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Diffstat (limited to 'math/tools/sin.sollya')
| -rw-r--r-- | math/tools/sin.sollya | 37 |
1 files changed, 37 insertions, 0 deletions
diff --git a/math/tools/sin.sollya b/math/tools/sin.sollya new file mode 100644 index 000000000000..a6e851145c11 --- /dev/null +++ b/math/tools/sin.sollya @@ -0,0 +1,37 @@ +// polynomial for approximating sin(x) +// +// Copyright (c) 2019, Arm Limited. +// SPDX-License-Identifier: MIT + +deg = 7; // polynomial degree +a = -pi/4; // interval +b = pi/4; + +// find even polynomial with minimal abs error compared to sin(x)/x + +// account for /x +deg = deg-1; + +// f = sin(x)/x; +f = 1; +c = 1; +for i from 1 to 60 do { c = 2*i*(2*i + 1)*c; f = f + (-1)^i*x^(2*i)/c; }; + +// return p that minimizes |f(x) - poly(x) - x^d*p(x)| +approx = proc(poly,d) { + return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10); +}; + +// first coeff is fixed, iteratively find optimal double prec coeffs +poly = 1; +for i from 1 to deg/2 do { + p = roundcoefficients(approx(poly,2*i), [|D ...|]); + poly = poly + x^(2*i)*coeff(p,0); +}; + +display = hexadecimal; +print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); +print("abs error:", accurateinfnorm(sin(x)-x*poly(x), [a;b], 30)); +print("in [",a,b,"]"); +print("coeffs:"); +for i from 0 to deg do coeff(poly,i); |
