ir_variable *x = in_var(type, "x");
MAKE_SIG(type, v130, 1, x);
- /* 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.
+ /* 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.
*/
ir_variable *t = body.make_temp(type, "tmp");
- body.emit(assign(t, min2(x, imm(10.0f))));
+ body.emit(assign(t, min2(max2(x, imm(-10.0f)), imm(10.0f))));
- body.emit(ret(div(sub(exp(mul(t, imm(2.0f))), imm(1.0f)),
- add(exp(mul(t, imm(2.0f))), imm(1.0f)))));
+ /* (e^x - e^(-x)) / (e^x + e^(-x)) */
+ body.emit(ret(div(sub(exp(t), exp(neg(t))),
+ add(exp(t), exp(neg(t))))));
return sig;
}