mirror of
https://github.com/lcn2/calc.git
synced 2025-08-16 01:03:29 +03:00
add trigonometric chord of a unit circle functions
Improve builtin function strings, as printed by help builtin,
that use an optional accuracy (epsilon) arg by adding a comma.
Added the following new trigonometric functions:
crd(x [,eps]) trigonometric chord of a unit circle
acrd(x [,eps]) inverse trigonometric chord of a unit circle
This commit is contained in:
Landon Curt Noll
142
comfunc.c
142
comfunc.c
@@ -1655,7 +1655,7 @@ c_ilog(COMPLEX *c, ZVALUE base)
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* versin(x) = 1 - cos(x)
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -1705,7 +1705,7 @@ c_versin(COMPLEX *c, NUMBER *epsilon)
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* aversin(x) = acos(1 - x)
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -1751,7 +1751,7 @@ c_aversin(COMPLEX *c, NUMBER *epsilon)
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* coversin(x) = 1 - cos(x)
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -1801,7 +1801,7 @@ c_coversin(COMPLEX *c, NUMBER *epsilon)
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* acoversin(x) = asin(1 - x)
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -1847,7 +1847,7 @@ c_acoversin(COMPLEX *c, NUMBER *epsilon)
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* vercos(x) = 1 + cos(x)
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -1897,7 +1897,7 @@ c_vercos(COMPLEX *c, NUMBER *epsilon)
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* avercos(x) = acos(x - 1)
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -1943,7 +1943,7 @@ c_avercos(COMPLEX *c, NUMBER *epsilon)
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* covercos(x) = 1 + sin(x)
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -1993,7 +1993,7 @@ c_covercos(COMPLEX *c, NUMBER *epsilon)
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* acovercos(x) = asin(x - 1)
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -2039,7 +2039,7 @@ c_acovercos(COMPLEX *c, NUMBER *epsilon)
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* haversin(x) = versin(x) / 2
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -2089,7 +2089,7 @@ c_haversin(COMPLEX *c, NUMBER *epsilon)
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* ahaversin(x) = acos(1 - 2*x)
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -2138,7 +2138,7 @@ c_ahaversin(COMPLEX *c, NUMBER *epsilon)
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* hacoversin(x) = coversin(x) / 2
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -2188,7 +2188,7 @@ c_hacoversin(COMPLEX *c, NUMBER *epsilon)
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* ahacoversin(x) = asin(1 - 2*x)
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -2237,7 +2237,7 @@ c_ahacoversin(COMPLEX *c, NUMBER *epsilon)
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* havercos(x) = vercos(x) / 2
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -2287,7 +2287,7 @@ c_havercos(COMPLEX *c, NUMBER *epsilon)
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* ahavercos(x) = acos(2*x - 1)
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -2336,7 +2336,7 @@ c_ahavercos(COMPLEX *c, NUMBER *epsilon)
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* hacovercos(x) = covercos(x) / 2
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -2386,7 +2386,7 @@ c_hacovercos(COMPLEX *c, NUMBER *epsilon)
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* ahacovercos(x) = asin(2*x - 1)
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -2435,7 +2435,7 @@ c_ahacovercos(COMPLEX *c, NUMBER *epsilon)
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* exsec(x) = sec(x) - 1
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -2485,7 +2485,7 @@ c_exsec(COMPLEX *c, NUMBER *epsilon)
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* aexsec(x) = asec(x + 1)
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -2531,7 +2531,7 @@ c_aexsec(COMPLEX *c, NUMBER *epsilon)
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* excsc(x) = csc(x) - 1
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -2581,7 +2581,7 @@ c_excsc(COMPLEX *c, NUMBER *epsilon)
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* aexcsc(x) = acsc(x + 1)
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*
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* given:
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* q complex value to pass to the trig function
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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@@ -2617,3 +2617,105 @@ c_aexcsc(COMPLEX *c, NUMBER *epsilon)
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*/
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return r;
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}
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/*
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* c_crd - COMPLEX valued trigonometric chord of a unit circle
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*
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* This uses the formula:
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*
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* crd(x) = 2 * sin(x / 2)
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*
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* given:
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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* complex value result of trig function on q with error epsilon
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*/
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COMPLEX *
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c_crd(COMPLEX *c, NUMBER *epsilon)
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{
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COMPLEX *r; /* return COMPLEX value */
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COMPLEX *cdiv2; /* complex c/2 */
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COMPLEX *ctmp; /* complex sin(c/2) */
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/*
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* firewall
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*/
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if (c == NULL) {
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math_error("%s: c is NULL", __func__);
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not_reached();
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}
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if (check_epsilon(epsilon) == false) {
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math_error("Invalid epsilon arg for %s", __func__);
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not_reached();
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}
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/*
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* calculate complex trig function value
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*/
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cdiv2 = c_divq(c, &_qtwo_);
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ctmp = c_sin(cdiv2, epsilon);
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comfree(cdiv2);
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if (ctmp == NULL) {
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math_error("Failed to compute complex sine for complex crd");
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not_reached();
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}
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r = c_mulq(ctmp, &_qtwo_);
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comfree(ctmp);
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/*
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* return trigonometric result
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*/
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return r;
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}
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/*
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* c_acrd - COMPLEX valued inverse trigonometric chord of a unit circle
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*
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* This uses the formula:
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*
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* acrd(x) = 2 * asin(x / 2)
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*
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* given:
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* c complex value to pass to the trig function
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* epsilon error tolerance / precision for trig calculation
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*
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* returns:
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* complex value result of trig function on q with error epsilon
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*/
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COMPLEX *
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c_acrd(COMPLEX *c, NUMBER *epsilon)
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{
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COMPLEX *r; /* inverse trig value result */
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COMPLEX *cdiv2; /* complex c/2 */
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COMPLEX *ctmp; /* complex asin(c/2) */
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/*
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* firewall
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*/
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if (c == NULL) {
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math_error("%s: c is NULL", __func__);
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not_reached();
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}
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if (check_epsilon(epsilon) == false) {
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math_error("Invalid epsilon arg for %s", __func__);
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not_reached();
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}
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/*
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* calculate complex inverse trig function value
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*/
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cdiv2 = c_divq(c, &_qtwo_);
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ctmp = c_asin(cdiv2, epsilon);
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comfree(cdiv2);
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r = c_mulq(ctmp, &_qtwo_);
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comfree(ctmp);
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/*
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* return inverse trigonometric result
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*/
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return r;
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}
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