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-rw-r--r--deps/jemalloc/test/include/test/math.h306
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diff --git a/deps/jemalloc/test/include/test/math.h b/deps/jemalloc/test/include/test/math.h
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-/*
- * Compute the natural log of Gamma(x), accurate to 10 decimal places.
- *
- * This implementation is based on:
- *
- * Pike, M.C., I.D. Hill (1966) Algorithm 291: Logarithm of Gamma function
- * [S14]. Communications of the ACM 9(9):684.
- */
-static inline double
-ln_gamma(double x) {
- double f, z;
-
- assert(x > 0.0);
-
- if (x < 7.0) {
- f = 1.0;
- z = x;
- while (z < 7.0) {
- f *= z;
- z += 1.0;
- }
- x = z;
- f = -log(f);
- } else {
- f = 0.0;
- }
-
- z = 1.0 / (x * x);
-
- return f + (x-0.5) * log(x) - x + 0.918938533204673 +
- (((-0.000595238095238 * z + 0.000793650793651) * z -
- 0.002777777777778) * z + 0.083333333333333) / x;
-}
-
-/*
- * Compute the incomplete Gamma ratio for [0..x], where p is the shape
- * parameter, and ln_gamma_p is ln_gamma(p).
- *
- * This implementation is based on:
- *
- * Bhattacharjee, G.P. (1970) Algorithm AS 32: The incomplete Gamma integral.
- * Applied Statistics 19:285-287.
- */
-static inline double
-i_gamma(double x, double p, double ln_gamma_p) {
- double acu, factor, oflo, gin, term, rn, a, b, an, dif;
- double pn[6];
- unsigned i;
-
- assert(p > 0.0);
- assert(x >= 0.0);
-
- if (x == 0.0) {
- return 0.0;
- }
-
- acu = 1.0e-10;
- oflo = 1.0e30;
- gin = 0.0;
- factor = exp(p * log(x) - x - ln_gamma_p);
-
- if (x <= 1.0 || x < p) {
- /* Calculation by series expansion. */
- gin = 1.0;
- term = 1.0;
- rn = p;
-
- while (true) {
- rn += 1.0;
- term *= x / rn;
- gin += term;
- if (term <= acu) {
- gin *= factor / p;
- return gin;
- }
- }
- } else {
- /* Calculation by continued fraction. */
- a = 1.0 - p;
- b = a + x + 1.0;
- term = 0.0;
- pn[0] = 1.0;
- pn[1] = x;
- pn[2] = x + 1.0;
- pn[3] = x * b;
- gin = pn[2] / pn[3];
-
- while (true) {
- a += 1.0;
- b += 2.0;
- term += 1.0;
- an = a * term;
- for (i = 0; i < 2; i++) {
- pn[i+4] = b * pn[i+2] - an * pn[i];
- }
- if (pn[5] != 0.0) {
- rn = pn[4] / pn[5];
- dif = fabs(gin - rn);
- if (dif <= acu && dif <= acu * rn) {
- gin = 1.0 - factor * gin;
- return gin;
- }
- gin = rn;
- }
- for (i = 0; i < 4; i++) {
- pn[i] = pn[i+2];
- }
-
- if (fabs(pn[4]) >= oflo) {
- for (i = 0; i < 4; i++) {
- pn[i] /= oflo;
- }
- }
- }
- }
-}
-
-/*
- * Given a value p in [0..1] of the lower tail area of the normal distribution,
- * compute the limit on the definite integral from [-inf..z] that satisfies p,
- * accurate to 16 decimal places.
- *
- * This implementation is based on:
- *
- * Wichura, M.J. (1988) Algorithm AS 241: The percentage points of the normal
- * distribution. Applied Statistics 37(3):477-484.
- */
-static inline double
-pt_norm(double p) {
- double q, r, ret;
-
- assert(p > 0.0 && p < 1.0);
-
- q = p - 0.5;
- if (fabs(q) <= 0.425) {
- /* p close to 1/2. */
- r = 0.180625 - q * q;
- return q * (((((((2.5090809287301226727e3 * r +
- 3.3430575583588128105e4) * r + 6.7265770927008700853e4) * r
- + 4.5921953931549871457e4) * r + 1.3731693765509461125e4) *
- r + 1.9715909503065514427e3) * r + 1.3314166789178437745e2)
- * r + 3.3871328727963666080e0) /
- (((((((5.2264952788528545610e3 * r +
- 2.8729085735721942674e4) * r + 3.9307895800092710610e4) * r
- + 2.1213794301586595867e4) * r + 5.3941960214247511077e3) *
- r + 6.8718700749205790830e2) * r + 4.2313330701600911252e1)
- * r + 1.0);
- } else {
- if (q < 0.0) {
- r = p;
- } else {
- r = 1.0 - p;
- }
- assert(r > 0.0);
-
- r = sqrt(-log(r));
- if (r <= 5.0) {
- /* p neither close to 1/2 nor 0 or 1. */
- r -= 1.6;
- ret = ((((((((7.74545014278341407640e-4 * r +
- 2.27238449892691845833e-2) * r +
- 2.41780725177450611770e-1) * r +
- 1.27045825245236838258e0) * r +
- 3.64784832476320460504e0) * r +
- 5.76949722146069140550e0) * r +
- 4.63033784615654529590e0) * r +
- 1.42343711074968357734e0) /
- (((((((1.05075007164441684324e-9 * r +
- 5.47593808499534494600e-4) * r +
- 1.51986665636164571966e-2)
- * r + 1.48103976427480074590e-1) * r +
- 6.89767334985100004550e-1) * r +
- 1.67638483018380384940e0) * r +
- 2.05319162663775882187e0) * r + 1.0));
- } else {
- /* p near 0 or 1. */
- r -= 5.0;
- ret = ((((((((2.01033439929228813265e-7 * r +
- 2.71155556874348757815e-5) * r +
- 1.24266094738807843860e-3) * r +
- 2.65321895265761230930e-2) * r +
- 2.96560571828504891230e-1) * r +
- 1.78482653991729133580e0) * r +
- 5.46378491116411436990e0) * r +
- 6.65790464350110377720e0) /
- (((((((2.04426310338993978564e-15 * r +
- 1.42151175831644588870e-7) * r +
- 1.84631831751005468180e-5) * r +
- 7.86869131145613259100e-4) * r +
- 1.48753612908506148525e-2) * r +
- 1.36929880922735805310e-1) * r +
- 5.99832206555887937690e-1)
- * r + 1.0));
- }
- if (q < 0.0) {
- ret = -ret;
- }
- return ret;
- }
-}
-
-/*
- * Given a value p in [0..1] of the lower tail area of the Chi^2 distribution
- * with df degrees of freedom, where ln_gamma_df_2 is ln_gamma(df/2.0), compute
- * the upper limit on the definite integral from [0..z] that satisfies p,
- * accurate to 12 decimal places.
- *
- * This implementation is based on:
- *
- * Best, D.J., D.E. Roberts (1975) Algorithm AS 91: The percentage points of
- * the Chi^2 distribution. Applied Statistics 24(3):385-388.
- *
- * Shea, B.L. (1991) Algorithm AS R85: A remark on AS 91: The percentage
- * points of the Chi^2 distribution. Applied Statistics 40(1):233-235.
- */
-static inline double
-pt_chi2(double p, double df, double ln_gamma_df_2) {
- double e, aa, xx, c, ch, a, q, p1, p2, t, x, b, s1, s2, s3, s4, s5, s6;
- unsigned i;
-
- assert(p >= 0.0 && p < 1.0);
- assert(df > 0.0);
-
- e = 5.0e-7;
- aa = 0.6931471805;
-
- xx = 0.5 * df;
- c = xx - 1.0;
-
- if (df < -1.24 * log(p)) {
- /* Starting approximation for small Chi^2. */
- ch = pow(p * xx * exp(ln_gamma_df_2 + xx * aa), 1.0 / xx);
- if (ch - e < 0.0) {
- return ch;
- }
- } else {
- if (df > 0.32) {
- x = pt_norm(p);
- /*
- * Starting approximation using Wilson and Hilferty
- * estimate.
- */
- p1 = 0.222222 / df;
- ch = df * pow(x * sqrt(p1) + 1.0 - p1, 3.0);
- /* Starting approximation for p tending to 1. */
- if (ch > 2.2 * df + 6.0) {
- ch = -2.0 * (log(1.0 - p) - c * log(0.5 * ch) +
- ln_gamma_df_2);
- }
- } else {
- ch = 0.4;
- a = log(1.0 - p);
- while (true) {
- q = ch;
- p1 = 1.0 + ch * (4.67 + ch);
- p2 = ch * (6.73 + ch * (6.66 + ch));
- t = -0.5 + (4.67 + 2.0 * ch) / p1 - (6.73 + ch
- * (13.32 + 3.0 * ch)) / p2;
- ch -= (1.0 - exp(a + ln_gamma_df_2 + 0.5 * ch +
- c * aa) * p2 / p1) / t;
- if (fabs(q / ch - 1.0) - 0.01 <= 0.0) {
- break;
- }
- }
- }
- }
-
- for (i = 0; i < 20; i++) {
- /* Calculation of seven-term Taylor series. */
- q = ch;
- p1 = 0.5 * ch;
- if (p1 < 0.0) {
- return -1.0;
- }
- p2 = p - i_gamma(p1, xx, ln_gamma_df_2);
- t = p2 * exp(xx * aa + ln_gamma_df_2 + p1 - c * log(ch));
- b = t / ch;
- a = 0.5 * t - b * c;
- s1 = (210.0 + a * (140.0 + a * (105.0 + a * (84.0 + a * (70.0 +
- 60.0 * a))))) / 420.0;
- s2 = (420.0 + a * (735.0 + a * (966.0 + a * (1141.0 + 1278.0 *
- a)))) / 2520.0;
- s3 = (210.0 + a * (462.0 + a * (707.0 + 932.0 * a))) / 2520.0;
- s4 = (252.0 + a * (672.0 + 1182.0 * a) + c * (294.0 + a *
- (889.0 + 1740.0 * a))) / 5040.0;
- s5 = (84.0 + 264.0 * a + c * (175.0 + 606.0 * a)) / 2520.0;
- s6 = (120.0 + c * (346.0 + 127.0 * c)) / 5040.0;
- ch += t * (1.0 + 0.5 * t * s1 - b * c * (s1 - b * (s2 - b * (s3
- - b * (s4 - b * (s5 - b * s6))))));
- if (fabs(q / ch - 1.0) <= e) {
- break;
- }
- }
-
- return ch;
-}
-
-/*
- * Given a value p in [0..1] and Gamma distribution shape and scale parameters,
- * compute the upper limit on the definite integral from [0..z] that satisfies
- * p.
- */
-static inline double
-pt_gamma(double p, double shape, double scale, double ln_gamma_shape) {
- return pt_chi2(p, shape * 2.0, ln_gamma_shape) * 0.5 * scale;
-}
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