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glsl: Use a simpler formula for tanh

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The formula we have used in the past is a trivial reduction from the
definition by simply multiplying both the numerator and denominator of the
formula by 2.  However, multiplying by e^x, you can further reduce it.
This allows us to get rid of one side of the clamp and two of exponential
functions which should make it faster.  The new formula still passes the
dEQP precision tests for tanh so it should be fine.

Reviewed-by: Roland Scheidegger <sroland@vmware.com>
Reviewed-by: Kenneth Graunke <kenneth@whitecape.org>
This commit is contained in:
Jason Ekstrand
2016-12-09 09:33:05 -08:00
parent efe9d1cde3
commit 9807f502eb
1 changed files with 10 additions and 8 deletions
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18
src/compiler/glsl/builtin_functions.cpp
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@@ -3563,17 +3563,19 @@ builtin_builder::_tanh(const glsl_type *type)
ir_variable *x = in_var(type, "x");
MAKE_SIG(type, v130, 1, x);
/* Clamp x to [-10, +10] to avoid precision problems.
* When x > 10, e^(-x) is so small relative to e^x that it gets flushed to
* zero in the computation e^x + e^(-x). The same happens in the other
* direction when x < -10.
/* tanh(x) := (0.5 * (e^x - e^(-x))) / (0.5 * (e^x + e^(-x)))
*
* With a little algebra this reduces to (e^2x - 1) / (e^2x + 1)
*
* Clamp x to (-inf, +10] to avoid precision problems. When x > 10, e^2x
* is so much larger than 1.0 that 1.0 gets flushed to zero in the
* computation e^2x +/- 1 so it can be ignored.
*/
ir_variable *t = body.make_temp(type, "tmp");
body.emit(assign(t, min2(max2(x, imm(-10.0f)), imm(10.0f))));
body.emit(assign(t, min2(x, imm(10.0f))));
/* (e^x - e^(-x)) / (e^x + e^(-x)) */
body.emit(ret(div(sub(exp(t), exp(neg(t))),
add(exp(t), exp(neg(t))))));
body.emit(ret(div(sub(exp(mul(t, imm(2.0f))), imm(1.0f)),
add(exp(mul(t, imm(2.0f))), imm(1.0f)))));
return sig;
}