| /* origin: FreeBSD /usr/src/lib/msun/src/e_jnf.c */ |
| /* |
| * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
| */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| use super::{fabsf, j0f, j1f, logf, y0f, y1f}; |
| |
| pub fn jnf(n: i32, mut x: f32) -> f32 { |
| let mut ix: u32; |
| let mut nm1: i32; |
| let mut sign: bool; |
| let mut i: i32; |
| let mut a: f32; |
| let mut b: f32; |
| let mut temp: f32; |
| |
| ix = x.to_bits(); |
| sign = (ix >> 31) != 0; |
| ix &= 0x7fffffff; |
| if ix > 0x7f800000 { |
| /* nan */ |
| return x; |
| } |
| |
| /* J(-n,x) = J(n,-x), use |n|-1 to avoid overflow in -n */ |
| if n == 0 { |
| return j0f(x); |
| } |
| if n < 0 { |
| nm1 = -(n + 1); |
| x = -x; |
| sign = !sign; |
| } else { |
| nm1 = n - 1; |
| } |
| if nm1 == 0 { |
| return j1f(x); |
| } |
| |
| sign &= (n & 1) != 0; /* even n: 0, odd n: signbit(x) */ |
| x = fabsf(x); |
| if ix == 0 || ix == 0x7f800000 { |
| /* if x is 0 or inf */ |
| b = 0.0; |
| } else if (nm1 as f32) < x { |
| /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ |
| a = j0f(x); |
| b = j1f(x); |
| i = 0; |
| while i < nm1 { |
| i += 1; |
| temp = b; |
| b = b * (2.0 * (i as f32) / x) - a; |
| a = temp; |
| } |
| } else { |
| if ix < 0x35800000 { |
| /* x < 2**-20 */ |
| /* x is tiny, return the first Taylor expansion of J(n,x) |
| * J(n,x) = 1/n!*(x/2)^n - ... |
| */ |
| if nm1 > 8 { |
| /* underflow */ |
| nm1 = 8; |
| } |
| temp = 0.5 * x; |
| b = temp; |
| a = 1.0; |
| i = 2; |
| while i <= nm1 + 1 { |
| a *= i as f32; /* a = n! */ |
| b *= temp; /* b = (x/2)^n */ |
| i += 1; |
| } |
| b = b / a; |
| } else { |
| /* use backward recurrence */ |
| /* x x^2 x^2 |
| * J(n,x)/J(n-1,x) = ---- ------ ------ ..... |
| * 2n - 2(n+1) - 2(n+2) |
| * |
| * 1 1 1 |
| * (for large x) = ---- ------ ------ ..... |
| * 2n 2(n+1) 2(n+2) |
| * -- - ------ - ------ - |
| * x x x |
| * |
| * Let w = 2n/x and h=2/x, then the above quotient |
| * is equal to the continued fraction: |
| * 1 |
| * = ----------------------- |
| * 1 |
| * w - ----------------- |
| * 1 |
| * w+h - --------- |
| * w+2h - ... |
| * |
| * To determine how many terms needed, let |
| * Q(0) = w, Q(1) = w(w+h) - 1, |
| * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), |
| * When Q(k) > 1e4 good for single |
| * When Q(k) > 1e9 good for double |
| * When Q(k) > 1e17 good for quadruple |
| */ |
| /* determine k */ |
| let mut t: f32; |
| let mut q0: f32; |
| let mut q1: f32; |
| let mut w: f32; |
| let h: f32; |
| let mut z: f32; |
| let mut tmp: f32; |
| let nf: f32; |
| let mut k: i32; |
| |
| nf = (nm1 as f32) + 1.0; |
| w = 2.0 * (nf as f32) / x; |
| h = 2.0 / x; |
| z = w + h; |
| q0 = w; |
| q1 = w * z - 1.0; |
| k = 1; |
| while q1 < 1.0e4 { |
| k += 1; |
| z += h; |
| tmp = z * q1 - q0; |
| q0 = q1; |
| q1 = tmp; |
| } |
| t = 0.0; |
| i = k; |
| while i >= 0 { |
| t = 1.0 / (2.0 * ((i as f32) + nf) / x - t); |
| i -= 1; |
| } |
| a = t; |
| b = 1.0; |
| /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) |
| * Hence, if n*(log(2n/x)) > ... |
| * single 8.8722839355e+01 |
| * double 7.09782712893383973096e+02 |
| * long double 1.1356523406294143949491931077970765006170e+04 |
| * then recurrent value may overflow and the result is |
| * likely underflow to zero |
| */ |
| tmp = nf * logf(fabsf(w)); |
| if tmp < 88.721679688 { |
| i = nm1; |
| while i > 0 { |
| temp = b; |
| b = 2.0 * (i as f32) * b / x - a; |
| a = temp; |
| i -= 1; |
| } |
| } else { |
| i = nm1; |
| while i > 0 { |
| temp = b; |
| b = 2.0 * (i as f32) * b / x - a; |
| a = temp; |
| /* scale b to avoid spurious overflow */ |
| let x1p60 = f32::from_bits(0x5d800000); // 0x1p60 == 2^60 |
| if b > x1p60 { |
| a /= b; |
| t /= b; |
| b = 1.0; |
| } |
| i -= 1; |
| } |
| } |
| z = j0f(x); |
| w = j1f(x); |
| if fabsf(z) >= fabsf(w) { |
| b = t * z / b; |
| } else { |
| b = t * w / a; |
| } |
| } |
| } |
| |
| if sign { |
| -b |
| } else { |
| b |
| } |
| } |
| |
| pub fn ynf(n: i32, x: f32) -> f32 { |
| let mut ix: u32; |
| let mut ib: u32; |
| let nm1: i32; |
| let mut sign: bool; |
| let mut i: i32; |
| let mut a: f32; |
| let mut b: f32; |
| let mut temp: f32; |
| |
| ix = x.to_bits(); |
| sign = (ix >> 31) != 0; |
| ix &= 0x7fffffff; |
| if ix > 0x7f800000 { |
| /* nan */ |
| return x; |
| } |
| if sign && ix != 0 { |
| /* x < 0 */ |
| return 0.0 / 0.0; |
| } |
| if ix == 0x7f800000 { |
| return 0.0; |
| } |
| |
| if n == 0 { |
| return y0f(x); |
| } |
| if n < 0 { |
| nm1 = -(n + 1); |
| sign = (n & 1) != 0; |
| } else { |
| nm1 = n - 1; |
| sign = false; |
| } |
| if nm1 == 0 { |
| if sign { |
| return -y1f(x); |
| } else { |
| return y1f(x); |
| } |
| } |
| |
| a = y0f(x); |
| b = y1f(x); |
| /* quit if b is -inf */ |
| ib = b.to_bits(); |
| i = 0; |
| while i < nm1 && ib != 0xff800000 { |
| i += 1; |
| temp = b; |
| b = (2.0 * (i as f32) / x) * b - a; |
| ib = b.to_bits(); |
| a = temp; |
| } |
| |
| if sign { |
| -b |
| } else { |
| b |
| } |
| } |
