4*3393 + 4096) >> 13; \
    /* 5793/8192 ~= Sin[Pi/4] ~= 0.707106781186547 */ \
    OD_DCT_OVERFLOW_CHECK(t3, 5793, 4096, 218); \
    t4 -= (t3*5793 + 4096) >> 13; \
    /* 3393/8192 ~= Tan[Pi/8] ~= 0.414213562373095 */ \
    OD_DCT_OVERFLOW_CHECK(t4, 3393, 4096, 219); \
    t3 += (t4*3393 + 4096) >> 13; \
  } \
  while (0)

#define OD_IDST_8_ASYM(t0, t4, t2, t6, t1, t5, t3, t7) \
  /* Embedded 8-point asymmetric Type-IV iDST. */ \
  do { \
    int t0h; \
    int t2h; \
    int t5h__; \
    int t7h__; \
    /* 3393/8192 ~= Tan[Pi/8] ~= 0.414213562373095 */ \
    t6 -= (t1*3393 + 4096) >> 13; \
    /* 5793/8192 ~= Sin[Pi/4] ~= 0.707106781186547 */ \
    t1 += (t6*5793 + 4096) >> 13; \
    /* 3393/8192 ~= Tan[Pi/8] ~= 0.414213562373095 */ \
    t6 -= (t1*3393 + 4096) >> 13; \
    /* 2737/4096 ~= Tan[3*Pi/16] ~= 0.668178637919299 */ \
    t5 -= (t2*2737 + 2048) >> 12; \
    /* 473/512 ~= Sin[3*Pi/8] ~= 0.923879532511287 */ \
    t2 += (t5*473 + 256) >> 9; \
    /* 2737/4096 ~= Tan[3*Pi/16] ~= 0.668178637919299 */ \
    t5 -= (t2*2737 + 2048) >> 12; \
    /* 3259/16384 ~= Tan[Pi/16] ~= 0.198912367379658 */ \
    t4 -= (t3*3259 + 8192) >> 14; \
    /* 3135/8192 ~= Sin[Pi/8] ~= 0.382683432365090 */ \
    t3 += (t4*3135 + 4096) >> 13; \
    /* 3259/16384 ~= Tan[Pi/16] ~= 0.198912367379658 */ \
    t4 -= (t3*3259 + 8192) >> 14; \
    t0 -= t6; \
    t0h = OD_DCT_RSHIFT(t0, 1); \
    t6 += t0h; \
    t2 = t3 - t2; \
    t2h = OD_DCT_RSHIFT(t2, 1); \
    t3 -= t2h; \
    t5 = t4 - t5; \
    t5h__ = OD_DCT_RSHIFT(t5, 1); \
    t4 -= t5h__; \
    t7 += t1; \
    t7h__ = OD_DCT_RSHIFT(t7, 1); \
    t1 = t7h__ - t1; \
    t3 = t7h__ - t3; \
    t7 -= t3; \
    t1 -= t5h__; \
    t5 += t1; \
    t6 -= t2h; \
    t2 += t6; \
    t4 += t0h; \
    t0 -= t4; \
    /* 2507/4096 ~= (1/Sqrt[2] - Sin[Pi/32])/Cos[Pi/32] */ \
    t7 -= (t0*2507 + 2048) >> 12; \
    /* 5765/4096 ~= Sqrt[2]*Cos[Pi/32] */ \
    t0 += (t7*5765 + 2048) >> 12; \
    /* 5417/8192 ~= (Sqrt[2] - Sin[Pi/32])/(2*Cos[Pi/32]) */ \
    t7 -= (t0*5417 + 4096) >> 13; \
    /* 3525/4096 ~= (Cos[3*Pi/32] - 1/Sqrt[2])/Sin[3*Pi/32] */ \
    t1 += (t6*3525 + 2048) >> 12; \
    /* 3363/8192 ~= Sqrt[2]*Sin[3*Pi/32] */ \
    t6 += (t1*3363 + 4096) >> 13; \
    /* 12905/16384 ~= (1/Sqrt[2] - Cos[3*Pi/32]/1)/Sin[3*Pi/32] */ \
    t1 -= (t6*12905 + 8192) >> 14; \
    /* 4379/16384 ~= (1/Sqrt[2] - Sin[5*Pi/32])/Cos[5*Pi/32] */ \
    t5 -= (t2*4379 + 8192) >> 14; \
    /* 10217/8192 ~= Sqrt[2]*Cos[5*Pi/32] */ \
    t2 += (t5*10217 + 4096) >> 13; \
    /* 4379/8192 ~= (Sqrt[2] - Sin[5*Pi/32])/(2*Cos[5*Pi/32]) */ \
    t5 -= (t2*4379 + 4096) >> 13; \
    /* 851/8192 ~= (Cos[7*Pi/32] - 1/Sqrt[2])/Sin[7*Pi/32] */ \
    t3 += (t4*851 + 4096) >> 13; \
    /* 3675/4096 ~= Sqrt[2]*Sin[7*Pi/32] */ \
    t4 += (t3*3675 + 2048) >> 12; \
    /* 1035/2048 ~= (Sqrt[2] - Cos[7*Pi/32])/(2*Sin[7*Pi/32]) */ \
    t3 -= (t4*1035 + 1024) >> 11; \
  } \
  while (0)

#define OD_FDCT_16(s0, s8, s4, sc, s2, sa, s6, se, \
  s1, s9, s5, sd, s3, sb, s7, sf) \
  /* Embedded 16-point orthonormal Type-II fDCT. */ \
  do { \
    int s8h; \
    int sah; \
    int sch; \
    int seh; \
    int sfh; \
    sf = s0 - sf; \
    sfh = OD_DCT_RSHIFT(sf, 1); \
    s0 -= sfh; \
    se += s1; \
    seh = OD_DCT_RSHIFT(se, 1); \
    s1 = seh - s1; \
    sd = s2 - sd; \
    s2 -= OD_DCT_RSHIFT(sd, 1); \
    sc += s3; \
    sch = OD_DCT_RSHIFT(sc, 1); \
    s3 = sch - s3; \
    sb = s4 - sb; \
    s4 -= OD_DCT_RSHIFT(sb, 1); \
    sa += s5; \
    sah = OD_DCT_RSHIFT(sa, 1); \
    s5 = sah - s5; \
    s9 = s6 - s9; \
    s6 -= OD_DCT_RSHIFT(s9, 1); \
    s8 += s7; \
    s8h = OD_DCT_RSHIFT(s8, 1); \
    s7 = s8h - s7; \
    OD_FDCT_8_ASYM(s0, s8, s8h, s4, sc, sch, s2, sa, sah, s6, se, seh); \
    OD_FDST_8_ASYM(sf, s7, sb, s3, sd, s5, s9, s1); \
  } \
  while (0)

#define OD_IDCT_16(s0, s8, s4, sc, s2, sa, s6, se, \
  s1, s9, s5, sd, s3, sb, s7, sf) \
  /* Embedded 16-point orthonormal Type-II iDCT. */ \
  do { \
    int s1h; \
    int s3h; \
    int s5h; \
    int s7h; \
    int sfh; \
    OD_IDST_8_ASYM(sf, sb, sd, s9, se, sa, sc, s8); \
    OD_IDCT_8_ASYM(s0, s4, s2, s6, s1, s1h, s5, s5h, s3, s3h, s7, s7h); \
    sfh = OD_DCT_RSHIFT(sf, 1); \
    s0 += sfh; \
    sf = s0 - sf; \
    se = s1h - se; \
    s1 -= se; \
    s2 += OD_DCT_RSHIFT(sd, 1); \
    sd = s2 - sd; \
    sc = s3h - sc; \
    s3 -= sc; \
    s4 += OD_DCT_RSHIFT(sb, 1); \
    sb = s4 - sb; \
    sa = s5h - sa; \
    s5 -= sa; \
    s6 += OD_DCT_RSHIFT(s9, 1); \
    s9 = s6 - s9; \
    s8 = s7h - s8; \
    s7 -= s8; \
  } \
  while (0)

#define OD_FDCT_16_ASYM(t0, t8, t8h, t4, tc, tch, t2, ta, tah, t6, te, teh, \
  t1, t9, t9h, t5, td, tdh, t3, tb, tbh, t7, tf, tfh) \
  /* Embedded 16-point asymmetric Type-II fDCT. */ \
  do { \
    t0 += tfh; \
    tf = t0 - tf; \
    t1 -= teh; \
    te += t1; \
    t2 += tdh; \
    td = t2 - td; \
    t3 -= tch; \
    tc += t3; \
    t4 += tbh; \
    tb = t4 - tb; \
    t5 -= tah; \
    ta += t5; \
    t6 += t9h; \
    t9 = t6 - t9; \
    t7 -= t8h; \
    t8 += t7; \
    OD_FDCT_8(t0, t8, t4, tc, t2, ta, t6, te); \
    OD_FDST_8(tf, t7, tb, t3, td, t5, t9, t1); \
  } \
  while (0)

#define OD_IDCT_16_ASYM(t0, t8, t4, tc, t2, ta, t6, te, \
  t1, t1h, t9, t9h, t5, t5h, td, tdh, t3, t3h, tb, tbh, t7, t7h, tf, tfh) \
  /* Embedded 16-point asymmetric Type-II iDCT. */ \
  do { \
    OD_IDST_8(tf, tb, td, t9, te, ta, tc, t8); \
    OD_IDCT_8(t0, t4, t2, t6, t1, t5, t3, t7); \
    t1 -= te; \
    t1h = OD_DCT_RSHIFT(t1, 1); \
    te += t1h; \
    t9 = t6 - t9; \
    t9h = OD_DCT_RSHIFT(t9, 1); \
    t6 -= t9h; \
    t5 -= ta; \
    t5h = OD_DCT_RSHIFT(t5, 1); \
    ta += t5h; \
    td = t2 - td; \
    tdh = OD_DCT_RSHIFT(td, 1); \
    t2 -= tdh; \
    t3 -= tc; \
    t3h = OD_DCT_RSHIFT(t3, 1); \
    tc += t3h; \
    tb = t4 - tb; \
    tbh = OD_DCT_RSHIFT(tb, 1); \
    t4 -= tbh; \
    t7 -= t8; \
    t7h = OD_DCT_RSHIFT(t7, 1); \
    t8 += t7h; \
    tf = t0 - tf; \
    tfh = OD_DCT_RSHIFT(tf, 1); \
    t0 -= tfh; \
  } \
  while (0)

#define OD_FDST_16(s0, s8, s4, sc, s2, sa, s6, se, \
  s1, s9, s5, sd, s3, sb, s7, sf) \
  /* Embedded 16-point orthonormal Type-IV fDST. */ \
  do { \
    int s0h; \
    int s2h; \
    int sdh; \
    int sfh; \
    /* 13573/32768 ~= Tan[Pi/8] ~= 0.414213562373095 */ \
    OD_DCT_OVERFLOW_CHECK(s3, 13573, 16384, 220); \
    s1 += (se*13573 + 16384) >> 15; \
    /* 11585/16384 ~= Sin[Pi/4] ~= 0.707106781186547 */ \
    OD_DCT_OVERFLOW_CHECK(s1, 11585, 8192, 221); \
    se -= (s1*11585 + 8192) >> 14; \
    /* 13573/32768 ~= Tan[Pi/8] ~= 0.414213562373095 */ \
    OD_DCT_OVERFLOW_CHECK(s3, 13573, 16384, 222); \
    s1 += (se*13573 + 16384) >> 15; \
    /* 21895/32768 ~= Tan[3*Pi/16] ~= 0.668178637919299 */ \
    OD_DCT_OVERFLOW_CHECK(s2, 21895, 16384, 223); \
    sd += (s2*21895 + 16384) >> 15; \
    /* 15137/16384 ~= Sin[3*Pi/8] ~= 0.923879532511287 */ \
    OD_DCT_OVERFLOW_CHECK(sd, 15137, 16384, 224); \
    s2 -= (sd*15137 + 8192) >> 14; \
    /* 21895/32768 ~= Tan[3*Pi/16] ~= 0.668178637919299 */ \
    OD_DCT_OVERFLOW_CHECK(s2, 21895, 16384, 225); \
    sd += (s2*21895 + 16384) >> 15; \
    /* 3259/16384 ~= Tan[Pi/16] ~= 0.198912367379658 */ \
    OD_DCT_OVERFLOW_CHECK(s3, 3259, 8192, 226); \
    sc += (s3*3259 + 8192) >> 14; \
    /* 3135/8192 ~= Sin[Pi/8] ~= 0.382683432365090 */ \
    OD_DCT_OVERFLOW_CHECK(sc, 3135, 4096, 227); \
    s3 -= (sc*3135 + 4096) >> 13; \
    /* 3259/16384 ~= Tan[Pi/16] ~= 0.198912367379658 */ \
    OD_DCT_OVERFLOW_CHECK(s3, 3259, 8192, 228); \
    sc += (s3*3259 + 8192) >> 14; \
    /* 13573/32768 ~= Tan[Pi/8] ~= 0.414213562373095 */ \
    OD_DCT_OVERFLOW_CHECK(s5, 13573, 16384, 229); \
    sa += (s5*13573 + 16384) >> 15; \
    /* 11585/16384 ~= Sin[Pi/4] ~= 0.707106781186547 */ \
    OD_DCT_OVERFLOW_CHECK(sa, 11585, 8192, 230); \
    s5 -= (sa*11585 + 8192) >> 14; \
    /* 13573/32768 ~= Tan[Pi/8] ~= 0.414213562373095 */ \
    OD_DCT_OVERFLOW_CHECK(s5, 13573, 16384, 231); \
    sa += (s5*13573 + 16384) >> 15; \
    /* 13573/32768 ~= Tan[pi/8] ~= 0.414213562373095 */ \
    OD_DCT_OVERFLOW_CHECK(s9, 13573, 16384, 232); \
    s6 += (s9*13573 + 16384) >> 15; \
    /* 11585/16384 ~= Sin[pi/4] ~= 0.707106781186547 */ \
    OD_DCT_OVERFLOW_CHECK(s6, 11585, 8192, 233); \
    s9 -= (s6*11585 + 8192) >> 14; \
    /* 13573/32768 ~= Tan[pi/8] ~= 0.414213562373095 */ \
    OD_DCT_OVERFLOW_CHECK(s9, 13573, 16384, 234); \
    s6 += (s9*13573 + 16384) >> 15; \
    sf += se; \
    sfh = OD_DCT_RSHIFT(sf, 1); \
    se = sfh - se; \
    s0 += s1; \
    s0h = OD_DCT_RSHIFT(s0, 1); \
    s1 = s0h - s1; \
    s2 = s3 - s2; \
    s2h = OD_DCT_RSHIFT(s2, 1); \
    s3 -= s2h; \
    sd -= sc; \
    sdh = OD_DCT_RSHIFT(sd, 1); \
    sc += sdh; \
    sa = s4 - sa; \
    s4 -= OD_DCT_RSHIFT(sa, 1); \
    s5 += sb; \
    sb = OD_DCT_RSHIFT(s5, 1) - sb; \
    s8 += s6; \
    s6 -= OD_DCT_RSHIFT(s8, 1); \
    s7 = s9 - s7; \
    s9 -= OD_DCT_RSHIFT(s7, 1); \
    /* 6723/8192 ~= Tan[7*Pi/32] ~= 0.820678790828660 */ \
    OD_DCT_OVERFLOW_CHECK(sb, 6723, 4096, 235); \
    s4 += (sb*6723 + 4096) >> 13; \
    /* 16069/16384 ~= Sin[7*Pi/16] ~= 0.980785280403230 */ \
    OD_DCT_OVERFLOW_CHECK(s4, 16069, 8192, 236); \
    sb -= (s4*16069 + 8192) >> 14; \
    /* 6723/8192 ~= Tan[7*Pi/32]) ~= 0.820678790828660 */ \
    OD_DCT_OVERFLOW_CHECK(sb, 6723, 4096, 237); \
    s4 += (sb*6723 + 4096) >> 13; \
    /* 8757/16384 ~= Tan[5*Pi/32]) ~= 0.534511135950792 */ \
    OD_DCT_OVERFLOW_CHECK(s5, 8757, 8192, 238); \
    sa += (s5*8757 + 8192) >> 14; \
    /* 6811/8192 ~= Sin[5*Pi/16] ~= 0.831469612302545 */ \
    OD_DCT_OVERFLOW_CHECK(sa, 6811, 4096, 239); \
    s5 -= (sa*6811 + 4096) >> 13; \
    /* 8757/16384 ~= Tan[5*Pi/32] ~= 0.534511135950792 */ \
    OD_DCT_OVERFLOW_CHECK(s5, 8757, 8192, 240); \
    sa += (s5*8757 + 8192) >> 14; \
    /* 2485/8192 ~= Tan[3*Pi/32] ~= 0.303346683607342 */ \
    OD_DCT_OVERFLOW_CHECK(s9, 2485, 4096, 241); \
    s6 += (s9*2485 + 4096) >> 13; \
    /* 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; \
    /* 3227/32768 ~= Tan[Pi/32] ~= 0.09849140335716425 */ \
    OD_DCT_OVERFLOW_CHECK(s8, 3227, 16384, 244); \
    s7 += (s8*3227 + 16384) >> 15; \
    /* 6393/32768 ~= Sin[Pi/16] ~= 0.19509032201612825 */ \
    OD_DCT_OVERFLOW_CHECK(s7, 6393, 16384, 245); \
    s8 -= (s7*6393 + 16384) >> 15; \
    /* 3227/32768 ~= Tan[Pi/32] ~= 0.09849140335716425 */ \
    OD_DCT_OVERFLOW_CHECK(s8, 3227, 16384, 246); \
    s7 += (s8*3227 + 16384) >> 15; \
    s1 -= s2h; \
    s2 += s1; \
    se += sdh; \
    sd = se - sd; \
    s3 += sfh; \
    sf -= s3; \
    sc = s0h - sc; \
    s0 -= sc; \
    sb += OD_DCT_RSHIFT(s8, 1); \
    s8 = sb - s8; \
    s4 += OD_DCT_RSHIFT(s7, 1); \
    s7 -= s4; \
    s6 += OD_DCT_RSHIFT(s5, 1); \
    s5 = s6 - s5; \
    s9 -= OD_DCT_RSHIFT(sa, 1); \
    sa += s9; \
    s8 += s0; \
    s0 -= OD_DCT_RSHIFT(s8, 1); \
    sf += s7; \
    s7 = OD_DCT_RSHIFT(sf, 1) - s7; \
    s1 -= s6; \
    s6 += OD_DCT_RSHIFT(s1, 1); \
    s9 += se; \
    se = OD_DCT_RSHIFT(s9, 1) - se; \
    s2 += sa; \
    sa = OD_DCT_RSHIFT(s2, 1) - sa; \
    s5 += sd; \
    sd -= OD_DCT_RSHIFT(s5, 1); \
    s4 = sc - s4; \
    sc -= OD_DCT_RSHIFT(s4, 1); \
    s3 -= sb; \
    sb += OD_DCT_RSHIFT(s3, 1); \
    /* 2799/4096 ~= (1/Sqrt[2] - Cos[31*Pi/64]/2)/Sin[31*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(sf, 2799, 2048, 247); \
    s0 -= (sf*2799 + 2048) >> 12; \
    /* 2893/2048 ~= Sqrt[2]*Sin[31*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s0, 2893, 1024, 248); \
    sf += (s0*2893 + 1024) >> 11; \
    /* 5397/8192 ~= (Cos[Pi/4] - Cos[31*Pi/64])/Sin[31*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(sf, 5397, 4096, 249); \
    s0 -= (sf*5397 + 4096) >> 13; \
    /* 41/64 ~= (1/Sqrt[2] - Cos[29*Pi/64]/2)/Sin[29*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s1, 41, 32, 250); \
    se += (s1*41 + 32) >> 6; \
    /* 2865/2048 ~= Sqrt[2]*Sin[29*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(se, 2865, 1024, 251); \
    s1 -= (se*2865 + 1024) >> 11; \
    /* 4641/8192 ~= (1/Sqrt[2] - Cos[29*Pi/64])/Sin[29*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s1, 4641, 4096, 252); \
    se += (s1*4641 + 4096) >> 13; \
    /* 2473/4096 ~= (1/Sqrt[2] - Cos[27*Pi/64]/2)/Sin[27*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s2, 2473, 2048, 253); \
    sd += (s2*2473 + 2048) >> 12; \
    /* 5619/4096 ~= Sqrt[2]*Sin[27*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(sd, 5619, 2048, 254); \
    s2 -= (sd*5619 + 2048) >> 12; \
    /* 7839/16384 ~= (1/Sqrt[2] - Cos[27*Pi/64])/Sin[27*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s2, 7839, 8192, 255); \
    sd += (s2*7839 + 8192) >> 14; \
    /* 5747/8192 ~= (1/Sqrt[2] - Cos[7*Pi/64]/2)/Sin[7*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s3, 5747, 4096, 256); \
    sc -= (s3*5747 + 4096) >> 13; \
    /* 3903/8192 ~= Sqrt[2]*Sin[7*Pi/64] ~= */ \
    OD_DCT_OVERFLOW_CHECK(sc, 3903, 4096, 257); \
    s3 += (sc*3903 + 4096) >> 13; \
    /* 5701/8192 ~= (1/Sqrt[2] - Cos[7*Pi/64])/Sin[7*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s3, 5701, 4096, 258); \
    sc += (s3*5701 + 4096) >> 13; \
    /* 4471/8192 ~= (1/Sqrt[2] - Cos[23*Pi/64]/2)/Sin[23*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s4, 4471, 4096, 259); \
    sb += (s4*4471 + 4096) >> 13; \
    /* 1309/1024 ~= Sqrt[2]*Sin[23*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(sb, 1309, 512, 260); \
    s4 -= (sb*1309 + 512) >> 10; \
    /* 5067/16384 ~= (1/Sqrt[2] - Cos[23*Pi/64])/Sin[23*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s4, 5067, 8192, 261); \
    sb += (s4*5067 + 8192) >> 14; \
    /* 2217/4096 ~= (1/Sqrt[2] - Cos[11*Pi/64]/2)/Sin[11*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s5, 2217, 2048, 262); \
    sa -= (s5*2217 + 2048) >> 12; \
    /* 1489/2048 ~= Sqrt[2]*Sin[11*Pi/64] ~= 0.72705107329128 */ \
    OD_DCT_OVERFLOW_CHECK(sa, 1489, 1024, 263); \
    s5 += (sa*1489 + 1024) >> 11; \
    /* 75/256 ~= (1/Sqrt[2] - Cos[11*Pi/64])/Sin[11*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s5, 75, 128, 264); \
    sa += (s5*75 + 128) >> 8; \
    /* 2087/4096 ~= (1/Sqrt[2] - Cos[19*Pi/64]/2)/Sin[19*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s9, 2087, 2048, 265); \
    s6 -= (s9*2087 + 2048) >> 12; \
    /* 4653/4096 ~= Sqrt[2]*Sin[19*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s6, 4653, 2048, 266); \
    s9 += (s6*4653 + 2048) >> 12; \
    /* 4545/32768 ~= (1/Sqrt[2] - Cos[19*Pi/64])/Sin[19*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s9, 4545, 16384, 267); \
    s6 -= (s9*4545 + 16384) >> 15; \
    /* 2053/4096 ~= (1/Sqrt[2] - Cos[15*Pi/64]/2)/Sin[15*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s8, 2053, 2048, 268); \
    s7 += (s8*2053 + 2048) >> 12; \
    /* 1945/2048 ~= Sqrt[2]*Sin[15*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s7, 1945, 1024, 269); \
    s8 -= (s7*1945 + 1024) >> 11; \
    /* 1651/32768 ~= (1/Sqrt[2] - Cos[15*Pi/64])/Sin[15*Pi/64] */ \
    OD_DCT_OVERFLOW_CHECK(s8, 1651, 16384, 270); \
    s7 -= (s8*1651 + 16384) >> 15; \
  } \
  while (0)

#define OD_IDST_16(s0, s8, s4, sc, s2, sa, s6, se, \
  s1, s9, s5, sd, s3, sb, s7, sf) \
  /* Embedded 16-point orthonormal Type-IV iDST. */ \
  do { \
    int s0h; \
    int s4h; \
    int sbh; \
    int sfh; \
    /* 1651/32768 ~= (1/Sqrt[2] - Cos[15*Pi/64])/Sin[15*Pi/64] */ \
    se += (s1*1651 + 16384) >> 15; \
    /* 1945/2048 ~= Sqrt[2]*Sin[15*Pi/64] */ \
    s1 += (se*1945 + 1024) >> 11; \
    /* 2053/4096 ~= (1/Sqrt[2] - Cos[15*Pi/64]/2)/Sin[15*Pi/64] */ \
    se -= (s1*2053 + 2048) >> 12; \
    /* 4545/32768 ~= (1/Sqrt[2] - Cos[19*Pi/64])/Sin[19*Pi/64] */ \
    s6 += (s9*4545 + 16384) >> 15; \
    /* 4653/32768 ~= Sqrt[2]*Sin[19*Pi/64] */ \
    s9 -= (s6*4653 + 2048) >> 12; \
    /* 2087/4096 ~= (1/Sqrt[2] - Cos[19*Pi/64]/2)/Sin[19*Pi/64] */ \
    s6 += (s9*2087 + 2048) >> 12; \
    /* 75/256 ~= (1/Sqrt[2] - Cos[11*Pi/64])/Sin[11*Pi/64] */ \
    s5 -= (sa*75 + 128) >> 8; \
    /* 1489/2048 ~= Sqrt[2]*Sin[11*Pi/64] */ \
    sa -= (s5*1489 + 1024) >> 11; \
    /* 2217/4096 ~= (1/Sqrt[2] - Cos[11*Pi/64]/2)/Sin[11*Pi/64] */ \
    s5 += (sa*2217 + 2048) >> 12; \
    /* 5067/16384 ~= (1/Sqrt[2] - Cos[23*Pi/64])/Sin[23*Pi/64] */ \
    sd -= (s2*5067 + 8192) >> 14; \
    /* 1309/1024 ~= Sqrt[2]*Sin[23*Pi/64] */ \
    s2 += (sd*1309 + 512) >> 10; \
    /* 4471/8192 ~= (1/Sqrt[2] - Cos[23*Pi/64]/2)/Sin[23*Pi/64] */ \
    sd -= (s2*4471 + 4096) >> 13; \
    /* 5701/8192 ~= (1/Sqrt[2] - Cos[7*Pi/64])/Sin[7*Pi/64] */  \
    s3 -= (sc*5701 + 4096) >> 13; \
    /* 3903/8192 ~= Sqrt[2]*Sin[7*Pi/64] */ \
    sc -= (s3*3903 + 4096) >> 13; \
    /* 5747/8192 ~= (1/Sqrt[2] - Cos[7*Pi/64]/2)/Sin[7*Pi/64] */ \
    s3 += (sc*5747 + 4096) >> 13; \
    /* 7839/16384 ~= (1/Sqrt[2] - Cos[27*Pi/64])/Sin[27*Pi/64] */ \
    sb -= (s4*7839 + 8192) >> 14; \
    /* 5619/4096 ~= Sqrt[2]*Sin[27*Pi/64] */ \
    s4 += (sb*5619 + 2048) >> 12; \
    /* 2473/4096 ~= (1/Sqrt[2] - Cos[27*Pi/64]/2)/Sin[27*Pi/64] */ \
    sb -= (s4*2473 + 2048) >> 12; \
    /* 4641/8192 ~= (1/Sqrt[2] - Cos[29*Pi/64])/Sin[29*Pi/64] */ \
    s7 -= (s8*4641 + 4096) >> 13; \
    /* 2865/2048 ~= Sqrt[2]*Sin[29*Pi/64] */ \
    s8 += (s7*2865 + 1024) >> 11; \
    /* 41/64 ~= (1/Sqrt[2] - Cos[29*Pi/64]/2)/Sin[29*Pi/64] */ \
    s7 -= (s8*41 + 32) >> 6; \
    /* 5397/8192 ~= (Cos[Pi/4] - Cos[31*Pi/64])/Sin[31*Pi/64] */ \
    s0 += (sf*5397 + 4096) >> 13; \
    /* 2893/2048 ~= Sqrt[2]*Sin[31*Pi/64] */ \
    sf -= (s0*2893 + 1024) >> 11; \
    /* 2799/4096 ~= (1/Sqrt[2] - Cos[31*Pi/64]/2)/Sin[31*Pi/64] */ \
    s0 += (sf*2799 + 2048) >> 12; \
    sd -= OD_DCT_RSHIFT(sc, 1); \
    sc += sd; \
    s3 += OD_DCT_RSHIFT(s2, 1); \
    s2 = s3 - s2; \
    sb += OD_DCT_RSHIFT(sa, 1); \
    sa -= sb; \
    s5 = OD_DCT_RSHIFT(s4, 1) - s5; \
    s4 -= s5; \
    s7 = OD_DCT_RSHIFT(s9, 1) - s7; \
    s9 -= s7; \
    s6 -= OD_DCT_RSHIFT(s8, 1); \
    s8 += s6; \
    se = OD_DCT_RSHIFT(sf, 1) - se; \
    sf -= se; \
    s0 += OD_DCT_RSHIFT(s1, 1); \
    s1 -= s0; \
    s5 -= s9; \
    s9 += OD_DCT_RSHIFT(s5, 1); \
    sa = s6 - sa; \
    s6 -= OD_DCT_RSHIFT(sa, 1); \
    se += s2; \
    s2 -= OD_DCT_RSHIFT(se, 1); \
    s1 = sd - s1; \
    sd -= OD_DCT_RSHIFT(s1, 1); \
    s0 += s3; \
    s0h = OD_DCT_RSHIFT(s0, 1); \
    s3 = s0h - s3; \
    sf += sc; \
    sfh = OD_DCT_RSHIFT(sf, 1); \
    sc -= sfh; \
    sb = s7 - sb; \
    sbh = OD_DCT_RSHIFT(sb, 1); \
    s7 -= sbh; \
    s4 -= s8; \
    s4h = OD_DCT_RSHIFT(s4, 1); \
    s8 += s4h; \
    /* 3227/32768 ~= Tan[Pi/32] ~= 0.09849140335716425 */ \
    se -= (s1*3227 + 16384) >> 15; \
    /* 6393/32768 ~= Sin[Pi/16] ~= 0.19509032201612825 */ \
    s1 += (se*6393 + 16384) >> 15; \
    /* 3227/32768 ~= Tan[Pi/32] ~= 0.09849140335716425 */ \
    se -= (s1*3227 + 16384) >> 15; \
    /* 2485/8192 ~= Tan[3*Pi/32] ~= 0.303346683607342 */ \
    s6 -= (s9*2485 + 4096) >> 13; \
    /* 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 */ \
    s5 -= (sa*8757 + 8192) >> 14; \
    /* 6811/8192 ~= Sin[5*Pi/16] ~= 0.831469612302545 */ \
    sa += (s5*6811 + 4096) >> 13; \
    /* 8757/16384 ~= Tan[5*Pi/32]) ~= 0.534511135950792 */ \
    s5 -= (sa*8757 + 8192) >> 14; \
    /* 6723/8192 ~= Tan[7*Pi/32]) ~= 0.820678790828660 */ \
    s2 -= (sd*6723 + 4096) >> 13; \
    /* 16069/16384 ~= Sin[7*Pi/16] ~= 0.980785280403230 */ \
    sd += (s2*16069 + 8192) >> 14; \
    /* 6723/8192 ~= Tan[7*Pi/32] ~= 0.820678790828660 */ \
    s2 -= (sd*6723 + 4096) >> 13; \
    s9 += OD_DCT_RSHIFT(se, 1); \
    se = s9 - se; \
    s6 += OD_DCT_RSHIFT(s1, 1); \
    s1 -= s6; \
    sd = OD_DCT_RSHIFT(sa, 1) - sd; \
    sa -= sd; \
    s2 += OD_DCT_RSHIFT(s5, 1); \
    s5 = s2 - s5; \
    s3 -= sbh; \
    sb += s3; \
    sc += s4h; \
    s4 = sc - s4; \
    s8 = s0h - s8; \
    s0 -= s8; \
    s7 = sfh - s7; \
    sf -= s7; \
    /* 13573/32768 ~= Tan[pi/8] ~= 0.414213562373095 */ \
    s6 -= (s9*13573 + 16384) >> 15; \
    /* 11585/16384 ~= Sin[pi/4] ~= 0.707106781186547 */ \
    s9 += (s6*11585 + 8192) >> 14; \
    /* 13573/32768 ~= Tan[pi/8] ~= 0.414213562373095 */ \
    s6 -= (s9*13573 + 16384) >> 15; \
    /* 13573/32768 ~= Tan[pi/8] ~= 0.414213562373095 */ \
    s5 -= (sa*13573 + 16384) >> 15; \
    /* 11585/16384 ~= Sin[pi/4] ~= 0.707106781186547 */ \
    sa += (s5*11585 + 8192) >> 14; \
    /* 13573/32768 ~= Tan[pi/8] ~= 0.414213562373095 */ \
    s5 -= (sa*13573 + 16384) >> 15; \
    /* 3259/16384 ~= Tan[Pi/16] ~= 0.198912367379658 */ \
    s3 -= (sc*3259 + 8192) >> 14; \
    /* 3135/8192 ~= Sin[Pi/8] ~= 0.382683432365090 */ \
    sc += (s3*3135 + 4096) >> 13; \
    /* 3259/16384 ~= Tan[Pi/16] ~= 0.198912367379658 */ \
    s3 -= (sc*3259 + 8192) >> 14; \
    /* 21895/32768 ~= Tan[3*Pi/16] ~= 0.668178637919299 */ \
    sb -= (s4*21895 + 16384) >> 15; \
    /* 15137/16384 ~= Sin[3*Pi/8] ~= 0.923879532511287 */ \
    s4 += (sb*15137 + 8192) >> 14; \
    /* 21895/32768 ~= Tan[3*Pi/16] ~= 0.668178637919299 */ \
    sb -= (s4*21895 + 16384) >> 15; \
    /* 13573/32768 ~= Tan[pi/8] ~= 0.414213562373095 */ \
    s8 -= (s7*13573 + 16384) >> 15; \
    /* 11585/16384 ~= Sin[pi/4] ~= 0.707106781186547 */ \
    s7 += (s8*11585 + 8192) >> 14; \
    /* 13573/32768 ~= Tan[pi/8] ~= 0.414213562373095 */ \
    s8 -= (s7*13573 + 16384) >> 15; \
  } \
  while (0)

/* TODO: rewrite this to match OD_FDST_16. */
#define OD_FDST_16_ASYM(t0, t0h, t8, t4, t4h, tc, t2, ta, t6, te, \
  t1, t9, t5, td, t3, tb, t7, t7h, tf) \
  /* Embedded 16-point asymmetric Type-IV fDST. */ \
  do { \
    int t2h; \
    int t3h; \
    int t6h; \
    int t8h; \
    int t9h; \
    int tch; \
    int tdh; \
    /* TODO: Can we move these into another operation */ \
    t8 = -t8; \
    t9 = -t9; \
    ta = -ta; \
    tb = -tb; \
    td = -td; \
    /* 13573/16384 ~= 2*Tan[Pi/8] ~= 0.828427124746190 */ \
    OD_DCT_OVERFLOW_CHECK(te, 13573, 8192, 136); \
    t1 -= (te*13573 + 8192) >> 14; \
    /* 11585/32768 ~= Sin[Pi/4]/2 ~= 0.353553390593274 */ \
    OD_DCT_OVERFLOW_CHECK(t1, 11585, 16384, 137); \
    te += (t1*11585 + 16384) >> 15; \
    /* 13573/16384 ~= 2*Tan[Pi/8] ~= 0.828427124746190 */ \
    OD_DCT_OVERFLOW_CHECK(te, 13573, 8192, 138); \
    t1 -= (te*13573 + 8192) >> 14; \
    /* 4161/16384 ~= Tan[3*Pi/16] - Tan[Pi/8] ~= 0.253965075546204 */ \
    OD_DCT_OVERFLOW_CHECK(td, 4161, 8192, 139); \
    t2 += (td*4161 + 8192) >> 14; \
    /* 15137/16384 ~= Sin[3*Pi/8] ~= 0.923879532511287 */ \
    OD_DCT_OVERFLOW_CHECK(t2, 15137, 8192, 140); \
    td -= (t2*15137 + 8192) >> 14; \
    /* 14341/16384 ~= Tan[3*Pi/16] + Tan[Pi/8]/2 ~= 0.875285419105846 */ \
    OD_DCT_OVERFLOW_CHECK(td, 14341, 8192, 141); \
    t2 += (td*14341 + 8192) >> 14; \
    /* 14341/16384 ~= Tan[3*Pi/16] + Tan[Pi/8]/2 ~= 0.875285419105846 */ \
    OD_DCT_OVERFLOW_CHECK(t3, 14341, 8192, 142); \
    tc -= (t3*14341 + 8192) >> 14; \
    /* 15137/16384 ~= Sin[3*Pi/8] ~= 0.923879532511287 */ \
    OD_DCT_OVERFLOW_CHECK(tc, 15137, 8192, 143); \
    t3 += (tc*15137 + 8192) >> 14; \
    /* 4161/16384 ~= Tan[3*Pi/16] - Tan[Pi/8] ~= 0.253965075546204 */ \
    OD_DCT_OVERFLOW_CHECK(t3, 4161, 8192, 144); \
    tc -= (t3*4161 + 8192) >> 14; \
    te = t0h - te; \
    t0 -= te; \
    tf = OD_DCT_RSHIFT(t1, 1) - tf; \
    t1 -= tf; \
    /* TODO: Can we move this into another operation */ \
    tc = -tc; \
    t2 = OD_DCT_RSHIFT(tc, 1) - t2; \
    tc -= t2; \
    t3 = OD_DCT_RSHIFT(td, 1) - t3; \
    td = t3 - td; \
    /* 7489/8192 ~= Tan[Pi/8] + Tan[Pi/4]/2 ~= 0.914213562373095 */ \
    OD_DCT_OVERFLOW_CHECK(t6, 7489, 4096, 145); \
    t9 -= (t6*7489 + 4096) >> 13; \
    /* 11585/16384 ~= Sin[Pi/4] ~= 0.707106781186548 */ \
    OD_DCT_OVERFLOW_CHECK(t9, 11585, 8192, 146); \
    t6 += (t9*11585 + 8192) >> 14; \
    /* -19195/32768 ~= Tan[Pi/8] - Tan[Pi/4] ~= -0.585786437626905 */ \
    OD_DCT_OVERFLOW_CHECK(t6, 19195, 16384, 147); \
    t9 += (t6*19195 + 16384) >> 15; \
    t8 += OD_DCT_RSHIFT(t9, 1); \
    t9 -= t8; \
    t6 = t7h - t6; \
    t7 -= t6; \
    /* 6723/8192 ~= Tan[7*Pi/32] ~= 0.820678790828660 */ \
    OD_DCT_OVERFLOW_CHECK(t7, 6723, 4096, 148); \
    t8 += (t7*6723 + 4096) >> 13; \
    /* 16069/16384 ~= Sin[7*Pi/16] ~= 0.980785280403230 */ \
    OD_DCT_OVERFLOW_CHECK(t8, 16069, 8192, 149); \
    t7 -= (t8*16069 + 8192) >> 14; \
    /* 6723/8192 ~= Tan[7*Pi/32]) ~= 0.820678790828660 */ \
    OD_DCT_OVERFLOW_CHECK(t7, 6723, 4096, 150); \
    t8 += (t7*6723 + 4096) >> 13; \
    /* 17515/32768 ~= Tan[5*Pi/32]) ~= 0.534511135950792 */ \
    OD_DCT_OVERFLOW_CHECK(t6, 17515, 16384, 151); \
    t9 += (t6*17515 + 16384) >> 15; \
    /* 13623/16384 ~= Sin[5*Pi/16] ~= 0.831469612302545 */ \
    OD_DCT_OVERFLOW_CHECK(t9, 13623, 8192, 152); \
    t6 -= (t9*13623 + 8192) >> 14; \
    /* 17515/32768 ~= Tan[5*Pi/32] ~= 0.534511135950792 */ \
    OD_DCT_OVERFLOW_CHECK(t6, 17515, 16384, 153); \
    t9 += (t6*17515 + 16384) >> 15; \
    /* 13573/16384 ~= 2*Tan[Pi/8] ~= 0.828427124746190 */ \
    OD_DCT_OVERFLOW_CHECK(ta, 13573, 8192, 154); \
    t5 += (ta*13573 + 8192) >> 14; \
    /* 11585/32768 ~= Sin[Pi/4]/2 ~= 0.353553390593274 */ \
    OD_DCT_OVERFLOW_CHECK(t5, 11585, 16384, 155); \
    ta -= (t5*11585 + 16384) >> 15; \
    /* 13573/16384 ~= 2*Tan[Pi/8] ~= 0.828427124746190 */ \
    OD_DCT_OVERFLOW_CHECK(ta, 13573, 8192, 156); \
    t5 += (ta*13573 + 8192) >> 14; \
    tb += OD_DCT_RSHIFT(t5, 1); \
    t5 = tb - t5; \
    ta += t4h; \
    t4 -= ta; \
    /* 2485/8192 ~= Tan[3*Pi/32] ~= 0.303346683607342 */ \
    OD_DCT_OVERFLOW_CHECK(t5, 2485, 4096, 157); \
    ta += (t5*2485 + 4096) >> 13; \
    /* 18205/32768 ~= Sin[3*Pi/16] ~= 0.555570233019602 */ \
    OD_DCT_OVERFLOW_CHECK(ta, 18205, 16384, 158); \
    t5 -= (ta*18205 + 16384) >> 15; \
    /* 2485/8192 ~= Tan[3*Pi/32] ~= 0.303346683607342 */ \
    OD_DCT_OVERFLOW_CHECK(t5, 2485, 4096, 159); \
    ta += (t5*2485 + 4096) >> 13; \
    /* 6723/8192 ~= Tan[7*Pi/32] ~= 0.820678790828660 */ \
    OD_DCT_OVERFLOW_CHECK(t4, 6723, 4096, 160); \
    tb -= (t4*6723 + 4096) >> 13; \
    /* 16069/16384 ~= Sin[7*Pi/16] ~= 0.980785280403230 */ \
    OD_DCT_OVERFLOW_CHECK(tb, 16069, 8192, 161); \
    t4 += (tb*16069 + 8192) >> 14; \
    /* 6723/8192 ~= Tan[7*Pi/32] ~= 0.820678790828660 */ \
    OD_DCT_OVERFLOW_CHECK(t4, 6723, 4096, 162); \
    tb -= (t4*6723 + 4096) >> 13; \
    /* TODO: Can we move this into another operation */ \
    t5 = -t5; \
    tc -= tf; \
    tch = OD_DCT_RSHIFT(tc, 1); \
    tf += tch; \
    t3 += t0; \
    t3h = OD_DCT_RSHIFT(t3, 1); \
    t0 -= t3h; \
    td -= t1; \
    tdh = OD_DCT_RSHIFT(td, 1); \
    t1 += tdh; \
    t2 += te; \
    t2h = OD_DCT_RSHIFT(t2, 1); \
    te -= t2h; \
    t8 += t4; \
    t8h = OD_DCT_RSHIFT(t8, 1); \
    t4 = t8h - t4; \
    t7 = tb - t7; \
    t7h = OD_DCT_RSHIFT(t7, 1); \
    tb = t7h - tb; \
    t6 -= ta; \
    t6h = OD_DCT_RSHIFT(t6, 1); \
    ta += t6h; \
    t9 = t5 - t9; \
    t9h = OD_DCT_RSHIFT(t9, 1); \
    t5 -= t9h; \
    t0 -= t7h; \
    t7 += t0; \
    tf += t8h; \
    t8 -= tf; \
    te -= t6h; \
    t6 += te; \
    t1 += t9h; \
    t9 -= t1; \
    tb -= tch; \
    tc += tb; \
    t4 += t3h; \
    t3 -= t4; \
    ta -= tdh; \
    td += ta; \
    t5 = t2h - t5; \
    t2 -= t5; \
    /* TODO: Can we move these into another operation */ \
    t8 = -t8; \
    t9 = -t9; \
    ta = -ta; \
    tb = -tb; \
    tc = -tc; \
    td = -td; \
    tf = -tf; \
    /* 7799/8192 ~= Tan[31*Pi/128] ~= 0.952079146700925 */ \
    OD_DCT_OVERFLOW_CHECK(tf, 7799, 4096, 163); \
    t0 -= (tf*7799 + 4096) >> 13; \
    /* 4091/4096 ~= Sin[31*Pi/64] ~= 0.998795456205172 */ \
    OD_DCT_OVERFLOW_CHECK(t0, 4091, 2048, 164); \
    tf += (t0*4091 + 2048) >> 12; \
    /* 7799/8192 ~= Tan[31*Pi/128] ~= 0.952079146700925 */ \
    OD_DCT_OVERFLOW_CHECK(tf, 7799, 4096, 165); \
    t0 -= (tf*7799 + 4096) >> 13; \
    /* 2417/32768 ~= Tan[3*Pi/128] ~= 0.0737644315224493 */ \
    OD_DCT_OVERFLOW_CHECK(te, 2417, 16384, 166); \
    t1 += (te*2417 + 16384) >> 15; \
    /* 601/4096 ~= Sin[3*Pi/64] ~= 0.146730474455362 */ \
    OD_DCT_OVERFLOW_CHECK(t1, 601, 2048, 167); \
    te -= (t1*601 + 2048) >> 12; \
    /* 2417/32768 ~= Tan[3*Pi/128] ~= 0.0737644315224493 */ \
    OD_DCT_OVERFLOW_CHECK(te, 2417, 16384, 168); \
    t1 += (te*2417 + 16384) >> 15; \
    /* 14525/32768 ~= Tan[17*Pi/128] ~= 0.443269513890864 */ \
    OD_DCT_OVERFLOW_CHECK(t8, 14525, 16384, 169); \
    t7 -= (t8*14525 + 16384) >> 15; \
    /* 3035/4096 ~= Sin[17*Pi/64] ~= 0.740951125354959 */ \
    OD_DCT_OVERFLOW_CHECK(t7, 3035, 2048, 170); \
    t8 += (t7*3035 + 2048) >> 12; \
    /* 7263/16384 ~= Tan[17*Pi/128] ~= 0.443269513890864 */ \
    OD_DCT_OVERFLOW_CHECK(t8, 7263, 8192, 171); \
    t7 -= (t8*7263 + 8192) >> 14; \
    /* 6393/8192 ~= Tan[27*Pi/128] ~= 0.780407659653944 */ \
    OD_DCT_OVERFLOW_CHECK(td, 6393, 4096, 172); \
    t2 -= (td*6393 + 4096) >> 13; \
    /* 3973/4096 ~= Sin[27*Pi/64] ~= 0.970031253194544 */ \
    OD_DCT_OVERFLOW_CHECK(t2, 3973, 2048, 173); \
    td += (t2*3973 + 2048) >> 12; \
    /* 6393/8192 ~= Tan[27*Pi/128] ~= 0.780407659653944 */ \
    OD_DCT_OVERFLOW_CHECK(td, 6393, 4096, 174); \
    t2 -= (td*6393 + 4096) >> 13; \
    /* 9281/16384 ~= Tan[21*Pi/128] ~= 0.566493002730344 */ \
    OD_DCT_OVERFLOW_CHECK(ta, 9281, 8192, 175); \
    t5 -= (ta*9281 + 8192) >> 14; \
    /* 7027/8192 ~= Sin[21*Pi/64] ~= 0.857728610000272 */ \
    OD_DCT_OVERFLOW_CHECK(t5, 7027, 4096, 176); \
    ta += (t5*7027 + 4096) >> 13; \
    /* 9281/16384 ~= Tan[21*Pi/128] ~= 0.566493002730344 */ \
    OD_DCT_OVERFLOW_CHECK(ta, 9281, 8192, 177); \
    t5 -= (ta*9281 + 8192) >> 14; \
    /* 11539/16384 ~= Tan[25*Pi/128] ~= 0.704279460865044 */ \
    OD_DCT_OVERFLOW_CHECK(tc, 11539, 8192, 178); \
    t3 -= (tc*11539 + 8192) >> 14; \
    /* 7713/8192 ~= Sin[25*Pi/64] ~= 0.941544065183021 */ \
    OD_DCT_OVERFLOW_CHECK(t3, 7713, 4096, 179); \
    tc += (t3*7713 + 4096) >> 13; \
    /* 11539/16384 ~= Tan[25*Pi/128] ~= 0.704279460865044 */ \
    OD_DCT_OVERFLOW_CHECK(tc, 11539, 8192, 180); \
    t3 -= (tc*11539 + 8192) >> 14; \
    /* 10375/16384 ~= Tan[23*Pi/128] ~= 0.633243016177569 */ \
    OD_DCT_OVERFLOW_CHECK(tb, 10375, 8192, 181); \
    t4 -= (tb*10375 + 8192) >> 14; \
    /* 7405/8192 ~= Sin[23*Pi/64] ~= 0.903989293123443 */ \
    OD_DCT_OVERFLOW_CHECK(t4, 7405, 4096, 182); \
    tb += (t4*7405 + 4096) >> 13; \
    /* 10375/16384 ~= Tan[23*Pi/128] ~= 0.633243016177569 */ \
    OD_DCT_OVERFLOW_CHECK(tb, 10375, 8192, 183); \
    t4 -= (tb*10375 + 8192) >> 14; \
    /* 8247/16384 ~= Tan[19*Pi/128] ~= 0.503357699799294 */ \
    OD_DCT_OVERFLOW_CHECK(t9, 8247, 8192, 184); \
    t6 -= (t9*8247 + 8192) >> 14; \
    /* 1645/2048 ~= Sin[19*Pi/64] ~= 0.803207531480645 */ \
    OD_DCT_OVERFLOW_CHECK(t6, 1645, 1024, 185); \
    t9 += (t6*1645 + 1024) >> 11; \
    /* 8247/16384 ~= Tan[19*Pi/128] ~= 0.503357699799294 */ \
    OD_DCT_OVERFLOW_CHECK(t9, 8247, 8192, 186); \
    t6 -= (t9*8247 + 8192) >> 14; \
  } \
  while (0)

#define OD_IDST_16_ASYM(t0, t0h, t8, t4, tc, t2, t2h, ta, t6, te, teh, \
  t1, t9, t5, td, t3, tb, t7, tf) \
  /* Embedded 16-point asymmetric Type-IV iDST. */ \
  do { \
    int t1h_; \
    int t3h_; \
    int t4h; \
    int t6h; \
    int t9h_; \
    int tbh_; \
    int tch; \
    /* 8247/16384 ~= Tan[19*Pi/128] ~= 0.503357699799294 */ \
    t6 += (t9*8247 + 8192) >> 14; \
    /* 1645/2048 ~= Sin[19*Pi/64] ~= 0.803207531480645 */ \
    t9 -= (t6*1645 + 1024) >> 11; \
    /* 8247/16384 ~= Tan[19*Pi/128] ~= 0.503357699799294 */ \
    t6 += (t9*8247 + 8192) >> 14; \
    /* 10375/16384 ~= Tan[23*Pi/128] ~= 0.633243016177569 */ \
    t2 += (td*10375 + 8192) >> 14; \
    /* 7405/8192 ~= Sin[23*Pi/64] ~= 0.903989293123443 */ \
    td -= (t2*7405 + 4096) >> 13; \
    /* 10375/16384 ~= Tan[23*Pi/128] ~= 0.633243016177569 */ \
    t2 += (td*10375 + 8192) >> 14; \
    /* 11539/16384 ~= Tan[25*Pi/128] ~= 0.704279460865044 */ \
    tc += (t3*11539 + 8192) >> 14; \
    /* 7713/8192 ~= Sin[25*Pi/64] ~= 0.941544065183021 */ \
    t3 -= (tc*7713 + 4096) >> 13; \
    /* 11539/16384 ~= Tan[25*Pi/128] ~= 0.704279460865044 */ \
    tc += (t3*11539 + 8192) >> 14; \
    /* 9281/16384 ~= Tan[21*Pi/128] ~= 0.566493002730344 */ \
    ta += (t5*9281 + 8192) >> 14; \
    /* 7027/8192 ~= Sin[21*Pi/64] ~= 0.857728610000272 */ \
    t5 -= (ta*7027 + 4096) >> 13; \
    /* 9281/16384 ~= Tan[21*Pi/128] ~= 0.566493002730344 */ \
    ta += (t5*9281 + 8192) >> 14; \
    /* 6393/8192 ~= Tan[27*Pi/128] ~= 0.780407659653944 */ \
    t4 += (tb*6393 + 4096) >> 13; \
    /* 3973/4096 ~= Sin[27*Pi/64] ~= 0.970031253194544 */ \
    tb -= (t4*3973 + 2048) >> 12; \
    /* 6393/8192 ~= Tan[27*Pi/128] ~= 0.780407659653944 */ \
    t4 += (tb*6393 + 4096) >> 13; \
    /* 7263/16384 ~= Tan[17*Pi/128] ~= 0.443269513890864 */ \
    te += (t1*7263 + 8192) >> 14; \
    /* 3035/4096 ~= Sin[17*Pi/64] ~= 0.740951125354959 */ \
    t1 -= (te*3035 + 2048) >> 12; \
    /* 14525/32768 ~= Tan[17*Pi/128] ~= 0.443269513890864 */ \
    te += (t1*14525 + 16384) >> 15; \
    /* 2417/32768 ~= Tan[3*Pi/128] ~= 0.0737644315224493 */ \
    t8 -= (t7*2417 + 16384) >> 15; \
    /* 601/4096 ~= Sin[3*Pi/64] ~= 0.146730474455362 */ \
    t7 += (t8*601 + 2048) >> 12; \
    /* 2417/32768 ~= Tan[3*Pi/128] ~= 0.0737644315224493 */ \
    t8 -= (t7*2417 + 16384) >> 15; \
    /* 7799/8192 ~= Tan[31*Pi/128] ~= 0.952079146700925 */ \
    t0 += (tf*7799 + 4096) >> 13; \
    /* 4091/4096 ~= Sin[31*Pi/64] ~= 0.998795456205172 */ \
    tf -= (t0*4091 + 2048) >> 12; \
    /* 7799/8192 ~= Tan[31*Pi/128] ~= 0.952079146700925 */ \
    t0 += (tf*7799 + 4096) >> 13; \
    /* TODO: Can we move these into another operation */ \
    t1 = -t1; \
    t3 = -t3; \
    t5 = -t5; \
    t9 = -t9; \
    tb = -tb; \
    td = -td; \
    tf = -tf; \
    t4 += ta; \
    t4h = OD_DCT_RSHIFT(t4, 1); \
    ta = t4h - ta; \
    tb -= t5; \
    tbh_ = OD_DCT_RSHIFT(tb, 1); \
    t5 += tbh_; \
    tc += t2; \
    tch = OD_DCT_RSHIFT(tc, 1); \
    t2 -= tch; \
    t3 -= td; \
    t3h_ = OD_DCT_RSHIFT(t3, 1); \
    td += t3h_; \
    t9 += t8; \
    t9h_ = OD_DCT_RSHIFT(t9, 1); \
    t8 -= t9h_; \
    t6 -= t7; \
    t6h = OD_DCT_RSHIFT(t6, 1); \
    t7 += t6h; \
    t1 += tf; \
    t1h_ = OD_DCT_RSHIFT(t1, 1); \
    tf -= t1h_; \
    te -= t0; \
    teh = OD_DCT_RSHIFT(te, 1); \
    t0 += teh; \
    ta += t9h_; \
    t9 = ta - t9; \
    t5 -= t6h; \
    t6 += t5; \
    td = teh - td; \
    te = td - te; \
    t2 = t1h_ - t2; \
    t1 -= t2; \
    t7 += t4h; \
    t4 -= t7; \
    t8 -= tbh_; \
    tb += t8; \
    t0 += tch; \
    tc -= t0; \
    tf -= t3h_; \
    t3 += tf; \
    /* TODO: Can we move this into another operation */ \
    ta = -ta; \
    /* 6723/8192 ~= Tan[7*Pi/32] ~= 0.820678790828660 */ \
    td += (t2*6723 + 4096) >> 13; \
    /* 16069/16384 ~= Sin[7*Pi/16] ~= 0.980785280403230 */ \
    t2 -= (td*16069 + 8192) >> 14; \
    /* 6723/8192 ~= Tan[7*Pi/32] ~= 0.820678790828660 */ \
    td += (t2*6723 + 4096) >> 13; \
    /* 2485/8192 ~= Tan[3*Pi/32] ~= 0.303346683607342 */ \
    t5 -= (ta*2485 + 4096) >> 13; \
    /* 18205/32768 ~= Sin[3*Pi/16] ~= 0.555570233019602 */ \
    ta += (t5*18205 + 16384) >> 15; \
    /* 2485/8192 ~= Tan[3*Pi/32] ~= 0.303346683607342 */ \
    t5 -= (ta*2485 + 4096) >> 13; \
    t2 += t5; \
    t2h = OD_DCT_RSHIFT(t2, 1); \
    t5 -= t2h; \
    ta = td - ta; \
    td -= OD_DCT_RSHIFT(ta, 1); \
    /* 13573/16384 ~= 2*Tan[Pi/8] ~= 0.828427124746190 */ \
    ta -= (t5*13573 + 8192) >> 14; \
    /* 11585/32768 ~= Sin[Pi/4]/2 ~= 0.353553390593274 */ \
    t5 += (ta*11585 + 16384) >> 15; \
    /* 13573/16384 ~= 2*Tan[Pi/8] ~= 0.828427124746190 */ \
    ta -= (t5*13573 + 8192) >> 14; \
    /* 17515/32768 ~= Tan[5*Pi/32] ~= 0.534511135950792 */ \
    t9 -= (t6*17515 + 16384) >> 15; \
    /* 13623/16384 ~= Sin[5*Pi/16] ~= 0.831469612302545 */ \
    t6 += (t9*13623 + 8192) >> 14; \
    /* 17515/32768 ~= Tan[5*Pi/32]) ~= 0.534511135950792 */ \
    t9 -= (t6*17515 + 16384) >> 15; \
    /* 6723/8192 ~= Tan[7*Pi/32]) ~= 0.820678790828660 */ \
    t1 -= (te*6723 + 4096) >> 13; \
    /* 16069/16384 ~= Sin[7*Pi/16] ~= 0.980785280403230 */ \
    te += (t1*16069 + 8192) >> 14; \
    /* 6723/8192 ~= Tan[7*Pi/32]) ~= 0.820678790828660 */ \
    t1 -= (te*6723 + 4096) >> 13; \
    te += t6; \
    teh = OD_DCT_RSHIFT(te, 1); \
    t6 = teh - t6; \
    t9 += t1; \
    t1 -= OD_DCT_RSHIFT(t9, 1); \
    /* -19195/32768 ~= Tan[Pi/8] - Tan[Pi/4] ~= -0.585786437626905 */ \
    t9 -= (t6*19195 + 16384) >> 15; \
    /* 11585/16384 ~= Sin[Pi/4] ~= 0.707106781186548 */ \
    t6 -= (t9*11585 + 8192) >> 14; \
    /* 7489/8192 ~= Tan[Pi/8] + Tan[Pi/4]/2 ~= 0.914213562373095 */ \
    t9 += (t6*7489 + 4096) >> 13; \
    tb = tc - tb; \
    tc = OD_DCT_RSHIFT(tb, 1) - tc; \
    t3 += t4; \
    t4 = OD_DCT_RSHIFT(t3, 1) - t4; \
    /* TODO: Can we move this into another operation */ \
    t3 = -t3; \
    t8 += tf; \
    tf = OD_DCT_RSHIFT(t8, 1) - tf; \
    t0 += t7; \
    t0h = OD_DCT_RSHIFT(t0, 1); \
    t7 = t0h - t7; \
    /* 4161/16384 ~= Tan[3*Pi/16] - Tan[Pi/8] ~= 0.253965075546204 */ \
    t3 += (tc*4161 + 8192) >> 14; \
    /* 15137/16384 ~= Sin[3*Pi/8] ~= 0.923879532511287 */ \
    tc -= (t3*15137 + 8192) >> 14; \
    /* 14341/16384 ~= Tan[3*Pi/16] + Tan[Pi/8]/2 ~= 0.875285419105846 */ \
    t3 += (tc*14341 + 8192) >> 14; \
    /* 14341/16384 ~= Tan[3*Pi/16] + Tan[Pi/8]/2 ~= 0.875285419105846 */ \
    t4 -= (tb*14341 + 8192) >> 14; \
    /* 15137/16384 ~= Sin[3*Pi/8] ~= 0.923879532511287 */ \
    tb += (t4*15137 + 8192) >> 14; \
    /* 4161/16384 ~= Tan[3*Pi/16] - Tan[Pi/8] ~= 0.253965075546204 */ \
    t4 -= (tb*4161 + 8192) >> 14; \
    /* 13573/16384 ~= 2*Tan[Pi/8] ~= 0.828427124746190 */ \
    t8 += (t7*13573 + 8192) >> 14; \
    /* 11585/32768 ~= Sin[Pi/4]/2 ~= 0.353553390593274 */ \
    t7 -= (t8*11585 + 16384) >> 15; \
    /* 13573/16384 ~= 2*Tan[Pi/8] ~= 0.828427124746190 */ \
    t8 += (t7*13573 + 8192) >> 14; \
    /* TODO: Can we move these into another operation */ \
    t1 = -t1; \
    t5 = -t5; \
    t9 = -t9; \
    tb = -tb; \
    td = -td; \
  } \
  while (0)

#define OD_FDCT_32(t0, tg, t8, to, t4, tk, tc, ts, t2, ti, ta, tq, t6, tm, \
  te, tu, t1, th, t9, tp, t5, tl, td, tt, t3, tj, tb, tr, t7, tn, tf, tv) \
  /* Embedded 32-point orthonormal Type-II fDCT. */ \
  do { \
    int tgh; \
    int thh; \
    int tih; \
    int tkh; \
    int tmh; \
    int tnh; \
    int toh; \
    int tqh; \
    int tsh; \
    int tuh; \
    int tvh; \
    tv = t0 - tv; \
    tvh = OD_DCT_RSHIFT(tv, 1); \
    t0 -= tvh; \
    tu += t1; \
    tuh = OD_DCT_RSHIFT(tu, 1); \
    t1 = tuh - t1; \
    tt = t2 - tt; \
    t2 -= OD_DCT_RSHIFT(tt, 1); \
    ts += t3; \
    tsh = OD_DCT_RSHIFT(ts, 1); \
    t3 = tsh - t3; \
    tr = t4 - tr; \
    t4 -= OD_DCT_RSHIFT(tr, 1); \
    tq += t5; \
    tqh = OD_DCT_RSHIFT(tq, 1); \
    t5 = tqh - t5; \
    tp = t6 - tp; \
    t6 -= OD_DCT_RSHIFT(tp, 1); \
    to += t7; \
    toh = OD_DCT_RSHIFT(to, 1); \
    t7 = toh - t7; \
    tn = t8 - tn; \
    tnh = OD_DCT_RSHIFT(tn, 1); \
    t8 -= tnh; \
    tm += t9; \
    tmh = OD_DCT_RSHIFT(tm, 1); \
    t9 = tmh - t9; \
    tl = ta - tl; \
    ta -= OD_DCT_RSHIFT(tl, 1); \
    tk += tb; \
    tkh = OD_DCT_RSHIFT(tk, 1); \
    tb = tkh - tb; \
    tj = tc - tj; \
    tc -= OD_DCT_RSHIFT(tj, 1); \
    ti += td; \
    tih = OD_DCT_RSHIFT(ti, 1); \
    td = tih - td; \
    th = te - th; \
    thh = OD_DCT_RSHIFT(th, 1); \
    te -= thh; \
    tg += tf; \
    tgh = OD_DCT_RSHIFT(tg, 1); \
    tf = tgh - tf; \
    OD_FDCT_16_ASYM(t0, tg, tgh, t8, to, toh, t4, tk, tkh, tc, ts, tsh, \
     t2, ti, tih, ta, tq, tqh, t6, tm, tmh, te, tu, tuh); \
    OD_FDST_16_ASYM(tv, tvh, tf, tn, tnh, t7, tr, tb, tj, t3, \
     tt, td, tl, t5, tp, t9, th, thh, t1); \
  } \
  while (0)

#define OD_IDCT_32(t0, tg, t8, to, t4, tk, tc, ts, t2, ti, ta, tq, t6, tm, \
  te, tu, t1, th, t9, tp, t5, tl, td, tt, t3, tj, tb, tr, t7, tn, tf, tv) \
  /* Embedded 32-point orthonormal Type-II iDCT. */ \
  do { \
    int t1h; \
    int t3h; \
    int t5h; \
    int t7h; \
    int t9h; \
    int tbh; \
    int tdh; \
    int tfh; \
    int thh; \
    int tth; \
    int tvh; \
    OD_IDST_16_ASYM(tv, tvh, tn, tr, tj, tt, tth, tl, tp, th, thh, \
     tu, tm, tq, ti, ts, tk, to, tg); \
    OD_IDCT_16_ASYM(t0, t8, t4, tc, t2, ta, t6, te, \
     t1, t1h, t9, t9h, t5, t5h, td, tdh, t3, t3h, tb, tbh, t7, t7h, tf, tfh); \
    tu = t1h - tu; \
    t1 -= tu; \
    te += thh; \
    th = te - th; \
    tm = t9h - tm; \
    t9 -= tm; \
    t6 += OD_DCT_RSHIFT(tp, 1); \
    tp = t6 - tp; \
    tq = t5h - tq; \
    t5 -= tq; \
    ta += OD_DCT_RSHIFT(tl, 1); \
    tl = ta - tl; \
    ti = tdh - ti; \
    td -= ti; \
    t2 += tth; \
    tt = t2 - tt; \
    ts = t3h - ts; \
    t3 -= ts; \
    tc += OD_DCT_RSHIFT(tj, 1); \
    tj = tc - tj; \
    tk = tbh - tk; \
    tb -= tk; \
    t4 += OD_DCT_RSHIFT(tr, 1); \
    tr = t4 - tr; \
    to = t7h - to; \
    t7 -= to; \
    t8 += OD_DCT_RSHIFT(tn, 1); \
    tn = t8 - tn; \
    tg = tfh - tg; \
    tf -= tg; \
    t0 += tvh; \
    tv = t0 - tv; \
  } \
  while (0)

void od_bin_fdct4(od_coeff y[4], const od_coeff *x, int xstride) {
  int q0;
  int q1;
  int q2;
  int q3;
  q0 = x[0*xstride];
  q2 = x[1*xstride];
  q1 = x[2*xstride];
  q3 = x[3*xstride];
  OD_FDCT_4(q0, q2, q1, q3);
  y[0] = (od_coeff)q0;
  y[1] = (od_coeff)q1;
  y[2] = (od_coeff)q2;
  y[3] = (od_coeff)q3;
}

void od_bin_idct4(od_coeff *x, int xstride, const od_coeff y[4]) {
  int q0;
  int q1;
  int q2;
  int q3;
  q0 = y[0];
  q2 = y[1];
  q1 = y[2];
  q3 = y[3];
  OD_IDCT_4(q0, q2, q1, q3);
  x[0*xstride] = q0;
  x[1*xstride] = q1;
  x[2*xstride] = q2;
  x[3*xstride] = q3;
}

void od_bin_fdct8(od_coeff y[8], const od_coeff *x, int xstride) {
  int r0;
  int r1;
  int r2;
  int r3;
  int r4;
  int r5;
  int r6;
  int r7;
  r0 = x[0*xstride];
  r4 = x[1*xstride];
  r2 = x[2*xstride];
  r6 = x[3*xstride];
  r1 = x[4*xstride];
  r5 = x[5*xstride];
  r3 = x[6*xstride];
  r7 = x[7*xstride];
  OD_FDCT_8(r0, r4, r2, r6, r1, r5, r3, r7);
  y[0] = (od_coeff)r0;
  y[1] = (od_coeff)r1;
  y[2] = (od_coeff)r2;
  y[3] = (od_coeff)r3;
  y[4] = (od_coeff)r4;
  y[5] = (od_coeff)r5;
  y[6] = (od_coeff)r6;
  y[7] = (od_coeff)r7;
}

void od_bin_idct8(od_coeff *x, int xstride, const od_coeff y[8]) {
  int r0;
  int r1;
  int r2;
  int r3;
  int r4;
  int r5;
  int r6;
  int r7;
  r0 = y[0];
  r4 = y[1];
  r2 = y[2];
  r6 = y[3];
  r1 = y[4];
  r5 = y[5];
  r3 = y[6];
  r7 = y[7];
  OD_IDCT_8(r0, r4, r2, r6, r1, r5, r3, r7);
  x[0*xstride] = (od_coeff)r0;
  x[1*xstride] = (od_coeff)r1;
  x[2*xstride] = (od_coeff)r2;
  x[3*xstride] = (od_coeff)r3;
  x[4*xstride] = (od_coeff)r4;
  x[5*xstride] = (od_coeff)r5;
  x[6*xstride] = (od_coeff)r6;
  x[7*xstride] = (od_coeff)r7;
}

void od_bin_fdst8(od_coeff y[8], const od_coeff *x, int xstride) {
  int r0;
  int r1;
  int r2;
  int r3;
  int r4;
  int r5;
  int r6;
  int r7;
  r0 = x[0*xstride];
  r4 = x[1*xstride];
  r2 = x[2*xstride];
  r6 = x[3*xstride];
  r1 = x[4*xstride];
  r5 = x[5*xstride];
  r3 = x[6*xstride];
  r7 = x[7*xstride];
  OD_FDST_8(r0, r4, r2, r6, r1, r5, r3, r7);
  y[0] = (od_coeff)r0;
  y[1] = (od_coeff)r1;
  y[2] = (od_coeff)r2;
  y[3] = (od_coeff)r3;
  y[4] = (od_coeff)r4;
  y[5] = (od_coeff)r5;
  y[6] = (od_coeff)r6;
  y[7] = (od_coeff)r7;
}

void od_bin_idst8(od_coeff *x, int xstride, const od_coeff y[8]) {
  int r0;
  int r1;
  int r2;
  int r3;
  int r4;
  int r5;
  int r6;
  int r7;
  r0 = y[0];
  r4 = y[1];
  r2 = y[2];
  r6 = y[3];
  r1 = y[4];
  r5 = y[5];
  r3 = y[6];
  r7 = y[7];
  OD_IDST_8(r0, r4, r2, r6, r1, r5, r3, r7);
  x[0*xstride] = (od_coeff)r0;
  x[1*xstride] = (od_coeff)r1;
  x[2*xstride] = (od_coeff)r2;
  x[3*xstride] = (od_coeff)r3;
  x[4*xstride] = (od_coeff)r4;
  x[5*xstride] = (od_coeff)r5;
  x[6*xstride] = (od_coeff)r6;
  x[7*xstride] = (od_coeff)r7;
}

void od_bin_fdct16(od_coeff y[16], const od_coeff *x, int xstride) {
  int s0;
  int s1;
  int s2;
  int s3;
  int s4;
  int s5;
  int s6;
  int s7;
  int s8;
  int s9;
  int sa;
  int sb;
  int sc;
  int sd;
  int se;
  int sf;
  s0 = x[0*xstride];
  s8 = x[1*xstride];
  s4 = x[2*xstride];
  sc = x[3*xstride];
  s2 = x[4*xstride];
  sa = x[5*xstride];
  s6 = x[6*xstride];
  se = x[7*xstride];
  s1 = x[8*xstride];
  s9 = x[9*xstride];
  s5 = x[10*xstride];
  sd = x[11*xstride];
  s3 = x[12*xstride];
  sb = x[13*xstride];
  s7 = x[14*xstride];
  sf = x[15*xstride];
  OD_FDCT_16(s0, s8, s4, sc, s2, sa, s6, se, s1, s9, s5, sd, s3, sb, s7, sf);
  y[0] = (od_coeff)s0;
  y[1] = (od_coeff)s1;
  y[2] = (od_coeff)s2;
  y[3] = (od_coeff)s3;
  y[4] = (od_coeff)s4;
  y[5] = (od_coeff)s5;
  y[6] = (od_coeff)s6;
  y[7] = (od_coeff)s7;
  y[8] = (od_coeff)s8;
  y[9] = (od_coeff)s9;
  y[10] = (od_coeff)sa;
  y[11] = (od_coeff)sb;
  y[12] = (od_coeff)sc;
  y[13] = (od_coeff)sd;
  y[14] = (od_coeff)se;
  y[15] = (od_coeff)sf;
}

void od_bin_idct16(od_coeff *x, int xstride, const od_coeff y[16]) {
  int s0;
  int s1;
  int s2;
  int s3;
  int s4;
  int s5;
  int s6;
  int s7;
  int s8;
  int s9;
  int sa;
  int sb;
  int sc;
  int sd;
  int se;
  int sf;
  s0 = y[0];
  s8 = y[1];
  s4 = y[2];
  sc = y[3];
  s2 = y[4];
  sa = y[5];
  s6 = y[6];
  se = y[7];
  s1 = y[8];
  s9 = y[9];
  s5 = y[10];
  sd = y[11];
  s3 = y[12];
  sb = y[13];
  s7 = y[14];
  sf = y[15];
  OD_IDCT_16(s0, s8, s4, sc, s2, sa, s6, se, s1, s9, s5, sd, s3, sb, s7, sf);
  x[0*xstride] = (od_coeff)s0;
  x[1*xstride] = (od_coeff)s1;
  x[2*xstride] = (od_coeff)s2;
  x[3*xstride] = (od_coeff)s3;
  x[4*xstride] = (od_coeff)s4;
  x[5*xstride] = (od_coeff)s5;
  x[6*xstride] = (od_coeff)s6;
  x[7*xstride] = (od_coeff)s7;
  x[8*xstride] = (od_coeff)s8;
  x[9*xstride] = (od_coeff)s9;
  x[10*xstride] = (od_coeff)sa;
  x[11*xstride] = (od_coeff)sb;
  x[12*xstride] = (od_coeff)sc;
  x[13*xstride] = (od_coeff)sd;
  x[14*xstride] = (od_coeff)se;
  x[15*xstride] = (od_coeff)sf;
}

void od_bin_fdst16(od_coeff y[16], const od_coeff *x, int xstride) {
  int s0;
  int s1;
  int s2;
  int s3;
  int s4;
  int s5;
  int s6;
  int s7;
  int s8;
  int s9;
  int sa;
  int sb;
  int sc;
  int sd;
  int se;
  int sf;
  s0 = x[15*xstride];
  s8 = x[14*xstride];
  s4 = x[13*xstride];
  sc = x[12*xstride];
  s2 = x[11*xstride];
  sa = x[10*xstride];
  s6 = x[9*xstride];
  se = x[8*xstride];
  s1 = x[7*xstride];
  s9 = x[6*xstride];
  s5 = x[5*xstride];
  sd = x[4*xstride];
  s3 = x[3*xstride];
  sb = x[2*xstride];
  s7 = x[1*xstride];
  sf = x[0*xstride];
  OD_FDST_16(s0, s8, s4, sc, s2, sa, s6, se, s1, s9, s5, sd, s3, sb, s7, sf);
  y[0] = (od_coeff)sf;
  y[1] = (od_coeff)se;
  y[2] = (od_coeff)sd;
  y[3] = (od_coeff)sc;
  y[4] = (od_coeff)sb;
  y[5] = (od_coeff)sa;
  y[6] = (od_coeff)s9;
  y[7] = (od_coeff)s8;
  y[8] = (od_coeff)s7;
  y[9] = (od_coeff)s6;
  y[10] = (od_coeff)s5;
  y[11] = (od_coeff)s4;
  y[12] = (od_coeff)s3;
  y[13] = (od_coeff)s2;
  y[14] = (od_coeff)s1;
  y[15] = (od_coeff)s0;
}

void od_bin_idst16(od_coeff *x, int xstride, const od_coeff y[16]) {
  int s0;
  int s1;
  int s2;
  int s3;
  int s4;
  int s5;
  int s6;
  int s7;
  int s8;
  int s9;
  int sa;
  int sb;
  int sc;
  int sd;
  int se;
  int sf;
  s0 = y[15];
  s8 = y[14];
  s4 = y[13];
  sc = y[12];
  s2 = y[11];
  sa = y[10];
  s6 = y[9];
  se = y[8];
  s1 = y[7];
  s9 = y[6];
  s5 = y[5];
  sd = y[4];
  s3 = y[3];
  sb = y[2];
  s7 = y[1];
  sf = y[0];
  OD_IDST_16(s0, s8, s4, sc, s2, sa, s6, se, s1, s9, s5, sd, s3, sb, s7, sf);
  x[0*xstride] = (od_coeff)sf;
  x[1*xstride] = (od_coeff)se;
  x[2*xstride] = (od_coeff)sd;
  x[3*xstride] = (od_coeff)sc;
  x[4*xstride] = (od_coeff)sb;
  x[5*xstride] = (od_coeff)sa;
  x[6*xstride] = (od_coeff)s9;
  x[7*xstride] = (od_coeff)s8;
  x[8*xstride] = (od_coeff)s7;
  x[9*xstride] = (od_coeff)s6;
  x[10*xstride] = (od_coeff)s5;
  x[11*xstride] = (od_coeff)s4;
  x[12*xstride] = (od_coeff)s3;
  x[13*xstride] = (od_coeff)s2;
  x[14*xstride] = (od_coeff)s1;
  x[15*xstride] = (od_coeff)s0;
}

void od_bin_fdct32(od_coeff y[32], const od_coeff *x, int xstride) {
  /*215 adds, 38 shifts, 87 "muls".*/
  int t0;
  int t1;
  int t2;
  int t3;
  int t4;
  int t5;
  int t6;
  int t7;
  int t8;
  int t9;
  int ta;
  int tb;
  int tc;
  int td;
  int te;
  int tf;
  int tg;
  int th;
  int ti;
  int tj;
  int tk;
  int tl;
  int tm;
  int tn;
  int to;
  int tp;
  int tq;
  int tr;
  int ts;
  int tt;
  int tu;
  int tv;
  t0 = x[0*xstride];
  tg = x[1*xstride];
  t8 = x[2*xstride];
  to = x[3*xstride];
  t4 = x[4*xstride];
  tk = x[5*xstride];
  tc = x[6*xstride];
  ts = x[7*xstride];
  t2 = x[8*xstride];
  ti = x[9*xstride];
  ta = x[10*xstride];
  tq = x[11*xstride];
  t6 = x[12*xstride];
  tm = x[13*xstride];
  te = x[14*xstride];
  tu = x[15*xstride];
  t1 = x[16*xstride];
  th = x[17*xstride];
  t9 = x[18*xstride];
  tp = x[19*xstride];
  t5 = x[20*xstride];
  tl = x[21*xstride];
  td = x[22*xstride];
  tt = x[23*xstride];
  t3 = x[24*xstride];
  tj = x[25*xstride];
  tb = x[26*xstride];
  tr = x[27*xstride];
  t7 = x[28*xstride];
  tn = x[29*xstride];
  tf = x[30*xstride];
  tv = x[31*xstride];
  OD_FDCT_32(t0, tg, t8, to, t4, tk, tc, ts, t2, ti, ta, tq, t6, tm, te, tu,
    t1, th, t9, tp, t5, tl, td, tt, t3, tj, tb, tr, t7, tn, tf, tv);
  y[0] = (od_coeff)t0;
  y[1] = (od_coeff)t1;
  y[2] = (od_coeff)t2;
  y[3] = (od_coeff)t3;
  y[4] = (od_coeff)t4;
  y[5] = (od_coeff)t5;
  y[6] = (od_coeff)t6;
  y[7] = (od_coeff)t7;
  y[8] = (od_coeff)t8;
  y[9] = (od_coeff)t9;
  y[10] = (od_coeff)ta;
  y[11] = (od_coeff)tb;
  y[12] = (od_coeff)tc;
  y[13] = (od_coeff)td;
  y[14] = (od_coeff)te;
  y[15] = (od_coeff)tf;
  y[16] = (od_coeff)tg;
  y[17] = (od_coeff)th;
  y[18] = (od_coeff)ti;
  y[19] = (od_coeff)tj;
  y[20] = (od_coeff)tk;
  y[21] = (od_coeff)tl;
  y[22] = (od_coeff)tm;
  y[23] = (od_coeff)tn;
  y[24] = (od_coeff)to;
  y[25] = (od_coeff)tp;
  y[26] = (od_coeff)tq;
  y[27] = (od_coeff)tr;
  y[28] = (od_coeff)ts;
  y[29] = (od_coeff)tt;
  y[30] = (od_coeff)tu;
  y[31] = (od_coeff)tv;
}

void od_bin_idct32(od_coeff *x, int xstride, const od_coeff y[32]) {
  int t0;
  int t1;
  int t2;
  int t3;
  int t4;
  int t5;
  int t6;
  int t7;
  int t8;
  int t9;
  int ta;
  int tb;
  int tc;
  int td;
  int te;
  int tf;
  int tg;
  int th;
  int ti;
  int tj;
  int tk;
  int tl;
  int tm;
  int tn;
  int to;
  int tp;
  int tq;
  int tr;
  int ts;
  int tt;
  int tu;
  int tv;
  t0 = y[0];
  tg = y[1];
  t8 = y[2];
  to = y[3];
  t4 = y[4];
  tk = y[5];
  tc = y[6];
  ts = y[7];
  t2 = y[8];
  ti = y[9];
  ta = y[10];
  tq = y[11];
  t6 = y[12];
  tm = y[13];
  te = y[14];
  tu = y[15];
  t1 = y[16];
  th = y[17];
  t9 = y[18];
  tp = y[19];
  t5 = y[20];
  tl = y[21];
  td = y[22];
  tt = y[23];
  t3 = y[24];
  tj = y[25];
  tb = y[26];
  tr = y[27];
  t7 = y[28];
  tn = y[29];
  tf = y[30];
  tv = y[31];
  OD_IDCT_32(t0, tg, t8, to, t4, tk, tc, ts, t2, ti, ta, tq, t6, tm, te, tu,
    t1, th, t9, tp, t5, tl, td, tt, t3, tj, tb, tr, t7, tn, tf, tv);
  x[0*xstride] = (od_coeff)t0;
  x[1*xstride] = (od_coeff)t1;
  x[2*xstride] = (od_coeff)t2;
  x[3*xstride] = (od_coeff)t3;
  x[4*xstride] = (od_coeff)t4;
  x[5*xstride] = (od_coeff)t5;
  x[6*xstride] = (od_coeff)t6;
  x[7*xstride] = (od_coeff)t7;
  x[8*xstride] = (od_coeff)t8;
  x[9*xstride] = (od_coeff)t9;
  x[10*xstride] = (od_coeff)ta;
  x[11*xstride] = (od_coeff)tb;
  x[12*xstride] = (od_coeff)tc;
  x[13*xstride] = (od_coeff)td;
  x[14*xstride] = (od_coeff)te;
  x[15*xstride] = (od_coeff)tf;
  x[16*xstride] = (od_coeff)tg;
  x[17*xstride] = (od_coeff)th;
  x[18*xstride] = (od_coeff)ti;
  x[19*xstride] = (od_coeff)tj;
  x[20*xstride] = (od_coeff)tk;
  x[21*xstride] = (od_coeff)tl;
  x[22*xstride] = (od_coeff)tm;
  x[23*xstride] = (od_coeff)tn;
  x[24*xstride] = (od_coeff)to;
  x[25*xstride] = (od_coeff)tp;
  x[26*xstride] = (od_coeff)tq;
  x[27*xstride] = (od_coeff)tr;
  x[28*xstride] = (od_coeff)ts;
  x[29*xstride] = (od_coeff)tt;
  x[30*xstride] = (od_coeff)tu;
  x[31*xstride] = (od_coeff)tv;
}