In arbitrary-precision arithmetics, the sign of the result of trigonometric and exponential functions is sometimes wrong.
Here's an excerpt of a formula printing some debug results:
complex m1 = exp(flip(#pi))
print("exp(i * #pi)=",m1)
float sin1=sin(#pi)
float cos1=cos(#pi)
print("cos(#pi)=",cos1, ", sin(#pi)=", sin1)
When I run this without additional precision, I get the following results:
exp(i * #pi)=(-1, 1.22460635382238E-016)
cos(#pi)=-1, sin(#pi)=1.22460635382238E-016
This (aside from some floating-point imprecision) is the result I and Leonhard Euler would expect.
If however I request enough additional precision to trigger arbitrary-precision math, I get:
exp(i * #pi)=(1, 0)
cos(#pi)=1, sin(#pi)=0
The exp and cos results don't have the correct sign.
The power function also doesn't work correctly with arbitrary precision. Example formula:
complex st=(-0.698827118771579245233, 0)
complex st_power2 = sqr(st)
complex st_power4 = sqr(st_power2)
complex st_power5 = st_power4*st
complex st_power5a = st^5
print("st=", st, ", st^2=", st_power2, ", st^4=", st_power4)
print(" st^5 should be ", st_power5, ", st^5 is ", st_power5a)
Result with double precision:
st=(-0.698827118771579, 0), st^2=(0.488359341930587, 0), st^4=(0.238494846850876, 0)
st^5 should be (-0.166666666666666, 0), st^5 is (-0.166666666666666, -9.03501810404586E-021)
---
Correct, except for floating-point imprecision.
With arbitrary precision:
st=(-0.698827118771579245233, 0), st^2=(0.4883593419305869251049, 0), st^4=(0.2384948468508759168409, 0)
st^5 should be (-0.1666666666666666666667, 0), st^5 is (0.1666666666666666666667, 0)
---
Again, the sign is wrong.
In arbitrary-precision arithmetics, the sign of the result of trigonometric and exponential functions is sometimes wrong.
Here's an excerpt of a formula printing some debug results:
complex m1 = exp(flip(#pi))
print("exp(i * #pi)=",m1)
float sin1=sin(#pi)
float cos1=cos(#pi)
print("cos(#pi)=",cos1, ", sin(#pi)=", sin1)
When I run this without additional precision, I get the following results:
exp(i * #pi)=(-1, 1.22460635382238E-016)
cos(#pi)=-1, sin(#pi)=1.22460635382238E-016
This (aside from some floating-point imprecision) is the result I and Leonhard Euler would expect.
If however I request enough additional precision to trigger arbitrary-precision math, I get:
exp(i * #pi)=(1, 0)
cos(#pi)=1, sin(#pi)=0
The exp and cos results don't have the correct sign.
The power function also doesn't work correctly with arbitrary precision. Example formula:
complex st=(-0.698827118771579245233, 0)
complex st_power2 = sqr(st)
complex st_power4 = sqr(st_power2)
complex st_power5 = st_power4*st
complex st_power5a = st^5
print("st=", st, ", st^2=", st_power2, ", st^4=", st_power4)
print(" st^5 should be ", st_power5, ", st^5 is ", st_power5a)
Result with double precision:
st=(-0.698827118771579, 0), st^2=(0.488359341930587, 0), st^4=(0.238494846850876, 0)
st^5 should be (-0.166666666666666, 0), st^5 is (-0.166666666666666, -9.03501810404586E-021)
---
Correct, except for floating-point imprecision.
With arbitrary precision:
st=(-0.698827118771579245233, 0), st^2=(0.4883593419305869251049, 0), st^4=(0.2384948468508759168409, 0)
st^5 should be (-0.1666666666666666666667, 0), st^5 is (0.1666666666666666666667, 0)
---
Again, the sign is wrong.
