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math: cleanup gamma.v: remove if true { and gotos; move constants closer to the places that do use them
This commit is contained in:
Delyan Angelov
parent
4c8c892b96
commit
d1ec41cd6a
@ -11,14 +11,12 @@ fn stirling(x f64) (f64, f64) {
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if x > 200 {
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return inf(1), 1.0
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}
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sqrt_two_pi := 2.506628274631000502417
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max_stirling := 143.01608
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mut w := 1.0 / x
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w = 1.0 + w * ((((gamma_s[0] * w + gamma_s[1]) * w + gamma_s[2]) * w + gamma_s[3]) * w +
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gamma_s[4])
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mut y1 := exp(x)
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mut y2 := 1.0
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if x > max_stirling { // avoid Pow() overflow
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if x > 143.01608 { // avoid Pow() overflow, the constant is max_stirling
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v := pow(x, 0.5 * x - 0.25)
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y1_ := y1
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y1 = v
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@ -26,7 +24,7 @@ fn stirling(x f64) (f64, f64) {
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} else {
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y1 = pow(x, x - 0.5) / y1
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}
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return y1, f64(sqrt_two_pi) * w * y2
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return y1, f64(2.506628274631000502417) * w * y2 // the constant is sqrt_two_pi
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}
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// gamma returns the gamma function of x.
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@ -40,7 +38,6 @@ fn stirling(x f64) (f64, f64) {
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// gamma(nan) = nan
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pub fn gamma(a f64) f64 {
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mut x := a
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euler := 0.57721566490153286060651209008240243104215933593992 // A001620
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if is_neg_int(x) || is_inf(x, -1) || is_nan(x) {
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return nan()
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}
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@ -92,18 +89,14 @@ pub fn gamma(a f64) f64 {
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}
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for x < 0 {
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if x > -1e-09 {
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unsafe {
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goto small
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}
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return gamma_too_small(x, z)
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}
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z = z / x
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x = x + 1
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}
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for x < 2 {
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if x < 1e-09 {
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unsafe {
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goto small
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}
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return gamma_too_small(x, z)
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}
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z = z / x
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x = x + 1
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@ -116,13 +109,14 @@ pub fn gamma(a f64) f64 {
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gamma_p[4]) * x + gamma_p[5]) * x + gamma_p[6]
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q = ((((((x * gamma_q[0] + gamma_q[1]) * x + gamma_q[2]) * x + gamma_q[3]) * x +
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gamma_q[4]) * x + gamma_q[5]) * x + gamma_q[6]) * x + gamma_q[7]
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if true {
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return z * p / q
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}
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small:
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return z * p / q
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}
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fn gamma_too_small(x f64, z f64) f64 {
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if x == 0 {
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return inf(1)
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}
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euler := 0.57721566490153286060651209008240243104215933593992 // A001620
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return z / ((1.0 + euler * x) * x)
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}
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@ -142,14 +136,6 @@ pub fn log_gamma(x f64) f64 {
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// log_gamma_sign returns the natural logarithm and sign (-1 or +1) of Gamma(x)
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pub fn log_gamma_sign(a f64) (f64, int) {
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mut x := a
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ymin := 1.461632144968362245
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tiny := exp2(-70)
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two52 := exp2(52) // 0x4330000000000000 ~4.5036e+15
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two58 := exp2(58) // 0x4390000000000000 ~2.8823e+17
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tc := 1.46163214496836224576e+00 // 0x3FF762D86356BE3F
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tf := -1.21486290535849611461e-01 // 0xBFBF19B9BCC38A42
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// tt := -(tail of tf)
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tt := -3.63867699703950536541e-18 // 0xBC50C7CAA48A971F
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mut sign := 1
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if is_nan(x) {
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return x, sign
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@ -165,7 +151,7 @@ pub fn log_gamma_sign(a f64) (f64, int) {
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x = -x
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neg = true
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}
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if x < tiny { // if |x| < 2**-70, return -log(|x|)
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if x < exp2(-70) { // if |x| < 2**-70, return -log(|x|)
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if neg {
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sign = -1
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}
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@ -173,7 +159,7 @@ pub fn log_gamma_sign(a f64) (f64, int) {
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}
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mut nadj := 0.0
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if neg {
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if x >= two52 {
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if x >= exp2(52) { // the constant is 0x4330000000000000 ~4.5036e+15
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// x| >= 2**52, must be -integer
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return inf(1), sign
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}
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@ -190,6 +176,8 @@ pub fn log_gamma_sign(a f64) (f64, int) {
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if x == 1 || x == 2 { // purge off 1 and 2
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return 0.0, sign
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} else if x < 2 { // use lgamma(x) = lgamma(x+1) - log(x)
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ymin := 1.461632144968362245
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tc := 1.46163214496836224576e+00 // 0x3FF762D86356BE3F
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mut y := 0.0
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mut i := 0
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if x <= 0.9 {
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@ -234,6 +222,9 @@ pub fn log_gamma_sign(a f64) (f64, int) {
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w * lgamma_t[13])))
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gamma_p3 := lgamma_t[2] + w * (lgamma_t[5] + w * (lgamma_t[8] + w * (lgamma_t[11] +
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w * lgamma_t[14])))
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tf := -1.21486290535849611461e-01 // 0xBFBF19B9BCC38A42
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// tt := -(tail of tf)
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tt := -3.63867699703950536541e-18 // 0xBC50C7CAA48A971F
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p := z * gamma_p1 - (tt - w * (gamma_p2 + y * gamma_p3))
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lgamma += (tf + p)
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} else if i == 2 {
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@ -278,7 +269,7 @@ pub fn log_gamma_sign(a f64) (f64, int) {
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z *= (y + 2)
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lgamma += log(z)
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}
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} else if x < two58 { // 8 <= x < 2**58
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} else if x < exp2(58) { // 8 <= x < 2**58, which is 0x4390000000000000 ~2.8823e+17
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t := log(x)
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z := 1.0 / x
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y := z * z
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@ -297,8 +288,6 @@ pub fn log_gamma_sign(a f64) (f64, int) {
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// sin_pi(x) is a helper function for negative x
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fn sin_pi(x_ f64) f64 {
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mut x := x_
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two52 := exp2(52) // 0x4330000000000000 ~4.5036e+15
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two53 := exp2(53) // 0x4340000000000000 ~9.0072e+15
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if x < 0.25 {
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return -sin(pi * x)
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}
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@ -309,10 +298,11 @@ fn sin_pi(x_ f64) f64 {
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x = mod(x, 2)
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n = int(x * 4)
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} else {
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if x >= two53 { // x must be even
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if x >= exp2(53) { // x must be even; the constant is 0x4340000000000000 ~9.0072e+15
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x = 0
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n = 0
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} else {
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two52 := exp2(52) // 0x4330000000000000 ~4.5036e+15
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if x < two52 {
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z = x + two52 // exact
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}
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