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mpv/video/csputils.c
Kacper Michajłow 05c8d5a93a csputils: add missing PL_COLOR_SYSTEM names
2024-03-09 05:58:52 +00:00

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/*
* Common code related to colorspaces and conversion
*
* Copyleft (C) 2009 Reimar Döffinger <Reimar.Doeffinger@gmx.de>
*
* This file is part of mpv.
*
* mpv is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* mpv is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with mpv. If not, see <http://www.gnu.org/licenses/>.
*/
#include <stdint.h>
#include <math.h>
#include <assert.h>
#include <libavutil/common.h>
#include <libavcodec/avcodec.h>
#include "mp_image.h"
#include "csputils.h"
#include "options/m_config.h"
#include "options/m_option.h"
const struct m_opt_choice_alternatives pl_csp_names[] = {
{"auto", PL_COLOR_SYSTEM_UNKNOWN},
{"bt.601", PL_COLOR_SYSTEM_BT_601},
{"bt.709", PL_COLOR_SYSTEM_BT_709},
{"smpte-240m", PL_COLOR_SYSTEM_SMPTE_240M},
{"bt.2020-ncl", PL_COLOR_SYSTEM_BT_2020_NC},
{"bt.2020-cl", PL_COLOR_SYSTEM_BT_2020_C},
{"bt.2100-pq", PL_COLOR_SYSTEM_BT_2100_PQ},
{"bt.2100-hlg", PL_COLOR_SYSTEM_BT_2100_HLG},
{"dolbyvision", PL_COLOR_SYSTEM_DOLBYVISION},
{"rgb", PL_COLOR_SYSTEM_RGB},
{"xyz", PL_COLOR_SYSTEM_XYZ},
{"ycgco", PL_COLOR_SYSTEM_YCGCO},
{0}
};
const struct m_opt_choice_alternatives pl_csp_levels_names[] = {
{"auto", PL_COLOR_LEVELS_UNKNOWN},
{"limited", PL_COLOR_LEVELS_LIMITED},
{"full", PL_COLOR_LEVELS_FULL},
{0}
};
const struct m_opt_choice_alternatives pl_csp_prim_names[] = {
{"auto", PL_COLOR_PRIM_UNKNOWN},
{"bt.601-525", PL_COLOR_PRIM_BT_601_525},
{"bt.601-625", PL_COLOR_PRIM_BT_601_625},
{"bt.709", PL_COLOR_PRIM_BT_709},
{"bt.2020", PL_COLOR_PRIM_BT_2020},
{"bt.470m", PL_COLOR_PRIM_BT_470M},
{"apple", PL_COLOR_PRIM_APPLE},
{"adobe", PL_COLOR_PRIM_ADOBE},
{"prophoto", PL_COLOR_PRIM_PRO_PHOTO},
{"cie1931", PL_COLOR_PRIM_CIE_1931},
{"dci-p3", PL_COLOR_PRIM_DCI_P3},
{"display-p3", PL_COLOR_PRIM_DISPLAY_P3},
{"v-gamut", PL_COLOR_PRIM_V_GAMUT},
{"s-gamut", PL_COLOR_PRIM_S_GAMUT},
{"ebu3213", PL_COLOR_PRIM_EBU_3213},
{"film-c", PL_COLOR_PRIM_FILM_C},
{"aces-ap0", PL_COLOR_PRIM_ACES_AP0},
{"aces-ap1", PL_COLOR_PRIM_ACES_AP1},
{0}
};
const struct m_opt_choice_alternatives pl_csp_trc_names[] = {
{"auto", PL_COLOR_TRC_UNKNOWN},
{"bt.1886", PL_COLOR_TRC_BT_1886},
{"srgb", PL_COLOR_TRC_SRGB},
{"linear", PL_COLOR_TRC_LINEAR},
{"gamma1.8", PL_COLOR_TRC_GAMMA18},
{"gamma2.0", PL_COLOR_TRC_GAMMA20},
{"gamma2.2", PL_COLOR_TRC_GAMMA22},
{"gamma2.4", PL_COLOR_TRC_GAMMA24},
{"gamma2.6", PL_COLOR_TRC_GAMMA26},
{"gamma2.8", PL_COLOR_TRC_GAMMA28},
{"prophoto", PL_COLOR_TRC_PRO_PHOTO},
{"pq", PL_COLOR_TRC_PQ},
{"hlg", PL_COLOR_TRC_HLG},
{"v-log", PL_COLOR_TRC_V_LOG},
{"s-log1", PL_COLOR_TRC_S_LOG1},
{"s-log2", PL_COLOR_TRC_S_LOG2},
{"st428", PL_COLOR_TRC_ST428},
{0}
};
const struct m_opt_choice_alternatives mp_csp_light_names[] = {
{"auto", MP_CSP_LIGHT_AUTO},
{"display", MP_CSP_LIGHT_DISPLAY},
{"hlg", MP_CSP_LIGHT_SCENE_HLG},
{"709-1886", MP_CSP_LIGHT_SCENE_709_1886},
{"gamma1.2", MP_CSP_LIGHT_SCENE_1_2},
{0}
};
const struct m_opt_choice_alternatives pl_chroma_names[] = {
{"unknown", PL_CHROMA_UNKNOWN},
{"uhd", PL_CHROMA_TOP_LEFT},
{"mpeg2/4/h264",PL_CHROMA_LEFT},
{"mpeg1/jpeg", PL_CHROMA_CENTER},
{"top", PL_CHROMA_TOP_CENTER},
{"bottom left", PL_CHROMA_BOTTOM_LEFT},
{"bottom", PL_CHROMA_BOTTOM_CENTER},
{0}
};
const struct m_opt_choice_alternatives pl_alpha_names[] = {
{"auto", PL_ALPHA_UNKNOWN},
{"straight", PL_ALPHA_INDEPENDENT},
{"premul", PL_ALPHA_PREMULTIPLIED},
{0}
};
// The short name _must_ match with what vf_stereo3d accepts (if supported).
// The long name in comments is closer to the Matroska spec (StereoMode element).
// The numeric index matches the Matroska StereoMode value. If you add entries
// that don't match Matroska, make sure demux_mkv.c rejects them properly.
const struct m_opt_choice_alternatives mp_stereo3d_names[] = {
{"no", -1}, // disable/invalid
{"mono", 0},
{"sbs2l", 1}, // "side_by_side_left"
{"ab2r", 2}, // "top_bottom_right"
{"ab2l", 3}, // "top_bottom_left"
{"checkr", 4}, // "checkboard_right" (unsupported by vf_stereo3d)
{"checkl", 5}, // "checkboard_left" (unsupported by vf_stereo3d)
{"irr", 6}, // "row_interleaved_right"
{"irl", 7}, // "row_interleaved_left"
{"icr", 8}, // "column_interleaved_right" (unsupported by vf_stereo3d)
{"icl", 9}, // "column_interleaved_left" (unsupported by vf_stereo3d)
{"arcc", 10}, // "anaglyph_cyan_red" (Matroska: unclear which mode)
{"sbs2r", 11}, // "side_by_side_right"
{"agmc", 12}, // "anaglyph_green_magenta" (Matroska: unclear which mode)
{"al", 13}, // "alternating frames left first"
{"ar", 14}, // "alternating frames right first"
{0}
};
enum pl_color_system mp_csp_guess_colorspace(int width, int height)
{
return width >= 1280 || height > 576 ? PL_COLOR_SYSTEM_BT_709 : PL_COLOR_SYSTEM_BT_601;
}
enum pl_color_primaries mp_csp_guess_primaries(int width, int height)
{
// HD content
if (width >= 1280 || height > 576)
return PL_COLOR_PRIM_BT_709;
switch (height) {
case 576: // Typical PAL content, including anamorphic/squared
return PL_COLOR_PRIM_BT_601_625;
case 480: // Typical NTSC content, including squared
case 486: // NTSC Pro or anamorphic NTSC
return PL_COLOR_PRIM_BT_601_525;
default: // No good metric, just pick BT.709 to minimize damage
return PL_COLOR_PRIM_BT_709;
}
}
// LMS<-XYZ revised matrix from CIECAM97, based on a linear transform and
// normalized for equal energy on monochrome inputs
static const pl_matrix3x3 m_cat97 = {{
{ 0.8562, 0.3372, -0.1934 },
{ -0.8360, 1.8327, 0.0033 },
{ 0.0357, -0.0469, 1.0112 },
}};
// M := M * XYZd<-XYZs
static void apply_chromatic_adaptation(struct pl_cie_xy src,
struct pl_cie_xy dest, pl_matrix3x3 *mat)
{
// If the white points are nearly identical, this is a wasteful identity
// operation.
if (fabs(src.x - dest.x) < 1e-6 && fabs(src.y - dest.y) < 1e-6)
return;
// XYZd<-XYZs = Ma^-1 * (I*[Cd/Cs]) * Ma
// http://www.brucelindbloom.com/index.html?Eqn_ChromAdapt.html
// For Ma, we use the CIECAM97 revised (linear) matrix
float C[3][2];
for (int i = 0; i < 3; i++) {
// source cone
C[i][0] = m_cat97.m[i][0] * pl_cie_X(src)
+ m_cat97.m[i][1] * 1
+ m_cat97.m[i][2] * pl_cie_Z(src);
// dest cone
C[i][1] = m_cat97.m[i][0] * pl_cie_X(dest)
+ m_cat97.m[i][1] * 1
+ m_cat97.m[i][2] * pl_cie_Z(dest);
}
// tmp := I * [Cd/Cs] * Ma
pl_matrix3x3 tmp = {0};
for (int i = 0; i < 3; i++)
tmp.m[i][i] = C[i][1] / C[i][0];
pl_matrix3x3_mul(&tmp, &m_cat97);
// M := M * Ma^-1 * tmp
pl_matrix3x3 ma_inv = m_cat97;
pl_matrix3x3_invert(&ma_inv);
pl_matrix3x3_mul(mat, &ma_inv);
pl_matrix3x3_mul(mat, &tmp);
}
// Get multiplication factor required if image data is fit within the LSBs of a
// higher smaller bit depth fixed-point texture data.
// This is broken. Use mp_get_csp_uint_mul().
double mp_get_csp_mul(enum pl_color_system csp, int input_bits, int texture_bits)
{
assert(texture_bits >= input_bits);
// Convenience for some irrelevant cases, e.g. rgb565 or disabling expansion.
if (!input_bits)
return 1;
// RGB always uses the full range available.
if (csp == PL_COLOR_SYSTEM_RGB)
return ((1LL << input_bits) - 1.) / ((1LL << texture_bits) - 1.);
if (csp == PL_COLOR_SYSTEM_XYZ)
return 1;
// High bit depth YUV uses a range shifted from 8 bit.
return (1LL << input_bits) / ((1LL << texture_bits) - 1.) * 255 / 256;
}
// Return information about color fixed point representation.his is needed for
// converting color from integer formats to or from float. Use as follows:
// float_val = uint_val * m + o
// uint_val = clamp(round((float_val - o) / m))
// See H.264/5 Annex E.
// csp: colorspace
// levels: full range flag
// component: ID of the channel, as in mp_regular_imgfmt:
// 1 is red/luminance/gray, 2 is green/Cb, 3 is blue/Cr, 4 is alpha.
// bits: number of significant bits, e.g. 10 for yuv420p10, 16 for p010
// out_m: returns factor to multiply the uint number with
// out_o: returns offset to add after multiplication
void mp_get_csp_uint_mul(enum pl_color_system csp, enum pl_color_levels levels,
int bits, int component, double *out_m, double *out_o)
{
uint16_t i_min = 0;
uint16_t i_max = (1u << bits) - 1;
double f_min = 0; // min. float value
if (csp != PL_COLOR_SYSTEM_RGB && component != 4) {
if (component == 2 || component == 3) {
f_min = (1u << (bits - 1)) / -(double)i_max; // force center => 0
if (levels != PL_COLOR_LEVELS_FULL && bits >= 8) {
i_min = 16 << (bits - 8); // => -0.5
i_max = 240 << (bits - 8); // => 0.5
f_min = -0.5;
}
} else {
if (levels != PL_COLOR_LEVELS_FULL && bits >= 8) {
i_min = 16 << (bits - 8); // => 0
i_max = 235 << (bits - 8); // => 1
}
}
}
*out_m = 1.0 / (i_max - i_min);
*out_o = (1 + f_min) - i_max * *out_m;
}
/* Fill in the Y, U, V vectors of a yuv-to-rgb conversion matrix
* based on the given luma weights of the R, G and B components (lr, lg, lb).
* lr+lg+lb is assumed to equal 1.
* This function is meant for colorspaces satisfying the following
* conditions (which are true for common YUV colorspaces):
* - The mapping from input [Y, U, V] to output [R, G, B] is linear.
* - Y is the vector [1, 1, 1]. (meaning input Y component maps to 1R+1G+1B)
* - U maps to a value with zero R and positive B ([0, x, y], y > 0;
* i.e. blue and green only).
* - V maps to a value with zero B and positive R ([x, y, 0], x > 0;
* i.e. red and green only).
* - U and V are orthogonal to the luma vector [lr, lg, lb].
* - The magnitudes of the vectors U and V are the minimal ones for which
* the image of the set Y=[0...1],U=[-0.5...0.5],V=[-0.5...0.5] under the
* conversion function will cover the set R=[0...1],G=[0...1],B=[0...1]
* (the resulting matrix can be converted for other input/output ranges
* outside this function).
* Under these conditions the given parameters lr, lg, lb uniquely
* determine the mapping of Y, U, V to R, G, B.
*/
static void luma_coeffs(struct pl_transform3x3 *mat, float lr, float lg, float lb)
{
assert(fabs(lr+lg+lb - 1) < 1e-6);
*mat = (struct pl_transform3x3) {
{ {{1, 0, 2 * (1-lr) },
{1, -2 * (1-lb) * lb/lg, -2 * (1-lr) * lr/lg },
{1, 2 * (1-lb), 0 }} },
// Constant coefficients (mat->c) not set here
};
}
// get the coefficients of the yuv -> rgb conversion matrix
void mp_get_csp_matrix(struct mp_csp_params *params, struct pl_transform3x3 *m)
{
enum pl_color_system colorspace = params->repr.sys;
if (colorspace <= PL_COLOR_SYSTEM_UNKNOWN || colorspace >= PL_COLOR_SYSTEM_COUNT)
colorspace = PL_COLOR_SYSTEM_BT_601;
// Not supported. TODO: replace with pl_color_repr_decode
if (colorspace == PL_COLOR_SYSTEM_BT_2100_PQ ||
colorspace == PL_COLOR_SYSTEM_BT_2100_HLG ||
colorspace == PL_COLOR_SYSTEM_DOLBYVISION) {
colorspace = PL_COLOR_SYSTEM_BT_2020_NC;
}
enum pl_color_levels levels_in = params->repr.levels;
if (levels_in <= PL_COLOR_LEVELS_UNKNOWN || levels_in >= PL_COLOR_LEVELS_COUNT)
levels_in = PL_COLOR_LEVELS_LIMITED;
switch (colorspace) {
case PL_COLOR_SYSTEM_BT_601: luma_coeffs(m, 0.299, 0.587, 0.114 ); break;
case PL_COLOR_SYSTEM_BT_709: luma_coeffs(m, 0.2126, 0.7152, 0.0722); break;
case PL_COLOR_SYSTEM_SMPTE_240M: luma_coeffs(m, 0.2122, 0.7013, 0.0865); break;
case PL_COLOR_SYSTEM_BT_2020_NC: luma_coeffs(m, 0.2627, 0.6780, 0.0593); break;
case PL_COLOR_SYSTEM_BT_2020_C: {
// Note: This outputs into the [-0.5,0.5] range for chroma information.
// If this clips on any VO, a constant 0.5 coefficient can be added
// to the chroma channels to normalize them into [0,1]. This is not
// currently needed by anything, though.
*m = (struct pl_transform3x3){{{{0, 0, 1}, {1, 0, 0}, {0, 1, 0}}}};
break;
}
case PL_COLOR_SYSTEM_RGB: {
*m = (struct pl_transform3x3){{{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}}};
levels_in = -1;
break;
}
case PL_COLOR_SYSTEM_XYZ: {
// For lack of anything saner to do, just assume the caller wants
// DCI-P3 primaries, which is a reasonable assumption.
const struct pl_raw_primaries *dst = pl_raw_primaries_get(PL_COLOR_PRIM_DCI_P3);
pl_matrix3x3 mat = pl_get_xyz2rgb_matrix(dst);
// DCDM X'Y'Z' is expected to have equal energy white point (EG 432-1 Annex H)
apply_chromatic_adaptation((struct pl_cie_xy){1.0/3.0, 1.0/3.0}, dst->white, &mat);
*m = (struct pl_transform3x3) { .mat = mat };
levels_in = -1;
break;
}
case PL_COLOR_SYSTEM_YCGCO: {
*m = (struct pl_transform3x3) {
{{{1, -1, 1},
{1, 1, 0},
{1, -1, -1}}},
};
break;
}
default:
MP_ASSERT_UNREACHABLE();
};
if (params->is_float)
levels_in = -1;
if ((colorspace == PL_COLOR_SYSTEM_BT_601 || colorspace == PL_COLOR_SYSTEM_BT_709 ||
colorspace == PL_COLOR_SYSTEM_SMPTE_240M || colorspace == PL_COLOR_SYSTEM_BT_2020_NC))
{
// Hue is equivalent to rotating input [U, V] subvector around the origin.
// Saturation scales [U, V].
float huecos = params->gray ? 0 : params->saturation * cos(params->hue);
float huesin = params->gray ? 0 : params->saturation * sin(params->hue);
for (int i = 0; i < 3; i++) {
float u = m->mat.m[i][1], v = m->mat.m[i][2];
m->mat.m[i][1] = huecos * u - huesin * v;
m->mat.m[i][2] = huesin * u + huecos * v;
}
}
// The values below are written in 0-255 scale - thus bring s into range.
double s =
mp_get_csp_mul(colorspace, params->input_bits, params->texture_bits) / 255;
// NOTE: The yuvfull ranges as presented here are arguably ambiguous,
// and conflict with at least the full-range YCbCr/ICtCp values as defined
// by ITU-R BT.2100. If somebody ever complains about full-range YUV looking
// different from their reference display, this comment is probably why.
struct yuvlevels { double ymin, ymax, cmax, cmid; }
yuvlim = { 16*s, 235*s, 240*s, 128*s },
yuvfull = { 0*s, 255*s, 255*s, 128*s },
anyfull = { 0*s, 255*s, 255*s/2, 0 }, // cmax picked to make cmul=ymul
yuvlev;
switch (levels_in) {
case PL_COLOR_LEVELS_LIMITED: yuvlev = yuvlim; break;
case PL_COLOR_LEVELS_FULL: yuvlev = yuvfull; break;
case -1: yuvlev = anyfull; break;
default:
MP_ASSERT_UNREACHABLE();
}
int levels_out = params->levels_out;
if (levels_out <= PL_COLOR_LEVELS_UNKNOWN || levels_out >= PL_COLOR_LEVELS_COUNT)
levels_out = PL_COLOR_LEVELS_FULL;
struct rgblevels { double min, max; }
rgblim = { 16/255., 235/255. },
rgbfull = { 0, 1 },
rgblev;
switch (levels_out) {
case PL_COLOR_LEVELS_LIMITED: rgblev = rgblim; break;
case PL_COLOR_LEVELS_FULL: rgblev = rgbfull; break;
default:
MP_ASSERT_UNREACHABLE();
}
double ymul = (rgblev.max - rgblev.min) / (yuvlev.ymax - yuvlev.ymin);
double cmul = (rgblev.max - rgblev.min) / (yuvlev.cmax - yuvlev.cmid) / 2;
// Contrast scales the output value range (gain)
ymul *= params->contrast;
cmul *= params->contrast;
for (int i = 0; i < 3; i++) {
m->mat.m[i][0] *= ymul;
m->mat.m[i][1] *= cmul;
m->mat.m[i][2] *= cmul;
// Set c so that Y=umin,UV=cmid maps to RGB=min (black to black),
// also add brightness offset (black lift)
m->c[i] = rgblev.min - m->mat.m[i][0] * yuvlev.ymin
- (m->mat.m[i][1] + m->mat.m[i][2]) * yuvlev.cmid
+ params->brightness;
}
}
// Set colorspace related fields in p from f. Don't touch other fields.
void mp_csp_set_image_params(struct mp_csp_params *params,
const struct mp_image_params *imgparams)
{
struct mp_image_params p = *imgparams;
mp_image_params_guess_csp(&p); // ensure consistency
params->repr = p.repr;
params->color = p.color;
}
enum mp_csp_equalizer_param {
MP_CSP_EQ_BRIGHTNESS,
MP_CSP_EQ_CONTRAST,
MP_CSP_EQ_HUE,
MP_CSP_EQ_SATURATION,
MP_CSP_EQ_GAMMA,
MP_CSP_EQ_COUNT,
};
// Default initialization with 0 is enough, except for the capabilities field
struct mp_csp_equalizer_opts {
// Value for each property is in the range [-100.0, 100.0].
// 0.0 is default, meaning neutral or no change.
float values[MP_CSP_EQ_COUNT];
int output_levels;
};
#define OPT_BASE_STRUCT struct mp_csp_equalizer_opts
const struct m_sub_options mp_csp_equalizer_conf = {
.opts = (const m_option_t[]) {
{"brightness", OPT_FLOAT(values[MP_CSP_EQ_BRIGHTNESS]),
M_RANGE(-100, 100)},
{"saturation", OPT_FLOAT(values[MP_CSP_EQ_SATURATION]),
M_RANGE(-100, 100)},
{"contrast", OPT_FLOAT(values[MP_CSP_EQ_CONTRAST]),
M_RANGE(-100, 100)},
{"hue", OPT_FLOAT(values[MP_CSP_EQ_HUE]),
M_RANGE(-100, 100)},
{"gamma", OPT_FLOAT(values[MP_CSP_EQ_GAMMA]),
M_RANGE(-100, 100)},
{"video-output-levels",
OPT_CHOICE_C(output_levels, pl_csp_levels_names)},
{0}
},
.size = sizeof(struct mp_csp_equalizer_opts),
.change_flags = UPDATE_VIDEO,
};
// Copy settings from eq into params.
static void mp_csp_copy_equalizer_values(struct mp_csp_params *params,
const struct mp_csp_equalizer_opts *eq)
{
params->brightness = eq->values[MP_CSP_EQ_BRIGHTNESS] / 100.0;
params->contrast = (eq->values[MP_CSP_EQ_CONTRAST] + 100) / 100.0;
params->hue = eq->values[MP_CSP_EQ_HUE] / 100.0 * M_PI;
params->saturation = (eq->values[MP_CSP_EQ_SATURATION] + 100) / 100.0;
params->gamma = exp(log(8.0) * eq->values[MP_CSP_EQ_GAMMA] / 100.0);
params->levels_out = eq->output_levels;
}
struct mp_csp_equalizer_state *mp_csp_equalizer_create(void *ta_parent,
struct mpv_global *global)
{
struct m_config_cache *c = m_config_cache_alloc(ta_parent, global,
&mp_csp_equalizer_conf);
// The terrible, terrible truth.
return (struct mp_csp_equalizer_state *)c;
}
bool mp_csp_equalizer_state_changed(struct mp_csp_equalizer_state *state)
{
struct m_config_cache *c = (struct m_config_cache *)state;
return m_config_cache_update(c);
}
void mp_csp_equalizer_state_get(struct mp_csp_equalizer_state *state,
struct mp_csp_params *params)
{
struct m_config_cache *c = (struct m_config_cache *)state;
m_config_cache_update(c);
struct mp_csp_equalizer_opts *opts = c->opts;
mp_csp_copy_equalizer_values(params, opts);
}
// Multiply the color in c with the given matrix.
// i/o is {R, G, B} or {Y, U, V} (depending on input/output and matrix), using
// a fixed point representation with the given number of bits (so for bits==8,
// [0,255] maps to [0,1]). The output is clipped to the range as needed.
void mp_map_fixp_color(struct pl_transform3x3 *matrix, int ibits, int in[3],
int obits, int out[3])
{
for (int i = 0; i < 3; i++) {
double val = matrix->c[i];
for (int x = 0; x < 3; x++)
val += matrix->mat.m[i][x] * in[x] / ((1 << ibits) - 1);
int ival = lrint(val * ((1 << obits) - 1));
out[i] = av_clip(ival, 0, (1 << obits) - 1);
}
}
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