Changes between Version 11 and Version 12 of research/trig Tweet

Timestamp:

Dec 30, 2011, 11:32:22 PM (9 years ago)

Author:

sam

Comment:

--

research/trig

@@ +1 @@
+[[TOC]]
 = Trigonometric functions =
 
@@ -7 +8 @@
  * OpenBSD [http://www.openbsd.org/cgi-bin/cvsweb/src/lib/libm/src/k_sin.c?rev=1.3;content-type=text%2Fplain sin(double)].
  * OpenBSD [http://www.openbsd.org/cgi-bin/cvsweb/src/lib/libm/src/k_sinf.c?rev=1.3;content-type=text%2Fplain sinf(float)].
+
+== Evaluating minimax polynomials ==
+
+Let’s check how much an error on the last bit affects `float` variables, using relative error:
+
+{{{
+#!cpp
+for (float f = 1e-25f; f < 50.0f; f *= 1.001f)
+{
+    union { float f; uint32_t x; } u = { f }, v = u, w = u;
+    ++v.x;
+    --w.x;
+    printf("%e: %e %e\n", u.f, (v.f - u.f) / u.f, (u.f - w.f) / u.f);
+}
+}}}
+
+Plotting the results gives the answer: between `5.96e-8` and `1.19e-7`.
+
+How about `double`?
+
+{{{
+#!cpp
+for (double d = 1e-25; d < 50.0; d *= 1.001)
+{   
+    union { double d; uint64_t x; } u = { d }, v = u, w = u;
+    ++v.x;
+    --w.x;
+    printf("%e: %e %e\n", u.d, (v.d - u.d) / u.d, (u.d - w.d) / u.d);
+}   
+}}}
+
+Result: between `1.11e-16` and `2.22e-16`.
 
 == Minimax polynomial for sin(x) ==