src/compiler/nir/nir_builtin_builder.c - platform/external/mesa3d - Git at Google

 /*
  * Copyright © 2018 Red Hat Inc.
  * Copyright © 2015 Intel Corporation
  *
  * Permission is hereby granted, free of charge, to any person obtaining a
  * copy of this software and associated documentation files (the "Software"),
  * to deal in the Software without restriction, including without limitation
  * the rights to use, copy, modify, merge, publish, distribute, sublicense,
  * and/or sell copies of the Software, and to permit persons to whom the
  * Software is furnished to do so, subject to the following conditions:
  *
  * The above copyright notice and this permission notice (including the next
  * paragraph) shall be included in all copies or substantial portions of the
  * Software.
  *
  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
  * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
  * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
  * IN THE SOFTWARE.
  */

 #include <math.h>

 #include "nir.h"
 #include "nir_builder.h"
 #include "nir_builtin_builder.h"

 nir_def *
 nir_cross3(nir_builder *b, nir_def *x, nir_def *y)
 {
    unsigned yzx[3] = { 1, 2, 0 };
    unsigned zxy[3] = { 2, 0, 1 };

    return nir_ffma(b, nir_swizzle(b, x, yzx, 3),
                    nir_swizzle(b, y, zxy, 3),
                    nir_fneg(b, nir_fmul(b, nir_swizzle(b, x, zxy, 3),
                                         nir_swizzle(b, y, yzx, 3))));
 }

 nir_def *
 nir_cross4(nir_builder *b, nir_def *x, nir_def *y)
 {
    nir_def *cross = nir_cross3(b, x, y);

    return nir_vec4(b,
                    nir_channel(b, cross, 0),
                    nir_channel(b, cross, 1),
                    nir_channel(b, cross, 2),
                    nir_imm_intN_t(b, 0, cross->bit_size));
 }

 nir_def *
 nir_fast_length(nir_builder *b, nir_def *vec)
 {
    return nir_fsqrt(b, nir_fdot(b, vec, vec));
 }

 nir_def *
 nir_nextafter(nir_builder *b, nir_def *x, nir_def *y)
 {
    nir_def *zero = nir_imm_intN_t(b, 0, x->bit_size);
    nir_def *one = nir_imm_intN_t(b, 1, x->bit_size);

    nir_def *condeq = nir_feq(b, x, y);
    nir_def *conddir = nir_flt(b, x, y);
    nir_def *condzero = nir_feq(b, x, zero);

    uint64_t sign_mask = 1ull << (x->bit_size - 1);
    uint64_t min_abs = 1;

    if (nir_is_denorm_flush_to_zero(b->shader->info.float_controls_execution_mode, x->bit_size)) {
       switch (x->bit_size) {
       case 16:
          min_abs = 1 << 10;
          break;
       case 32:
          min_abs = 1 << 23;
          break;
       case 64:
          min_abs = 1ULL << 52;
          break;
       }

       /* Flush denorm to zero to avoid returning a denorm when condeq is true. */
       x = nir_fmul_imm(b, x, 1.0);
    }

    /* beware of: +/-0.0 - 1 == NaN */
    nir_def *xn =
       nir_bcsel(b,
                 condzero,
                 nir_imm_intN_t(b, sign_mask | min_abs, x->bit_size),
                 nir_isub(b, x, one));

    /* beware of -0.0 + 1 == -0x1p-149 */
    nir_def *xp = nir_bcsel(b, condzero,
                            nir_imm_intN_t(b, min_abs, x->bit_size),
                            nir_iadd(b, x, one));

    /* nextafter can be implemented by just +/- 1 on the int value */
    nir_def *res =
       nir_bcsel(b, nir_ixor(b, conddir, nir_flt(b, x, zero)), xp, xn);

    return nir_nan_check2(b, x, y, nir_bcsel(b, condeq, x, res));
 }

 nir_def *
 nir_normalize(nir_builder *b, nir_def *vec)
 {
    if (vec->num_components == 1)
       return nir_fsign(b, vec);

    nir_def *f0 = nir_imm_floatN_t(b, 0.0, vec->bit_size);
    nir_def *f1 = nir_imm_floatN_t(b, 1.0, vec->bit_size);
    nir_def *finf = nir_imm_floatN_t(b, INFINITY, vec->bit_size);

    /* scale the input to increase precision */
    nir_def *maxc = nir_fmax_abs_vec_comp(b, vec);
    nir_def *svec = nir_fdiv(b, vec, maxc);
    /* for inf */
    nir_def *finfvec = nir_copysign(b, nir_bcsel(b, nir_feq(b, vec, finf), f1, f0), f1);

    nir_def *temp = nir_bcsel(b, nir_feq(b, maxc, finf), finfvec, svec);
    nir_def *res = nir_fmul(b, temp, nir_frsq(b, nir_fdot(b, temp, temp)));

    return nir_bcsel(b, nir_feq(b, maxc, f0), vec, res);
 }

 nir_def *
 nir_smoothstep(nir_builder *b, nir_def *edge0, nir_def *edge1, nir_def *x)
 {
    nir_def *f2 = nir_imm_floatN_t(b, 2.0, x->bit_size);
    nir_def *f3 = nir_imm_floatN_t(b, 3.0, x->bit_size);

    /* t = clamp((x - edge0) / (edge1 - edge0), 0, 1) */
    nir_def *t =
       nir_fsat(b, nir_fdiv(b, nir_fsub(b, x, edge0),
                            nir_fsub(b, edge1, edge0)));

    /* result = t * t * (3 - 2 * t) */
    return nir_fmul(b, t, nir_fmul(b, t, nir_a_minus_bc(b, f3, f2, t)));
 }

 nir_def *
 nir_upsample(nir_builder *b, nir_def *hi, nir_def *lo)
 {
    assert(lo->num_components == hi->num_components);
    assert(lo->bit_size == hi->bit_size);

    nir_def *res[NIR_MAX_VEC_COMPONENTS];
    for (unsigned i = 0; i < lo->num_components; ++i) {
       nir_def *vec = nir_vec2(b, nir_channel(b, lo, i), nir_channel(b, hi, i));
       res[i] = nir_pack_bits(b, vec, vec->bit_size * 2);
    }

    return nir_vec(b, res, lo->num_components);
 }

 nir_def *
 nir_atan(nir_builder *b, nir_def *y_over_x)
 {
    const uint32_t bit_size = y_over_x->bit_size;

    nir_def *abs_y_over_x = nir_fabs(b, y_over_x);

    /*
     * range-reduction, first step:
     *
     *      / y_over_x         if |y_over_x| <= 1.0;
     * u = <
     *      \ 1.0 / y_over_x   otherwise
     *
     * x = |u| for the corrected sign.
     */
    nir_def *le_1 = nir_fle_imm(b, abs_y_over_x, 1.0);
    nir_def *u = nir_bcsel(b, le_1, y_over_x, nir_frcp(b, y_over_x));

    /*
     * approximate atan by evaluating polynomial using Horner's method:
     *
     * x   * 0.9999793128310355 - x^3  * 0.3326756418091246 +
     * x^5 * 0.1938924977115610 - x^7  * 0.1173503194786851 +
     * x^9 * 0.0536813784310406 - x^11 * 0.0121323213173444
     */
    float coeffs[] = {
       -0.0121323213173444f, 0.0536813784310406f,
       -0.1173503194786851f, 0.1938924977115610f,
       -0.3326756418091246f, 0.9999793128310355f
    };

    nir_def *x_2 = nir_fmul(b, u, u);
    nir_def *res = nir_imm_floatN_t(b, coeffs[0], bit_size);

    for (unsigned i = 1; i < ARRAY_SIZE(coeffs); ++i) {
       res = nir_ffma_imm2(b, res, x_2, coeffs[i]);
    }

    /* range-reduction fixup value */
    nir_def *bias = nir_bcsel(b, le_1, nir_imm_floatN_t(b, 0, bit_size),
                              nir_imm_floatN_t(b, -M_PI_2, bit_size));

    /* multiply through by x while fixing up the range reduction */
    nir_def *tmp = nir_ffma(b, nir_fabs(b, u), res, bias);

    /* sign fixup */
    return nir_copysign(b, tmp, y_over_x);
 }

 nir_def *
 nir_atan2(nir_builder *b, nir_def *y, nir_def *x)
 {
    assert(y->bit_size == x->bit_size);
    const uint32_t bit_size = x->bit_size;

    nir_def *zero = nir_imm_floatN_t(b, 0, bit_size);
    nir_def *one = nir_imm_floatN_t(b, 1, bit_size);

    /* If we're on the left half-plane rotate the coordinates π/2 clock-wise
     * for the y=0 discontinuity to end up aligned with the vertical
     * discontinuity of atan(s/t) along t=0.  This also makes sure that we
     * don't attempt to divide by zero along the vertical line, which may give
     * unspecified results on non-GLSL 4.1-capable hardware.
     */
    nir_def *flip = nir_fge(b, zero, x);
    nir_def *s = nir_bcsel(b, flip, nir_fabs(b, x), y);
    nir_def *t = nir_bcsel(b, flip, y, nir_fabs(b, x));

    /* If the magnitude of the denominator exceeds some huge value, scale down
     * the arguments in order to prevent the reciprocal operation from flushing
     * its result to zero, which would cause precision problems, and for s
     * infinite would cause us to return a NaN instead of the correct finite
     * value.
     *
     * If fmin and fmax are respectively the smallest and largest positive
     * normalized floating point values representable by the implementation,
     * the constants below should be in agreement with:
     *
     *    huge <= 1 / fmin
     *    scale <= 1 / fmin / fmax (for |t| >= huge)
     *
     * In addition scale should be a negative power of two in order to avoid
     * loss of precision.  The values chosen below should work for most usual
     * floating point representations with at least the dynamic range of ATI's
     * 24-bit representation.
     */
    const double huge_val = bit_size >= 32 ? 1e18 : 16384;
    nir_def *scale = nir_bcsel(b, nir_fge_imm(b, nir_fabs(b, t), huge_val),
                               nir_imm_floatN_t(b, 0.25, bit_size), one);
    nir_def *rcp_scaled_t = nir_frcp(b, nir_fmul(b, t, scale));
    nir_def *abs_s_over_t = nir_fmul(b, nir_fabs(b, nir_fmul(b, s, scale)),
                                     nir_fabs(b, rcp_scaled_t));

    /* For |x| = |y| assume tan = 1 even if infinite (i.e. pretend momentarily
     * that ∞/∞ = 1) in order to comply with the rather artificial rules
     * inherited from IEEE 754-2008, namely:
     *
     *  "atan2(±∞, −∞) is ±3π/4
     *   atan2(±∞, +∞) is ±π/4"
     *
     * Note that this is inconsistent with the rules for the neighborhood of
     * zero that are based on iterated limits:
     *
     *  "atan2(±0, −0) is ±π
     *   atan2(±0, +0) is ±0"
     *
     * but GLSL specifically allows implementations to deviate from IEEE rules
     * at (0,0), so we take that license (i.e. pretend that 0/0 = 1 here as
     * well).
     */
    nir_def *tan = nir_bcsel(b, nir_feq(b, nir_fabs(b, x), nir_fabs(b, y)),
                             one, abs_s_over_t);

    /* Calculate the arctangent and fix up the result if we had flipped the
     * coordinate system.
     */
    nir_def *arc =
       nir_ffma_imm1(b, nir_b2fN(b, flip, bit_size), M_PI_2, nir_atan(b, tan));

    /* Rather convoluted calculation of the sign of the result.  When x < 0 we
     * cannot use fsign because we need to be able to distinguish between
     * negative and positive zero.  We don't use bitwise arithmetic tricks for
     * consistency with the GLSL front-end.  When x >= 0 rcp_scaled_t will
     * always be non-negative so this won't be able to distinguish between
     * negative and positive zero, but we don't care because atan2 is
     * continuous along the whole positive y = 0 half-line, so it won't affect
     * the result significantly.
     */
    return nir_bcsel(b, nir_flt(b, nir_fmin(b, y, rcp_scaled_t), zero),
                     nir_fneg(b, arc), arc);
 }

 nir_def *
 nir_build_texture_query(nir_builder *b, nir_tex_instr *tex, nir_texop texop,
                         unsigned components, nir_alu_type dest_type,
                         bool include_coord, bool include_lod)
 {
    nir_tex_instr *query;

    unsigned num_srcs = include_lod ? 1 : 0;
    for (unsigned i = 0; i < tex->num_srcs; i++) {
       if ((tex->src[i].src_type == nir_tex_src_coord && include_coord) ||
           tex->src[i].src_type == nir_tex_src_texture_deref ||
           tex->src[i].src_type == nir_tex_src_sampler_deref ||
           tex->src[i].src_type == nir_tex_src_texture_offset ||
           tex->src[i].src_type == nir_tex_src_sampler_offset ||
           tex->src[i].src_type == nir_tex_src_texture_handle ||
           tex->src[i].src_type == nir_tex_src_sampler_handle)
          num_srcs++;
    }

    query = nir_tex_instr_create(b->shader, num_srcs);
    query->op = texop;
    query->sampler_dim = tex->sampler_dim;
    query->is_array = tex->is_array;
    query->is_shadow = tex->is_shadow;
    query->is_new_style_shadow = tex->is_new_style_shadow;
    query->texture_index = tex->texture_index;
    query->sampler_index = tex->sampler_index;
    query->dest_type = dest_type;

    if (include_coord) {
       query->coord_components = tex->coord_components;
    }

    unsigned idx = 0;
    for (unsigned i = 0; i < tex->num_srcs; i++) {
       if ((tex->src[i].src_type == nir_tex_src_coord && include_coord) ||
           tex->src[i].src_type == nir_tex_src_texture_deref ||
           tex->src[i].src_type == nir_tex_src_sampler_deref ||
           tex->src[i].src_type == nir_tex_src_texture_offset ||
           tex->src[i].src_type == nir_tex_src_sampler_offset ||
           tex->src[i].src_type == nir_tex_src_texture_handle ||
           tex->src[i].src_type == nir_tex_src_sampler_handle) {
          query->src[idx].src = nir_src_for_ssa(tex->src[i].src.ssa);
          query->src[idx].src_type = tex->src[i].src_type;
          idx++;
       }
    }

    /* Add in an LOD because some back-ends require it */
    if (include_lod) {
       query->src[idx] = nir_tex_src_for_ssa(nir_tex_src_lod, nir_imm_int(b, 0));
    }

    nir_def_init(&query->instr, &query->def, nir_tex_instr_dest_size(query),
                 nir_alu_type_get_type_size(dest_type));

    nir_builder_instr_insert(b, &query->instr);
    return &query->def;
 }

 nir_def *
 nir_get_texture_size(nir_builder *b, nir_tex_instr *tex)
 {
    b->cursor = nir_before_instr(&tex->instr);

    return nir_build_texture_query(b, tex, nir_texop_txs,
                                   nir_tex_instr_dest_size(tex),
                                   nir_type_int32, false, true);
 }

 nir_def *
 nir_get_texture_lod(nir_builder *b, nir_tex_instr *tex)
 {
    b->cursor = nir_before_instr(&tex->instr);

    nir_def *tql = nir_build_texture_query(b, tex, nir_texop_lod, 2,
                                           nir_type_float32, true, false);

    /* The LOD is the y component of the result */
    return nir_channel(b, tql, 1);
 }
	/*
	* Copyright © 2018 Red Hat Inc.
	* Copyright © 2015 Intel Corporation
	*
	* Permission is hereby granted, free of charge, to any person obtaining a
	* copy of this software and associated documentation files (the "Software"),
	* to deal in the Software without restriction, including without limitation
	* the rights to use, copy, modify, merge, publish, distribute, sublicense,
	* and/or sell copies of the Software, and to permit persons to whom the
	* Software is furnished to do so, subject to the following conditions:
	*
	* The above copyright notice and this permission notice (including the next
	* paragraph) shall be included in all copies or substantial portions of the
	* Software.
	*
	* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
	* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
	* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
	* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
	* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
	* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
	* IN THE SOFTWARE.
	*/

	#include <math.h>

	#include "nir.h"
	#include "nir_builder.h"
	#include "nir_builtin_builder.h"

	nir_def *
	nir_cross3(nir_builder b, nir_def x, nir_def *y)
	{
	unsigned yzx[3] = { 1, 2, 0 };
	unsigned zxy[3] = { 2, 0, 1 };

	return nir_ffma(b, nir_swizzle(b, x, yzx, 3),
	nir_swizzle(b, y, zxy, 3),
	nir_fneg(b, nir_fmul(b, nir_swizzle(b, x, zxy, 3),
	nir_swizzle(b, y, yzx, 3))));
	}

	nir_def *
	nir_cross4(nir_builder b, nir_def x, nir_def *y)
	{
	nir_def *cross = nir_cross3(b, x, y);

	return nir_vec4(b,
	nir_channel(b, cross, 0),
	nir_channel(b, cross, 1),
	nir_channel(b, cross, 2),
	nir_imm_intN_t(b, 0, cross->bit_size));
	}

	nir_def *
	nir_fast_length(nir_builder b, nir_def vec)
	{
	return nir_fsqrt(b, nir_fdot(b, vec, vec));
	}

	nir_def *
	nir_nextafter(nir_builder b, nir_def x, nir_def *y)
	{
	nir_def *zero = nir_imm_intN_t(b, 0, x->bit_size);
	nir_def *one = nir_imm_intN_t(b, 1, x->bit_size);

	nir_def *condeq = nir_feq(b, x, y);
	nir_def *conddir = nir_flt(b, x, y);
	nir_def *condzero = nir_feq(b, x, zero);

	uint64_t sign_mask = 1ull << (x->bit_size - 1);
	uint64_t min_abs = 1;

	if (nir_is_denorm_flush_to_zero(b->shader->info.float_controls_execution_mode, x->bit_size)) {
	switch (x->bit_size) {
	case 16:
	min_abs = 1 << 10;
	break;
	case 32:
	min_abs = 1 << 23;
	break;
	case 64:
	min_abs = 1ULL << 52;
	break;
	}

	/* Flush denorm to zero to avoid returning a denorm when condeq is true. */
	x = nir_fmul_imm(b, x, 1.0);
	}

	/* beware of: +/-0.0 - 1 == NaN */
	nir_def *xn =
	nir_bcsel(b,
	condzero,
	nir_imm_intN_t(b, sign_mask \| min_abs, x->bit_size),
	nir_isub(b, x, one));

	/* beware of -0.0 + 1 == -0x1p-149 */
	nir_def *xp = nir_bcsel(b, condzero,
	nir_imm_intN_t(b, min_abs, x->bit_size),
	nir_iadd(b, x, one));

	/* nextafter can be implemented by just +/- 1 on the int value */
	nir_def *res =
	nir_bcsel(b, nir_ixor(b, conddir, nir_flt(b, x, zero)), xp, xn);

	return nir_nan_check2(b, x, y, nir_bcsel(b, condeq, x, res));
	}

	nir_def *
	nir_normalize(nir_builder b, nir_def vec)
	{
	if (vec->num_components == 1)
	return nir_fsign(b, vec);

	nir_def *f0 = nir_imm_floatN_t(b, 0.0, vec->bit_size);
	nir_def *f1 = nir_imm_floatN_t(b, 1.0, vec->bit_size);
	nir_def *finf = nir_imm_floatN_t(b, INFINITY, vec->bit_size);

	/* scale the input to increase precision */
	nir_def *maxc = nir_fmax_abs_vec_comp(b, vec);
	nir_def *svec = nir_fdiv(b, vec, maxc);
	/* for inf */
	nir_def *finfvec = nir_copysign(b, nir_bcsel(b, nir_feq(b, vec, finf), f1, f0), f1);

	nir_def *temp = nir_bcsel(b, nir_feq(b, maxc, finf), finfvec, svec);
	nir_def *res = nir_fmul(b, temp, nir_frsq(b, nir_fdot(b, temp, temp)));

	return nir_bcsel(b, nir_feq(b, maxc, f0), vec, res);
	}

	nir_def *
	nir_smoothstep(nir_builder b, nir_def edge0, nir_def edge1, nir_def x)
	{
	nir_def *f2 = nir_imm_floatN_t(b, 2.0, x->bit_size);
	nir_def *f3 = nir_imm_floatN_t(b, 3.0, x->bit_size);

	/* t = clamp((x - edge0) / (edge1 - edge0), 0, 1) */
	nir_def *t =
	nir_fsat(b, nir_fdiv(b, nir_fsub(b, x, edge0),
	nir_fsub(b, edge1, edge0)));

	/* result = t * t * (3 - 2 * t) */
	return nir_fmul(b, t, nir_fmul(b, t, nir_a_minus_bc(b, f3, f2, t)));
	}

	nir_def *
	nir_upsample(nir_builder b, nir_def hi, nir_def *lo)
	{
	assert(lo->num_components == hi->num_components);
	assert(lo->bit_size == hi->bit_size);

	nir_def *res[NIR_MAX_VEC_COMPONENTS];
	for (unsigned i = 0; i < lo->num_components; ++i) {
	nir_def *vec = nir_vec2(b, nir_channel(b, lo, i), nir_channel(b, hi, i));
	res[i] = nir_pack_bits(b, vec, vec->bit_size * 2);
	}

	return nir_vec(b, res, lo->num_components);
	}

	nir_def *
	nir_atan(nir_builder b, nir_def y_over_x)
	{
	const uint32_t bit_size = y_over_x->bit_size;

	nir_def *abs_y_over_x = nir_fabs(b, y_over_x);

	/*
	* range-reduction, first step:
	*
	* / y_over_x if \|y_over_x\| <= 1.0;
	* u = <
	* \ 1.0 / y_over_x otherwise
	*
	* x = \|u\| for the corrected sign.
	*/
	nir_def *le_1 = nir_fle_imm(b, abs_y_over_x, 1.0);
	nir_def *u = nir_bcsel(b, le_1, y_over_x, nir_frcp(b, y_over_x));

	/*
	* approximate atan by evaluating polynomial using Horner's method:
	*
	* x * 0.9999793128310355 - x^3 * 0.3326756418091246 +
	* x^5 * 0.1938924977115610 - x^7 * 0.1173503194786851 +
	* x^9 * 0.0536813784310406 - x^11 * 0.0121323213173444
	*/
	float coeffs[] = {
	-0.0121323213173444f, 0.0536813784310406f,
	-0.1173503194786851f, 0.1938924977115610f,
	-0.3326756418091246f, 0.9999793128310355f
	};

	nir_def *x_2 = nir_fmul(b, u, u);
	nir_def *res = nir_imm_floatN_t(b, coeffs[0], bit_size);

	for (unsigned i = 1; i < ARRAY_SIZE(coeffs); ++i) {
	res = nir_ffma_imm2(b, res, x_2, coeffs[i]);
	}

	/* range-reduction fixup value */
	nir_def *bias = nir_bcsel(b, le_1, nir_imm_floatN_t(b, 0, bit_size),
	nir_imm_floatN_t(b, -M_PI_2, bit_size));

	/* multiply through by x while fixing up the range reduction */
	nir_def *tmp = nir_ffma(b, nir_fabs(b, u), res, bias);

	/* sign fixup */
	return nir_copysign(b, tmp, y_over_x);
	}

	nir_def *
	nir_atan2(nir_builder b, nir_def y, nir_def *x)
	{
	assert(y->bit_size == x->bit_size);
	const uint32_t bit_size = x->bit_size;

	nir_def *zero = nir_imm_floatN_t(b, 0, bit_size);
	nir_def *one = nir_imm_floatN_t(b, 1, bit_size);

	/* If we're on the left half-plane rotate the coordinates π/2 clock-wise
	* for the y=0 discontinuity to end up aligned with the vertical
	* discontinuity of atan(s/t) along t=0. This also makes sure that we
	* don't attempt to divide by zero along the vertical line, which may give
	* unspecified results on non-GLSL 4.1-capable hardware.
	*/
	nir_def *flip = nir_fge(b, zero, x);
	nir_def *s = nir_bcsel(b, flip, nir_fabs(b, x), y);
	nir_def *t = nir_bcsel(b, flip, y, nir_fabs(b, x));

	/* If the magnitude of the denominator exceeds some huge value, scale down
	* the arguments in order to prevent the reciprocal operation from flushing
	* its result to zero, which would cause precision problems, and for s
	* infinite would cause us to return a NaN instead of the correct finite
	* value.
	*
	* If fmin and fmax are respectively the smallest and largest positive
	* normalized floating point values representable by the implementation,
	* the constants below should be in agreement with:
	*
	* huge <= 1 / fmin
	* scale <= 1 / fmin / fmax (for \|t\| >= huge)
	*
	* In addition scale should be a negative power of two in order to avoid
	* loss of precision. The values chosen below should work for most usual
	* floating point representations with at least the dynamic range of ATI's
	* 24-bit representation.
	*/
	const double huge_val = bit_size >= 32 ? 1e18 : 16384;
	nir_def *scale = nir_bcsel(b, nir_fge_imm(b, nir_fabs(b, t), huge_val),
	nir_imm_floatN_t(b, 0.25, bit_size), one);
	nir_def *rcp_scaled_t = nir_frcp(b, nir_fmul(b, t, scale));
	nir_def *abs_s_over_t = nir_fmul(b, nir_fabs(b, nir_fmul(b, s, scale)),
	nir_fabs(b, rcp_scaled_t));

	/* For \|x\| = \|y\| assume tan = 1 even if infinite (i.e. pretend momentarily
	* that ∞/∞ = 1) in order to comply with the rather artificial rules
	* inherited from IEEE 754-2008, namely:
	*
	* "atan2(±∞, −∞) is ±3π/4
	* atan2(±∞, +∞) is ±π/4"
	*
	* Note that this is inconsistent with the rules for the neighborhood of
	* zero that are based on iterated limits:
	*
	* "atan2(±0, −0) is ±π
	* atan2(±0, +0) is ±0"
	*
	* but GLSL specifically allows implementations to deviate from IEEE rules
	* at (0,0), so we take that license (i.e. pretend that 0/0 = 1 here as
	* well).
	*/
	nir_def *tan = nir_bcsel(b, nir_feq(b, nir_fabs(b, x), nir_fabs(b, y)),
	one, abs_s_over_t);

	/* Calculate the arctangent and fix up the result if we had flipped the
	* coordinate system.
	*/
	nir_def *arc =
	nir_ffma_imm1(b, nir_b2fN(b, flip, bit_size), M_PI_2, nir_atan(b, tan));

	/* Rather convoluted calculation of the sign of the result. When x < 0 we
	* cannot use fsign because we need to be able to distinguish between
	* negative and positive zero. We don't use bitwise arithmetic tricks for
	* consistency with the GLSL front-end. When x >= 0 rcp_scaled_t will
	* always be non-negative so this won't be able to distinguish between
	* negative and positive zero, but we don't care because atan2 is
	* continuous along the whole positive y = 0 half-line, so it won't affect
	* the result significantly.
	*/
	return nir_bcsel(b, nir_flt(b, nir_fmin(b, y, rcp_scaled_t), zero),
	nir_fneg(b, arc), arc);
	}

	nir_def *
	nir_build_texture_query(nir_builder b, nir_tex_instr tex, nir_texop texop,
	unsigned components, nir_alu_type dest_type,
	bool include_coord, bool include_lod)
	{
	nir_tex_instr *query;

	unsigned num_srcs = include_lod ? 1 : 0;
	for (unsigned i = 0; i < tex->num_srcs; i++) {
	if ((tex->src[i].src_type == nir_tex_src_coord && include_coord) \|\|
	tex->src[i].src_type == nir_tex_src_texture_deref \|\|
	tex->src[i].src_type == nir_tex_src_sampler_deref \|\|
	tex->src[i].src_type == nir_tex_src_texture_offset \|\|
	tex->src[i].src_type == nir_tex_src_sampler_offset \|\|
	tex->src[i].src_type == nir_tex_src_texture_handle \|\|
	tex->src[i].src_type == nir_tex_src_sampler_handle)
	num_srcs++;
	}

	query = nir_tex_instr_create(b->shader, num_srcs);
	query->op = texop;
	query->sampler_dim = tex->sampler_dim;
	query->is_array = tex->is_array;
	query->is_shadow = tex->is_shadow;
	query->is_new_style_shadow = tex->is_new_style_shadow;
	query->texture_index = tex->texture_index;
	query->sampler_index = tex->sampler_index;
	query->dest_type = dest_type;

	if (include_coord) {
	query->coord_components = tex->coord_components;
	}

	unsigned idx = 0;
	for (unsigned i = 0; i < tex->num_srcs; i++) {
	if ((tex->src[i].src_type == nir_tex_src_coord && include_coord) \|\|
	tex->src[i].src_type == nir_tex_src_texture_deref \|\|
	tex->src[i].src_type == nir_tex_src_sampler_deref \|\|
	tex->src[i].src_type == nir_tex_src_texture_offset \|\|
	tex->src[i].src_type == nir_tex_src_sampler_offset \|\|
	tex->src[i].src_type == nir_tex_src_texture_handle \|\|
	tex->src[i].src_type == nir_tex_src_sampler_handle) {
	query->src[idx].src = nir_src_for_ssa(tex->src[i].src.ssa);
	query->src[idx].src_type = tex->src[i].src_type;
	idx++;
	}
	}

	/* Add in an LOD because some back-ends require it */
	if (include_lod) {
	query->src[idx] = nir_tex_src_for_ssa(nir_tex_src_lod, nir_imm_int(b, 0));
	}

	nir_def_init(&query->instr, &query->def, nir_tex_instr_dest_size(query),
	nir_alu_type_get_type_size(dest_type));

	nir_builder_instr_insert(b, &query->instr);
	return &query->def;
	}

	nir_def *
	nir_get_texture_size(nir_builder b, nir_tex_instr tex)
	{
	b->cursor = nir_before_instr(&tex->instr);

	return nir_build_texture_query(b, tex, nir_texop_txs,
	nir_tex_instr_dest_size(tex),
	nir_type_int32, false, true);
	}

	nir_def *
	nir_get_texture_lod(nir_builder b, nir_tex_instr tex)
	{
	b->cursor = nir_before_instr(&tex->instr);

	nir_def *tql = nir_build_texture_query(b, tex, nir_texop_lod, 2,
	nir_type_float32, true, false);

	/* The LOD is the y component of the result */
	return nir_channel(b, tql, 1);
	}