mirror of https://github.com/flysand7/ciabatta.git
CORDIC trig functions
This commit is contained in:
bumbread
parent
a16e2d5a6e
commit
e79c192472
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@ -0,0 +1,202 @@
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double tK = 0x1.b7b2b62cef828p-1;
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double hK = 0x1.a2166ada47ca4p-1;
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double ttable[] = {
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0x1.dac670561bb4fp-2,
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0x1.f5b75f92c80ddp-3,
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0x1.fd5ba9aac2f6ep-4,
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0x1.ff55bb72cfdeap-5,
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0x1.ffd55bba97625p-6,
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0x1.fff555bbb729bp-7,
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0x1.fffd555bbba97p-8,
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0x1.ffff5555bbbb7p-9,
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0x1.ffffd5555bbbcp-10,
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0x1.fffff55555bbcp-11,
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0x1.fffffd55555bcp-12,
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0x1.ffffff555555cp-13,
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0x1.ffffffd555556p-14,
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0x1.fffffff555555p-15,
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0x1.fffffffd55555p-16,
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0x1.ffffffff55555p-17,
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0x1.ffffffffd5555p-18,
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0x1.fffffffff5555p-19,
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0x1.fffffffffd555p-20,
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0x1.ffffffffff555p-21,
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0x1.ffffffffffd55p-22,
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0x1.fffffffffff55p-23,
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0x1.fffffffffffd5p-24,
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0x1.ffffffffffff5p-25,
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0x1.ffffffffffffdp-26,
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0x1.fffffffffffffp-27,
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0x1.0000000000000p-27,
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0x1.0000000000000p-28,
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0x1.0000000000000p-29,
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0x1.0000000000000p-30,
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0x1.0000000000000p-31,
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0x1.0000000000000p-32,
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0x1.0000000000000p-33,
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0x1.0000000000000p-34,
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0x1.0000000000000p-35,
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0x1.0000000000000p-36,
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0x1.0000000000000p-37,
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0x1.0000000000000p-38,
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0x1.0000000000000p-39,
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0x1.0000000000000p-40,
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0x1.0000000000000p-41,
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0x1.0000000000000p-42,
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0x1.0000000000000p-43,
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0x1.0000000000000p-44,
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0x1.0000000000000p-45,
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0x1.0000000000000p-46,
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0x1.0000000000000p-47,
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0x1.0000000000000p-48,
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0x1.0000000000000p-49,
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0x1.0000000000000p-50,
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0x1.0000000000000p-51,
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0x1.0000000000000p-52,
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0x1.0000000000000p-53,
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0x1.0000000000000p-54,
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0x1.0000000000000p-55,
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0x1.0000000000000p-56,
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0x1.0000000000000p-57,
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0x1.0000000000000p-58,
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0x1.0000000000000p-59,
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0x1.0000000000000p-60,
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0x1.0000000000000p-61,
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0x1.0000000000000p-62,
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0x1.0000000000000p-63,
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};
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double htable[] = {
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0x1.193ea7aad030bp-1,
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0x1.058aefa811452p-2,
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0x1.015891c9eaef8p-3,
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0x1.005588ad375adp-4,
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0x1.001558891aee2p-5,
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0x1.000555888ad1dp-6,
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0x1.000155588891bp-7,
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0x1.000055558888bp-8,
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0x1.0000155558889p-9,
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0x1.0000055555889p-10,
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0x1.0000015555589p-11,
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0x1.0000005555559p-12,
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0x1.0000001555556p-13,
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0x1.0000000555555p-14,
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0x1.0000000155555p-15,
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0x1.0000000055555p-16,
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0x1.0000000015555p-17,
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0x1.0000000005555p-18,
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0x1.0000000001555p-19,
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0x1.0000000000555p-20,
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0x1.0000000000155p-21,
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0x1.0000000000055p-22,
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0x1.0000000000015p-23,
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0x1.0000000000005p-24,
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0x1.0000000000001p-25,
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0x1.0000000000000p-26,
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0x1.0000000000000p-27,
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0x1.0000000000000p-28,
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0x1.0000000000000p-29,
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0x1.0000000000000p-30,
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0x1.0000000000000p-31,
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0x1.0000000000000p-32,
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0x1.0000000000000p-33,
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0x1.0000000000000p-34,
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0x1.0000000000000p-35,
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0x1.0000000000000p-36,
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0x1.0000000000000p-37,
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0x1.0000000000000p-38,
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0x1.0000000000000p-39,
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0x1.0000000000000p-40,
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0x1.0000000000000p-41,
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0x1.0000000000000p-42,
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0x1.0000000000000p-43,
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0x1.0000000000000p-44,
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0x1.0000000000000p-45,
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0x1.0000000000000p-46,
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0x1.0000000000000p-47,
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0x1.0000000000000p-48,
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0x1.0000000000000p-49,
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0x1.0000000000000p-50,
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0x1.0000000000000p-51,
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0x1.0000000000000p-52,
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0x1.0000000000000p-53,
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0x1.0000000000000p-54,
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0x1.0000000000000p-55,
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0x1.0000000000000p-56,
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0x1.0000000000000p-57,
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0x1.0000000000000p-58,
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0x1.0000000000000p-59,
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0x1.0000000000000p-60,
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0x1.0000000000000p-61,
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0x1.0000000000000p-62,
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0x1.0000000000000p-63,
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};
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double ptable[] = {
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0x1.0000000000000p-1,
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0x1.0000000000000p-2,
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0x1.0000000000000p-3,
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0x1.0000000000000p-4,
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0x1.0000000000000p-5,
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0x1.0000000000000p-6,
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0x1.0000000000000p-7,
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0x1.0000000000000p-8,
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0x1.0000000000000p-9,
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0x1.0000000000000p-10,
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0x1.0000000000000p-11,
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0x1.0000000000000p-12,
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0x1.0000000000000p-13,
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0x1.0000000000000p-14,
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0x1.0000000000000p-15,
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0x1.0000000000000p-16,
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0x1.0000000000000p-17,
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0x1.0000000000000p-18,
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0x1.0000000000000p-19,
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0x1.0000000000000p-20,
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0x1.0000000000000p-21,
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0x1.0000000000000p-22,
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0x1.0000000000000p-23,
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0x1.0000000000000p-24,
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0x1.0000000000000p-25,
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0x1.0000000000000p-26,
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0x1.0000000000000p-27,
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0x1.0000000000000p-28,
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0x1.0000000000000p-29,
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0x1.0000000000000p-30,
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0x1.0000000000000p-31,
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0x1.0000000000000p-32,
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0x1.0000000000000p-33,
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0x1.0000000000000p-34,
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0x1.0000000000000p-35,
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0x1.0000000000000p-36,
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0x1.0000000000000p-37,
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0x1.0000000000000p-38,
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0x1.0000000000000p-39,
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0x1.0000000000000p-40,
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0x1.0000000000000p-41,
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0x1.0000000000000p-42,
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0x1.0000000000000p-43,
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0x1.0000000000000p-44,
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0x1.0000000000000p-45,
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0x1.0000000000000p-46,
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0x1.0000000000000p-47,
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0x1.0000000000000p-48,
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0x1.0000000000000p-49,
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0x1.0000000000000p-50,
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0x1.0000000000000p-51,
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0x1.0000000000000p-52,
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0x1.0000000000000p-53,
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0x1.0000000000000p-54,
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0x1.0000000000000p-55,
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0x1.0000000000000p-56,
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0x1.0000000000000p-57,
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0x1.0000000000000p-58,
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0x1.0000000000000p-59,
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0x1.0000000000000p-60,
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0x1.0000000000000p-61,
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0x1.0000000000000p-62,
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0x1.0000000000000p-63,
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};
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@ -0,0 +1,106 @@
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float tKf = 0x1.b7b2b62cef828p-1;
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float hKf = 0x1.a2166ada47ca4p-1;
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float ttablef[] = {
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0x1.dac670561bb4fp-2,
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0x1.f5b75f92c80ddp-3,
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0x1.fd5ba9aac2f6ep-4,
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0x1.ff55bb72cfdeap-5,
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0x1.ffd55bba97625p-6,
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0x1.fff555bbb729bp-7,
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0x1.fffd555bbba97p-8,
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0x1.ffff5555bbbb7p-9,
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0x1.ffffd5555bbbcp-10,
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0x1.fffff55555bbcp-11,
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0x1.fffffd55555bcp-12,
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0x1.ffffff555555cp-13,
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0x1.ffffffd555556p-14,
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0x1.fffffff555555p-15,
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0x1.fffffffd55555p-16,
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0x1.ffffffff55555p-17,
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0x1.ffffffffd5555p-18,
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0x1.fffffffff5555p-19,
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0x1.fffffffffd555p-20,
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0x1.ffffffffff555p-21,
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0x1.ffffffffffd55p-22,
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0x1.fffffffffff55p-23,
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0x1.fffffffffffd5p-24,
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0x1.ffffffffffff5p-25,
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0x1.ffffffffffffdp-26,
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0x1.fffffffffffffp-27,
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0x1.0000000000000p-27,
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0x1.0000000000000p-28,
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0x1.0000000000000p-29,
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0x1.0000000000000p-30,
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0x1.0000000000000p-31,
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};
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float htablef[] = {
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0x1.193ea7aad030bp-1,
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0x1.058aefa811452p-2,
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0x1.015891c9eaef8p-3,
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0x1.005588ad375adp-4,
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0x1.001558891aee2p-5,
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0x1.000555888ad1dp-6,
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0x1.000155588891bp-7,
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0x1.000055558888bp-8,
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0x1.0000155558889p-9,
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0x1.0000055555889p-10,
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0x1.0000015555589p-11,
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0x1.0000005555559p-12,
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0x1.0000001555556p-13,
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0x1.0000000555555p-14,
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0x1.0000000155555p-15,
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0x1.0000000055555p-16,
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0x1.0000000015555p-17,
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0x1.0000000005555p-18,
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0x1.0000000001555p-19,
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0x1.0000000000555p-20,
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0x1.0000000000155p-21,
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0x1.0000000000055p-22,
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0x1.0000000000015p-23,
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0x1.0000000000005p-24,
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0x1.0000000000001p-25,
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0x1.0000000000000p-26,
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0x1.0000000000000p-27,
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0x1.0000000000000p-28,
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0x1.0000000000000p-29,
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0x1.0000000000000p-30,
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0x1.0000000000000p-31,
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};
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float ptablef[] = {
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0x1.0000000000000p-1,
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0x1.0000000000000p-2,
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0x1.0000000000000p-3,
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0x1.0000000000000p-4,
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0x1.0000000000000p-5,
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0x1.0000000000000p-6,
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0x1.0000000000000p-7,
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0x1.0000000000000p-8,
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0x1.0000000000000p-9,
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0x1.0000000000000p-10,
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0x1.0000000000000p-11,
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0x1.0000000000000p-12,
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0x1.0000000000000p-13,
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0x1.0000000000000p-14,
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0x1.0000000000000p-15,
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0x1.0000000000000p-16,
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0x1.0000000000000p-17,
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0x1.0000000000000p-18,
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0x1.0000000000000p-19,
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0x1.0000000000000p-20,
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0x1.0000000000000p-21,
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0x1.0000000000000p-22,
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0x1.0000000000000p-23,
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0x1.0000000000000p-24,
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0x1.0000000000000p-25,
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0x1.0000000000000p-26,
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0x1.0000000000000p-27,
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0x1.0000000000000p-28,
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0x1.0000000000000p-29,
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0x1.0000000000000p-30,
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0x1.0000000000000p-31,
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};
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@ -0,0 +1,202 @@
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long double tKl = 0x1.b7b2b62cef828p-1;
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long double hKl = 0x1.a2166ada47ca4p-1;
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long double ttablel[] = {
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0x1.dac670561bb4fp-2,
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0x1.f5b75f92c80ddp-3,
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0x1.fd5ba9aac2f6ep-4,
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0x1.ff55bb72cfdeap-5,
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0x1.ffd55bba97625p-6,
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0x1.fff555bbb729bp-7,
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0x1.fffd555bbba97p-8,
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0x1.ffff5555bbbb7p-9,
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0x1.ffffd5555bbbcp-10,
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0x1.fffff55555bbcp-11,
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0x1.fffffd55555bcp-12,
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0x1.ffffff555555cp-13,
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0x1.ffffffd555556p-14,
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0x1.fffffff555555p-15,
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0x1.fffffffd55555p-16,
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0x1.ffffffff55555p-17,
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0x1.ffffffffd5555p-18,
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0x1.fffffffff5555p-19,
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0x1.fffffffffd555p-20,
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0x1.ffffffffff555p-21,
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0x1.ffffffffffd55p-22,
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0x1.fffffffffff55p-23,
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0x1.fffffffffffd5p-24,
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0x1.ffffffffffff5p-25,
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0x1.ffffffffffffdp-26,
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0x1.fffffffffffffp-27,
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0x1.0000000000000p-27,
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0x1.0000000000000p-28,
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0x1.0000000000000p-29,
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0x1.0000000000000p-30,
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0x1.0000000000000p-31,
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0x1.0000000000000p-32,
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0x1.0000000000000p-33,
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0x1.0000000000000p-34,
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0x1.0000000000000p-35,
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0x1.0000000000000p-36,
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0x1.0000000000000p-37,
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0x1.0000000000000p-38,
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0x1.0000000000000p-39,
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0x1.0000000000000p-40,
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0x1.0000000000000p-41,
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0x1.0000000000000p-42,
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0x1.0000000000000p-43,
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0x1.0000000000000p-44,
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0x1.0000000000000p-45,
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0x1.0000000000000p-46,
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0x1.0000000000000p-47,
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0x1.0000000000000p-48,
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0x1.0000000000000p-49,
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0x1.0000000000000p-50,
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0x1.0000000000000p-51,
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0x1.0000000000000p-52,
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0x1.0000000000000p-53,
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0x1.0000000000000p-54,
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0x1.0000000000000p-55,
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0x1.0000000000000p-56,
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0x1.0000000000000p-57,
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0x1.0000000000000p-58,
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0x1.0000000000000p-59,
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0x1.0000000000000p-60,
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0x1.0000000000000p-61,
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0x1.0000000000000p-62,
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0x1.0000000000000p-63,
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};
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long double htablel[] = {
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0x1.193ea7aad030bp-1,
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0x1.058aefa811452p-2,
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0x1.015891c9eaef8p-3,
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0x1.005588ad375adp-4,
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0x1.001558891aee2p-5,
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0x1.000555888ad1dp-6,
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0x1.000155588891bp-7,
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0x1.000055558888bp-8,
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0x1.0000155558889p-9,
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0x1.0000055555889p-10,
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0x1.0000015555589p-11,
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0x1.0000005555559p-12,
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0x1.0000001555556p-13,
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0x1.0000000555555p-14,
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0x1.0000000155555p-15,
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0x1.0000000055555p-16,
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0x1.0000000015555p-17,
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0x1.0000000005555p-18,
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0x1.0000000001555p-19,
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0x1.0000000000555p-20,
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0x1.0000000000155p-21,
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0x1.0000000000055p-22,
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0x1.0000000000015p-23,
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0x1.0000000000005p-24,
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0x1.0000000000001p-25,
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0x1.0000000000000p-26,
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0x1.0000000000000p-27,
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0x1.0000000000000p-28,
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0x1.0000000000000p-29,
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0x1.0000000000000p-30,
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0x1.0000000000000p-31,
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0x1.0000000000000p-32,
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0x1.0000000000000p-33,
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0x1.0000000000000p-34,
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0x1.0000000000000p-35,
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||||
0x1.0000000000000p-36,
|
||||
0x1.0000000000000p-37,
|
||||
0x1.0000000000000p-38,
|
||||
0x1.0000000000000p-39,
|
||||
0x1.0000000000000p-40,
|
||||
0x1.0000000000000p-41,
|
||||
0x1.0000000000000p-42,
|
||||
0x1.0000000000000p-43,
|
||||
0x1.0000000000000p-44,
|
||||
0x1.0000000000000p-45,
|
||||
0x1.0000000000000p-46,
|
||||
0x1.0000000000000p-47,
|
||||
0x1.0000000000000p-48,
|
||||
0x1.0000000000000p-49,
|
||||
0x1.0000000000000p-50,
|
||||
0x1.0000000000000p-51,
|
||||
0x1.0000000000000p-52,
|
||||
0x1.0000000000000p-53,
|
||||
0x1.0000000000000p-54,
|
||||
0x1.0000000000000p-55,
|
||||
0x1.0000000000000p-56,
|
||||
0x1.0000000000000p-57,
|
||||
0x1.0000000000000p-58,
|
||||
0x1.0000000000000p-59,
|
||||
0x1.0000000000000p-60,
|
||||
0x1.0000000000000p-61,
|
||||
0x1.0000000000000p-62,
|
||||
0x1.0000000000000p-63,
|
||||
};
|
||||
|
||||
long double ptablel[] = {
|
||||
0x1.0000000000000p-1,
|
||||
0x1.0000000000000p-2,
|
||||
0x1.0000000000000p-3,
|
||||
0x1.0000000000000p-4,
|
||||
0x1.0000000000000p-5,
|
||||
0x1.0000000000000p-6,
|
||||
0x1.0000000000000p-7,
|
||||
0x1.0000000000000p-8,
|
||||
0x1.0000000000000p-9,
|
||||
0x1.0000000000000p-10,
|
||||
0x1.0000000000000p-11,
|
||||
0x1.0000000000000p-12,
|
||||
0x1.0000000000000p-13,
|
||||
0x1.0000000000000p-14,
|
||||
0x1.0000000000000p-15,
|
||||
0x1.0000000000000p-16,
|
||||
0x1.0000000000000p-17,
|
||||
0x1.0000000000000p-18,
|
||||
0x1.0000000000000p-19,
|
||||
0x1.0000000000000p-20,
|
||||
0x1.0000000000000p-21,
|
||||
0x1.0000000000000p-22,
|
||||
0x1.0000000000000p-23,
|
||||
0x1.0000000000000p-24,
|
||||
0x1.0000000000000p-25,
|
||||
0x1.0000000000000p-26,
|
||||
0x1.0000000000000p-27,
|
||||
0x1.0000000000000p-28,
|
||||
0x1.0000000000000p-29,
|
||||
0x1.0000000000000p-30,
|
||||
0x1.0000000000000p-31,
|
||||
0x1.0000000000000p-32,
|
||||
0x1.0000000000000p-33,
|
||||
0x1.0000000000000p-34,
|
||||
0x1.0000000000000p-35,
|
||||
0x1.0000000000000p-36,
|
||||
0x1.0000000000000p-37,
|
||||
0x1.0000000000000p-38,
|
||||
0x1.0000000000000p-39,
|
||||
0x1.0000000000000p-40,
|
||||
0x1.0000000000000p-41,
|
||||
0x1.0000000000000p-42,
|
||||
0x1.0000000000000p-43,
|
||||
0x1.0000000000000p-44,
|
||||
0x1.0000000000000p-45,
|
||||
0x1.0000000000000p-46,
|
||||
0x1.0000000000000p-47,
|
||||
0x1.0000000000000p-48,
|
||||
0x1.0000000000000p-49,
|
||||
0x1.0000000000000p-50,
|
||||
0x1.0000000000000p-51,
|
||||
0x1.0000000000000p-52,
|
||||
0x1.0000000000000p-53,
|
||||
0x1.0000000000000p-54,
|
||||
0x1.0000000000000p-55,
|
||||
0x1.0000000000000p-56,
|
||||
0x1.0000000000000p-57,
|
||||
0x1.0000000000000p-58,
|
||||
0x1.0000000000000p-59,
|
||||
0x1.0000000000000p-60,
|
||||
0x1.0000000000000p-61,
|
||||
0x1.0000000000000p-62,
|
||||
0x1.0000000000000p-63,
|
||||
};
|
||||
|
||||
|
|
@ -0,0 +1,58 @@
|
|||
|
||||
import math;
|
||||
|
||||
import os;
|
||||
import sys;
|
||||
|
||||
abspath = os.path.abspath(sys.argv[0])
|
||||
dname = os.path.dirname(abspath)
|
||||
os.chdir(dname)
|
||||
|
||||
data=[
|
||||
('cordic_dataf.c', 'float', 'f', 32),
|
||||
('cordic_data.c', 'double', '', 64),
|
||||
('cordic_datal.c', 'long double', 'l', 64),
|
||||
]
|
||||
|
||||
for f in data:
|
||||
fname = f[0]
|
||||
ftype = f[1]
|
||||
s = f[2]
|
||||
N = f[3]
|
||||
|
||||
f = open(fname, 'w')
|
||||
|
||||
tK = 1
|
||||
for i in range(1, N):
|
||||
tK *= math.cos(math.atan(2**(-i)));
|
||||
f.write(ftype + ' tK' + s + ' = ' + float.hex(tK) + ';\n')
|
||||
f.write('\n')
|
||||
|
||||
hK = 1
|
||||
for i in range(1, N):
|
||||
hK *= math.cos(math.atanh(2**(-i)));
|
||||
f.write(ftype + ' hK' + s + ' = ' + float.hex(hK) + ';\n')
|
||||
f.write('\n')
|
||||
|
||||
f.write(ftype + ' ttable' + s + '[] = {\n');
|
||||
for i in range(1, N):
|
||||
v = math.atan(2**(-i));
|
||||
f.write(' ' + float.hex(v) + ',\n')
|
||||
f.write('};\n')
|
||||
f.write('\n')
|
||||
|
||||
f.write(ftype + ' htable' + s + '[] = {\n');
|
||||
for i in range(1, N):
|
||||
v = math.atanh(2**(-i));
|
||||
f.write(' ' + float.hex(v) + ',\n')
|
||||
f.write('};\n')
|
||||
f.write('\n')
|
||||
|
||||
f.write(ftype + ' ptable' + s + '[] = {\n');
|
||||
for i in range(1, N):
|
||||
v = 2**(-i);
|
||||
f.write(' ' + float.hex(v) + ',\n')
|
||||
f.write('};\n')
|
||||
f.write('\n')
|
||||
|
||||
f.close();
|
||||
|
|
@ -5,21 +5,29 @@
|
|||
#include <stdint.h>
|
||||
|
||||
#define ln2 0.69314718055994530941723212145817
|
||||
static double HALF_PI = 1.570796326794896619231321691639751;
|
||||
static double PI = 3.141592653589793238462643383279502;
|
||||
static double LOG2E = 1.442695040888963407359924681001892;
|
||||
|
||||
#define countof(arr) (sizeof arr/sizeof arr[0])
|
||||
|
||||
#define ftype float
|
||||
#define suffix(name) name ## f
|
||||
#include "cordic/cordic_dataf.c"
|
||||
#include "generic.h"
|
||||
#undef ftype
|
||||
#undef suffix
|
||||
|
||||
#define ftype double
|
||||
#define suffix(name) name
|
||||
#include "cordic/cordic_data.c"
|
||||
#include "generic.h"
|
||||
#undef ftype
|
||||
#undef suffix
|
||||
|
||||
#define ftype long double
|
||||
#define suffix(name) name ## l
|
||||
#include "cordic/cordic_datal.c"
|
||||
#include "generic.h"
|
||||
#undef ftype
|
||||
#undef suffix
|
||||
|
|
|
|||
|
|
@ -1,38 +1,225 @@
|
|||
|
||||
|
||||
static ftype suffix(cordic)(
|
||||
ftype x0, // x initial value
|
||||
ftype y0, // y initial value
|
||||
ftype z0, // initial 'angle'
|
||||
int m, // system: 1 for trig, -1 for hyperbolic
|
||||
int v, // mode: 1 for vectoring, 0 for rotation
|
||||
ftype *c, // output x
|
||||
ftype *s // output y
|
||||
) {
|
||||
int tab_count = 0;
|
||||
ftype *tab = NULL;
|
||||
if(m == 1) {
|
||||
tab = suffix(ttable);
|
||||
tab_count = countof(suffix(ttable));
|
||||
}
|
||||
else if(m == -1) {
|
||||
tab = suffix(htable);
|
||||
tab_count = countof(suffix(htable));
|
||||
}
|
||||
ftype x = x0;
|
||||
ftype y = y0;
|
||||
ftype z = z0;
|
||||
for(int i = 0; i != tab_count; ++i) {
|
||||
ftype sign;
|
||||
if(v) sign = (y < 0)? 1 : -1;
|
||||
else sign = (z < 0)? -1 : 1;
|
||||
ftype x1 = suffix(fma)(suffix(ptable)[i], -m*sign*y, x);
|
||||
ftype y1 = suffix(fma)(suffix(ptable)[i], x*sign, y);
|
||||
x = x1;
|
||||
y = y1;
|
||||
z = suffix(fma)(tab[i], -sign, z);
|
||||
}
|
||||
if(c!=NULL) *c = x;
|
||||
if(s!=NULL) *s = y;
|
||||
return z;
|
||||
}
|
||||
|
||||
ftype suffix(sin)(ftype x) {
|
||||
if(isinf(x)) return NAN;
|
||||
if(isnan(x)) return NAN;
|
||||
int k;
|
||||
ftype alpha = suffix(remquo)(x, HALF_PI, &k);
|
||||
if(x == 0) return x;
|
||||
k = (((k % 4) +4) %4);
|
||||
ftype sinx;
|
||||
ftype cosx;
|
||||
suffix(cordic)(suffix(tK), 0, alpha, 1, 0, &cosx, &sinx);
|
||||
switch(k) {
|
||||
case 0: return sinx;
|
||||
case 1: return cosx;
|
||||
case 2: return -sinx;
|
||||
case 3: return -cosx;
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
|
||||
ftype suffix(cos)(ftype x) {
|
||||
if(isinf(x)) return NAN;
|
||||
if(isnan(x)) return NAN;
|
||||
int k;
|
||||
ftype alpha = suffix(remquo)(x, HALF_PI, &k);
|
||||
k = (((k % 4) +4) %4);
|
||||
ftype sinx;
|
||||
ftype cosx;
|
||||
suffix(cordic)(suffix(tK), 0, alpha, 1, 0, &cosx, &sinx);
|
||||
switch(k) {
|
||||
case 0: return cosx;
|
||||
case 1: return -sinx;
|
||||
case 2: return -cosx;
|
||||
case 3: return sinx;
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
|
||||
ftype suffix(tan)(ftype x) {
|
||||
if(isinf(x)) return NAN;
|
||||
if(isnan(x)) return NAN;
|
||||
int k;
|
||||
ftype alpha = suffix(remquo)(x, HALF_PI, &k);
|
||||
if(x == 0) return x;
|
||||
k = (((k % 2) +2) %2);
|
||||
ftype sinx;
|
||||
ftype cosx;
|
||||
suffix(cordic)(suffix(tK), 0, alpha, 1, 0, &cosx, &sinx);
|
||||
switch(k) {
|
||||
case 0: return sinx/cosx;
|
||||
case 1: return -cosx/sinx;
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
|
||||
ftype suffix(cot)(ftype x) {
|
||||
if(x == 0) return x;
|
||||
if(isinf(x)) return NAN;
|
||||
if(isnan(x)) return NAN;
|
||||
int k;
|
||||
ftype alpha = suffix(remquo)(x, HALF_PI, &k);
|
||||
k = (((k % 2) +2) %2);
|
||||
ftype sinx;
|
||||
ftype cosx;
|
||||
suffix(cordic)(suffix(tK), 0, alpha, 1, 0, &cosx, &sinx);
|
||||
switch(k) {
|
||||
case 0: return cosx/sinx;
|
||||
case 1: return -sinx/cosx;
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
|
||||
ftype suffix(exp)(ftype x) {
|
||||
if(x == 0) return x;
|
||||
if(isinf(x)) return NAN;
|
||||
if(isnan(x)) return NAN;
|
||||
if(x > 0 && isinf(x)) return +INFINITY;
|
||||
if(x < 0 && isinf(x)) return +0.0;
|
||||
if(x == 0) return 1.0;
|
||||
if(x > 709.8) {
|
||||
#if math_errhandling & MATH_ERREXCEPT
|
||||
feraiseexcept(FE_OVERFLOW);
|
||||
#endif
|
||||
#if math_errhandling & MATH_ERRNO
|
||||
errno = ERANGE;
|
||||
#endif
|
||||
return +INFINITY;
|
||||
}
|
||||
if(x < -708.4) {
|
||||
#if math_errhandling & MATH_ERREXCEPT
|
||||
feraiseexcept(FE_OVERFLOW);
|
||||
#endif
|
||||
#if math_errhandling & MATH_ERRNO
|
||||
errno = ERANGE;
|
||||
#endif
|
||||
return 0;
|
||||
}
|
||||
ftype e = 1.0;
|
||||
ftype xp = 1.0;
|
||||
ftype f = 1;
|
||||
for(uint64_t i = 1; i != 10; ++i) {
|
||||
f *= i;
|
||||
xp *= x;
|
||||
e += xp / f;
|
||||
}
|
||||
return e;
|
||||
ftype t = x*LOG2E;
|
||||
int64_t k = (int64_t)t;
|
||||
x = (t - (ftype)k) / LOG2E;
|
||||
ftype xx = x*x;
|
||||
ftype xxx = xx*x;
|
||||
ftype xxxx = xx*xx;
|
||||
ftype xxxxx = xxx*xx;
|
||||
ftype expx = 1+x + xx/2.0 + xxx/6.0+ xxxx/24.0 + xxxxx/720.0;
|
||||
if(k>0) expx *= 2.0;
|
||||
if(k>0) while(k-- > 0) expx *= 2.0;
|
||||
if(k<0) while(k++ < 0) expx /= 2.0;
|
||||
return expx;
|
||||
}
|
||||
|
||||
ftype suffix(atan)(ftype x) {
|
||||
if(x == 0) return x;
|
||||
if(isinf(x)) return INFINITY;
|
||||
if(isnan(x)) return NAN;
|
||||
ftype atan;
|
||||
if(x > 1) {
|
||||
atan = HALF_PI - suffix(cordic)(x, 1, 0, 1, 1, NULL, NULL);
|
||||
}
|
||||
else if(x < -1) {
|
||||
atan = -HALF_PI + suffix(cordic)(-x, 1, 0, 1, 1, NULL, NULL);
|
||||
}
|
||||
else {
|
||||
atan = suffix(cordic)(1, x, 0, 1, 1, NULL, NULL);
|
||||
}
|
||||
return atan;
|
||||
}
|
||||
|
||||
ftype suffix(acos)(ftype x) {
|
||||
if(x == 0) return HALF_PI;
|
||||
if(x == -1) return PI;
|
||||
if(x == 1) return 0;
|
||||
if(isinf(x)) return INFINITY;
|
||||
if(isnan(x)) return NAN;
|
||||
if(fabs(x) > 1) return NAN;
|
||||
ftype atan;
|
||||
x = sqrt(fma(-x,x,1))/x;
|
||||
if(x > 1) {
|
||||
atan = HALF_PI - suffix(cordic)(x, 1, 0, 1, 1, NULL, NULL);
|
||||
}
|
||||
else if(x < -1) {
|
||||
atan = -HALF_PI + suffix(cordic)(-x, 1, 0, 1, 1, NULL, NULL);
|
||||
}
|
||||
else {
|
||||
atan = suffix(cordic)(1, x, 0, 1, 1, NULL, NULL);
|
||||
}
|
||||
if(x < 0) atan += PI;
|
||||
return atan;
|
||||
}
|
||||
|
||||
ftype suffix(asin)(ftype x) {
|
||||
if(x == 0) return 0;
|
||||
if(x == -1) return -HALF_PI;
|
||||
if(x == 1) return HALF_PI;
|
||||
if(isinf(x)) return INFINITY;
|
||||
if(isnan(x)) return NAN;
|
||||
if(fabs(x) > 1) return NAN;
|
||||
ftype atan;
|
||||
x /= sqrt(fma(-x,x,1));
|
||||
if(x > 1) {
|
||||
atan = HALF_PI - suffix(cordic)(x, 1, 0, 1, 1, NULL, NULL);
|
||||
}
|
||||
else if(x < -1) {
|
||||
atan = -HALF_PI + suffix(cordic)(-x, 1, 0, 1, 1, NULL, NULL);
|
||||
}
|
||||
else {
|
||||
atan = suffix(cordic)(1, x, 0, 1, 1, NULL, NULL);
|
||||
}
|
||||
return atan;
|
||||
}
|
||||
|
||||
// ftype suffix(exp)(ftype x) {
|
||||
// if(isnan(x)) return NAN;
|
||||
// if(x > 0 && isinf(x)) return +INFINITY;
|
||||
// if(x < 0 && isinf(x)) return +0.0;
|
||||
// if(x == 0) return 1.0;
|
||||
// if(x > 709.8) {
|
||||
// #if math_errhandling & MATH_ERREXCEPT
|
||||
// feraiseexcept(FE_OVERFLOW);
|
||||
// #endif
|
||||
// #if math_errhandling & MATH_ERRNO
|
||||
// errno = ERANGE;
|
||||
// #endif
|
||||
// return +INFINITY;
|
||||
// }
|
||||
// if(x < -708.4) {
|
||||
// #if math_errhandling & MATH_ERREXCEPT
|
||||
// feraiseexcept(FE_OVERFLOW);
|
||||
// #endif
|
||||
// #if math_errhandling & MATH_ERRNO
|
||||
// errno = ERANGE;
|
||||
// #endif
|
||||
// return 0;
|
||||
// }
|
||||
// ftype e = 1.0;
|
||||
// ftype xp = 1.0;
|
||||
// ftype f = 1;
|
||||
// for(uint64_t i = 1; i != 10; ++i) {
|
||||
// f *= i;
|
||||
// xp *= x;
|
||||
// e += xp / f;
|
||||
// }
|
||||
// return e;
|
||||
// }
|
||||
|
||||
ftype suffix(exp2)(ftype x) {
|
||||
return suffix(exp)(x * ln2);
|
||||
}
|
||||
|
|
|
|||
|
|
@ -0,0 +1,47 @@
|
|||
|
||||
import matplotlib.pyplot as plt
|
||||
import numpy as np
|
||||
import subprocess;
|
||||
import math;
|
||||
import csv;
|
||||
|
||||
plt.style.use('_mpl-gallery')
|
||||
pi=math.pi
|
||||
|
||||
with open('bin/data.csv', newline='') as csvfile:
|
||||
reader = csv.reader(csvfile, delimiter=' ', quotechar='|')
|
||||
rows = [row for row in reader];
|
||||
|
||||
# make data
|
||||
x = [float.fromhex(xi[:-1]) for xi in rows[0][:-1]]
|
||||
y = [float.fromhex(yi[:-1]) for yi in rows[1][:-1]]
|
||||
yex = [math.asin(x0) for x0 in x]
|
||||
|
||||
err = np.subtract(y, yex);
|
||||
maxerrv = max(err)
|
||||
minerrv = min(err)
|
||||
maxerr = [maxerrv for xi in rows[0][:-1]]
|
||||
minerr = [minerrv for xi in rows[0][:-1]]
|
||||
errscale = 10**-14
|
||||
|
||||
lo = x[0]
|
||||
hi = x[-1]
|
||||
|
||||
fig, a = plt.subplots(2, 1, constrained_layout=True)
|
||||
# a.step(x, y, linewidth=1)
|
||||
a[0].set_xlim(lo, hi);
|
||||
# a[0].set_ylim(-1.000001, 1.000001);
|
||||
a[0].set_xlabel('x');
|
||||
a[0].set_ylabel('f(x)');
|
||||
a[0].plot(x, y, x, yex)
|
||||
|
||||
a[1].set_xlim(lo, hi);
|
||||
a[1].ticklabel_format(useOffset=False)
|
||||
a[1].set_ylim(-errscale, errscale);
|
||||
a[1].set_xlabel('x');
|
||||
a[1].set_ylabel('absolute error');
|
||||
a[1].plot(x, err, x, maxerr, x, minerr);
|
||||
|
||||
plt.show()
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,26 @@
|
|||
|
||||
#include <stdlib.h>
|
||||
#include <stdio.h>
|
||||
#include <math.h>
|
||||
#include <stdint.h>
|
||||
#include <stdio.h>
|
||||
#include <math.h>
|
||||
|
||||
// TODO: won't work until %a is implemented
|
||||
int main(int argc, char **argv) {
|
||||
double lo = -1;
|
||||
double hi = 1;
|
||||
double step = 0.0001;
|
||||
FILE *out = fopen("bin/data.csv", "w");
|
||||
for(double i = lo; i < hi; i += step) {
|
||||
fprintf(out, "%f", i);
|
||||
fprintf(out, ", ");
|
||||
}
|
||||
fprintf(out, "\n");
|
||||
for(double i = lo; i < hi; i += step) {
|
||||
fprintf(out, "%a", asin(i));
|
||||
fprintf(out, ", ");
|
||||
}
|
||||
fclose(out);
|
||||
return 0;
|
||||
}
|
||||
Loading…
Reference in New Issue