ir_function_signature *
builtin_builder::_atan2(const glsl_type *type)
{
- ir_variable *vec_y = in_var(type, "vec_y");
- ir_variable *vec_x = in_var(type, "vec_x");
- MAKE_SIG(type, always_available, 2, vec_y, vec_x);
-
- ir_variable *vec_result = body.make_temp(type, "vec_result");
- ir_variable *r = body.make_temp(glsl_type::float_type, "r");
- for (int i = 0; i < type->vector_elements; i++) {
- ir_variable *y = body.make_temp(glsl_type::float_type, "y");
- ir_variable *x = body.make_temp(glsl_type::float_type, "x");
- body.emit(assign(y, swizzle(vec_y, i, 1)));
- body.emit(assign(x, swizzle(vec_x, i, 1)));
-
- /* If |x| >= 1.0e-8 * |y|: */
- ir_if *outer_if =
- new(mem_ctx) ir_if(greater(abs(x), mul(imm(1.0e-8f), abs(y))));
-
- ir_factory outer_then(&outer_if->then_instructions, mem_ctx);
-
- /* Then...call atan(y/x) */
- do_atan(outer_then, glsl_type::float_type, r, div(y, x));
-
- /* ...and fix it up: */
- ir_if *inner_if = new(mem_ctx) ir_if(less(x, imm(0.0f)));
- inner_if->then_instructions.push_tail(
- if_tree(gequal(y, imm(0.0f)),
- assign(r, add(r, imm(M_PIf))),
- assign(r, sub(r, imm(M_PIf)))));
- outer_then.emit(inner_if);
-
- /* Else... */
- outer_if->else_instructions.push_tail(
- assign(r, mul(sign(y), imm(M_PI_2f))));
+ const unsigned n = type->vector_elements;
+ ir_variable *y = in_var(type, "y");
+ ir_variable *x = in_var(type, "x");
+ MAKE_SIG(type, always_available, 2, y, x);
- body.emit(outer_if);
+ /* 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.
+ */
+ ir_variable *flip = body.make_temp(glsl_type::bvec(n), "flip");
+ body.emit(assign(flip, gequal(imm(0.0f, n), x)));
+ ir_variable *s = body.make_temp(type, "s");
+ body.emit(assign(s, csel(flip, abs(x), y)));
+ ir_variable *t = body.make_temp(type, "t");
+ body.emit(assign(t, csel(flip, y, abs(x))));
- body.emit(assign(vec_result, r, 1 << i));
- }
- body.emit(ret(vec_result));
+ /* 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.
+ */
+ ir_constant *huge = imm(1e18f, n);
+ ir_variable *scale = body.make_temp(type, "scale");
+ body.emit(assign(scale, csel(gequal(abs(t), huge),
+ imm(0.25f, n), imm(1.0f, n))));
+ ir_variable *rcp_scaled_t = body.make_temp(type, "rcp_scaled_t");
+ body.emit(assign(rcp_scaled_t, rcp(mul(t, scale))));
+ ir_expression *s_over_t = mul(mul(s, scale), rcp_scaled_t);
+
+ /* Calculate the arctangent and fix up the result if we had flipped the
+ * coordinate system.
+ */
+ ir_variable *arc = body.make_temp(type, "arc");
+ do_atan(body, type, arc, abs(s_over_t));
+ body.emit(assign(arc, add(arc, mul(b2f(flip), imm(M_PI_2f)))));
+
+ /* 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. Unfortunately we cannot use bitwise
+ * arithmetic tricks either because of back-ends without integer support.
+ * 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.
+ */
+ body.emit(ret(csel(less(min2(y, rcp_scaled_t), imm(0.0f, n)),
+ neg(arc), arc)));
return sig;
}
projects / mesa.git / blobdiff