diff --git a/vlib/math/log.js.v b/vlib/math/log.js.v deleted file mode 100644 index a1a0cbb184..0000000000 --- a/vlib/math/log.js.v +++ /dev/null @@ -1,9 +0,0 @@ -module math - -fn JS.Math.log(x f64) f64 - -// log calculates natural (base-e) logarithm of the provided value. -[inline] -pub fn log(x f64) f64 { - return JS.Math.log(x) -} diff --git a/vlib/math/log.v b/vlib/math/log.v index 47ef731226..f274d0fc2a 100644 --- a/vlib/math/log.v +++ b/vlib/math/log.v @@ -74,3 +74,85 @@ fn ilog_b_(x_ f64) int { x, exp := normalize(x_) return int((f64_bits(x) >> shift) & mask) - bias + exp } + +// log returns the logarithm of x +// +// Method : +// 1. Argument Reduction: find k and f such that +// x = 2^k * (1+f), +// where sqrt(2)/2 < 1+f < sqrt(2) . +// +// 2. Approximation of log(1+f). +// Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) +// = 2s + 2/3 s**3 + 2/5 s**5 + ....., +// = 2s + s*R +// We use a special Remez algorithm on [0,0.1716] to generate +// a polynomial of degree 14 to approximate R The maximum error +// of this polynomial approximation is bounded by 2**-58.45. In +// other words, +// 2 4 6 8 10 12 14 +// R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s +// (the values of Lg1 to Lg7 are listed in the program) +// and +// | 2 14 | -58.45 +// | Lg1*s +...+Lg7*s - R(z) | <= 2 +// | | +// Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. +// In order to guarantee error in log below 1ulp, we compute log +// by +// log(1+f) = f - s*(f - R) (if f is not too large) +// log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) +// +// 3. Finally, log(x) = k*ln2 + log(1+f). +// = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) +// Here ln2 is split into two floating point number: +// ln2_hi + ln2_lo, +// where n*ln2_hi is always exact for |n| < 2000. +// +// Special cases: +// log(x) is NaN with signal if x < 0 (including -inf) ; +// log(+inf) is +inf; log(0) is -inf with signal; +// log(NaN) is that NaN with no signal. +// +// Accuracy: +// according to an error analysis, the error is always less than +// 1 ulp (unit in the last place). +pub fn log(a f64) f64 { + ln2_hi := 6.93147180369123816490e-01 // 3fe62e42 fee00000 + ln2_lo := 1.90821492927058770002e-10 // 3dea39ef 35793c76 + l1 := 6.666666666666735130e-01 // 3FE55555 55555593 + l2 := 3.999999999940941908e-01 // 3FD99999 9997FA04 + l3 := 2.857142874366239149e-01 // 3FD24924 94229359 + l4 := 2.222219843214978396e-01 // 3FCC71C5 1D8E78AF + l5 := 1.818357216161805012e-01 // 3FC74664 96CB03DE + l6 := 1.531383769920937332e-01 // 3FC39A09 D078C69F + l7 := 1.479819860511658591e-01 // 3FC2F112 DF3E5244 + + x := a + if is_nan(x) || is_inf(x, 1) { + return x + } else if x < 0 { + return nan() + } else if x == 0 { + return inf(-1) + } + + mut f1, mut ki := frexp(x) + if f1 < sqrt2 / 2 { + f1 *= 2 + ki-- + } + + f := f1 - 1 + k := f64(ki) + + // compute + s := f / (2 + f) + s2 := s * s + s4 := s2 * s2 + t1 := s2 * (l1 + s4 * (l3 + s4 * (l5 + s4 * l7))) + t2 := s4 * (l2 + s4 * (l4 + s4 * l6)) + r := t1 + t2 + hfsq := 0.5 * f * f + return k * ln2_hi - ((hfsq - (s * (hfsq + r) + k * ln2_lo)) - f) +}