/*
 * Copyright (c) 2017, Alliance for Open Media. All rights reserved
 *
 * This source code is subject to the terms of the BSD 2 Clause License and
 * the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
 * was not distributed with this source code in the LICENSE file, you can
 * obtain it at www.aomedia.org/license/software. If the Alliance for Open
 * Media Patent License 1.0 was not distributed with this source code in the
 * PATENTS file, you can obtain it at www.aomedia.org/license/patent.
 */

/* clang-format off */

#ifndef AOM_DSP_DAALA_TX_KERNELS_H_
#define AOM_DSP_DAALA_TX_KERNELS_H_

#include "aom_dsp/aom_dsp_common.h"
#include "av1/common/odintrin.h"

#define AVG_BIAS (0)

static INLINE od_coeff od_add(od_coeff p0, od_coeff p1) {
  return p0 + p1;
}

static INLINE od_coeff od_sub(od_coeff p0, od_coeff p1) {
  return p0 - p1;
}

static INLINE od_coeff od_add_avg(od_coeff p0, od_coeff p1) {
  return (od_add(p0, p1) + AVG_BIAS) >> 1;
}

static INLINE od_coeff od_sub_avg(od_coeff p0, od_coeff p1) {
  return (od_sub(p0, p1) + AVG_BIAS) >> 1;
}

static INLINE od_coeff od_rshift1(od_coeff v) {
  return (v + (v < 0)) >> 1;
}

/* Fixed point multiply. */
static INLINE od_coeff od_mul(od_coeff n, int c, int q) {
  return (n*c + ((1 << q) >> 1)) >> q;
}

/* Two multiply rotation primative (used when rotating by Pi/4). */
static INLINE void od_rot2(od_coeff *p0, od_coeff *p1, od_coeff t, int c0,
 int q0, int c1, int q1) {
  *p1 = od_mul(*p0, c0, q0);
  *p0 = od_mul(t, c1, q1);
}

/* Three multiply rotation primative. */
static INLINE void od_rot3(od_coeff *p0, od_coeff *p1, od_coeff *t, od_coeff *u,
 int c0, int q0, int c1, int q1, int c2, int q2) {
  *u = od_mul(*p0, c0, q0);
  *p0 = od_mul(*p1, c1, q1);
  *t = od_mul(*t, c2, q2);
}

#define NONE (0)
#define AVG (!NONE)
#define SHIFT (!NONE)

#define ADD (0)
#define SUB (1)

/* Rotate by Pi/4 and add. */
static INLINE void od_rotate_pi4_kernel(od_coeff *p0, od_coeff *p1, int c0,
 int q0, int c1, int q1, int type, int avg) {
  od_coeff t;
  t = type == ADD ?
   avg ? od_add_avg(*p1, *p0) : od_add(*p1, *p0) :
   avg ? od_sub_avg(*p1, *p0) : od_sub(*p1, *p0);
  od_rot2(p0, p1, t, c0, q0, c1, q1);
  *p1 = type == ADD ? od_sub(*p1, *p0) : od_add(*p1, *p0);
}

#define od_rotate_pi4_add(p0, p1, c0, q0, c1, q1) \
 od_rotate_pi4_kernel(p0, p1, c0, q0, c1, q1, ADD, NONE)
#define od_rotate_pi4_sub(p0, p1, c0, q0, c1, q1) \
 od_rotate_pi4_kernel(p0, p1, c0, q0, c1, q1, SUB, NONE)

#define od_rotate_pi4_add_avg(p0, p1, c0, q0, c1, q1) \
 od_rotate_pi4_kernel(p0, p1, c0, q0, c1, q1, ADD, AVG)
#define od_rotate_pi4_sub_avg(p0, p1, c0, q0, c1, q1) \
 od_rotate_pi4_kernel(p0, p1, c0, q0, c1, q1, SUB, AVG)

/* Rotate and add. */
static INLINE void od_rotate_kernel(od_coeff *p0, od_coeff *p1, od_coeff v,
 int c0, int q0, int c1, int q1, int c2, int q2, int type, int avg, int shift) {
  od_coeff u;
  od_coeff t;
  t = type == ADD ?
   avg ? od_add_avg(*p1, v) : od_add(*p1, v) :
   avg ? od_sub_avg(*p1, v) : od_sub(*p1, v);
  od_rot3(p0, p1, &t, &u, c0, q0, c1, q1, c2, q2);
  *p0 = od_add(*p0, t);
  if (shift) t = od_rshift1(t);
  *p1 = type == ADD ? od_sub(u, t) : od_add(u, t);
}

#define od_rotate_add(p0, p1, c0, q0, c1, q1, c2, q2, shift) \
 od_rotate_kernel(p0, p1, *p0, c0, q0, c1, q1, c2, q2, ADD, NONE, shift)
#define od_rotate_sub(p0, p1, c0, q0, c1, q1, c2, q2, shift) \
 od_rotate_kernel(p0, p1, *p0, c0, q0, c1, q1, c2, q2, SUB, NONE, shift)

#define od_rotate_add_avg(p0, p1, c0, q0, c1, q1, c2, q2, shift) \
 od_rotate_kernel(p0, p1, *p0, c0, q0, c1, q1, c2, q2, ADD, AVG, shift)
#define od_rotate_sub_avg(p0, p1, c0, q0, c1, q1, c2, q2, shift) \
 od_rotate_kernel(p0, p1, *p0, c0, q0, c1, q1, c2, q2, SUB, AVG, shift)

#define od_rotate_add_half(p0, p1, v, c0, q0, c1, q1, c2, q2, shift) \
 od_rotate_kernel(p0, p1, v, c0, q0, c1, q1, c2, q2, ADD, NONE, shift)
#define od_rotate_sub_half(p0, p1, v, c0, q0, c1, q1, c2, q2, shift) \
 od_rotate_kernel(p0, p1, v, c0, q0, c1, q1, c2, q2, SUB, NONE, shift)

/* Rotate and subtract with negation. */
static INLINE void od_rotate_neg_kernel(od_coeff *p0, od_coeff *p1,
 int c0, int q0, int c1, int q1, int c2, int q2, int avg) {
  od_coeff u;
  od_coeff t;
  t = avg ? od_sub_avg(*p0, *p1) : od_sub(*p0, *p1);
  od_rot3(p0, p1, &t, &u, c0, q0, c1, q1, c2, q2);
  *p0 = od_sub(*p0, t);
  *p1 = od_sub(t, u);
}

#define od_rotate_neg(p0, p1, c0, q0, c1, q1, c2, q2) \
 od_rotate_neg_kernel(p0, p1, c0, q0, c1, q1, c2, q2, NONE)
#define od_rotate_neg_avg(p0, p1, c0, q0, c1, q1, c2, q2) \
 od_rotate_neg_kernel(p0, p1, c0, q0, c1, q1, c2, q2, AVG)

/* Computes the +/- addition butterfly (asymmetric output).
   The inverse to this function is od_butterfly_add_asym().

    p0 = p0 + p1;
    p1 = p1 - p0/2; */
static INLINE void od_butterfly_add(od_coeff *p0, od_coeff *p0h, od_coeff *p1) {
  od_coeff p0h_;
  *p0 = od_add(*p0, *p1);
  p0h_ = od_rshift1(*p0);
  *p1 = od_sub(*p1, p0h_);
  if (p0h != NULL) *p0h = p0h_;
}

/* Computes the asymmetric +/- addition butterfly (unscaled output).
   The inverse to this function is od_butterfly_add().

    p1 = p1 + p0/2;
    p0 = p0 - p1; */
static INLINE void od_butterfly_add_asym(od_coeff *p0, od_coeff p0h,
 od_coeff *p1) {
  *p1 = od_add(*p1, p0h);
  *p0 = od_sub(*p0, *p1);
}

/* Computes the +/- subtraction butterfly (asymmetric output).
   The inverse to this function is od_butterfly_sub_asym().

    p0 = p0 - p1;
    p1 = p1 + p0/2; */
static INLINE void od_butterfly_sub(od_coeff *p0, od_coeff *p0h, od_coeff *p1) {
  od_coeff p0h_;
  *p0 = od_sub(*p0, *p1);
  p0h_ = od_rshift1(*p0);
  *p1 = od_add(*p1, p0h_);
  if (p0h != NULL) *p0h = p0h_;
}

/* Computes the asymmetric +/- subtraction butterfly (unscaled output).
   The inverse to this function is od_butterfly_sub().

    p1 = p1 - p0/2;
    p0 = p0 + p1; */
static INLINE void od_butterfly_sub_asym(od_coeff *p0, od_coeff p0h,
 od_coeff *p1) {
  *p1 = od_sub(*p1, p0h);
  *p0 = od_add(*p0, *p1);
}

/* Computes the +/- subtract and negate butterfly (asymmetric output).
   The inverse to this function is od_butterfly_neg_asym().

    p1 = p1 - p0;
    p0 = p0 + p1/2;
    p1 = -p1; */
static INLINE void od_butterfly_neg(od_coeff *p0, od_coeff *p1, od_coeff *p1h) {
  *p1 = od_sub(*p0, *p1);
  *p1h = od_rshift1(*p1);
  *p0 = od_sub(*p0, *p1h);
}

/*  Computes the asymmetric +/- negate and subtract butterfly (unscaled output).
    The inverse to this function is od_butterfly_neg().

    p1 = -p1;
    p0 = p0 - p1/2;
    p1 = p1 + p0; */
static INLINE void od_butterfly_neg_asym(od_coeff *p0, od_coeff *p1,
 od_coeff p1h) {
  *p0 = od_add(*p0, p1h);
  *p1 = od_sub(*p0, *p1);
}

/* --- 2-point Transforms --- */

/**
 * 2-point orthonormal Type-II fDCT
 */
static INLINE void od_fdct_2(od_coeff *p0, od_coeff *p1) {
  /* 11585/8192 = Sin[Pi/4] + Cos[Pi/4]  = 1.4142135623730951 */
  /* 11585/8192 = 2*Cos[Pi/4]            = 1.4142135623730951 */
  od_rotate_pi4_sub_avg(p1, p0, 11585, 13, 11585, 13);
}

/**
 * 2-point orthonormal Type-II iDCT
 */
static INLINE void od_idct_2(od_coeff *p0, od_coeff *p1) {
  /*  11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/16384 = Cos[Pi/4]             = 0.7071067811865475 */
  od_rotate_pi4_add(p0, p1, 11585, 13, 11585, 14);
}

/**
 * 2-point asymmetric Type-II fDCT
 */
static INLINE void od_fdct_2_asym(od_coeff *p0, od_coeff *p1, od_coeff p1h) {
  od_butterfly_neg_asym(p0, p1, p1h);
}

/**
 * 2-point asymmetric Type-II iDCT
 */
static INLINE void od_idct_2_asym(od_coeff *p0, od_coeff *p1, od_coeff *p1h) {
  od_butterfly_neg(p0, p1, p1h);
}

/**
 * 2-point orthonormal Type-IV fDCT
 */
static INLINE void od_fdst_2(od_coeff *p0, od_coeff *p1) {

  /* Stage 0 */

  /* 21407/16384 = Sin[3*Pi/8] + Cos[3*Pi/8]  = 1.3065629648763766 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8]  = 0.5411961001461971 */
  /*   3135/4096 = 2*Cos[3*Pi/8]              = 0.7653668647301796 */
  od_rotate_add_avg(p0, p1, 21407, 14, 8867, 14, 3135, 12, NONE);
}

/**
 * 2-point orthonormal Type-IV iDCT
 */
static INLINE void od_idst_2(od_coeff *p0, od_coeff *p1) {
  od_fdst_2(p0, p1);
}

/**
 * 2-point asymmetric Type-IV fDCT
 */
static INLINE void od_fdst_2_asym(od_coeff *p0, od_coeff p0h, od_coeff *p1) {

  /* Stage 0 */

  /* 15137/16384 = (Sin[3*Pi/8] + Cos[3*Pi/8])/Sqrt[2] = 0.9238795325112867 */
  /*   3135/4096 = (Sin[3*Pi/8] - Cos[3*Pi/8])*Sqrt[2] = 0.7653668647301795 */
  /*  8867/16384 = Cos[3*Pi/8]*Sqrt[2]                 = 0.5411961001461971 */
  od_rotate_add_half(p0, p1, p0h, 15137, 14, 3135, 12, 8867, 14, NONE);
}

/**
 * 2-point asymmetric Type-IV iDCT
 */
static INLINE void od_idst_2_asym(od_coeff *p0, od_coeff *p1) {

  /* Stage 0 */

  /* 15137/16384 = (Sin[3*Pi/8] + Cos[3*Pi/8])/Sqrt[2] = 0.9238795325112867 */
  /*   3135/4096 = (Sin[3*Pi/8] - Cos[3*Pi/8])*Sqrt[2] = 0.7653668647301795 */
  /*   8867/8192 = 2*Cos[3*Pi/8]*Sqrt[2]               = 1.0823922002923940 */
  od_rotate_add_avg(p0, p1, 15137, 14, 3135, 12, 8867, 13, SHIFT);
}

/* --- 4-point Transforms --- */

/**
 * 4-point orthonormal Type-II fDCT
 */
static INLINE void od_fdct_4(od_coeff *q0, od_coeff *q1, od_coeff *q2,
 od_coeff *q3) {
  od_coeff q1h;
  od_coeff q3h;

  /* +/- Butterflies with asymmetric output. */
  od_butterfly_neg(q0, q3, &q3h);
  od_butterfly_add(q1, &q1h, q2);

  /* Embedded 2-point transforms with asymmetric input. */
  od_fdct_2_asym(q0, q1, q1h);
  od_fdst_2_asym(q3, q3h, q2);
}

/**
 * 4-point orthonormal Type-II iDCT
 */
static INLINE void od_idct_4(od_coeff *q0, od_coeff *q2,
                             od_coeff *q1, od_coeff *q3)  {
  od_coeff q1h;

  /* Embedded 2-point transforms with asymmetric output. */
  od_idst_2_asym(q3, q2);
  od_idct_2_asym(q0, q1, &q1h);

  /* +/- Butterflies with asymmetric input. */
  od_butterfly_add_asym(q1, q1h, q2);
  od_butterfly_neg_asym(q0, q3, od_rshift1(*q3));
}

/**
 * 4-point asymmetric Type-II fDCT
 */
static INLINE void od_fdct_4_asym(od_coeff *q0, od_coeff *q1, od_coeff q1h,
                                  od_coeff *q2, od_coeff *q3, od_coeff q3h) {

  /* +/- Butterflies with asymmetric input. */
  od_butterfly_neg_asym(q0, q3, q3h);
  od_butterfly_sub_asym(q1, q1h, q2);

  /* Embedded 2-point orthonormal transforms. */
  od_fdct_2(q0, q1);
  od_fdst_2(q3, q2);
}

/**
 * 4-point asymmetric Type-II iDCT
 */
static INLINE void od_idct_4_asym(od_coeff *q0, od_coeff *q2,
                                  od_coeff *q1, od_coeff *q1h,
                                  od_coeff *q3, od_coeff *q3h)  {

  /* Embedded 2-point orthonormal transforms. */
  od_idst_2(q3, q2);
  od_idct_2(q0, q1);

  /* +/- Butterflies with asymmetric output. */
  od_butterfly_sub(q1, q1h, q2);
  od_butterfly_neg(q0, q3, q3h);
}

/**
 * 4-point orthonormal Type-IV fDST
 */
static INLINE void od_fdst_4(od_coeff *q0, od_coeff *q1,
                             od_coeff *q2, od_coeff *q3) {

  /* Stage 0 */

  /* 13623/16384 = (Sin[7*Pi/16] + Cos[7*Pi/16])/Sqrt[2] = 0.831469612302545 */
  /* 18205/16384 = (Sin[7*Pi/16] - Cos[7*Pi/16])*Sqrt[2] = 1.111140466039204 */
  /*  9041/32768 = Cos[7*Pi/16]*Sqrt[2]                  = 0.275899379282943 */
  od_rotate_add(q0, q3, 13623, 14, 18205, 14, 9041, 15, SHIFT);

  /* 16069/16384 = (Sin[5*Pi/16] + Cos[5*Pi/16])/Sqrt[2] = 0.9807852804032304 */
  /* 12785/32768 = (Sin[5*Pi/16] - Cos[5*Pi/16])*Sqrt[2] = 0.3901806440322566 */
  /* 12873/16384 = Cos[5*Pi/16]*Sqrt[2]                  = 0.7856949583871021 */
  od_rotate_sub(q2, q1, 16069, 14, 12785, 15, 12873, 14, SHIFT);

  /* Stage 1 */

  od_butterfly_sub_asym(q0, od_rshift1(*q0), q1);
  od_butterfly_sub_asym(q2, od_rshift1(*q2), q3);

  /* Stage 2 */

  /* 11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/8192 = 2*Cos[Pi/4]           = 1.4142135623730951 */
  od_rotate_pi4_add_avg(q2, q1, 11585, 13, 11585, 13);
}

/**
 * 4-point orthonormal Type-IV iDST
 */
static INLINE void od_idst_4(od_coeff *q0, od_coeff *q2,
                             od_coeff *q1, od_coeff *q3) {
  od_coeff q0h;
  od_coeff q2h;

  /* Stage 0 */

  /* 11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/8192 = 2*Cos[Pi/4]           = 1.4142135623730951 */
  od_rotate_pi4_add_avg(q2, q1, 11585, 13, 11585, 13);

  /* Stage 1 */

  od_butterfly_sub(q2, &q2h, q3);
  od_butterfly_sub(q0, &q0h, q1);

  /* Stage 2 */

  /* 16069/16384 = (Sin[5*Pi/16] + Cos[5*Pi/16])/Sqrt[2] = 0.9807852804032304 */
  /* 12785/32768 = (Sin[5*Pi/16] - Cos[5*Pi/16])*Sqrt[2] = 0.3901806440322566 */
  /* 12873/16384 = Cos[5*Pi/16]*Sqrt[2]                  = 0.7856949583871021 */
  od_rotate_sub_half(q2, q1, q2h, 16069, 14, 12785, 15, 12873, 14, NONE);

  /* 13623/16384 = (Sin[7*Pi/16] + Cos[7*Pi/16])/Sqrt[2] = 0.831469612302545 */
  /* 18205/16384 = (Sin[7*Pi/16] - Cos[7*Pi/16])*Sqrt[2] = 1.111140466039204 */
  /*  9041/32768 = Cos[7*Pi/16]*Sqrt[2]                  = 0.275899379282943 */
  od_rotate_add_half(q0, q3, q0h, 13623, 14, 18205, 14, 9041, 15, NONE);
}

/**
 * 4-point asymmetric Type-IV fDST
 */
static INLINE void od_fdst_4_asym(od_coeff *q0, od_coeff q0h, od_coeff *q1,
                                  od_coeff *q2, od_coeff q2h, od_coeff *q3) {

  /* Stage 0 */

  /*  9633/16384 = (Sin[7*Pi/16] + Cos[7*Pi/16])/2 = 0.5879378012096793 */
  /*  12873/8192 = (Sin[7*Pi/16] - Cos[7*Pi/16])*2 = 1.5713899167742045 */
  /* 12785/32768 = Cos[7*Pi/16]*2                  = 0.3901806440322565 */
  od_rotate_add_half(q0, q3, q0h, 9633, 14, 12873, 13, 12785, 15, SHIFT);

  /* 22725/32768 = (Sin[5*Pi/16] + Cos[5*Pi/16])/2 = 0.6935199226610738 */
  /* 18081/32768 = (Sin[5*Pi/16] - Cos[5*Pi/16])*2 = 0.5517987585658861 */
  /* 18205/16384 = Cos[5*Pi/16]*2                  = 1.1111404660392044 */
  od_rotate_sub_half(q2, q1, q2h, 22725, 15, 18081, 15, 18205, 14, SHIFT);

  /* Stage 1 */

  od_butterfly_sub_asym(q0, od_rshift1(*q0), q1);
  od_butterfly_sub_asym(q2, od_rshift1(*q2), q3);

  /* Stage 2 */

  /* 11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/8192 = 2*Cos[Pi/4]           = 1.4142135623730951 */
  od_rotate_pi4_add_avg(q2, q1, 11585, 13, 11585, 13);
}

/**
 * 4-point asymmetric Type-IV iDST
 */
static INLINE void od_idst_4_asym(od_coeff *q0, od_coeff *q2,
                                  od_coeff *q1, od_coeff *q3) {
  od_coeff q0h;
  od_coeff q2h;

  /* Stage 0 */

  /* 11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/8192 = 2*Cos[Pi/4]           = 1.4142135623730951 */
  od_rotate_pi4_add_avg(q2, q1, 11585, 13, 11585, 13);

  /* Stage 1 */

  od_butterfly_sub(q2, &q2h, q3);
  od_butterfly_sub(q0, &q0h, q1);

  /* Stage 2 */

  /* 22725/32768 = (Sin[5*Pi/16] + Cos[5*Pi/16])/2 = 0.6935199226610738 */
  /* 18081/32768 = (Sin[5*Pi/16] - Cos[5*Pi/16])*2 = 0.5517987585658861 */
  /* 18205/16384 = Cos[5*Pi/16]*2                  = 1.1111404660392044 */
  od_rotate_sub_half(q2, q1, q2h, 22725, 15, 18081, 15, 18205, 14, SHIFT);

  /*  9633/16384 = (Sin[7*Pi/16] + Cos[7*Pi/16])/2 = 0.5879378012096793 */
  /*  12873/8192 = (Sin[7*Pi/16] - Cos[7*Pi/16])*2 = 1.5713899167742045 */
  /* 12785/32768 = Cos[7*Pi/16]*2                  = 0.3901806440322565 */
  od_rotate_add_half(q0, q3, q0h, 9633, 14, 12873, 13, 12785, 15, SHIFT);
}

/* --- 8-point Transforms --- */

/**
 * 8-point orthonormal Type-II fDCT
 */
static INLINE void od_fdct_8(od_coeff *r0, od_coeff *r1,
                             od_coeff *r2, od_coeff *r3,
                             od_coeff *r4, od_coeff *r5,
                             od_coeff *r6, od_coeff *r7) {
  od_coeff r1h;
  od_coeff r3h;
  od_coeff r5h;
  od_coeff r7h;

  /* +/- Butterflies with asymmetric output. */
  od_butterfly_neg(r0, r7, &r7h);
  od_butterfly_add(r1, &r1h, r6);
  od_butterfly_neg(r2, r5, &r5h);
  od_butterfly_add(r3, &r3h, r4);

  /* Embedded 4-point forward transforms with asymmetric input. */
  od_fdct_4_asym(r0, r1, r1h, r2, r3, r3h);
  od_fdst_4_asym(r7, r7h, r6, r5, r5h, r4);
}

/**
 * 8-point orthonormal Type-II iDCT
 */
static INLINE void od_idct_8(od_coeff *r0, od_coeff *r4,
                             od_coeff *r2, od_coeff *r6,
                             od_coeff *r1, od_coeff *r5,
                             od_coeff *r3, od_coeff *r7) {
  od_coeff r1h;
  od_coeff r3h;

  /* Embedded 4-point inverse transforms with asymmetric output. */
  od_idst_4_asym(r7, r5, r6, r4);
  od_idct_4_asym(r0, r2, r1, &r1h, r3, &r3h);

  /* +/- Butterflies with asymmetric input. */
  od_butterfly_add_asym(r3, r3h, r4);
  od_butterfly_neg_asym(r2, r5, od_rshift1(*r5));
  od_butterfly_add_asym(r1, r1h, r6);
  od_butterfly_neg_asym(r0, r7, od_rshift1(*r7));
}

/**
 * 8-point asymmetric Type-II fDCT
 */
static INLINE void od_fdct_8_asym(od_coeff *r0, od_coeff *r1, od_coeff r1h,
                                  od_coeff *r2, od_coeff *r3, od_coeff r3h,
                                  od_coeff *r4, od_coeff *r5, od_coeff r5h,
                                  od_coeff *r6, od_coeff *r7, od_coeff r7h) {

  /* +/- Butterflies with asymmetric input. */
  od_butterfly_neg_asym(r0, r7, r7h);
  od_butterfly_sub_asym(r1, r1h, r6);
  od_butterfly_neg_asym(r2, r5, r5h);
  od_butterfly_sub_asym(r3, r3h, r4);

  /* Embedded 4-point orthonormal transforms. */
  od_fdct_4(r0, r1, r2, r3);
  od_fdst_4(r7, r6, r5, r4);
}

/**
 * 8-point asymmetric Type-II iDCT
 */
static INLINE void od_idct_8_asym(od_coeff *r0, od_coeff *r4,
                                  od_coeff *r2, od_coeff *r6,
                                  od_coeff *r1, od_coeff *r1h,
                                  od_coeff *r5, od_coeff *r5h,
                                  od_coeff *r3, od_coeff *r3h,
                                  od_coeff *r7, od_coeff *r7h)  {

  /* Embedded 4-point inverse orthonormal transforms. */
  od_idst_4(r7, r5, r6, r4);
  od_idct_4(r0, r2, r1, r3);

  /* +/- Butterflies with asymmetric output. */
  od_butterfly_sub(r3, r3h, r4);
  od_butterfly_neg(r2, r5, r5h);
  od_butterfly_sub(r1, r1h, r6);
  od_butterfly_neg(r0, r7, r7h);
}

/**
 * 8-point orthonormal Type-IV fDST
 */
static INLINE void od_fdst_8(od_coeff *r0, od_coeff *r1,
                             od_coeff *r2, od_coeff *r3,
                             od_coeff *r4, od_coeff *r5,
                             od_coeff *r6, od_coeff *r7) {
  od_coeff r0h;
  od_coeff r2h;
  od_coeff r5h;
  od_coeff r7h;

  /* Stage 0 */

  /* 17911/16384 = Sin[15*Pi/32] + Cos[15*Pi/32] = 1.0932018670017576 */
  /* 14699/16384 = Sin[15*Pi/32] - Cos[15*Pi/32] = 0.8971675863426363 */
  /*    803/8192 = Cos[15*Pi/32]                 = 0.0980171403295606 */
  od_rotate_add(r0, r7, 17911, 14, 14699, 14, 803, 13, NONE);

  /* 40869/32768 = Sin[13*Pi/32] + Cos[13*Pi/32] = 1.24722501298667123 */
  /* 21845/32768 = Sin[13*Pi/32] - Cos[13*Pi/32] = 0.66665565847774650 */
  /*   1189/4096 = Cos[13*Pi/32]                 = 0.29028467725446233 */
  od_rotate_sub(r6, r1, 40869, 15, 21845, 15, 1189, 12, NONE);

  /* 22173/16384 = Sin[11*Pi/32] + Cos[11*Pi/32] = 1.3533180011743526 */
  /*   3363/8192 = Sin[11*Pi/32] - Cos[11*Pi/32] = 0.4105245275223574 */
  /* 15447/32768 = Cos[11*Pi/32]                 = 0.47139673682599764 */
  od_rotate_add(r2, r5, 22173, 14, 3363, 13, 15447, 15, NONE);

  /* 23059/16384 = Sin[9*Pi/32] + Cos[9*Pi/32] = 1.4074037375263826 */
  /*  2271/16384 = Sin[9*Pi/32] - Cos[9*Pi/32] = 0.1386171691990915 */
  /*   5197/8192 = Cos[9*Pi/32]                = 0.6343932841636455 */
  od_rotate_sub(r4, r3, 23059, 14, 2271, 14, 5197, 13, NONE);

  /* Stage 1 */

  od_butterfly_add(r0, &r0h, r3);
  od_butterfly_sub(r2, &r2h, r1);
  od_butterfly_add(r5, &r5h, r6);
  od_butterfly_sub(r7, &r7h, r4);

  /* Stage 2 */

  od_butterfly_add_asym(r7, r7h, r6);
  od_butterfly_add_asym(r5, r5h, r3);
  od_butterfly_add_asym(r2, r2h, r4);
  od_butterfly_sub_asym(r0, r0h, r1);

  /* Stage 3 */

  /* 21407/16384 = Sin[3*Pi/8] + Cos[3*Pi/8] = 1.3065629648763766 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8] = 0.5411961001461969 */
  /*   3135/4096 = 2*Cos[3*Pi/8]             = 0.7653668647301796 */
  od_rotate_sub_avg(r3, r4, 21407, 14, 8867, 14, 3135, 12, NONE);

  /* 21407/16384 = Sin[3*Pi/8] + Cos[3*Pi/8] = 1.3065629648763766 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8] = 0.5411961001461969 */
  /*   3135/4096 = 2*Cos[3*Pi/8]             = 0.7653668647301796 */
  od_rotate_neg_avg(r2, r5, 21407, 14, 8867, 14, 3135, 12);

  /* 46341/32768 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 46341/32768 = 2*Cos[Pi/4]           = 1.4142135623730951 */
  od_rotate_pi4_sub_avg(r1, r6, 46341, 15, 46341, 15);
}

/**
 * 8-point orthonormal Type-IV iDST
 */
static INLINE void od_idst_8(od_coeff *r0, od_coeff *r4,
                             od_coeff *r2, od_coeff *r6,
                             od_coeff *r1, od_coeff *r5,
                             od_coeff *r3, od_coeff *r7) {
  od_coeff r0h;
  od_coeff r2h;
  od_coeff r5h;
  od_coeff r7h;

  /* Stage 3 */

  /* 46341/32768 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 46341/32768 = 2*Cos[Pi/4]           = 1.4142135623730951 */
  od_rotate_pi4_add_avg(r6, r1, 11585, 13, 46341, 15);

  /* 21407/16384 = Sin[3*Pi/8] + Cos[3*Pi/8] = 1.3065629648763766 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8] = 0.5411961001461969 */
  /*   3135/4096 = 2*Cos[3*Pi/8]             = 0.7653668647301796 */
  od_rotate_neg_avg(r5, r2, 21407, 14, 8867, 14, 3135, 12);

  /* 21407/16384 = Sin[3*Pi/8] + Cos[3*Pi/8] = 1.3065629648763766 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8] = 0.5411961001461969 */
  /*   3135/4096 = 2*Cos[3*Pi/8]             = 0.7653668647301796 */
  od_rotate_add_avg(r4, r3, 21407, 14, 8867, 14, 3135, 12, NONE);

  /* Stage 2 */

  od_butterfly_sub(r0, &r0h, r1);
  od_butterfly_add(r2, &r2h, r4);
  od_butterfly_add(r5, &r5h, r3);
  od_butterfly_add(r7, &r7h, r6);

  /* Stage 1 */

  od_butterfly_sub_asym(r7, r7h, r4);
  od_butterfly_add_asym(r5, r5h, r6);
  od_butterfly_sub_asym(r2, r2h, r1);
  od_butterfly_add_asym(r0, r0h, r3);

  /* Stage 0 */

  /* 23059/16384 = Sin[9*Pi/32] + Cos[9*Pi/32] = 1.4074037375263826 */
  /*  2271/16384 = Sin[9*Pi/32] - Cos[9*Pi/32] = 0.1386171691990915 */
  /*   5197/8192 = Cos[9*Pi/32]                = 0.6343932841636455 */
  od_rotate_sub(r4, r3, 23059, 14, 2271, 14, 5197, 13, NONE);

  /* 22173/16384 = Sin[11*Pi/32] + Cos[11*Pi/32] = 1.3533180011743526 */
  /*   3363/8192 = Sin[11*Pi/32] - Cos[11*Pi/32] = 0.4105245275223574 */
  /* 15447/32768 = Cos[11*Pi/32]                 = 0.47139673682599764 */
  od_rotate_add(r2, r5, 22173, 14, 3363, 13, 15447, 15, NONE);

  /* 40869/32768 = Sin[13*Pi/32] + Cos[13*Pi/32] = 1.24722501298667123 */
  /* 21845/32768 = Sin[13*Pi/32] - Cos[13*Pi/32] = 0.66665565847774650 */
  /*   1189/4096 = Cos[13*Pi/32]                 = 0.29028467725446233 */
  od_rotate_sub(r6, r1, 40869, 15, 21845, 15, 1189, 12, NONE);

  /* 17911/16384 = Sin[15*Pi/32] + Cos[15*Pi/32] = 1.0932018670017576 */
  /* 14699/16384 = Sin[15*Pi/32] - Cos[15*Pi/32] = 0.8971675863426363 */
  /*    803/8192 = Cos[15*Pi/32]                 = 0.0980171403295606 */
  od_rotate_add(r0, r7, 17911, 14, 14699, 14, 803, 13, NONE);
}

/**
 * 8-point asymmetric Type-IV fDST
 */
static INLINE void od_fdst_8_asym(od_coeff *r0, od_coeff r0h, od_coeff *r1,
                                  od_coeff *r2, od_coeff r2h, od_coeff *r3,
                                  od_coeff *r4, od_coeff r4h, od_coeff *r5,
                                  od_coeff *r6, od_coeff r6h, od_coeff *r7) {
  od_coeff r5h;
  od_coeff r7h;

  /* Stage 0 */

  /* 12665/16384 = (Sin[15*Pi/32] + Cos[15*Pi/32])/Sqrt[2] = 0.77301045336274 */
  /*   5197/4096 = (Sin[15*Pi/32] - Cos[15*Pi/32])*Sqrt[2] = 1.26878656832729 */
  /*  2271/16384 = Cos[15*Pi/32]*Sqrt[2]                   = 0.13861716919909 */
  od_rotate_add_half(r0, r7, r0h, 12665, 14, 5197, 12, 2271, 14, NONE);

  /* 28899/32768 = Sin[13*Pi/32] + Cos[13*Pi/32])/Sqrt[2] = 0.881921264348355 */
  /* 30893/32768 = Sin[13*Pi/32] - Cos[13*Pi/32])*Sqrt[2] = 0.942793473651995 */
  /*   3363/8192 = Cos[13*Pi/32]*Sqrt[2]                  = 0.410524527522357 */
  od_rotate_sub_half(r6, r1, r6h, 28899, 15, 30893, 15, 3363, 13, NONE);

  /* 31357/32768 = Sin[11*Pi/32] + Cos[11*Pi/32])/Sqrt[2] = 0.956940335732209 */
  /*   1189/2048 = Sin[11*Pi/32] - Cos[11*Pi/32])*Sqrt[2] = 0.580569354508925 */
  /* 21845/32768 = Cos[11*Pi/32]*Sqrt[2]                  = 0.666655658477747 */
  od_rotate_add_half(r2, r5, r2h, 31357, 15, 1189, 11, 21845, 15, NONE);

  /* 16305/16384 = (Sin[9*Pi/32] + Cos[9*Pi/32])/Sqrt[2] = 0.9951847266721969 */
  /*    803/4096 = (Sin[9*Pi/32] - Cos[9*Pi/32])*Sqrt[2] = 0.1960342806591213 */
  /* 14699/16384 = Cos[9*Pi/32]*Sqrt[2]                  = 0.8971675863426364 */
  od_rotate_sub_half(r4, r3, r4h, 16305, 14, 803, 12, 14699, 14, NONE);

  /* Stage 1 */

  od_butterfly_add(r0, &r0h, r3);
  od_butterfly_sub(r2, &r2h, r1);
  od_butterfly_add(r5, &r5h, r6);
  od_butterfly_sub(r7, &r7h, r4);

  /* Stage 2 */

  od_butterfly_add_asym(r7, r7h, r6);
  od_butterfly_add_asym(r5, r5h, r3);
  od_butterfly_add_asym(r2, r2h, r4);
  od_butterfly_sub_asym(r0, r0h, r1);

  /* Stage 3 */

  /* 21407/16384 = Sin[3*Pi/8] + Cos[3*Pi/8] = 1.3065629648763766 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8] = 0.5411961001461969 */
  /*   3135/4096 = 2*Cos[3*Pi/8]             = 0.7653668647301796 */
  od_rotate_sub_avg(r3, r4, 21407, 14, 8867, 14, 3135, 12, NONE);

  /* 21407/16384 = Sin[3*Pi/8] + Cos[3*Pi/8] = 1.3065629648763766 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8] = 0.5411961001461969 */
  /*   3135/4096 = 2*Cos[3*Pi/8]             = 0.7653668647301796 */
  od_rotate_neg_avg(r2, r5, 21407, 14, 8867, 14, 3135, 12);

  /* 46341/32768 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 46341/32768 = 2*Cos[Pi/4]           = 1.4142135623730951 */
  od_rotate_pi4_sub_avg(r1, r6, 46341, 15, 46341, 15);
}

/**
 * 8-point asymmetric Type-IV iDST
 */
static INLINE void od_idst_8_asym(od_coeff *r0, od_coeff *r4,
                                  od_coeff *r2, od_coeff *r6,
                                  od_coeff *r1, od_coeff *r5,
                                  od_coeff *r3, od_coeff *r7) {
  od_coeff r0h;
  od_coeff r2h;
  od_coeff r5h;
  od_coeff r7h;

  /* Stage 3 */

  /* 46341/32768 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 46341/32768 = 2*Cos[Pi/4]           = 1.4142135623730951 */
  od_rotate_pi4_add_avg(r6, r1, 11585, 13, 11585, 13);

  /* 21407/16384 = Sin[3*Pi/8] + Cos[3*Pi/8] = 1.3065629648763766 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8] = 0.5411961001461969 */
  /*   3135/4096 = 2*Cos[3*Pi/8]             = 0.7653668647301796 */
  od_rotate_neg_avg(r5, r2, 21407, 14, 8867, 14, 3135, 12);

  /* 21407/16384 = Sin[3*Pi/8] + Cos[3*Pi/8] = 1.3065629648763766 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8] = 0.5411961001461969 */
  /*   3135/4096 = 2*Cos[3*Pi/8]             = 0.7653668647301796 */
  od_rotate_add_avg(r4, r3, 21407, 14, 8867, 14, 3135, 12, NONE);

  /* Stage 2 */

  od_butterfly_sub(r0, &r0h, r1);
  od_butterfly_add(r2, &r2h, r4);
  od_butterfly_add(r5, &r5h, r3);
  od_butterfly_add(r7, &r7h, r6);

  /* Stage 1 */

  od_butterfly_sub_asym(r7, r7h, r4);
  od_butterfly_add_asym(r5, r5h, r6);
  od_butterfly_sub_asym(r2, r2h, r1);
  od_butterfly_add_asym(r0, r0h, r3);

  /* Stage 0 */

  /* 16305/16384 = (Sin[9*Pi/32] + Cos[9*Pi/32])/Sqrt[2] = 0.9951847266721969 */
  /*    803/4096 = (Sin[9*Pi/32] - Cos[9*Pi/32])*Sqrt[2] = 0.1960342806591213 */
  /* 14699/16384 = Cos[9*Pi/32]*Sqrt[2]                  = 0.8971675863426364 */
  od_rotate_sub(r4, r3, 16305, 14, 803, 12, 14699, 14, SHIFT);

  /* 31357/32768 = Sin[11*Pi/32] + Cos[11*Pi/32])/Sqrt[2] = 0.956940335732209 */
  /*   1189/2048 = Sin[11*Pi/32] - Cos[11*Pi/32])*Sqrt[2] = 0.580569354508925 */
  /* 21845/32768 = Cos[11*Pi/32]*Sqrt[2]                  = 0.666655658477747 */
  od_rotate_add(r2, r5, 31357, 15, 1189, 11, 21845, 15, SHIFT);

  /* 28899/32768 = Sin[13*Pi/32] + Cos[13*Pi/32])/Sqrt[2] = 0.881921264348355 */
  /* 30893/32768 = Sin[13*Pi/32] - Cos[13*Pi/32])*Sqrt[2] = 0.942793473651995 */
  /*   3363/8192 = Cos[13*Pi/32]*Sqrt[2]                  = 0.410524527522357 */
  od_rotate_sub(r6, r1, 28899, 15, 30893, 15, 3363, 13, SHIFT);

  /* 12665/16384 = (Sin[15*Pi/32] + Cos[15*Pi/32])/Sqrt[2] = 0.77301045336274 */
  /*   5197/4096 = (Sin[15*Pi/32] - Cos[15*Pi/32])*Sqrt[2] = 1.26878656832729 */
  /*  2271/16384 = Cos[15*Pi/32]*Sqrt[2]                   = 0.13861716919909 */
  od_rotate_add(r0, r7, 12665, 14, 5197, 12, 2271, 14, SHIFT);
}

/* --- 16-point Transforms --- */

/**
 * 16-point orthonormal Type-II fDCT
 */
static INLINE void od_fdct_16(od_coeff *s0, od_coeff *s1,
                              od_coeff *s2, od_coeff *s3,
                              od_coeff *s4, od_coeff *s5,
                              od_coeff *s6, od_coeff *s7,
                              od_coeff *s8, od_coeff *s9,
                              od_coeff *sa, od_coeff *sb,
                              od_coeff *sc, od_coeff *sd,
                              od_coeff *se, od_coeff *sf) {
  od_coeff s1h;
  od_coeff s3h;
  od_coeff s5h;
  od_coeff s7h;
  od_coeff s9h;
  od_coeff sbh;
  od_coeff sdh;
  od_coeff sfh;

  /* +/- Butterflies with asymmetric output. */
  od_butterfly_neg(s0, sf, &sfh);
  od_butterfly_add(s1, &s1h, se);
  od_butterfly_neg(s2, sd, &sdh);
  od_butterfly_add(s3, &s3h, sc);
  od_butterfly_neg(s4, sb, &sbh);
  od_butterfly_add(s5, &s5h, sa);
  od_butterfly_neg(s6, s9, &s9h);
  od_butterfly_add(s7, &s7h, s8);

  /* Embedded 8-point transforms with asymmetric input. */
  od_fdct_8_asym(s0, s1, s1h, s2, s3, s3h, s4, s5, s5h, s6, s7, s7h);
  od_fdst_8_asym(sf, sfh, se, sd, sdh, sc, sb, sbh, sa, s9, s9h, s8);
}

/**
 * 16-point orthonormal Type-II iDCT
 */
static INLINE void od_idct_16(od_coeff *s0, od_coeff *s8,
                              od_coeff *s4, od_coeff *sc,
                              od_coeff *s2, od_coeff *sa,
                              od_coeff *s6, od_coeff *se,
                              od_coeff *s1, od_coeff *s9,
                              od_coeff *s5, od_coeff *sd,
                              od_coeff *s3, od_coeff *sb,
                              od_coeff *s7, od_coeff *sf) {
  od_coeff s1h;
  od_coeff s3h;
  od_coeff s5h;
  od_coeff s7h;

  /* Embedded 8-point transforms with asymmetric output. */
  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);

  /* +/- Butterflies with asymmetric input. */
  od_butterfly_add_asym(s7, s7h, s8);
  od_butterfly_neg_asym(s6, s9, od_rshift1(*s9));
  od_butterfly_add_asym(s5, s5h, sa);
  od_butterfly_neg_asym(s4, sb, od_rshift1(*sb));
  od_butterfly_add_asym(s3, s3h, sc);
  od_butterfly_neg_asym(s2, sd, od_rshift1(*sd));
  od_butterfly_add_asym(s1, s1h, se);
  od_butterfly_neg_asym(s0, sf, od_rshift1(*sf));
}

/**
 * 16-point asymmetric Type-II fDCT
 */
static INLINE void od_fdct_16_asym(od_coeff *s0, od_coeff *s1, od_coeff s1h,
                                   od_coeff *s2, od_coeff *s3, od_coeff s3h,
                                   od_coeff *s4, od_coeff *s5, od_coeff s5h,
                                   od_coeff *s6, od_coeff *s7, od_coeff s7h,
                                   od_coeff *s8, od_coeff *s9, od_coeff s9h,
                                   od_coeff *sa, od_coeff *sb, od_coeff sbh,
                                   od_coeff *sc, od_coeff *sd, od_coeff sdh,
                                   od_coeff *se, od_coeff *sf, od_coeff sfh) {

  /* +/- Butterflies with asymmetric input. */
  od_butterfly_neg_asym(s0, sf, sfh);
  od_butterfly_sub_asym(s1, s1h, se);
  od_butterfly_neg_asym(s2, sd, sdh);
  od_butterfly_sub_asym(s3, s3h, sc);
  od_butterfly_neg_asym(s4, sb, sbh);
  od_butterfly_sub_asym(s5, s5h, sa);
  od_butterfly_neg_asym(s6, s9, s9h);
  od_butterfly_sub_asym(s7, s7h, s8);

  /* Embedded 8-point orthonormal transforms. */
  od_fdct_8(s0, s1, s2, s3, s4, s5, s6, s7);
  od_fdst_8(sf, se, sd, sc, sb, sa, s9, s8);
}

/**
 * 16-point asymmetric Type-II iDCT
 */
static INLINE void od_idct_16_asym(od_coeff *s0, od_coeff *s8,
                                   od_coeff *s4, od_coeff *sc,
                                   od_coeff *s2, od_coeff *sa,
                                   od_coeff *s6, od_coeff *se,
                                   od_coeff *s1, od_coeff *s1h,
                                   od_coeff *s9, od_coeff *s9h,
                                   od_coeff *s5, od_coeff *s5h,
                                   od_coeff *sd, od_coeff *sdh,
                                   od_coeff *s3, od_coeff *s3h,
                                   od_coeff *sb, od_coeff *sbh,
                                   od_coeff *s7, od_coeff *s7h,
                                   od_coeff *sf, od_coeff *sfh) {

  /* Embedded 8-point orthonormal transforms. */
  od_idst_8(sf, sb, sd, s9, se, sa, sc, s8);
  od_idct_8(s0, s4, s2, s6, s1, s5, s3, s7);

  /* +/- Butterflies with asymmetric output. */
  od_butterfly_sub(s7, s7h, s8);
  od_butterfly_neg(s6, s9, s9h);
  od_butterfly_sub(s5, s5h, sa);
  od_butterfly_neg(s4, sb, sbh);
  od_butterfly_sub(s3, s3h, sc);
  od_butterfly_neg(s2, sd, sdh);
  od_butterfly_sub(s1, s1h, se);
  od_butterfly_neg(s0, sf, sfh);
}

/**
 * 16-point orthonormal Type-IV fDST
 */
static INLINE void od_fdst_16(od_coeff *s0, od_coeff *s1,
                              od_coeff *s2, od_coeff *s3,
                              od_coeff *s4, od_coeff *s5,
                              od_coeff *s6, od_coeff *s7,
                              od_coeff *s8, od_coeff *s9,
                              od_coeff *sa, od_coeff *sb,
                              od_coeff *sc, od_coeff *sd,
                              od_coeff *se, od_coeff *sf) {
  od_coeff s0h;
  od_coeff s2h;
  od_coeff sdh;
  od_coeff sfh;

  /* Stage 0 */

  /* 24279/32768 = (Sin[31*Pi/64] + Cos[31*Pi/64])/Sqrt[2] = 0.74095112535496 */
  /* 44011/32768 = (Sin[31*Pi/64] - Cos[31*Pi/64])*Sqrt[2] = 1.34311790969404 */
  /*  1137/16384 = Cos[31*Pi/64]*Sqrt[2]                   = 0.06939217050794 */
  od_rotate_add(s0, sf, 24279, 15, 44011, 15, 1137, 14, SHIFT);

  /* 1645/2048 = (Sin[29*Pi/64] + Cos[29*Pi/64])/Sqrt[2] = 0.8032075314806449 */
  /*   305/256 = (Sin[29*Pi/64] - Cos[29*Pi/64])*Sqrt[2] = 1.1913986089848667 */
  /*  425/2048 = Cos[29*Pi/64]*Sqrt[2]                   = 0.2075082269882116 */
  od_rotate_sub(se, s1, 1645, 11, 305, 8, 425, 11, SHIFT);

  /* 14053/32768 = (Sin[27*Pi/64] + Cos[27*Pi/64])/Sqrt[2] = 0.85772861000027 */
  /*   8423/8192 = (Sin[27*Pi/64] - Cos[27*Pi/64])*Sqrt[2] = 1.02820548838644 */
  /*   2815/8192 = Cos[27*Pi/64]*Sqrt[2]                   = 0.34362586580705 */
  od_rotate_add(s2, sd, 14053, 14, 8423, 13, 2815, 13, SHIFT);

  /* 14811/16384 = (Sin[25*Pi/64] + Cos[25*Pi/64])/Sqrt[2] = 0.90398929312344 */
  /*   7005/8192 = (Sin[25*Pi/64] - Cos[25*Pi/64])*Sqrt[2] = 0.85511018686056 */
  /*   3903/8192 = Cos[25*Pi/64]*Sqrt[2]                   = 0.47643419969316 */
  od_rotate_sub(sc, s3, 14811, 14, 7005, 13, 3903, 13, SHIFT);

  /* 30853/32768 = (Sin[23*Pi/64] + Cos[23*Pi/64])/Sqrt[2] = 0.94154406518302 */
  /* 11039/16384 = (Sin[23*Pi/64] - Cos[23*Pi/64])*Sqrt[2] = 0.67377970678444 */
  /* 19813/32768 = Cos[23*Pi/64]*Sqrt[2]                   = 0.60465421179080 */
  od_rotate_add(s4, sb, 30853, 15, 11039, 14, 19813, 15, SHIFT);

  /* 15893/16384 = (Sin[21*Pi/64] + Cos[21*Pi/64])/Sqrt[2] = 0.97003125319454 */
  /*   3981/8192 = (Sin[21*Pi/64] - Cos[21*Pi/64])*Sqrt[2] = 0.89716758634264 */
  /*   1489/2048 = Cos[21*Pi/64]*Sqrt[2]                   = 0.72705107329128 */
  od_rotate_sub(sa, s5, 15893, 14, 3981, 13, 1489, 11, SHIFT);

  /* 32413/32768 = (Sin[19*Pi/64] + Cos[19*Pi/64])/Sqrt[2] = 0.98917650996478 */
  /*    601/2048 = (Sin[19*Pi/64] - Cos[19*Pi/64])*Sqrt[2] = 0.29346094891072 */
  /* 27605/32768 = Cos[19*Pi/64]*Sqrt[2]                   = 0.84244603550942 */
  od_rotate_add(s6, s9, 32413, 15, 601, 11, 27605, 15, SHIFT);

  /* 32729/32768 = (Sin[17*Pi/64] + Cos[17*Pi/64])/Sqrt[2] = 0.99879545620517 */
  /*    201/2048 = (Sin[17*Pi/64] - Cos[17*Pi/64])*Sqrt[2] = 0.09813534865484 */
  /* 31121/32768 = Cos[17*Pi/64]*Sqrt[2]                   = 0.94972778187775 */
  od_rotate_sub(s8, s7, 32729, 15, 201, 11, 31121, 15, SHIFT);

  /* Stage 1 */

  od_butterfly_sub_asym(s0, od_rshift1(*s0), s7);
  od_butterfly_sub_asym(s8, od_rshift1(*s8), sf);
  od_butterfly_add_asym(s4, od_rshift1(*s4), s3);
  od_butterfly_add_asym(sc, od_rshift1(*sc), sb);
  od_butterfly_sub_asym(s2, od_rshift1(*s2), s5);
  od_butterfly_sub_asym(sa, od_rshift1(*sa), sd);
  od_butterfly_add_asym(s6, od_rshift1(*s6), s1);
  od_butterfly_add_asym(se, od_rshift1(*se), s9);

  /* Stage 2 */

  od_butterfly_add(s8, NULL, s4);
  od_butterfly_add(s7, NULL, sb);
  od_butterfly_sub(sa, NULL, s6);
  od_butterfly_sub(s5, NULL, s9);
  od_butterfly_add(s0, &s0h, s3);
  od_butterfly_add(sd, &sdh, se);
  od_butterfly_sub(s2, &s2h, s1);
  od_butterfly_sub(sf, &sfh, sc);

  /* Stage 3 */

  /*   9633/8192 = Sin[7*Pi/16] + Cos[7*Pi/16] = 1.1758756024193586 */
  /* 12873/16384 = Sin[7*Pi/16] - Cos[7*Pi/16] = 0.7856949583871022 */
  /* 12785/32768 = 2*Cos[7*Pi/16]              = 0.3901806440322565 */
  od_rotate_add_avg(s8, s7, 9633, 13, 12873, 14, 12785, 15, NONE);

  /* 45451/32768 = Sin[5*Pi/16] + Cos[5*Pi/16] = 1.3870398453221475 */
  /*  9041/32768 = Sin[5*Pi/16] - Cos[5*Pi/16] = 0.2758993792829431 */
  /* 18205/32768 = Cos[5*Pi/16]                = 0.5555702330196022 */
  od_rotate_add(s9, s6, 45451, 15, 9041, 15, 18205, 15, NONE);

  /* 22725/16384 = Sin[5*Pi/16] + Cos[5*Pi/16] = 1.3870398453221475 */
  /*  9041/32768 = Sin[5*Pi/16] - Cos[5*Pi/16] = 0.2758993792829431 */
  /* 18205/32768 = 2*Cos[5*Pi/16]              = 1.1111404660392044 */
  od_rotate_neg_avg(s5, sa, 22725, 14, 9041, 15, 18205, 14);

  /* 38531/32768 = Sin[7*Pi/16] + Cos[7*Pi/16] = 1.1758756024193586 */
  /* 12873/16384 = Sin[7*Pi/16] - Cos[7*Pi/16] = 0.7856949583871022 */
  /*  6393/32768 = Cos[7*Pi/16]                = 0.1950903220161283 */
  od_rotate_neg(s4, sb, 38531, 15, 12873, 14, 6393, 15);

  /* Stage 4 */

  od_butterfly_add_asym(s2, s2h, sc);
  od_butterfly_sub_asym(s0, s0h, s1);
  od_butterfly_add_asym(sf, sfh, se);
  od_butterfly_add_asym(sd, sdh, s3);
  od_butterfly_add_asym(s7, od_rshift1(*s7), s6);
  od_butterfly_sub_asym(s8, od_rshift1(*s8), s9);
  od_butterfly_sub_asym(sa, od_rshift1(*sa), sb);
  od_butterfly_add_asym(s5, od_rshift1(*s5), s4);

  /* Stage 5 */

  /* 21407/16384 = Sin[3*Pi/8] + Cos[3*Pi/8] = 1.3065629648763766 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8] = 0.5411961001461969 */
  /*   3135/4096 = 2*Cos[7*Pi/8]             = 0.7653668647301796 */
  od_rotate_add_avg(sc, s3, 21407, 14, 8867, 14, 3135, 12, NONE);

  /* 21407/16384 = Sin[3*Pi/8] + Cos[3*Pi/8] = 1.3870398453221475 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8] = 0.5411961001461969 */
  /*   3135/4096 = 2*Cos[3*Pi/8]             = 0.7653668647301796 */
  od_rotate_neg_avg(s2, sd, 21407, 14, 8867, 14, 3135, 12);

  /* 11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/8192 = 2*Cos[Pi/4]           = 1.4142135623730951 */
  od_rotate_pi4_add_avg(sa, s5, 11585, 13, 11585, 13);

  /* 11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/8192 = 2*Cos[Pi/4]           = 1.4142135623730951 */
  od_rotate_pi4_add_avg(s6, s9, 11585, 13, 11585, 13);

  /* 11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/8192 = 2*Cos[Pi/4]           = 1.4142135623730951 */
  od_rotate_pi4_add_avg(se, s1, 11585, 13, 11585, 13);
}

/**
 * 16-point orthonormal Type-IV iDST
 */
static INLINE void od_idst_16(od_coeff *s0, od_coeff *s8,
                              od_coeff *s4, od_coeff *sc,
                              od_coeff *s2, od_coeff *sa,
                              od_coeff *s6, od_coeff *se,
                              od_coeff *s1, od_coeff *s9,
                              od_coeff *s5, od_coeff *sd,
                              od_coeff *s3, od_coeff *sb,
                              od_coeff *s7, od_coeff *sf) {
  od_coeff s0h;
  od_coeff s2h;
  od_coeff s4h;
  od_coeff s6h;
  od_coeff s8h;
  od_coeff sah;
  od_coeff sch;
  od_coeff sdh;
  od_coeff seh;
  od_coeff sfh;

  /* Stage 5 */

  /* 11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/8192 = 2*Cos[Pi/4]           = 1.4142135623730951 */
  od_rotate_pi4_add_avg(s6, s9, 11585, 13, 11585, 13);

  /* 11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/8192 = 2*Cos[Pi/4]           = 1.4142135623730951 */
  od_rotate_pi4_add_avg(sa, s5, 11585, 13, 11585, 13);

  /* 11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/8192 = 2*Cos[Pi/4]           = 1.4142135623730951 */
  od_rotate_pi4_add_avg(se, s1, 11585, 13, 11585, 13);

  /* 21407/16384 = Sin[3*Pi/8] + Cos[3*Pi/8] = 1.3065629648763766 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8] = 0.5411961001461969 */
  /*   3135/4096 = 2*Cos[7*Pi/8]             = 0.7653668647301796 */
  od_rotate_add_avg(sc, s3, 21407, 14, 8867, 14, 3135, 12, NONE);

  /* 21407/16384 = Sin[3*Pi/8] + Cos[3*Pi/8] = 1.3870398453221475 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8] = 0.5411961001461969 */
  /*   3135/4096 = 2*Cos[3*Pi/8]             = 0.7653668647301796 */
  od_rotate_neg_avg(sd, s2, 21407, 14, 8867, 14, 3135, 12);

  /* Stage 4 */

  od_butterfly_add(s5, NULL, s4);
  od_butterfly_sub(sa, NULL, sb);
  od_butterfly_sub(s8, NULL, s9);
  od_butterfly_add(s7, NULL, s6);
  od_butterfly_add(sd, &sdh, s3);
  od_butterfly_add(sf, &sfh, se);
  od_butterfly_sub(s0, &s0h, s1);
  od_butterfly_add(s2, &s2h, sc);

  /* Stage 3 */

  /*   9633/8192 = Sin[7*Pi/16] + Cos[7*Pi/16] = 1.1758756024193586 */
  /* 12873/16384 = Sin[7*Pi/16] - Cos[7*Pi/16] = 0.7856949583871022 */
  /* 12785/32768 = 2*Cos[7*Pi/16]              = 0.3901806440322565 */
  od_rotate_add_avg(s8, s7, 9633, 13, 12873, 14, 12785, 15, NONE);

  /* 45451/32768 = Sin[5*Pi/16] + Cos[5*Pi/16] = 1.3870398453221475 */
  /*  9041/32768 = Sin[5*Pi/16] - Cos[5*Pi/16] = 0.2758993792829431 */
  /* 18205/32768 = Cos[5*Pi/16]                = 0.5555702330196022 */
  od_rotate_add(s9, s6, 45451, 15, 9041, 15, 18205, 15, NONE);

  /* 22725/16384 = Sin[5*Pi/16] + Cos[5*Pi/16] = 1.3870398453221475 */
  /*  9041/32768 = Sin[5*Pi/16] - Cos[5*Pi/16] = 0.2758993792829431 */
  /* 18205/32768 = 2*Cos[5*Pi/16]              = 1.1111404660392044 */
  od_rotate_neg_avg(sa, s5, 22725, 14, 9041, 15, 18205, 14);

  /* 38531/32768 = Sin[7*Pi/16] + Cos[7*Pi/16] = 1.1758756024193586 */
  /* 12873/16384 = Sin[7*Pi/16] - Cos[7*Pi/16] = 0.7856949583871022 */
  /*  6393/32768 = Cos[7*Pi/16]                = 0.1950903220161283 */
  od_rotate_neg(sb, s4, 38531, 15, 12873, 14, 6393, 15);

  /* Stage 2 */

  od_butterfly_add_asym(s8, od_rshift1(*s8), s4);
  od_butterfly_add_asym(s7, od_rshift1(*s7), sb);
  od_butterfly_sub_asym(sa, od_rshift1(*sa), s6);
  od_butterfly_sub_asym(s5, od_rshift1(*s5), s9);
  od_butterfly_add_asym(s0, s0h, s3);
  od_butterfly_add_asym(sd, sdh, se);
  od_butterfly_sub_asym(s2, s2h, s1);
  od_butterfly_sub_asym(sf, sfh, sc);

  /* Stage 1 */

  od_butterfly_sub(s0, &s0h, s7);
  od_butterfly_sub(s8, &s8h, sf);
  od_butterfly_add(s4, &s4h, s3);
  od_butterfly_add(sc, &sch, sb);
  od_butterfly_sub(s2, &s2h, s5);
  od_butterfly_sub(sa, &sah, sd);
  od_butterfly_add(s6, &s6h, s1);
  od_butterfly_add(se, &seh, s9);

  /* Stage 0 */

  /* 32729/32768 = (Sin[17*Pi/64] + Cos[17*Pi/64])/Sqrt[2] = 0.99879545620517 */
  /*    201/2048 = (Sin[17*Pi/64] - Cos[17*Pi/64])*Sqrt[2] = 0.09813534865484 */
  /* 31121/32768 = Cos[17*Pi/64]*Sqrt[2]                   = 0.94972778187775 */
  od_rotate_sub_half(s8, s7, s8h, 32729, 15, 201, 11, 31121, 15, NONE);

  /* 32413/32768 = (Sin[19*Pi/64] + Cos[19*Pi/64])/Sqrt[2] = 0.98917650996478 */
  /*    601/2048 = (Sin[19*Pi/64] - Cos[19*Pi/64])*Sqrt[2] = 0.29346094891072 */
  /* 27605/32768 = Cos[19*Pi/64]*Sqrt[2]                   = 0.84244603550942 */
  od_rotate_add_half(s6, s9, s6h, 32413, 15, 601, 11, 27605, 15, NONE);

  /* 15893/16384 = (Sin[21*Pi/64] + Cos[21*Pi/64])/Sqrt[2] = 0.97003125319454 */
  /*   3981/8192 = (Sin[21*Pi/64] - Cos[21*Pi/64])*Sqrt[2] = 0.89716758634264 */
  /*   1489/2048 = Cos[21*Pi/64]*Sqrt[2]                   = 0.72705107329128 */
  od_rotate_sub_half(sa, s5, sah, 15893, 14, 3981, 13, 1489, 11, NONE);

  /* 30853/32768 = (Sin[23*Pi/64] + Cos[23*Pi/64])/Sqrt[2] = 0.94154406518302 */
  /* 11039/16384 = (Sin[23*Pi/64] - Cos[23*Pi/64])*Sqrt[2] = 0.67377970678444 */
  /* 19813/32768 = Cos[23*Pi/64]*Sqrt[2]                   = 0.60465421179080 */
  od_rotate_add_half(s4, sb, s4h, 30853, 15, 11039, 14, 19813, 15, NONE);

  /* 14811/16384 = (Sin[25*Pi/64] + Cos[25*Pi/64])/Sqrt[2] = 0.90398929312344 */
  /*   7005/8192 = (Sin[25*Pi/64] - Cos[25*Pi/64])*Sqrt[2] = 0.85511018686056 */
  /*   3903/8192 = Cos[25*Pi/64]*Sqrt[2]                   = 0.47643419969316 */
  od_rotate_sub_half(sc, s3, sch, 14811, 14, 7005, 13, 3903, 13, NONE);

  /* 14053/32768 = (Sin[27*Pi/64] + Cos[27*Pi/64])/Sqrt[2] = 0.85772861000027 */
  /*   8423/8192 = (Sin[27*Pi/64] - Cos[27*Pi/64])*Sqrt[2] = 1.02820548838644 */
  /*   2815/8192 = Cos[27*Pi/64]*Sqrt[2]                   = 0.34362586580705 */
  od_rotate_add_half(s2, sd, s2h, 14053, 14, 8423, 13, 2815, 13, NONE);

  /* 1645/2048 = (Sin[29*Pi/64] + Cos[29*Pi/64])/Sqrt[2] = 0.8032075314806449 */
  /*   305/256 = (Sin[29*Pi/64] - Cos[29*Pi/64])*Sqrt[2] = 1.1913986089848667 */
  /*  425/2048 = Cos[29*Pi/64]*Sqrt[2]                   = 0.2075082269882116 */
  od_rotate_sub_half(se, s1, seh, 1645, 11, 305, 8, 425, 11, NONE);

  /* 24279/32768 = (Sin[31*Pi/64] + Cos[31*Pi/64])/Sqrt[2] = 0.74095112535496 */
  /* 44011/32768 = (Sin[31*Pi/64] - Cos[31*Pi/64])*Sqrt[2] = 1.34311790969404 */
  /*  1137/16384 = Cos[31*Pi/64]*Sqrt[2]                   = 0.06939217050794 */
  od_rotate_add_half(s0, sf, s0h, 24279, 15, 44011, 15, 1137, 14, NONE);
}

/**
 * 16-point asymmetric Type-IV fDST
 */
static INLINE void od_fdst_16_asym(od_coeff *s0, od_coeff s0h, od_coeff *s1,
                                   od_coeff *s2, od_coeff s2h, od_coeff *s3,
                                   od_coeff *s4, od_coeff s4h, od_coeff *s5,
                                   od_coeff *s6, od_coeff s6h, od_coeff *s7,
                                   od_coeff *s8, od_coeff s8h, od_coeff *s9,
                                   od_coeff *sa, od_coeff sah, od_coeff *sb,
                                   od_coeff *sc, od_coeff sch, od_coeff *sd,
                                   od_coeff *se, od_coeff seh, od_coeff *sf) {
  od_coeff sdh;
  od_coeff sfh;

  /* Stage 0 */

  /*   1073/2048 = (Sin[31*Pi/64] + Cos[31*Pi/64])/2 = 0.5239315652662953 */
  /* 62241/32768 = (Sin[31*Pi/64] - Cos[31*Pi/64])*2 = 1.8994555637555088 */
  /*   201/16384 = Cos[31*Pi/64]*2                   = 0.0981353486548360 */
  od_rotate_add_half(s0, sf, s0h, 1073, 11, 62241, 15, 201, 11, SHIFT);

  /* 18611/32768 = (Sin[29*Pi/64] + Cos[29*Pi/64])/2 = 0.5679534922100714 */
  /* 55211/32768 = (Sin[29*Pi/64] - Cos[29*Pi/64])*2 = 1.6848920710188384 */
  /*    601/2048 = Cos[29*Pi/64]*2                   = 0.2934609489107235 */
  od_rotate_sub_half(se, s1, seh, 18611, 15, 55211, 15, 601, 11, SHIFT);

  /*  9937/16384 = (Sin[27*Pi/64] + Cos[27*Pi/64])/2 = 0.6065057165489039 */
  /*   1489/1024 = (Sin[27*Pi/64] - Cos[27*Pi/64])*2 = 1.4541021465825602 */
  /*   3981/8192 = Cos[27*Pi/64]*2                   = 0.4859603598065277 */
  od_rotate_add_half(s2, sd, s2h, 9937, 14, 1489, 10, 3981, 13, SHIFT);

  /* 10473/16384 = (Sin[25*Pi/64] + Cos[25*Pi/64])/2 = 0.6392169592876205 */
  /* 39627/32768 = (Sin[25*Pi/64] - Cos[25*Pi/64])*2 = 1.2093084235816014 */
  /* 11039/16384 = Cos[25*Pi/64]*2                   = 0.6737797067844401 */
  od_rotate_sub_half(sc, s3, sch, 10473, 14, 39627, 15, 11039, 14, SHIFT);

  /* 2727/4096 = (Sin[23*Pi/64] + Cos[23*Pi/64])/2 = 0.6657721932768628 */
  /* 3903/4096 = (Sin[23*Pi/64] - Cos[23*Pi/64])*2 = 0.9528683993863225 */
  /* 7005/8192 = Cos[23*Pi/64]*2                   = 0.8551101868605642 */
  od_rotate_add_half(s4, sb, s4h, 2727, 12, 3903, 12, 7005, 13, SHIFT);

  /* 5619/8192 = (Sin[21*Pi/64] + Cos[21*Pi/64])/2 = 0.6859156770967569 */
  /* 2815/4096 = (Sin[21*Pi/64] - Cos[21*Pi/64])*2 = 0.6872517316141069 */
  /* 8423/8192 = Cos[21*Pi/64]*2                   = 1.0282054883864433 */
  od_rotate_sub_half(sa, s5, sah, 5619, 13, 2815, 12, 8423, 13, SHIFT);

  /*   2865/4096 = (Sin[19*Pi/64] + Cos[19*Pi/64])/2 = 0.6994534179865391 */
  /* 13588/32768 = (Sin[19*Pi/64] - Cos[19*Pi/64])*2 = 0.4150164539764232 */
  /*     305/256 = Cos[19*Pi/64]*2                   = 1.1913986089848667 */
  od_rotate_add_half(s6, s9, s6h, 2865, 12, 13599, 15, 305, 8, SHIFT);

  /* 23143/32768 = (Sin[17*Pi/64] + Cos[17*Pi/64])/2 = 0.7062550401009887 */
  /*   1137/8192 = (Sin[17*Pi/64] - Cos[17*Pi/64])*2 = 0.1387843410158816 */
  /* 44011/32768 = Cos[17*Pi/64]*2                   = 1.3431179096940367 */
  od_rotate_sub_half(s8, s7, s8h, 23143, 15, 1137, 13, 44011, 15, SHIFT);

  /* Stage 1 */

  od_butterfly_sub_asym(s0, od_rshift1(*s0), s7);
  od_butterfly_sub_asym(s8, od_rshift1(*s8), sf);
  od_butterfly_add_asym(s4, od_rshift1(*s4), s3);
  od_butterfly_add_asym(sc, od_rshift1(*sc), sb);
  od_butterfly_sub_asym(s2, od_rshift1(*s2), s5);
  od_butterfly_sub_asym(sa, od_rshift1(*sa), sd);
  od_butterfly_add_asym(s6, od_rshift1(*s6), s1);
  od_butterfly_add_asym(se, od_rshift1(*se), s9);

  /* Stage 2 */

  od_butterfly_add(s8, NULL, s4);
  od_butterfly_add(s7, NULL, sb);
  od_butterfly_sub(sa, NULL, s6);
  od_butterfly_sub(s5, NULL, s9);
  od_butterfly_add(s0, &s0h, s3);
  od_butterfly_add(sd, &sdh, se);
  od_butterfly_sub(s2, &s2h, s1);
  od_butterfly_sub(sf, &sfh, sc);

  /* Stage 3 */

  /*   9633/8192 = Sin[7*Pi/16] + Cos[7*Pi/16] = 1.1758756024193586 */
  /* 12873/16384 = Sin[7*Pi/16] - Cos[7*Pi/16] = 0.7856949583871022 */
  /*  6393/32768 = Cos[7*Pi/16]                = 0.1950903220161283 */
  od_rotate_add(s8, s7, 9633, 13, 12873, 14, 6393, 15, NONE);

  /* 45451/32768 = Sin[5*Pi/16] + Cos[5*Pi/16] = 1.3870398453221475 */
  /*  9041/32768 = Sin[5*Pi/16] - Cos[5*Pi/16] = 0.2758993792829431 */
  /* 18205/32768 = Cos[5*Pi/16]                = 0.5555702330196022 */
  od_rotate_add(s9, s6, 45451, 15, 9041, 15, 18205, 15, NONE);

  /*  11363/8192 = Sin[5*Pi/16] + Cos[5*Pi/16] = 1.3870398453221475 */
  /*  9041/32768 = Sin[5*Pi/16] - Cos[5*Pi/16] = 0.2758993792829431 */
  /*   4551/8192 = Cos[5*Pi/16]                = 0.5555702330196022 */
  od_rotate_neg(s5, sa, 11363, 13, 9041, 15, 4551, 13);

  /*  9633/32768 = Sin[7*Pi/16] + Cos[7*Pi/16] = 1.1758756024193586 */
  /* 12873/16384 = Sin[7*Pi/16] - Cos[7*Pi/16] = 0.7856949583871022 */
  /*  6393/32768 = Cos[7*Pi/16]                = 0.1950903220161283 */
  od_rotate_neg(s4, sb, 9633, 13, 12873, 14, 6393, 15);

  /* Stage 4 */

  od_butterfly_add_asym(s2, s2h, sc);
  od_butterfly_sub_asym(s0, s0h, s1);
  od_butterfly_add_asym(sf, sfh, se);
  od_butterfly_add_asym(sd, sdh, s3);
  od_butterfly_add_asym(s7, od_rshift1(*s7), s6);
  od_butterfly_sub_asym(s8, od_rshift1(*s8), s9);
  od_butterfly_sub_asym(sa, od_rshift1(*sa), sb);
  od_butterfly_add_asym(s5, od_rshift1(*s5), s4);

  /* Stage 5 */

  /*  10703/8192 = Sin[3*Pi/8] + Cos[3*Pi/8] = 1.3065629648763766 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8] = 0.5411961001461969 */
  /*   3135/8192 = Cos[7*Pi/8]               = 0.3826834323650898 */
  od_rotate_add(sc, s3, 10703, 13, 8867, 14, 3135, 13, NONE);

  /*  10703/8192 = Sin[3*Pi/8] + Cos[3*Pi/8] = 1.3870398453221475 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8] = 0.5411961001461969 */
  /*   3135/8192 = Cos[3*Pi/8]               = 0.3826834323650898 */
  od_rotate_neg(s2, sd, 10703, 13, 8867, 14, 3135, 13);

  /*  11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/16384 = Cos[Pi/4]             = 0.7071067811865475 */
  od_rotate_pi4_add(sa, s5, 11585, 13, 11585, 14);

  /*  11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/16384 = Cos[Pi/4]             = 0.7071067811865475 */
  od_rotate_pi4_add(s6, s9, 11585, 13, 11585, 14);

  /*  11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/16384 = Cos[Pi/4]             = 0.7071067811865475 */
  od_rotate_pi4_add(se, s1, 11585, 13, 11585, 14);
}

/**
 * 16-point asymmetric Type-IV iDST
 */
static INLINE void od_idst_16_asym(od_coeff *s0, od_coeff *s8,
                                   od_coeff *s4, od_coeff *sc,
                                   od_coeff *s2, od_coeff *sa,
                                   od_coeff *s6, od_coeff *se,
                                   od_coeff *s1, od_coeff *s9,
                                   od_coeff *s5, od_coeff *sd,
                                   od_coeff *s3, od_coeff *sb,
                                   od_coeff *s7, od_coeff *sf) {
  od_coeff s0h;
  od_coeff s2h;
  od_coeff s4h;
  od_coeff s6h;
  od_coeff s8h;
  od_coeff sah;
  od_coeff sch;
  od_coeff sdh;
  od_coeff seh;
  od_coeff sfh;

  /* Stage 5 */

  /*  11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/16384 = Cos[Pi/4]           = 0.7071067811865475 */
  od_rotate_pi4_add(s6, s9, 11585, 13, 11585, 14);

  /*  11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/16384 = 2*Cos[Pi/4]           = 0.7071067811865475 */
  od_rotate_pi4_add(sa, s5, 11585, 13, 11585, 14);

  /*  11585/8192 = Sin[Pi/4] + Cos[Pi/4] = 1.4142135623730951 */
  /* 11585/16384 = 2*Cos[Pi/4]           = 0.7071067811865475 */
  od_rotate_pi4_add(se, s1, 11585, 13, 11585, 14);

  /*  10703/8192 = Sin[3*Pi/8] + Cos[3*Pi/8] = 1.3065629648763766 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8] = 0.5411961001461969 */
  /*   3135/8192 = Cos[7*Pi/8]               = 0.7653668647301796 */
  od_rotate_add(sc, s3, 10703, 13, 8867, 14, 3135, 13, NONE);

  /*  10703/8192 = Sin[3*Pi/8] + Cos[3*Pi/8] = 1.3870398453221475 */
  /*  8867/16384 = Sin[3*Pi/8] - Cos[3*Pi/8] = 0.5411961001461969 */
  /*   3135/8192 = Cos[3*Pi/8]               = 0.7653668647301796 */
  od_rotate_neg(sd, s2, 10703, 13, 8867, 14, 3135, 13);

  /* Stage 4 */

  od_butterfly_add(s5, NULL, s4);
  od_butterfly_sub(sa, NULL, sb);
  od_butterfly_sub(s8, NULL, s9);
  od_butterfly_add(s7, NULL, s6);
  od_butterfly_add(sd, &sdh, s3);
  od_butterfly_add(sf, &sfh, se);
  od_butterfly_sub(s0, &s0h, s1);
  od_butterfly_add(s2, &s2h, sc);

  /* Stage 3 */

  /*   9633/8192 = Sin[7*Pi/16] + Cos[7*Pi/16] = 1.1758756024193586 */
  /* 12873/16384 = Sin[7*Pi/16] - Cos[7*Pi/16] = 0.7856949583871022 */
  /*  6393/32768 = Cos[7*Pi/16]                = 0.1950903220161283 */
  od_rotate_neg(sb, s4, 9633, 13, 12873, 14, 6393, 15);

  /*  11363/8192 = Sin[5*Pi/16] + Cos[5*Pi/16] = 1.3870398453221475 */
  /*  9041/32768 = Sin[5*Pi/16] - Cos[5*Pi/16] = 0.2758993792829431 */
  /*   4551/8192 = Cos[5*Pi/16]                = 0.5555702330196022 */
  od_rotate_neg(sa, s5, 11363, 13, 9041, 15, 4551, 13);

  /* 22725/16384 = Sin[5*Pi/16] + Cos[5*Pi/16] = 1.3870398453221475 */
  /*  9041/32768 = Sin[5*Pi/16] - Cos[5*Pi/16] = 0.2758993792829431 */
  /* 18205/32768 = Cos[5*Pi/16]                = 0.5555702330196022 */
  od_rotate_add(s9, s6, 22725, 14, 9041, 15, 18205, 15, NONE);

  /*   9633/8192 = Sin[7*Pi/16] + Cos[7*Pi/16] = 1.1758756024193586 */
  /* 12873/16384 = Sin[7*Pi/16] - Cos[7*Pi/16] = 0.7856949583871022 */
  /*  6393/32768 = Cos[7*Pi/16]                = 0.1950903220161283 */
  od_rotate_add(s8, s7, 9633, 13, 12873, 14, 6393, 15, NONE);

  /* Stage 2 */

  od_butterfly_add_asym(s8, od_rshift1(*s8), s4);
  od_butterfly_add_asym(s7, od_rshift1(*s7), sb);
  od_butterfly_sub_asym(sa, od_rshift1(*sa), s6);
  od_butterfly_sub_asym(s5, od_rshift1(*s5), s9);
  od_butterfly_add_asym(s0, s0h, s3);
  od_butterfly_add_asym(sd, sdh, se);
  od_butterfly_sub_asym(s2, s2h, s1);
  od_butterfly_sub_asym(sf, sfh, sc);

  /* Stage 1 */

  od_butterfly_sub(s0, &s0h, s7);
  od_butterfly_sub(s8, &s8h, sf);
  od_butterfly_add(s4, &s4h, s3);
  od_butterfly_add(sc, &sch, sb);
  od_butterfly_sub(s2, &s2h, s5);
  od_butterfly_sub(sa, &sah, sd);
  od_butterfly_add(s6, &s6h, s1);
  od_butterfly_add(se, &seh, s9);

  /* Stage 0 */

  /* 23143/32768 = (Sin[17*Pi/64] + Cos[17*Pi/64])/2 = 0.7062550401009887 */
  /*   1137/8192 = (Sin[17*Pi/64] - Cos[17*Pi/64])*2 = 0.1387843410158816 */
  /* 44011/32768 = Cos[17*Pi/64]*2                   = 1.3431179096940367 */
  od_rotate_sub_half(s8, s7, s8h, 23143, 15, 1137, 13, 44011, 15, SHIFT);

  /*   2865/4096 = (Sin[19*Pi/64] + Cos[19*Pi/64])/2 = 0.6994534179865391 */
  /* 13599/32768 = (Sin[19*Pi/64] - Cos[19*Pi/64])*2 = 0.4150164539764232 */
  /*     305/256 = Cos[19*Pi/64]*2                   = 1.1913986089848667 */
  od_rotate_add_half(s6, s9, s6h, 2865, 12, 13599, 15, 305, 8, SHIFT);

  /* 5619/8192 = (Sin[21*Pi/64] + Cos[21*Pi/64])/2 = 0.6859156770967569 */
  /* 2815/4096 = (Sin[21*Pi/64] - Cos[21*Pi/64])*2 = 0.6872517316141069 */
  /* 8423/8192 = Cos[21*Pi/64]*2                   = 1.0282054883864433 */
  od_rotate_sub_half(sa, s5, sah, 5619, 13, 2815, 12, 8423, 13, SHIFT);

  /* 2727/4096 = (Sin[23*Pi/64] + Cos[23*Pi/64])/2 = 0.6657721932768628 */
  /* 3903/4096 = (Sin[23*Pi/64] - Cos[23*Pi/64])*2 = 0.9528683993863225 */
  /* 7005/8192 = Cos[23*Pi/64]*2                   = 0.8551101868605642 */
  od_rotate_add_half(s4, sb, s4h, 2727, 12, 3903, 12, 7005, 13, SHIFT);

  /* 10473/16384 = (Sin[25*Pi/64] + Cos[25*Pi/64])/2 = 0.6392169592876205 */
  /* 39627/32768 = (Sin[25*Pi/64] - Cos[25*Pi/64])*2 = 1.2093084235816014 */
  /* 11039/16384 = Cos[25*Pi/64]*2                   = 0.6737797067844401 */
  od_rotate_sub_half(sc, s3, sch, 10473, 14, 39627, 15, 11039, 14, SHIFT);

  /*  9937/16384 = (Sin[27*Pi/64] + Cos[27*Pi/64])/2 = 0.6065057165489039 */
  /*   1489/1024 = (Sin[27*Pi/64] - Cos[27*Pi/64])*2 = 1.4541021465825602 */
  /*   3981/8192 = Cos[27*Pi/64]*2                   = 0.4859603598065277 */
  od_rotate_add_half(s2, sd, s2h, 9937, 14, 1489, 10, 3981, 13, SHIFT);

  /* 18611/32768 = (Sin[29*Pi/64] + Cos[29*Pi/64])/2 = 0.5679534922100714 */
  /* 55211/32768 = (Sin[29*Pi/64] - Cos[29*Pi/64])*2 = 1.6848920710188384 */
  /*    601/2048 = Cos[29*Pi/64]*2                   = 0.2934609489107235 */
  od_rotate_sub_half(se, s1, seh, 18611, 15, 55211, 15, 601, 11, SHIFT);

  /*   1073/2048 = (Sin[31*Pi/64] + Cos[31*Pi/64])/2 = 0.5239315652662953 */
  /* 62241/32768 = (Sin[31*Pi/64] - Cos[31*Pi/64])*2 = 1.8994555637555088 */
  /*    201/2048 = Cos[31*Pi/64]*2                   = 0.0981353486548360 */
  od_rotate_add_half(s0, sf, s0h, 1073, 11, 62241, 15, 201, 11, SHIFT);
}

/* --- 32-point Transforms --- */

/**
 * 32-point orthonormal Type-II fDCT
 */
static INLINE void od_fdct_32(od_coeff *t0, od_coeff *t1,
                              od_coeff *t2, od_coeff *t3,
                              od_coeff *t4, od_coeff *t5,
                              od_coeff *t6, od_coeff *t7,
                              od_coeff *t8, od_coeff *t9,
                              od_coeff *ta, od_coeff *tb,
                              od_coeff *tc, od_coeff *td,
                              od_coeff *te, od_coeff *tf,
                              od_coeff *tg, od_coeff *th,
                              od_coeff *ti, od_coeff *tj,
                              od_coeff *tk, od_coeff *tl,
                              od_coeff *tm, od_coeff *tn,
                              od_coeff *to, od_coeff *tp,
                              od_coeff *tq, od_coeff *tr,
                              od_coeff *ts, od_coeff *tt,
                              od_coeff *tu, od_coeff *tv) {
  od_coeff t1h;
  od_coeff t3h;
  od_coeff t5h;
  od_coeff t7h;
  od_coeff t9h;
  od_coeff tbh;
  od_coeff tdh;
  od_coeff tfh;
  od_coeff thh;
  od_coeff tjh;
  od_coeff tlh;
  od_coeff tnh;
  od_coeff tph;
  od_coeff trh;
  od_coeff tth;
  od_coeff tvh;

  /* +/- Butterflies with asymmetric output. */
  od_butterfly_neg(t0, tv, &tvh);
  od_butterfly_add(t1, &t1h, tu);
  od_butterfly_neg(t2, tt, &tth);
  od_butterfly_add(t3, &t3h, ts);
  od_butterfly_neg(t4, tr, &trh);
  od_butterfly_add(t5, &t5h, tq);
  od_butterfly_neg(t6, tp, &tph);
  od_butterfly_add(t7, &t7h, to);
  od_butterfly_neg(t8, tn, &tnh);
  od_butterfly_add(t9, &t9h, tm);
  od_butterfly_neg(ta, tl, &tlh);
  od_butterfly_add(tb, &tbh, tk);
  od_butterfly_neg(tc, tj, &tjh);
  od_butterfly_add(td, &tdh, ti);
  od_butterfly_neg(te, th, &thh);
  od_butterfly_add(tf, &tfh, tg);

  /* Embedded 16-point transforms with asymmetric input. */
  od_fdct_16_asym(
   t0, t1, t1h, t2, t3, t3h, t4, t5, t5h, t6, t7, t7h,
   t8, t9, t9h, ta, tb, tbh, tc, td, tdh, te, tf, tfh);
  od_fdst_16_asym(
   tv, tvh, tu, tt, tth, ts, tr, trh, tq, tp, tph, to,
   tn, tnh, tm, tl, tlh, tk, tj, tjh, ti, th, thh, tg);
}

/**
 * 32-point orthonormal Type-II iDCT
 */
static INLINE void od_idct_32(od_coeff *t0, od_coeff *tg,
                              od_coeff *t8, od_coeff *to,
                              od_coeff *t4, od_coeff *tk,
                              od_coeff *tc, od_coeff *ts,
                              od_coeff *t2, od_coeff *ti,
                              od_coeff *ta, od_coeff *tq,
                              od_coeff *t6, od_coeff *tm,
                              od_coeff *te, od_coeff *tu,
                              od_coeff *t1, od_coeff *th,
                              od_coeff *t9, od_coeff *tp,
                              od_coeff *t5, od_coeff *tl,
                              od_coeff *td, od_coeff *tt,
                              od_coeff *t3, od_coeff *tj,
                              od_coeff *tb, od_coeff *tr,
                              od_coeff *t7, od_coeff *tn,
                              od_coeff *tf, od_coeff *tv) {
  od_coeff t1h;
  od_coeff t3h;
  od_coeff t5h;
  od_coeff t7h;
  od_coeff t9h;
  od_coeff tbh;
  od_coeff tdh;
  od_coeff tfh;

  /* Embedded 16-point transforms with asymmetric output. */
  od_idst_16_asym(
   tv, tn, tr, tj, tt, tl, tp, th, 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);

  /* +/- Butterflies with asymmetric input. */
  od_butterfly_add_asym(tf, tfh, tg);
  od_butterfly_neg_asym(te, th, od_rshift1(*th));
  od_butterfly_add_asym(td, tdh, ti);
  od_butterfly_neg_asym(tc, tj, od_rshift1(*tj));
  od_butterfly_add_asym(tb, tbh, tk);
  od_butterfly_neg_asym(ta, tl, od_rshift1(*tl));
  od_butterfly_add_asym(t9, t9h, tm);
  od_butterfly_neg_asym(t8, tn, od_rshift1(*tn));
  od_butterfly_add_asym(t7, t7h, to);
  od_butterfly_neg_asym(t6, tp, od_rshift1(*tp));
  od_butterfly_add_asym(t5, t5h, tq);
  od_butterfly_neg_asym(t4, tr, od_rshift1(*tr));
  od_butterfly_add_asym(t3, t3h, ts);
  od_butterfly_neg_asym(t2, tt, od_rshift1(*tt));
  od_butterfly_add_asym(t1, t1h, tu);
  od_butterfly_neg_asym(t0, tv, od_rshift1(*tv));
}

#endif